org.apache.mxnet

SymbolAPI

Related Doc: package mxnet

object SymbolAPI extends SymbolAPIBase

Linear Supertypes
SymbolAPIBase, AnyRef, Any
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. SymbolAPI
  2. SymbolAPIBase
  3. AnyRef
  4. Any
  1. Hide All
  2. Show all
Learn more about member selection
Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def Activation(data: Option[Symbol] = None, act_type: String, name: String = null, attr: Map[String, String] = null): Symbol

    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:L184
    

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:L184

data

The input array.

act_type

Activation function to be applied.

returns

org.apache.mxnet.Symbol

Definition Classes
SymbolAPIBase
Annotations
@Experimental()
  • abstract def BatchNorm(data: Option[Symbol] = None, gamma: Option[Symbol] = None, beta: Option[Symbol] = None, moving_mean: Option[Symbol] = None, moving_var: Option[Symbol] = None, eps: Option[Double] = None, momentum: Option[MXFloat] = None, fix_gamma: Option[Boolean] = None, use_global_stats: Option[Boolean] = None, output_mean_var: Option[Boolean] = None, axis: Option[Int] = None, cudnn_off: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L574
    

  • 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:L574
    

    data

    Input data to batch normalization

    gamma

    gamma array

    beta

    beta array

    moving_mean

    running mean of input

    moving_var

    running variance of input

    eps

    Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5)

    momentum

    Momentum for moving average

    fix_gamma

    Fix gamma while training

    use_global_stats

    Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.

    output_mean_var

    Output the mean and inverse std

    axis

    Specify which shape axis the channel is specified

    cudnn_off

    Do not select CUDNN operator, if available

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def BatchNorm_v1(data: Option[Symbol] = None, gamma: Option[Symbol] = None, beta: Option[Symbol] = None, eps: Option[MXFloat] = None, momentum: Option[MXFloat] = None, fix_gamma: Option[Boolean] = None, use_global_stats: Option[Boolean] = None, output_mean_var: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to batch normalization

    gamma

    gamma array

    beta

    beta array

    eps

    Epsilon to prevent div 0

    momentum

    Momentum for moving average

    fix_gamma

    Fix gamma while training

    use_global_stats

    Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.

    output_mean_var

    Output All,normal mean and var

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def BilinearSampler(data: Option[Symbol] = None, grid: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L245
    

  • 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:L245
    

    data

    Input data to the BilinearsamplerOp.

    grid

    Input grid to the BilinearsamplerOp.grid has two channels: x_src, y_src

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def BlockGrad(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L265
    

  • 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:L265
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Cast(data: Option[Symbol] = None, dtype: String, name: String = null, attr: Map[String, String] = null): Symbol

    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:L592
    

  • 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:L592
    

    data

    The input.

    dtype

    Output data type.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Concat(data: Array[Symbol], num_args: Int, dim: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    List of arrays to concatenate

    num_args

    Number of inputs to be concated.

    dim

    the dimension to be concated.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Convolution(data: Option[Symbol] = None, weight: Option[Symbol] = None, bias: Option[Symbol] = None, kernel: Shape, stride: Option[Shape] = None, dilate: Option[Shape] = None, pad: Option[Shape] = None, num_filter: Int, num_group: Option[Int] = None, workspace: Option[Long] = None, no_bias: Option[Boolean] = None, cudnn_tune: Option[String] = None, cudnn_off: Option[Boolean] = None, layout: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L474
    

  • 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:L474
    

    data

    Input data to the ConvolutionOp.

    weight

    Weight matrix.

    bias

    Bias parameter.

    kernel

    Convolution kernel size: (w,), (h, w) or (d, h, w)

    stride

    Convolution stride: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

    dilate

    Convolution dilate: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

    pad

    Zero pad for convolution: (w,), (h, w) or (d, h, w). Defaults to no padding.

    num_filter

    Convolution filter(channel) number

    num_group

    Number of group partitions.

    workspace

    Maximum temporary workspace allowed (MB) in convolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the convolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when limited_workspace strategy is used.

    no_bias

    Whether to disable bias parameter.

    cudnn_tune

    Whether to pick convolution algo by running performance test.

    cudnn_off

    Turn off cudnn for this layer.

    layout

    Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Convolution_v1(data: Option[Symbol] = None, weight: Option[Symbol] = None, bias: Option[Symbol] = None, kernel: Shape, stride: Option[Shape] = None, dilate: Option[Shape] = None, pad: Option[Shape] = None, num_filter: Int, num_group: Option[Int] = None, workspace: Option[Long] = None, no_bias: Option[Boolean] = None, cudnn_tune: Option[String] = None, cudnn_off: Option[Boolean] = None, layout: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

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

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

    data

    Input data to the ConvolutionV1Op.

    weight

    Weight matrix.

    bias

    Bias parameter.

    kernel

    convolution kernel size: (h, w) or (d, h, w)

    stride

    convolution stride: (h, w) or (d, h, w)

    dilate

    convolution dilate: (h, w) or (d, h, w)

    pad

    pad for convolution: (h, w) or (d, h, w)

    num_filter

    convolution filter(channel) number

    num_group

    Number of group partitions. Equivalent to slicing input into num_group partitions, apply convolution on each, then concatenate the results

    workspace

    Maximum temporary workspace allowed for convolution (MB).This parameter determines the effective batch size of the convolution kernel, which may be smaller than the given batch size. Also, the workspace will be automatically enlarged to make sure that we can run the kernel with batch_size=1

    no_bias

    Whether to disable bias parameter.

    cudnn_tune

    Whether to pick convolution algo by running performance test. 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. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest.

    cudnn_off

    Turn off cudnn for this layer.

    layout

    Set layout for input, output and weight. Empty for default layout: NCHW for 2d and NCDHW for 3d.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Correlation(data1: Option[Symbol] = None, data2: Option[Symbol] = None, kernel_size: Option[Int] = None, max_displacement: Option[Int] = None, stride1: Option[Int] = None, stride2: Option[Int] = None, pad_size: Option[Int] = None, is_multiply: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data1

    Input data1 to the correlation.

    data2

    Input data2 to the correlation.

    kernel_size

    kernel size for Correlation must be an odd number

    max_displacement

    Max displacement of Correlation

    stride1

    stride1 quantize data1 globally

    stride2

    stride2 quantize data2 within the neighborhood centered around data1

    pad_size

    pad for Correlation

    is_multiply

    operation type is either multiplication or subduction

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Crop(data: Array[Symbol], num_args: Int, offset: Option[Shape] = None, h_w: Option[Shape] = None, center_crop: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    
    
    .. 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
    

    data

    Tensor or List of Tensors, the second input will be used as crop_like shape reference

    num_args

    Number of inputs for crop, if equals one, then we will use the h_wfor crop height and width, else if equals two, then we will use the heightand width of the second input symbol, we name crop_like here

    offset

    crop offset coordinate: (y, x)

    h_w

    crop height and width: (h, w)

    center_crop

    If set to true, then it will use be the center_crop,or it will crop using the shape of crop_like

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Deconvolution(data: Option[Symbol] = None, weight: Option[Symbol] = None, bias: Option[Symbol] = None, kernel: Shape, stride: Option[Shape] = None, dilate: Option[Shape] = None, pad: Option[Shape] = None, adj: Option[Shape] = None, target_shape: Option[Shape] = None, num_filter: Int, num_group: Option[Int] = None, workspace: Option[Long] = None, no_bias: Option[Boolean] = None, cudnn_tune: Option[String] = None, cudnn_off: Option[Boolean] = None, layout: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.
    

    data

    Input tensor to the deconvolution operation.

    weight

    Weights representing the kernel.

    bias

    Bias added to the result after the deconvolution operation.

    kernel

    Deconvolution kernel size: (w,), (h, w) or (d, h, w). This is same as the kernel size used for the corresponding convolution

    stride

    The stride used for the corresponding convolution: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

    dilate

    Dilation factor for each dimension of the input: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.

    pad

    The amount of implicit zero padding added during convolution for each dimension of the input: (w,), (h, w) or (d, h, w). (kernel-1)/2 is usually a good choice. If target_shape is set, pad will be ignored and a padding that will generate the target shape will be used. Defaults to no padding.

    adj

    Adjustment for output shape: (w,), (h, w) or (d, h, w). If target_shape is set, adj will be ignored and computed accordingly.

    target_shape

    Shape of the output tensor: (w,), (h, w) or (d, h, w).

    num_filter

    Number of output filters.

    num_group

    Number of groups partition.

    workspace

    Maximum temporary workspace allowed (MB) in deconvolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the deconvolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when limited_workspace strategy is used.

    no_bias

    Whether to disable bias parameter.

    cudnn_tune

    Whether to pick convolution algorithm by running performance test.

    cudnn_off

    Turn off cudnn for this layer.

    layout

    Set layout for input, output and weight. Empty for default layout, NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Dropout(data: Option[Symbol] = None, p: Option[MXFloat] = None, mode: Option[String] = None, axes: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array to which dropout will be applied.

    p

    Fraction of the input that gets dropped out during training time.

    mode

    Whether to only turn on dropout during training or to also turn on for inference.

    axes

    Axes for variational dropout kernel.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def ElementWiseSum(args: Array[Symbol], name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    args

    Positional input arguments

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Embedding(data: Option[Symbol] = None, weight: Option[Symbol] = None, input_dim: Int, output_dim: Int, dtype: Option[String] = None, sparse_grad: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array to the embedding operator.

    weight

    The embedding weight matrix.

    input_dim

    Vocabulary size of the input indices.

    output_dim

    Dimension of the embedding vectors.

    dtype

    Data type of weight.

    sparse_grad

    Compute row sparse gradient in the backward calculation. If set to True, the grad's storage type is row_sparse.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Flatten(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def FullyConnected(data: Option[Symbol] = None, weight: Option[Symbol] = None, bias: Option[Symbol] = None, num_hidden: Int, no_bias: Option[Boolean] = None, flatten: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L272
    

  • 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:L272
    

    data

    Input data.

    weight

    Weight matrix.

    bias

    Bias parameter.

    num_hidden

    Number of hidden nodes of the output.

    no_bias

    Whether to disable bias parameter.

    flatten

    Whether to collapse all but the first axis of the input data tensor.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def GridGenerator(data: Option[Symbol] = None, transform_type: String, target_shape: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Generates 2D sampling grid for bilinear sampling.
    

