org.apache.mxnet

NDArrayBase

Related Doc: package mxnet

abstract class NDArrayBase extends AnyRef

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  1. new NDArrayBase()

Abstract Value Members

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

    Applies an activation function element-wise to the input.
    
    The following activation functions are supported:
    
    - `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
    - `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
    - `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}`
    - `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
    - `softsign`: :math:`y = \frac{x}{1 + abs(x)}`
    
    
    
    Defined in src/operator/nn/activation.cc:L168
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Applies an activation function element-wise to the input.
    
    The following activation functions are supported:
    
    - `relu`: Rectified Linear Unit, :math:`y = max(x, 0)`
    - `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}`
    - `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}`
    - `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))`
    - `softsign`: :math:`y = \frac{x}{1 + abs(x)}`
    
    
    
    Defined in src/operator/nn/activation.cc:L168
    returns

    org.apache.mxnet.NDArrayFuncReturn

  3. abstract def BatchNorm(args: Any*): NDArrayFuncReturn

    Batch normalization.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these
    two outputs are blocked.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
    axis to be the last item in the input shape.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    .. Note::
      When ``fix_gamma`` is set to True, no sparse support is provided. If ``fix_gamma is`` set to False,
      the sparse tensors will fallback.
    
    
    
    Defined in src/operator/nn/batch_norm.cc:L571
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Batch normalization.
    
    Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis:
    
    .. math::
    
      data\_mean[i] = mean(data[:,i,:,...]) \\
      data\_var[i] = var(data[:,i,:,...])
    
    Then compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]
    
    Both *mean* and *var* returns a scalar by treating the input as a vector.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these
    two outputs are blocked.
    
    Besides the inputs and the outputs, this operator accepts two auxiliary
    states, ``moving_mean`` and ``moving_var``, which are *k*-length
    vectors. They are global statistics for the whole dataset, which are updated
    by::
    
      moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
      moving_var = moving_var * momentum + data_var * (1 - momentum)
    
    If ``use_global_stats`` is set to be true, then ``moving_mean`` and
    ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute
    the output. It is often used during inference.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
    axis to be the last item in the input shape.
    
    Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true,
    then set ``gamma`` to 1 and its gradient to 0.
    
    .. Note::
      When ``fix_gamma`` is set to True, no sparse support is provided. If ``fix_gamma is`` set to False,
      the sparse tensors will fallback.
    
    
    
    Defined in src/operator/nn/batch_norm.cc:L571
    returns

    org.apache.mxnet.NDArrayFuncReturn

  5. abstract def BatchNorm_v1(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  7. abstract def BilinearSampler(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  9. abstract def BlockGrad(args: Any*): NDArrayFuncReturn

    Stops gradient computation.
    
    Stops the accumulated gradient of the inputs from flowing through this operator
    in the backward direction. In other words, this operator prevents the contribution
    of its inputs to be taken into account for computing gradients.
    
    Example::
    
      v1 = [1, 2]
      v2 = [0, 1]
      a = Variable('a')
      b = Variable('b')
      b_stop_grad = stop_gradient(3 * b)
      loss = MakeLoss(b_stop_grad + a)
    
      executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
      executor.forward(is_train=True, a=v1, b=v2)
      executor.outputs
      [ 1.  5.]
    
      executor.backward()
      executor.grad_arrays
      [ 0.  0.]
      [ 1.  1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L327
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Stops gradient computation.
    
    Stops the accumulated gradient of the inputs from flowing through this operator
    in the backward direction. In other words, this operator prevents the contribution
    of its inputs to be taken into account for computing gradients.
    
    Example::
    
      v1 = [1, 2]
      v2 = [0, 1]
      a = Variable('a')
      b = Variable('b')
      b_stop_grad = stop_gradient(3 * b)
      loss = MakeLoss(b_stop_grad + a)
    
      executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
      executor.forward(is_train=True, a=v1, b=v2)
      executor.outputs
      [ 1.  5.]
    
      executor.backward()
      executor.grad_arrays
      [ 0.  0.]
      [ 1.  1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L327
    returns

    org.apache.mxnet.NDArrayFuncReturn

  11. abstract def CTCLoss(args: Any*): NDArrayFuncReturn

    Connectionist Temporal Classification Loss.
    
    .. note:: The existing alias ``contrib_CTCLoss`` is deprecated.
    
