org.apache.mxnet

NDArrayBase

Related Doc: package mxnet

abstract class NDArrayBase extends AnyRef

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  1. new NDArrayBase()

Abstract Value Members

  1. abstract def Activation(args: Any*): NDArrayFuncReturn

    Applies an activation function element-wise to the input.
    
    The following activation functions are supported:
    
    - `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
    - `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
    - `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}`
    - `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
    - `softsign`: :math:`y = \frac{x}{1 + abs(x)}`
    
    
    
    Defined in src/operator/nn/activation.cc:L147
    

Applies an activation function element-wise to the input.

The following activation functions are supported:

- `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
- `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
- `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}`
- `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
- `softsign`: :math:`y = \frac{x}{1 + abs(x)}`



Defined in src/operator/nn/activation.cc:L147

returns

org.apache.mxnet.NDArray

  • abstract def Activation(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies an activation function element-wise to the input.
    
    The following activation functions are supported:
    
    - `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
    - `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
    - `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}`
    - `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
    - `softsign`: :math:`y = \frac{x}{1 + abs(x)}`
    
    
    
    Defined in src/operator/nn/activation.cc:L147
    

  • Applies an activation function element-wise to the input.
    
    The following activation functions are supported:
    
    - `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
    - `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
    - `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}`
    - `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
    - `softsign`: :math:`y = \frac{x}{1 + abs(x)}`
    
    
    
    Defined in src/operator/nn/activation.cc:L147
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BatchNorm(args: Any*): NDArrayFuncReturn

    Batch normalization.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these
    two outputs are blocked.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
    axis to be the last item in the input shape.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    Note::
    
    When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False,
    the sparse tensors will fallback.
    
    
    
    Defined in src/operator/nn/batch_norm.cc:L575
    

  • Batch normalization.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these
    two outputs are blocked.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
    axis to be the last item in the input shape.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    Note::
    
    When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False,
    the sparse tensors will fallback.
    
    
    
    Defined in src/operator/nn/batch_norm.cc:L575
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BatchNorm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Batch normalization.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these
    two outputs are blocked.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
    axis to be the last item in the input shape.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    Note::
    
    When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False,
    the sparse tensors will fallback.
    
    
    
    Defined in src/operator/nn/batch_norm.cc:L575
    

  • Batch normalization.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these
    two outputs are blocked.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
    axis to be the last item in the input shape.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    Note::
    
    When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False,
    the sparse tensors will fallback.
    
    
    
    Defined in src/operator/nn/batch_norm.cc:L575
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BatchNorm_v1(args: Any*): NDArrayFuncReturn

    Batch normalization.
    
    This operator is DEPRECATED. Perform BatchNorm on the input.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_var`` as well, which are needed for the backward pass.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    There's no sparse support for this operator, and it will exhibit problematic behavior if used with
    sparse tensors.
    
    
    
    Defined in src/operator/batch_norm_v1.cc:L95
    

  • Batch normalization.
    
    This operator is DEPRECATED. Perform BatchNorm on the input.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_var`` as well, which are needed for the backward pass.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    There's no sparse support for this operator, and it will exhibit problematic behavior if used with
    sparse tensors.
    
    
    
    Defined in src/operator/batch_norm_v1.cc:L95
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BatchNorm_v1(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Batch normalization.
    
    This operator is DEPRECATED. Perform BatchNorm on the input.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_var`` as well, which are needed for the backward pass.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    There's no sparse support for this operator, and it will exhibit problematic behavior if used with
    sparse tensors.
    
    
    
    Defined in src/operator/batch_norm_v1.cc:L95
    

  • Batch normalization.
    
    This operator is DEPRECATED. Perform BatchNorm on the input.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_var`` as well, which are needed for the backward pass.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    There's no sparse support for this operator, and it will exhibit problematic behavior if used with
    sparse tensors.
    
    
    
    Defined in src/operator/batch_norm_v1.cc:L95
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BilinearSampler(args: Any*): NDArrayFuncReturn

    Applies bilinear sampling to input feature map.
    
    Bilinear Sampling is the key of  [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
    except that the operator has the backward pass.
    
    Given :math:`data` and :math:`grid`, then the output is computed by
    
    .. math::
      x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
      y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
      output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})
    
    :math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in :math:`output`, and :math:`G()` denotes the bilinear interpolation kernel.
    The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).
    
    The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has been normalized to [-1, 1].
    
    BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
    GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
    If users want to design a CustomOp to manipulate :math:`grid`, please firstly refer to the code of GridGenerator.
    
    Example 1::
    
      ## Zoom out data two times
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      affine_matrix = array([[2, 0, 0],
                             [0, 2, 0]])
    
      affine_matrix = reshape(affine_matrix, shape=(1, 6))
    
      grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))
    
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 0,   0,     0,   0],
         [ 0,   3.5,   6.5, 0],
         [ 0,   1.25,  2.5, 0],
         [ 0,   0,     0,   0]]]
    
    
    Example 2::
    
      ## shift data horizontally by -1 pixel
    
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      warp_maxtrix = array([[[[1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1]],
                             [[0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0]]]])
    
      grid = GridGenerator(data=warp_matrix, transform_type='warp')
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 4,  3,  6,  0],
         [ 8,  8,  9,  0],
         [ 4,  1,  5,  0],
         [ 0,  1,  3,  0]]]
    
    
    Defined in src/operator/bilinear_sampler.cc:L256
    

  • Applies bilinear sampling to input feature map.
    
    Bilinear Sampling is the key of  [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
    except that the operator has the backward pass.
    
    Given :math:`data` and :math:`grid`, then the output is computed by
    
    .. math::
      x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
      y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
      output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})
    
    :math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in :math:`output`, and :math:`G()` denotes the bilinear interpolation kernel.
    The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).
    
    The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has been normalized to [-1, 1].
    
    BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
    GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
    If users want to design a CustomOp to manipulate :math:`grid`, please firstly refer to the code of GridGenerator.
    
    Example 1::
    
      ## Zoom out data two times
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      affine_matrix = array([[2, 0, 0],
                             [0, 2, 0]])
    
      affine_matrix = reshape(affine_matrix, shape=(1, 6))
    
      grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))
    
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 0,   0,     0,   0],
         [ 0,   3.5,   6.5, 0],
         [ 0,   1.25,  2.5, 0],
         [ 0,   0,     0,   0]]]
    
    
    Example 2::
    
      ## shift data horizontally by -1 pixel
    
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      warp_maxtrix = array([[[[1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1]],
                             [[0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0]]]])
    
      grid = GridGenerator(data=warp_matrix, transform_type='warp')
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 4,  3,  6,  0],
         [ 8,  8,  9,  0],
         [ 4,  1,  5,  0],
         [ 0,  1,  3,  0]]]
    
    
    Defined in src/operator/bilinear_sampler.cc:L256
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BilinearSampler(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies bilinear sampling to input feature map.
    
    Bilinear Sampling is the key of  [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
    except that the operator has the backward pass.
    
    Given :math:`data` and :math:`grid`, then the output is computed by
    
    .. math::
      x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
      y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
      output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})
    
    :math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in :math:`output`, and :math:`G()` denotes the bilinear interpolation kernel.
    The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).
    
    The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has been normalized to [-1, 1].
    
    BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
    GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
    If users want to design a CustomOp to manipulate :math:`grid`, please firstly refer to the code of GridGenerator.
    
    Example 1::
    
      ## Zoom out data two times
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      affine_matrix = array([[2, 0, 0],
                             [0, 2, 0]])
    
      affine_matrix = reshape(affine_matrix, shape=(1, 6))
    
      grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))
    
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 0,   0,     0,   0],
         [ 0,   3.5,   6.5, 0],
         [ 0,   1.25,  2.5, 0],
         [ 0,   0,     0,   0]]]
    
    
    Example 2::
    
      ## shift data horizontally by -1 pixel
    
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      warp_maxtrix = array([[[[1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1]],
                             [[0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0]]]])
    
      grid = GridGenerator(data=warp_matrix, transform_type='warp')
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 4,  3,  6,  0],
         [ 8,  8,  9,  0],
         [ 4,  1,  5,  0],
         [ 0,  1,  3,  0]]]
    
    
    Defined in src/operator/bilinear_sampler.cc:L256
    

  • Applies bilinear sampling to input feature map.
    
    Bilinear Sampling is the key of  [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
    except that the operator has the backward pass.
    
    Given :math:`data` and :math:`grid`, then the output is computed by
    
    .. math::
      x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
      y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
      output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})
    
    :math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in :math:`output`, and :math:`G()` denotes the bilinear interpolation kernel.
    The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).
    
    The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has been normalized to [-1, 1].
    
    BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
    GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
    If users want to design a CustomOp to manipulate :math:`grid`, please firstly refer to the code of GridGenerator.
    
    Example 1::
    
      ## Zoom out data two times
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      affine_matrix = array([[2, 0, 0],
                             [0, 2, 0]])
    
      affine_matrix = reshape(affine_matrix, shape=(1, 6))
    
      grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))
    
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 0,   0,     0,   0],
         [ 0,   3.5,   6.5, 0],
         [ 0,   1.25,  2.5, 0],
         [ 0,   0,     0,   0]]]
    
    
    Example 2::
    
      ## shift data horizontally by -1 pixel
    
      data = array([[[[1, 4, 3, 6],
                      [1, 8, 8, 9],
                      [0, 4, 1, 5],
                      [1, 0, 1, 3]]]])
    
      warp_maxtrix = array([[[[1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1],
                              [1, 1, 1, 1]],
                             [[0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0],
                              [0, 0, 0, 0]]]])
    
      grid = GridGenerator(data=warp_matrix, transform_type='warp')
      out = BilinearSampler(data, grid)
    
      out
      [[[[ 4,  3,  6,  0],
         [ 8,  8,  9,  0],
         [ 4,  1,  5,  0],
         [ 0,  1,  3,  0]]]
    
    
    Defined in src/operator/bilinear_sampler.cc:L256
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BlockGrad(args: Any*): NDArrayFuncReturn

    Stops gradient computation.
    
    Stops the accumulated gradient of the inputs from flowing through this operator
    in the backward direction. In other words, this operator prevents the contribution
    of its inputs to be taken into account for computing gradients.
    
    Example::
    
      v1 = [1, 2]
      v2 = [0, 1]
      a = Variable('a')
      b = Variable('b')
      b_stop_grad = stop_gradient(3 * b)
      loss = MakeLoss(b_stop_grad + a)
    
      executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
      executor.forward(is_train=True, a=v1, b=v2)
      executor.outputs
      [ 1.  5.]
    
      executor.backward()
      executor.grad_arrays
      [ 0.  0.]
      [ 1.  1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L267
    

  • Stops gradient computation.
    
    Stops the accumulated gradient of the inputs from flowing through this operator
    in the backward direction. In other words, this operator prevents the contribution
    of its inputs to be taken into account for computing gradients.
    
    Example::
    
      v1 = [1, 2]
      v2 = [0, 1]
      a = Variable('a')
      b = Variable('b')
      b_stop_grad = stop_gradient(3 * b)
      loss = MakeLoss(b_stop_grad + a)
    
      executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
      executor.forward(is_train=True, a=v1, b=v2)
      executor.outputs
      [ 1.  5.]
    
      executor.backward()
      executor.grad_arrays
      [ 0.  0.]
      [ 1.  1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L267
    

    returns

    org.apache.mxnet.NDArray

  • abstract def BlockGrad(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Stops gradient computation.
    
    Stops the accumulated gradient of the inputs from flowing through this operator
    in the backward direction. In other words, this operator prevents the contribution
    of its inputs to be taken into account for computing gradients.
    
    Example::
    
      v1 = [1, 2]
      v2 = [0, 1]
      a = Variable('a')
      b = Variable('b')
      b_stop_grad = stop_gradient(3 * b)
      loss = MakeLoss(b_stop_grad + a)
    
      executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
      executor.forward(is_train=True, a=v1, b=v2)
      executor.outputs
      [ 1.  5.]
    
      executor.backward()
      executor.grad_arrays
      [ 0.  0.]
      [ 1.  1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L267
    

  • Stops gradient computation.
    
    Stops the accumulated gradient of the inputs from flowing through this operator
    in the backward direction. In other words, this operator prevents the contribution
    of its inputs to be taken into account for computing gradients.
    
    Example::
    
      v1 = [1, 2]
      v2 = [0, 1]
      a = Variable('a')
      b = Variable('b')
      b_stop_grad = stop_gradient(3 * b)
      loss = MakeLoss(b_stop_grad + a)
    
      executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
      executor.forward(is_train=True, a=v1, b=v2)
      executor.outputs
      [ 1.  5.]
    
      executor.backward()
      executor.grad_arrays
      [ 0.  0.]
      [ 1.  1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L267
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Cast(args: Any*): NDArrayFuncReturn

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

  • Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Cast(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

  • Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Concat(args: Any*): NDArrayFuncReturn

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

  • Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Concat(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

  • Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Convolution(args: Any*): NDArrayFuncReturn

    Compute *N*-D convolution on *(N+2)*-D input.
    
    In the 2-D convolution, given input data with shape *(batch_size,
    channel, height, width)*, the output is computed by
    
    .. math::
    
       out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
       weight[i,j,:,:]
    
    where :math:`\star` is the 2-D cross-correlation operator.
    
    For general 2-D convolution, the shapes are
    
    - **data**: *(batch_size, channel, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*.
    
    Define::
    
      f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
    
    then we have::
    
      out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
      out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
    width)*. We can choose other layouts such as *NWC*.
    
    If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
    evenly into *g* parts along the channel axis, and also evenly split ``weight``
    along the first dimension. Next compute the convolution on the *i*-th part of
    the data with the *i*-th weight part. The output is obtained by concatenating all
    the *g* results.
    
    1-D convolution does not have *height* dimension but only *width* in space.
    
    - **data**: *(batch_size, channel, width)*
    - **weight**: *(num_filter, channel, kernel[0])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_width)*.
    
    3-D convolution adds an additional *depth* dimension besides *height* and
    *width*. The shapes are
    
    - **data**: *(batch_size, channel, depth, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
    
    Both ``weight`` and ``bias`` are learnable parameters.
    
    There are other options to tune the performance.
    
    - **cudnn_tune**: enable this option leads to higher startup time but may give
      faster speed. Options are
    
      - **off**: no tuning
      - **limited_workspace**:run test and pick the fastest algorithm that doesn't
        exceed workspace limit.
      - **fastest**: pick the fastest algorithm and ignore workspace limit.
      - **None** (default): the behavior is determined by environment variable
        ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
        (default), 2 for fastest.
    
    - **workspace**: A large number leads to more (GPU) memory usage but may improve
      the performance.
    
    
    
    Defined in src/operator/nn/convolution.cc:L461
    

  • Compute *N*-D convolution on *(N+2)*-D input.
    
    In the 2-D convolution, given input data with shape *(batch_size,
    channel, height, width)*, the output is computed by
    
    .. math::
    
       out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
       weight[i,j,:,:]
    
    where :math:`\star` is the 2-D cross-correlation operator.
    
    For general 2-D convolution, the shapes are
    
    - **data**: *(batch_size, channel, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*.
    
    Define::
    
      f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
    
    then we have::
    
      out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
      out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
    width)*. We can choose other layouts such as *NWC*.
    
    If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
    evenly into *g* parts along the channel axis, and also evenly split ``weight``
    along the first dimension. Next compute the convolution on the *i*-th part of
    the data with the *i*-th weight part. The output is obtained by concatenating all
    the *g* results.
    
    1-D convolution does not have *height* dimension but only *width* in space.
    
    - **data**: *(batch_size, channel, width)*
    - **weight**: *(num_filter, channel, kernel[0])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_width)*.
    
    3-D convolution adds an additional *depth* dimension besides *height* and
    *width*. The shapes are
    
    - **data**: *(batch_size, channel, depth, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
    
    Both ``weight`` and ``bias`` are learnable parameters.
    
    There are other options to tune the performance.
    
    - **cudnn_tune**: enable this option leads to higher startup time but may give
      faster speed. Options are
    
      - **off**: no tuning
      - **limited_workspace**:run test and pick the fastest algorithm that doesn't
        exceed workspace limit.
      - **fastest**: pick the fastest algorithm and ignore workspace limit.
      - **None** (default): the behavior is determined by environment variable
        ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
        (default), 2 for fastest.
    
    - **workspace**: A large number leads to more (GPU) memory usage but may improve
      the performance.
    
    
    
    Defined in src/operator/nn/convolution.cc:L461
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Convolution(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Compute *N*-D convolution on *(N+2)*-D input.
    
    In the 2-D convolution, given input data with shape *(batch_size,
    channel, height, width)*, the output is computed by
    
    .. math::
    
       out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
       weight[i,j,:,:]
    
    where :math:`\star` is the 2-D cross-correlation operator.
    
    For general 2-D convolution, the shapes are
    
    - **data**: *(batch_size, channel, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*.
    
    Define::
    
      f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
    
    then we have::
    
      out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
      out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
    width)*. We can choose other layouts such as *NWC*.
    
    If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
    evenly into *g* parts along the channel axis, and also evenly split ``weight``
    along the first dimension. Next compute the convolution on the *i*-th part of
    the data with the *i*-th weight part. The output is obtained by concatenating all
    the *g* results.
    
    1-D convolution does not have *height* dimension but only *width* in space.
    
    - **data**: *(batch_size, channel, width)*
    - **weight**: *(num_filter, channel, kernel[0])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_width)*.
    
    3-D convolution adds an additional *depth* dimension besides *height* and
    *width*. The shapes are
    
    - **data**: *(batch_size, channel, depth, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
    
    Both ``weight`` and ``bias`` are learnable parameters.
    
    There are other options to tune the performance.
    
    - **cudnn_tune**: enable this option leads to higher startup time but may give
      faster speed. Options are
    
      - **off**: no tuning
      - **limited_workspace**:run test and pick the fastest algorithm that doesn't
        exceed workspace limit.
      - **fastest**: pick the fastest algorithm and ignore workspace limit.
      - **None** (default): the behavior is determined by environment variable
        ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
        (default), 2 for fastest.
    
    - **workspace**: A large number leads to more (GPU) memory usage but may improve
      the performance.
    
    
    
    Defined in src/operator/nn/convolution.cc:L461
    

  • Compute *N*-D convolution on *(N+2)*-D input.
    
    In the 2-D convolution, given input data with shape *(batch_size,
    channel, height, width)*, the output is computed by
    
    .. math::
    
       out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
       weight[i,j,:,:]
    
    where :math:`\star` is the 2-D cross-correlation operator.
    
    For general 2-D convolution, the shapes are
    
    - **data**: *(batch_size, channel, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*.
    
    Define::
    
      f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
    
    then we have::
    
      out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
      out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
    width)*. We can choose other layouts such as *NWC*.
    
    If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
    evenly into *g* parts along the channel axis, and also evenly split ``weight``
    along the first dimension. Next compute the convolution on the *i*-th part of
    the data with the *i*-th weight part. The output is obtained by concatenating all
    the *g* results.
    
    1-D convolution does not have *height* dimension but only *width* in space.
    
    - **data**: *(batch_size, channel, width)*
    - **weight**: *(num_filter, channel, kernel[0])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_width)*.
    
    3-D convolution adds an additional *depth* dimension besides *height* and
    *width*. The shapes are
    
    - **data**: *(batch_size, channel, depth, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
    
    Both ``weight`` and ``bias`` are learnable parameters.
    
    There are other options to tune the performance.
    
    - **cudnn_tune**: enable this option leads to higher startup time but may give
      faster speed. Options are
    
      - **off**: no tuning
      - **limited_workspace**:run test and pick the fastest algorithm that doesn't
        exceed workspace limit.
      - **fastest**: pick the fastest algorithm and ignore workspace limit.
      - **None** (default): the behavior is determined by environment variable
        ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
        (default), 2 for fastest.
    
    - **workspace**: A large number leads to more (GPU) memory usage but may improve
      the performance.
    
    
    
    Defined in src/operator/nn/convolution.cc:L461
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Convolution_v1(args: Any*): NDArrayFuncReturn

    This operator is DEPRECATED. Apply convolution to input then add a bias.
    

  • This operator is DEPRECATED. Apply convolution to input then add a bias.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Convolution_v1(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    This operator is DEPRECATED. Apply convolution to input then add a bias.
    

  • This operator is DEPRECATED. Apply convolution to input then add a bias.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Correlation(args: Any*): NDArrayFuncReturn

    Applies correlation to inputs.
    
    The correlation layer performs multiplicative patch comparisons between two feature maps.
    
    Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels,
    the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`.
    
    For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and
    :math:`x_{2}` in the second map is then defined as:
    
    .. math::
    
       c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} 
    
    for a square patch of size :math:`K:=2k+1`.
    
    Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other
    data. For this reason, it has no training weights.
    
    Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations.
    
    Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size :math:`D:=2d+1`,
    by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the neighborhood
    centered around :math:`x_{1}`.
    
    The final output is defined by the following expression:
    
    .. math::
      out[n, q, i, j] = c(x_{i, j}, x_{q})
    
    where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`.
    
    
    Defined in src/operator/correlation.cc:L198
    

  • Applies correlation to inputs.
    
    The correlation layer performs multiplicative patch comparisons between two feature maps.
    
    Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels,
    the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`.
    
    For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and
    :math:`x_{2}` in the second map is then defined as:
    
    .. math::
    
       c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} 
    
    for a square patch of size :math:`K:=2k+1`.
    
    Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other
    data. For this reason, it has no training weights.
    
    Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations.
    
    Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size :math:`D:=2d+1`,
    by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the neighborhood
    centered around :math:`x_{1}`.
    
    The final output is defined by the following expression:
    
    .. math::
      out[n, q, i, j] = c(x_{i, j}, x_{q})
    
    where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`.
    
    
    Defined in src/operator/correlation.cc:L198
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Correlation(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies correlation to inputs.
    
    The correlation layer performs multiplicative patch comparisons between two feature maps.
    
    Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels,
    the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`.
    
    For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and
    :math:`x_{2}` in the second map is then defined as:
    
    .. math::
    
       c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} 
    
    for a square patch of size :math:`K:=2k+1`.
    
    Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other
    data. For this reason, it has no training weights.
    
    Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations.
    
    Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size :math:`D:=2d+1`,
    by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the neighborhood
    centered around :math:`x_{1}`.
    
    The final output is defined by the following expression:
    
    .. math::
      out[n, q, i, j] = c(x_{i, j}, x_{q})
    
    where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`.
    
    
    Defined in src/operator/correlation.cc:L198
    

  • Applies correlation to inputs.
    
    The correlation layer performs multiplicative patch comparisons between two feature maps.
    
    Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels,
    the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`.
    
    For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and
    :math:`x_{2}` in the second map is then defined as:
    
    .. math::
    
       c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} 
    
    for a square patch of size :math:`K:=2k+1`.
    
    Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other
    data. For this reason, it has no training weights.
    
    Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations.
    
    Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size :math:`D:=2d+1`,
    by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the neighborhood
    centered around :math:`x_{1}`.
    
    The final output is defined by the following expression:
    
    .. math::
      out[n, q, i, j] = c(x_{i, j}, x_{q})
    
    where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`.
    
    
    Defined in src/operator/correlation.cc:L198
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Crop(args: Any*): NDArrayFuncReturn

    
    
    .. note:: `Crop` is deprecated. Use `slice` instead.
    
    Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or
    with width and height of the second input symbol, i.e., with one input, we need h_w to
    specify the crop height and width, otherwise the second input symbol's size will be used
    
    
    Defined in src/operator/crop.cc:L50
    

  • 
    
    .. note:: `Crop` is deprecated. Use `slice` instead.
    
    Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or
    with width and height of the second input symbol, i.e., with one input, we need h_w to
    specify the crop height and width, otherwise the second input symbol's size will be used
    
    
    Defined in src/operator/crop.cc:L50
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Crop(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    
    
    .. note:: `Crop` is deprecated. Use `slice` instead.
    
    Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or
    with width and height of the second input symbol, i.e., with one input, we need h_w to
    specify the crop height and width, otherwise the second input symbol's size will be used
    
    
    Defined in src/operator/crop.cc:L50
    

  • 
    
    .. note:: `Crop` is deprecated. Use `slice` instead.
    
    Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or
    with width and height of the second input symbol, i.e., with one input, we need h_w to
    specify the crop height and width, otherwise the second input symbol's size will be used
    
    
    Defined in src/operator/crop.cc:L50
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Custom(args: Any*): NDArrayFuncReturn

    Apply a custom operator implemented in a frontend language (like Python).
    
    Custom operators should override required methods like `forward` and `backward`.
    The custom operator must be registered before it can be used.
    Please check the tutorial here: https://mxnet.incubator.apache.org/faq/new_op.html.
    
    
    
    Defined in src/operator/custom/custom.cc:L547
    

  • Apply a custom operator implemented in a frontend language (like Python).
    
    Custom operators should override required methods like `forward` and `backward`.
    The custom operator must be registered before it can be used.
    Please check the tutorial here: https://mxnet.incubator.apache.org/faq/new_op.html.
    
    
    
    Defined in src/operator/custom/custom.cc:L547
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Custom(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Apply a custom operator implemented in a frontend language (like Python).
    
    Custom operators should override required methods like `forward` and `backward`.
    The custom operator must be registered before it can be used.
    Please check the tutorial here: https://mxnet.incubator.apache.org/faq/new_op.html.
    
    
    
    Defined in src/operator/custom/custom.cc:L547
    

  • Apply a custom operator implemented in a frontend language (like Python).
    
    Custom operators should override required methods like `forward` and `backward`.
    The custom operator must be registered before it can be used.
    Please check the tutorial here: https://mxnet.incubator.apache.org/faq/new_op.html.
    
    
    
    Defined in src/operator/custom/custom.cc:L547
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Deconvolution(args: Any*): NDArrayFuncReturn

    Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern.
    

  • Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Deconvolution(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern.
    

  • Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Dropout(args: Any*): NDArrayFuncReturn

    Applies dropout operation to input array.
    
    - During training, each element of the input is set to zero with probability p.
      The whole array is rescaled by :math:`1/(1-p)` to keep the expected
      sum of the input unchanged.
    
    - During testing, this operator does not change the input if mode is 'training'.
      If mode is 'always', the same computaion as during training will be applied.
    
    Example::
    
      random.seed(998)
      input_array = array([[3., 0.5,  -0.5,  2., 7.],
                          [2., -0.4,   7.,  3., 0.2]])
      a = symbol.Variable('a')
      dropout = symbol.Dropout(a, p = 0.2)
      executor = dropout.simple_bind(a = input_array.shape)
    
      ## If training
      executor.forward(is_train = True, a = input_array)
      executor.outputs
      [[ 3.75   0.625 -0.     2.5    8.75 ]
       [ 2.5   -0.5    8.75   3.75   0.   ]]
    
      ## If testing
      executor.forward(is_train = False, a = input_array)
      executor.outputs
      [[ 3.     0.5   -0.5    2.     7.   ]
       [ 2.    -0.4    7.     3.     0.2  ]]
    
    
    Defined in src/operator/nn/dropout.cc:L76
    

  • Applies dropout operation to input array.
    
    - During training, each element of the input is set to zero with probability p.
      The whole array is rescaled by :math:`1/(1-p)` to keep the expected
      sum of the input unchanged.
    
    - During testing, this operator does not change the input if mode is 'training'.
      If mode is 'always', the same computaion as during training will be applied.
    
    Example::
    
      random.seed(998)
      input_array = array([[3., 0.5,  -0.5,  2., 7.],
                          [2., -0.4,   7.,  3., 0.2]])
      a = symbol.Variable('a')
      dropout = symbol.Dropout(a, p = 0.2)
      executor = dropout.simple_bind(a = input_array.shape)
    
      ## If training
      executor.forward(is_train = True, a = input_array)
      executor.outputs
      [[ 3.75   0.625 -0.     2.5    8.75 ]
       [ 2.5   -0.5    8.75   3.75   0.   ]]
    
      ## If testing
      executor.forward(is_train = False, a = input_array)
      executor.outputs
      [[ 3.     0.5   -0.5    2.     7.   ]
       [ 2.    -0.4    7.     3.     0.2  ]]
    
    
    Defined in src/operator/nn/dropout.cc:L76
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Dropout(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies dropout operation to input array.
    
    - During training, each element of the input is set to zero with probability p.
      The whole array is rescaled by :math:`1/(1-p)` to keep the expected
      sum of the input unchanged.
    
    - During testing, this operator does not change the input if mode is 'training'.
      If mode is 'always', the same computaion as during training will be applied.
    
    Example::
    
      random.seed(998)
      input_array = array([[3., 0.5,  -0.5,  2., 7.],
                          [2., -0.4,   7.,  3., 0.2]])
      a = symbol.Variable('a')
      dropout = symbol.Dropout(a, p = 0.2)
      executor = dropout.simple_bind(a = input_array.shape)
    
      ## If training
      executor.forward(is_train = True, a = input_array)
      executor.outputs
      [[ 3.75   0.625 -0.     2.5    8.75 ]
       [ 2.5   -0.5    8.75   3.75   0.   ]]
    
      ## If testing
      executor.forward(is_train = False, a = input_array)
      executor.outputs
      [[ 3.     0.5   -0.5    2.     7.   ]
       [ 2.    -0.4    7.     3.     0.2  ]]
    
    
    Defined in src/operator/nn/dropout.cc:L76
    

  • Applies dropout operation to input array.
    
    - During training, each element of the input is set to zero with probability p.
      The whole array is rescaled by :math:`1/(1-p)` to keep the expected
      sum of the input unchanged.
    
    - During testing, this operator does not change the input if mode is 'training'.
      If mode is 'always', the same computaion as during training will be applied.
    
    Example::
    
      random.seed(998)
      input_array = array([[3., 0.5,  -0.5,  2., 7.],
                          [2., -0.4,   7.,  3., 0.2]])
      a = symbol.Variable('a')
      dropout = symbol.Dropout(a, p = 0.2)
      executor = dropout.simple_bind(a = input_array.shape)
    
      ## If training
      executor.forward(is_train = True, a = input_array)
      executor.outputs
      [[ 3.75   0.625 -0.     2.5    8.75 ]
       [ 2.5   -0.5    8.75   3.75   0.   ]]
    
      ## If testing
      executor.forward(is_train = False, a = input_array)
      executor.outputs
      [[ 3.     0.5   -0.5    2.     7.   ]
       [ 2.    -0.4    7.     3.     0.2  ]]
    
    
    Defined in src/operator/nn/dropout.cc:L76
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ElementWiseSum(args: Any*): NDArrayFuncReturn

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

  • Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ElementWiseSum(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

  • Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Embedding(args: Any*): NDArrayFuncReturn

    Maps integer indices to vector representations (embeddings).
    
    This operator maps words to real-valued vectors in a high-dimensional space,
    called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
    For example, it has been noted that in the learned embedding spaces, similar words tend
    to be close to each other and dissimilar words far apart.
    
    For an input array of shape (d1, ..., dK),
    the shape of an output array is (d1, ..., dK, output_dim).
    All the input values should be integers in the range [0, input_dim).
    
    If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
    (ip0, op0).
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last vector in an embedding matrix.
    
    Examples::
    
      input_dim = 4
      output_dim = 5
    
      // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
      y = [[  0.,   1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.,   9.],
           [ 10.,  11.,  12.,  13.,  14.],
           [ 15.,  16.,  17.,  18.,  19.]]
    
      // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
      x = [[ 1.,  3.],
           [ 0.,  2.]]
    
      // Mapped input x to its vector representation y.
      Embedding(x, y, 4, 5) = [[[  5.,   6.,   7.,   8.,   9.],
                                [ 15.,  16.,  17.,  18.,  19.]],
    
                               [[  0.,   1.,   2.,   3.,   4.],
                                [ 10.,  11.,  12.,  13.,  14.]]]
    
    
    The storage type of weight can be either row_sparse or default.
    
    .. Note::
    
        If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L267
    

  • Maps integer indices to vector representations (embeddings).
    
    This operator maps words to real-valued vectors in a high-dimensional space,
    called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
    For example, it has been noted that in the learned embedding spaces, similar words tend
    to be close to each other and dissimilar words far apart.
    
    For an input array of shape (d1, ..., dK),
    the shape of an output array is (d1, ..., dK, output_dim).
    All the input values should be integers in the range [0, input_dim).
    
    If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
    (ip0, op0).
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last vector in an embedding matrix.
    
    Examples::
    
      input_dim = 4
      output_dim = 5
    
      // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
      y = [[  0.,   1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.,   9.],
           [ 10.,  11.,  12.,  13.,  14.],
           [ 15.,  16.,  17.,  18.,  19.]]
    
      // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
      x = [[ 1.,  3.],
           [ 0.,  2.]]
    
      // Mapped input x to its vector representation y.
      Embedding(x, y, 4, 5) = [[[  5.,   6.,   7.,   8.,   9.],
                                [ 15.,  16.,  17.,  18.,  19.]],
    
                               [[  0.,   1.,   2.,   3.,   4.],
                                [ 10.,  11.,  12.,  13.,  14.]]]
    
    
    The storage type of weight can be either row_sparse or default.
    
    .. Note::
    
        If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L267
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Embedding(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Maps integer indices to vector representations (embeddings).
    
    This operator maps words to real-valued vectors in a high-dimensional space,
    called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
    For example, it has been noted that in the learned embedding spaces, similar words tend
    to be close to each other and dissimilar words far apart.
    
    For an input array of shape (d1, ..., dK),
    the shape of an output array is (d1, ..., dK, output_dim).
    All the input values should be integers in the range [0, input_dim).
    
    If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
    (ip0, op0).
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last vector in an embedding matrix.
    
    Examples::
    
      input_dim = 4
      output_dim = 5
    
      // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
      y = [[  0.,   1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.,   9.],
           [ 10.,  11.,  12.,  13.,  14.],
           [ 15.,  16.,  17.,  18.,  19.]]
    
      // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
      x = [[ 1.,  3.],
           [ 0.,  2.]]
    
      // Mapped input x to its vector representation y.
      Embedding(x, y, 4, 5) = [[[  5.,   6.,   7.,   8.,   9.],
                                [ 15.,  16.,  17.,  18.,  19.]],
    
                               [[  0.,   1.,   2.,   3.,   4.],
                                [ 10.,  11.,  12.,  13.,  14.]]]
    
    
    The storage type of weight can be either row_sparse or default.
    
    .. Note::
    
        If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L267
    

  • Maps integer indices to vector representations (embeddings).
    
    This operator maps words to real-valued vectors in a high-dimensional space,
    called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
    For example, it has been noted that in the learned embedding spaces, similar words tend
    to be close to each other and dissimilar words far apart.
    
    For an input array of shape (d1, ..., dK),
    the shape of an output array is (d1, ..., dK, output_dim).
    All the input values should be integers in the range [0, input_dim).
    
    If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
    (ip0, op0).
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last vector in an embedding matrix.
    
    Examples::
    
      input_dim = 4
      output_dim = 5
    
      // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
      y = [[  0.,   1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.,   9.],
           [ 10.,  11.,  12.,  13.,  14.],
           [ 15.,  16.,  17.,  18.,  19.]]
    
      // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
      x = [[ 1.,  3.],
           [ 0.,  2.]]
    
      // Mapped input x to its vector representation y.
      Embedding(x, y, 4, 5) = [[[  5.,   6.,   7.,   8.,   9.],
                                [ 15.,  16.,  17.,  18.,  19.]],
    
                               [[  0.,   1.,   2.,   3.,   4.],
                                [ 10.,  11.,  12.,  13.,  14.]]]
    
    
    The storage type of weight can be either row_sparse or default.
    
    .. Note::
    
        If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L267
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Flatten(args: Any*): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

  • Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Flatten(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

  • Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

    returns

    org.apache.mxnet.NDArray

  • abstract def FullyConnected(args: Any*): NDArrayFuncReturn

    Applies a linear transformation: :math:`Y = XW^T + b`.
    
    If ``flatten`` is set to be true, then the shapes are:
    
    - **data**: `(batch_size, x1, x2, ..., xn)`
    - **weight**: `(num_hidden, x1 * x2 * ... * xn)`
    - **bias**: `(num_hidden,)`
    - **out**: `(batch_size, num_hidden)`
    
    If ``flatten`` is set to be false, then the shapes are:
    
    - **data**: `(x1, x2, ..., xn, input_dim)`
    - **weight**: `(num_hidden, input_dim)`
    - **bias**: `(num_hidden,)`
    - **out**: `(x1, x2, ..., xn, num_hidden)`
    
    The learnable parameters include both ``weight`` and ``bias``.
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    .. Note::
    
        The sparse support for FullyConnected is limited to forward evaluation with `row_sparse`
        weight and bias, where the length of `weight.indices` and `bias.indices` must be equal
        to `num_hidden`. This could be useful for model inference with `row_sparse` weights
        trained with importance sampling or noise contrastive estimation.
    