  • Generates 2D sampling grid for bilinear sampling.
    

    data

    Input data to the function.

    transform_type

    The type of transformation. For affine, input data should be an affine matrix of size (batch, 6). For warp, input data should be an optical flow of size (batch, 2, h, w).

    target_shape

    Specifies the output shape (H, W). This is required if transformation type is affine. If transformation type is warp, this parameter is ignored.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def IdentityAttachKLSparseReg(data: Option[Symbol] = None, sparseness_target: Option[MXFloat] = None, penalty: Option[MXFloat] = None, momentum: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

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

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

    data

    Input data.

    sparseness_target

    The sparseness target

    penalty

    The tradeoff parameter for the sparseness penalty

    momentum

    The momentum for running average

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def InstanceNorm(data: Option[Symbol] = None, gamma: Option[Symbol] = None, beta: Option[Symbol] = None, eps: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    An n-dimensional input array (n > 2) of the form [batch, channel, spatial_dim1, spatial_dim2, ...].

    gamma

    A vector of length 'channel', which multiplies the normalized input.

    beta

    A vector of length 'channel', which is added to the product of the normalized input and the weight.

    eps

    An epsilon parameter to prevent division by 0.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def L2Normalization(data: Option[Symbol] = None, eps: Option[MXFloat] = None, mode: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array to normalize.

    eps

    A small constant for numerical stability.

    mode

    Specify the dimension along which to compute L2 norm.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def LRN(data: Option[Symbol] = None, alpha: Option[MXFloat] = None, beta: Option[MXFloat] = None, knorm: Option[MXFloat] = None, nsize: Int, name: String = null, attr: Map[String, String] = null): Symbol

    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:L178
    

  • 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:L178
    

    data

    Input data to LRN

    alpha

    The variance scaling parameter :math:lpha in the LRN expression.

    beta

    The power parameter :math:eta in the LRN expression.

    knorm

    The parameter :math:k in the LRN expression.

    nsize

    normalization window width in elements.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def LayerNorm(data: Option[Symbol] = None, gamma: Option[Symbol] = None, beta: Option[Symbol] = None, axis: Option[Int] = None, eps: Option[MXFloat] = None, output_mean_var: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to layer normalization

    gamma

    gamma array

    beta

    beta array

    axis

    The axis to perform layer normalization. Usually, this should be be axis of the channel dimension. Negative values means indexing from right to left.

    eps

    An epsilon parameter to prevent division by 0.

    output_mean_var

    Output the mean and std calculated along the given axis.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def LeakyReLU(data: Option[Symbol] = None, gamma: Option[Symbol] = None, act_type: Option[String] = None, slope: Option[MXFloat] = None, lower_bound: Option[MXFloat] = None, upper_bound: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to activation function.

    gamma

    Slope parameter for PReLU. Only required when act_type is 'prelu'. It should be either a vector of size 1, or the same size as the second dimension of data.

    act_type

    Activation function to be applied.

    slope

    Init slope for the activation. (For leaky and elu only)

    lower_bound

    Lower bound of random slope. (For rrelu only)

    upper_bound

    Upper bound of random slope. (For rrelu only)

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def LinearRegressionOutput(data: Option[Symbol] = None, label: Option[Symbol] = None, grad_scale: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to the function.

    label

    Input label to the function.

    grad_scale

    Scale the gradient by a float factor

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def LogisticRegressionOutput(data: Option[Symbol] = None, label: Option[Symbol] = None, grad_scale: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    
    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:L148
    

  • 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
    
    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:L148
    

    data

    Input data to the function.

    label

    Input label to the function.

    grad_scale

    Scale the gradient by a float factor

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def MAERegressionOutput(data: Option[Symbol] = None, label: Option[Symbol] = None, grad_scale: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to the function.

    label

    Input label to the function.

    grad_scale

    Scale the gradient by a float factor

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def MakeLoss(data: Option[Symbol] = None, grad_scale: Option[MXFloat] = None, valid_thresh: Option[MXFloat] = None, normalization: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    grad_scale

    Gradient scale as a supplement to unary and binary operators

    valid_thresh

    clip each element in the array to 0 when it is less than valid_thresh. This is used when normalization is set to 'valid'.

    normalization

    If this is set to null, the output gradient will not be normalized. If this is set to batch, the output gradient will be divided by the batch size. If this is set to valid, the output gradient will be divided by the number of valid input elements.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Pad(data: Option[Symbol] = None, mode: String, pad_width: Shape, constant_value: Option[Double] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    An n-dimensional input array.

    mode

    Padding type to use. "constant" pads with constant_value "edge" pads using the edge values of the input array "reflect" pads by reflecting values with respect to the edges.

    pad_width

    Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). It should be of length 2*N where N is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened.

    constant_value

    The value used for padding when mode is "constant".

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Pooling(data: Option[Symbol] = None, kernel: Option[Shape] = None, pool_type: Option[String] = None, global_pool: Option[Boolean] = None, cudnn_off: Option[Boolean] = None, pooling_convention: Option[String] = None, stride: Option[Shape] = None, pad: Option[Shape] = None, p_value: Option[Int] = None, count_include_pad: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L388
    

  • 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:L388
    

    data

    Input data to the pooling operator.

    kernel

    Pooling kernel size: (y, x) or (d, y, x)

    pool_type

    Pooling type to be applied.

    global_pool

    Ignore kernel size, do global pooling based on current input feature map.

    cudnn_off

    Turn off cudnn pooling and use MXNet pooling operator.

    pooling_convention

    Pooling convention to be applied.

    stride

    Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each dimension.

    pad

    Pad for pooling: (y, x) or (d, y, x). Defaults to no padding.

    p_value

    Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling.

    count_include_pad

    Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set to true,or it will be divided by 9 if this is set to false. Defaults to true.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Pooling_v1(data: Option[Symbol] = None, kernel: Option[Shape] = None, pool_type: Option[String] = None, global_pool: Option[Boolean] = None, pooling_convention: Option[String] = None, stride: Option[Shape] = None, pad: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to the pooling operator.

    kernel

    pooling kernel size: (y, x) or (d, y, x)

    pool_type

    Pooling type to be applied.

    global_pool

    Ignore kernel size, do global pooling based on current input feature map.

    pooling_convention

    Pooling convention to be applied.

    stride

    stride: for pooling (y, x) or (d, y, x)

    pad

    pad for pooling: (y, x) or (d, y, x)

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def RNN(data: Option[Symbol] = None, parameters: Option[Symbol] = None, state: Option[Symbol] = None, state_cell: Option[Symbol] = None, state_size: Int, num_layers: Int, bidirectional: Option[Boolean] = None, mode: String, p: Option[MXFloat] = None, state_outputs: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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}
    

    data

    Input data to RNN

    parameters

    Vector of all RNN trainable parameters concatenated

    state

    initial hidden state of the RNN

    state_cell

    initial cell state for LSTM networks (only for LSTM)

    state_size

    size of the state for each layer

    num_layers

    number of stacked layers

    bidirectional

    whether to use bidirectional recurrent layers

    mode

    the type of RNN to compute

    p

    Dropout probability, fraction of the input that gets dropped out at training time

    state_outputs

    Whether to have the states as symbol outputs.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def ROIPooling(data: Option[Symbol] = None, rois: Option[Symbol] = None, pooled_size: Shape, spatial_scale: MXFloat, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array to the pooling operator, a 4D Feature maps

    rois

    Bounding box coordinates, a 2D array of x1, y1, x2, y2, where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest. batch_index indicates the index of corresponding image in the input array

    pooled_size

    ROI pooling output shape (h,w)

    spatial_scale

    Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Reshape(data: Option[Symbol] = None, shape: Option[Shape] = None, reverse: Option[Boolean] = None, target_shape: Option[Shape] = None, keep_highest: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to reshape.

    shape

    The target shape

    reverse

    If true then the special values are inferred from right to left

    target_shape

    (Deprecated! Use shape instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims

    keep_highest

    (Deprecated! Use shape instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SVMOutput(data: Option[Symbol] = None, label: Option[Symbol] = None, margin: Option[MXFloat] = None, regularization_coefficient: Option[MXFloat] = None, use_linear: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.
    

    data

    Input data for SVM transformation.

    label

    Class label for the input data.

    margin

    The loss function penalizes outputs that lie outside this margin. Default margin is 1.

    regularization_coefficient

    Regularization parameter for the SVM. This balances the tradeoff between coefficient size and error.

    use_linear

    Whether to use L1-SVM objective. L2-SVM objective is used by default.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SequenceLast(data: Option[Symbol] = None, sequence_length: Option[Symbol] = None, use_sequence_length: Option[Boolean] = None, axis: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2

    sequence_length

    vector of sequence lengths of the form [batch_size]

    use_sequence_length

    If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence

    axis

    The sequence axis. Only values of 0 and 1 are currently supported.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SequenceMask(data: Option[Symbol] = None, sequence_length: Option[Symbol] = None, use_sequence_length: Option[Boolean] = None, value: Option[MXFloat] = None, axis: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2

    sequence_length

    vector of sequence lengths of the form [batch_size]

    use_sequence_length

    If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence

    value

    The value to be used as a mask.

    axis

    The sequence axis. Only values of 0 and 1 are currently supported.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SequenceReverse(data: Option[Symbol] = None, sequence_length: Option[Symbol] = None, use_sequence_length: Option[Boolean] = None, axis: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    n-dimensional input array of the form [max_sequence_length, batch_size, other dims] where n>2

    sequence_length

    vector of sequence lengths of the form [batch_size]

    use_sequence_length

    If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence

    axis

    The sequence axis. Only 0 is currently supported.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SliceChannel(data: Option[Symbol] = None, num_outputs: Int, axis: Option[Int] = None, squeeze_axis: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input

    num_outputs

    Number of splits. Note that this should evenly divide the length of the axis.

    axis

    Axis along which to split.

    squeeze_axis

    If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting squeeze_axis to true 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.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def Softmax(data: Option[Symbol] = None, grad_scale: Option[MXFloat] = None, ignore_label: Option[MXFloat] = None, multi_output: Option[Boolean] = None, use_ignore: Option[Boolean] = None, preserve_shape: Option[Boolean] = None, normalization: Option[String] = None, out_grad: Option[Boolean] = None, smooth_alpha: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    grad_scale

    Scales the gradient by a float factor.

    ignore_label

    The instances whose labels == ignore_label will be ignored during backward, if use_ignore is set to true).

    multi_output

    If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the shape of label array.

    use_ignore

    If set to true, the ignore_label value will not contribute to the backward gradient.

    preserve_shape

    If set to true, the softmax function will be computed along the last axis (-1).

    normalization

    Normalizes the gradient.

    out_grad

    Multiplies gradient with output gradient element-wise.

    smooth_alpha

    Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SoftmaxActivation(data: Option[Symbol] = None, mode: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    mode

    Specifies how to compute the softmax. If set to instance, it computes softmax for each instance. If set to channel, It computes cross channel softmax for each position of each instance.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SoftmaxOutput(data: Option[Symbol] = None, label: Option[Symbol] = None, grad_scale: Option[MXFloat] = None, ignore_label: Option[MXFloat] = None, multi_output: Option[Boolean] = None, use_ignore: Option[Boolean] = None, preserve_shape: Option[Boolean] = None, normalization: Option[String] = None, out_grad: Option[Boolean] = None, smooth_alpha: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    label

    Ground truth label.

    grad_scale

    Scales the gradient by a float factor.

    ignore_label

    The instances whose labels == ignore_label will be ignored during backward, if use_ignore is set to true).

    multi_output

    If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the shape of label array.

    use_ignore

    If set to true, the ignore_label value will not contribute to the backward gradient.

    preserve_shape

    If set to true, the softmax function will be computed along the last axis (-1).

    normalization

    Normalizes the gradient.

    out_grad

    Multiplies gradient with output gradient element-wise.

    smooth_alpha

    Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SpatialTransformer(data: Option[Symbol] = None, loc: Option[Symbol] = None, target_shape: Option[Shape] = None, transform_type: String, sampler_type: String, name: String = null, attr: Map[String, String] = null): Symbol

    Applies a spatial transformer to input feature map.
    