    The shapes of the inputs and outputs:
    
    - **data**: `(sequence_length, batch_size, alphabet_size)`
    - **label**: `(batch_size, label_sequence_length)`
    - **out**: `(batch_size)`
    
    The `data` tensor consists of sequences of activation vectors (without applying softmax),
    with i-th channel in the last dimension corresponding to i-th label
    for i between 0 and alphabet_size-1 (i.e always 0-indexed).
    Alphabet size should include one additional value reserved for blank label.
    When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for
    activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be
    reserved for blank label.
    
    ``label`` is an index matrix of integers. When `blank_label` is ``"first"``,
    the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
    when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label.
    
    If a sequence of labels is shorter than *label_sequence_length*, use the special
    padding value at the end of the sequence to conform it to the correct
    length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise.
    
    For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences
    'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as
    `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]
    
    When `blank_label` is ``"last"``, we can index the labels as
    `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]
    
    ``out`` is a list of CTC loss values, one per example in the batch.
    
    See *Connectionist Temporal Classification: Labelling Unsegmented
    Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
    information on the definition and the algorithm.
    
    
    
    Defined in src/operator/nn/ctc_loss.cc:L100
    returns

    org.apache.mxnet.NDArrayFuncReturn

  12. abstract def CTCLoss(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Connectionist Temporal Classification Loss.
    
    .. note:: The existing alias ``contrib_CTCLoss`` is deprecated.
    
    The shapes of the inputs and outputs:
    
    - **data**: `(sequence_length, batch_size, alphabet_size)`
    - **label**: `(batch_size, label_sequence_length)`
    - **out**: `(batch_size)`
    
    The `data` tensor consists of sequences of activation vectors (without applying softmax),
    with i-th channel in the last dimension corresponding to i-th label
    for i between 0 and alphabet_size-1 (i.e always 0-indexed).
    Alphabet size should include one additional value reserved for blank label.
    When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for
    activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be
    reserved for blank label.
    
    ``label`` is an index matrix of integers. When `blank_label` is ``"first"``,
    the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
    when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label.
    
    If a sequence of labels is shorter than *label_sequence_length*, use the special
    padding value at the end of the sequence to conform it to the correct
    length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise.
    
    For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences
    'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as
    `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]
    
    When `blank_label` is ``"last"``, we can index the labels as
    `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]
    
    ``out`` is a list of CTC loss values, one per example in the batch.
    
    See *Connectionist Temporal Classification: Labelling Unsegmented
    Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
    information on the definition and the algorithm.
    
    
    
    Defined in src/operator/nn/ctc_loss.cc:L100
    returns

    org.apache.mxnet.NDArrayFuncReturn

  13. abstract def Cast(args: Any*): NDArrayFuncReturn

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L665
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L665
    returns

    org.apache.mxnet.NDArrayFuncReturn

  15. abstract def Concat(args: Any*): NDArrayFuncReturn

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = `[ [1,1],[2,2] ]
       y = `[ [3,3],[4,4],[5,5] ]
       z = `[ [6,6], [7,7],[8,8] ]
    
       concat(x,y,z,dim=0) = `[ [ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.] ]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = `[ [ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.] ]
    
    
    
    Defined in src/operator/nn/concat.cc:L383
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = `[ [1,1],[2,2] ]
       y = `[ [3,3],[4,4],[5,5] ]
       z = `[ [6,6], [7,7],[8,8] ]
    
       concat(x,y,z,dim=0) = `[ [ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.] ]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = `[ [ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.] ]
    
    
    
    Defined in src/operator/nn/concat.cc:L383
    returns

    org.apache.mxnet.NDArrayFuncReturn

  17. abstract def Convolution(args: Any*): NDArrayFuncReturn

    Compute *N*-D convolution on *(N+2)*-D input.
    
    In the 2-D convolution, given input data with shape *(batch_size,
    channel, height, width)*, the output is computed by
    
    .. math::
    
       out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
       weight[i,j,:,:]
    
    where :math:`\star` is the 2-D cross-correlation operator.
    
    For general 2-D convolution, the shapes are
    
    - **data**: *(batch_size, channel, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*.
    
    Define::
    
      f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
    
    then we have::
    
      out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
      out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
    width)*. We can choose other layouts such as *NWC*.
    
    If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
    evenly into *g* parts along the channel axis, and also evenly split ``weight``
    along the first dimension. Next compute the convolution on the *i*-th part of
    the data with the *i*-th weight part. The output is obtained by concatenating all
    the *g* results.
    