        To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
        of sparse.FullyConnected.
    
    
    
    Defined in src/operator/nn/fully_connected.cc:L271
    

  • Applies a linear transformation: :math:`Y = XW^T + b`.
    
    If ``flatten`` is set to be true, then the shapes are:
    
    - **data**: `(batch_size, x1, x2, ..., xn)`
    - **weight**: `(num_hidden, x1 * x2 * ... * xn)`
    - **bias**: `(num_hidden,)`
    - **out**: `(batch_size, num_hidden)`
    
    If ``flatten`` is set to be false, then the shapes are:
    
    - **data**: `(x1, x2, ..., xn, input_dim)`
    - **weight**: `(num_hidden, input_dim)`
    - **bias**: `(num_hidden,)`
    - **out**: `(x1, x2, ..., xn, num_hidden)`
    
    The learnable parameters include both ``weight`` and ``bias``.
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    .. Note::
    
        The sparse support for FullyConnected is limited to forward evaluation with `row_sparse`
        weight and bias, where the length of `weight.indices` and `bias.indices` must be equal
        to `num_hidden`. This could be useful for model inference with `row_sparse` weights
        trained with importance sampling or noise contrastive estimation.
    
        To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
        of sparse.FullyConnected.
    
    
    
    Defined in src/operator/nn/fully_connected.cc:L271
    

    returns

    org.apache.mxnet.NDArray

  • abstract def FullyConnected(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies a linear transformation: :math:`Y = XW^T + b`.
    
    If ``flatten`` is set to be true, then the shapes are:
    
    - **data**: `(batch_size, x1, x2, ..., xn)`
    - **weight**: `(num_hidden, x1 * x2 * ... * xn)`
    - **bias**: `(num_hidden,)`
    - **out**: `(batch_size, num_hidden)`
    
    If ``flatten`` is set to be false, then the shapes are:
    
    - **data**: `(x1, x2, ..., xn, input_dim)`
    - **weight**: `(num_hidden, input_dim)`
    - **bias**: `(num_hidden,)`
    - **out**: `(x1, x2, ..., xn, num_hidden)`
    
    The learnable parameters include both ``weight`` and ``bias``.
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    .. Note::
    
        The sparse support for FullyConnected is limited to forward evaluation with `row_sparse`
        weight and bias, where the length of `weight.indices` and `bias.indices` must be equal
        to `num_hidden`. This could be useful for model inference with `row_sparse` weights
        trained with importance sampling or noise contrastive estimation.
    
        To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
        of sparse.FullyConnected.
    
    
    
    Defined in src/operator/nn/fully_connected.cc:L271
    

  • Applies a linear transformation: :math:`Y = XW^T + b`.
    
    If ``flatten`` is set to be true, then the shapes are:
    
    - **data**: `(batch_size, x1, x2, ..., xn)`
    - **weight**: `(num_hidden, x1 * x2 * ... * xn)`
    - **bias**: `(num_hidden,)`
    - **out**: `(batch_size, num_hidden)`
    
    If ``flatten`` is set to be false, then the shapes are:
    
    - **data**: `(x1, x2, ..., xn, input_dim)`
    - **weight**: `(num_hidden, input_dim)`
    - **bias**: `(num_hidden,)`
    - **out**: `(x1, x2, ..., xn, num_hidden)`
    
    The learnable parameters include both ``weight`` and ``bias``.
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    .. Note::
    
        The sparse support for FullyConnected is limited to forward evaluation with `row_sparse`
        weight and bias, where the length of `weight.indices` and `bias.indices` must be equal
        to `num_hidden`. This could be useful for model inference with `row_sparse` weights
        trained with importance sampling or noise contrastive estimation.
    
        To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
        of sparse.FullyConnected.
    
    
    
    Defined in src/operator/nn/fully_connected.cc:L271
    

    returns

    org.apache.mxnet.NDArray

  • abstract def GridGenerator(args: Any*): NDArrayFuncReturn

    Generates 2D sampling grid for bilinear sampling.
    

  • Generates 2D sampling grid for bilinear sampling.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def GridGenerator(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Generates 2D sampling grid for bilinear sampling.
    

  • Generates 2D sampling grid for bilinear sampling.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def IdentityAttachKLSparseReg(args: Any*): NDArrayFuncReturn

    Apply a sparse regularization to the output a sigmoid activation function.
    

  • Apply a sparse regularization to the output a sigmoid activation function.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def IdentityAttachKLSparseReg(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Apply a sparse regularization to the output a sigmoid activation function.
    

  • Apply a sparse regularization to the output a sigmoid activation function.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def InstanceNorm(args: Any*): NDArrayFuncReturn

    Applies instance normalization to the n-dimensional input array.
    
    This operator takes an n-dimensional input array where (n>2) and normalizes
    the input using the following formula:
    
    .. math::
    
      out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta
    
    This layer is similar to batch normalization layer (`BatchNorm`)
    with two differences: first, the normalization is
    carried out per example (instance), not over a batch. Second, the
    same normalization is applied both at test and train time. This
    operation is also known as `contrast normalization`.
    
    If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
    `gamma` and `beta` parameters must be vectors of shape [channel].
    
    This implementation is based on paper:
    
    .. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
       D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).
    
    Examples::
    
      // Input of shape (2,1,2)
      x = [[[ 1.1,  2.2]],
           [[ 3.3,  4.4]]]
    
      // gamma parameter of length 1
      gamma = [1.5]
    
      // beta parameter of length 1
      beta = [0.5]
    
      // Instance normalization is calculated with the above formula
      InstanceNorm(x,gamma,beta) = [[[-0.997527  ,  1.99752665]],
                                    [[-0.99752653,  1.99752724]]]
    
    
    
    Defined in src/operator/instance_norm.cc:L95
    

  • Applies instance normalization to the n-dimensional input array.
    
    This operator takes an n-dimensional input array where (n>2) and normalizes
    the input using the following formula:
    
    .. math::
    
      out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta
    
    This layer is similar to batch normalization layer (`BatchNorm`)
    with two differences: first, the normalization is
    carried out per example (instance), not over a batch. Second, the
    same normalization is applied both at test and train time. This
    operation is also known as `contrast normalization`.
    
    If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
    `gamma` and `beta` parameters must be vectors of shape [channel].
    
    This implementation is based on paper:
    
    .. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
       D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).
    
    Examples::
    
      // Input of shape (2,1,2)
      x = [[[ 1.1,  2.2]],
           [[ 3.3,  4.4]]]
    
      // gamma parameter of length 1
      gamma = [1.5]
    
      // beta parameter of length 1
      beta = [0.5]
    
      // Instance normalization is calculated with the above formula
      InstanceNorm(x,gamma,beta) = [[[-0.997527  ,  1.99752665]],
                                    [[-0.99752653,  1.99752724]]]
    
    
    
    Defined in src/operator/instance_norm.cc:L95
    

    returns

    org.apache.mxnet.NDArray

  • abstract def InstanceNorm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies instance normalization to the n-dimensional input array.
    
    This operator takes an n-dimensional input array where (n>2) and normalizes
    the input using the following formula:
    
    .. math::
    
      out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta
    
    This layer is similar to batch normalization layer (`BatchNorm`)
    with two differences: first, the normalization is
    carried out per example (instance), not over a batch. Second, the
    same normalization is applied both at test and train time. This
    operation is also known as `contrast normalization`.
    
    If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
    `gamma` and `beta` parameters must be vectors of shape [channel].
    
    This implementation is based on paper:
    
    .. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
       D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).
    
    Examples::
    
      // Input of shape (2,1,2)
      x = [[[ 1.1,  2.2]],
           [[ 3.3,  4.4]]]
    
      // gamma parameter of length 1
      gamma = [1.5]
    
      // beta parameter of length 1
      beta = [0.5]
    
      // Instance normalization is calculated with the above formula
      InstanceNorm(x,gamma,beta) = [[[-0.997527  ,  1.99752665]],
                                    [[-0.99752653,  1.99752724]]]
    
    
    
    Defined in src/operator/instance_norm.cc:L95
    

  • Applies instance normalization to the n-dimensional input array.
    
    This operator takes an n-dimensional input array where (n>2) and normalizes
    the input using the following formula:
    
    .. math::
    
      out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta
    
    This layer is similar to batch normalization layer (`BatchNorm`)
    with two differences: first, the normalization is
    carried out per example (instance), not over a batch. Second, the
    same normalization is applied both at test and train time. This
    operation is also known as `contrast normalization`.
    
    If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
    `gamma` and `beta` parameters must be vectors of shape [channel].
    
    This implementation is based on paper:
    
    .. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
       D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).
    
    Examples::
    
      // Input of shape (2,1,2)
      x = [[[ 1.1,  2.2]],
           [[ 3.3,  4.4]]]
    
      // gamma parameter of length 1
      gamma = [1.5]
    
      // beta parameter of length 1
      beta = [0.5]
    
      // Instance normalization is calculated with the above formula
      InstanceNorm(x,gamma,beta) = [[[-0.997527  ,  1.99752665]],
                                    [[-0.99752653,  1.99752724]]]
    
    
    
    Defined in src/operator/instance_norm.cc:L95
    

    returns

    org.apache.mxnet.NDArray

  • abstract def L2Normalization(args: Any*): NDArrayFuncReturn

    Normalize the input array using the L2 norm.
    
    For 1-D NDArray, it computes::
    
      out = data / sqrt(sum(data ** 2) + eps)
    
    For N-D NDArray, if the input array has shape (N, N, ..., N),
    
    with ``mode`` = ``instance``, it normalizes each instance in the multidimensional
    array by its L2 norm.::
    
      for i in 0...N
        out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.::
    
      for i in 0...N
        out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position
    in the array by its L2 norm.::
    
      for dim in 2...N
        for i in 0...N
          out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
              -dim-
    
    Example::
    
      x = [[[1,2],
            [3,4]],
           [[2,2],
            [5,6]]]
    
      L2Normalization(x, mode='instance')
      =[[[ 0.18257418  0.36514837]
         [ 0.54772252  0.73029673]]
        [[ 0.24077171  0.24077171]
         [ 0.60192931  0.72231513]]]
    
      L2Normalization(x, mode='channel')
      =[[[ 0.31622776  0.44721359]
         [ 0.94868326  0.89442718]]
        [[ 0.37139067  0.31622776]
         [ 0.92847669  0.94868326]]]
    
      L2Normalization(x, mode='spatial')
      =[[[ 0.44721359  0.89442718]
         [ 0.60000002  0.80000001]]
        [[ 0.70710677  0.70710677]
         [ 0.6401844   0.76822126]]]
    
    
    
    Defined in src/operator/l2_normalization.cc:L98
    

  • Normalize the input array using the L2 norm.
    
    For 1-D NDArray, it computes::
    
      out = data / sqrt(sum(data ** 2) + eps)
    
    For N-D NDArray, if the input array has shape (N, N, ..., N),
    
    with ``mode`` = ``instance``, it normalizes each instance in the multidimensional
    array by its L2 norm.::
    
      for i in 0...N
        out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.::
    
      for i in 0...N
        out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position
    in the array by its L2 norm.::
    
      for dim in 2...N
        for i in 0...N
          out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
              -dim-
    
    Example::
    
      x = [[[1,2],
            [3,4]],
           [[2,2],
            [5,6]]]
    
      L2Normalization(x, mode='instance')
      =[[[ 0.18257418  0.36514837]
         [ 0.54772252  0.73029673]]
        [[ 0.24077171  0.24077171]
         [ 0.60192931  0.72231513]]]
    
      L2Normalization(x, mode='channel')
      =[[[ 0.31622776  0.44721359]
         [ 0.94868326  0.89442718]]
        [[ 0.37139067  0.31622776]
         [ 0.92847669  0.94868326]]]
    
      L2Normalization(x, mode='spatial')
      =[[[ 0.44721359  0.89442718]
         [ 0.60000002  0.80000001]]
        [[ 0.70710677  0.70710677]
         [ 0.6401844   0.76822126]]]
    
    
    
    Defined in src/operator/l2_normalization.cc:L98
    

    returns

    org.apache.mxnet.NDArray

  • abstract def L2Normalization(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Normalize the input array using the L2 norm.
    
    For 1-D NDArray, it computes::
    
      out = data / sqrt(sum(data ** 2) + eps)
    
    For N-D NDArray, if the input array has shape (N, N, ..., N),
    
    with ``mode`` = ``instance``, it normalizes each instance in the multidimensional
    array by its L2 norm.::
    
      for i in 0...N
        out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.::
    
      for i in 0...N
        out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position
    in the array by its L2 norm.::
    
      for dim in 2...N
        for i in 0...N
          out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
              -dim-
    
    Example::
    
      x = [[[1,2],
            [3,4]],
           [[2,2],
            [5,6]]]
    
      L2Normalization(x, mode='instance')
      =[[[ 0.18257418  0.36514837]
         [ 0.54772252  0.73029673]]
        [[ 0.24077171  0.24077171]
         [ 0.60192931  0.72231513]]]
    
      L2Normalization(x, mode='channel')
      =[[[ 0.31622776  0.44721359]
         [ 0.94868326  0.89442718]]
        [[ 0.37139067  0.31622776]
         [ 0.92847669  0.94868326]]]
    
      L2Normalization(x, mode='spatial')
      =[[[ 0.44721359  0.89442718]
         [ 0.60000002  0.80000001]]
        [[ 0.70710677  0.70710677]
         [ 0.6401844   0.76822126]]]
    
    
    
    Defined in src/operator/l2_normalization.cc:L98
    

  • Normalize the input array using the L2 norm.
    
    For 1-D NDArray, it computes::
    
      out = data / sqrt(sum(data ** 2) + eps)
    
    For N-D NDArray, if the input array has shape (N, N, ..., N),
    
    with ``mode`` = ``instance``, it normalizes each instance in the multidimensional
    array by its L2 norm.::
    
      for i in 0...N
        out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.::
    
      for i in 0...N
        out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position
    in the array by its L2 norm.::
    
      for dim in 2...N
        for i in 0...N
          out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
              -dim-
    
    Example::
    
      x = [[[1,2],
            [3,4]],
           [[2,2],
            [5,6]]]
    
      L2Normalization(x, mode='instance')
      =[[[ 0.18257418  0.36514837]
         [ 0.54772252  0.73029673]]
        [[ 0.24077171  0.24077171]
         [ 0.60192931  0.72231513]]]
    
      L2Normalization(x, mode='channel')
      =[[[ 0.31622776  0.44721359]
         [ 0.94868326  0.89442718]]
        [[ 0.37139067  0.31622776]
         [ 0.92847669  0.94868326]]]
    
      L2Normalization(x, mode='spatial')
      =[[[ 0.44721359  0.89442718]
         [ 0.60000002  0.80000001]]
        [[ 0.70710677  0.70710677]
         [ 0.6401844   0.76822126]]]
    
    
    
    Defined in src/operator/l2_normalization.cc:L98
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LRN(args: Any*): NDArrayFuncReturn

    Applies local response normalization to the input.
    
    The local response normalization layer performs "lateral inhibition" by normalizing
    over local input regions.
    
    If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel :math:`i` at position
    :math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized
    activity :math:`b_{x,y}^{i}` is given by the expression:
    
    .. math::
       b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}
    
    where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial position, and :math:`N` is the total
    number of kernels in the layer.
    
    
    
    Defined in src/operator/nn/lrn.cc:L164
    

  • Applies local response normalization to the input.
    
    The local response normalization layer performs "lateral inhibition" by normalizing
    over local input regions.
    
    If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel :math:`i` at position
    :math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized
    activity :math:`b_{x,y}^{i}` is given by the expression:
    
    .. math::
       b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}
    
    where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial position, and :math:`N` is the total
    number of kernels in the layer.
    
    
    
    Defined in src/operator/nn/lrn.cc:L164
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LRN(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies local response normalization to the input.
    
    The local response normalization layer performs "lateral inhibition" by normalizing
    over local input regions.
    
    If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel :math:`i` at position
    :math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized
    activity :math:`b_{x,y}^{i}` is given by the expression:
    
    .. math::
       b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}
    
    where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial position, and :math:`N` is the total
    number of kernels in the layer.
    
    
    
    Defined in src/operator/nn/lrn.cc:L164
    

  • Applies local response normalization to the input.
    
    The local response normalization layer performs "lateral inhibition" by normalizing
    over local input regions.
    
    If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel :math:`i` at position
    :math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized
    activity :math:`b_{x,y}^{i}` is given by the expression:
    
    .. math::
       b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}
    
    where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial position, and :math:`N` is the total
    number of kernels in the layer.
    
    
    
    Defined in src/operator/nn/lrn.cc:L164
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LayerNorm(args: Any*): NDArrayFuncReturn

    Layer normalization.
    
    Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis and then
    compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_std``. Note that no gradient will be passed through these two outputs.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is -1, which sets the channel
    axis to be the last item in the input shape.
    
    
    
    Defined in src/operator/nn/layer_norm.cc:L94
    

  • Layer normalization.
    
    Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis and then
    compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_std``. Note that no gradient will be passed through these two outputs.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is -1, which sets the channel
    axis to be the last item in the input shape.
    
    
    
    Defined in src/operator/nn/layer_norm.cc:L94
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LayerNorm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Layer normalization.
    
    Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis and then
    compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_std``. Note that no gradient will be passed through these two outputs.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is -1, which sets the channel
    axis to be the last item in the input shape.
    
    
    
    Defined in src/operator/nn/layer_norm.cc:L94
    

  • Layer normalization.
    
    Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis and then
    compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_std``. Note that no gradient will be passed through these two outputs.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is -1, which sets the channel
    axis to be the last item in the input shape.
    
    
    
    Defined in src/operator/nn/layer_norm.cc:L94
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LeakyReLU(args: Any*): NDArrayFuncReturn

    Applies Leaky rectified linear unit activation element-wise to the input.
    
    Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope`
    when the input is negative and has a slope of one when input is positive.
    
    The following modified ReLU Activation functions are supported:
    
    - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)`
    - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where
      *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
    - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x`
    - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training.
    - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from
      *[lower_bound, upper_bound)* for training, while fixed to be
      *(lower_bound+upper_bound)/2* for inference.
    
    
    
    Defined in src/operator/leaky_relu.cc:L65
    

  • Applies Leaky rectified linear unit activation element-wise to the input.
    
    Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope`
    when the input is negative and has a slope of one when input is positive.
    
    The following modified ReLU Activation functions are supported:
    
    - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)`
    - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where
      *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
    - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x`
    - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training.
    - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from
      *[lower_bound, upper_bound)* for training, while fixed to be
      *(lower_bound+upper_bound)/2* for inference.
    
    
    
    Defined in src/operator/leaky_relu.cc:L65
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LeakyReLU(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies Leaky rectified linear unit activation element-wise to the input.
    
    Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope`
    when the input is negative and has a slope of one when input is positive.
    
    The following modified ReLU Activation functions are supported:
    
    - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)`
    - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where
      *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
    - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x`
    - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training.
    - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from
      *[lower_bound, upper_bound)* for training, while fixed to be
      *(lower_bound+upper_bound)/2* for inference.
    
    
    
    Defined in src/operator/leaky_relu.cc:L65
    

  • Applies Leaky rectified linear unit activation element-wise to the input.
    
    Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope`
    when the input is negative and has a slope of one when input is positive.
    
    The following modified ReLU Activation functions are supported:
    
    - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)`
    - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where
      *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
    - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x`
    - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training.
    - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from
      *[lower_bound, upper_bound)* for training, while fixed to be
      *(lower_bound+upper_bound)/2* for inference.
    
    
    
    Defined in src/operator/leaky_relu.cc:L65
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LinearRegressionOutput(args: Any*): NDArrayFuncReturn

    Computes and optimizes for squared loss during backward propagation.
    Just outputs ``data`` during forward propagation.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the squared loss estimated over :math:`n` samples is defined as
    
    :math:`\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert  \textbf{y}_i - \hat{\textbf{y}}_i  \rVert_2`
    
    .. note::
       Use the LinearRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LinearRegressionOutput(default, default) = default
    - LinearRegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L92
    

  • Computes and optimizes for squared loss during backward propagation.
    Just outputs ``data`` during forward propagation.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the squared loss estimated over :math:`n` samples is defined as
    
    :math:`\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert  \textbf{y}_i - \hat{\textbf{y}}_i  \rVert_2`
    
    .. note::
       Use the LinearRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LinearRegressionOutput(default, default) = default
    - LinearRegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L92
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LinearRegressionOutput(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes and optimizes for squared loss during backward propagation.
    Just outputs ``data`` during forward propagation.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the squared loss estimated over :math:`n` samples is defined as
    
    :math:`\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert  \textbf{y}_i - \hat{\textbf{y}}_i  \rVert_2`
    
    .. note::
       Use the LinearRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LinearRegressionOutput(default, default) = default
    - LinearRegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L92
    

  • Computes and optimizes for squared loss during backward propagation.
    Just outputs ``data`` during forward propagation.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the squared loss estimated over :math:`n` samples is defined as
    
    :math:`\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert  \textbf{y}_i - \hat{\textbf{y}}_i  \rVert_2`
    
    .. note::
       Use the LinearRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LinearRegressionOutput(default, default) = default
    - LinearRegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L92
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LogisticRegressionOutput(args: Any*): NDArrayFuncReturn

    Applies a logistic function to the input.
    
    The logistic function, also known as the sigmoid function, is computed as
    :math:`\frac{1}{1+exp(-\textbf{x})}`.
    
    Commonly, the sigmoid is used to squash the real-valued output of a linear model
    :math:`wTx+b` into the [0,1] range so that it can be interpreted as a probability.
    It is suitable for binary classification or probability prediction tasks.
    
    .. note::
       Use the LogisticRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LogisticRegressionOutput(default, default) = default
    - LogisticRegressionOutput(default, csr) = default
    
    The loss function used is the Binary Cross Entropy Loss:
    
    :math:`-{(y\log(p) + (1 - y)\log(1 - p))}`
    
    Where `y` is the ground truth probability of positive outcome for a given example, and `p` the probability predicted by the model. By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L152
    

  • Applies a logistic function to the input.
    
    The logistic function, also known as the sigmoid function, is computed as
    :math:`\frac{1}{1+exp(-\textbf{x})}`.
    
    Commonly, the sigmoid is used to squash the real-valued output of a linear model
    :math:`wTx+b` into the [0,1] range so that it can be interpreted as a probability.
    It is suitable for binary classification or probability prediction tasks.
    
    .. note::
       Use the LogisticRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LogisticRegressionOutput(default, default) = default
    - LogisticRegressionOutput(default, csr) = default
    
    The loss function used is the Binary Cross Entropy Loss:
    
    :math:`-{(y\log(p) + (1 - y)\log(1 - p))}`
    
    Where `y` is the ground truth probability of positive outcome for a given example, and `p` the probability predicted by the model. By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L152
    

    returns

    org.apache.mxnet.NDArray

  • abstract def LogisticRegressionOutput(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies a logistic function to the input.
    
    The logistic function, also known as the sigmoid function, is computed as
    :math:`\frac{1}{1+exp(-\textbf{x})}`.
    
    Commonly, the sigmoid is used to squash the real-valued output of a linear model
    :math:`wTx+b` into the [0,1] range so that it can be interpreted as a probability.
    It is suitable for binary classification or probability prediction tasks.
    
    .. note::
       Use the LogisticRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LogisticRegressionOutput(default, default) = default
    - LogisticRegressionOutput(default, csr) = default
    
    The loss function used is the Binary Cross Entropy Loss:
    
    :math:`-{(y\log(p) + (1 - y)\log(1 - p))}`
    
    Where `y` is the ground truth probability of positive outcome for a given example, and `p` the probability predicted by the model. By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L152
    

  • Applies a logistic function to the input.
    
    The logistic function, also known as the sigmoid function, is computed as
    :math:`\frac{1}{1+exp(-\textbf{x})}`.
    
    Commonly, the sigmoid is used to squash the real-valued output of a linear model
    :math:`wTx+b` into the [0,1] range so that it can be interpreted as a probability.
    It is suitable for binary classification or probability prediction tasks.
    
    .. note::
       Use the LogisticRegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - LogisticRegressionOutput(default, default) = default
    - LogisticRegressionOutput(default, csr) = default
    
    The loss function used is the Binary Cross Entropy Loss:
    
    :math:`-{(y\log(p) + (1 - y)\log(1 - p))}`
    
    Where `y` is the ground truth probability of positive outcome for a given example, and `p` the probability predicted by the model. By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L152
    

    returns

    org.apache.mxnet.NDArray

  • abstract def MAERegressionOutput(args: Any*): NDArrayFuncReturn

    Computes mean absolute error of the input.
    
    MAE is a risk metric corresponding to the expected value of the absolute error.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the mean absolute error (MAE) estimated over :math:`n` samples is defined as
    
    :math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1`
    
    .. note::
       Use the MAERegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - MAERegressionOutput(default, default) = default
    - MAERegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L120
    

  • Computes mean absolute error of the input.
    
    MAE is a risk metric corresponding to the expected value of the absolute error.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the mean absolute error (MAE) estimated over :math:`n` samples is defined as
    
    :math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1`
    
    .. note::
       Use the MAERegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - MAERegressionOutput(default, default) = default
    - MAERegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L120
    

    returns

    org.apache.mxnet.NDArray

  • abstract def MAERegressionOutput(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes mean absolute error of the input.
    
    MAE is a risk metric corresponding to the expected value of the absolute error.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the mean absolute error (MAE) estimated over :math:`n` samples is defined as
    
    :math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1`
    
    .. note::
       Use the MAERegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - MAERegressionOutput(default, default) = default
    - MAERegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L120
    

  • Computes mean absolute error of the input.
    
    MAE is a risk metric corresponding to the expected value of the absolute error.
    
    If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value,
    then the mean absolute error (MAE) estimated over :math:`n` samples is defined as
    
    :math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1`
    
    .. note::
       Use the MAERegressionOutput as the final output layer of a net.
    
    The storage type of ``label`` can be ``default`` or ``csr``
    
    - MAERegressionOutput(default, default) = default
    - MAERegressionOutput(default, csr) = default
    
    By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
    The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.
    
    
    
    Defined in src/operator/regression_output.cc:L120
    

    returns

    org.apache.mxnet.NDArray

  • abstract def MakeLoss(args: Any*): NDArrayFuncReturn

    Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = MakeLoss(cross_entropy)
    
    We will need to use ``MakeLoss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    In addition, we can give a scale to the loss by setting ``grad_scale``,
    so that the gradient of the loss will be rescaled in the backpropagation.
    
    .. note:: This operator should be used as a Symbol instead of NDArray.
    
    
    
    Defined in src/operator/make_loss.cc:L71
    

  • Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = MakeLoss(cross_entropy)
    
    We will need to use ``MakeLoss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    In addition, we can give a scale to the loss by setting ``grad_scale``,
    so that the gradient of the loss will be rescaled in the backpropagation.
    
    .. note:: This operator should be used as a Symbol instead of NDArray.
    
    
    
    Defined in src/operator/make_loss.cc:L71
    

    returns

    org.apache.mxnet.NDArray

  • abstract def MakeLoss(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = MakeLoss(cross_entropy)
    
    We will need to use ``MakeLoss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    In addition, we can give a scale to the loss by setting ``grad_scale``,
    so that the gradient of the loss will be rescaled in the backpropagation.
    
    .. note:: This operator should be used as a Symbol instead of NDArray.
    
    
    
    Defined in src/operator/make_loss.cc:L71
    

  • Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = MakeLoss(cross_entropy)
    
    We will need to use ``MakeLoss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    In addition, we can give a scale to the loss by setting ``grad_scale``,
    so that the gradient of the loss will be rescaled in the backpropagation.
    
    .. note:: This operator should be used as a Symbol instead of NDArray.
    
    
    
    Defined in src/operator/make_loss.cc:L71
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Pad(args: Any*): NDArrayFuncReturn

    Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

  • Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Pad(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

  • Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Pooling(args: Any*): NDArrayFuncReturn

    Performs pooling on the input.
    
    The shapes for 1-D pooling are
    
    - **data**: *(batch_size, channel, width)*,
    - **out**: *(batch_size, num_filter, out_width)*.
    
    The shapes for 2-D pooling are
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    - **lp**: Lp pooling
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    Notes on Lp pooling:
    
    Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf.
    L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
    We can see that Lp pooling stands between those two, in practice the most common value for p is 2.
    
    For each window ``X``, the mathematical expression for Lp pooling is:
    
    :math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}`
    
    
    
    Defined in src/operator/nn/pooling.cc:L368
    

  • Performs pooling on the input.
    
    The shapes for 1-D pooling are
    
    - **data**: *(batch_size, channel, width)*,
    - **out**: *(batch_size, num_filter, out_width)*.
    
    The shapes for 2-D pooling are
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    - **lp**: Lp pooling
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    Notes on Lp pooling:
    
    Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf.
    L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
    We can see that Lp pooling stands between those two, in practice the most common value for p is 2.
    
    For each window ``X``, the mathematical expression for Lp pooling is:
    
    :math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}`
    
    
    
    Defined in src/operator/nn/pooling.cc:L368
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Pooling(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs pooling on the input.
    
    The shapes for 1-D pooling are
    
    - **data**: *(batch_size, channel, width)*,
    - **out**: *(batch_size, num_filter, out_width)*.
    
    The shapes for 2-D pooling are
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    - **lp**: Lp pooling
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    Notes on Lp pooling:
    
    Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf.
    L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
    We can see that Lp pooling stands between those two, in practice the most common value for p is 2.
    
    For each window ``X``, the mathematical expression for Lp pooling is:
    
    :math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}`
    
    
    
    Defined in src/operator/nn/pooling.cc:L368
    

  • Performs pooling on the input.
    
    The shapes for 1-D pooling are
    
    - **data**: *(batch_size, channel, width)*,
    - **out**: *(batch_size, num_filter, out_width)*.
    
    The shapes for 2-D pooling are
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    - **lp**: Lp pooling
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    Notes on Lp pooling:
    
    Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf.
    L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
    We can see that Lp pooling stands between those two, in practice the most common value for p is 2.
    
    For each window ``X``, the mathematical expression for Lp pooling is:
    
    :math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}`
    
    
    
    Defined in src/operator/nn/pooling.cc:L368
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Pooling_v1(args: Any*): NDArrayFuncReturn

    This operator is DEPRECATED.
    Perform pooling on the input.
    
    The shapes for 2-D pooling is
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    
    1-D pooling is special case of 2-D pooling with *weight=1* and
    *kernel[1]=1*.
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    
    
    Defined in src/operator/pooling_v1.cc:L104
    

  • This operator is DEPRECATED.
    Perform pooling on the input.
    
    The shapes for 2-D pooling is
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    
    1-D pooling is special case of 2-D pooling with *weight=1* and
    *kernel[1]=1*.
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    
    
    Defined in src/operator/pooling_v1.cc:L104
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Pooling_v1(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    This operator is DEPRECATED.
    Perform pooling on the input.
    
    The shapes for 2-D pooling is
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    
    1-D pooling is special case of 2-D pooling with *weight=1* and
    *kernel[1]=1*.
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    
    
    Defined in src/operator/pooling_v1.cc:L104
    

  • This operator is DEPRECATED.
    Perform pooling on the input.
    
    The shapes for 2-D pooling is
    
    - **data**: *(batch_size, channel, height, width)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*, with::
    
        out_height = f(height, kernel[0], pad[0], stride[0])
        out_width = f(width, kernel[1], pad[1], stride[1])
    
    The definition of *f* depends on ``pooling_convention``, which has two options:
    
    - **valid** (default)::
    
        f(x, k, p, s) = floor((x+2*p-k)/s)+1
    
    - **full**, which is compatible with Caffe::
    
        f(x, k, p, s) = ceil((x+2*p-k)/s)+1
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    
    1-D pooling is special case of 2-D pooling with *weight=1* and
    *kernel[1]=1*.
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data will have shape *(batch_size, channel, depth,
    height, width)*.
    
    
    
    Defined in src/operator/pooling_v1.cc:L104
    

    returns

    org.apache.mxnet.NDArray

  • abstract def RNN(args: Any*): NDArrayFuncReturn

    Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
    implemented, with both multi-layer and bidirectional support.
    
    **Vanilla RNN**
    
    Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported:
    ReLU and Tanh.
    
    With ReLU activation function:
    
    .. math::
        h_t = relu(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    With Tanh activtion function:
    
    .. math::
        h_t = \tanh(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    Reference paper: Finding structure in time - Elman, 1988.
    https://crl.ucsd.edu/~elman/Papers/fsit.pdf
    
    **LSTM**
    
    Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf
    
    .. math::
      \begin{array}{ll}
                i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\
                f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\
                g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\
                o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\
                c_t = f_t * c_{(t-1)} + i_t * g_t \\
                h_t = o_t * \tanh(c_t)
                \end{array}
    
    **GRU**
    
    Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078
    
    The definition of GRU here is slightly different from paper but compatible with CUDNN.
    
    .. math::
      \begin{array}{ll}
                r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
                z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
                n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
                h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\
                \end{array}
    

  • Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
    implemented, with both multi-layer and bidirectional support.
    
    **Vanilla RNN**
    
    Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported:
    ReLU and Tanh.
    
    With ReLU activation function:
    
    .. math::
        h_t = relu(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    With Tanh activtion function:
    
    .. math::
        h_t = \tanh(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    Reference paper: Finding structure in time - Elman, 1988.
    https://crl.ucsd.edu/~elman/Papers/fsit.pdf
    
    **LSTM**
    
    Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf
    
    .. math::
      \begin{array}{ll}
                i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\
                f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\
                g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\
                o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\
                c_t = f_t * c_{(t-1)} + i_t * g_t \\
                h_t = o_t * \tanh(c_t)
                \end{array}
    
    **GRU**
    
    Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078
    
    The definition of GRU here is slightly different from paper but compatible with CUDNN.
    
    .. math::
      \begin{array}{ll}
                r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
                z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
                n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
                h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\
                \end{array}
    

    returns

    org.apache.mxnet.NDArray

  • abstract def RNN(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
    implemented, with both multi-layer and bidirectional support.
    
    **Vanilla RNN**
    
    Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported:
    ReLU and Tanh.
    
    With ReLU activation function:
    
    .. math::
        h_t = relu(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    With Tanh activtion function:
    
    .. math::
        h_t = \tanh(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    Reference paper: Finding structure in time - Elman, 1988.
    https://crl.ucsd.edu/~elman/Papers/fsit.pdf
    
    **LSTM**
    
    Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf
    
    .. math::
      \begin{array}{ll}
                i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\
                f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\
                g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\
                o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\
                c_t = f_t * c_{(t-1)} + i_t * g_t \\
                h_t = o_t * \tanh(c_t)
                \end{array}
    
    **GRU**
    
    Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078
    
    The definition of GRU here is slightly different from paper but compatible with CUDNN.
    
    .. math::
      \begin{array}{ll}
                r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
                z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
                n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
                h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\
                \end{array}
    

  • Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
    implemented, with both multi-layer and bidirectional support.
    
    **Vanilla RNN**
    
    Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported:
    ReLU and Tanh.
    
    With ReLU activation function:
    
    .. math::
        h_t = relu(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    With Tanh activtion function:
    
    .. math::
        h_t = \tanh(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})
    
    Reference paper: Finding structure in time - Elman, 1988.
    https://crl.ucsd.edu/~elman/Papers/fsit.pdf
    
    **LSTM**
    
    Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf
    
    .. math::
      \begin{array}{ll}
                i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\
                f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\
                g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\
                o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\
                c_t = f_t * c_{(t-1)} + i_t * g_t \\
                h_t = o_t * \tanh(c_t)
                \end{array}
    
    **GRU**
    
    Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078
    
    The definition of GRU here is slightly different from paper but compatible with CUDNN.
    
    .. math::
      \begin{array}{ll}
                r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
                z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
                n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
                h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\
                \end{array}
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ROIPooling(args: Any*): NDArrayFuncReturn

    Performs region of interest(ROI) pooling on the input array.
    
    ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
    region of interest is a parameter. Its purpose is to perform max pooling on the inputs
    of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
    layer mostly used in training a `Fast R-CNN` network for object detection.
    
    This operator takes a 4D feature map as an input array and region proposals as `rois`,
    then it pools over sub-regions of input and produces a fixed-sized output array
    regardless of the ROI size.
    
    To crop the feature map accordingly, you can resize the bounding box coordinates
    by changing the parameters `rois` and `spatial_scale`.
    