  • Applies a spatial transformer to input feature map.
    

    data

    Input data to the SpatialTransformerOp.

    loc

    localisation net, the output dim should be 6 when transform_type is affine. You shold initialize the weight and bias with identity tranform.

    target_shape

    output shape(h, w) of spatial transformer: (y, x)

    transform_type

    transformation type

    sampler_type

    sampling type

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def SwapAxis(data: Option[Symbol] = None, dim1: Option[Int] = None, dim2: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    dim1

    the first axis to be swapped.

    dim2

    the second axis to be swapped.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def UpSampling(data: Array[Symbol], scale: Int, num_filter: Option[Int] = None, sample_type: String, multi_input_mode: Option[String] = None, num_args: Int, workspace: Option[Long] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Performs nearest neighbor/bilinear up sampling to inputs.
    

  • Performs nearest neighbor/bilinear up sampling to inputs.
    

    data

    Array of tensors to upsample

    scale

    Up sampling scale

    num_filter

    Input filter. Only used by bilinear sample_type.

    sample_type

    upsampling method

    multi_input_mode

    How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images together, only available for nearest neighbor upsampling.

    num_args

    Number of inputs to be upsampled. For nearest neighbor upsampling, this can be 1-N; the size of output will be(scale*h_0,scale*w_0) and all other inputs will be upsampled to thesame size. For bilinear upsampling this must be 2; 1 input and 1 weight.

    workspace

    Tmp workspace for deconvolution (MB)

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def abs(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L666
    

  • 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:L666
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def adam_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, mean: Option[Symbol] = None, vari: Option[Symbol] = None, lr: MXFloat, beta1: Option[MXFloat] = None, beta2: Option[MXFloat] = None, epsilon: Option[MXFloat] = None, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, lazy_update: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    weight

    Weight

    grad

    Gradient

    mean

    Moving mean

    vari

    Moving variance

    lr

    Learning rate

    beta1

    The decay rate for the 1st moment estimates.

    beta2

    The decay rate for the 2nd moment estimates.

    epsilon

    A small constant for numerical stability.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    lazy_update

    If true, lazy updates are applied if gradient's stype is row_sparse and all of w, m and v have the same stype

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def add_n(args: Array[Symbol], name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    args

    Positional input arguments

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def arccos(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def arccosh(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def arcsin(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def arcsinh(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def arctan(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def arctanh(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def argmax(data: Option[Symbol] = None, axis: Option[Int] = None, keepdims: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input

    axis

    The axis along which to perform the reduction. Negative values means indexing from right to left. Requires axis to be set as int, because global reduction is not supported yet.

    keepdims

    If this is set to True, the reduced axis is left in the result as dimension with size one.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def argmax_channel(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def argmin(data: Option[Symbol] = None, axis: Option[Int] = None, keepdims: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input

    axis

    The axis along which to perform the reduction. Negative values means indexing from right to left. Requires axis to be set as int, because global reduction is not supported yet.

    keepdims

    If this is set to True, the reduced axis is left in the result as dimension with size one.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def argsort(data: Option[Symbol] = None, axis: Option[Int] = None, is_ascend: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L176
    

  • 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:L176
    

    data

    The input array

    axis

    Axis along which to sort the input tensor. If not given, the flattened array is used. Default is -1.

    is_ascend

    Whether to sort in ascending or descending order.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def batch_dot(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, forward_stype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    The first input

    rhs

    The second input

    transpose_a

    If true then transpose the first input before dot.

    transpose_b

    If true then transpose the second input before dot.

    forward_stype

    The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def batch_take(a: Option[Symbol] = None, indices: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    a

    The input array

    indices

    The index array

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_add(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_axes(data: Option[Symbol] = None, axis: Option[Shape] = None, size: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L237
    

  • 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:L237
    

    data

    The input

    axis

    The axes to perform the broadcasting.

    size

    Target sizes of the broadcasting axes.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_axis(data: Option[Symbol] = None, axis: Option[Shape] = None, size: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L237
    

  • 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:L237
    

    data

    The input

    axis

    The axes to perform the broadcasting.

    size

    Target sizes of the broadcasting axes.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_div(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_equal(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_greater(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_greater_equal(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_hypot(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

     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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_lesser(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_lesser_equal(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_like(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.]])
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L312
    

  • 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.]])
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L312
    

    lhs

    First input.

    rhs

    Second input.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_logical_and(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_logical_or(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_logical_xor(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_maximum(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_minimum(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_minus(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_mod(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_mul(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_not_equal(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_plus(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_power(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_sub(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def broadcast_to(data: Option[Symbol] = None, shape: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L261
    

  • 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:L261
    

    data

    The input

    shape

    The shape of the desired array. We can set the dim to zero if it's same as the original. E.g A = broadcast_to(B, shape=(10, 0, 0)) has the same meaning as A = broadcast_axis(B, axis=0, size=10).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def cast(data: Option[Symbol] = None, dtype: String, name: String = null, attr: Map[String, String] = null): Symbol

    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:L592
    

  • 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:L592
    

    data

    The input.

    dtype

    Output data type.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def cast_storage(data: Option[Symbol] = None, stype: String, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input.

    stype

    Output storage type.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def cbrt(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L887
    

  • 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:L887
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def ceil(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L744
    

  • 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:L744
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def choose_element_0index(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.
    

    lhs

    Left operand to the function.

    rhs

    Right operand to the function.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def clip(data: Option[Symbol] = None, a_min: MXFloat, a_max: MXFloat, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    a_min

    Minimum value

    a_max

    Maximum value

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def concat(data: Array[Symbol], num_args: Int, dim: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    List of arrays to concatenate

    num_args

    Number of inputs to be concated.

    dim

    the dimension to be concated.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def cos(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def cosh(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def crop(data: Option[Symbol] = None, begin: Shape, end: Shape, step: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Source input

    begin

    starting indices for the slice operation, supports negative indices.

    end

    ending indices for the slice operation, supports negative indices.

    step

    step for the slice operation, supports negative values.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def degrees(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def depth_to_space(data: Option[Symbol] = None, block_size: Int, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input ndarray

    block_size

    Blocks of [block_size. block_size] are moved

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def diag(data: Option[Symbol] = None, k: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    - 2-D arrays: returns elements in the diagonal as a new 1-D array
    - N-D arrays: not supported yet
    
    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]]
    
    
    
    Defined in src/operator/tensor/diag_op.cc:L68
    

  • 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
    - 2-D arrays: returns elements in the diagonal as a new 1-D array
    - N-D arrays: not supported yet
    
    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]]
    
    
    
    Defined in src/operator/tensor/diag_op.cc:L68
    

    data

    Input ndarray

    k

    Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. If input has shape (S0 S1) k must be between -S0 and S1

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def dot(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, forward_stype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    The first input

    rhs

    The second input

    transpose_a

    If true then transpose the first input before dot.

    transpose_b

    If true then transpose the second input before dot.

    forward_stype

    The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def elemwise_add(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    first input

    rhs

    second input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def elemwise_div(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    first input

    rhs

    second input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def elemwise_mul(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    first input

    rhs

    second input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def elemwise_sub(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lhs

    first input

    rhs

    second input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def exp(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L927
    

  • 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:L927
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def expand_dims(data: Option[Symbol] = None, axis: Int, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Source input

    axis

    Position where new axis is to be inserted. Suppose that the input NDArray's dimension is ndim, the range of the inserted axis is [-ndim, ndim]

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def expm1(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L1006
    

  • 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:L1006
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def fill_element_0index(lhs: Option[Symbol] = None, mhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.
    

    lhs

    Left operand to the function.

    mhs

    Middle operand to the function.

    rhs

    Right operand to the function.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def fix(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L801
    

  • 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:L801
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def flatten(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def flip(data: Option[Symbol] = None, axis: Shape, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data array

    axis

    The axis which to reverse elements.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def floor(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L763
    

  • 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:L763
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def ftml_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, d: Option[Symbol] = None, v: Option[Symbol] = None, z: Option[Symbol] = None, lr: MXFloat, beta1: Option[MXFloat] = None, beta2: Option[MXFloat] = None, epsilon: Option[Double] = None, t: Int, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_grad: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    weight

    Weight

    grad

    Gradient

    d

    Internal state d_t

    v

    Internal state v_t

    z

    Internal state z_t

    lr

    Learning rate.

    beta1

    Generally close to 0.5.

    beta2

    Generally close to 1.

    epsilon

    Epsilon to prevent div 0.

    t

    Number of update.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_grad

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def ftrl_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, z: Option[Symbol] = None, n: Option[Symbol] = None, lr: MXFloat, lamda1: Option[MXFloat] = None, beta: Option[MXFloat] = None, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    weight

    Weight

    grad

    Gradient

    z

    z

    n

    Square of grad

    lr

    Learning rate

    lamda1

    The L1 regularization coefficient.

    beta

    Per-Coordinate Learning Rate beta.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def gamma(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def gammaln(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def gather_nd(data: Option[Symbol] = None, indices: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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]]
    

    data

    data

    indices

    indices

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def hard_sigmoid(data: Option[Symbol] = None, alpha: Option[MXFloat] = None, beta: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    alpha

    Slope of hard sigmoid

    beta

    Bias of hard sigmoid.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def identity(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def khatri_rao(args: Array[Symbol], name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    args

    Positional input matrices

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_gelqf(A: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of input matrices to be factorized

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_gemm(A: Option[Symbol] = None, B: Option[Symbol] = None, C: Option[Symbol] = None, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, alpha: Option[Double] = None, beta: Option[Double] = None, axis: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of input matrices

    B

    Tensor of input matrices

    C

    Tensor of input matrices

    transpose_a

    Multiply with transposed of first input (A).

    transpose_b

    Multiply with transposed of second input (B).

    alpha

    Scalar factor multiplied with A*B.

    beta

    Scalar factor multiplied with C.

    axis

    Axis corresponding to the matrix rows.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_gemm2(A: Option[Symbol] = None, B: Option[Symbol] = None, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, alpha: Option[Double] = None, axis: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of input matrices

    B

    Tensor of input matrices

    transpose_a

    Multiply with transposed of first input (A).

    transpose_b

    Multiply with transposed of second input (B).

    alpha

    Scalar factor multiplied with A*B.

    axis

    Axis corresponding to the matrix row indices.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_potrf(A: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of input matrices to be decomposed

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_potri(A: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of lower triangular matrices

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_sumlogdiag(A: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of square matrices

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_syrk(A: Option[Symbol] = None, transpose: Option[Boolean] = None, alpha: Option[Double] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of input matrices

    transpose

    Use transpose of input matrix.