    1-D convolution does not have *height* dimension but only *width* in space.
    
    - **data**: *(batch_size, channel, width)*
    - **weight**: *(num_filter, channel, kernel[0])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_width)*.
    
    3-D convolution adds an additional *depth* dimension besides *height* and
    *width*. The shapes are
    
    - **data**: *(batch_size, channel, depth, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
    
    Both ``weight`` and ``bias`` are learnable parameters.
    
    There are other options to tune the performance.
    
    - **cudnn_tune**: enable this option leads to higher startup time but may give
      faster speed. Options are
    
      - **off**: no tuning
      - **limited_workspace**:run test and pick the fastest algorithm that doesn't
        exceed workspace limit.
      - **fastest**: pick the fastest algorithm and ignore workspace limit.
      - **None** (default): the behavior is determined by environment variable
        ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
        (default), 2 for fastest.
    
    - **workspace**: A large number leads to more (GPU) memory usage but may improve
      the performance.
    
    
    
    Defined in src/operator/nn/convolution.cc:L473
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Compute *N*-D convolution on *(N+2)*-D input.
    
    In the 2-D convolution, given input data with shape *(batch_size,
    channel, height, width)*, the output is computed by
    
    .. math::
    
       out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
       weight[i,j,:,:]
    
    where :math:`\star` is the 2-D cross-correlation operator.
    
    For general 2-D convolution, the shapes are
    
    - **data**: *(batch_size, channel, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_height, out_width)*.
    
    Define::
    
      f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1
    
    then we have::
    
      out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])
      out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
    width)*. We can choose other layouts such as *NWC*.
    
    If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
    evenly into *g* parts along the channel axis, and also evenly split ``weight``
    along the first dimension. Next compute the convolution on the *i*-th part of
    the data with the *i*-th weight part. The output is obtained by concatenating all
    the *g* results.
    
    1-D convolution does not have *height* dimension but only *width* in space.
    
    - **data**: *(batch_size, channel, width)*
    - **weight**: *(num_filter, channel, kernel[0])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_width)*.
    
    3-D convolution adds an additional *depth* dimension besides *height* and
    *width*. The shapes are
    
    - **data**: *(batch_size, channel, depth, height, width)*
    - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
    - **bias**: *(num_filter,)*
    - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.
    
    Both ``weight`` and ``bias`` are learnable parameters.
    
    There are other options to tune the performance.
    
    - **cudnn_tune**: enable this option leads to higher startup time but may give
      faster speed. Options are
    
      - **off**: no tuning
      - **limited_workspace**:run test and pick the fastest algorithm that doesn't
        exceed workspace limit.
      - **fastest**: pick the fastest algorithm and ignore workspace limit.
      - **None** (default): the behavior is determined by environment variable
        ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
        (default), 2 for fastest.
    
    - **workspace**: A large number leads to more (GPU) memory usage but may improve
      the performance.
    
    
    
    Defined in src/operator/nn/convolution.cc:L473
    returns

    org.apache.mxnet.NDArrayFuncReturn

  19. abstract def Convolution_v1(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  21. abstract def Correlation(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  23. abstract def Crop(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  25. abstract def Custom(args: Any*): NDArrayFuncReturn

    Apply a custom operator implemented in a frontend language (like Python).
    
    Custom operators should override required methods like `forward` and `backward`.
    The custom operator must be registered before it can be used.
    Please check the tutorial here: https://mxnet.incubator.apache.org/api/faq/new_op
    
    
    
    Defined in src/operator/custom/custom.cc:L546
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Apply a custom operator implemented in a frontend language (like Python).
    
    Custom operators should override required methods like `forward` and `backward`.
    The custom operator must be registered before it can be used.
    Please check the tutorial here: https://mxnet.incubator.apache.org/api/faq/new_op
    
    
    
    Defined in src/operator/custom/custom.cc:L546
    returns

    org.apache.mxnet.NDArrayFuncReturn

  27. abstract def Deconvolution(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  29. abstract def Dropout(args: Any*): NDArrayFuncReturn

    Applies dropout operation to input array.
    
    - During training, each element of the input is set to zero with probability p.
      The whole array is rescaled by :math:`1/(1-p)` to keep the expected
      sum of the input unchanged.
    
    - During testing, this operator does not change the input if mode is 'training'.
      If mode is 'always', the same computaion as during training will be applied.
    