    The cropped feature maps are pooled by standard max pooling operation to a fixed size output
    indicated by a `pooled_size` parameter. batch_size will change to the number of region
    bounding boxes after `ROIPooling`.
    
    The size of each region of interest doesn't have to be perfectly divisible by
    the number of pooling sections(`pooled_size`).
    
    Example::
    
      x = [[[[  0.,   1.,   2.,   3.,   4.,   5.],
             [  6.,   7.,   8.,   9.,  10.,  11.],
             [ 12.,  13.,  14.,  15.,  16.,  17.],
             [ 18.,  19.,  20.,  21.,  22.,  23.],
             [ 24.,  25.,  26.,  27.,  28.,  29.],
             [ 30.,  31.,  32.,  33.,  34.,  35.],
             [ 36.,  37.,  38.,  39.,  40.,  41.],
             [ 42.,  43.,  44.,  45.,  46.,  47.]]]]
    
      // region of interest i.e. bounding box coordinates.
      y = [[0,0,0,4,4]]
    
      // returns array of shape (2,2) according to the given roi with max pooling.
      ROIPooling(x, y, (2,2), 1.0) = [[[[ 14.,  16.],
                                        [ 26.,  28.]]]]
    
      // region of interest is changed due to the change in `spacial_scale` parameter.
      ROIPooling(x, y, (2,2), 0.7) = [[[[  7.,   9.],
                                        [ 19.,  21.]]]]
    
    
    
    Defined in src/operator/roi_pooling.cc:L295
    

  • Performs region of interest(ROI) pooling on the input array.
    
    ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
    region of interest is a parameter. Its purpose is to perform max pooling on the inputs
    of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
    layer mostly used in training a `Fast R-CNN` network for object detection.
    
    This operator takes a 4D feature map as an input array and region proposals as `rois`,
    then it pools over sub-regions of input and produces a fixed-sized output array
    regardless of the ROI size.
    
    To crop the feature map accordingly, you can resize the bounding box coordinates
    by changing the parameters `rois` and `spatial_scale`.
    
    The cropped feature maps are pooled by standard max pooling operation to a fixed size output
    indicated by a `pooled_size` parameter. batch_size will change to the number of region
    bounding boxes after `ROIPooling`.
    
    The size of each region of interest doesn't have to be perfectly divisible by
    the number of pooling sections(`pooled_size`).
    
    Example::
    
      x = [[[[  0.,   1.,   2.,   3.,   4.,   5.],
             [  6.,   7.,   8.,   9.,  10.,  11.],
             [ 12.,  13.,  14.,  15.,  16.,  17.],
             [ 18.,  19.,  20.,  21.,  22.,  23.],
             [ 24.,  25.,  26.,  27.,  28.,  29.],
             [ 30.,  31.,  32.,  33.,  34.,  35.],
             [ 36.,  37.,  38.,  39.,  40.,  41.],
             [ 42.,  43.,  44.,  45.,  46.,  47.]]]]
    
      // region of interest i.e. bounding box coordinates.
      y = [[0,0,0,4,4]]
    
      // returns array of shape (2,2) according to the given roi with max pooling.
      ROIPooling(x, y, (2,2), 1.0) = [[[[ 14.,  16.],
                                        [ 26.,  28.]]]]
    
      // region of interest is changed due to the change in `spacial_scale` parameter.
      ROIPooling(x, y, (2,2), 0.7) = [[[[  7.,   9.],
                                        [ 19.,  21.]]]]
    
    
    
    Defined in src/operator/roi_pooling.cc:L295
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ROIPooling(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs region of interest(ROI) pooling on the input array.
    
    ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
    region of interest is a parameter. Its purpose is to perform max pooling on the inputs
    of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
    layer mostly used in training a `Fast R-CNN` network for object detection.
    
    This operator takes a 4D feature map as an input array and region proposals as `rois`,
    then it pools over sub-regions of input and produces a fixed-sized output array
    regardless of the ROI size.
    
    To crop the feature map accordingly, you can resize the bounding box coordinates
    by changing the parameters `rois` and `spatial_scale`.
    
    The cropped feature maps are pooled by standard max pooling operation to a fixed size output
    indicated by a `pooled_size` parameter. batch_size will change to the number of region
    bounding boxes after `ROIPooling`.
    
    The size of each region of interest doesn't have to be perfectly divisible by
    the number of pooling sections(`pooled_size`).
    
    Example::
    
      x = [[[[  0.,   1.,   2.,   3.,   4.,   5.],
             [  6.,   7.,   8.,   9.,  10.,  11.],
             [ 12.,  13.,  14.,  15.,  16.,  17.],
             [ 18.,  19.,  20.,  21.,  22.,  23.],
             [ 24.,  25.,  26.,  27.,  28.,  29.],
             [ 30.,  31.,  32.,  33.,  34.,  35.],
             [ 36.,  37.,  38.,  39.,  40.,  41.],
             [ 42.,  43.,  44.,  45.,  46.,  47.]]]]
    
      // region of interest i.e. bounding box coordinates.
      y = [[0,0,0,4,4]]
    
      // returns array of shape (2,2) according to the given roi with max pooling.
      ROIPooling(x, y, (2,2), 1.0) = [[[[ 14.,  16.],
                                        [ 26.,  28.]]]]
    
      // region of interest is changed due to the change in `spacial_scale` parameter.
      ROIPooling(x, y, (2,2), 0.7) = [[[[  7.,   9.],
                                        [ 19.,  21.]]]]
    
    
    
    Defined in src/operator/roi_pooling.cc:L295
    

  • Performs region of interest(ROI) pooling on the input array.
    
    ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
    region of interest is a parameter. Its purpose is to perform max pooling on the inputs
    of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
    layer mostly used in training a `Fast R-CNN` network for object detection.
    
    This operator takes a 4D feature map as an input array and region proposals as `rois`,
    then it pools over sub-regions of input and produces a fixed-sized output array
    regardless of the ROI size.
    
    To crop the feature map accordingly, you can resize the bounding box coordinates
    by changing the parameters `rois` and `spatial_scale`.
    
    The cropped feature maps are pooled by standard max pooling operation to a fixed size output
    indicated by a `pooled_size` parameter. batch_size will change to the number of region
    bounding boxes after `ROIPooling`.
    
    The size of each region of interest doesn't have to be perfectly divisible by
    the number of pooling sections(`pooled_size`).
    
    Example::
    
      x = [[[[  0.,   1.,   2.,   3.,   4.,   5.],
             [  6.,   7.,   8.,   9.,  10.,  11.],
             [ 12.,  13.,  14.,  15.,  16.,  17.],
             [ 18.,  19.,  20.,  21.,  22.,  23.],
             [ 24.,  25.,  26.,  27.,  28.,  29.],
             [ 30.,  31.,  32.,  33.,  34.,  35.],
             [ 36.,  37.,  38.,  39.,  40.,  41.],
             [ 42.,  43.,  44.,  45.,  46.,  47.]]]]
    
      // region of interest i.e. bounding box coordinates.
      y = [[0,0,0,4,4]]
    
      // returns array of shape (2,2) according to the given roi with max pooling.
      ROIPooling(x, y, (2,2), 1.0) = [[[[ 14.,  16.],
                                        [ 26.,  28.]]]]
    
      // region of interest is changed due to the change in `spacial_scale` parameter.
      ROIPooling(x, y, (2,2), 0.7) = [[[[  7.,   9.],
                                        [ 19.,  21.]]]]
    
    
    
    Defined in src/operator/roi_pooling.cc:L295
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Reshape(args: Any*): NDArrayFuncReturn

    Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

  • Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Reshape(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

  • Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SVMOutput(args: Any*): NDArrayFuncReturn

    Computes support vector machine based transformation of the input.
    
    This tutorial demonstrates using SVM as output layer for classification instead of softmax:
    https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
    

  • Computes support vector machine based transformation of the input.
    
    This tutorial demonstrates using SVM as output layer for classification instead of softmax:
    https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SVMOutput(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes support vector machine based transformation of the input.
    
    This tutorial demonstrates using SVM as output layer for classification instead of softmax:
    https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
    

  • Computes support vector machine based transformation of the input.
    
    This tutorial demonstrates using SVM as output layer for classification instead of softmax:
    https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SequenceLast(args: Any*): NDArrayFuncReturn

    Takes the last element of a sequence.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
    of the form [batch_size, other_feature_dims].
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be
    an input array of positive ints of dimension [batch_size]. To use this parameter,
    set `use_sequence_length` to `True`, otherwise each example in the batch is assumed
    to have the max sequence length.
    
    .. note:: Alternatively, you can also use `take` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.],
             [  7.,   8.,   9.]],
    
            [[ 10.,   11.,   12.],
             [ 13.,   14.,   15.],
             [ 16.,   17.,   18.]],
    
            [[  19.,   20.,   21.],
             [  22.,   23.,   24.],
             [  25.,   26.,   27.]]]
    
       // returns last sequence when sequence_length parameter is not used
       SequenceLast(x) = [[  19.,   20.,   21.],
                          [  22.,   23.,   24.],
                          [  25.,   26.,   27.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
                [[  1.,   2.,   3.],
                 [  4.,   5.,   6.],
                 [  7.,   8.,   9.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
                [[  1.,    2.,   3.],
                 [  13.,  14.,  15.],
                 [  25.,  26.,  27.]]
    
    
    
    Defined in src/operator/sequence_last.cc:L92
    

  • Takes the last element of a sequence.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
    of the form [batch_size, other_feature_dims].
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be
    an input array of positive ints of dimension [batch_size]. To use this parameter,
    set `use_sequence_length` to `True`, otherwise each example in the batch is assumed
    to have the max sequence length.
    
    .. note:: Alternatively, you can also use `take` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.],
             [  7.,   8.,   9.]],
    
            [[ 10.,   11.,   12.],
             [ 13.,   14.,   15.],
             [ 16.,   17.,   18.]],
    
            [[  19.,   20.,   21.],
             [  22.,   23.,   24.],
             [  25.,   26.,   27.]]]
    
       // returns last sequence when sequence_length parameter is not used
       SequenceLast(x) = [[  19.,   20.,   21.],
                          [  22.,   23.,   24.],
                          [  25.,   26.,   27.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
                [[  1.,   2.,   3.],
                 [  4.,   5.,   6.],
                 [  7.,   8.,   9.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
                [[  1.,    2.,   3.],
                 [  13.,  14.,  15.],
                 [  25.,  26.,  27.]]
    
    
    
    Defined in src/operator/sequence_last.cc:L92
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SequenceLast(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Takes the last element of a sequence.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
    of the form [batch_size, other_feature_dims].
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be
    an input array of positive ints of dimension [batch_size]. To use this parameter,
    set `use_sequence_length` to `True`, otherwise each example in the batch is assumed
    to have the max sequence length.
    
    .. note:: Alternatively, you can also use `take` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.],
             [  7.,   8.,   9.]],
    
            [[ 10.,   11.,   12.],
             [ 13.,   14.,   15.],
             [ 16.,   17.,   18.]],
    
            [[  19.,   20.,   21.],
             [  22.,   23.,   24.],
             [  25.,   26.,   27.]]]
    
       // returns last sequence when sequence_length parameter is not used
       SequenceLast(x) = [[  19.,   20.,   21.],
                          [  22.,   23.,   24.],
                          [  25.,   26.,   27.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
                [[  1.,   2.,   3.],
                 [  4.,   5.,   6.],
                 [  7.,   8.,   9.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
                [[  1.,    2.,   3.],
                 [  13.,  14.,  15.],
                 [  25.,  26.,  27.]]
    
    
    
    Defined in src/operator/sequence_last.cc:L92
    

  • Takes the last element of a sequence.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
    of the form [batch_size, other_feature_dims].
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be
    an input array of positive ints of dimension [batch_size]. To use this parameter,
    set `use_sequence_length` to `True`, otherwise each example in the batch is assumed
    to have the max sequence length.
    
    .. note:: Alternatively, you can also use `take` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.],
             [  7.,   8.,   9.]],
    
            [[ 10.,   11.,   12.],
             [ 13.,   14.,   15.],
             [ 16.,   17.,   18.]],
    
            [[  19.,   20.,   21.],
             [  22.,   23.,   24.],
             [  25.,   26.,   27.]]]
    
       // returns last sequence when sequence_length parameter is not used
       SequenceLast(x) = [[  19.,   20.,   21.],
                          [  22.,   23.,   24.],
                          [  25.,   26.,   27.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
                [[  1.,   2.,   3.],
                 [  4.,   5.,   6.],
                 [  7.,   8.,   9.]]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
                [[  1.,    2.,   3.],
                 [  13.,  14.,  15.],
                 [  25.,  26.,  27.]]
    
    
    
    Defined in src/operator/sequence_last.cc:L92
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SequenceMask(args: Any*): NDArrayFuncReturn

    Sets all elements outside the sequence to a constant value.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length`
    should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length and
    this operator works as the `identity` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // works as identity operator when sequence_length parameter is not used
       SequenceMask(x) = [[[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [1,1] means 1 of each batch will be kept
       // and other rows are masked with default mask value = 0
       SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]]]
    
       // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
       // and other rows are masked with value = 1
       SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  7.,   8.,   9.],
                      [  10.,  11.,  12.]],
    
                     [[   1.,   1.,   1.],
                      [  16.,  17.,  18.]]]
    
    
    
    Defined in src/operator/sequence_mask.cc:L114
    

  • Sets all elements outside the sequence to a constant value.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length`
    should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length and
    this operator works as the `identity` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // works as identity operator when sequence_length parameter is not used
       SequenceMask(x) = [[[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [1,1] means 1 of each batch will be kept
       // and other rows are masked with default mask value = 0
       SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]]]
    
       // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
       // and other rows are masked with value = 1
       SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  7.,   8.,   9.],
                      [  10.,  11.,  12.]],
    
                     [[   1.,   1.,   1.],
                      [  16.,  17.,  18.]]]
    
    
    
    Defined in src/operator/sequence_mask.cc:L114
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SequenceMask(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Sets all elements outside the sequence to a constant value.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length`
    should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length and
    this operator works as the `identity` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // works as identity operator when sequence_length parameter is not used
       SequenceMask(x) = [[[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [1,1] means 1 of each batch will be kept
       // and other rows are masked with default mask value = 0
       SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]]]
    
       // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
       // and other rows are masked with value = 1
       SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  7.,   8.,   9.],
                      [  10.,  11.,  12.]],
    
                     [[   1.,   1.,   1.],
                      [  16.,  17.,  18.]]]
    
    
    
    Defined in src/operator/sequence_mask.cc:L114
    

  • Sets all elements outside the sequence to a constant value.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length`
    should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length and
    this operator works as the `identity` operator.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // works as identity operator when sequence_length parameter is not used
       SequenceMask(x) = [[[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [1,1] means 1 of each batch will be kept
       // and other rows are masked with default mask value = 0
       SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]],
    
                     [[  0.,   0.,   0.],
                      [  0.,   0.,   0.]]]
    
       // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
       // and other rows are masked with value = 1
       SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) =
                    [[[  1.,   2.,   3.],
                      [  4.,   5.,   6.]],
    
                     [[  7.,   8.,   9.],
                      [  10.,  11.,  12.]],
    
                     [[   1.,   1.,   1.],
                      [  16.,  17.,  18.]]]
    
    
    
    Defined in src/operator/sequence_mask.cc:L114
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SequenceReverse(args: Any*): NDArrayFuncReturn

    Reverses the elements of each sequence.
    
    This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
    and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences.
    `sequence_length` should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // returns reverse sequence when sequence_length parameter is not used
       SequenceReverse(x) = [[[ 13.,  14.,   15.],
                              [ 16.,  17.,   18.]],
    
                             [[  7.,   8.,   9.],
                              [ 10.,  11.,  12.]],
    
                             [[  1.,   2.,   3.],
                              [  4.,   5.,   6.]]]
    
       // sequence_length [2,2] means 2 rows of
       // both batch B1 and B2 will be reversed.
       SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
                         [[[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
       // will be reversed.
       SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
                        [[[  7.,   8.,   9.],
                          [ 16.,  17.,  18.]],
    
                         [[  1.,   2.,   3.],
                          [ 10.,  11.,  12.]],
    
                         [[ 13.,  14,   15.],
                          [  4.,   5.,   6.]]]
    
    
    
    Defined in src/operator/sequence_reverse.cc:L113
    

  • Reverses the elements of each sequence.
    
    This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
    and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences.
    `sequence_length` should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // returns reverse sequence when sequence_length parameter is not used
       SequenceReverse(x) = [[[ 13.,  14.,   15.],
                              [ 16.,  17.,   18.]],
    
                             [[  7.,   8.,   9.],
                              [ 10.,  11.,  12.]],
    
                             [[  1.,   2.,   3.],
                              [  4.,   5.,   6.]]]
    
       // sequence_length [2,2] means 2 rows of
       // both batch B1 and B2 will be reversed.
       SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
                         [[[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
       // will be reversed.
       SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
                        [[[  7.,   8.,   9.],
                          [ 16.,  17.,  18.]],
    
                         [[  1.,   2.,   3.],
                          [ 10.,  11.,  12.]],
    
                         [[ 13.,  14,   15.],
                          [  4.,   5.,   6.]]]
    
    
    
    Defined in src/operator/sequence_reverse.cc:L113
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SequenceReverse(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Reverses the elements of each sequence.
    
    This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
    and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences.
    `sequence_length` should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // returns reverse sequence when sequence_length parameter is not used
       SequenceReverse(x) = [[[ 13.,  14.,   15.],
                              [ 16.,  17.,   18.]],
    
                             [[  7.,   8.,   9.],
                              [ 10.,  11.,  12.]],
    
                             [[  1.,   2.,   3.],
                              [  4.,   5.,   6.]]]
    
       // sequence_length [2,2] means 2 rows of
       // both batch B1 and B2 will be reversed.
       SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
                         [[[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
       // will be reversed.
       SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
                        [[[  7.,   8.,   9.],
                          [ 16.,  17.,  18.]],
    
                         [[  1.,   2.,   3.],
                          [ 10.,  11.,  12.]],
    
                         [[ 13.,  14,   15.],
                          [  4.,   5.,   6.]]]
    
    
    
    Defined in src/operator/sequence_reverse.cc:L113
    

  • Reverses the elements of each sequence.
    
    This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
    and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences.
    `sequence_length` should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length.
    
    Example::
    
       x = [[[  1.,   2.,   3.],
             [  4.,   5.,   6.]],
    
            [[  7.,   8.,   9.],
             [ 10.,  11.,  12.]],
    
            [[ 13.,  14.,   15.],
             [ 16.,  17.,   18.]]]
    
       // Batch 1
       B1 = [[  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.]]
    
       // Batch 2
       B2 = [[  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.]]
    
       // returns reverse sequence when sequence_length parameter is not used
       SequenceReverse(x) = [[[ 13.,  14.,   15.],
                              [ 16.,  17.,   18.]],
    
                             [[  7.,   8.,   9.],
                              [ 10.,  11.,  12.]],
    
                             [[  1.,   2.,   3.],
                              [  4.,   5.,   6.]]]
    
       // sequence_length [2,2] means 2 rows of
       // both batch B1 and B2 will be reversed.
       SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
                         [[[  7.,   8.,   9.],
                           [ 10.,  11.,  12.]],
    
                          [[  1.,   2.,   3.],
                           [  4.,   5.,   6.]],
    
                          [[ 13.,  14.,   15.],
                           [ 16.,  17.,   18.]]]
    
       // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
       // will be reversed.
       SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
                        [[[  7.,   8.,   9.],
                          [ 16.,  17.,  18.]],
    
                         [[  1.,   2.,   3.],
                          [ 10.,  11.,  12.]],
    
                         [[ 13.,  14,   15.],
                          [  4.,   5.,   6.]]]
    
    
    
    Defined in src/operator/sequence_reverse.cc:L113
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SliceChannel(args: Any*): NDArrayFuncReturn

    Splits an array along a particular axis into multiple sub-arrays.
    
    .. note:: ``SliceChannel`` is deprecated. Use ``split`` instead.
    
    **Note** that `num_outputs` should evenly divide the length of the axis
    along which to split the array.
    
    Example::
    
       x  = [[[ 1.]
              [ 2.]]
             [[ 3.]
              [ 4.]]
             [[ 5.]
              [ 6.]]]
       x.shape = (3, 2, 1)
    
       y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
       y = [[[ 1.]]
            [[ 3.]]
            [[ 5.]]]
    
           [[[ 2.]]
            [[ 4.]]
            [[ 6.]]]
    
       y[0].shape = (3, 1, 1)
    
       z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
       z = [[[ 1.]
             [ 2.]]]
    
           [[[ 3.]
             [ 4.]]]
    
           [[[ 5.]
             [ 6.]]]
    
       z[0].shape = (1, 2, 1)
    
    `squeeze_axis=1` removes the axis with length 1 from the shapes of the output arrays.
    **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only
    along the `axis` which it is split.
    Also `squeeze_axis` can be set to true only if ``input.shape[axis] == num_outputs``.
    
    Example::
    
       z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
       z = [[ 1.]
            [ 2.]]
    
           [[ 3.]
            [ 4.]]
    
           [[ 5.]
            [ 6.]]
       z[0].shape = (2 ,1 )
    
    
    
    Defined in src/operator/slice_channel.cc:L107
    

  • Splits an array along a particular axis into multiple sub-arrays.
    
    .. note:: ``SliceChannel`` is deprecated. Use ``split`` instead.
    
    **Note** that `num_outputs` should evenly divide the length of the axis
    along which to split the array.
    
    Example::
    
       x  = [[[ 1.]
              [ 2.]]
             [[ 3.]
              [ 4.]]
             [[ 5.]
              [ 6.]]]
       x.shape = (3, 2, 1)
    
       y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
       y = [[[ 1.]]
            [[ 3.]]
            [[ 5.]]]
    
           [[[ 2.]]
            [[ 4.]]
            [[ 6.]]]
    
       y[0].shape = (3, 1, 1)
    
       z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
       z = [[[ 1.]
             [ 2.]]]
    
           [[[ 3.]
             [ 4.]]]
    
           [[[ 5.]
             [ 6.]]]
    
       z[0].shape = (1, 2, 1)
    
    `squeeze_axis=1` removes the axis with length 1 from the shapes of the output arrays.
    **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only
    along the `axis` which it is split.
    Also `squeeze_axis` can be set to true only if ``input.shape[axis] == num_outputs``.
    
    Example::
    
       z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
       z = [[ 1.]
            [ 2.]]
    
           [[ 3.]
            [ 4.]]
    
           [[ 5.]
            [ 6.]]
       z[0].shape = (2 ,1 )
    
    
    
    Defined in src/operator/slice_channel.cc:L107
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SliceChannel(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Splits an array along a particular axis into multiple sub-arrays.
    
    .. note:: ``SliceChannel`` is deprecated. Use ``split`` instead.
    
    **Note** that `num_outputs` should evenly divide the length of the axis
    along which to split the array.
    
    Example::
    
       x  = [[[ 1.]
              [ 2.]]
             [[ 3.]
              [ 4.]]
             [[ 5.]
              [ 6.]]]
       x.shape = (3, 2, 1)
    
       y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
       y = [[[ 1.]]
            [[ 3.]]
            [[ 5.]]]
    
           [[[ 2.]]
            [[ 4.]]
            [[ 6.]]]
    
       y[0].shape = (3, 1, 1)
    
       z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
       z = [[[ 1.]
             [ 2.]]]
    
           [[[ 3.]
             [ 4.]]]
    
           [[[ 5.]
             [ 6.]]]
    
       z[0].shape = (1, 2, 1)
    
    `squeeze_axis=1` removes the axis with length 1 from the shapes of the output arrays.
    **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only
    along the `axis` which it is split.
    Also `squeeze_axis` can be set to true only if ``input.shape[axis] == num_outputs``.
    
    Example::
    
       z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
       z = [[ 1.]
            [ 2.]]
    
           [[ 3.]
            [ 4.]]
    
           [[ 5.]
            [ 6.]]
       z[0].shape = (2 ,1 )
    
    
    
    Defined in src/operator/slice_channel.cc:L107
    

  • Splits an array along a particular axis into multiple sub-arrays.
    
    .. note:: ``SliceChannel`` is deprecated. Use ``split`` instead.
    
    **Note** that `num_outputs` should evenly divide the length of the axis
    along which to split the array.
    
    Example::
    
       x  = [[[ 1.]
              [ 2.]]
             [[ 3.]
              [ 4.]]
             [[ 5.]
              [ 6.]]]
       x.shape = (3, 2, 1)
    
       y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
       y = [[[ 1.]]
            [[ 3.]]
            [[ 5.]]]
    
           [[[ 2.]]
            [[ 4.]]
            [[ 6.]]]
    
       y[0].shape = (3, 1, 1)
    
       z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
       z = [[[ 1.]
             [ 2.]]]
    
           [[[ 3.]
             [ 4.]]]
    
           [[[ 5.]
             [ 6.]]]
    
       z[0].shape = (1, 2, 1)
    
    `squeeze_axis=1` removes the axis with length 1 from the shapes of the output arrays.
    **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only
    along the `axis` which it is split.
    Also `squeeze_axis` can be set to true only if ``input.shape[axis] == num_outputs``.
    
    Example::
    
       z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
       z = [[ 1.]
            [ 2.]]
    
           [[ 3.]
            [ 4.]]
    
           [[ 5.]
            [ 6.]]
       z[0].shape = (2 ,1 )
    
    
    
    Defined in src/operator/slice_channel.cc:L107
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Softmax(args: Any*): NDArrayFuncReturn

    Please use `SoftmaxOutput`.
    
    .. note::
    
      This operator has been renamed to `SoftmaxOutput`, which
      computes the gradient of cross-entropy loss w.r.t softmax output.
      To just compute softmax output, use the `softmax` operator.
    
    
    
    Defined in src/operator/softmax_output.cc:L138
    

  • Please use `SoftmaxOutput`.
    
    .. note::
    
      This operator has been renamed to `SoftmaxOutput`, which
      computes the gradient of cross-entropy loss w.r.t softmax output.
      To just compute softmax output, use the `softmax` operator.
    
    
    
    Defined in src/operator/softmax_output.cc:L138
    

    returns

    org.apache.mxnet.NDArray

  • abstract def Softmax(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Please use `SoftmaxOutput`.
    
    .. note::
    
      This operator has been renamed to `SoftmaxOutput`, which
      computes the gradient of cross-entropy loss w.r.t softmax output.
      To just compute softmax output, use the `softmax` operator.
    
    
    
    Defined in src/operator/softmax_output.cc:L138
    

  • Please use `SoftmaxOutput`.
    
    .. note::
    
      This operator has been renamed to `SoftmaxOutput`, which
      computes the gradient of cross-entropy loss w.r.t softmax output.
      To just compute softmax output, use the `softmax` operator.
    
    
    
    Defined in src/operator/softmax_output.cc:L138
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SoftmaxActivation(args: Any*): NDArrayFuncReturn

    Applies softmax activation to input. This is intended for internal layers.
    
    .. note::
    
      This operator has been deprecated, please use `softmax`.
    
    If `mode` = ``instance``, this operator will compute a softmax for each instance in the batch.
    This is the default mode.
    
    If `mode` = ``channel``, this operator will compute a k-class softmax at each position
    of each instance, where `k` = ``num_channel``. This mode can only be used when the input array
    has at least 3 dimensions.
    This can be used for `fully convolutional network`, `image segmentation`, etc.
    
    Example::
    
      >>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.],
      >>>                            [2., -.4, 7.,   3., 0.2]])
      >>> softmax_act = mx.nd.SoftmaxActivation(input_array)
      >>> print softmax_act.asnumpy()
      [[  1.78322066e-02   1.46375655e-03   5.38485940e-04   6.56010211e-03   9.73605454e-01]
       [  6.56221947e-03   5.95310994e-04   9.73919690e-01   1.78379621e-02   1.08472735e-03]]
    
    
    
    Defined in src/operator/nn/softmax_activation.cc:L59
    

  • Applies softmax activation to input. This is intended for internal layers.
    
    .. note::
    
      This operator has been deprecated, please use `softmax`.
    
    If `mode` = ``instance``, this operator will compute a softmax for each instance in the batch.
    This is the default mode.
    
    If `mode` = ``channel``, this operator will compute a k-class softmax at each position
    of each instance, where `k` = ``num_channel``. This mode can only be used when the input array
    has at least 3 dimensions.
    This can be used for `fully convolutional network`, `image segmentation`, etc.
    
    Example::
    
      >>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.],
      >>>                            [2., -.4, 7.,   3., 0.2]])
      >>> softmax_act = mx.nd.SoftmaxActivation(input_array)
      >>> print softmax_act.asnumpy()
      [[  1.78322066e-02   1.46375655e-03   5.38485940e-04   6.56010211e-03   9.73605454e-01]
       [  6.56221947e-03   5.95310994e-04   9.73919690e-01   1.78379621e-02   1.08472735e-03]]
    
    
    
    Defined in src/operator/nn/softmax_activation.cc:L59
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SoftmaxActivation(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies softmax activation to input. This is intended for internal layers.
    
    .. note::
    
      This operator has been deprecated, please use `softmax`.
    
    If `mode` = ``instance``, this operator will compute a softmax for each instance in the batch.
    This is the default mode.
    
    If `mode` = ``channel``, this operator will compute a k-class softmax at each position
    of each instance, where `k` = ``num_channel``. This mode can only be used when the input array
    has at least 3 dimensions.
    This can be used for `fully convolutional network`, `image segmentation`, etc.
    
    Example::
    
      >>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.],
      >>>                            [2., -.4, 7.,   3., 0.2]])
      >>> softmax_act = mx.nd.SoftmaxActivation(input_array)
      >>> print softmax_act.asnumpy()
      [[  1.78322066e-02   1.46375655e-03   5.38485940e-04   6.56010211e-03   9.73605454e-01]
       [  6.56221947e-03   5.95310994e-04   9.73919690e-01   1.78379621e-02   1.08472735e-03]]
    
    
    
    Defined in src/operator/nn/softmax_activation.cc:L59
    

  • Applies softmax activation to input. This is intended for internal layers.
    
    .. note::
    
      This operator has been deprecated, please use `softmax`.
    
    If `mode` = ``instance``, this operator will compute a softmax for each instance in the batch.
    This is the default mode.
    
    If `mode` = ``channel``, this operator will compute a k-class softmax at each position
    of each instance, where `k` = ``num_channel``. This mode can only be used when the input array
    has at least 3 dimensions.
    This can be used for `fully convolutional network`, `image segmentation`, etc.
    
    Example::
    
      >>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.],
      >>>                            [2., -.4, 7.,   3., 0.2]])
      >>> softmax_act = mx.nd.SoftmaxActivation(input_array)
      >>> print softmax_act.asnumpy()
      [[  1.78322066e-02   1.46375655e-03   5.38485940e-04   6.56010211e-03   9.73605454e-01]
       [  6.56221947e-03   5.95310994e-04   9.73919690e-01   1.78379621e-02   1.08472735e-03]]
    
    
    
    Defined in src/operator/nn/softmax_activation.cc:L59
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SoftmaxOutput(args: Any*): NDArrayFuncReturn

    Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          [[ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]]
          ## backward gradient output
          [[ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75]]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L123
    

  • Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          [[ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]]
          ## backward gradient output
          [[ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75]]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L123
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SoftmaxOutput(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          [[ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]]
          ## backward gradient output
          [[ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75]]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L123
    

  • Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          [[ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]]
          ## backward gradient output
          [[ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75]]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L123
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SpatialTransformer(args: Any*): NDArrayFuncReturn

    Applies a spatial transformer to input feature map.
    

  • Applies a spatial transformer to input feature map.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SpatialTransformer(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Applies a spatial transformer to input feature map.
    

  • Applies a spatial transformer to input feature map.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SwapAxis(args: Any*): NDArrayFuncReturn

    Interchanges two axes of an array.
    
    Examples::
    
      x = [[1, 2, 3]])
      swapaxes(x, 0, 1) = [[ 1],
                           [ 2],
                           [ 3]]
    
      x = [[[ 0, 1],
            [ 2, 3]],
           [[ 4, 5],
            [ 6, 7]]]  // (2,2,2) array
    
     swapaxes(x, 0, 2) = [[[ 0, 4],
                           [ 2, 6]],
                          [[ 1, 5],
                           [ 3, 7]]]
    
    
    Defined in src/operator/swapaxis.cc:L70
    

  • Interchanges two axes of an array.
    
    Examples::
    
      x = [[1, 2, 3]])
      swapaxes(x, 0, 1) = [[ 1],
                           [ 2],
                           [ 3]]
    
      x = [[[ 0, 1],
            [ 2, 3]],
           [[ 4, 5],
            [ 6, 7]]]  // (2,2,2) array
    
     swapaxes(x, 0, 2) = [[[ 0, 4],
                           [ 2, 6]],
                          [[ 1, 5],
                           [ 3, 7]]]
    
    
    Defined in src/operator/swapaxis.cc:L70
    

    returns

    org.apache.mxnet.NDArray

  • abstract def SwapAxis(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Interchanges two axes of an array.
    
    Examples::
    
      x = [[1, 2, 3]])
      swapaxes(x, 0, 1) = [[ 1],
                           [ 2],
                           [ 3]]
    
      x = [[[ 0, 1],
            [ 2, 3]],
           [[ 4, 5],
            [ 6, 7]]]  // (2,2,2) array
    
     swapaxes(x, 0, 2) = [[[ 0, 4],
                           [ 2, 6]],
                          [[ 1, 5],
                           [ 3, 7]]]
    
    
    Defined in src/operator/swapaxis.cc:L70
    

  • Interchanges two axes of an array.
    
    Examples::
    
      x = [[1, 2, 3]])
      swapaxes(x, 0, 1) = [[ 1],
                           [ 2],
                           [ 3]]
    
      x = [[[ 0, 1],
            [ 2, 3]],
           [[ 4, 5],
            [ 6, 7]]]  // (2,2,2) array
    
     swapaxes(x, 0, 2) = [[[ 0, 4],
                           [ 2, 6]],
                          [[ 1, 5],
                           [ 3, 7]]]
    
    
    Defined in src/operator/swapaxis.cc:L70
    

    returns

    org.apache.mxnet.NDArray

  • abstract def UpSampling(args: Any*): NDArrayFuncReturn

    Performs nearest neighbor/bilinear up sampling to inputs.
    

  • Performs nearest neighbor/bilinear up sampling to inputs.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def UpSampling(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs nearest neighbor/bilinear up sampling to inputs.
    

  • Performs nearest neighbor/bilinear up sampling to inputs.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def abs(args: Any*): NDArrayFuncReturn

    Returns element-wise absolute value of the input.
    
    Example::
    
       abs([-2, 0, 3]) = [2, 0, 3]
    
    The storage type of ``abs`` output depends upon the input storage type:
    
       - abs(default) = default
       - abs(row_sparse) = row_sparse
       - abs(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L668
    

  • Returns element-wise absolute value of the input.
    
    Example::
    
       abs([-2, 0, 3]) = [2, 0, 3]
    
    The storage type of ``abs`` output depends upon the input storage type:
    
       - abs(default) = default
       - abs(row_sparse) = row_sparse
       - abs(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L668
    

    returns

    org.apache.mxnet.NDArray

  • abstract def abs(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise absolute value of the input.
    
    Example::
    
       abs([-2, 0, 3]) = [2, 0, 3]
    
    The storage type of ``abs`` output depends upon the input storage type:
    
       - abs(default) = default
       - abs(row_sparse) = row_sparse
       - abs(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L668
    

  • Returns element-wise absolute value of the input.
    
    Example::
    
       abs([-2, 0, 3]) = [2, 0, 3]
    
    The storage type of ``abs`` output depends upon the input storage type:
    
       - abs(default) = default
       - abs(row_sparse) = row_sparse
       - abs(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L668
    

    returns

    org.apache.mxnet.NDArray

  • abstract def adam_update(args: Any*): NDArrayFuncReturn

    Update function for Adam optimizer. Adam is seen as a generalization
    of AdaGrad.
    
    Adam update consists of the following steps, where g represents gradient and m, v
    are 1st and 2nd order moment estimates (mean and variance).
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }
    
    It updates the weights using::
    
     m = beta1*m + (1-beta1)*grad
     v = beta2*v + (1-beta2)*(grad**2)
     w += - learning_rate * m / (sqrt(v) + epsilon)
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage
    type of weight is the same as those of m and v,
    only the row slices whose indices appear in grad.indices are updated (for w, m and v)::
    
     for row in grad.indices:
         m[row] = beta1*m[row] + (1-beta1)*grad[row]
         v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
         w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
    
    
    
    Defined in src/operator/optimizer_op.cc:L495
    

  • Update function for Adam optimizer. Adam is seen as a generalization
    of AdaGrad.
    