    alpha

    Scalar factor to be applied to the result.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_trmm(A: Option[Symbol] = None, B: Option[Symbol] = None, transpose: Option[Boolean] = None, rightside: Option[Boolean] = None, alpha: Option[Double] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of lower triangular matrices

    B

    Tensor of matrices

    transpose

    Use transposed of the triangular matrix

    rightside

    Multiply triangular matrix from the right to non-triangular one.

    alpha

    Scalar factor to be applied to the result.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def linalg_trsm(A: Option[Symbol] = None, B: Option[Symbol] = None, transpose: Option[Boolean] = None, rightside: Option[Boolean] = None, alpha: Option[Double] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    A

    Tensor of lower triangular matrices

    B

    Tensor of matrices

    transpose

    Use transposed of the triangular matrix

    rightside

    Multiply triangular matrix from the right to non-triangular one.

    alpha

    Scalar factor to be applied to the result.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def log(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L939
    

  • 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:L939
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def log10(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L951
    

  • 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:L951
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def log1p(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L988
    

  • 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:L988
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def log2(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L963
    

  • 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:L963
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def log_softmax(data: Option[Symbol] = None, axis: Option[Int] = None, temperature: Option[Double] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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)
    

    data

    The input array.

    axis

    The axis along which to compute softmax.

    temperature

    Temperature parameter in softmax

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def logical_not(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.]
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def make_loss(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L298
    

  • 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:L298
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def max(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
    

  • Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def max_axis(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
    

  • Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L190
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def mean(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L131
    

  • Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L131
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def min(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
    

  • Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def min_axis(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
    

  • Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L204
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def mp_sgd_mom_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, mom: Option[Symbol] = None, weight32: Option[Symbol] = None, lr: MXFloat, momentum: Option[MXFloat] = None, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, lazy_update: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Updater function for multi-precision sgd optimizer
    

  • Updater function for multi-precision sgd optimizer
    

    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    weight32

    Weight32

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    lazy_update

    If true, lazy updates are applied if gradient's stype is row_sparse and both weight and momentum have the same stype

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def mp_sgd_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, weight32: Option[Symbol] = None, lr: MXFloat, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, lazy_update: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Updater function for multi-precision sgd optimizer
    

  • Updater function for multi-precision sgd optimizer
    

    weight

    Weight

    grad

    gradient

    weight32

    Weight32

    lr

    Learning rate

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    lazy_update

    If true, lazy updates are applied if gradient's stype is row_sparse.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def nanprod(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L176
    

  • 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:L176
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def nansum(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L161
    

  • 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:L161
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def negative(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def norm(data: Option[Symbol] = None, ord: Option[Int] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L345
    

  • 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:L345
    

    data

    The input

    ord

    Order of the norm. Currently ord=1 and ord=2 is supported.

    axis

    The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed.

    keepdims

    If this is set to True, the reduced axis is left in the result as dimension with size one.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def normal(loc: Option[MXFloat] = None, scale: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    loc

    Mean of the distribution.

    scale

    Standard deviation of the distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def one_hot(indices: Option[Symbol] = None, depth: Int, on_value: Option[Double] = None, off_value: Option[Double] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    indices

    array of locations where to set on_value

    depth

    Depth of the one hot dimension.

    on_value

    The value assigned to the locations represented by indices.

    off_value

    The value assigned to the locations not represented by indices.

    dtype

    DType of the output

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def ones_like(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.]]
    

    data

    The input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def pad(data: Option[Symbol] = None, mode: String, pad_width: Shape, constant_value: Option[Double] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    An n-dimensional input array.

    mode

    Padding type to use. "constant" pads with constant_value "edge" pads using the edge values of the input array "reflect" pads by reflecting values with respect to the edges.

    pad_width

    Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). It should be of length 2*N where N is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened.

    constant_value

    The value used for padding when mode is "constant".

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def pick(data: Option[Symbol] = None, index: Option[Symbol] = None, axis: Option[Int] = None, keepdims: Option[Boolean] = None, mode: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array

    index

    The index array

    axis

    int or None. The axis to picking the elements. Negative values means indexing from right to left. If is None, the elements in the index w.r.t the flattened input will be picked.

    keepdims

    If true, the axis where we pick the elements is left in the result as dimension with size one.

    mode

    Specify how out-of-bound indices behave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" means to wrap around.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def prod(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L146
    

  • Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L146
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def radians(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def random_exponential(lam: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lam

    Lambda parameter (rate) of the exponential distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def random_gamma(alpha: Option[MXFloat] = None, beta: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    alpha

    Alpha parameter (shape) of the gamma distribution.

    beta

    Beta parameter (scale) of the gamma distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def random_generalized_negative_binomial(mu: Option[MXFloat] = None, alpha: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    mu

    Mean of the negative binomial distribution.

    alpha

    Alpha (dispersion) parameter of the negative binomial distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def random_negative_binomial(k: Option[Int] = None, p: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    k

    Limit of unsuccessful experiments.

    p

    Failure probability in each experiment.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def random_normal(loc: Option[MXFloat] = None, scale: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    loc

    Mean of the distribution.

    scale

    Standard deviation of the distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def random_poisson(lam: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lam

    Lambda parameter (rate) of the Poisson distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def random_uniform(low: Option[MXFloat] = None, high: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    low

    Lower bound of the distribution.

    high

    Upper bound of the distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def ravel_multi_index(data: Option[Symbol] = None, shape: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Batch of multi-indices

    shape

    Shape of the array into which the multi-indices apply.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def rcbrt(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L904
    

  • 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:L904
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def reciprocal(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L644
    

  • 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:L644
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def relu(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def repeat(data: Option[Symbol] = None, repeats: Int, axis: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data array

    repeats

    The number of repetitions for each element.

    axis

    The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input array, and return a flat output array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def reshape(data: Option[Symbol] = None, shape: Option[Shape] = None, reverse: Option[Boolean] = None, target_shape: Option[Shape] = None, keep_highest: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data to reshape.

    shape

    The target shape

    reverse

    If true then the special values are inferred from right to left

    target_shape

    (Deprecated! Use shape instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims

    keep_highest

    (Deprecated! Use shape instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def reshape_like(lhs: Option[Symbol] = None, rhs: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L453
    

  • 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:L453
    

    lhs

    First input.

    rhs

    Second input.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def reverse(data: Option[Symbol] = None, axis: Shape, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input data array

    axis

    The axis which to reverse elements.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def rint(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L725
    

  • 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:L725
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def rmsprop_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, n: Option[Symbol] = None, lr: MXFloat, gamma1: Option[MXFloat] = None, epsilon: Option[MXFloat] = None, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, clip_weights: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    weight

    Weight

    grad

    Gradient

    n

    n

    lr

    Learning rate

    gamma1

    The decay rate of momentum estimates.

    epsilon

    A small constant for numerical stability.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    clip_weights

    Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def rmspropalex_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, n: Option[Symbol] = None, g: Option[Symbol] = None, delta: Option[Symbol] = None, lr: MXFloat, gamma1: Option[MXFloat] = None, gamma2: Option[MXFloat] = None, epsilon: Option[MXFloat] = None, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, clip_weights: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    weight

    Weight

    grad

    Gradient

    n

    n

    g

    g

    delta

    delta

    lr

    Learning rate

    gamma1

    Decay rate.

    gamma2

    Decay rate.

    epsilon

    A small constant for numerical stability.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    clip_weights

    Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def round(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L704
    

  • 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:L704
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def rsqrt(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L864
    

  • 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:L864
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_exponential(lam: Option[Symbol] = None, shape: Option[Shape] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lam

    Lambda (rate) parameters of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_gamma(alpha: Option[Symbol] = None, shape: Option[Shape] = None, dtype: Option[String] = None, beta: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    alpha

    Alpha (shape) parameters of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    beta

    Beta (scale) parameters of the distributions.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_generalized_negative_binomial(mu: Option[Symbol] = None, shape: Option[Shape] = None, dtype: Option[String] = None, alpha: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    mu

    Means of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    alpha

    Alpha (dispersion) parameters of the distributions.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_multinomial(data: Option[Symbol] = None, shape: Option[Shape] = None, get_prob: Option[Boolean] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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]
    

    data

    Distribution probabilities. Must sum to one on the last axis.

    shape

    Shape to be sampled from each random distribution.

    get_prob

    Whether to also return the log probability of sampled result. This is usually used for differentiating through stochastic variables, e.g. in reinforcement learning.

    dtype

    DType of the output in case this can't be inferred.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_negative_binomial(k: Option[Symbol] = None, shape: Option[Shape] = None, dtype: Option[String] = None, p: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    k

    Limits of unsuccessful experiments.

    shape

    Shape to be sampled from each random distribution.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    p

    Failure probabilities in each experiment.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_normal(mu: Option[Symbol] = None, shape: Option[Shape] = None, dtype: Option[String] = None, sigma: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    mu

    Means of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    sigma

    Standard deviations of the distributions.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_poisson(lam: Option[Symbol] = None, shape: Option[Shape] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    lam

    Lambda (rate) parameters of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sample_uniform(low: Option[Symbol] = None, shape: Option[Shape] = None, dtype: Option[String] = None, high: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    low

    Lower bounds of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    high

    Upper bounds of the distributions.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def scatter_nd(data: Option[Symbol] = None, indices: Option[Symbol] = None, shape: Shape, name: String = null, attr: Map[String, String] = null): Symbol

    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]]]]
    

    data

    data

    indices

    indices

    shape

    Shape of output.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sgd_mom_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, mom: Option[Symbol] = None, lr: MXFloat, momentum: Option[MXFloat] = None, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, lazy_update: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    lazy_update

    If true, lazy updates are applied if gradient's stype is row_sparse and both weight and momentum have the same stype

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sgd_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, lr: MXFloat, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, lazy_update: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    weight

    Weight

    grad

    Gradient

    lr

    Learning rate

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    lazy_update

    If true, lazy updates are applied if gradient's stype is row_sparse.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def shape_array(data: Option[Symbol] = None, lhs_begin: Option[Int] = None, lhs_end: Option[Int] = None, rhs_begin: Option[Int] = None, rhs_end: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L503
    

  • 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:L503
    

    data

    Input Array.

    lhs_begin

    Defaults to 0. The beginning index along which the lhs dimensions are to be reshaped. Supports negative indices.

    lhs_end

    Defaults to None. The ending index along which the lhs dimensions are to be used for reshaping. Supports negative indices.

    rhs_begin

    Defaults to 0. The beginning index along which the rhs dimensions are to be used for reshaping. Supports negative indices.

    rhs_end

    Defaults to None. The ending index along which the rhs dimensions are to be used for reshaping. Supports negative indices.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def shuffle(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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.
    

    data

    Data to be shuffled.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sigmoid(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes sigmoid of x element-wise.
    
    .. math::
       y = 1 / (1 + exp(-x))
    
    The storage type of ``sigmoid`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L101
    

  • Computes sigmoid of x element-wise.
    
    .. math::
       y = 1 / (1 + exp(-x))
    
    The storage type of ``sigmoid`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L101
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sign(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns element-wise sign of the input.
    