    Example::
    
      random.seed(998)
      input_array = array(`[ [3., 0.5,  -0.5,  2., 7.],
                          [2., -0.4,   7.,  3., 0.2] ])
      a = symbol.Variable('a')
      dropout = symbol.Dropout(a, p = 0.2)
      executor = dropout.simple_bind(a = input_array.shape)
    
      ## If training
      executor.forward(is_train = True, a = input_array)
      executor.outputs
      `[ [ 3.75   0.625 -0.     2.5    8.75 ]
       [ 2.5   -0.5    8.75   3.75   0.   ] ]
    
      ## If testing
      executor.forward(is_train = False, a = input_array)
      executor.outputs
      `[ [ 3.     0.5   -0.5    2.     7.   ]
       [ 2.    -0.4    7.     3.     0.2  ] ]
    
    
    Defined in src/operator/nn/dropout.cc:L96
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Applies dropout operation to input array.
    
    - During training, each element of the input is set to zero with probability p.
      The whole array is rescaled by :math:`1/(1-p)` to keep the expected
      sum of the input unchanged.
    
    - During testing, this operator does not change the input if mode is 'training'.
      If mode is 'always', the same computaion as during training will be applied.
    
    Example::
    
      random.seed(998)
      input_array = array(`[ [3., 0.5,  -0.5,  2., 7.],
                          [2., -0.4,   7.,  3., 0.2] ])
      a = symbol.Variable('a')
      dropout = symbol.Dropout(a, p = 0.2)
      executor = dropout.simple_bind(a = input_array.shape)
    
      ## If training
      executor.forward(is_train = True, a = input_array)
      executor.outputs
      `[ [ 3.75   0.625 -0.     2.5    8.75 ]
       [ 2.5   -0.5    8.75   3.75   0.   ] ]
    
      ## If testing
      executor.forward(is_train = False, a = input_array)
      executor.outputs
      `[ [ 3.     0.5   -0.5    2.     7.   ]
       [ 2.    -0.4    7.     3.     0.2  ] ]
    
    
    Defined in src/operator/nn/dropout.cc:L96
    returns

    org.apache.mxnet.NDArrayFuncReturn

  31. abstract def ElementWiseSum(args: Any*): NDArrayFuncReturn

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

  33. abstract def Embedding(args: Any*): NDArrayFuncReturn

    Maps integer indices to vector representations (embeddings).
    
    This operator maps words to real-valued vectors in a high-dimensional space,
    called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
    For example, it has been noted that in the learned embedding spaces, similar words tend
    to be close to each other and dissimilar words far apart.
    
    For an input array of shape (d1, ..., dK),
    the shape of an output array is (d1, ..., dK, output_dim).
    All the input values should be integers in the range [0, input_dim).
    
    If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
    (ip0, op0).
    
    When "sparse_grad" is False, if any index mentioned is too large, it is replaced by the index that
    addresses the last vector in an embedding matrix.
    When "sparse_grad" is True, an error will be raised if invalid indices are found.
    
    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:L539
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Maps integer indices to vector representations (embeddings).
    
    This operator maps words to real-valued vectors in a high-dimensional space,
    called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
    For example, it has been noted that in the learned embedding spaces, similar words tend
    to be close to each other and dissimilar words far apart.
    
    For an input array of shape (d1, ..., dK),
    the shape of an output array is (d1, ..., dK, output_dim).
    All the input values should be integers in the range [0, input_dim).
    
    If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
    (ip0, op0).
    
    When "sparse_grad" is False, if any index mentioned is too large, it is replaced by the index that
    addresses the last vector in an embedding matrix.
    When "sparse_grad" is True, an error will be raised if invalid indices are found.
    
    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:L539
    returns

    org.apache.mxnet.NDArrayFuncReturn

  35. abstract def Flatten(args: Any*): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    Note that the behavior 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:L250
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    Note that the behavior 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:L250
    returns

    org.apache.mxnet.NDArrayFuncReturn

  37. abstract def FullyConnected(args: Any*): NDArrayFuncReturn

    Applies a linear transformation: :math:`Y = XW^T + b`.
    