    Adam update consists of the following steps, where g represents gradient and m, v
    are 1st and 2nd order moment estimates (mean and variance).
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }
    
    It updates the weights using::
    
     m = beta1*m + (1-beta1)*grad
     v = beta2*v + (1-beta2)*(grad**2)
     w += - learning_rate * m / (sqrt(v) + epsilon)
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage
    type of weight is the same as those of m and v,
    only the row slices whose indices appear in grad.indices are updated (for w, m and v)::
    
     for row in grad.indices:
         m[row] = beta1*m[row] + (1-beta1)*grad[row]
         v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
         w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
    
    
    
    Defined in src/operator/optimizer_op.cc:L495
    

    returns

    org.apache.mxnet.NDArray

  • abstract def adam_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for Adam optimizer. Adam is seen as a generalization
    of AdaGrad.
    
    Adam update consists of the following steps, where g represents gradient and m, v
    are 1st and 2nd order moment estimates (mean and variance).
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }
    
    It updates the weights using::
    
     m = beta1*m + (1-beta1)*grad
     v = beta2*v + (1-beta2)*(grad**2)
     w += - learning_rate * m / (sqrt(v) + epsilon)
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage
    type of weight is the same as those of m and v,
    only the row slices whose indices appear in grad.indices are updated (for w, m and v)::
    
     for row in grad.indices:
         m[row] = beta1*m[row] + (1-beta1)*grad[row]
         v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
         w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
    
    
    
    Defined in src/operator/optimizer_op.cc:L495
    

  • Update function for Adam optimizer. Adam is seen as a generalization
    of AdaGrad.
    
    Adam update consists of the following steps, where g represents gradient and m, v
    are 1st and 2nd order moment estimates (mean and variance).
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }
    
    It updates the weights using::
    
     m = beta1*m + (1-beta1)*grad
     v = beta2*v + (1-beta2)*(grad**2)
     w += - learning_rate * m / (sqrt(v) + epsilon)
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage
    type of weight is the same as those of m and v,
    only the row slices whose indices appear in grad.indices are updated (for w, m and v)::
    
     for row in grad.indices:
         m[row] = beta1*m[row] + (1-beta1)*grad[row]
         v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
         w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
    
    
    
    Defined in src/operator/optimizer_op.cc:L495
    

    returns

    org.apache.mxnet.NDArray

  • abstract def add_n(args: Any*): NDArrayFuncReturn

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

  • Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

    returns

    org.apache.mxnet.NDArray

  • abstract def add_n(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

  • Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L156
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arccos(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse cosine of the input array.
    
    The input should be in range `[-1, 1]`.
    The output is in the closed interval :math:`[0, \pi]`
    
    .. math::
       arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]
    
    The storage type of ``arccos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L123
    

  • Returns element-wise inverse cosine of the input array.
    
    The input should be in range `[-1, 1]`.
    The output is in the closed interval :math:`[0, \pi]`
    
    .. math::
       arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]
    
    The storage type of ``arccos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L123
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arccos(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse cosine of the input array.
    
    The input should be in range `[-1, 1]`.
    The output is in the closed interval :math:`[0, \pi]`
    
    .. math::
       arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]
    
    The storage type of ``arccos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L123
    

  • Returns element-wise inverse cosine of the input array.
    
    The input should be in range `[-1, 1]`.
    The output is in the closed interval :math:`[0, \pi]`
    
    .. math::
       arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]
    
    The storage type of ``arccos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L123
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arccosh(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic cosine of the input array, \
    computed element-wise.
    
    The storage type of ``arccosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L264
    

  • Returns the element-wise inverse hyperbolic cosine of the input array, \
    computed element-wise.
    
    The storage type of ``arccosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L264
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arccosh(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic cosine of the input array, \
    computed element-wise.
    
    The storage type of ``arccosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L264
    

  • Returns the element-wise inverse hyperbolic cosine of the input array, \
    computed element-wise.
    
    The storage type of ``arccosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L264
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arcsin(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse sine of the input array.
    
    The input should be in the range `[-1, 1]`.
    The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`].
    
    .. math::
       arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]
    
    The storage type of ``arcsin`` output depends upon the input storage type:
    
       - arcsin(default) = default
       - arcsin(row_sparse) = row_sparse
       - arcsin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104
    

  • Returns element-wise inverse sine of the input array.
    
    The input should be in the range `[-1, 1]`.
    The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`].
    
    .. math::
       arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]
    
    The storage type of ``arcsin`` output depends upon the input storage type:
    
       - arcsin(default) = default
       - arcsin(row_sparse) = row_sparse
       - arcsin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arcsin(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse sine of the input array.
    
    The input should be in the range `[-1, 1]`.
    The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`].
    
    .. math::
       arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]
    
    The storage type of ``arcsin`` output depends upon the input storage type:
    
       - arcsin(default) = default
       - arcsin(row_sparse) = row_sparse
       - arcsin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104
    

  • Returns element-wise inverse sine of the input array.
    
    The input should be in the range `[-1, 1]`.
    The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`].
    
    .. math::
       arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]
    
    The storage type of ``arcsin`` output depends upon the input storage type:
    
       - arcsin(default) = default
       - arcsin(row_sparse) = row_sparse
       - arcsin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L104
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arcsinh(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic sine of the input array, \
    computed element-wise.
    
    The storage type of ``arcsinh`` output depends upon the input storage type:
    
       - arcsinh(default) = default
       - arcsinh(row_sparse) = row_sparse
       - arcsinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250
    

  • Returns the element-wise inverse hyperbolic sine of the input array, \
    computed element-wise.
    
    The storage type of ``arcsinh`` output depends upon the input storage type:
    
       - arcsinh(default) = default
       - arcsinh(row_sparse) = row_sparse
       - arcsinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arcsinh(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic sine of the input array, \
    computed element-wise.
    
    The storage type of ``arcsinh`` output depends upon the input storage type:
    
       - arcsinh(default) = default
       - arcsinh(row_sparse) = row_sparse
       - arcsinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250
    

  • Returns the element-wise inverse hyperbolic sine of the input array, \
    computed element-wise.
    
    The storage type of ``arcsinh`` output depends upon the input storage type:
    
       - arcsinh(default) = default
       - arcsinh(row_sparse) = row_sparse
       - arcsinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L250
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arctan(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse tangent of the input array.
    
    The output is in the closed interval :math:`[-\pi/2, \pi/2]`
    
    .. math::
       arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]
    
    The storage type of ``arctan`` output depends upon the input storage type:
    
       - arctan(default) = default
       - arctan(row_sparse) = row_sparse
       - arctan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144
    

  • Returns element-wise inverse tangent of the input array.
    
    The output is in the closed interval :math:`[-\pi/2, \pi/2]`
    
    .. math::
       arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]
    
    The storage type of ``arctan`` output depends upon the input storage type:
    
       - arctan(default) = default
       - arctan(row_sparse) = row_sparse
       - arctan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arctan(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse tangent of the input array.
    
    The output is in the closed interval :math:`[-\pi/2, \pi/2]`
    
    .. math::
       arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]
    
    The storage type of ``arctan`` output depends upon the input storage type:
    
       - arctan(default) = default
       - arctan(row_sparse) = row_sparse
       - arctan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144
    

  • Returns element-wise inverse tangent of the input array.
    
    The output is in the closed interval :math:`[-\pi/2, \pi/2]`
    
    .. math::
       arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]
    
    The storage type of ``arctan`` output depends upon the input storage type:
    
       - arctan(default) = default
       - arctan(row_sparse) = row_sparse
       - arctan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L144
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arctanh(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic tangent of the input array, \
    computed element-wise.
    
    The storage type of ``arctanh`` output depends upon the input storage type:
    
       - arctanh(default) = default
       - arctanh(row_sparse) = row_sparse
       - arctanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281
    

  • Returns the element-wise inverse hyperbolic tangent of the input array, \
    computed element-wise.
    
    The storage type of ``arctanh`` output depends upon the input storage type:
    
       - arctanh(default) = default
       - arctanh(row_sparse) = row_sparse
       - arctanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281
    

    returns

    org.apache.mxnet.NDArray

  • abstract def arctanh(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic tangent of the input array, \
    computed element-wise.
    
    The storage type of ``arctanh`` output depends upon the input storage type:
    
       - arctanh(default) = default
       - arctanh(row_sparse) = row_sparse
       - arctanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281
    

  • Returns the element-wise inverse hyperbolic tangent of the input array, \
    computed element-wise.
    
    The storage type of ``arctanh`` output depends upon the input storage type:
    
       - arctanh(default) = default
       - arctanh(row_sparse) = row_sparse
       - arctanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L281
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argmax(args: Any*): NDArrayFuncReturn

    Returns indices of the maximum values along an axis.
    
    In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmax along axis 0
      argmax(x, axis=0) = [ 1.,  1.,  1.]
    
      // argmax along axis 1
      argmax(x, axis=1) = [ 2.,  2.]
    
      // argmax along axis 1 keeping same dims as an input array
      argmax(x, axis=1, keepdims=True) = [[ 2.],
                                          [ 2.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
    

  • Returns indices of the maximum values along an axis.
    
    In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmax along axis 0
      argmax(x, axis=0) = [ 1.,  1.,  1.]
    
      // argmax along axis 1
      argmax(x, axis=1) = [ 2.,  2.]
    
      // argmax along axis 1 keeping same dims as an input array
      argmax(x, axis=1, keepdims=True) = [[ 2.],
                                          [ 2.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argmax(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns indices of the maximum values along an axis.
    
    In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmax along axis 0
      argmax(x, axis=0) = [ 1.,  1.,  1.]
    
      // argmax along axis 1
      argmax(x, axis=1) = [ 2.,  2.]
    
      // argmax along axis 1 keeping same dims as an input array
      argmax(x, axis=1, keepdims=True) = [[ 2.],
                                          [ 2.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
    

  • Returns indices of the maximum values along an axis.
    
    In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmax along axis 0
      argmax(x, axis=0) = [ 1.,  1.,  1.]
    
      // argmax along axis 1
      argmax(x, axis=1) = [ 2.,  2.]
    
      // argmax along axis 1 keeping same dims as an input array
      argmax(x, axis=1, keepdims=True) = [[ 2.],
                                          [ 2.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argmax_channel(args: Any*): NDArrayFuncReturn

    Returns argmax indices of each channel from the input array.
    
    The result will be an NDArray of shape (num_channel,).
    
    In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      argmax_channel(x) = [ 2.,  2.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
    

  • Returns argmax indices of each channel from the input array.
    
    The result will be an NDArray of shape (num_channel,).
    
    In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      argmax_channel(x) = [ 2.,  2.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argmax_channel(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns argmax indices of each channel from the input array.
    
    The result will be an NDArray of shape (num_channel,).
    
    In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      argmax_channel(x) = [ 2.,  2.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
    

  • Returns argmax indices of each channel from the input array.
    
    The result will be an NDArray of shape (num_channel,).
    
    In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      argmax_channel(x) = [ 2.,  2.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argmin(args: Any*): NDArrayFuncReturn

    Returns indices of the minimum values along an axis.
    
    In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmin along axis 0
      argmin(x, axis=0) = [ 0.,  0.,  0.]
    
      // argmin along axis 1
      argmin(x, axis=1) = [ 0.,  0.]
    
      // argmin along axis 1 keeping same dims as an input array
      argmin(x, axis=1, keepdims=True) = [[ 0.],
                                          [ 0.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
    

  • Returns indices of the minimum values along an axis.
    
    In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmin along axis 0
      argmin(x, axis=0) = [ 0.,  0.,  0.]
    
      // argmin along axis 1
      argmin(x, axis=1) = [ 0.,  0.]
    
      // argmin along axis 1 keeping same dims as an input array
      argmin(x, axis=1, keepdims=True) = [[ 0.],
                                          [ 0.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argmin(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns indices of the minimum values along an axis.
    
    In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmin along axis 0
      argmin(x, axis=0) = [ 0.,  0.,  0.]
    
      // argmin along axis 1
      argmin(x, axis=1) = [ 0.,  0.]
    
      // argmin along axis 1 keeping same dims as an input array
      argmin(x, axis=1, keepdims=True) = [[ 0.],
                                          [ 0.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
    

  • Returns indices of the minimum values along an axis.
    
    In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence
    are returned.
    
    Examples::
    
      x = [[ 0.,  1.,  2.],
           [ 3.,  4.,  5.]]
    
      // argmin along axis 0
      argmin(x, axis=0) = [ 0.,  0.,  0.]
    
      // argmin along axis 1
      argmin(x, axis=1) = [ 0.,  0.]
    
      // argmin along axis 1 keeping same dims as an input array
      argmin(x, axis=1, keepdims=True) = [[ 0.],
                                          [ 0.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argsort(args: Any*): NDArrayFuncReturn

    Returns the indices that would sort an input array along the given axis.
    
    This function performs sorting along the given axis and returns an array of indices having same shape
    as an input array that index data in sorted order.
    
    Examples::
    
      x = [[ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2]]
    
      // sort along axis -1
      argsort(x) = [[ 1.,  0.,  2.],
                    [ 0.,  2.,  1.]]
    
      // sort along axis 0
      argsort(x, axis=0) = [[ 1.,  0.,  1.]
                            [ 0.,  1.,  0.]]
    
      // flatten and then sort
      argsort(x) = [ 3.,  1.,  5.,  0.,  4.,  2.]
    
    
    Defined in src/operator/tensor/ordering_op.cc:L177
    

  • Returns the indices that would sort an input array along the given axis.
    
    This function performs sorting along the given axis and returns an array of indices having same shape
    as an input array that index data in sorted order.
    
    Examples::
    
      x = [[ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2]]
    
      // sort along axis -1
      argsort(x) = [[ 1.,  0.,  2.],
                    [ 0.,  2.,  1.]]
    
      // sort along axis 0
      argsort(x, axis=0) = [[ 1.,  0.,  1.]
                            [ 0.,  1.,  0.]]
    
      // flatten and then sort
      argsort(x) = [ 3.,  1.,  5.,  0.,  4.,  2.]
    
    
    Defined in src/operator/tensor/ordering_op.cc:L177
    

    returns

    org.apache.mxnet.NDArray

  • abstract def argsort(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the indices that would sort an input array along the given axis.
    
    This function performs sorting along the given axis and returns an array of indices having same shape
    as an input array that index data in sorted order.
    
    Examples::
    
      x = [[ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2]]
    
      // sort along axis -1
      argsort(x) = [[ 1.,  0.,  2.],
                    [ 0.,  2.,  1.]]
    
      // sort along axis 0
      argsort(x, axis=0) = [[ 1.,  0.,  1.]
                            [ 0.,  1.,  0.]]
    
      // flatten and then sort
      argsort(x) = [ 3.,  1.,  5.,  0.,  4.,  2.]
    
    
    Defined in src/operator/tensor/ordering_op.cc:L177
    

  • Returns the indices that would sort an input array along the given axis.
    
    This function performs sorting along the given axis and returns an array of indices having same shape
    as an input array that index data in sorted order.
    
    Examples::
    
      x = [[ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2]]
    
      // sort along axis -1
      argsort(x) = [[ 1.,  0.,  2.],
                    [ 0.,  2.,  1.]]
    
      // sort along axis 0
      argsort(x, axis=0) = [[ 1.,  0.,  1.]
                            [ 0.,  1.,  0.]]
    
      // flatten and then sort
      argsort(x) = [ 3.,  1.,  5.,  0.,  4.,  2.]
    
    
    Defined in src/operator/tensor/ordering_op.cc:L177
    

    returns

    org.apache.mxnet.NDArray

  • abstract def batch_dot(args: Any*): NDArrayFuncReturn

    Batchwise dot product.
    
    ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and
    ``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`.
    
    For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape
    `(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`,
    which is computed by::
    
       batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:])
    
    
    
    Defined in src/operator/tensor/dot.cc:L125
    

  • Batchwise dot product.
    
    ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and
    ``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`.
    
    For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape
    `(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`,
    which is computed by::
    
       batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:])
    
    
    
    Defined in src/operator/tensor/dot.cc:L125
    

    returns

    org.apache.mxnet.NDArray

  • abstract def batch_dot(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Batchwise dot product.
    
    ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and
    ``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`.
    
    For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape
    `(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`,
    which is computed by::
    
       batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:])
    
    
    
    Defined in src/operator/tensor/dot.cc:L125
    

  • Batchwise dot product.
    
    ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and
    ``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`.
    
    For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape
    `(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`,
    which is computed by::
    
       batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:])
    
    
    
    Defined in src/operator/tensor/dot.cc:L125
    

    returns

    org.apache.mxnet.NDArray

  • abstract def batch_take(args: Any*): NDArrayFuncReturn

    Takes elements from a data batch.
    
    .. note::
      `batch_take` is deprecated. Use `pick` instead.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // takes elements with specified indices
      batch_take(x, [0,1,0]) = [ 1.  4.  5.]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L490
    

  • Takes elements from a data batch.
    
    .. note::
      `batch_take` is deprecated. Use `pick` instead.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // takes elements with specified indices
      batch_take(x, [0,1,0]) = [ 1.  4.  5.]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L490
    

    returns

    org.apache.mxnet.NDArray

  • abstract def batch_take(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Takes elements from a data batch.
    
    .. note::
      `batch_take` is deprecated. Use `pick` instead.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // takes elements with specified indices
      batch_take(x, [0,1,0]) = [ 1.  4.  5.]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L490
    

  • Takes elements from a data batch.
    
    .. note::
      `batch_take` is deprecated. Use `pick` instead.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // takes elements with specified indices
      batch_take(x, [0,1,0]) = [ 1.  4.  5.]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L490
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_add(args: Any*): NDArrayFuncReturn

    Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

  • Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_add(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

  • Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_axes(args: Any*): NDArrayFuncReturn

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

  • Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_axes(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

  • Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_axis(args: Any*): NDArrayFuncReturn

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

  • Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_axis(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

  • Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    Example::
    
       // given x of shape (1,2,1)
       x = [[[ 1.],
             [ 2.]]]
    
       // broadcast x on on axis 2
       broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                             [ 2.,  2.,  2.]]]
       // broadcast x on on axes 0 and 2
       broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]],
                                                    [[ 1.,  1.,  1.],
                                                     [ 2.,  2.,  2.]]]
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_div(args: Any*): NDArrayFuncReturn

    Returns element-wise division of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 6.,  6.,  6.],
            [ 6.,  6.,  6.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_div(x, y) = [[ 3.,  3.,  3.],
                              [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_div(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
    

  • Returns element-wise division of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 6.,  6.,  6.],
            [ 6.,  6.,  6.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_div(x, y) = [[ 3.,  3.,  3.],
                              [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_div(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_div(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise division of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 6.,  6.,  6.],
            [ 6.,  6.,  6.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_div(x, y) = [[ 3.,  3.,  3.],
                              [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_div(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
    

  • Returns element-wise division of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 6.,  6.,  6.],
            [ 6.,  6.,  6.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_div(x, y) = [[ 3.,  3.,  3.],
                              [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_div(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_equal(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **equal to** (==) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_equal(x, y) = [[ 0.,  0.,  0.],
                                [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
    

  • Returns the result of element-wise **equal to** (==) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_equal(x, y) = [[ 0.,  0.,  0.],
                                [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_equal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **equal to** (==) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_equal(x, y) = [[ 0.,  0.,  0.],
                                [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
    

  • Returns the result of element-wise **equal to** (==) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_equal(x, y) = [[ 0.,  0.,  0.],
                                [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_greater(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **greater than** (>) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater(x, y) = [[ 1.,  1.,  1.],
                                  [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
    

  • Returns the result of element-wise **greater than** (>) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater(x, y) = [[ 1.,  1.,  1.],
                                  [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_greater(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **greater than** (>) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater(x, y) = [[ 1.,  1.,  1.],
                                  [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
    

  • Returns the result of element-wise **greater than** (>) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater(x, y) = [[ 1.,  1.,  1.],
                                  [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_greater_equal(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater_equal(x, y) = [[ 1.,  1.,  1.],
                                        [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
    

  • Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater_equal(x, y) = [[ 1.,  1.,  1.],
                                        [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_greater_equal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater_equal(x, y) = [[ 1.,  1.,  1.],
                                        [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
    

  • Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_greater_equal(x, y) = [[ 1.,  1.,  1.],
                                        [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_hypot(args: Any*): NDArrayFuncReturn

     Returns the hypotenuse of a right angled triangle, given its "legs"
    with broadcasting.
    
    It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`.
    
    Example::
    
       x = [[ 3.,  3.,  3.]]
    
       y = [[ 4.],
            [ 4.]]
    
       broadcast_hypot(x, y) = [[ 5.,  5.,  5.],
                                [ 5.,  5.,  5.]]
    
       z = [[ 0.],
            [ 4.]]
    
       broadcast_hypot(x, z) = [[ 3.,  3.,  3.],
                                [ 5.,  5.,  5.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156
    

  •  Returns the hypotenuse of a right angled triangle, given its "legs"
    with broadcasting.
    
    It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`.
    
    Example::
    
       x = [[ 3.,  3.,  3.]]
    
       y = [[ 4.],
            [ 4.]]
    
       broadcast_hypot(x, y) = [[ 5.,  5.,  5.],
                                [ 5.,  5.,  5.]]
    
       z = [[ 0.],
            [ 4.]]
    
       broadcast_hypot(x, z) = [[ 3.,  3.,  3.],
                                [ 5.,  5.,  5.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_hypot(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

     Returns the hypotenuse of a right angled triangle, given its "legs"
    with broadcasting.
    
    It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`.
    
    Example::
    
       x = [[ 3.,  3.,  3.]]
    
       y = [[ 4.],
            [ 4.]]
    
       broadcast_hypot(x, y) = [[ 5.,  5.,  5.],
                                [ 5.,  5.,  5.]]
    
       z = [[ 0.],
            [ 4.]]
    
       broadcast_hypot(x, z) = [[ 3.,  3.,  3.],
                                [ 5.,  5.,  5.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156
    

  •  Returns the hypotenuse of a right angled triangle, given its "legs"
    with broadcasting.
    
    It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`.
    
    Example::
    
       x = [[ 3.,  3.,  3.]]
    
       y = [[ 4.],
            [ 4.]]
    
       broadcast_hypot(x, y) = [[ 5.,  5.,  5.],
                                [ 5.,  5.,  5.]]
    
       z = [[ 0.],
            [ 4.]]
    
       broadcast_hypot(x, z) = [[ 3.,  3.,  3.],
                                [ 5.,  5.,  5.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_lesser(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser(x, y) = [[ 0.,  0.,  0.],
                                 [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
    

  • Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser(x, y) = [[ 0.,  0.,  0.],
                                 [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_lesser(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser(x, y) = [[ 0.,  0.,  0.],
                                 [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
    

  • Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser(x, y) = [[ 0.,  0.,  0.],
                                 [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_lesser_equal(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser_equal(x, y) = [[ 0.,  0.,  0.],
                                       [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
    

  • Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser_equal(x, y) = [[ 0.,  0.,  0.],
                                       [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_lesser_equal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser_equal(x, y) = [[ 0.,  0.,  0.],
                                       [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
    

  • Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_lesser_equal(x, y) = [[ 0.,  0.,  0.],
                                       [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_like(args: Any*): NDArrayFuncReturn

    Broadcasts lhs to have the same shape as rhs.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1.,  2.,  3.],
                                                       [ 1.,  2.,  3.]])
    
       broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L315
    

  • Broadcasts lhs to have the same shape as rhs.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1.,  2.,  3.],
                                                       [ 1.,  2.,  3.]])
    
       broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L315
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_like(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Broadcasts lhs to have the same shape as rhs.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1.,  2.,  3.],
                                                       [ 1.,  2.,  3.]])
    
       broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L315
    

  • Broadcasts lhs to have the same shape as rhs.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1.,  2.,  3.],
                                                       [ 1.,  2.,  3.]])
    
       broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L315
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_logical_and(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **logical and** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_logical_and(x, y) = [[ 0.,  0.,  0.],
                                      [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
    

  • Returns the result of element-wise **logical and** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_logical_and(x, y) = [[ 0.,  0.,  0.],
                                      [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_logical_and(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **logical and** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_logical_and(x, y) = [[ 0.,  0.,  0.],
                                      [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
    

  • Returns the result of element-wise **logical and** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_logical_and(x, y) = [[ 0.,  0.,  0.],
                                      [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_logical_or(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **logical or** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_or(x, y) = [[ 1.,  1.,  1.],
                                     [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
    

  • Returns the result of element-wise **logical or** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_or(x, y) = [[ 1.,  1.,  1.],
                                     [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_logical_or(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **logical or** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_or(x, y) = [[ 1.,  1.,  1.],
                                     [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
    

  • Returns the result of element-wise **logical or** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_or(x, y) = [[ 1.,  1.,  1.],
                                     [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_logical_xor(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **logical xor** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_xor(x, y) = [[ 0.,  0.,  1.],
                                      [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
    

  • Returns the result of element-wise **logical xor** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_xor(x, y) = [[ 0.,  0.,  1.],
                                      [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_logical_xor(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **logical xor** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_xor(x, y) = [[ 0.,  0.,  1.],
                                      [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
    

  • Returns the result of element-wise **logical xor** with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  0.],
            [ 1.,  1.,  0.]]
    
       y = [[ 1.],
            [ 0.]]
    
       broadcast_logical_xor(x, y) = [[ 0.,  0.,  1.],
                                      [ 1.,  1.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_maximum(args: Any*): NDArrayFuncReturn

    Returns element-wise maximum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise maxima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 1.,  1.,  1.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80
    

  • Returns element-wise maximum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise maxima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 1.,  1.,  1.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_maximum(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise maximum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise maxima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 1.,  1.,  1.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80
    

  • Returns element-wise maximum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise maxima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 1.,  1.,  1.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_minimum(args: Any*): NDArrayFuncReturn

    Returns element-wise minimum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise minima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 0.,  0.,  0.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115
    

  • Returns element-wise minimum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise minima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 0.,  0.,  0.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_minimum(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise minimum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise minima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 0.,  0.,  0.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115
    

  • Returns element-wise minimum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise minima.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_maximum(x, y) = [[ 0.,  0.,  0.],
                                  [ 1.,  1.,  1.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_minus(args: Any*): NDArrayFuncReturn

    Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

  • Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_minus(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

  • Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_mod(args: Any*): NDArrayFuncReturn

    Returns element-wise modulo of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 8.,  8.,  8.],
            [ 8.,  8.,  8.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_mod(x, y) = [[ 0.,  0.,  0.],
                              [ 2.,  2.,  2.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
    

  • Returns element-wise modulo of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 8.,  8.,  8.],
            [ 8.,  8.,  8.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_mod(x, y) = [[ 0.,  0.,  0.],
                              [ 2.,  2.,  2.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_mod(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise modulo of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 8.,  8.,  8.],
            [ 8.,  8.,  8.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_mod(x, y) = [[ 0.,  0.,  0.],
                              [ 2.,  2.,  2.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
    

  • Returns element-wise modulo of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 8.,  8.,  8.],
            [ 8.,  8.,  8.]]
    
       y = [[ 2.],
            [ 3.]]
    
       broadcast_mod(x, y) = [[ 0.,  0.,  0.],
                              [ 2.,  2.,  2.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_mul(args: Any*): NDArrayFuncReturn

    Returns element-wise product of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_mul(x, y) = [[ 0.,  0.,  0.],
                              [ 1.,  1.,  1.]]
    
    Supported sparse operations:
    
       broadcast_mul(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
    

  • Returns element-wise product of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_mul(x, y) = [[ 0.,  0.,  0.],
                              [ 1.,  1.,  1.]]
    
    Supported sparse operations:
    
       broadcast_mul(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_mul(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise product of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_mul(x, y) = [[ 0.,  0.,  0.],
                              [ 1.,  1.,  1.]]
    
    Supported sparse operations:
    
       broadcast_mul(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
    

  • Returns element-wise product of the input arrays with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_mul(x, y) = [[ 0.,  0.,  0.],
                              [ 1.,  1.,  1.]]
    
    Supported sparse operations:
    
       broadcast_mul(csr, dense(1D)) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_not_equal(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_not_equal(x, y) = [[ 1.,  1.,  1.],
                                    [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
    

  • Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_not_equal(x, y) = [[ 1.,  1.,  1.],
                                    [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_not_equal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_not_equal(x, y) = [[ 1.,  1.,  1.],
                                    [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
    

  • Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_not_equal(x, y) = [[ 1.,  1.,  1.],
                                    [ 0.,  0.,  0.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_plus(args: Any*): NDArrayFuncReturn

    Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

  • Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_plus(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

  • Returns element-wise sum of the input arrays with broadcasting.
    
    `broadcast_plus` is an alias to the function `broadcast_add`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_add(x, y) = [[ 1.,  1.,  1.],
                              [ 2.,  2.,  2.]]
    
       broadcast_plus(x, y) = [[ 1.,  1.,  1.],
                               [ 2.,  2.,  2.]]
    
    Supported sparse operations:
    
       broadcast_add(csr, dense(1D)) = dense
       broadcast_add(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_power(args: Any*): NDArrayFuncReturn

    Returns result of first array elements raised to powers from second array, element-wise with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_power(x, y) = [[ 2.,  2.,  2.],
                                [ 4.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
    

  • Returns result of first array elements raised to powers from second array, element-wise with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_power(x, y) = [[ 2.,  2.,  2.],
                                [ 4.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_power(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns result of first array elements raised to powers from second array, element-wise with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_power(x, y) = [[ 2.,  2.,  2.],
                                [ 4.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
    

  • Returns result of first array elements raised to powers from second array, element-wise with broadcasting.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_power(x, y) = [[ 2.,  2.,  2.],
                                [ 4.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_sub(args: Any*): NDArrayFuncReturn

    Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

  • Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_sub(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

  • Returns element-wise difference of the input arrays with broadcasting.
    
    `broadcast_minus` is an alias to the function `broadcast_sub`.
    
    Example::
    
       x = [[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]]
    
       y = [[ 0.],
            [ 1.]]
    
       broadcast_sub(x, y) = [[ 1.,  1.,  1.],
                              [ 0.,  0.,  0.]]
    
       broadcast_minus(x, y) = [[ 1.,  1.,  1.],
                                [ 0.,  0.,  0.]]
    
    Supported sparse operations:
    
       broadcast_sub/minus(csr, dense(1D)) = dense
       broadcast_sub/minus(dense(1D), csr) = dense
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_to(args: Any*): NDArrayFuncReturn

    Broadcasts the input array to a new shape.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1.,  2.,  3.],
                                               [ 1.,  2.,  3.]])
    
    The dimension which you do not want to change can also be kept as `0` which means copy the original value.
    So with `shape=(2,0)`, we will obtain the same result as in the above example.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L262
    

  • Broadcasts the input array to a new shape.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1.,  2.,  3.],
                                               [ 1.,  2.,  3.]])
    
    The dimension which you do not want to change can also be kept as `0` which means copy the original value.
    So with `shape=(2,0)`, we will obtain the same result as in the above example.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L262
    

    returns

    org.apache.mxnet.NDArray

  • abstract def broadcast_to(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Broadcasts the input array to a new shape.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1.,  2.,  3.],
                                               [ 1.,  2.,  3.]])
    
    The dimension which you do not want to change can also be kept as `0` which means copy the original value.
    So with `shape=(2,0)`, we will obtain the same result as in the above example.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L262
    

  • Broadcasts the input array to a new shape.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting `_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1.,  2.,  3.],
                                               [ 1.,  2.,  3.]])
    
    The dimension which you do not want to change can also be kept as `0` which means copy the original value.
    So with `shape=(2,0)`, we will obtain the same result as in the above example.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L262
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cast(args: Any*): NDArrayFuncReturn

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

  • Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cast(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

  • Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L594
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cast_storage(args: Any*): NDArrayFuncReturn

    Casts tensor storage type to the new type.
    
    When an NDArray with default storage type is cast to csr or row_sparse storage,
    the result is compact, which means:
    
    - for csr, zero values will not be retained
    - for row_sparse, row slices of all zeros will not be retained
    
    The storage type of ``cast_storage`` output depends on stype parameter:
    
    - cast_storage(csr, 'default') = default
    - cast_storage(row_sparse, 'default') = default
    - cast_storage(default, 'csr') = csr
    - cast_storage(default, 'row_sparse') = row_sparse
    - cast_storage(csr, 'csr') = csr
    - cast_storage(row_sparse, 'row_sparse') = row_sparse
    
    Example::
    
        dense = [[ 0.,  1.,  0.],
                 [ 2.,  0.,  3.],
                 [ 0.,  0.,  0.],
                 [ 0.,  0.,  0.]]
    
        # cast to row_sparse storage type
        rsp = cast_storage(dense, 'row_sparse')
        rsp.indices = [0, 1]
        rsp.values = [[ 0.,  1.,  0.],
                      [ 2.,  0.,  3.]]
    
        # cast to csr storage type
        csr = cast_storage(dense, 'csr')
        csr.indices = [1, 0, 2]
        csr.values = [ 1.,  2.,  3.]
        csr.indptr = [0, 1, 3, 3, 3]
    
    
    
    Defined in src/operator/tensor/cast_storage.cc:L71
    

  • Casts tensor storage type to the new type.
    
    When an NDArray with default storage type is cast to csr or row_sparse storage,
    the result is compact, which means:
    
    - for csr, zero values will not be retained
    - for row_sparse, row slices of all zeros will not be retained
    
    The storage type of ``cast_storage`` output depends on stype parameter:
    
    - cast_storage(csr, 'default') = default
    - cast_storage(row_sparse, 'default') = default
    - cast_storage(default, 'csr') = csr
    - cast_storage(default, 'row_sparse') = row_sparse
    - cast_storage(csr, 'csr') = csr
    - cast_storage(row_sparse, 'row_sparse') = row_sparse
    
    Example::
    
        dense = [[ 0.,  1.,  0.],
                 [ 2.,  0.,  3.],
                 [ 0.,  0.,  0.],
                 [ 0.,  0.,  0.]]
    
        # cast to row_sparse storage type
        rsp = cast_storage(dense, 'row_sparse')
        rsp.indices = [0, 1]
        rsp.values = [[ 0.,  1.,  0.],
                      [ 2.,  0.,  3.]]
    
        # cast to csr storage type
        csr = cast_storage(dense, 'csr')
        csr.indices = [1, 0, 2]
        csr.values = [ 1.,  2.,  3.]
        csr.indptr = [0, 1, 3, 3, 3]
    
    
    
    Defined in src/operator/tensor/cast_storage.cc:L71
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cast_storage(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Casts tensor storage type to the new type.
    
    When an NDArray with default storage type is cast to csr or row_sparse storage,
    the result is compact, which means:
    
    - for csr, zero values will not be retained
    - for row_sparse, row slices of all zeros will not be retained
    
    The storage type of ``cast_storage`` output depends on stype parameter:
    
    - cast_storage(csr, 'default') = default
    - cast_storage(row_sparse, 'default') = default
    - cast_storage(default, 'csr') = csr
    - cast_storage(default, 'row_sparse') = row_sparse
    - cast_storage(csr, 'csr') = csr
    - cast_storage(row_sparse, 'row_sparse') = row_sparse
    
    Example::
    
        dense = [[ 0.,  1.,  0.],
                 [ 2.,  0.,  3.],
                 [ 0.,  0.,  0.],
                 [ 0.,  0.,  0.]]
    
        # cast to row_sparse storage type
        rsp = cast_storage(dense, 'row_sparse')
        rsp.indices = [0, 1]
        rsp.values = [[ 0.,  1.,  0.],
                      [ 2.,  0.,  3.]]
    
        # cast to csr storage type
        csr = cast_storage(dense, 'csr')
        csr.indices = [1, 0, 2]
        csr.values = [ 1.,  2.,  3.]
        csr.indptr = [0, 1, 3, 3, 3]
    
    
    
    Defined in src/operator/tensor/cast_storage.cc:L71
    

  • Casts tensor storage type to the new type.
    
    When an NDArray with default storage type is cast to csr or row_sparse storage,
    the result is compact, which means:
    
    - for csr, zero values will not be retained
    - for row_sparse, row slices of all zeros will not be retained
    
    The storage type of ``cast_storage`` output depends on stype parameter:
    
    - cast_storage(csr, 'default') = default
    - cast_storage(row_sparse, 'default') = default
    - cast_storage(default, 'csr') = csr
    - cast_storage(default, 'row_sparse') = row_sparse
    - cast_storage(csr, 'csr') = csr
    - cast_storage(row_sparse, 'row_sparse') = row_sparse
    
    Example::
    
        dense = [[ 0.,  1.,  0.],
                 [ 2.,  0.,  3.],
                 [ 0.,  0.,  0.],
                 [ 0.,  0.,  0.]]
    