    Example::
    
       sign([-2, 0, 3]) = [-1, 0, 1]
    
    The storage type of ``sign`` output depends upon the input storage type:
    
       - sign(default) = default
       - sign(row_sparse) = row_sparse
       - sign(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L685
    

  • Returns element-wise sign of the input.
    
    Example::
    
       sign([-2, 0, 3]) = [-1, 0, 1]
    
    The storage type of ``sign`` output depends upon the input storage type:
    
       - sign(default) = default
       - sign(row_sparse) = row_sparse
       - sign(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L685
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def signsgd_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, lr: MXFloat, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Update function for SignSGD optimizer.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     W_t = W_{t-1} - \eta_t \text{sign}(g_t)
    
    It updates the weights using::
    
     weight = weight - learning_rate * sign(gradient)
    
    .. note::
       - sparse ndarray not supported for this optimizer yet.
    
    
    Defined in src/operator/optimizer_op.cc:L57
    

  • Update function for SignSGD optimizer.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     W_t = W_{t-1} - \eta_t \text{sign}(g_t)
    
    It updates the weights using::
    
     weight = weight - learning_rate * sign(gradient)
    
    .. note::
       - sparse ndarray not supported for this optimizer yet.
    
    
    Defined in src/operator/optimizer_op.cc:L57
    

    weight

    Weight

    grad

    Gradient

    lr

    Learning rate

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def signum_update(weight: Option[Symbol] = None, grad: Option[Symbol] = None, mom: Option[Symbol] = None, lr: MXFloat, momentum: Option[MXFloat] = None, wd: Option[MXFloat] = None, rescale_grad: Option[MXFloat] = None, clip_gradient: Option[MXFloat] = None, wd_lh: Option[MXFloat] = None, name: String = null, attr: Map[String, String] = null): Symbol

    SIGN momentUM (Signum) optimizer.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta m_{t-1} + (1 - \beta) g_t\\
     W_t = W_{t-1} - \eta_t \text{sign}(m_t)
    
    It updates the weights using::
     state = momentum * state + (1-momentum) * gradient
     weight = weight - learning_rate * sign(state)
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    .. note::
       - sparse ndarray not supported for this optimizer yet.
    
    
    Defined in src/operator/optimizer_op.cc:L86
    

  • SIGN momentUM (Signum) optimizer.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta m_{t-1} + (1 - \beta) g_t\\
     W_t = W_{t-1} - \eta_t \text{sign}(m_t)
    
    It updates the weights using::
     state = momentum * state + (1-momentum) * gradient
     weight = weight - learning_rate * sign(state)
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    .. note::
       - sparse ndarray not supported for this optimizer yet.
    
    
    Defined in src/operator/optimizer_op.cc:L86
    

    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

    Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

    Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).

    wd_lh

    The amount of weight decay that does not go into gradient/momentum calculationsotherwise do weight decay algorithmically only.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sin(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the element-wise sine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       sin([0, \pi/4, \pi/2]) = [0, 0.707, 1]
    
    The storage type of ``sin`` output depends upon the input storage type:
    
       - sin(default) = default
       - sin(row_sparse) = row_sparse
       - sin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L46
    

  • Computes the element-wise sine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       sin([0, \pi/4, \pi/2]) = [0, 0.707, 1]
    
    The storage type of ``sin`` output depends upon the input storage type:
    
       - sin(default) = default
       - sin(row_sparse) = row_sparse
       - sin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L46
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sinh(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns the hyperbolic sine of the input array, computed element-wise.
    
    .. math::
       sinh(x) = 0.5\times(exp(x) - exp(-x))
    
    The storage type of ``sinh`` output depends upon the input storage type:
    
       - sinh(default) = default
       - sinh(row_sparse) = row_sparse
       - sinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L201
    

  • Returns the hyperbolic sine of the input array, computed element-wise.
    
    .. math::
       sinh(x) = 0.5\times(exp(x) - exp(-x))
    
    The storage type of ``sinh`` output depends upon the input storage type:
    
       - sinh(default) = default
       - sinh(row_sparse) = row_sparse
       - sinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L201
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def size_array(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns a 1D int64 array containing the size of data.
    
    Example::
    
      size_array([[1,2,3,4], [5,6,7,8]]) = [8]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L554
    

  • Returns a 1D int64 array containing the size of data.
    
    Example::
    
      size_array([[1,2,3,4], [5,6,7,8]]) = [8]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L554
    

    data

    Input Array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def slice(data: Option[Symbol] = None, begin: Shape, end: Shape, step: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Source input

    begin

    starting indices for the slice operation, supports negative indices.

    end

    ending indices for the slice operation, supports negative indices.

    step

    step for the slice operation, supports negative values.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def slice_axis(data: Option[Symbol] = None, axis: Int, begin: Int, end: Int, name: String = null, attr: Map[String, String] = null): Symbol

    Slices along a given axis.
    
    Returns an array slice along a given `axis` starting from the `begin` index
    to the `end` index.
    
    Examples::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      slice_axis(x, axis=0, begin=1, end=3) = [[  5.,   6.,   7.,   8.],
                                               [  9.,  10.,  11.,  12.]]
    
      slice_axis(x, axis=1, begin=0, end=2) = [[  1.,   2.],
                                               [  5.,   6.],
                                               [  9.,  10.]]
    
      slice_axis(x, axis=1, begin=-3, end=-1) = [[  2.,   3.],
                                                 [  6.,   7.],
                                                 [ 10.,  11.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L500
    

  • Slices along a given axis.
    
    Returns an array slice along a given `axis` starting from the `begin` index
    to the `end` index.
    
    Examples::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      slice_axis(x, axis=0, begin=1, end=3) = [[  5.,   6.,   7.,   8.],
                                               [  9.,  10.,  11.,  12.]]
    
      slice_axis(x, axis=1, begin=0, end=2) = [[  1.,   2.],
                                               [  5.,   6.],
                                               [  9.,  10.]]
    
      slice_axis(x, axis=1, begin=-3, end=-1) = [[  2.,   3.],
                                                 [  6.,   7.],
                                                 [ 10.,  11.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L500
    

    data

    Source input

    axis

    Axis along which to be sliced, supports negative indexes.

    begin

    The beginning index along the axis to be sliced, supports negative indexes.

    end

    The ending index along the axis to be sliced, supports negative indexes.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def slice_like(data: Option[Symbol] = None, shape_like: Option[Symbol] = None, axes: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Slices a region of the array like the shape of another array.
    
    This function is similar to ``slice``, however, the `begin` are always `0`s
    and `end` of specific axes are inferred from the second input `shape_like`.
    
    Given the second `shape_like` input of ``shape=(d_0, d_1, ..., d_n-1)``,
    a ``slice_like`` operator with default empty `axes`, it performs the
    following operation:
    
    `` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``.
    
    When `axes` is not empty, it is used to speficy which axes are being sliced.
    
    Given a 4-d input data, ``slice_like`` operator with ``axes=(0, 2, -1)``
    will perform the following operation:
    
    `` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``.
    
    Note that it is allowed to have first and second input with different dimensions,
    however, you have to make sure the `axes` are specified and not exceeding the
    dimension limits.
    
    For example, given `input_1` with ``shape=(2,3,4,5)`` and `input_2` with
    ``shape=(1,2,3)``, it is not allowed to use:
    
    `` out = slice_like(a, b)`` because ndim of `input_1` is 4, and ndim of `input_2`
    is 3.
    
    The following is allowed in this situation:
    
    `` out = slice_like(a, b, axes=(0, 2))``
    
    Example::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      y = [[  0.,   0.,   0.],
           [  0.,   0.,   0.]]
    
      slice_like(x, y) = [[ 1.,  2.,  3.]
                          [ 5.,  6.,  7.]]
      slice_like(x, y, axes=(0, 1)) = [[ 1.,  2.,  3.]
                                       [ 5.,  6.,  7.]]
      slice_like(x, y, axes=(0)) = [[ 1.,  2.,  3.,  4.]
                                    [ 5.,  6.,  7.,  8.]]
      slice_like(x, y, axes=(-1)) = [[  1.,   2.,   3.]
                                     [  5.,   6.,   7.]
                                     [  9.,  10.,  11.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L569
    

  • Slices a region of the array like the shape of another array.
    
    This function is similar to ``slice``, however, the `begin` are always `0`s
    and `end` of specific axes are inferred from the second input `shape_like`.
    
    Given the second `shape_like` input of ``shape=(d_0, d_1, ..., d_n-1)``,
    a ``slice_like`` operator with default empty `axes`, it performs the
    following operation:
    
    `` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``.
    
    When `axes` is not empty, it is used to speficy which axes are being sliced.
    
    Given a 4-d input data, ``slice_like`` operator with ``axes=(0, 2, -1)``
    will perform the following operation:
    
    `` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``.
    
    Note that it is allowed to have first and second input with different dimensions,
    however, you have to make sure the `axes` are specified and not exceeding the
    dimension limits.
    
    For example, given `input_1` with ``shape=(2,3,4,5)`` and `input_2` with
    ``shape=(1,2,3)``, it is not allowed to use:
    
    `` out = slice_like(a, b)`` because ndim of `input_1` is 4, and ndim of `input_2`
    is 3.
    
    The following is allowed in this situation:
    
    `` out = slice_like(a, b, axes=(0, 2))``
    
    Example::
    
      x = [[  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.]]
    
      y = [[  0.,   0.,   0.],
           [  0.,   0.,   0.]]
    
      slice_like(x, y) = [[ 1.,  2.,  3.]
                          [ 5.,  6.,  7.]]
      slice_like(x, y, axes=(0, 1)) = [[ 1.,  2.,  3.]
                                       [ 5.,  6.,  7.]]
      slice_like(x, y, axes=(0)) = [[ 1.,  2.,  3.,  4.]
                                    [ 5.,  6.,  7.,  8.]]
      slice_like(x, y, axes=(-1)) = [[  1.,   2.,   3.]
                                     [  5.,   6.,   7.]
                                     [  9.,  10.,  11.]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L569
    

    data

    Source input

    shape_like

    Shape like input

    axes

    List of axes on which input data will be sliced according to the corresponding size of the second input. By default will slice on all axes. Negative axes are supported.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def smooth_l1(data: Option[Symbol] = None, scalar: MXFloat, name: String = null, attr: Map[String, String] = null): Symbol

    Calculate Smooth L1 Loss(lhs, scalar) by summing
    
    .. math::
    
        f(x) =
        \begin{cases}
        (\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
        |x|-0.5/\sigma^2,& \text{otherwise}
        \end{cases}
    
    where :math:`x` is an element of the tensor *lhs* and :math:`\sigma` is the scalar.
    
    Example::
    
      smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L103
    

  • Calculate Smooth L1 Loss(lhs, scalar) by summing
    
    .. math::
    
        f(x) =
        \begin{cases}
        (\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
        |x|-0.5/\sigma^2,& \text{otherwise}
        \end{cases}
    
    where :math:`x` is an element of the tensor *lhs* and :math:`\sigma` is the scalar.
    