        # cast to row_sparse storage type
        rsp = cast_storage(dense, 'row_sparse')
        rsp.indices = [0, 1]
        rsp.values = [[ 0.,  1.,  0.],
                      [ 2.,  0.,  3.]]
    
        # cast to csr storage type
        csr = cast_storage(dense, 'csr')
        csr.indices = [1, 0, 2]
        csr.values = [ 1.,  2.,  3.]
        csr.indptr = [0, 1, 3, 3, 3]
    
    
    
    Defined in src/operator/tensor/cast_storage.cc:L71
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cbrt(args: Any*): NDArrayFuncReturn

    Returns element-wise cube-root value of the input.
    
    .. math::
       cbrt(x) = \sqrt[3]{x}
    
    Example::
    
       cbrt([1, 8, -125]) = [1, 2, -5]
    
    The storage type of ``cbrt`` output depends upon the input storage type:
    
       - cbrt(default) = default
       - cbrt(row_sparse) = row_sparse
       - cbrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L889
    

  • Returns element-wise cube-root value of the input.
    
    .. math::
       cbrt(x) = \sqrt[3]{x}
    
    Example::
    
       cbrt([1, 8, -125]) = [1, 2, -5]
    
    The storage type of ``cbrt`` output depends upon the input storage type:
    
       - cbrt(default) = default
       - cbrt(row_sparse) = row_sparse
       - cbrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L889
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cbrt(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise cube-root value of the input.
    
    .. math::
       cbrt(x) = \sqrt[3]{x}
    
    Example::
    
       cbrt([1, 8, -125]) = [1, 2, -5]
    
    The storage type of ``cbrt`` output depends upon the input storage type:
    
       - cbrt(default) = default
       - cbrt(row_sparse) = row_sparse
       - cbrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L889
    

  • Returns element-wise cube-root value of the input.
    
    .. math::
       cbrt(x) = \sqrt[3]{x}
    
    Example::
    
       cbrt([1, 8, -125]) = [1, 2, -5]
    
    The storage type of ``cbrt`` output depends upon the input storage type:
    
       - cbrt(default) = default
       - cbrt(row_sparse) = row_sparse
       - cbrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L889
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ceil(args: Any*): NDArrayFuncReturn

    Returns element-wise ceiling of the input.
    
    The ceil of the scalar x is the smallest integer i, such that i >= x.
    
    Example::
    
       ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]
    
    The storage type of ``ceil`` output depends upon the input storage type:
    
       - ceil(default) = default
       - ceil(row_sparse) = row_sparse
       - ceil(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
    

  • Returns element-wise ceiling of the input.
    
    The ceil of the scalar x is the smallest integer i, such that i >= x.
    
    Example::
    
       ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]
    
    The storage type of ``ceil`` output depends upon the input storage type:
    
       - ceil(default) = default
       - ceil(row_sparse) = row_sparse
       - ceil(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ceil(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise ceiling of the input.
    
    The ceil of the scalar x is the smallest integer i, such that i >= x.
    
    Example::
    
       ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]
    
    The storage type of ``ceil`` output depends upon the input storage type:
    
       - ceil(default) = default
       - ceil(row_sparse) = row_sparse
       - ceil(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
    

  • Returns element-wise ceiling of the input.
    
    The ceil of the scalar x is the smallest integer i, such that i >= x.
    
    Example::
    
       ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]
    
    The storage type of ``ceil`` output depends upon the input storage type:
    
       - ceil(default) = default
       - ceil(row_sparse) = row_sparse
       - ceil(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
    

    returns

    org.apache.mxnet.NDArray

  • abstract def choose_element_0index(args: Any*): NDArrayFuncReturn

    Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based index.
    

  • Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based index.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def choose_element_0index(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based index.
    

  • Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based index.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def clip(args: Any*): NDArrayFuncReturn

    Clips (limits) the values in an array.
    
    Given an interval, values outside the interval are clipped to the interval edges.
    Clipping ``x`` between `a_min` and `a_x` would be::
    
       clip(x, a_min, a_max) = max(min(x, a_max), a_min))
    
    Example::
    
        x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    
        clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]
    
    The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \
    parameter values:
    
       - clip(default) = default
       - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
       - clip(csr, a_min <= 0, a_max >= 0) = csr
       - clip(row_sparse, a_min < 0, a_max < 0) = default
       - clip(row_sparse, a_min > 0, a_max > 0) = default
       - clip(csr, a_min < 0, a_max < 0) = csr
       - clip(csr, a_min > 0, a_max > 0) = csr
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L618
    

  • Clips (limits) the values in an array.
    
    Given an interval, values outside the interval are clipped to the interval edges.
    Clipping ``x`` between `a_min` and `a_x` would be::
    
       clip(x, a_min, a_max) = max(min(x, a_max), a_min))
    
    Example::
    
        x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    
        clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]
    
    The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \
    parameter values:
    
       - clip(default) = default
       - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
       - clip(csr, a_min <= 0, a_max >= 0) = csr
       - clip(row_sparse, a_min < 0, a_max < 0) = default
       - clip(row_sparse, a_min > 0, a_max > 0) = default
       - clip(csr, a_min < 0, a_max < 0) = csr
       - clip(csr, a_min > 0, a_max > 0) = csr
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L618
    

    returns

    org.apache.mxnet.NDArray

  • abstract def clip(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Clips (limits) the values in an array.
    
    Given an interval, values outside the interval are clipped to the interval edges.
    Clipping ``x`` between `a_min` and `a_x` would be::
    
       clip(x, a_min, a_max) = max(min(x, a_max), a_min))
    
    Example::
    
        x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    
        clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]
    
    The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \
    parameter values:
    
       - clip(default) = default
       - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
       - clip(csr, a_min <= 0, a_max >= 0) = csr
       - clip(row_sparse, a_min < 0, a_max < 0) = default
       - clip(row_sparse, a_min > 0, a_max > 0) = default
       - clip(csr, a_min < 0, a_max < 0) = csr
       - clip(csr, a_min > 0, a_max > 0) = csr
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L618
    

  • Clips (limits) the values in an array.
    
    Given an interval, values outside the interval are clipped to the interval edges.
    Clipping ``x`` between `a_min` and `a_x` would be::
    
       clip(x, a_min, a_max) = max(min(x, a_max), a_min))
    
    Example::
    
        x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    
        clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]
    
    The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \
    parameter values:
    
       - clip(default) = default
       - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
       - clip(csr, a_min <= 0, a_max >= 0) = csr
       - clip(row_sparse, a_min < 0, a_max < 0) = default
       - clip(row_sparse, a_min > 0, a_max > 0) = default
       - clip(csr, a_min < 0, a_max < 0) = csr
       - clip(csr, a_min > 0, a_max > 0) = csr
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L618
    

    returns

    org.apache.mxnet.NDArray

  • abstract def concat(args: Any*): NDArrayFuncReturn

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

  • Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

    returns

    org.apache.mxnet.NDArray

  • abstract def concat(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

  • Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = [[1,1],[2,2]]
       y = [[3,3],[4,4],[5,5]]
       z = [[6,6], [7,7],[8,8]]
    
       concat(x,y,z,dim=0) = [[ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.]]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.]]
    
    
    
    Defined in src/operator/nn/concat.cc:L365
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cos(args: Any*): NDArrayFuncReturn

    Computes the element-wise cosine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]
    
    The storage type of ``cos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L63
    

  • Computes the element-wise cosine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]
    
    The storage type of ``cos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L63
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cos(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the element-wise cosine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]
    
    The storage type of ``cos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L63
    

  • Computes the element-wise cosine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]
    
    The storage type of ``cos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L63
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cosh(args: Any*): NDArrayFuncReturn

    Returns the hyperbolic cosine  of the input array, computed element-wise.
    
    .. math::
       cosh(x) = 0.5\times(exp(x) + exp(-x))
    
    The storage type of ``cosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L216
    

  • Returns the hyperbolic cosine  of the input array, computed element-wise.
    
    .. math::
       cosh(x) = 0.5\times(exp(x) + exp(-x))
    
    The storage type of ``cosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L216
    

    returns

    org.apache.mxnet.NDArray

  • abstract def cosh(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the hyperbolic cosine  of the input array, computed element-wise.
    
    .. math::
       cosh(x) = 0.5\times(exp(x) + exp(-x))
    
    The storage type of ``cosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L216
    

  • Returns the hyperbolic cosine  of the input array, computed element-wise.
    
    .. math::
       cosh(x) = 0.5\times(exp(x) + exp(-x))
    
    The storage type of ``cosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L216
    

    returns

    org.apache.mxnet.NDArray

  • abstract def crop(args: Any*): NDArrayFuncReturn

    Slices a region of the array.
    
    .. note:: ``crop`` is deprecated. Use ``slice`` instead.
    
    This function returns a sliced array between the indices given
    by `begin` and `end` with the corresponding `step`.
    
    For an input array of ``shape=(d_0, d_1, ..., d_n-1)``,
    slice operation with ``begin=(b_0, b_1...b_m-1)``,
    ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``,
    where m <= n, results in an array with the shape
    ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``.
    
    The resulting array's *k*-th dimension contains elements
    from the *k*-th dimension of the input array starting
    from index ``b_k`` (inclusive) with step ``s_k``
    until reaching ``e_k`` (exclusive).
    
    If the *k*-th elements are `None` in the sequence of `begin`, `end`,
    and `step`, the following rule will be used to set default values.
    If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`;
    else, set `b_k=d_k-1`, `e_k=-1`.
    
    The storage type of ``slice`` output depends on storage types of inputs
    
    - slice(csr) = csr
    - otherwise, ``slice`` generates output with default storage
    
    .. note:: When input data storage type is csr, it only supports
    step=(), or step=(None,), or step=(1,) to generate a csr output.
    For other step parameter values, it falls back to slicing
    a dense tensor.
    
    Example::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      slice(x, begin=(0,1), end=(2,4)) = [[ 2.,  3.,  4.],
                                         [ 6.,  7.,  8.]]
      slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.],
                                                                [5.,  7.],
                                                                [1.,  3.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L413
    

  • Slices a region of the array.
    
    .. note:: ``crop`` is deprecated. Use ``slice`` instead.
    
    This function returns a sliced array between the indices given
    by `begin` and `end` with the corresponding `step`.
    
    For an input array of ``shape=(d_0, d_1, ..., d_n-1)``,
    slice operation with ``begin=(b_0, b_1...b_m-1)``,
    ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``,
    where m <= n, results in an array with the shape
    ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``.
    
    The resulting array's *k*-th dimension contains elements
    from the *k*-th dimension of the input array starting
    from index ``b_k`` (inclusive) with step ``s_k``
    until reaching ``e_k`` (exclusive).
    
    If the *k*-th elements are `None` in the sequence of `begin`, `end`,
    and `step`, the following rule will be used to set default values.
    If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`;
    else, set `b_k=d_k-1`, `e_k=-1`.
    
    The storage type of ``slice`` output depends on storage types of inputs
    
    - slice(csr) = csr
    - otherwise, ``slice`` generates output with default storage
    
    .. note:: When input data storage type is csr, it only supports
    step=(), or step=(None,), or step=(1,) to generate a csr output.
    For other step parameter values, it falls back to slicing
    a dense tensor.
    
    Example::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      slice(x, begin=(0,1), end=(2,4)) = [[ 2.,  3.,  4.],
                                         [ 6.,  7.,  8.]]
      slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.],
                                                                [5.,  7.],
                                                                [1.,  3.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L413
    

    returns

    org.apache.mxnet.NDArray

  • abstract def crop(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Slices a region of the array.
    
    .. note:: ``crop`` is deprecated. Use ``slice`` instead.
    
    This function returns a sliced array between the indices given
    by `begin` and `end` with the corresponding `step`.
    
    For an input array of ``shape=(d_0, d_1, ..., d_n-1)``,
    slice operation with ``begin=(b_0, b_1...b_m-1)``,
    ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``,
    where m <= n, results in an array with the shape
    ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``.
    
    The resulting array's *k*-th dimension contains elements
    from the *k*-th dimension of the input array starting
    from index ``b_k`` (inclusive) with step ``s_k``
    until reaching ``e_k`` (exclusive).
    
    If the *k*-th elements are `None` in the sequence of `begin`, `end`,
    and `step`, the following rule will be used to set default values.
    If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`;
    else, set `b_k=d_k-1`, `e_k=-1`.
    
    The storage type of ``slice`` output depends on storage types of inputs
    
    - slice(csr) = csr
    - otherwise, ``slice`` generates output with default storage
    
    .. note:: When input data storage type is csr, it only supports
    step=(), or step=(None,), or step=(1,) to generate a csr output.
    For other step parameter values, it falls back to slicing
    a dense tensor.
    
    Example::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      slice(x, begin=(0,1), end=(2,4)) = [[ 2.,  3.,  4.],
                                         [ 6.,  7.,  8.]]
      slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.],
                                                                [5.,  7.],
                                                                [1.,  3.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L413
    

  • Slices a region of the array.
    
    .. note:: ``crop`` is deprecated. Use ``slice`` instead.
    
    This function returns a sliced array between the indices given
    by `begin` and `end` with the corresponding `step`.
    
    For an input array of ``shape=(d_0, d_1, ..., d_n-1)``,
    slice operation with ``begin=(b_0, b_1...b_m-1)``,
    ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``,
    where m <= n, results in an array with the shape
    ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``.
    
    The resulting array's *k*-th dimension contains elements
    from the *k*-th dimension of the input array starting
    from index ``b_k`` (inclusive) with step ``s_k``
    until reaching ``e_k`` (exclusive).
    
    If the *k*-th elements are `None` in the sequence of `begin`, `end`,
    and `step`, the following rule will be used to set default values.
    If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`;
    else, set `b_k=d_k-1`, `e_k=-1`.
    
    The storage type of ``slice`` output depends on storage types of inputs
    
    - slice(csr) = csr
    - otherwise, ``slice`` generates output with default storage
    
    .. note:: When input data storage type is csr, it only supports
    step=(), or step=(None,), or step=(1,) to generate a csr output.
    For other step parameter values, it falls back to slicing
    a dense tensor.
    
    Example::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      slice(x, begin=(0,1), end=(2,4)) = [[ 2.,  3.,  4.],
                                         [ 6.,  7.,  8.]]
      slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.],
                                                                [5.,  7.],
                                                                [1.,  3.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L413
    

    returns

    org.apache.mxnet.NDArray

  • abstract def degrees(args: Any*): NDArrayFuncReturn

    Converts each element of the input array from radians to degrees.
    
    .. math::
       degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]
    
    The storage type of ``degrees`` output depends upon the input storage type:
    
       - degrees(default) = default
       - degrees(row_sparse) = row_sparse
       - degrees(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163
    

  • Converts each element of the input array from radians to degrees.
    
    .. math::
       degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]
    
    The storage type of ``degrees`` output depends upon the input storage type:
    
       - degrees(default) = default
       - degrees(row_sparse) = row_sparse
       - degrees(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163
    

    returns

    org.apache.mxnet.NDArray

  • abstract def degrees(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Converts each element of the input array from radians to degrees.
    
    .. math::
       degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]
    
    The storage type of ``degrees`` output depends upon the input storage type:
    
       - degrees(default) = default
       - degrees(row_sparse) = row_sparse
       - degrees(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163
    

  • Converts each element of the input array from radians to degrees.
    
    .. math::
       degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]
    
    The storage type of ``degrees`` output depends upon the input storage type:
    
       - degrees(default) = default
       - degrees(row_sparse) = row_sparse
       - degrees(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L163
    

    returns

    org.apache.mxnet.NDArray

  • abstract def depth_to_space(args: Any*): NDArrayFuncReturn

    Rearranges(permutes) data from depth into blocks of spatial data.
    Similar to ONNX DepthToSpace operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace.
    The output is a new tensor where the values from depth dimension are moved in spatial blocks
    to height and width dimension. The reverse of this operation is ``space_to_depth``.
    
    .. math::
    
        \begin{gather*}
        x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\
        y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size])
        \end{gather*}
    
    where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width]
    and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]`
    
    Example::
    
      x = [[[[0, 1, 2],
             [3, 4, 5]],
            [[6, 7, 8],
             [9, 10, 11]],
            [[12, 13, 14],
             [15, 16, 17]],
            [[18, 19, 20],
             [21, 22, 23]]]]
    
      depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8],
                                [12, 18, 13, 19, 14, 20],
                                [3, 9, 4, 10, 5, 11],
                                [15, 21, 16, 22, 17, 23]]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L945
    

  • Rearranges(permutes) data from depth into blocks of spatial data.
    Similar to ONNX DepthToSpace operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace.
    The output is a new tensor where the values from depth dimension are moved in spatial blocks
    to height and width dimension. The reverse of this operation is ``space_to_depth``.
    
    .. math::
    
        \begin{gather*}
        x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\
        y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size])
        \end{gather*}
    
    where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width]
    and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]`
    
    Example::
    
      x = [[[[0, 1, 2],
             [3, 4, 5]],
            [[6, 7, 8],
             [9, 10, 11]],
            [[12, 13, 14],
             [15, 16, 17]],
            [[18, 19, 20],
             [21, 22, 23]]]]
    
      depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8],
                                [12, 18, 13, 19, 14, 20],
                                [3, 9, 4, 10, 5, 11],
                                [15, 21, 16, 22, 17, 23]]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L945
    

    returns

    org.apache.mxnet.NDArray

  • abstract def depth_to_space(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Rearranges(permutes) data from depth into blocks of spatial data.
    Similar to ONNX DepthToSpace operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace.
    The output is a new tensor where the values from depth dimension are moved in spatial blocks
    to height and width dimension. The reverse of this operation is ``space_to_depth``.
    
    .. math::
    
        \begin{gather*}
        x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\
        y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size])
        \end{gather*}
    
    where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width]
    and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]`
    
    Example::
    
      x = [[[[0, 1, 2],
             [3, 4, 5]],
            [[6, 7, 8],
             [9, 10, 11]],
            [[12, 13, 14],
             [15, 16, 17]],
            [[18, 19, 20],
             [21, 22, 23]]]]
    
      depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8],
                                [12, 18, 13, 19, 14, 20],
                                [3, 9, 4, 10, 5, 11],
                                [15, 21, 16, 22, 17, 23]]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L945
    

  • Rearranges(permutes) data from depth into blocks of spatial data.
    Similar to ONNX DepthToSpace operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace.
    The output is a new tensor where the values from depth dimension are moved in spatial blocks
    to height and width dimension. The reverse of this operation is ``space_to_depth``.
    
    .. math::
    
        \begin{gather*}
        x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\
        y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size])
        \end{gather*}
    
    where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width]
    and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]`
    
    Example::
    
      x = [[[[0, 1, 2],
             [3, 4, 5]],
            [[6, 7, 8],
             [9, 10, 11]],
            [[12, 13, 14],
             [15, 16, 17]],
            [[18, 19, 20],
             [21, 22, 23]]]]
    
      depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8],
                                [12, 18, 13, 19, 14, 20],
                                [3, 9, 4, 10, 5, 11],
                                [15, 21, 16, 22, 17, 23]]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L945
    

    returns

    org.apache.mxnet.NDArray

  • abstract def diag(args: Any*): NDArrayFuncReturn

    Extracts a diagonal or constructs a diagonal array.
    
    ``diag``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
    - N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``.
      The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the
      input shape and appending to the result a new axis with the size of the diagonals in question.
    
      For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2
      respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`.
    
    Examples::
    
      x = [[1, 2, 3],
           [4, 5, 6]]
    
      diag(x) = [1, 5]
    
      diag(x, k=1) = [2, 6]
    
      diag(x, k=-1) = [4]
    
      x = [1, 2, 3]
    
      diag(x) = [[1, 0, 0],
                 [0, 2, 0],
                 [0, 0, 3]]
    
      diag(x, k=1) = [[0, 1, 0],
                      [0, 0, 2],
                      [0, 0, 0]]
    
      diag(x, k=-1) = [[0, 0, 0],
                       [1, 0, 0],
                       [0, 2, 0]]
    
      x = [[[1, 2],
            [3, 4]],
    
           [[5, 6],
            [7, 8]]]
    
      diag(x) = [[1, 7],
                 [2, 8]]
    
      diag(x, k=1) = [[3],
                      [4]]
    
      diag(x, axis1=-2, axis2=-1) = [[1, 4],
                                     [5, 8]]
    
    
    
    Defined in src/operator/tensor/diag_op.cc:L87
    

  • Extracts a diagonal or constructs a diagonal array.
    
    ``diag``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
    - N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``.
      The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the
      input shape and appending to the result a new axis with the size of the diagonals in question.
    
      For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2
      respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`.
    
    Examples::
    
      x = [[1, 2, 3],
           [4, 5, 6]]
    
      diag(x) = [1, 5]
    
      diag(x, k=1) = [2, 6]
    
      diag(x, k=-1) = [4]
    
      x = [1, 2, 3]
    
      diag(x) = [[1, 0, 0],
                 [0, 2, 0],
                 [0, 0, 3]]
    
      diag(x, k=1) = [[0, 1, 0],
                      [0, 0, 2],
                      [0, 0, 0]]
    
      diag(x, k=-1) = [[0, 0, 0],
                       [1, 0, 0],
                       [0, 2, 0]]
    
      x = [[[1, 2],
            [3, 4]],
    
           [[5, 6],
            [7, 8]]]
    
      diag(x) = [[1, 7],
                 [2, 8]]
    
      diag(x, k=1) = [[3],
                      [4]]
    
      diag(x, axis1=-2, axis2=-1) = [[1, 4],
                                     [5, 8]]
    
    
    
    Defined in src/operator/tensor/diag_op.cc:L87
    

    returns

    org.apache.mxnet.NDArray

  • abstract def diag(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Extracts a diagonal or constructs a diagonal array.
    
    ``diag``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
    - N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``.
      The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the
      input shape and appending to the result a new axis with the size of the diagonals in question.
    
      For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2
      respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`.
    
    Examples::
    
      x = [[1, 2, 3],
           [4, 5, 6]]
    
      diag(x) = [1, 5]
    
      diag(x, k=1) = [2, 6]
    
      diag(x, k=-1) = [4]
    
      x = [1, 2, 3]
    
      diag(x) = [[1, 0, 0],
                 [0, 2, 0],
                 [0, 0, 3]]
    
      diag(x, k=1) = [[0, 1, 0],
                      [0, 0, 2],
                      [0, 0, 0]]
    
      diag(x, k=-1) = [[0, 0, 0],
                       [1, 0, 0],
                       [0, 2, 0]]
    
      x = [[[1, 2],
            [3, 4]],
    
           [[5, 6],
            [7, 8]]]
    
      diag(x) = [[1, 7],
                 [2, 8]]
    
      diag(x, k=1) = [[3],
                      [4]]
    
      diag(x, axis1=-2, axis2=-1) = [[1, 4],
                                     [5, 8]]
    
    
    
    Defined in src/operator/tensor/diag_op.cc:L87
    

  • Extracts a diagonal or constructs a diagonal array.
    
    ``diag``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
    - N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``.
      The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the
      input shape and appending to the result a new axis with the size of the diagonals in question.
    
      For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2
      respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`.
    
    Examples::
    
      x = [[1, 2, 3],
           [4, 5, 6]]
    
      diag(x) = [1, 5]
    
      diag(x, k=1) = [2, 6]
    
      diag(x, k=-1) = [4]
    
      x = [1, 2, 3]
    
      diag(x) = [[1, 0, 0],
                 [0, 2, 0],
                 [0, 0, 3]]
    
      diag(x, k=1) = [[0, 1, 0],
                      [0, 0, 2],
                      [0, 0, 0]]
    
      diag(x, k=-1) = [[0, 0, 0],
                       [1, 0, 0],
                       [0, 2, 0]]
    
      x = [[[1, 2],
            [3, 4]],
    
           [[5, 6],
            [7, 8]]]
    
      diag(x) = [[1, 7],
                 [2, 8]]
    
      diag(x, k=1) = [[3],
                      [4]]
    
      diag(x, axis1=-2, axis2=-1) = [[1, 4],
                                     [5, 8]]
    
    
    
    Defined in src/operator/tensor/diag_op.cc:L87
    

    returns

    org.apache.mxnet.NDArray

  • abstract def dot(args: Any*): NDArrayFuncReturn

    Dot product of two arrays.
    
    ``dot``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: inner product of vectors
    - 2-D arrays: matrix multiplication
    - N-D arrays: a sum product over the last axis of the first input and the first
      axis of the second input
    
      For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape `(k,r,s)`, the
      result array will have shape `(n,m,r,s)`. It is computed by::
    
        dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])
    
      Example::
    
        x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
        y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
        dot(x,y)[0,0,1,1] = 0
        sum(x[0,0,:]*y[:,1,1]) = 0
    
    The storage type of ``dot`` output depends on storage types of inputs, transpose option and
    forward_stype option for output storage type. Implemented sparse operations include:
    
    - dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
    - dot(csr, default, transpose_a=True) = default
    - dot(csr, default, transpose_a=True) = row_sparse
    - dot(csr, default) = default
    - dot(csr, row_sparse) = default
    - dot(default, csr) = csr (CPU only)
    - dot(default, csr, forward_stype='default') = default
    - dot(default, csr, transpose_b=True, forward_stype='default') = default
    
    If the combination of input storage types and forward_stype does not match any of the
    above patterns, ``dot`` will fallback and generate output with default storage.
    
    .. Note::
    
        If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/dot.cc:L77
    

  • Dot product of two arrays.
    
    ``dot``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: inner product of vectors
    - 2-D arrays: matrix multiplication
    - N-D arrays: a sum product over the last axis of the first input and the first
      axis of the second input
    
      For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape `(k,r,s)`, the
      result array will have shape `(n,m,r,s)`. It is computed by::
    
        dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])
    
      Example::
    
        x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
        y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
        dot(x,y)[0,0,1,1] = 0
        sum(x[0,0,:]*y[:,1,1]) = 0
    
    The storage type of ``dot`` output depends on storage types of inputs, transpose option and
    forward_stype option for output storage type. Implemented sparse operations include:
    
    - dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
    - dot(csr, default, transpose_a=True) = default
    - dot(csr, default, transpose_a=True) = row_sparse
    - dot(csr, default) = default
    - dot(csr, row_sparse) = default
    - dot(default, csr) = csr (CPU only)
    - dot(default, csr, forward_stype='default') = default
    - dot(default, csr, transpose_b=True, forward_stype='default') = default
    
    If the combination of input storage types and forward_stype does not match any of the
    above patterns, ``dot`` will fallback and generate output with default storage.
    
    .. Note::
    
        If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/dot.cc:L77
    

    returns

    org.apache.mxnet.NDArray

  • abstract def dot(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Dot product of two arrays.
    
    ``dot``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: inner product of vectors
    - 2-D arrays: matrix multiplication
    - N-D arrays: a sum product over the last axis of the first input and the first
      axis of the second input
    
      For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape `(k,r,s)`, the
      result array will have shape `(n,m,r,s)`. It is computed by::
    
        dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])
    
      Example::
    
        x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
        y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
        dot(x,y)[0,0,1,1] = 0
        sum(x[0,0,:]*y[:,1,1]) = 0
    
    The storage type of ``dot`` output depends on storage types of inputs, transpose option and
    forward_stype option for output storage type. Implemented sparse operations include:
    
    - dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
    - dot(csr, default, transpose_a=True) = default
    - dot(csr, default, transpose_a=True) = row_sparse
    - dot(csr, default) = default
    - dot(csr, row_sparse) = default
    - dot(default, csr) = csr (CPU only)
    - dot(default, csr, forward_stype='default') = default
    - dot(default, csr, transpose_b=True, forward_stype='default') = default
    
    If the combination of input storage types and forward_stype does not match any of the
    above patterns, ``dot`` will fallback and generate output with default storage.
    
    .. Note::
    
        If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/dot.cc:L77
    

  • Dot product of two arrays.
    
    ``dot``'s behavior depends on the input array dimensions:
    
    - 1-D arrays: inner product of vectors
    - 2-D arrays: matrix multiplication
    - N-D arrays: a sum product over the last axis of the first input and the first
      axis of the second input
    
      For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape `(k,r,s)`, the
      result array will have shape `(n,m,r,s)`. It is computed by::
    
        dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])
    
      Example::
    
        x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
        y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
        dot(x,y)[0,0,1,1] = 0
        sum(x[0,0,:]*y[:,1,1]) = 0
    
    The storage type of ``dot`` output depends on storage types of inputs, transpose option and
    forward_stype option for output storage type. Implemented sparse operations include:
    
    - dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
    - dot(csr, default, transpose_a=True) = default
    - dot(csr, default, transpose_a=True) = row_sparse
    - dot(csr, default) = default
    - dot(csr, row_sparse) = default
    - dot(default, csr) = csr (CPU only)
    - dot(default, csr, forward_stype='default') = default
    - dot(default, csr, transpose_b=True, forward_stype='default') = default
    
    If the combination of input storage types and forward_stype does not match any of the
    above patterns, ``dot`` will fallback and generate output with default storage.
    
    .. Note::
    
        If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/dot.cc:L77
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_add(args: Any*): NDArrayFuncReturn

    Adds arguments element-wise.
    
    The storage type of ``elemwise_add`` output depends on storage types of inputs
    
       - elemwise_add(row_sparse, row_sparse) = row_sparse
       - elemwise_add(csr, csr) = csr
       - elemwise_add(default, csr) = default
       - elemwise_add(csr, default) = default
       - elemwise_add(default, rsp) = default
       - elemwise_add(rsp, default) = default
       - otherwise, ``elemwise_add`` generates output with default storage
    

  • Adds arguments element-wise.
    
    The storage type of ``elemwise_add`` output depends on storage types of inputs
    
       - elemwise_add(row_sparse, row_sparse) = row_sparse
       - elemwise_add(csr, csr) = csr
       - elemwise_add(default, csr) = default
       - elemwise_add(csr, default) = default
       - elemwise_add(default, rsp) = default
       - elemwise_add(rsp, default) = default
       - otherwise, ``elemwise_add`` generates output with default storage
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_add(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Adds arguments element-wise.
    
    The storage type of ``elemwise_add`` output depends on storage types of inputs
    
       - elemwise_add(row_sparse, row_sparse) = row_sparse
       - elemwise_add(csr, csr) = csr
       - elemwise_add(default, csr) = default
       - elemwise_add(csr, default) = default
       - elemwise_add(default, rsp) = default
       - elemwise_add(rsp, default) = default
       - otherwise, ``elemwise_add`` generates output with default storage
    

  • Adds arguments element-wise.
    
    The storage type of ``elemwise_add`` output depends on storage types of inputs
    
       - elemwise_add(row_sparse, row_sparse) = row_sparse
       - elemwise_add(csr, csr) = csr
       - elemwise_add(default, csr) = default
       - elemwise_add(csr, default) = default
       - elemwise_add(default, rsp) = default
       - elemwise_add(rsp, default) = default
       - otherwise, ``elemwise_add`` generates output with default storage
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_div(args: Any*): NDArrayFuncReturn

    Divides arguments element-wise.
    
    The storage type of ``elemwise_div`` output is always dense
    

  • Divides arguments element-wise.
    
    The storage type of ``elemwise_div`` output is always dense
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_div(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Divides arguments element-wise.
    
    The storage type of ``elemwise_div`` output is always dense
    

  • Divides arguments element-wise.
    
    The storage type of ``elemwise_div`` output is always dense
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_mul(args: Any*): NDArrayFuncReturn

    Multiplies arguments element-wise.
    
    The storage type of ``elemwise_mul`` output depends on storage types of inputs
    
       - elemwise_mul(default, default) = default
       - elemwise_mul(row_sparse, row_sparse) = row_sparse
       - elemwise_mul(default, row_sparse) = row_sparse
       - elemwise_mul(row_sparse, default) = row_sparse
       - elemwise_mul(csr, csr) = csr
       - otherwise, ``elemwise_mul`` generates output with default storage
    

  • Multiplies arguments element-wise.
    
    The storage type of ``elemwise_mul`` output depends on storage types of inputs
    
       - elemwise_mul(default, default) = default
       - elemwise_mul(row_sparse, row_sparse) = row_sparse
       - elemwise_mul(default, row_sparse) = row_sparse
       - elemwise_mul(row_sparse, default) = row_sparse
       - elemwise_mul(csr, csr) = csr
       - otherwise, ``elemwise_mul`` generates output with default storage
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_mul(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Multiplies arguments element-wise.
    
    The storage type of ``elemwise_mul`` output depends on storage types of inputs
    
       - elemwise_mul(default, default) = default
       - elemwise_mul(row_sparse, row_sparse) = row_sparse
       - elemwise_mul(default, row_sparse) = row_sparse
       - elemwise_mul(row_sparse, default) = row_sparse
       - elemwise_mul(csr, csr) = csr
       - otherwise, ``elemwise_mul`` generates output with default storage
    

  • Multiplies arguments element-wise.
    
    The storage type of ``elemwise_mul`` output depends on storage types of inputs
    
       - elemwise_mul(default, default) = default
       - elemwise_mul(row_sparse, row_sparse) = row_sparse
       - elemwise_mul(default, row_sparse) = row_sparse
       - elemwise_mul(row_sparse, default) = row_sparse
       - elemwise_mul(csr, csr) = csr
       - otherwise, ``elemwise_mul`` generates output with default storage
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_sub(args: Any*): NDArrayFuncReturn

    Subtracts arguments element-wise.
    
    The storage type of ``elemwise_sub`` output depends on storage types of inputs
    
       - elemwise_sub(row_sparse, row_sparse) = row_sparse
       - elemwise_sub(csr, csr) = csr
       - elemwise_sub(default, csr) = default
       - elemwise_sub(csr, default) = default
       - elemwise_sub(default, rsp) = default
       - elemwise_sub(rsp, default) = default
       - otherwise, ``elemwise_sub`` generates output with default storage
    

  • Subtracts arguments element-wise.
    
    The storage type of ``elemwise_sub`` output depends on storage types of inputs
    
       - elemwise_sub(row_sparse, row_sparse) = row_sparse
       - elemwise_sub(csr, csr) = csr
       - elemwise_sub(default, csr) = default
       - elemwise_sub(csr, default) = default
       - elemwise_sub(default, rsp) = default
       - elemwise_sub(rsp, default) = default
       - otherwise, ``elemwise_sub`` generates output with default storage
    

    returns

    org.apache.mxnet.NDArray

  • abstract def elemwise_sub(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Subtracts arguments element-wise.
    
    The storage type of ``elemwise_sub`` output depends on storage types of inputs
    
       - elemwise_sub(row_sparse, row_sparse) = row_sparse
       - elemwise_sub(csr, csr) = csr
       - elemwise_sub(default, csr) = default
       - elemwise_sub(csr, default) = default
       - elemwise_sub(default, rsp) = default
       - elemwise_sub(rsp, default) = default
       - otherwise, ``elemwise_sub`` generates output with default storage
    

  • Subtracts arguments element-wise.
    
    The storage type of ``elemwise_sub`` output depends on storage types of inputs
    
       - elemwise_sub(row_sparse, row_sparse) = row_sparse
       - elemwise_sub(csr, csr) = csr
       - elemwise_sub(default, csr) = default
       - elemwise_sub(csr, default) = default
       - elemwise_sub(default, rsp) = default
       - elemwise_sub(rsp, default) = default
       - otherwise, ``elemwise_sub`` generates output with default storage
    

    returns

    org.apache.mxnet.NDArray

  • abstract def exp(args: Any*): NDArrayFuncReturn

    Returns element-wise exponential value of the input.
    
    .. math::
       exp(x) = e^x \approx 2.718^x
    
    Example::
    
       exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
    
    The storage type of ``exp`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L929
    

  • Returns element-wise exponential value of the input.
    
    .. math::
       exp(x) = e^x \approx 2.718^x
    
    Example::
    
       exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
    
    The storage type of ``exp`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L929
    

    returns

    org.apache.mxnet.NDArray

  • abstract def exp(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise exponential value of the input.
    
    .. math::
       exp(x) = e^x \approx 2.718^x
    
    Example::
    
       exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
    
    The storage type of ``exp`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L929
    

  • Returns element-wise exponential value of the input.
    