    Example::
    
      smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L103
    

    data

    source input

    scalar

    scalar input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def softmax(data: Option[Symbol] = None, axis: Option[Int] = None, temperature: Option[Double] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Applies the softmax function.
    
    The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.
    
    .. math::
       softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}
    
    for :math:`j = 1, ..., K`
    
    t is the temperature parameter in softmax function. By default, t equals 1.0
    
    Example::
    
      x = [[ 1.  1.  1.]
           [ 1.  1.  1.]]
    
      softmax(x,axis=0) = [[ 0.5  0.5  0.5]
                           [ 0.5  0.5  0.5]]
    
      softmax(x,axis=1) = [[ 0.33333334,  0.33333334,  0.33333334],
                           [ 0.33333334,  0.33333334,  0.33333334]]
    
    
    
    Defined in src/operator/nn/softmax.cc:L100
    

  • Applies the softmax function.
    
    The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.
    
    .. math::
       softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}
    
    for :math:`j = 1, ..., K`
    
    t is the temperature parameter in softmax function. By default, t equals 1.0
    
    Example::
    
      x = [[ 1.  1.  1.]
           [ 1.  1.  1.]]
    
      softmax(x,axis=0) = [[ 0.5  0.5  0.5]
                           [ 0.5  0.5  0.5]]
    
      softmax(x,axis=1) = [[ 0.33333334,  0.33333334,  0.33333334],
                           [ 0.33333334,  0.33333334,  0.33333334]]
    
    
    
    Defined in src/operator/nn/softmax.cc:L100
    

    data

    The input array.

    axis

    The axis along which to compute softmax.

    temperature

    Temperature parameter in softmax

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def softmax_cross_entropy(data: Option[Symbol] = None, label: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Calculate cross entropy of softmax output and one-hot label.
    
    - This operator computes the cross entropy in two steps:
      - Applies softmax function on the input array.
      - Computes and returns the cross entropy loss between the softmax output and the labels.
    
    - The softmax function and cross entropy loss 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)
    
    Example::
    
      x = [[1, 2, 3],
           [11, 7, 5]]
    
      label = [2, 0]
    
      softmax(x) = [[0.09003057, 0.24472848, 0.66524094],
                    [0.97962922, 0.01794253, 0.00242826]]
    
      softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871
    
    
    
    Defined in src/operator/loss_binary_op.cc:L59
    

  • Calculate cross entropy of softmax output and one-hot label.
    
    - This operator computes the cross entropy in two steps:
      - Applies softmax function on the input array.
      - Computes and returns the cross entropy loss between the softmax output and the labels.
    
    - The softmax function and cross entropy loss 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)
    
    Example::
    
      x = [[1, 2, 3],
           [11, 7, 5]]
    
      label = [2, 0]
    
      softmax(x) = [[0.09003057, 0.24472848, 0.66524094],
                    [0.97962922, 0.01794253, 0.00242826]]
    
      softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871
    
    
    
    Defined in src/operator/loss_binary_op.cc:L59
    

    data

    Input data

    label

    Input label

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def softsign(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes softsign of x element-wise.
    
    .. math::
       y = x / (1 + abs(x))
    
    The storage type of ``softsign`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L145
    

  • Computes softsign of x element-wise.
    
    .. math::
       y = x / (1 + abs(x))
    
    The storage type of ``softsign`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L145
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sort(data: Option[Symbol] = None, axis: Option[Int] = None, is_ascend: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns a sorted copy of an input array along the given axis.
    
    Examples::
    
      x = [[ 1, 4],
           [ 3, 1]]
    
      // sorts along the last axis
      sort(x) = [[ 1.,  4.],
                 [ 1.,  3.]]
    
      // flattens and then sorts
      sort(x) = [ 1.,  1.,  3.,  4.]
    
      // sorts along the first axis
      sort(x, axis=0) = [[ 1.,  1.],
                         [ 3.,  4.]]
    
      // in a descend order
      sort(x, is_ascend=0) = [[ 4.,  1.],
                              [ 3.,  1.]]
    
    
    
    Defined in src/operator/tensor/ordering_op.cc:L126
    

  • Returns a sorted copy of an input array along the given axis.
    
    Examples::
    
      x = [[ 1, 4],
           [ 3, 1]]
    
      // sorts along the last axis
      sort(x) = [[ 1.,  4.],
                 [ 1.,  3.]]
    
      // flattens and then sorts
      sort(x) = [ 1.,  1.,  3.,  4.]
    
      // sorts along the first axis
      sort(x, axis=0) = [[ 1.,  1.],
                         [ 3.,  4.]]
    
      // in a descend order
      sort(x, is_ascend=0) = [[ 4.,  1.],
                              [ 3.,  1.]]
    
    
    
    Defined in src/operator/tensor/ordering_op.cc:L126
    

    data

    The input array

    axis

    Axis along which to choose sort the input tensor. If not given, the flattened array is used. Default is -1.

    is_ascend

    Whether to sort in ascending or descending order.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def space_to_depth(data: Option[Symbol] = None, block_size: Int, name: String = null, attr: Map[String, String] = null): Symbol

    Rearranges(permutes) blocks of spatial data into depth.
    Similar to ONNX SpaceToDepth operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth
    
    The output is a new tensor where the values from height and width dimension are
    moved to the depth dimension. The reverse of this operation is ``depth_to_space``.
    
    .. math::
    
        \begin{gather*}
        x \prime = reshape(x, [N, C, H / block\_size, block\_size, W / block\_size, block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 5, 1, 2, 4]) \\
        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, 6, 1, 7, 2, 8],
             [12, 18, 13, 19, 14, 20],
             [3, 9, 4, 10, 5, 11],
             [15, 21, 16, 22, 17, 23]]]]
    
    
      space_to_depth(x, 2) = [[[[0, 1, 2],
                                [3, 4, 5]],
                               [[6, 7, 8],
                                [9, 10, 11]],
                               [[12, 13, 14],
                                [15, 16, 17]],
                               [[18, 19, 20],
                                [21, 22, 23]]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L999
    

  • Rearranges(permutes) blocks of spatial data into depth.
    Similar to ONNX SpaceToDepth operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth
    
    The output is a new tensor where the values from height and width dimension are
    moved to the depth dimension. The reverse of this operation is ``depth_to_space``.
    
    .. math::
    
        \begin{gather*}
        x \prime = reshape(x, [N, C, H / block\_size, block\_size, W / block\_size, block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 5, 1, 2, 4]) \\
        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, 6, 1, 7, 2, 8],
             [12, 18, 13, 19, 14, 20],
             [3, 9, 4, 10, 5, 11],
             [15, 21, 16, 22, 17, 23]]]]
    
    
      space_to_depth(x, 2) = [[[[0, 1, 2],
                                [3, 4, 5]],
                               [[6, 7, 8],
                                [9, 10, 11]],
                               [[12, 13, 14],
                                [15, 16, 17]],
                               [[18, 19, 20],
                                [21, 22, 23]]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L999
    

    data

    Input ndarray

    block_size

    Blocks of [block_size. block_size] are moved

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def split(data: Option[Symbol] = None, num_outputs: Int, axis: Option[Int] = None, squeeze_axis: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    The input

    num_outputs

    Number of splits. Note that this should evenly divide the length of the axis.

    axis

    Axis along which to split.

    squeeze_axis

    If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting squeeze_axis to true 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.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sqrt(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns element-wise square-root value of the input.
    
    .. math::
       \textrm{sqrt}(x) = \sqrt{x}
    
    Example::
    
       sqrt([4, 9, 16]) = [2, 3, 4]
    
    The storage type of ``sqrt`` output depends upon the input storage type:
    
       - sqrt(default) = default
       - sqrt(row_sparse) = row_sparse
       - sqrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L844
    

  • Returns element-wise square-root value of the input.
    
    .. math::
       \textrm{sqrt}(x) = \sqrt{x}
    
    Example::
    
       sqrt([4, 9, 16]) = [2, 3, 4]
    
    The storage type of ``sqrt`` output depends upon the input storage type:
    
       - sqrt(default) = default
       - sqrt(row_sparse) = row_sparse
       - sqrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L844
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def square(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns element-wise squared value of the input.
    
    .. math::
       square(x) = x^2
    
    Example::
    
       square([2, 3, 4]) = [4, 9, 16]
    
    The storage type of ``square`` output depends upon the input storage type:
    
       - square(default) = default
       - square(row_sparse) = row_sparse
       - square(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L821
    

  • Returns element-wise squared value of the input.
    
    .. math::
       square(x) = x^2
    
    Example::
    
       square([2, 3, 4]) = [4, 9, 16]
    
    The storage type of ``square`` output depends upon the input storage type:
    
       - square(default) = default
       - square(row_sparse) = row_sparse
       - square(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L821
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def squeeze(data: Array[Symbol], axis: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Remove single-dimensional entries from the shape of an array.
    Same behavior of defining the output tensor shape as numpy.squeeze for the most of cases.
    See the following note for exception.
    
    Examples::
    
      data = [[[0], [1], [2]]]
      squeeze(data) = [0, 1, 2]
      squeeze(data, axis=0) = [[0], [1], [2]]
      squeeze(data, axis=2) = [[0, 1, 2]]
      squeeze(data, axis=(0, 2)) = [0, 1, 2]
    
    .. Note::
      The output of this operator will keep at least one dimension not removed. For example,
      squeeze([[[4]]]) = [4], while in numpy.squeeze, the output will become a scalar.
    

  • Remove single-dimensional entries from the shape of an array.
    Same behavior of defining the output tensor shape as numpy.squeeze for the most of cases.
    See the following note for exception.
    
    Examples::
    
      data = [[[0], [1], [2]]]
      squeeze(data) = [0, 1, 2]
      squeeze(data, axis=0) = [[0], [1], [2]]
      squeeze(data, axis=2) = [[0, 1, 2]]
      squeeze(data, axis=(0, 2)) = [0, 1, 2]
    
    .. Note::
      The output of this operator will keep at least one dimension not removed. For example,
      squeeze([[[4]]]) = [4], while in numpy.squeeze, the output will become a scalar.
    

    data

    data to squeeze

    axis

    Selects a subset of the single-dimensional entries in the shape. If an axis is selected with shape entry greater than one, an error is raised.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def stack(data: Array[Symbol], axis: Option[Int] = None, num_args: Int, name: String = null, attr: Map[String, String] = null): Symbol

    Join a sequence of arrays along a new axis.
    
    The axis parameter specifies the index of the new axis in the dimensions of the
    result. For example, if axis=0 it will be the first dimension and if axis=-1 it
    will be the last dimension.
    
    Examples::
    
      x = [1, 2]
      y = [3, 4]
    
      stack(x, y) = [[1, 2],
                     [3, 4]]
      stack(x, y, axis=1) = [[1, 3],
                             [2, 4]]
    

  • Join a sequence of arrays along a new axis.
    
    The axis parameter specifies the index of the new axis in the dimensions of the
    result. For example, if axis=0 it will be the first dimension and if axis=-1 it
    will be the last dimension.
    
    Examples::
    
      x = [1, 2]
      y = [3, 4]
    
      stack(x, y) = [[1, 2],
                     [3, 4]]
      stack(x, y, axis=1) = [[1, 3],
                             [2, 4]]
    

    data

    List of arrays to stack

    axis

    The axis in the result array along which the input arrays are stacked.

    num_args

    Number of inputs to be stacked.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def stop_gradient(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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:L265
    

  • 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:L265
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sum(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the sum of array elements over given axes.
    
    .. Note::
    
      `sum` and `sum_axis` are equivalent.
      For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
      Setting keepdims or exclude to True will cause a fallback to dense operator.
    
    Example::
    
      data = [[[1, 2], [2, 3], [1, 3]],
              [[1, 4], [4, 3], [5, 2]],
              [[7, 1], [7, 2], [7, 3]]]
    
      sum(data, axis=1)
      [[  4.   8.]
       [ 10.   9.]
       [ 21.   6.]]
    
      sum(data, axis=[1,2])
      [ 12.  19.  27.]
    
      data = [[1, 2, 0],
              [3, 0, 1],
              [4, 1, 0]]
    
      csr = cast_storage(data, 'csr')
    
      sum(csr, axis=0)
      [ 8.  3.  1.]
    
      sum(csr, axis=1)
      [ 3.  4.  5.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
    

  • Computes the sum of array elements over given axes.
    
    .. Note::
    
      `sum` and `sum_axis` are equivalent.
      For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
      Setting keepdims or exclude to True will cause a fallback to dense operator.
    
    Example::
    
      data = [[[1, 2], [2, 3], [1, 3]],
              [[1, 4], [4, 3], [5, 2]],
              [[7, 1], [7, 2], [7, 3]]]
    
      sum(data, axis=1)
      [[  4.   8.]
       [ 10.   9.]
       [ 21.   6.]]
    
      sum(data, axis=[1,2])
      [ 12.  19.  27.]
    
      data = [[1, 2, 0],
              [3, 0, 1],
              [4, 1, 0]]
    
      csr = cast_storage(data, 'csr')
    
      sum(csr, axis=0)
      [ 8.  3.  1.]
    
      sum(csr, axis=1)
      [ 3.  4.  5.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def sum_axis(data: Option[Symbol] = None, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the sum of array elements over given axes.
    
    .. Note::
    
      `sum` and `sum_axis` are equivalent.
      For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
      Setting keepdims or exclude to True will cause a fallback to dense operator.
    
    Example::
    
      data = [[[1, 2], [2, 3], [1, 3]],
              [[1, 4], [4, 3], [5, 2]],
              [[7, 1], [7, 2], [7, 3]]]
    
      sum(data, axis=1)
      [[  4.   8.]
       [ 10.   9.]
       [ 21.   6.]]
    
      sum(data, axis=[1,2])
      [ 12.  19.  27.]
    
      data = [[1, 2, 0],
              [3, 0, 1],
              [4, 1, 0]]
    
      csr = cast_storage(data, 'csr')
    
      sum(csr, axis=0)
      [ 8.  3.  1.]
    
      sum(csr, axis=1)
      [ 3.  4.  5.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
    

  • Computes the sum of array elements over given axes.
    
    .. Note::
    
      `sum` and `sum_axis` are equivalent.
      For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
      Setting keepdims or exclude to True will cause a fallback to dense operator.
    
    Example::
    
      data = [[[1, 2], [2, 3], [1, 3]],
              [[1, 4], [4, 3], [5, 2]],
              [[7, 1], [7, 2], [7, 3]]]
    
      sum(data, axis=1)
      [[  4.   8.]
       [ 10.   9.]
       [ 21.   6.]]
    
      sum(data, axis=[1,2])
      [ 12.  19.  27.]
    
      data = [[1, 2, 0],
              [3, 0, 1],
              [4, 1, 0]]
    
      csr = cast_storage(data, 'csr')
    
      sum(csr, axis=0)
      [ 8.  3.  1.]
    
      sum(csr, axis=1)
      [ 3.  4.  5.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L115
    

    data

    The input

    axis

    The axis or axes along which to perform the reduction.

    The default, axis=(), will compute over all elements into a scalar array with shape (1,).

    If axis is int, a reduction is performed on a particular axis.

    If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple.

    If exclude is true, reduction will be performed on the axes that are NOT in axis instead.

    Negative values means indexing from right to left.

    keepdims

    If this is set to True, the reduced axes are left in the result as dimension with size one.

    exclude

    Whether to perform reduction on axis that are NOT in axis instead.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def swapaxes(data: Option[Symbol] = None, dim1: Option[Int] = None, dim2: Option[Int] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    data

    Input array.

    dim1

    the first axis to be swapped.

    dim2

    the second axis to be swapped.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def take(a: Option[Symbol] = None, indices: Option[Symbol] = None, axis: Option[Int] = None, mode: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Takes elements from an input array along the given axis.
    
    This function slices the input array along a particular axis with the provided indices.
    
    Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis
    dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them
    in an output tensor of rank q + (r - 1).
    
    Examples::
      x = [4.  5.  6.]
    
      // Trivial case, take the second element along the first axis.
    
      take(x, [1]) = [ 5. ]
    
      // The other trivial case, axis=-1, take the third element along the first axis
    
      take(x, [3], axis=-1, mode='clip') = [ 6. ]
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // In this case we will get rows 0 and 1, then 1 and 2. Along axis 0
    
      take(x, [[0,1],[1,2]]) = [[[ 1.,  2.],
                                 [ 3.,  4.]],
    
                                [[ 3.,  4.],
                                 [ 5.,  6.]]]
    
      // In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around).
      // Along axis 1
    
      take(x, [[0, 3], [-1, -2]], axis=1, mode='wrap') = [[[ 1.,  2.],
                                                           [ 3.,  4.]],
    
                                                          [[ 3.,  4.],
                                                           [ 5.,  6.]]]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L434
    

  • Takes elements from an input array along the given axis.
    
    This function slices the input array along a particular axis with the provided indices.
    
    Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis
    dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them
    in an output tensor of rank q + (r - 1).
    
    Examples::
      x = [4.  5.  6.]
    
      // Trivial case, take the second element along the first axis.
    
      take(x, [1]) = [ 5. ]
    
      // The other trivial case, axis=-1, take the third element along the first axis
    
      take(x, [3], axis=-1, mode='clip') = [ 6. ]
    
      x = [[ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.]]
    
      // In this case we will get rows 0 and 1, then 1 and 2. Along axis 0
    
      take(x, [[0,1],[1,2]]) = [[[ 1.,  2.],
                                 [ 3.,  4.]],
    
                                [[ 3.,  4.],
                                 [ 5.,  6.]]]
    
      // In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around).
      // Along axis 1
    
      take(x, [[0, 3], [-1, -2]], axis=1, mode='wrap') = [[[ 1.,  2.],
                                                           [ 3.,  4.]],
    
                                                          [[ 3.,  4.],
                                                           [ 5.,  6.]]]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L434
    

    a

    The input array.

    indices

    The indices of the values to be extracted.

    axis

    The axis of input array to be taken.For input tensor of rank r, it could be in the range of [-r, r-1]

    mode

    Specify how out-of-bound indices bahave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" means to wrap around. "raise" means to raise an error, not supported yet.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def tan(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Computes the element-wise tangent of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       tan([0, \pi/4, \pi/2]) = [0, 1, -inf]
    
    The storage type of ``tan`` output depends upon the input storage type:
    
       - tan(default) = default
       - tan(row_sparse) = row_sparse
       - tan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L83
    

  • Computes the element-wise tangent of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       tan([0, \pi/4, \pi/2]) = [0, 1, -inf]
    
    The storage type of ``tan`` output depends upon the input storage type:
    
       - tan(default) = default
       - tan(row_sparse) = row_sparse
       - tan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L83
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def tanh(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns the hyperbolic tangent of the input array, computed element-wise.
    
    .. math::
       tanh(x) = sinh(x) / cosh(x)
    
    The storage type of ``tanh`` output depends upon the input storage type:
    
       - tanh(default) = default
       - tanh(row_sparse) = row_sparse
       - tanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L234
    

  • Returns the hyperbolic tangent of the input array, computed element-wise.
    
    .. math::
       tanh(x) = sinh(x) / cosh(x)
    
    The storage type of ``tanh`` output depends upon the input storage type:
    
       - tanh(default) = default
       - tanh(row_sparse) = row_sparse
       - tanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L234
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def tile(data: Option[Symbol] = None, reps: Shape, name: String = null, attr: Map[String, String] = null): Symbol

    Repeats the whole array multiple times.
    
    If ``reps`` has length *d*, and input array has dimension of *n*. There are
    three cases:
    
    - **n=d**. Repeat *i*-th dimension of the input by ``reps[i]`` times::
    
        x = [[1, 2],
             [3, 4]]
    
        tile(x, reps=(2,3)) = [[ 1.,  2.,  1.,  2.,  1.,  2.],
                               [ 3.,  4.,  3.,  4.,  3.,  4.],
                               [ 1.,  2.,  1.,  2.,  1.,  2.],
                               [ 3.,  4.,  3.,  4.,  3.,  4.]]
    
    - **n>d**. ``reps`` is promoted to length *n* by pre-pending 1's to it. Thus for
      an input shape ``(2,3)``, ``repos=(2,)`` is treated as ``(1,2)``::
    
    
        tile(x, reps=(2,)) = [[ 1.,  2.,  1.,  2.],
                              [ 3.,  4.,  3.,  4.]]
    
    - **n

    Repeats the whole array multiple times.
    
    If ``reps`` has length *d*, and input array has dimension of *n*. There are
    three cases:
    
    - **n=d**. Repeat *i*-th dimension of the input by ``reps[i]`` times::
    
        x = [[1, 2],
             [3, 4]]
    
        tile(x, reps=(2,3)) = [[ 1.,  2.,  1.,  2.,  1.,  2.],
                               [ 3.,  4.,  3.,  4.,  3.,  4.],
                               [ 1.,  2.,  1.,  2.,  1.,  2.],
                               [ 3.,  4.,  3.,  4.,  3.,  4.]]
    
    - **n>d**. ``reps`` is promoted to length *n* by pre-pending 1's to it. Thus for
      an input shape ``(2,3)``, ``repos=(2,)`` is treated as ``(1,2)``::
    
    
        tile(x, reps=(2,)) = [[ 1.,  2.,  1.,  2.],
                              [ 3.,  4.,  3.,  4.]]
    
    - **n

    data

    Input data array

    reps

    The number of times for repeating the tensor a. Each dim size of reps must be a positive integer. If reps has length d, the result will have dimension of max(d, a.ndim); If a.ndim < d, a is promoted to be d-dimensional by prepending new axes. If a.ndim > d, reps is promoted to a.ndim by pre-pending 1's to it.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def topk(data: Option[Symbol] = None, axis: Option[Int] = None, k: Option[Int] = None, ret_typ: Option[String] = None, is_ascend: Option[Boolean] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Returns the top *k* elements in an input array along the given axis.
    