    .. math::
       exp(x) = e^x \approx 2.718^x
    
    Example::
    
       exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
    
    The storage type of ``exp`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L929
    

    returns

    org.apache.mxnet.NDArray

  • abstract def expand_dims(args: Any*): NDArrayFuncReturn

    Inserts a new axis of size 1 into the array shape
    
    For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)``
    will return a new array with shape ``(2,1,3,4)``.
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L347
    

  • Inserts a new axis of size 1 into the array shape
    
    For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)``
    will return a new array with shape ``(2,1,3,4)``.
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L347
    

    returns

    org.apache.mxnet.NDArray

  • abstract def expand_dims(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Inserts a new axis of size 1 into the array shape
    
    For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)``
    will return a new array with shape ``(2,1,3,4)``.
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L347
    

  • Inserts a new axis of size 1 into the array shape
    
    For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)``
    will return a new array with shape ``(2,1,3,4)``.
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L347
    

    returns

    org.apache.mxnet.NDArray

  • abstract def expm1(args: Any*): NDArrayFuncReturn

    Returns ``exp(x) - 1`` computed element-wise on the input.
    
    This function provides greater precision than ``exp(x) - 1`` for small values of ``x``.
    
    The storage type of ``expm1`` output depends upon the input storage type:
    
       - expm1(default) = default
       - expm1(row_sparse) = row_sparse
       - expm1(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1008
    

  • Returns ``exp(x) - 1`` computed element-wise on the input.
    
    This function provides greater precision than ``exp(x) - 1`` for small values of ``x``.
    
    The storage type of ``expm1`` output depends upon the input storage type:
    
       - expm1(default) = default
       - expm1(row_sparse) = row_sparse
       - expm1(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1008
    

    returns

    org.apache.mxnet.NDArray

  • abstract def expm1(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns ``exp(x) - 1`` computed element-wise on the input.
    
    This function provides greater precision than ``exp(x) - 1`` for small values of ``x``.
    
    The storage type of ``expm1`` output depends upon the input storage type:
    
       - expm1(default) = default
       - expm1(row_sparse) = row_sparse
       - expm1(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1008
    

  • Returns ``exp(x) - 1`` computed element-wise on the input.
    
    This function provides greater precision than ``exp(x) - 1`` for small values of ``x``.
    
    The storage type of ``expm1`` output depends upon the input storage type:
    
       - expm1(default) = default
       - expm1(row_sparse) = row_sparse
       - expm1(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1008
    

    returns

    org.apache.mxnet.NDArray

  • abstract def fill_element_0index(args: Any*): NDArrayFuncReturn

    Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.
    

  • Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def fill_element_0index(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.
    

  • Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def fix(args: Any*): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest \
    integer towards zero of the input.
    
    Example::
    
       fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]
    
    The storage type of ``fix`` output depends upon the input storage type:
    
       - fix(default) = default
       - fix(row_sparse) = row_sparse
       - fix(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L803
    

  • Returns element-wise rounded value to the nearest \
    integer towards zero of the input.
    
    Example::
    
       fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]
    
    The storage type of ``fix`` output depends upon the input storage type:
    
       - fix(default) = default
       - fix(row_sparse) = row_sparse
       - fix(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L803
    

    returns

    org.apache.mxnet.NDArray

  • abstract def fix(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest \
    integer towards zero of the input.
    
    Example::
    
       fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]
    
    The storage type of ``fix`` output depends upon the input storage type:
    
       - fix(default) = default
       - fix(row_sparse) = row_sparse
       - fix(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L803
    

  • Returns element-wise rounded value to the nearest \
    integer towards zero of the input.
    
    Example::
    
       fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]
    
    The storage type of ``fix`` output depends upon the input storage type:
    
       - fix(default) = default
       - fix(row_sparse) = row_sparse
       - fix(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L803
    

    returns

    org.apache.mxnet.NDArray

  • abstract def flatten(args: Any*): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

  • Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

    returns

    org.apache.mxnet.NDArray

  • abstract def flatten(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

  • Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = [[
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ]],
    
        flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L259
    

    returns

    org.apache.mxnet.NDArray

  • abstract def flip(args: Any*): NDArrayFuncReturn

    Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

  • Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

    returns

    org.apache.mxnet.NDArray

  • abstract def flip(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

  • Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

    returns

    org.apache.mxnet.NDArray

  • abstract def floor(args: Any*): NDArrayFuncReturn

    Returns element-wise floor of the input.
    
    The floor of the scalar x is the largest integer i, such that i <= x.
    
    Example::
    
       floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]
    
    The storage type of ``floor`` output depends upon the input storage type:
    
       - floor(default) = default
       - floor(row_sparse) = row_sparse
       - floor(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L765
    

  • Returns element-wise floor of the input.
    
    The floor of the scalar x is the largest integer i, such that i <= x.
    
    Example::
    
       floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]
    
    The storage type of ``floor`` output depends upon the input storage type:
    
       - floor(default) = default
       - floor(row_sparse) = row_sparse
       - floor(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L765
    

    returns

    org.apache.mxnet.NDArray

  • abstract def floor(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise floor of the input.
    
    The floor of the scalar x is the largest integer i, such that i <= x.
    
    Example::
    
       floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]
    
    The storage type of ``floor`` output depends upon the input storage type:
    
       - floor(default) = default
       - floor(row_sparse) = row_sparse
       - floor(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L765
    

  • Returns element-wise floor of the input.
    
    The floor of the scalar x is the largest integer i, such that i <= x.
    
    Example::
    
       floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]
    
    The storage type of ``floor`` output depends upon the input storage type:
    
       - floor(default) = default
       - floor(row_sparse) = row_sparse
       - floor(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L765
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ftml_update(args: Any*): NDArrayFuncReturn

    The FTML optimizer described in
    *FTML - Follow the Moving Leader in Deep Learning*,
    available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
     \sigma_t = d_t - \beta_1 d_{t-1}
     z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
     W_t = - \frac{ z_t }{ d_t }
    
    
    
    Defined in src/operator/optimizer_op.cc:L447
    

  • The FTML optimizer described in
    *FTML - Follow the Moving Leader in Deep Learning*,
    available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
     \sigma_t = d_t - \beta_1 d_{t-1}
     z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
     W_t = - \frac{ z_t }{ d_t }
    
    
    
    Defined in src/operator/optimizer_op.cc:L447
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ftml_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    The FTML optimizer described in
    *FTML - Follow the Moving Leader in Deep Learning*,
    available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
     \sigma_t = d_t - \beta_1 d_{t-1}
     z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
     W_t = - \frac{ z_t }{ d_t }
    
    
    
    Defined in src/operator/optimizer_op.cc:L447
    

  • The FTML optimizer described in
    *FTML - Follow the Moving Leader in Deep Learning*,
    available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
     \sigma_t = d_t - \beta_1 d_{t-1}
     z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
     W_t = - \frac{ z_t }{ d_t }
    
    
    
    Defined in src/operator/optimizer_op.cc:L447
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ftrl_update(args: Any*): NDArrayFuncReturn

    Update function for Ftrl optimizer.
    Referenced from *Ad Click Prediction: a View from the Trenches*, available at
    http://dl.acm.org/citation.cfm?id=2488200.
    
    It updates the weights using::
    
     rescaled_grad = clip(grad * rescale_grad, clip_gradient)
     z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
     n += rescaled_grad**2
     w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
    
    If w, z and n are all of ``row_sparse`` storage type,
    only the row slices whose indices appear in grad.indices are updated (for w, z and n)::
    
     for row in grad.indices:
         rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
         z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
         n[row] += rescaled_grad[row]**2
         w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
    
    
    
    Defined in src/operator/optimizer_op.cc:L632
    

  • Update function for Ftrl optimizer.
    Referenced from *Ad Click Prediction: a View from the Trenches*, available at
    http://dl.acm.org/citation.cfm?id=2488200.
    
    It updates the weights using::
    
     rescaled_grad = clip(grad * rescale_grad, clip_gradient)
     z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
     n += rescaled_grad**2
     w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
    
    If w, z and n are all of ``row_sparse`` storage type,
    only the row slices whose indices appear in grad.indices are updated (for w, z and n)::
    
     for row in grad.indices:
         rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
         z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
         n[row] += rescaled_grad[row]**2
         w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
    
    
    
    Defined in src/operator/optimizer_op.cc:L632
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ftrl_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for Ftrl optimizer.
    Referenced from *Ad Click Prediction: a View from the Trenches*, available at
    http://dl.acm.org/citation.cfm?id=2488200.
    
    It updates the weights using::
    
     rescaled_grad = clip(grad * rescale_grad, clip_gradient)
     z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
     n += rescaled_grad**2
     w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
    
    If w, z and n are all of ``row_sparse`` storage type,
    only the row slices whose indices appear in grad.indices are updated (for w, z and n)::
    
     for row in grad.indices:
         rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
         z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
         n[row] += rescaled_grad[row]**2
         w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
    
    
    
    Defined in src/operator/optimizer_op.cc:L632
    

  • Update function for Ftrl optimizer.
    Referenced from *Ad Click Prediction: a View from the Trenches*, available at
    http://dl.acm.org/citation.cfm?id=2488200.
    
    It updates the weights using::
    
     rescaled_grad = clip(grad * rescale_grad, clip_gradient)
     z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
     n += rescaled_grad**2
     w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
    
    If w, z and n are all of ``row_sparse`` storage type,
    only the row slices whose indices appear in grad.indices are updated (for w, z and n)::
    
     for row in grad.indices:
         rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
         z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
         n[row] += rescaled_grad[row]**2
         w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
    
    
    
    Defined in src/operator/optimizer_op.cc:L632
    

    returns

    org.apache.mxnet.NDArray

  • abstract def gamma(args: Any*): NDArrayFuncReturn

    Returns the gamma function (extension of the factorial function \
    to the reals), computed element-wise on the input array.
    
    The storage type of ``gamma`` output is always dense
    

  • Returns the gamma function (extension of the factorial function \
    to the reals), computed element-wise on the input array.
    
    The storage type of ``gamma`` output is always dense
    

    returns

    org.apache.mxnet.NDArray

  • abstract def gamma(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the gamma function (extension of the factorial function \
    to the reals), computed element-wise on the input array.
    
    The storage type of ``gamma`` output is always dense
    

  • Returns the gamma function (extension of the factorial function \
    to the reals), computed element-wise on the input array.
    
    The storage type of ``gamma`` output is always dense
    

    returns

    org.apache.mxnet.NDArray

  • abstract def gammaln(args: Any*): NDArrayFuncReturn

    Returns element-wise log of the absolute value of the gamma function \
    of the input.
    
    The storage type of ``gammaln`` output is always dense
    

  • Returns element-wise log of the absolute value of the gamma function \
    of the input.
    
    The storage type of ``gammaln`` output is always dense
    

    returns

    org.apache.mxnet.NDArray

  • abstract def gammaln(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise log of the absolute value of the gamma function \
    of the input.
    
    The storage type of ``gammaln`` output is always dense
    

  • Returns element-wise log of the absolute value of the gamma function \
    of the input.
    
    The storage type of ``gammaln`` output is always dense
    

    returns

    org.apache.mxnet.NDArray

  • abstract def gather_nd(args: Any*): NDArrayFuncReturn

    Gather elements or slices from `data` and store to a tensor whose
    shape is defined by `indices`.
    
    Given `data` with shape `(X_0, X_1, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, output shape will simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
                                                          ...,
                                                          indices[M-1, y_0, ..., y_{K-1}],
                                                          x_M, ..., x_{N-1}]
    
    Examples::
    
      data = [[0, 1], [2, 3]]
      indices = [[1, 1, 0], [0, 1, 0]]
      gather_nd(data, indices) = [2, 3, 0]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 0]]
      gather_nd(data, indices) = [[3, 4], [5, 6]]
    

  • Gather elements or slices from `data` and store to a tensor whose
    shape is defined by `indices`.
    
    Given `data` with shape `(X_0, X_1, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, output shape will simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
                                                          ...,
                                                          indices[M-1, y_0, ..., y_{K-1}],
                                                          x_M, ..., x_{N-1}]
    
    Examples::
    
      data = [[0, 1], [2, 3]]
      indices = [[1, 1, 0], [0, 1, 0]]
      gather_nd(data, indices) = [2, 3, 0]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 0]]
      gather_nd(data, indices) = [[3, 4], [5, 6]]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def gather_nd(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Gather elements or slices from `data` and store to a tensor whose
    shape is defined by `indices`.
    
    Given `data` with shape `(X_0, X_1, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, output shape will simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
                                                          ...,
                                                          indices[M-1, y_0, ..., y_{K-1}],
                                                          x_M, ..., x_{N-1}]
    
    Examples::
    
      data = [[0, 1], [2, 3]]
      indices = [[1, 1, 0], [0, 1, 0]]
      gather_nd(data, indices) = [2, 3, 0]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 0]]
      gather_nd(data, indices) = [[3, 4], [5, 6]]
    

  • Gather elements or slices from `data` and store to a tensor whose
    shape is defined by `indices`.
    
    Given `data` with shape `(X_0, X_1, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, output shape will simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
                                                          ...,
                                                          indices[M-1, y_0, ..., y_{K-1}],
                                                          x_M, ..., x_{N-1}]
    
    Examples::
    
      data = [[0, 1], [2, 3]]
      indices = [[1, 1, 0], [0, 1, 0]]
      gather_nd(data, indices) = [2, 3, 0]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 0]]
      gather_nd(data, indices) = [[3, 4], [5, 6]]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def hard_sigmoid(args: Any*): NDArrayFuncReturn

    Computes hard sigmoid of x element-wise.
    
    .. math::
       y = max(0, min(1, alpha * x + beta))
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115
    

  • Computes hard sigmoid of x element-wise.
    
    .. math::
       y = max(0, min(1, alpha * x + beta))
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115
    

    returns

    org.apache.mxnet.NDArray

  • abstract def hard_sigmoid(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes hard sigmoid of x element-wise.
    
    .. math::
       y = max(0, min(1, alpha * x + beta))
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115
    

  • Computes hard sigmoid of x element-wise.
    
    .. math::
       y = max(0, min(1, alpha * x + beta))
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L115
    

    returns

    org.apache.mxnet.NDArray

  • abstract def identity(args: Any*): NDArrayFuncReturn

    Returns a copy of the input.
    
    From:src/operator/tensor/elemwise_unary_op_basic.cc:200
    

  • Returns a copy of the input.
    
    From:src/operator/tensor/elemwise_unary_op_basic.cc:200
    

    returns

    org.apache.mxnet.NDArray

  • abstract def identity(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns a copy of the input.
    
    From:src/operator/tensor/elemwise_unary_op_basic.cc:200
    

  • Returns a copy of the input.
    
    From:src/operator/tensor/elemwise_unary_op_basic.cc:200
    

    returns

    org.apache.mxnet.NDArray

  • abstract def khatri_rao(args: Any*): NDArrayFuncReturn

    Computes the Khatri-Rao product of the input matrices.
    
    Given a collection of :math:`n` input matrices,
    
    .. math::
       A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},
    
    the (column-wise) Khatri-Rao product is defined as the matrix,
    
    .. math::
       X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},
    
    where the :math:`k` th column is equal to the column-wise outer product
    :math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth
    column of the ith matrix.
    
    Example::
    
      >>> A = mx.nd.array([[1, -1],
      >>>                  [2, -3]])
      >>> B = mx.nd.array([[1, 4],
      >>>                  [2, 5],
      >>>                  [3, 6]])
      >>> C = mx.nd.khatri_rao(A, B)
      >>> print(C.asnumpy())
      [[  1.  -4.]
       [  2.  -5.]
       [  3.  -6.]
       [  2. -12.]
       [  4. -15.]
       [  6. -18.]]
    
    
    
    Defined in src/operator/contrib/krprod.cc:L108
    

  • Computes the Khatri-Rao product of the input matrices.
    
    Given a collection of :math:`n` input matrices,
    
    .. math::
       A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},
    
    the (column-wise) Khatri-Rao product is defined as the matrix,
    
    .. math::
       X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},
    
    where the :math:`k` th column is equal to the column-wise outer product
    :math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth
    column of the ith matrix.
    
    Example::
    
      >>> A = mx.nd.array([[1, -1],
      >>>                  [2, -3]])
      >>> B = mx.nd.array([[1, 4],
      >>>                  [2, 5],
      >>>                  [3, 6]])
      >>> C = mx.nd.khatri_rao(A, B)
      >>> print(C.asnumpy())
      [[  1.  -4.]
       [  2.  -5.]
       [  3.  -6.]
       [  2. -12.]
       [  4. -15.]
       [  6. -18.]]
    
    
    
    Defined in src/operator/contrib/krprod.cc:L108
    

    returns

    org.apache.mxnet.NDArray

  • abstract def khatri_rao(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the Khatri-Rao product of the input matrices.
    
    Given a collection of :math:`n` input matrices,
    
    .. math::
       A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},
    
    the (column-wise) Khatri-Rao product is defined as the matrix,
    
    .. math::
       X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},
    
    where the :math:`k` th column is equal to the column-wise outer product
    :math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth
    column of the ith matrix.
    
    Example::
    
      >>> A = mx.nd.array([[1, -1],
      >>>                  [2, -3]])
      >>> B = mx.nd.array([[1, 4],
      >>>                  [2, 5],
      >>>                  [3, 6]])
      >>> C = mx.nd.khatri_rao(A, B)
      >>> print(C.asnumpy())
      [[  1.  -4.]
       [  2.  -5.]
       [  3.  -6.]
       [  2. -12.]
       [  4. -15.]
       [  6. -18.]]
    
    
    
    Defined in src/operator/contrib/krprod.cc:L108
    

  • Computes the Khatri-Rao product of the input matrices.
    
    Given a collection of :math:`n` input matrices,
    
    .. math::
       A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},
    
    the (column-wise) Khatri-Rao product is defined as the matrix,
    
    .. math::
       X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},
    
    where the :math:`k` th column is equal to the column-wise outer product
    :math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth
    column of the ith matrix.
    
    Example::
    
      >>> A = mx.nd.array([[1, -1],
      >>>                  [2, -3]])
      >>> B = mx.nd.array([[1, 4],
      >>>                  [2, 5],
      >>>                  [3, 6]])
      >>> C = mx.nd.khatri_rao(A, B)
      >>> print(C.asnumpy())
      [[  1.  -4.]
       [  2.  -5.]
       [  3.  -6.]
       [  2. -12.]
       [  4. -15.]
       [  6. -18.]]
    
    
    
    Defined in src/operator/contrib/krprod.cc:L108
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_gelqf(args: Any*): NDArrayFuncReturn

    LQ factorization for general matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
    must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
    factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
    that:
    
       *A* = *L* \* *Q*
    
    Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
    and *Q* is row-orthonormal, meaning that
    
       *Q* \* *Q*\ :sup:`T`
    
    is equal to the identity matrix of shape *(x, x)*.
    
    If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single LQ factorization
       A = [[1., 2., 3.], [4., 5., 6.]]
       Q, L = gelqf(A)
       Q = [[-0.26726124, -0.53452248, -0.80178373],
            [0.87287156, 0.21821789, -0.43643578]]
       L = [[-3.74165739, 0.],
            [-8.55235974, 1.96396101]]
    
       // Batch LQ factorization
       A = [[[1., 2., 3.], [4., 5., 6.]],
            [[7., 8., 9.], [10., 11., 12.]]]
       Q, L = gelqf(A)
       Q = [[[-0.26726124, -0.53452248, -0.80178373],
             [0.87287156, 0.21821789, -0.43643578]],
            [[-0.50257071, -0.57436653, -0.64616234],
             [0.7620735, 0.05862104, -0.64483142]]]
       L = [[[-3.74165739, 0.],
             [-8.55235974, 1.96396101]],
            [[-13.92838828, 0.],
             [-19.09768702, 0.52758934]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L552
    

  • LQ factorization for general matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
    must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
    factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
    that:
    
       *A* = *L* \* *Q*
    
    Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
    and *Q* is row-orthonormal, meaning that
    
       *Q* \* *Q*\ :sup:`T`
    
    is equal to the identity matrix of shape *(x, x)*.
    
    If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single LQ factorization
       A = [[1., 2., 3.], [4., 5., 6.]]
       Q, L = gelqf(A)
       Q = [[-0.26726124, -0.53452248, -0.80178373],
            [0.87287156, 0.21821789, -0.43643578]]
       L = [[-3.74165739, 0.],
            [-8.55235974, 1.96396101]]
    
       // Batch LQ factorization
       A = [[[1., 2., 3.], [4., 5., 6.]],
            [[7., 8., 9.], [10., 11., 12.]]]
       Q, L = gelqf(A)
       Q = [[[-0.26726124, -0.53452248, -0.80178373],
             [0.87287156, 0.21821789, -0.43643578]],
            [[-0.50257071, -0.57436653, -0.64616234],
             [0.7620735, 0.05862104, -0.64483142]]]
       L = [[[-3.74165739, 0.],
             [-8.55235974, 1.96396101]],
            [[-13.92838828, 0.],
             [-19.09768702, 0.52758934]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L552
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_gelqf(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    LQ factorization for general matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
    must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
    factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
    that:
    
       *A* = *L* \* *Q*
    
    Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
    and *Q* is row-orthonormal, meaning that
    
       *Q* \* *Q*\ :sup:`T`
    
    is equal to the identity matrix of shape *(x, x)*.
    
    If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single LQ factorization
       A = [[1., 2., 3.], [4., 5., 6.]]
       Q, L = gelqf(A)
       Q = [[-0.26726124, -0.53452248, -0.80178373],
            [0.87287156, 0.21821789, -0.43643578]]
       L = [[-3.74165739, 0.],
            [-8.55235974, 1.96396101]]
    
       // Batch LQ factorization
       A = [[[1., 2., 3.], [4., 5., 6.]],
            [[7., 8., 9.], [10., 11., 12.]]]
       Q, L = gelqf(A)
       Q = [[[-0.26726124, -0.53452248, -0.80178373],
             [0.87287156, 0.21821789, -0.43643578]],
            [[-0.50257071, -0.57436653, -0.64616234],
             [0.7620735, 0.05862104, -0.64483142]]]
       L = [[[-3.74165739, 0.],
             [-8.55235974, 1.96396101]],
            [[-13.92838828, 0.],
             [-19.09768702, 0.52758934]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L552
    

  • LQ factorization for general matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
    must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
    factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
    that:
    
       *A* = *L* \* *Q*
    
    Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
    and *Q* is row-orthonormal, meaning that
    
       *Q* \* *Q*\ :sup:`T`
    
    is equal to the identity matrix of shape *(x, x)*.
    
    If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single LQ factorization
       A = [[1., 2., 3.], [4., 5., 6.]]
       Q, L = gelqf(A)
       Q = [[-0.26726124, -0.53452248, -0.80178373],
            [0.87287156, 0.21821789, -0.43643578]]
       L = [[-3.74165739, 0.],
            [-8.55235974, 1.96396101]]
    
       // Batch LQ factorization
       A = [[[1., 2., 3.], [4., 5., 6.]],
            [[7., 8., 9.], [10., 11., 12.]]]
       Q, L = gelqf(A)
       Q = [[[-0.26726124, -0.53452248, -0.80178373],
             [0.87287156, 0.21821789, -0.43643578]],
            [[-0.50257071, -0.57436653, -0.64616234],
             [0.7620735, 0.05862104, -0.64483142]]]
       L = [[[-3.74165739, 0.],
             [-8.55235974, 1.96396101]],
            [[-13.92838828, 0.],
             [-19.09768702, 0.52758934]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L552
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_gemm(args: Any*): NDArrayFuncReturn

    Performs general matrix multiplication and accumulation.
    Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C*
    
    Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or
    matrix transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = swapaxes(C, dim1=1, dim2=3)
        C = gemm(A1, B1, C)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply-add
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
               = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]
    
       // Batch matrix multiply-add
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       C = [[[10.0]], [[0.01]]]
       gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
               = [[[104.0]], [[0.14]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L81
    

  • Performs general matrix multiplication and accumulation.
    Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C*
    
    Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or
    matrix transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = swapaxes(C, dim1=1, dim2=3)
        C = gemm(A1, B1, C)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply-add
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
               = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]
    
       // Batch matrix multiply-add
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       C = [[[10.0]], [[0.01]]]
       gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
               = [[[104.0]], [[0.14]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L81
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_gemm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs general matrix multiplication and accumulation.
    Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C*
    
    Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or
    matrix transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = swapaxes(C, dim1=1, dim2=3)
        C = gemm(A1, B1, C)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply-add
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
               = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]
    
       // Batch matrix multiply-add
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       C = [[[10.0]], [[0.01]]]
       gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
               = [[[104.0]], [[0.14]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L81
    

  • Performs general matrix multiplication and accumulation.
    Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C*
    
    Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or
    matrix transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = swapaxes(C, dim1=1, dim2=3)
        C = gemm(A1, B1, C)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply-add
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
               = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]
    
       // Batch matrix multiply-add
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       C = [[[10.0]], [[0.01]]]
       gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
               = [[[104.0]], [[0.14]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L81
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_gemm2(args: Any*): NDArrayFuncReturn

    Performs general matrix multiplication.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)
    
    Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
    transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = gemm2(A1, B1)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
                = [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]
    
       // Batch matrix multiply
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
               = [[[4.0]], [[0.04 ]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L151
    

  • Performs general matrix multiplication.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)
    
    Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
    transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = gemm2(A1, B1)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
                = [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]
    
       // Batch matrix multiply
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
               = [[[4.0]], [[0.04 ]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L151
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_gemm2(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs general matrix multiplication.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)
    
    Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
    transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = gemm2(A1, B1)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
                = [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]
    
       // Batch matrix multiply
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
               = [[[4.0]], [[0.04 ]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L151
    

  • Performs general matrix multiplication.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)
    
    Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
    transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to
    
        A1 = swapaxes(A, dim1=1, dim2=3)
        B1 = swapaxes(B, dim1=1, dim2=3)
        C = gemm2(A1, B1)
        C = swapaxis(C, dim1=1, dim2=3)
    
    without the overhead of the additional swapaxis operations.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1.0, 1.0], [1.0, 1.0]]
       B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
                = [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]
    
       // Batch matrix multiply
       A = [[[1.0, 1.0]], [[0.1, 0.1]]]
       B = [[[1.0, 1.0]], [[0.1, 0.1]]]
       gemm2(A, B, transpose_b=True, alpha=2.0)
               = [[[4.0]], [[0.04 ]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L151
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_potrf(args: Any*): NDArrayFuncReturn

    Performs Cholesky factorization of a symmetric positive-definite matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the Cholesky factor *L* of the symmetric, positive definite matrix *A* is
    computed. *L* is lower triangular (entries of upper triangle are all zero), has
    positive diagonal entries, and:
    
      *A* = *L* \* *L*\ :sup:`T`
    
    If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix factorization
       A = [[4.0, 1.0], [1.0, 4.25]]
       potrf(A) = [[2.0, 0], [0.5, 2.0]]
    
       // Batch matrix factorization
       A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
       potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L201
    

  • Performs Cholesky factorization of a symmetric positive-definite matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the Cholesky factor *L* of the symmetric, positive definite matrix *A* is
    computed. *L* is lower triangular (entries of upper triangle are all zero), has
    positive diagonal entries, and:
    
      *A* = *L* \* *L*\ :sup:`T`
    
    If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix factorization
       A = [[4.0, 1.0], [1.0, 4.25]]
       potrf(A) = [[2.0, 0], [0.5, 2.0]]
    
       // Batch matrix factorization
       A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
       potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L201
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_potrf(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs Cholesky factorization of a symmetric positive-definite matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the Cholesky factor *L* of the symmetric, positive definite matrix *A* is
    computed. *L* is lower triangular (entries of upper triangle are all zero), has
    positive diagonal entries, and:
    
      *A* = *L* \* *L*\ :sup:`T`
    
    If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix factorization
       A = [[4.0, 1.0], [1.0, 4.25]]
       potrf(A) = [[2.0, 0], [0.5, 2.0]]
    
       // Batch matrix factorization
       A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
       potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L201
    

  • Performs Cholesky factorization of a symmetric positive-definite matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the Cholesky factor *L* of the symmetric, positive definite matrix *A* is
    computed. *L* is lower triangular (entries of upper triangle are all zero), has
    positive diagonal entries, and:
    
      *A* = *L* \* *L*\ :sup:`T`
    
    If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix factorization
       A = [[4.0, 1.0], [1.0, 4.25]]
       potrf(A) = [[2.0, 0], [0.5, 2.0]]
    
       // Batch matrix factorization
       A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
       potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L201
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_potri(args: Any*): NDArrayFuncReturn

    Performs matrix inversion from a Cholesky factorization.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a lower triangular matrix (entries of upper triangle are all zero)
    with positive diagonal. We compute:
    
      *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1`
    
    In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix
    *B* (obtained by *potrf*), then
    
      *out* = *B*\ :sup:`-1`
    
    If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    .. note:: Use this operator only if you are certain you need the inverse of *B*, and
              cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution
              (*trsm*). The latter is numerically much safer, and also cheaper.
    
    Examples::
    
       // Single matrix inverse
       A = [[2.0, 0], [0.5, 2.0]]
       potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]
    
       // Batch matrix inverse
       A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
       potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
                   [[0.06641, -0.01562], [-0.01562, 0,0625]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L259
    

  • Performs matrix inversion from a Cholesky factorization.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a lower triangular matrix (entries of upper triangle are all zero)
    with positive diagonal. We compute:
    
      *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1`
    
    In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix
    *B* (obtained by *potrf*), then
    
      *out* = *B*\ :sup:`-1`
    
    If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    .. note:: Use this operator only if you are certain you need the inverse of *B*, and
              cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution
              (*trsm*). The latter is numerically much safer, and also cheaper.
    
    Examples::
    
       // Single matrix inverse
       A = [[2.0, 0], [0.5, 2.0]]
       potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]
    
       // Batch matrix inverse
       A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
       potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
                   [[0.06641, -0.01562], [-0.01562, 0,0625]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L259
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_potri(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs matrix inversion from a Cholesky factorization.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a lower triangular matrix (entries of upper triangle are all zero)
    with positive diagonal. We compute:
    
      *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1`
    
    In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix
    *B* (obtained by *potrf*), then
    
      *out* = *B*\ :sup:`-1`
    
    If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    .. note:: Use this operator only if you are certain you need the inverse of *B*, and
              cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution
              (*trsm*). The latter is numerically much safer, and also cheaper.
    
    Examples::
    
       // Single matrix inverse
       A = [[2.0, 0], [0.5, 2.0]]
       potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]
    
       // Batch matrix inverse
       A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
       potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
                   [[0.06641, -0.01562], [-0.01562, 0,0625]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L259
    

  • Performs matrix inversion from a Cholesky factorization.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a lower triangular matrix (entries of upper triangle are all zero)
    with positive diagonal. We compute:
    
      *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1`
    
    In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix
    *B* (obtained by *potrf*), then
    
      *out* = *B*\ :sup:`-1`
    
    If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    .. note:: Use this operator only if you are certain you need the inverse of *B*, and
              cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution
              (*trsm*). The latter is numerically much safer, and also cheaper.
    
    Examples::
    
       // Single matrix inverse
       A = [[2.0, 0], [0.5, 2.0]]
       potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]
    
       // Batch matrix inverse
       A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
       potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
                   [[0.06641, -0.01562], [-0.01562, 0,0625]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L259
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_sumlogdiag(args: Any*): NDArrayFuncReturn

    Computes the sum of the logarithms of the diagonal elements of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
    logarithms of the diagonal elements, the result has shape (1,).
    
    If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix reduction
       A = [[1.0, 1.0], [1.0, 7.0]]
       sumlogdiag(A) = [1.9459]
    
       // Batch matrix reduction
       A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]]
       sumlogdiag(A) = [1.9459, 3.9318]
    
    
    Defined in src/operator/tensor/la_op.cc:L428
    

  • Computes the sum of the logarithms of the diagonal elements of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
    logarithms of the diagonal elements, the result has shape (1,).
    
    If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix reduction
       A = [[1.0, 1.0], [1.0, 7.0]]
       sumlogdiag(A) = [1.9459]
    
       // Batch matrix reduction
       A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]]
       sumlogdiag(A) = [1.9459, 3.9318]
    
    
    Defined in src/operator/tensor/la_op.cc:L428
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_sumlogdiag(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the sum of the logarithms of the diagonal elements of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
    logarithms of the diagonal elements, the result has shape (1,).
    
    If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix reduction
       A = [[1.0, 1.0], [1.0, 7.0]]
       sumlogdiag(A) = [1.9459]
    
       // Batch matrix reduction
       A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]]
       sumlogdiag(A) = [1.9459, 3.9318]
    
    
    Defined in src/operator/tensor/la_op.cc:L428
    

  • Computes the sum of the logarithms of the diagonal elements of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
    logarithms of the diagonal elements, the result has shape (1,).
    
    If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix reduction
       A = [[1.0, 1.0], [1.0, 7.0]]
       sumlogdiag(A) = [1.9459]
    
       // Batch matrix reduction
       A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]]
       sumlogdiag(A) = [1.9459, 3.9318]
    
    
    Defined in src/operator/tensor/la_op.cc:L428
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_syrk(args: Any*): NDArrayFuncReturn

    Multiplication of matrix with its transpose.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the operator performs the BLAS3 function *syrk*:
    
      *out* = *alpha* \* *A* \* *A*\ :sup:`T`
    
    if *transpose=False*, or
    
      *out* = *alpha* \* *A*\ :sup:`T` \ \* *A*
    
    if *transpose=True*.
    
    If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1., 2., 3.], [4., 5., 6.]]
       syrk(A, alpha=1., transpose=False)
                = [[14., 32.],
                   [32., 77.]]
       syrk(A, alpha=1., transpose=True)
                = [[17., 22., 27.],
                   [22., 29., 36.],
                   [27., 36., 45.]]
    
       // Batch matrix multiply
       A = [[[1., 1.]], [[0.1, 0.1]]]
       syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L484
    

  • Multiplication of matrix with its transpose.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the operator performs the BLAS3 function *syrk*:
    
      *out* = *alpha* \* *A* \* *A*\ :sup:`T`
    
    if *transpose=False*, or
    
      *out* = *alpha* \* *A*\ :sup:`T` \ \* *A*
    
    if *transpose=True*.
    
    If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1., 2., 3.], [4., 5., 6.]]
       syrk(A, alpha=1., transpose=False)
                = [[14., 32.],
                   [32., 77.]]
       syrk(A, alpha=1., transpose=True)
                = [[17., 22., 27.],
                   [22., 29., 36.],
                   [27., 36., 45.]]
    
       // Batch matrix multiply
       A = [[[1., 1.]], [[0.1, 0.1]]]
       syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L484
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_syrk(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Multiplication of matrix with its transpose.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the operator performs the BLAS3 function *syrk*:
    
      *out* = *alpha* \* *A* \* *A*\ :sup:`T`
    
    if *transpose=False*, or
    
      *out* = *alpha* \* *A*\ :sup:`T` \ \* *A*
    
    if *transpose=True*.
    
    If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1., 2., 3.], [4., 5., 6.]]
       syrk(A, alpha=1., transpose=False)
                = [[14., 32.],
                   [32., 77.]]
       syrk(A, alpha=1., transpose=True)
                = [[17., 22., 27.],
                   [22., 29., 36.],
                   [27., 36., 45.]]
    
       // Batch matrix multiply
       A = [[[1., 1.]], [[0.1, 0.1]]]
       syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L484
    

  • Multiplication of matrix with its transpose.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the operator performs the BLAS3 function *syrk*:
    
      *out* = *alpha* \* *A* \* *A*\ :sup:`T`
    
    if *transpose=False*, or
    
      *out* = *alpha* \* *A*\ :sup:`T` \ \* *A*
    
    if *transpose=True*.
    
    If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix multiply
       A = [[1., 2., 3.], [4., 5., 6.]]
       syrk(A, alpha=1., transpose=False)
                = [[14., 32.],
                   [32., 77.]]
       syrk(A, alpha=1., transpose=True)
                = [[17., 22., 27.],
                   [22., 29., 36.],
                   [27., 36., 45.]]
    
       // Batch matrix multiply
       A = [[[1., 1.]], [[0.1, 0.1]]]
       syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L484
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_trmm(args: Any*): NDArrayFuncReturn

    Performs multiplication with a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trmm*:
    
       *out* = *alpha* \* *op*\ (*A*) \* *B*
    
    if *rightside=False*, or
    
       *out* = *alpha* \* *B* \* *op*\ (*A*)
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    
    Examples::
    
       // Single triangular matrix multiply
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
    
       // Batch triangular matrix multiply
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
       trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
                                [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L316
    

  • Performs multiplication with a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trmm*:
    
       *out* = *alpha* \* *op*\ (*A*) \* *B*
    
    if *rightside=False*, or
    
       *out* = *alpha* \* *B* \* *op*\ (*A*)
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    
    Examples::
    
       // Single triangular matrix multiply
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
    
       // Batch triangular matrix multiply
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
       trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
                                [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L316
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_trmm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Performs multiplication with a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trmm*:
    
       *out* = *alpha* \* *op*\ (*A*) \* *B*
    
    if *rightside=False*, or
    
       *out* = *alpha* \* *B* \* *op*\ (*A*)
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    
    Examples::
    
       // Single triangular matrix multiply
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
    
       // Batch triangular matrix multiply
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
       trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
                                [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L316
    

  • Performs multiplication with a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trmm*:
    
       *out* = *alpha* \* *op*\ (*A*) \* *B*
    
    if *rightside=False*, or
    
       *out* = *alpha* \* *B* \* *op*\ (*A*)
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    
    Examples::
    
       // Single triangular matrix multiply
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
       trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
    
       // Batch triangular matrix multiply
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
       trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
                                [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L316
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_trsm(args: Any*): NDArrayFuncReturn

    Solves matrix equation involving a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trsm*, solving for *out* in:
    
       *op*\ (*A*) \* *out* = *alpha* \* *B*
    
    if *rightside=False*, or
    
       *out* \* *op*\ (*A*) = *alpha* \* *B*
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix solve
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
       trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
    
       // Batch matrix solve
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
            [[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
       trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
                                [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L379
    

  • Solves matrix equation involving a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trsm*, solving for *out* in:
    
       *op*\ (*A*) \* *out* = *alpha* \* *B*
    
    if *rightside=False*, or
    
       *out* \* *op*\ (*A*) = *alpha* \* *B*
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix solve
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
       trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
    
       // Batch matrix solve
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
            [[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
       trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
                                [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L379
    

    returns

    org.apache.mxnet.NDArray

  • abstract def linalg_trsm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Solves matrix equation involving a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trsm*, solving for *out* in:
    
       *op*\ (*A*) \* *out* = *alpha* \* *B*
    
    if *rightside=False*, or
    
       *out* \* *op*\ (*A*) = *alpha* \* *B*
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix solve
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
       trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
    
       // Batch matrix solve
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
            [[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
       trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
                                [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L379
    

  • Solves matrix equation involving a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be lower triangular. The operator performs the BLAS3 function
    *trsm*, solving for *out* in:
    
       *op*\ (*A*) \* *out* = *alpha* \* *B*
    
    if *rightside=False*, or
    
       *out* \* *op*\ (*A*) = *alpha* \* *B*
    
    if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
    identity or the matrix transposition (depending on *transpose*).
    
    If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs
    (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       // Single matrix solve
       A = [[1.0, 0], [1.0, 1.0]]
       B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
       trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
    
       // Batch matrix solve
       A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
       B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
            [[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
       trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
                                [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]
    
    
    Defined in src/operator/tensor/la_op.cc:L379
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log(args: Any*): NDArrayFuncReturn

    Returns element-wise Natural logarithmic value of the input.
    
    The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
    
    The storage type of ``log`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L941
    

  • Returns element-wise Natural logarithmic value of the input.
    
    The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
    
    The storage type of ``log`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L941
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise Natural logarithmic value of the input.
    
    The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
    
    The storage type of ``log`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L941
    

  • Returns element-wise Natural logarithmic value of the input.
    
    The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
    
    The storage type of ``log`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L941
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log10(args: Any*): NDArrayFuncReturn

    Returns element-wise Base-10 logarithmic value of the input.
    
    ``10**log10(x) = x``
    
    The storage type of ``log10`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L953
    

  • Returns element-wise Base-10 logarithmic value of the input.
    
    ``10**log10(x) = x``
    
    The storage type of ``log10`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L953
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log10(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise Base-10 logarithmic value of the input.
    
    ``10**log10(x) = x``
    
    The storage type of ``log10`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L953
    

  • Returns element-wise Base-10 logarithmic value of the input.
    
    ``10**log10(x) = x``
    
    The storage type of ``log10`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L953
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log1p(args: Any*): NDArrayFuncReturn

    Returns element-wise ``log(1 + x)`` value of the input.
    
    This function is more accurate than ``log(1 + x)``  for small ``x`` so that
    :math:`1+x\approx 1`
    
    The storage type of ``log1p`` output depends upon the input storage type:
    
       - log1p(default) = default
       - log1p(row_sparse) = row_sparse
       - log1p(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L990
    

  • Returns element-wise ``log(1 + x)`` value of the input.
    
    This function is more accurate than ``log(1 + x)``  for small ``x`` so that
    :math:`1+x\approx 1`
    
    The storage type of ``log1p`` output depends upon the input storage type:
    
       - log1p(default) = default
       - log1p(row_sparse) = row_sparse
       - log1p(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L990
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log1p(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise ``log(1 + x)`` value of the input.
    
    This function is more accurate than ``log(1 + x)``  for small ``x`` so that
    :math:`1+x\approx 1`
    
    The storage type of ``log1p`` output depends upon the input storage type:
    
       - log1p(default) = default
       - log1p(row_sparse) = row_sparse
       - log1p(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L990
    

  • Returns element-wise ``log(1 + x)`` value of the input.
    
    This function is more accurate than ``log(1 + x)``  for small ``x`` so that
    :math:`1+x\approx 1`
    
    The storage type of ``log1p`` output depends upon the input storage type:
    
       - log1p(default) = default
       - log1p(row_sparse) = row_sparse
       - log1p(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L990
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log2(args: Any*): NDArrayFuncReturn

    Returns element-wise Base-2 logarithmic value of the input.
    
    ``2**log2(x) = x``
    
    The storage type of ``log2`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L965
    

  • Returns element-wise Base-2 logarithmic value of the input.
    
    ``2**log2(x) = x``
    
    The storage type of ``log2`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L965
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log2(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise Base-2 logarithmic value of the input.
    
    ``2**log2(x) = x``
    
    The storage type of ``log2`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L965
    

  • Returns element-wise Base-2 logarithmic value of the input.
    
    ``2**log2(x) = x``
    
    The storage type of ``log2`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L965
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log_softmax(args: Any*): NDArrayFuncReturn

    Computes the log softmax of the input.
    This is equivalent to computing softmax followed by log.
    
    Examples::
    
      >>> x = mx.nd.array([1, 2, .1])
      >>> mx.nd.log_softmax(x).asnumpy()
      array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)
    
      >>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] )
      >>> mx.nd.log_softmax(x, axis=0).asnumpy()
      array([[-0.34115392, -0.69314718, -1.24115396],
             [-1.24115396, -0.69314718, -0.34115392]], dtype=float32)
    

  • Computes the log softmax of the input.
    This is equivalent to computing softmax followed by log.
    
    Examples::
    
      >>> x = mx.nd.array([1, 2, .1])
      >>> mx.nd.log_softmax(x).asnumpy()
      array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)
    
      >>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] )
      >>> mx.nd.log_softmax(x, axis=0).asnumpy()
      array([[-0.34115392, -0.69314718, -1.24115396],
             [-1.24115396, -0.69314718, -0.34115392]], dtype=float32)
    

    returns

    org.apache.mxnet.NDArray

  • abstract def log_softmax(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the log softmax of the input.
    This is equivalent to computing softmax followed by log.
    
    Examples::
    
      >>> x = mx.nd.array([1, 2, .1])
      >>> mx.nd.log_softmax(x).asnumpy()
      array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)
    
      >>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] )
      >>> mx.nd.log_softmax(x, axis=0).asnumpy()
      array([[-0.34115392, -0.69314718, -1.24115396],
             [-1.24115396, -0.69314718, -0.34115392]], dtype=float32)
    

  • Computes the log softmax of the input.
    This is equivalent to computing softmax followed by log.
    
    Examples::
    
      >>> x = mx.nd.array([1, 2, .1])
      >>> mx.nd.log_softmax(x).asnumpy()
      array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)
    
      >>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] )
      >>> mx.nd.log_softmax(x, axis=0).asnumpy()
      array([[-0.34115392, -0.69314718, -1.24115396],
             [-1.24115396, -0.69314718, -0.34115392]], dtype=float32)
    

    returns

    org.apache.mxnet.NDArray

  • abstract def logical_not(args: Any*): NDArrayFuncReturn

    Returns the result of logical NOT (!) function
    
    Example:
      logical_not([-2., 0., 1.]) = [0., 1., 0.]
    

  • Returns the result of logical NOT (!) function
    
    Example:
      logical_not([-2., 0., 1.]) = [0., 1., 0.]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def logical_not(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the result of logical NOT (!) function
    
    Example:
      logical_not([-2., 0., 1.]) = [0., 1., 0.]
    

  • Returns the result of logical NOT (!) function
    
    Example:
      logical_not([-2., 0., 1.]) = [0., 1., 0.]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def make_loss(args: Any*): NDArrayFuncReturn

    Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = make_loss(cross_entropy)
    
    We will need to use ``make_loss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    The storage type of ``make_loss`` output depends upon the input storage type:
    
       - make_loss(default) = default
       - make_loss(row_sparse) = row_sparse
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L300
    

  • Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = make_loss(cross_entropy)
    
    We will need to use ``make_loss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    The storage type of ``make_loss`` output depends upon the input storage type:
    
       - make_loss(default) = default
       - make_loss(row_sparse) = row_sparse
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L300
    

    returns

    org.apache.mxnet.NDArray

  • abstract def make_loss(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = make_loss(cross_entropy)
    
    We will need to use ``make_loss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    The storage type of ``make_loss`` output depends upon the input storage type:
    
       - make_loss(default) = default
       - make_loss(row_sparse) = row_sparse
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L300
    

  • Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = make_loss(cross_entropy)
    
    We will need to use ``make_loss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    The storage type of ``make_loss`` output depends upon the input storage type:
    
       - make_loss(default) = default
       - make_loss(row_sparse) = row_sparse
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L300
    

    returns

    org.apache.mxnet.NDArray

  • abstract def max(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

  • Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

    returns

    org.apache.mxnet.NDArray

  • abstract def max(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

  • Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

    returns

    org.apache.mxnet.NDArray

  • abstract def max_axis(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

  • Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

    returns

    org.apache.mxnet.NDArray

  • abstract def max_axis(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

  • Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    

    returns

    org.apache.mxnet.NDArray

  • abstract def mean(args: Any*): NDArrayFuncReturn

    Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132
    

  • Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132
    

    returns

    org.apache.mxnet.NDArray

  • abstract def mean(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132
    

  • Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132
    

    returns

    org.apache.mxnet.NDArray

  • abstract def min(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

  • Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

    returns

    org.apache.mxnet.NDArray

  • abstract def min(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

  • Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

    returns

    org.apache.mxnet.NDArray

  • abstract def min_axis(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

  • Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

    returns

    org.apache.mxnet.NDArray

  • abstract def min_axis(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

  • Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    

    returns

    org.apache.mxnet.NDArray

  • abstract def mp_sgd_mom_update(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    

  • Updater function for multi-precision sgd optimizer
    

    returns

    org.apache.mxnet.NDArray

  • abstract def mp_sgd_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    

  • Updater function for multi-precision sgd optimizer
    

    returns

    org.apache.mxnet.NDArray

  • abstract def mp_sgd_update(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    

  • Updater function for multi-precision sgd optimizer
    

    returns

    org.apache.mxnet.NDArray

  • abstract def mp_sgd_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    

  • Updater function for multi-precision sgd optimizer
    

    returns

    org.apache.mxnet.NDArray

  • abstract def nanprod(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177
    

  • Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177
    

    returns

    org.apache.mxnet.NDArray

  • abstract def nanprod(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177
    

  • Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177
    

    returns

    org.apache.mxnet.NDArray

  • abstract def nansum(args: Any*): NDArrayFuncReturn

    Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162
    

  • Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162
    

    returns

    org.apache.mxnet.NDArray

  • abstract def nansum(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162
    

  • Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162
    

    returns

    org.apache.mxnet.NDArray

  • abstract def negative(args: Any*): NDArrayFuncReturn

    Numerical negative of the argument, element-wise.
    
    The storage type of ``negative`` output depends upon the input storage type:
    
       - negative(default) = default
       - negative(row_sparse) = row_sparse
       - negative(csr) = csr
    

  • Numerical negative of the argument, element-wise.
    
    The storage type of ``negative`` output depends upon the input storage type:
    
       - negative(default) = default
       - negative(row_sparse) = row_sparse
       - negative(csr) = csr
    

    returns

    org.apache.mxnet.NDArray

  • abstract def negative(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Numerical negative of the argument, element-wise.
    
    The storage type of ``negative`` output depends upon the input storage type:
    
       - negative(default) = default
       - negative(row_sparse) = row_sparse
       - negative(csr) = csr
    

  • Numerical negative of the argument, element-wise.
    
    The storage type of ``negative`` output depends upon the input storage type:
    
       - negative(default) = default
       - negative(row_sparse) = row_sparse
       - negative(csr) = csr
    

    returns

    org.apache.mxnet.NDArray

  • abstract def norm(args: Any*): NDArrayFuncReturn

    Computes the norm on an NDArray.
    
    This operator computes the norm on an NDArray with the specified axis, depending
    on the value of the ord parameter. By default, it computes the L2 norm on the entire
    array. Currently only ord=2 supports sparse ndarrays.
    
    Examples::
    
      x = [[[1, 2],
            [3, 4]],
           [[2, 2],
            [5, 6]]]
    
      norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ]
                                [5.3851647 6.3245554]]
    
      norm(x, ord=1, axis=1) = [[4., 6.],
                                [7., 8.]]
    
      rsp = x.cast_storage('row_sparse')
    
      norm(rsp) = [5.47722578]
    
      csr = x.cast_storage('csr')
    
      norm(csr) = [5.47722578]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L350
    

  • Computes the norm on an NDArray.
    
    This operator computes the norm on an NDArray with the specified axis, depending
    on the value of the ord parameter. By default, it computes the L2 norm on the entire
    array. Currently only ord=2 supports sparse ndarrays.
    
    Examples::
    
      x = [[[1, 2],
            [3, 4]],
           [[2, 2],
            [5, 6]]]
    
      norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ]
                                [5.3851647 6.3245554]]
    
      norm(x, ord=1, axis=1) = [[4., 6.],
                                [7., 8.]]
    
      rsp = x.cast_storage('row_sparse')
    
      norm(rsp) = [5.47722578]
    
      csr = x.cast_storage('csr')
    
      norm(csr) = [5.47722578]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L350
    

    returns

    org.apache.mxnet.NDArray

  • abstract def norm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the norm on an NDArray.
    
    This operator computes the norm on an NDArray with the specified axis, depending
    on the value of the ord parameter. By default, it computes the L2 norm on the entire
    array. Currently only ord=2 supports sparse ndarrays.
    
    Examples::
    
      x = [[[1, 2],
            [3, 4]],
           [[2, 2],
            [5, 6]]]
    
      norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ]
                                [5.3851647 6.3245554]]
    
      norm(x, ord=1, axis=1) = [[4., 6.],
                                [7., 8.]]
    
      rsp = x.cast_storage('row_sparse')
    
      norm(rsp) = [5.47722578]
    
      csr = x.cast_storage('csr')
    
      norm(csr) = [5.47722578]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L350
    

  • Computes the norm on an NDArray.
    
    This operator computes the norm on an NDArray with the specified axis, depending
    on the value of the ord parameter. By default, it computes the L2 norm on the entire
    array. Currently only ord=2 supports sparse ndarrays.
    
    Examples::
    
      x = [[[1, 2],
            [3, 4]],
           [[2, 2],
            [5, 6]]]
    
      norm(x, ord=2, axis=1) = [[3.1622777 4.472136 ]
                                [5.3851647 6.3245554]]
    
      norm(x, ord=1, axis=1) = [[4., 6.],
                                [7., 8.]]
    
      rsp = x.cast_storage('row_sparse')
    
      norm(rsp) = [5.47722578]
    
      csr = x.cast_storage('csr')
    
      norm(csr) = [5.47722578]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L350
    

    returns

    org.apache.mxnet.NDArray

  • abstract def normal(args: Any*): NDArrayFuncReturn

    Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

  • Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

    returns

    org.apache.mxnet.NDArray

  • abstract def normal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

  • Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

    returns

    org.apache.mxnet.NDArray

  • abstract def one_hot(args: Any*): NDArrayFuncReturn

    Returns a one-hot array.
    
    The locations represented by `indices` take value `on_value`, while all
    other locations take value `off_value`.
    
    `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth`  of ``d`` would result
    in an output array of shape ``(i0, i1, d)`` with::
    
      output[i,j,:] = off_value
      output[i,j,indices[i,j]] = on_value
    
    Examples::
    
      one_hot([1,0,2,0], 3) = [[ 0.  1.  0.]
                               [ 1.  0.  0.]
                               [ 0.  0.  1.]
                               [ 1.  0.  0.]]
    
      one_hot([1,0,2,0], 3, on_value=8, off_value=1,
              dtype='int32') = [[1 8 1]
                                [8 1 1]
                                [1 1 8]
                                [8 1 1]]
    
      one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  0.  1.]
                                          [ 1.  0.  0.]]]
    
    
    Defined in src/operator/tensor/indexing_op.cc:L536
    

  • Returns a one-hot array.
    
    The locations represented by `indices` take value `on_value`, while all
    other locations take value `off_value`.
    
    `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth`  of ``d`` would result
    in an output array of shape ``(i0, i1, d)`` with::
    
      output[i,j,:] = off_value
      output[i,j,indices[i,j]] = on_value
    
    Examples::
    
      one_hot([1,0,2,0], 3) = [[ 0.  1.  0.]
                               [ 1.  0.  0.]
                               [ 0.  0.  1.]
                               [ 1.  0.  0.]]
    
      one_hot([1,0,2,0], 3, on_value=8, off_value=1,
              dtype='int32') = [[1 8 1]
                                [8 1 1]
                                [1 1 8]
                                [8 1 1]]
    
      one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  0.  1.]
                                          [ 1.  0.  0.]]]
    
    
    Defined in src/operator/tensor/indexing_op.cc:L536
    

    returns

    org.apache.mxnet.NDArray

  • abstract def one_hot(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns a one-hot array.
    
    The locations represented by `indices` take value `on_value`, while all
    other locations take value `off_value`.
    
    `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth`  of ``d`` would result
    in an output array of shape ``(i0, i1, d)`` with::
    
      output[i,j,:] = off_value
      output[i,j,indices[i,j]] = on_value
    
    Examples::
    
      one_hot([1,0,2,0], 3) = [[ 0.  1.  0.]
                               [ 1.  0.  0.]
                               [ 0.  0.  1.]
                               [ 1.  0.  0.]]
    
      one_hot([1,0,2,0], 3, on_value=8, off_value=1,
              dtype='int32') = [[1 8 1]
                                [8 1 1]
                                [1 1 8]
                                [8 1 1]]
    
      one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  0.  1.]
                                          [ 1.  0.  0.]]]
    
    
    Defined in src/operator/tensor/indexing_op.cc:L536
    

  • Returns a one-hot array.
    
    The locations represented by `indices` take value `on_value`, while all
    other locations take value `off_value`.
    
    `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth`  of ``d`` would result
    in an output array of shape ``(i0, i1, d)`` with::
    
      output[i,j,:] = off_value
      output[i,j,indices[i,j]] = on_value
    
    Examples::
    
      one_hot([1,0,2,0], 3) = [[ 0.  1.  0.]
                               [ 1.  0.  0.]
                               [ 0.  0.  1.]
                               [ 1.  0.  0.]]
    
      one_hot([1,0,2,0], 3, on_value=8, off_value=1,
              dtype='int32') = [[1 8 1]
                                [8 1 1]
                                [1 1 8]
                                [8 1 1]]
    
      one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  1.  0.]
                                          [ 1.  0.  0.]]
    
                                         [[ 0.  0.  1.]
                                          [ 1.  0.  0.]]]
    
    
    Defined in src/operator/tensor/indexing_op.cc:L536
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ones_like(args: Any*): NDArrayFuncReturn

    Return an array of ones with the same shape and type
    as the input array.
    
    Examples::
    
      x = [[ 0.,  0.,  0.],
           [ 0.,  0.,  0.]]
    
      ones_like(x) = [[ 1.,  1.,  1.],
                      [ 1.,  1.,  1.]]
    

  • Return an array of ones with the same shape and type
    as the input array.
    
    Examples::
    
      x = [[ 0.,  0.,  0.],
           [ 0.,  0.,  0.]]
    
      ones_like(x) = [[ 1.,  1.,  1.],
                      [ 1.,  1.,  1.]]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ones_like(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Return an array of ones with the same shape and type
    as the input array.
    
    Examples::
    
      x = [[ 0.,  0.,  0.],
           [ 0.,  0.,  0.]]
    
      ones_like(x) = [[ 1.,  1.,  1.],
                      [ 1.,  1.,  1.]]
    

  • Return an array of ones with the same shape and type
    as the input array.
    
    Examples::
    
      x = [[ 0.,  0.,  0.],
           [ 0.,  0.,  0.]]
    
      ones_like(x) = [[ 1.,  1.,  1.],
                      [ 1.,  1.,  1.]]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def pad(args: Any*): NDArrayFuncReturn

    Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

  • Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

    returns

    org.apache.mxnet.NDArray

  • abstract def pad(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

  • Pads an input array with a constant or edge values of the array.
    
    .. note:: `Pad` is deprecated. Use `pad` instead.
    
    .. note:: Current implementation only supports 4D and 5D input arrays with padding applied
       only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero.
    
    This operation pads an input array with either a `constant_value` or edge values
    along each axis of the input array. The amount of padding is specified by `pad_width`.
    
    `pad_width` is a tuple of integer padding widths for each axis of the format
    ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N``
    where ``N`` is the number of dimensions of the array.
    
    For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values
    to add before and after the elements of the array along dimension ``N``.
    The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``,
    ``after_2`` must be 0.
    
    Example::
    
       x = [[[[  1.   2.   3.]
              [  4.   5.   6.]]
    
             [[  7.   8.   9.]
              [ 10.  11.  12.]]]
    
    
            [[[ 11.  12.  13.]
              [ 14.  15.  16.]]
    
             [[ 17.  18.  19.]
              [ 20.  21.  22.]]]]
    
       pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  1.   1.   2.   3.   3.]
                [  1.   1.   2.   3.   3.]
                [  4.   4.   5.   6.   6.]
                [  4.   4.   5.   6.   6.]]
    
               [[  7.   7.   8.   9.   9.]
                [  7.   7.   8.   9.   9.]
                [ 10.  10.  11.  12.  12.]
                [ 10.  10.  11.  12.  12.]]]
    
    
              [[[ 11.  11.  12.  13.  13.]
                [ 11.  11.  12.  13.  13.]
                [ 14.  14.  15.  16.  16.]
                [ 14.  14.  15.  16.  16.]]
    
               [[ 17.  17.  18.  19.  19.]
                [ 17.  17.  18.  19.  19.]
                [ 20.  20.  21.  22.  22.]
                [ 20.  20.  21.  22.  22.]]]]
    
       pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =
    
             [[[[  0.   0.   0.   0.   0.]
                [  0.   1.   2.   3.   0.]
                [  0.   4.   5.   6.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.   7.   8.   9.   0.]
                [  0.  10.  11.  12.   0.]
                [  0.   0.   0.   0.   0.]]]
    
    
              [[[  0.   0.   0.   0.   0.]
                [  0.  11.  12.  13.   0.]
                [  0.  14.  15.  16.   0.]
                [  0.   0.   0.   0.   0.]]
    
               [[  0.   0.   0.   0.   0.]
                [  0.  17.  18.  19.   0.]
                [  0.  20.  21.  22.   0.]
                [  0.   0.   0.   0.   0.]]]]
    
    
    
    
    Defined in src/operator/pad.cc:L766
    

    returns

    org.apache.mxnet.NDArray

  • abstract def pick(args: Any*): NDArrayFuncReturn

    Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = [[ 2.],
                                     [ 3.],
                                     [ 6.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153
    

  • Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = [[ 2.],
                                     [ 3.],
                                     [ 6.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153
    

    returns

    org.apache.mxnet.NDArray

  • abstract def pick(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = [[ 2.],
                                     [ 3.],
                                     [ 6.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153
    

  • Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i]]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = [[ 1.],
           [ 0.],
           [ 2.]]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = [[ 2.],
                                     [ 3.],
                                     [ 6.]]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L153
    

    returns

    org.apache.mxnet.NDArray

  • abstract def prod(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147
    

  • Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147
    

    returns

    org.apache.mxnet.NDArray

  • abstract def prod(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147
    

  • Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147
    

    returns

    org.apache.mxnet.NDArray

  • abstract def radians(args: Any*): NDArrayFuncReturn

    Converts each element of the input array from degrees to radians.
    
    .. math::
       radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]
    
    The storage type of ``radians`` output depends upon the input storage type:
    
       - radians(default) = default
       - radians(row_sparse) = row_sparse
       - radians(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182
    

  • Converts each element of the input array from degrees to radians.
    
    .. math::
       radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]
    
    The storage type of ``radians`` output depends upon the input storage type:
    
       - radians(default) = default
       - radians(row_sparse) = row_sparse
       - radians(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182
    

    returns

    org.apache.mxnet.NDArray

  • abstract def radians(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Converts each element of the input array from degrees to radians.
    
    .. math::
       radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]
    
    The storage type of ``radians`` output depends upon the input storage type:
    
       - radians(default) = default
       - radians(row_sparse) = row_sparse
       - radians(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182
    

  • Converts each element of the input array from degrees to radians.
    
    .. math::
       radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]
    
    The storage type of ``radians`` output depends upon the input storage type:
    
       - radians(default) = default
       - radians(row_sparse) = row_sparse
       - radians(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L182
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_exponential(args: Any*): NDArrayFuncReturn

    Draw random samples from an exponential distribution.
    
    Samples are distributed according to an exponential distribution parametrized by *lambda* (rate).
    
    Example::
    
       exponential(lam=4, shape=(2,2)) = [[ 0.0097189 ,  0.08999364],
                                          [ 0.04146638,  0.31715935]]
    
    
    Defined in src/operator/random/sample_op.cc:L115
    

  • Draw random samples from an exponential distribution.
    
    Samples are distributed according to an exponential distribution parametrized by *lambda* (rate).
    
    Example::
    
       exponential(lam=4, shape=(2,2)) = [[ 0.0097189 ,  0.08999364],
                                          [ 0.04146638,  0.31715935]]
    
    
    Defined in src/operator/random/sample_op.cc:L115
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_exponential(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from an exponential distribution.
    
    Samples are distributed according to an exponential distribution parametrized by *lambda* (rate).
    
    Example::
    
       exponential(lam=4, shape=(2,2)) = [[ 0.0097189 ,  0.08999364],
                                          [ 0.04146638,  0.31715935]]
    
    
    Defined in src/operator/random/sample_op.cc:L115
    

  • Draw random samples from an exponential distribution.
    
    Samples are distributed according to an exponential distribution parametrized by *lambda* (rate).
    
    Example::
    
       exponential(lam=4, shape=(2,2)) = [[ 0.0097189 ,  0.08999364],
                                          [ 0.04146638,  0.31715935]]
    
    
    Defined in src/operator/random/sample_op.cc:L115
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_gamma(args: Any*): NDArrayFuncReturn

    Draw random samples from a gamma distribution.
    
    Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale).
    
    Example::
    
       gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984,  3.37695289],
                                                [ 3.91697288,  3.65933681]]
    
    
    Defined in src/operator/random/sample_op.cc:L100
    

  • Draw random samples from a gamma distribution.
    
    Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale).
    
    Example::
    
       gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984,  3.37695289],
                                                [ 3.91697288,  3.65933681]]
    
    
    Defined in src/operator/random/sample_op.cc:L100
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_gamma(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a gamma distribution.
    
    Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale).
    
    Example::
    
       gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984,  3.37695289],
                                                [ 3.91697288,  3.65933681]]
    
    
    Defined in src/operator/random/sample_op.cc:L100
    

  • Draw random samples from a gamma distribution.
    
    Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale).
    
    Example::
    
       gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984,  3.37695289],
                                                [ 3.91697288,  3.65933681]]
    
    
    Defined in src/operator/random/sample_op.cc:L100
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_generalized_negative_binomial(args: Any*): NDArrayFuncReturn

    Draw random samples from a generalized negative binomial distribution.
    
    Samples are distributed according to a generalized negative binomial distribution parametrized by
    *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the
    number of unsuccessful experiments (generalized to real numbers).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2.,  1.],
                                                                        [ 6.,  4.]]
    
    
    Defined in src/operator/random/sample_op.cc:L168
    

  • Draw random samples from a generalized negative binomial distribution.
    
    Samples are distributed according to a generalized negative binomial distribution parametrized by
    *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the
    number of unsuccessful experiments (generalized to real numbers).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2.,  1.],
                                                                        [ 6.,  4.]]
    
    
    Defined in src/operator/random/sample_op.cc:L168
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_generalized_negative_binomial(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a generalized negative binomial distribution.
    
    Samples are distributed according to a generalized negative binomial distribution parametrized by
    *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the
    number of unsuccessful experiments (generalized to real numbers).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2.,  1.],
                                                                        [ 6.,  4.]]
    
    
    Defined in src/operator/random/sample_op.cc:L168
    

  • Draw random samples from a generalized negative binomial distribution.
    
    Samples are distributed according to a generalized negative binomial distribution parametrized by
    *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the
    number of unsuccessful experiments (generalized to real numbers).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2.,  1.],
                                                                        [ 6.,  4.]]
    
    
    Defined in src/operator/random/sample_op.cc:L168
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_negative_binomial(args: Any*): NDArrayFuncReturn

    Draw random samples from a negative binomial distribution.
    
    Samples are distributed according to a negative binomial distribution parametrized by
    *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4.,  7.],
                                                     [ 2.,  5.]]
    
    
    Defined in src/operator/random/sample_op.cc:L149
    

  • Draw random samples from a negative binomial distribution.
    
    Samples are distributed according to a negative binomial distribution parametrized by
    *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4.,  7.],
                                                     [ 2.,  5.]]
    
    
    Defined in src/operator/random/sample_op.cc:L149
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_negative_binomial(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a negative binomial distribution.
    
    Samples are distributed according to a negative binomial distribution parametrized by
    *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4.,  7.],
                                                     [ 2.,  5.]]
    
    
    Defined in src/operator/random/sample_op.cc:L149
    

  • Draw random samples from a negative binomial distribution.
    
    Samples are distributed according to a negative binomial distribution parametrized by
    *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4.,  7.],
                                                     [ 2.,  5.]]
    
    
    Defined in src/operator/random/sample_op.cc:L149
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_normal(args: Any*): NDArrayFuncReturn

    Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

  • Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_normal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

  • Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114]]
    
    
    Defined in src/operator/random/sample_op.cc:L85
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_poisson(args: Any*): NDArrayFuncReturn

    Draw random samples from a Poisson distribution.
    
    Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       poisson(lam=4, shape=(2,2)) = [[ 5.,  2.],
                                      [ 4.,  6.]]
    
    
    Defined in src/operator/random/sample_op.cc:L132
    

  • Draw random samples from a Poisson distribution.
    
    Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       poisson(lam=4, shape=(2,2)) = [[ 5.,  2.],
                                      [ 4.,  6.]]
    
    
    Defined in src/operator/random/sample_op.cc:L132
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_poisson(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a Poisson distribution.
    
    Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       poisson(lam=4, shape=(2,2)) = [[ 5.,  2.],
                                      [ 4.,  6.]]
    
    
    Defined in src/operator/random/sample_op.cc:L132
    

  • Draw random samples from a Poisson distribution.
    
    Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       poisson(lam=4, shape=(2,2)) = [[ 5.,  2.],
                                      [ 4.,  6.]]
    
    
    Defined in src/operator/random/sample_op.cc:L132
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_uniform(args: Any*): NDArrayFuncReturn

    Draw random samples from a uniform distribution.
    
    .. note:: The existing alias ``uniform`` is deprecated.
    
    Samples are uniformly distributed over the half-open interval *[low, high)*
    (includes *low*, but excludes *high*).
    
    Example::
    
       uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
                                              [ 0.54488319,  0.84725171]]
    
    
    
    Defined in src/operator/random/sample_op.cc:L66
    

  • Draw random samples from a uniform distribution.
    
    .. note:: The existing alias ``uniform`` is deprecated.
    
    Samples are uniformly distributed over the half-open interval *[low, high)*
    (includes *low*, but excludes *high*).
    
    Example::
    
       uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
                                              [ 0.54488319,  0.84725171]]
    
    
    
    Defined in src/operator/random/sample_op.cc:L66
    

    returns

    org.apache.mxnet.NDArray

  • abstract def random_uniform(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a uniform distribution.
    
    .. note:: The existing alias ``uniform`` is deprecated.
    
    Samples are uniformly distributed over the half-open interval *[low, high)*
    (includes *low*, but excludes *high*).
    
    Example::
    
       uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
                                              [ 0.54488319,  0.84725171]]
    
    
    
    Defined in src/operator/random/sample_op.cc:L66
    

  • Draw random samples from a uniform distribution.
    
    .. note:: The existing alias ``uniform`` is deprecated.
    
    Samples are uniformly distributed over the half-open interval *[low, high)*
    (includes *low*, but excludes *high*).
    
    Example::
    
       uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
                                              [ 0.54488319,  0.84725171]]
    
    
    
    Defined in src/operator/random/sample_op.cc:L66
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ravel_multi_index(args: Any*): NDArrayFuncReturn

    Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix.
    
    Examples::
    
       A = [[3,6,6],[4,5,1]]
       ravel(A, shape=(7,6)) = [22,41,37]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L41
    

  • Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix.
    
    Examples::
    
       A = [[3,6,6],[4,5,1]]
       ravel(A, shape=(7,6)) = [22,41,37]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L41
    

    returns

    org.apache.mxnet.NDArray

  • abstract def ravel_multi_index(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix.
    
    Examples::
    
       A = [[3,6,6],[4,5,1]]
       ravel(A, shape=(7,6)) = [22,41,37]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L41
    

  • Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix.
    
    Examples::
    
       A = [[3,6,6],[4,5,1]]
       ravel(A, shape=(7,6)) = [22,41,37]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L41
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rcbrt(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse cube-root value of the input.
    
    .. math::
       rcbrt(x) = 1/\sqrt[3]{x}
    
    Example::
    
       rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L906
    

  • Returns element-wise inverse cube-root value of the input.
    
    .. math::
       rcbrt(x) = 1/\sqrt[3]{x}
    
    Example::
    
       rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L906
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rcbrt(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse cube-root value of the input.
    
    .. math::
       rcbrt(x) = 1/\sqrt[3]{x}
    
    Example::
    
       rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L906
    

  • Returns element-wise inverse cube-root value of the input.
    
    .. math::
       rcbrt(x) = 1/\sqrt[3]{x}
    
    Example::
    
       rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L906
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reciprocal(args: Any*): NDArrayFuncReturn

    Returns the reciprocal of the argument, element-wise.
    
    Calculates 1/x.
    
    Example::
    
        reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L646
    

  • Returns the reciprocal of the argument, element-wise.
    
    Calculates 1/x.
    
    Example::
    
        reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L646
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reciprocal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns the reciprocal of the argument, element-wise.
    
    Calculates 1/x.
    
    Example::
    
        reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L646
    

  • Returns the reciprocal of the argument, element-wise.
    
    Calculates 1/x.
    
    Example::
    
        reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L646
    

    returns

    org.apache.mxnet.NDArray

  • abstract def relu(args: Any*): NDArrayFuncReturn

    Computes rectified linear.
    
    .. math::
       max(features, 0)
    
    The storage type of ``relu`` output depends upon the input storage type:
    
       - relu(default) = default
       - relu(row_sparse) = row_sparse
       - relu(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
    

  • Computes rectified linear.
    
    .. math::
       max(features, 0)
    
    The storage type of ``relu`` output depends upon the input storage type:
    
       - relu(default) = default
       - relu(row_sparse) = row_sparse
       - relu(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
    

    returns

    org.apache.mxnet.NDArray

  • abstract def relu(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes rectified linear.
    
    .. math::
       max(features, 0)
    
    The storage type of ``relu`` output depends upon the input storage type:
    
       - relu(default) = default
       - relu(row_sparse) = row_sparse
       - relu(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
    

  • Computes rectified linear.
    