    Examples::
    
      x = [[ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2]]
    
      // returns an index of the largest element on last axis
      topk(x) = [[ 2.],
                 [ 1.]]
    
      // returns the value of top-2 largest elements on last axis
      topk(x, ret_typ='value', k=2) = [[ 0.4,  0.3],
                                       [ 0.3,  0.2]]
    
      // returns the value of top-2 smallest elements on last axis
      topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 ,  0.3],
                                                   [ 0.1 ,  0.2]]
    
      // returns the value of top-2 largest elements on axis 0
      topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3,  0.3,  0.4],
                                               [ 0.1,  0.2,  0.2]]
    
      // flattens and then returns list of both values and indices
      topk(x, ret_typ='both', k=2) = [[[ 0.4,  0.3], [ 0.3,  0.2]] ,  [[ 2.,  0.], [ 1.,  2.]]]
    
    
    
    Defined in src/operator/tensor/ordering_op.cc:L63
    

  • Returns the top *k* elements in an input array along the given axis.
    
    Examples::
    
      x = [[ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2]]
    
      // returns an index of the largest element on last axis
      topk(x) = [[ 2.],
                 [ 1.]]
    
      // returns the value of top-2 largest elements on last axis
      topk(x, ret_typ='value', k=2) = [[ 0.4,  0.3],
                                       [ 0.3,  0.2]]
    
      // returns the value of top-2 smallest elements on last axis
      topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 ,  0.3],
                                                   [ 0.1 ,  0.2]]
    
      // returns the value of top-2 largest elements on axis 0
      topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3,  0.3,  0.4],
                                               [ 0.1,  0.2,  0.2]]
    
      // flattens and then returns list of both values and indices
      topk(x, ret_typ='both', k=2) = [[[ 0.4,  0.3], [ 0.3,  0.2]] ,  [[ 2.,  0.], [ 1.,  2.]]]
    
    
    
    Defined in src/operator/tensor/ordering_op.cc:L63
    

    data

    The input array

    axis

    Axis along which to choose the top k indices. If not given, the flattened array is used. Default is -1.

    k

    Number of top elements to select, should be always smaller than or equal to the element number in the given axis. A global sort is performed if set k < 1.

    ret_typ

    The return type. "value" means to return the top k values, "indices" means to return the indices of the top k values, "mask" means to return a mask array containing 0 and 1. 1 means the top k values. "both" means to return a list of both values and indices of top k elements.

    is_ascend

    Whether to choose k largest or k smallest elements. Top K largest elements will be chosen if set to false.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def transpose(data: Option[Symbol] = None, axes: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Permutes the dimensions of an array.
    
    Examples::
    
      x = [[ 1, 2],
           [ 3, 4]]
    
      transpose(x) = [[ 1.,  3.],
                      [ 2.,  4.]]
    
      x = [[[ 1.,  2.],
            [ 3.,  4.]],
    
           [[ 5.,  6.],
            [ 7.,  8.]]]
    
      transpose(x) = [[[ 1.,  5.],
                       [ 3.,  7.]],
    
                      [[ 2.,  6.],
                       [ 4.,  8.]]]
    
      transpose(x, axes=(1,0,2)) = [[[ 1.,  2.],
                                     [ 5.,  6.]],
    
                                    [[ 3.,  4.],
                                     [ 7.,  8.]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L311
    

  • Permutes the dimensions of an array.
    
    Examples::
    
      x = [[ 1, 2],
           [ 3, 4]]
    
      transpose(x) = [[ 1.,  3.],
                      [ 2.,  4.]]
    
      x = [[[ 1.,  2.],
            [ 3.,  4.]],
    
           [[ 5.,  6.],
            [ 7.,  8.]]]
    
      transpose(x) = [[[ 1.,  5.],
                       [ 3.,  7.]],
    
                      [[ 2.,  6.],
                       [ 4.,  8.]]]
    
      transpose(x, axes=(1,0,2)) = [[[ 1.,  2.],
                                     [ 5.,  6.]],
    
                                    [[ 3.,  4.],
                                     [ 7.,  8.]]]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L311
    

    data

    Source input

    axes

    Target axis order. By default the axes will be inverted.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def trunc(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Return the element-wise truncated value of the input.
    
    The truncated value of the scalar x is the nearest integer i which is closer to
    zero than x is. In short, the fractional part of the signed number x is discarded.
    
    Example::
    
       trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  1.,  1.,  2.]
    
    The storage type of ``trunc`` output depends upon the input storage type:
    
       - trunc(default) = default
       - trunc(row_sparse) = row_sparse
       - trunc(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L783
    

  • Return the element-wise truncated value of the input.
    
    The truncated value of the scalar x is the nearest integer i which is closer to
    zero than x is. In short, the fractional part of the signed number x is discarded.
    
    Example::
    
       trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  1.,  1.,  2.]
    
    The storage type of ``trunc`` output depends upon the input storage type:
    
       - trunc(default) = default
       - trunc(row_sparse) = row_sparse
       - trunc(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L783
    

    data

    The input array.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def uniform(low: Option[MXFloat] = None, high: Option[MXFloat] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, name: String = null, attr: Map[String, String] = null): Symbol

    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
    

    low

    Lower bound of the distribution.

    high

    Upper bound of the distribution.

    shape

    Shape of the output.

    ctx

    Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.

    dtype

    DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def unravel_index(data: Option[Symbol] = None, shape: Option[Shape] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix.
    
    Examples::
    
       A = [22,41,37]
       unravel(A, shape=(7,6)) = [[3,6,6],[4,5,1]]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L65
    

  • Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix.
    
    Examples::
    
       A = [22,41,37]
       unravel(A, shape=(7,6)) = [[3,6,6],[4,5,1]]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L65
    

    data

    Array of flat indices

    shape

    Shape of the array into which the multi-indices apply.

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def where(condition: Option[Symbol] = None, x: Option[Symbol] = None, y: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Return the elements, either from x or y, depending on the condition.
    
    Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y,
    depending on the elements from condition are true or false. x and y must have the same shape.
    If condition has the same shape as x, each element in the output array is from x if the
    corresponding element in the condition is true, and from y if false.
    
    If condition does not have the same shape as x, it must be a 1D array whose size is
    the same as x's first dimension size. Each row of the output array is from x's row
    if the corresponding element from condition is true, and from y's row if false.
    
    Note that all non-zero values are interpreted as ``True`` in condition.
    
    Examples::
    
      x = [[1, 2], [3, 4]]
      y = [[5, 6], [7, 8]]
      cond = [[0, 1], [-1, 0]]
    
      where(cond, x, y) = [[5, 2], [3, 8]]
    
      csr_cond = cast_storage(cond, 'csr')
    
      where(csr_cond, x, y) = [[5, 2], [3, 8]]
    
    
    
    Defined in src/operator/tensor/control_flow_op.cc:L57
    

  • Return the elements, either from x or y, depending on the condition.
    
    Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y,
    depending on the elements from condition are true or false. x and y must have the same shape.
    If condition has the same shape as x, each element in the output array is from x if the
    corresponding element in the condition is true, and from y if false.
    
    If condition does not have the same shape as x, it must be a 1D array whose size is
    the same as x's first dimension size. Each row of the output array is from x's row
    if the corresponding element from condition is true, and from y's row if false.
    
    Note that all non-zero values are interpreted as ``True`` in condition.
    
    Examples::
    
      x = [[1, 2], [3, 4]]
      y = [[5, 6], [7, 8]]
      cond = [[0, 1], [-1, 0]]
    
      where(cond, x, y) = [[5, 2], [3, 8]]
    
      csr_cond = cast_storage(cond, 'csr')
    
      where(csr_cond, x, y) = [[5, 2], [3, 8]]
    
    
    
    Defined in src/operator/tensor/control_flow_op.cc:L57
    

    condition

    condition array

    x
    y
    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()
  • abstract def zeros_like(data: Option[Symbol] = None, name: String = null, attr: Map[String, String] = null): Symbol

    Return an array of zeros with the same shape, type and storage type
    as the input array.
    
    The storage type of ``zeros_like`` output depends on the storage type of the input
    
    - zeros_like(row_sparse) = row_sparse
    - zeros_like(csr) = csr
    - zeros_like(default) = default
    
    Examples::
    
      x = [[ 1.,  1.,  1.],
           [ 1.,  1.,  1.]]
    
      zeros_like(x) = [[ 0.,  0.,  0.],
                       [ 0.,  0.,  0.]]
    

  • Return an array of zeros with the same shape, type and storage type
    as the input array.
    
    The storage type of ``zeros_like`` output depends on the storage type of the input
    
    - zeros_like(row_sparse) = row_sparse
    - zeros_like(csr) = csr
    - zeros_like(default) = default
    
    Examples::
    
      x = [[ 1.,  1.,  1.],
           [ 1.,  1.,  1.]]
    
      zeros_like(x) = [[ 0.,  0.,  0.],
                       [ 0.,  0.,  0.]]
    

    data

    The input

    returns

    org.apache.mxnet.Symbol

    Definition Classes
    SymbolAPIBase
    Annotations
    @Experimental()

    Concrete Value Members

    1. final def !=(arg0: Any): Boolean

      Definition Classes
      AnyRef → Any
    2. final def ##(): Int

      Definition Classes
      AnyRef → Any
    3. final def ==(arg0: Any): Boolean

      Definition Classes
      AnyRef → Any
    4. def Custom(op_type: String, kwargs: Map[String, Any], name: String = null, attr: Map[String, String] = null): Symbol

      typesafe Symbol API: Symbol.api._ Main code will be generated during compile time through Macros

    5. final def asInstanceOf[T0]: T0

      Definition Classes
      Any
    6. def clone(): AnyRef

      Attributes
      protected[java.lang]
      Definition Classes
      AnyRef
      Annotations
      @throws( ... )
    7. final def eq(arg0: AnyRef): Boolean

      Definition Classes
      AnyRef
    8. def equals(arg0: Any): Boolean

      Definition Classes
      AnyRef → Any
    9. def finalize(): Unit

      Attributes
      protected[java.lang]
      Definition Classes
      AnyRef
      Annotations
      @throws( classOf[java.lang.Throwable] )
    10. final def getClass(): Class[_]

      Definition Classes
      AnyRef → Any
    11. def hashCode(): Int

      Definition Classes
      AnyRef → Any
    12. final def isInstanceOf[T0]: Boolean

      Definition Classes
      Any
    13. final def ne(arg0: AnyRef): Boolean

      Definition Classes
      AnyRef
    14. final def notify(): Unit

      Definition Classes
      AnyRef
    15. final def notifyAll(): Unit

      Definition Classes
      AnyRef
    16. final def synchronized[T0](arg0: ⇒ T0): T0

      Definition Classes
      AnyRef
    17. def toString(): String

      Definition Classes
      AnyRef → Any
    18. final def wait(): Unit

      Definition Classes
      AnyRef
      Annotations
      @throws( ... )
    19. final def wait(arg0: Long, arg1: Int): Unit

      Definition Classes
      AnyRef
      Annotations
      @throws( ... )
    20. final def wait(arg0: Long): Unit

      Definition Classes
      AnyRef<