    .. math::
       max(features, 0)
    
    The storage type of ``relu`` output depends upon the input storage type:
    
       - relu(default) = default
       - relu(row_sparse) = row_sparse
       - relu(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
    

    returns

    org.apache.mxnet.NDArray

  • abstract def repeat(args: Any*): NDArrayFuncReturn

    Repeats elements of an array.
    
    By default, ``repeat`` flattens the input array into 1-D and then repeats the
    elements::
    
      x = [[ 1, 2],
           [ 3, 4]]
    
      repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]
    
    The parameter ``axis`` specifies the axis along which to perform repeat::
    
      repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
                                      [ 3.,  3.,  4.,  4.]]
    
      repeat(x, repeats=2, axis=0) = [[ 1.,  2.],
                                      [ 1.,  2.],
                                      [ 3.,  4.],
                                      [ 3.,  4.]]
    
      repeat(x, repeats=2, axis=-1) = [[ 1.,  1.,  2.,  2.],
                                       [ 3.,  3.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L691
    

  • Repeats elements of an array.
    
    By default, ``repeat`` flattens the input array into 1-D and then repeats the
    elements::
    
      x = [[ 1, 2],
           [ 3, 4]]
    
      repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]
    
    The parameter ``axis`` specifies the axis along which to perform repeat::
    
      repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
                                      [ 3.,  3.,  4.,  4.]]
    
      repeat(x, repeats=2, axis=0) = [[ 1.,  2.],
                                      [ 1.,  2.],
                                      [ 3.,  4.],
                                      [ 3.,  4.]]
    
      repeat(x, repeats=2, axis=-1) = [[ 1.,  1.,  2.,  2.],
                                       [ 3.,  3.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L691
    

    returns

    org.apache.mxnet.NDArray

  • abstract def repeat(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Repeats elements of an array.
    
    By default, ``repeat`` flattens the input array into 1-D and then repeats the
    elements::
    
      x = [[ 1, 2],
           [ 3, 4]]
    
      repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]
    
    The parameter ``axis`` specifies the axis along which to perform repeat::
    
      repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
                                      [ 3.,  3.,  4.,  4.]]
    
      repeat(x, repeats=2, axis=0) = [[ 1.,  2.],
                                      [ 1.,  2.],
                                      [ 3.,  4.],
                                      [ 3.,  4.]]
    
      repeat(x, repeats=2, axis=-1) = [[ 1.,  1.,  2.,  2.],
                                       [ 3.,  3.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L691
    

  • Repeats elements of an array.
    
    By default, ``repeat`` flattens the input array into 1-D and then repeats the
    elements::
    
      x = [[ 1, 2],
           [ 3, 4]]
    
      repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]
    
    The parameter ``axis`` specifies the axis along which to perform repeat::
    
      repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
                                      [ 3.,  3.,  4.,  4.]]
    
      repeat(x, repeats=2, axis=0) = [[ 1.,  2.],
                                      [ 1.,  2.],
                                      [ 3.,  4.],
                                      [ 3.,  4.]]
    
      repeat(x, repeats=2, axis=-1) = [[ 1.,  1.,  2.,  2.],
                                       [ 3.,  3.,  4.,  4.]]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L691
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reshape(args: Any*): NDArrayFuncReturn

    Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

  • Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reshape(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

  • Reshapes the input array.
    
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    
    Example::
    
      reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]
    
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    
    - ``0``  copy this dimension from the input to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
    
      Example::
    
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
    
      Example::
    
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
    
      Example::
    
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
    
      Example::
    
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
    
      Example::
    
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L169
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reshape_like(args: Any*): NDArrayFuncReturn

    Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`.
    
    Returns a **view** of the `lhs` array with a new shape without altering any data.
    
    Example::
    
      x = [1, 2, 3, 4, 5, 6]
      y = [[0, -4], [3, 2], [2, 2]]
      reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]]
    
    More precise control over how dimensions are inherited is achieved by specifying \
    slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \
    are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same.
    
      Examples::
    
      - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
      - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)
    
    Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range.
    
      Example::
    
      - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L455
    

  • Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`.
    
    Returns a **view** of the `lhs` array with a new shape without altering any data.
    
    Example::
    
      x = [1, 2, 3, 4, 5, 6]
      y = [[0, -4], [3, 2], [2, 2]]
      reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]]
    
    More precise control over how dimensions are inherited is achieved by specifying \
    slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \
    are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same.
    
      Examples::
    
      - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
      - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)
    
    Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range.
    
      Example::
    
      - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L455
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reshape_like(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`.
    
    Returns a **view** of the `lhs` array with a new shape without altering any data.
    
    Example::
    
      x = [1, 2, 3, 4, 5, 6]
      y = [[0, -4], [3, 2], [2, 2]]
      reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]]
    
    More precise control over how dimensions are inherited is achieved by specifying \
    slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \
    are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same.
    
      Examples::
    
      - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
      - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)
    
    Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range.
    
      Example::
    
      - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L455
    

  • Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`.
    
    Returns a **view** of the `lhs` array with a new shape without altering any data.
    
    Example::
    
      x = [1, 2, 3, 4, 5, 6]
      y = [[0, -4], [3, 2], [2, 2]]
      reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]]
    
    More precise control over how dimensions are inherited is achieved by specifying \
    slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \
    are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same.
    
      Examples::
    
      - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
      - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)
    
    Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range.
    
      Example::
    
      - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L455
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reverse(args: Any*): NDArrayFuncReturn

    Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

  • Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

    returns

    org.apache.mxnet.NDArray

  • abstract def reverse(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

  • Reverses the order of elements along given axis while preserving array shape.
    
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    
    Examples::
    
      x = [[ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.]]
    
      reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.]]
    
      reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L793
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rint(args: Any*): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest integer of the input.
    
    .. note::
       - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``.
       - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``.
    
    Example::
    
       rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  1., -2.,  2.,  2.]
    
    The storage type of ``rint`` output depends upon the input storage type:
    
       - rint(default) = default
       - rint(row_sparse) = row_sparse
       - rint(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
    

  • Returns element-wise rounded value to the nearest integer of the input.
    
    .. note::
       - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``.
       - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``.
    
    Example::
    
       rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  1., -2.,  2.,  2.]
    
    The storage type of ``rint`` output depends upon the input storage type:
    
       - rint(default) = default
       - rint(row_sparse) = row_sparse
       - rint(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rint(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest integer of the input.
    
    .. note::
       - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``.
       - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``.
    
    Example::
    
       rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  1., -2.,  2.,  2.]
    
    The storage type of ``rint`` output depends upon the input storage type:
    
       - rint(default) = default
       - rint(row_sparse) = row_sparse
       - rint(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
    

  • Returns element-wise rounded value to the nearest integer of the input.
    
    .. note::
       - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``.
       - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``.
    
    Example::
    
       rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  1., -2.,  2.,  2.]
    
    The storage type of ``rint`` output depends upon the input storage type:
    
       - rint(default) = default
       - rint(row_sparse) = row_sparse
       - rint(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rmsprop_update(args: Any*): NDArrayFuncReturn

    Update function for `RMSProp` optimizer.
    
    `RMSprop` is a variant of stochastic gradient descent where the gradients are
    divided by a cache which grows with the sum of squares of recent gradients?
    
    `RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
    tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for
    each parameter monotonically over the course of training.
    While this is analytically motivated for convex optimizations, it may not be ideal
    for non-convex problems. `RMSProp` deals with this heuristically by allowing the
    learning rates to rebound as the denominator decays over time.
    
    Define the Root Mean Square (RMS) error criterion of the gradient as
    :math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
    gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient.
    
    The :math:`E[g^2]_t` is given by:
    
    .. math::
      E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t
    
    The RMSProp code follows the version in
    http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
    Tieleman & Hinton, 2012.
    
    Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
    :math:`\eta` to be 0.001.
    
    
    
    Defined in src/operator/optimizer_op.cc:L553
    

  • Update function for `RMSProp` optimizer.
    
    `RMSprop` is a variant of stochastic gradient descent where the gradients are
    divided by a cache which grows with the sum of squares of recent gradients?
    
    `RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
    tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for
    each parameter monotonically over the course of training.
    While this is analytically motivated for convex optimizations, it may not be ideal
    for non-convex problems. `RMSProp` deals with this heuristically by allowing the
    learning rates to rebound as the denominator decays over time.
    
    Define the Root Mean Square (RMS) error criterion of the gradient as
    :math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
    gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient.
    
    The :math:`E[g^2]_t` is given by:
    
    .. math::
      E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t
    
    The RMSProp code follows the version in
    http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
    Tieleman & Hinton, 2012.
    
    Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
    :math:`\eta` to be 0.001.
    
    
    
    Defined in src/operator/optimizer_op.cc:L553
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rmsprop_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for `RMSProp` optimizer.
    
    `RMSprop` is a variant of stochastic gradient descent where the gradients are
    divided by a cache which grows with the sum of squares of recent gradients?
    
    `RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
    tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for
    each parameter monotonically over the course of training.
    While this is analytically motivated for convex optimizations, it may not be ideal
    for non-convex problems. `RMSProp` deals with this heuristically by allowing the
    learning rates to rebound as the denominator decays over time.
    
    Define the Root Mean Square (RMS) error criterion of the gradient as
    :math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
    gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient.
    
    The :math:`E[g^2]_t` is given by:
    
    .. math::
      E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t
    
    The RMSProp code follows the version in
    http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
    Tieleman & Hinton, 2012.
    
    Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
    :math:`\eta` to be 0.001.
    
    
    
    Defined in src/operator/optimizer_op.cc:L553
    

  • Update function for `RMSProp` optimizer.
    
    `RMSprop` is a variant of stochastic gradient descent where the gradients are
    divided by a cache which grows with the sum of squares of recent gradients?
    
    `RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
    tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for
    each parameter monotonically over the course of training.
    While this is analytically motivated for convex optimizations, it may not be ideal
    for non-convex problems. `RMSProp` deals with this heuristically by allowing the
    learning rates to rebound as the denominator decays over time.
    
    Define the Root Mean Square (RMS) error criterion of the gradient as
    :math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
    gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient.
    
    The :math:`E[g^2]_t` is given by:
    
    .. math::
      E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t
    
    The RMSProp code follows the version in
    http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
    Tieleman & Hinton, 2012.
    
    Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
    :math:`\eta` to be 0.001.
    
    
    
    Defined in src/operator/optimizer_op.cc:L553
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rmspropalex_update(args: Any*): NDArrayFuncReturn

    Update function for RMSPropAlex optimizer.
    
    `RMSPropAlex` is non-centered version of `RMSProp`.
    
    Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
    :math:`E[g]_t` is the decaying average over past gradient.
    
    .. math::
      E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
      E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
      \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t + \Delta_t
    
    The RMSPropAlex code follows the version in
    http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
    
    Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
    to be 0.9 and the learning rate :math:`\eta` to be 0.0001.
    
    
    Defined in src/operator/optimizer_op.cc:L592
    

  • Update function for RMSPropAlex optimizer.
    
    `RMSPropAlex` is non-centered version of `RMSProp`.
    
    Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
    :math:`E[g]_t` is the decaying average over past gradient.
    
    .. math::
      E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
      E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
      \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t + \Delta_t
    
    The RMSPropAlex code follows the version in
    http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
    
    Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
    to be 0.9 and the learning rate :math:`\eta` to be 0.0001.
    
    
    Defined in src/operator/optimizer_op.cc:L592
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rmspropalex_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for RMSPropAlex optimizer.
    
    `RMSPropAlex` is non-centered version of `RMSProp`.
    
    Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
    :math:`E[g]_t` is the decaying average over past gradient.
    
    .. math::
      E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
      E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
      \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t + \Delta_t
    
    The RMSPropAlex code follows the version in
    http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
    
    Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
    to be 0.9 and the learning rate :math:`\eta` to be 0.0001.
    
    
    Defined in src/operator/optimizer_op.cc:L592
    

  • Update function for RMSPropAlex optimizer.
    
    `RMSPropAlex` is non-centered version of `RMSProp`.
    
    Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
    :math:`E[g]_t` is the decaying average over past gradient.
    
    .. math::
      E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
      E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
      \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t + \Delta_t
    
    The RMSPropAlex code follows the version in
    http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
    
    Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
    to be 0.9 and the learning rate :math:`\eta` to be 0.0001.
    
    
    Defined in src/operator/optimizer_op.cc:L592
    

    returns

    org.apache.mxnet.NDArray

  • abstract def round(args: Any*): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest integer of the input.
    
    Example::
    
       round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]
    
    The storage type of ``round`` output depends upon the input storage type:
    
      - round(default) = default
      - round(row_sparse) = row_sparse
      - round(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L706
    

  • Returns element-wise rounded value to the nearest integer of the input.
    
    Example::
    
       round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]
    
    The storage type of ``round`` output depends upon the input storage type:
    
      - round(default) = default
      - round(row_sparse) = row_sparse
      - round(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L706
    

    returns

    org.apache.mxnet.NDArray

  • abstract def round(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest integer of the input.
    
    Example::
    
       round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]
    
    The storage type of ``round`` output depends upon the input storage type:
    
      - round(default) = default
      - round(row_sparse) = row_sparse
      - round(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L706
    

  • Returns element-wise rounded value to the nearest integer of the input.
    
    Example::
    
       round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]
    
    The storage type of ``round`` output depends upon the input storage type:
    
      - round(default) = default
      - round(row_sparse) = row_sparse
      - round(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L706
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rsqrt(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse square-root value of the input.
    
    .. math::
       rsqrt(x) = 1/\sqrt{x}
    
    Example::
    
       rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
    
    The storage type of ``rsqrt`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L866
    

  • Returns element-wise inverse square-root value of the input.
    
    .. math::
       rsqrt(x) = 1/\sqrt{x}
    
    Example::
    
       rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
    
    The storage type of ``rsqrt`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L866
    

    returns

    org.apache.mxnet.NDArray

  • abstract def rsqrt(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse square-root value of the input.
    
    .. math::
       rsqrt(x) = 1/\sqrt{x}
    
    Example::
    
       rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
    
    The storage type of ``rsqrt`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L866
    

  • Returns element-wise inverse square-root value of the input.
    
    .. math::
       rsqrt(x) = 1/\sqrt{x}
    
    Example::
    
       rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
    
    The storage type of ``rsqrt`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L866
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_exponential(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    exponential distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_exponential(lam) = [ 0.51837951,  0.09994757]
    
       // Draw a vector containing two samples for each distribution
       sample_exponential(lam, shape=(2)) = [[ 0.51837951,  0.19866663],
                                             [ 0.09994757,  0.50447971]]
    
    
    Defined in src/operator/random/multisample_op.cc:L284
    

  • Concurrent sampling from multiple
    exponential distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_exponential(lam) = [ 0.51837951,  0.09994757]
    
       // Draw a vector containing two samples for each distribution
       sample_exponential(lam, shape=(2)) = [[ 0.51837951,  0.19866663],
                                             [ 0.09994757,  0.50447971]]
    
    
    Defined in src/operator/random/multisample_op.cc:L284
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_exponential(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    exponential distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_exponential(lam) = [ 0.51837951,  0.09994757]
    
       // Draw a vector containing two samples for each distribution
       sample_exponential(lam, shape=(2)) = [[ 0.51837951,  0.19866663],
                                             [ 0.09994757,  0.50447971]]
    
    
    Defined in src/operator/random/multisample_op.cc:L284
    

  • Concurrent sampling from multiple
    exponential distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_exponential(lam) = [ 0.51837951,  0.09994757]
    
       // Draw a vector containing two samples for each distribution
       sample_exponential(lam, shape=(2)) = [[ 0.51837951,  0.19866663],
                                             [ 0.09994757,  0.50447971]]
    
    
    Defined in src/operator/random/multisample_op.cc:L284
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_gamma(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    gamma distributions with parameters *alpha* (shape) and *beta* (scale).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       alpha = [ 0.0, 2.5 ]
       beta = [ 1.0, 0.7 ]
    
       // Draw a single sample for each distribution
       sample_gamma(alpha, beta) = [ 0.        ,  2.25797319]
    
       // Draw a vector containing two samples for each distribution
       sample_gamma(alpha, beta, shape=(2)) = [[ 0.        ,  0.        ],
                                               [ 2.25797319,  1.70734084]]
    
    
    Defined in src/operator/random/multisample_op.cc:L282
    

  • Concurrent sampling from multiple
    gamma distributions with parameters *alpha* (shape) and *beta* (scale).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       alpha = [ 0.0, 2.5 ]
       beta = [ 1.0, 0.7 ]
    
       // Draw a single sample for each distribution
       sample_gamma(alpha, beta) = [ 0.        ,  2.25797319]
    
       // Draw a vector containing two samples for each distribution
       sample_gamma(alpha, beta, shape=(2)) = [[ 0.        ,  0.        ],
                                               [ 2.25797319,  1.70734084]]
    
    
    Defined in src/operator/random/multisample_op.cc:L282
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_gamma(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    gamma distributions with parameters *alpha* (shape) and *beta* (scale).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       alpha = [ 0.0, 2.5 ]
       beta = [ 1.0, 0.7 ]
    
       // Draw a single sample for each distribution
       sample_gamma(alpha, beta) = [ 0.        ,  2.25797319]
    
       // Draw a vector containing two samples for each distribution
       sample_gamma(alpha, beta, shape=(2)) = [[ 0.        ,  0.        ],
                                               [ 2.25797319,  1.70734084]]
    
    
    Defined in src/operator/random/multisample_op.cc:L282
    

  • Concurrent sampling from multiple
    gamma distributions with parameters *alpha* (shape) and *beta* (scale).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       alpha = [ 0.0, 2.5 ]
       beta = [ 1.0, 0.7 ]
    
       // Draw a single sample for each distribution
       sample_gamma(alpha, beta) = [ 0.        ,  2.25797319]
    
       // Draw a vector containing two samples for each distribution
       sample_gamma(alpha, beta, shape=(2)) = [[ 0.        ,  0.        ],
                                               [ 2.25797319,  1.70734084]]
    
    
    Defined in src/operator/random/multisample_op.cc:L282
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_generalized_negative_binomial(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       mu = [ 2.0, 2.5 ]
       alpha = [ 1.0, 0.1 ]
    
       // Draw a single sample for each distribution
       sample_generalized_negative_binomial(mu, alpha) = [ 0.,  3.]
    
       // Draw a vector containing two samples for each distribution
       sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [[ 0.,  3.],
                                                                     [ 3.,  1.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L293
    

  • Concurrent sampling from multiple
    generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       mu = [ 2.0, 2.5 ]
       alpha = [ 1.0, 0.1 ]
    
       // Draw a single sample for each distribution
       sample_generalized_negative_binomial(mu, alpha) = [ 0.,  3.]
    
       // Draw a vector containing two samples for each distribution
       sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [[ 0.,  3.],
                                                                     [ 3.,  1.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L293
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_generalized_negative_binomial(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       mu = [ 2.0, 2.5 ]
       alpha = [ 1.0, 0.1 ]
    
       // Draw a single sample for each distribution
       sample_generalized_negative_binomial(mu, alpha) = [ 0.,  3.]
    
       // Draw a vector containing two samples for each distribution
       sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [[ 0.,  3.],
                                                                     [ 3.,  1.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L293
    

  • Concurrent sampling from multiple
    generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       mu = [ 2.0, 2.5 ]
       alpha = [ 1.0, 0.1 ]
    
       // Draw a single sample for each distribution
       sample_generalized_negative_binomial(mu, alpha) = [ 0.,  3.]
    
       // Draw a vector containing two samples for each distribution
       sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [[ 0.,  3.],
                                                                     [ 3.,  1.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L293
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_multinomial(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple multinomial distributions.
    
    *data* is an *n* dimensional array whose last dimension has length *k*, where
    *k* is the number of possible outcomes of each multinomial distribution. This
    operator will draw *shape* samples from each distribution. If shape is empty
    one sample will be drawn from each distribution.
    
    If *get_prob* is true, a second array containing log likelihood of the drawn
    samples will also be returned. This is usually used for reinforcement learning
    where you can provide reward as head gradient for this array to estimate
    gradient.
    
    Note that the input distribution must be normalized, i.e. *data* must sum to
    1 along its last axis.
    
    Examples::
    
       probs = [[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]]
    
       // Draw a single sample for each distribution
       sample_multinomial(probs) = [3, 0]
    
       // Draw a vector containing two samples for each distribution
       sample_multinomial(probs, shape=(2)) = [[4, 2],
                                               [0, 0]]
    
       // requests log likelihood
       sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
    

  • Concurrent sampling from multiple multinomial distributions.
    
    *data* is an *n* dimensional array whose last dimension has length *k*, where
    *k* is the number of possible outcomes of each multinomial distribution. This
    operator will draw *shape* samples from each distribution. If shape is empty
    one sample will be drawn from each distribution.
    
    If *get_prob* is true, a second array containing log likelihood of the drawn
    samples will also be returned. This is usually used for reinforcement learning
    where you can provide reward as head gradient for this array to estimate
    gradient.
    
    Note that the input distribution must be normalized, i.e. *data* must sum to
    1 along its last axis.
    
    Examples::
    
       probs = [[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]]
    
       // Draw a single sample for each distribution
       sample_multinomial(probs) = [3, 0]
    
       // Draw a vector containing two samples for each distribution
       sample_multinomial(probs, shape=(2)) = [[4, 2],
                                               [0, 0]]
    
       // requests log likelihood
       sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_multinomial(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple multinomial distributions.
    
    *data* is an *n* dimensional array whose last dimension has length *k*, where
    *k* is the number of possible outcomes of each multinomial distribution. This
    operator will draw *shape* samples from each distribution. If shape is empty
    one sample will be drawn from each distribution.
    
    If *get_prob* is true, a second array containing log likelihood of the drawn
    samples will also be returned. This is usually used for reinforcement learning
    where you can provide reward as head gradient for this array to estimate
    gradient.
    
    Note that the input distribution must be normalized, i.e. *data* must sum to
    1 along its last axis.
    
    Examples::
    
       probs = [[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]]
    
       // Draw a single sample for each distribution
       sample_multinomial(probs) = [3, 0]
    
       // Draw a vector containing two samples for each distribution
       sample_multinomial(probs, shape=(2)) = [[4, 2],
                                               [0, 0]]
    
       // requests log likelihood
       sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
    

  • Concurrent sampling from multiple multinomial distributions.
    
    *data* is an *n* dimensional array whose last dimension has length *k*, where
    *k* is the number of possible outcomes of each multinomial distribution. This
    operator will draw *shape* samples from each distribution. If shape is empty
    one sample will be drawn from each distribution.
    
    If *get_prob* is true, a second array containing log likelihood of the drawn
    samples will also be returned. This is usually used for reinforcement learning
    where you can provide reward as head gradient for this array to estimate
    gradient.
    
    Note that the input distribution must be normalized, i.e. *data* must sum to
    1 along its last axis.
    
    Examples::
    
       probs = [[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]]
    
       // Draw a single sample for each distribution
       sample_multinomial(probs) = [3, 0]
    
       // Draw a vector containing two samples for each distribution
       sample_multinomial(probs, shape=(2)) = [[4, 2],
                                               [0, 0]]
    
       // requests log likelihood
       sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_negative_binomial(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       k = [ 20, 49 ]
       p = [ 0.4 , 0.77 ]
    
       // Draw a single sample for each distribution
       sample_negative_binomial(k, p) = [ 15.,  16.]
    
       // Draw a vector containing two samples for each distribution
       sample_negative_binomial(k, p, shape=(2)) = [[ 15.,  50.],
                                                    [ 16.,  12.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L289
    

  • Concurrent sampling from multiple
    negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       k = [ 20, 49 ]
       p = [ 0.4 , 0.77 ]
    
       // Draw a single sample for each distribution
       sample_negative_binomial(k, p) = [ 15.,  16.]
    
       // Draw a vector containing two samples for each distribution
       sample_negative_binomial(k, p, shape=(2)) = [[ 15.,  50.],
                                                    [ 16.,  12.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L289
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_negative_binomial(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       k = [ 20, 49 ]
       p = [ 0.4 , 0.77 ]
    
       // Draw a single sample for each distribution
       sample_negative_binomial(k, p) = [ 15.,  16.]
    
       // Draw a vector containing two samples for each distribution
       sample_negative_binomial(k, p, shape=(2)) = [[ 15.,  50.],
                                                    [ 16.,  12.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L289
    

  • Concurrent sampling from multiple
    negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       k = [ 20, 49 ]
       p = [ 0.4 , 0.77 ]
    
       // Draw a single sample for each distribution
       sample_negative_binomial(k, p) = [ 15.,  16.]
    
       // Draw a vector containing two samples for each distribution
       sample_negative_binomial(k, p, shape=(2)) = [[ 15.,  50.],
                                                    [ 16.,  12.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L289
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_normal(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       mu = [ 0.0, 2.5 ]
       sigma = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_normal(mu, sigma) = [-0.56410581,  0.95934606]
    
       // Draw a vector containing two samples for each distribution
       sample_normal(mu, sigma, shape=(2)) = [[-0.56410581,  0.2928229 ],
                                              [ 0.95934606,  4.48287058]]
    
    
    Defined in src/operator/random/multisample_op.cc:L279
    

  • Concurrent sampling from multiple
    normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       mu = [ 0.0, 2.5 ]
       sigma = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_normal(mu, sigma) = [-0.56410581,  0.95934606]
    
       // Draw a vector containing two samples for each distribution
       sample_normal(mu, sigma, shape=(2)) = [[-0.56410581,  0.2928229 ],
                                              [ 0.95934606,  4.48287058]]
    
    
    Defined in src/operator/random/multisample_op.cc:L279
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_normal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       mu = [ 0.0, 2.5 ]
       sigma = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_normal(mu, sigma) = [-0.56410581,  0.95934606]
    
       // Draw a vector containing two samples for each distribution
       sample_normal(mu, sigma, shape=(2)) = [[-0.56410581,  0.2928229 ],
                                              [ 0.95934606,  4.48287058]]
    
    
    Defined in src/operator/random/multisample_op.cc:L279
    

  • Concurrent sampling from multiple
    normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       mu = [ 0.0, 2.5 ]
       sigma = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_normal(mu, sigma) = [-0.56410581,  0.95934606]
    
       // Draw a vector containing two samples for each distribution
       sample_normal(mu, sigma, shape=(2)) = [[-0.56410581,  0.2928229 ],
                                              [ 0.95934606,  4.48287058]]
    
    
    Defined in src/operator/random/multisample_op.cc:L279
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_poisson(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    Poisson distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_poisson(lam) = [  0.,  13.]
    
       // Draw a vector containing two samples for each distribution
       sample_poisson(lam, shape=(2)) = [[  0.,   4.],
                                         [ 13.,   8.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L286
    

  • Concurrent sampling from multiple
    Poisson distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_poisson(lam) = [  0.,  13.]
    
       // Draw a vector containing two samples for each distribution
       sample_poisson(lam, shape=(2)) = [[  0.,   4.],
                                         [ 13.,   8.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L286
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_poisson(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    Poisson distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_poisson(lam) = [  0.,  13.]
    
       // Draw a vector containing two samples for each distribution
       sample_poisson(lam, shape=(2)) = [[  0.,   4.],
                                         [ 13.,   8.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L286
    

  • Concurrent sampling from multiple
    Poisson distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_poisson(lam) = [  0.,  13.]
    
       // Draw a vector containing two samples for each distribution
       sample_poisson(lam, shape=(2)) = [[  0.,   4.],
                                         [ 13.,   8.]]
    
    
    Defined in src/operator/random/multisample_op.cc:L286
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_uniform(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    uniform distributions on the intervals given by *[low,high)*.
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       low = [ 0.0, 2.5 ]
       high = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_uniform(low, high) = [ 0.40451524,  3.18687344]
    
       // Draw a vector containing two samples for each distribution
       sample_uniform(low, high, shape=(2)) = [[ 0.40451524,  0.18017688],
                                               [ 3.18687344,  3.68352246]]
    
    
    Defined in src/operator/random/multisample_op.cc:L277
    

  • Concurrent sampling from multiple
    uniform distributions on the intervals given by *[low,high)*.
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       low = [ 0.0, 2.5 ]
       high = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_uniform(low, high) = [ 0.40451524,  3.18687344]
    
       // Draw a vector containing two samples for each distribution
       sample_uniform(low, high, shape=(2)) = [[ 0.40451524,  0.18017688],
                                               [ 3.18687344,  3.68352246]]
    
    
    Defined in src/operator/random/multisample_op.cc:L277
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sample_uniform(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Concurrent sampling from multiple
    uniform distributions on the intervals given by *[low,high)*.
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       low = [ 0.0, 2.5 ]
       high = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_uniform(low, high) = [ 0.40451524,  3.18687344]
    
       // Draw a vector containing two samples for each distribution
       sample_uniform(low, high, shape=(2)) = [[ 0.40451524,  0.18017688],
                                               [ 3.18687344,  3.68352246]]
    
    
    Defined in src/operator/random/multisample_op.cc:L277
    

  • Concurrent sampling from multiple
    uniform distributions on the intervals given by *[low,high)*.
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       low = [ 0.0, 2.5 ]
       high = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_uniform(low, high) = [ 0.40451524,  3.18687344]
    
       // Draw a vector containing two samples for each distribution
       sample_uniform(low, high, shape=(2)) = [[ 0.40451524,  0.18017688],
                                               [ 3.18687344,  3.68352246]]
    
    
    Defined in src/operator/random/multisample_op.cc:L277
    

    returns

    org.apache.mxnet.NDArray

  • abstract def scatter_nd(args: Any*): NDArrayFuncReturn

    Scatters data into a new tensor according to indices.
    
    Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[indices[0, y_0, ..., y_{K-1}],
             ...,
             indices[M-1, y_0, ..., y_{K-1}],
             x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
    
    all other entries in output are 0.
    
    .. warning::
    
        If the indices have duplicates, the result will be non-deterministic and
        the gradient of `scatter_nd` will not be correct!!
    
    
    Examples::
    
      data = [2, 3, 0]
      indices = [[1, 1, 0], [0, 1, 0]]
      shape = (2, 2)
      scatter_nd(data, indices, shape) = [[0, 0], [2, 3]]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 1]]
      shape = (2, 2, 2, 2)
      scatter_nd(data, indices, shape) = [[[[0, 0],
                                            [0, 0]],
    
                                           [[1, 2],
                                            [3, 4]]],
    
                                          [[[0, 0],
                                            [0, 0]],
    
                                           [[5, 6],
                                            [7, 8]]]]
    

  • Scatters data into a new tensor according to indices.
    
    Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[indices[0, y_0, ..., y_{K-1}],
             ...,
             indices[M-1, y_0, ..., y_{K-1}],
             x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
    
    all other entries in output are 0.
    
    .. warning::
    
        If the indices have duplicates, the result will be non-deterministic and
        the gradient of `scatter_nd` will not be correct!!
    
    
    Examples::
    
      data = [2, 3, 0]
      indices = [[1, 1, 0], [0, 1, 0]]
      shape = (2, 2)
      scatter_nd(data, indices, shape) = [[0, 0], [2, 3]]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 1]]
      shape = (2, 2, 2, 2)
      scatter_nd(data, indices, shape) = [[[[0, 0],
                                            [0, 0]],
    
                                           [[1, 2],
                                            [3, 4]]],
    
                                          [[[0, 0],
                                            [0, 0]],
    
                                           [[5, 6],
                                            [7, 8]]]]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def scatter_nd(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Scatters data into a new tensor according to indices.
    
    Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[indices[0, y_0, ..., y_{K-1}],
             ...,
             indices[M-1, y_0, ..., y_{K-1}],
             x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
    
    all other entries in output are 0.
    
    .. warning::
    
        If the indices have duplicates, the result will be non-deterministic and
        the gradient of `scatter_nd` will not be correct!!
    
    
    Examples::
    
      data = [2, 3, 0]
      indices = [[1, 1, 0], [0, 1, 0]]
      shape = (2, 2)
      scatter_nd(data, indices, shape) = [[0, 0], [2, 3]]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 1]]
      shape = (2, 2, 2, 2)
      scatter_nd(data, indices, shape) = [[[[0, 0],
                                            [0, 0]],
    
                                           [[1, 2],
                                            [3, 4]]],
    
                                          [[[0, 0],
                                            [0, 0]],
    
                                           [[5, 6],
                                            [7, 8]]]]
    

  • Scatters data into a new tensor according to indices.
    
    Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[indices[0, y_0, ..., y_{K-1}],
             ...,
             indices[M-1, y_0, ..., y_{K-1}],
             x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
    
    all other entries in output are 0.
    
    .. warning::
    
        If the indices have duplicates, the result will be non-deterministic and
        the gradient of `scatter_nd` will not be correct!!
    
    
    Examples::
    
      data = [2, 3, 0]
      indices = [[1, 1, 0], [0, 1, 0]]
      shape = (2, 2)
      scatter_nd(data, indices, shape) = [[0, 0], [2, 3]]
    
      data = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]
      indices = [[0, 1], [1, 1]]
      shape = (2, 2, 2, 2)
      scatter_nd(data, indices, shape) = [[[[0, 0],
                                            [0, 0]],
    
                                           [[1, 2],
                                            [3, 4]]],
    
                                          [[[0, 0],
                                            [0, 0]],
    
                                           [[5, 6],
                                            [7, 8]]]]
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sgd_mom_update(args: Any*): NDArrayFuncReturn

    Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage
    type is the same as momentum's storage type,
    only the row slices whose indices appear in grad.indices are updated (for both weight and momentum)::
    
      for row in gradient.indices:
          v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
          weight[row] += v[row]
    
    
    
    Defined in src/operator/optimizer_op.cc:L372
    

  • Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage
    type is the same as momentum's storage type,
    only the row slices whose indices appear in grad.indices are updated (for both weight and momentum)::
    
      for row in gradient.indices:
          v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
          weight[row] += v[row]
    
    
    
    Defined in src/operator/optimizer_op.cc:L372
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sgd_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage
    type is the same as momentum's storage type,
    only the row slices whose indices appear in grad.indices are updated (for both weight and momentum)::
    
      for row in gradient.indices:
          v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
          weight[row] += v[row]
    
    
    
    Defined in src/operator/optimizer_op.cc:L372
    

  • Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage
    type is the same as momentum's storage type,
    only the row slices whose indices appear in grad.indices are updated (for both weight and momentum)::
    
      for row in gradient.indices:
          v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
          weight[row] += v[row]
    
    
    
    Defined in src/operator/optimizer_op.cc:L372
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sgd_update(args: Any*): NDArrayFuncReturn

    Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is True,
    only the row slices whose indices appear in grad.indices are updated::
    
     for row in gradient.indices:
         weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])
    
    
    
    Defined in src/operator/optimizer_op.cc:L331
    

  • Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is True,
    only the row slices whose indices appear in grad.indices are updated::
    
     for row in gradient.indices:
         weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])
    
    
    
    Defined in src/operator/optimizer_op.cc:L331
    

    returns

    org.apache.mxnet.NDArray

  • abstract def sgd_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is True,
    only the row slices whose indices appear in grad.indices are updated::
    
     for row in gradient.indices:
         weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])
    
    
    
    Defined in src/operator/optimizer_op.cc:L331
    

  • Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is True,
    only the row slices whose indices appear in grad.indices are updated::
    
     for row in gradient.indices:
         weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])
    
    
    
    Defined in src/operator/optimizer_op.cc:L331
    

    returns

    org.apache.mxnet.NDArray

  • abstract def shape_array(args: Any*): NDArrayFuncReturn

    Returns a 1D int64 array containing the shape of data.
    
    Example::
    
      shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L505
    

  • Returns a 1D int64 array containing the shape of data.
    
    Example::
    
      shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L505
    

    returns

    org.apache.mxnet.NDArray

  • abstract def shape_array(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns a 1D int64 array containing the shape of data.
    
    Example::
    
      shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L505
    

  • Returns a 1D int64 array containing the shape of data.
    
    Example::
    
      shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L505
    

    returns

    org.apache.mxnet.NDArray

  • abstract def shuffle(args: Any*): NDArrayFuncReturn

    Randomly shuffle the elements.
    
    This shuffles the array along the first axis.
    The order of the elements in each subarray does not change.
    For example, if a 2D array is given, the order of the rows randomly changes,
    but the order of the elements in each row does not change.
    

  • Randomly shuffle the elements.
    
    This shuffles the array along the first axis.
    The order of the elements in each subarray does not change.
    For example, if a 2D array is given, the order of the rows randomly changes,
    but the order of the elements in each row does not change.
    

    returns

    org.apache.mxnet.NDArray

  • abstract def shuffle(kwargs: Map[String, Any] = null)(args: Any