    If ``flatten`` is set to be true, then the shapes are:
    
    - **data**: `(batch_size, x1, x2, ..., xn)`
    - **weight**: `(num_hidden, x1 * x2 * ... * xn)`
    - **bias**: `(num_hidden,)`
    - **out**: `(batch_size, num_hidden)`
    
    If ``flatten`` is set to be false, then the shapes are:
    
    - **data**: `(x1, x2, ..., xn, input_dim)`
    - **weight**: `(num_hidden, input_dim)`
    - **bias**: `(num_hidden,)`
    - **out**: `(x1, x2, ..., xn, num_hidden)`
    
    The learnable parameters include both ``weight`` and ``bias``.
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    .. Note::
    
        The sparse support for FullyConnected is limited to forward evaluation with `row_sparse`
        weight and bias, where the length of `weight.indices` and `bias.indices` must be equal
        to `num_hidden`. This could be useful for model inference with `row_sparse` weights
        trained with importance sampling or noise contrastive estimation.
    
        To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
        of sparse.FullyConnected.
    
    
    
    Defined in src/operator/nn/fully_connected.cc:L291
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Applies a linear transformation: :math:`Y = XW^T + b`.
    
    If ``flatten`` is set to be true, then the shapes are:
    
    - **data**: `(batch_size, x1, x2, ..., xn)`
    - **weight**: `(num_hidden, x1 * x2 * ... * xn)`
    - **bias**: `(num_hidden,)`
    - **out**: `(batch_size, num_hidden)`
    
    If ``flatten`` is set to be false, then the shapes are:
    
    - **data**: `(x1, x2, ..., xn, input_dim)`
    - **weight**: `(num_hidden, input_dim)`
    - **bias**: `(num_hidden,)`
    - **out**: `(x1, x2, ..., xn, num_hidden)`
    
    The learnable parameters include both ``weight`` and ``bias``.
    
    If ``no_bias`` is set to be true, then the ``bias`` term is ignored.
    
    .. Note::
    
        The sparse support for FullyConnected is limited to forward evaluation with `row_sparse`
        weight and bias, where the length of `weight.indices` and `bias.indices` must be equal
        to `num_hidden`. This could be useful for model inference with `row_sparse` weights
        trained with importance sampling or noise contrastive estimation.
    
        To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
        of sparse.FullyConnected.
    
    
    
    Defined in src/operator/nn/fully_connected.cc:L291
    returns

    org.apache.mxnet.NDArrayFuncReturn

  39. abstract def GridGenerator(args: Any*): NDArrayFuncReturn

    Generates 2D sampling grid for bilinear sampling.
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Generates 2D sampling grid for bilinear sampling.
    returns

    org.apache.mxnet.NDArrayFuncReturn

  41. abstract def GroupNorm(args: Any*): NDArrayFuncReturn

    Group normalization.
    
    The input channels are separated into ``num_groups`` groups, each containing ``num_channels / num_groups`` channels.
    The mean and standard-deviation are calculated separately over the each group.
    
    .. math::
    
      data = data.reshape((N, num_groups, C // num_groups, ...))
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    
    
    Defined in src/operator/nn/group_norm.cc:L77
    returns

    org.apache.mxnet.NDArrayFuncReturn

  42. abstract def GroupNorm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Group normalization.
    
    The input channels are separated into ``num_groups`` groups, each containing ``num_channels / num_groups`` channels.
    The mean and standard-deviation are calculated separately over the each group.
    
    .. math::
    
      data = data.reshape((N, num_groups, C // num_groups, ...))
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    
    
    Defined in src/operator/nn/group_norm.cc:L77
    returns

    org.apache.mxnet.NDArrayFuncReturn

  43. abstract def IdentityAttachKLSparseReg(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  45. abstract def InstanceNorm(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  47. abstract def L2Normalization(args: Any*): NDArrayFuncReturn

    Normalize the input array using the L2 norm.
    
    For 1-D NDArray, it computes::
    
      out = data / sqrt(sum(data ** 2) + eps)
    
    For N-D NDArray, if the input array has shape (N, N, ..., N),
    
    with ``mode`` = ``instance``, it normalizes each instance in the multidimensional
    array by its L2 norm.::
    
      for i in 0...N
        out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.::
    
      for i in 0...N
        out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position
    in the array by its L2 norm.::
    
      for dim in 2...N
        for i in 0...N
          out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
              -dim-
    
    Example::
    
      x = `[ `[ [1,2],
            [3,4] ],
           `[ [2,2],
            [5,6] ] ]
    
      L2Normalization(x, mode='instance')
      =`[ `[ [ 0.18257418  0.36514837]
         [ 0.54772252  0.73029673] ]
        `[ [ 0.24077171  0.24077171]
         [ 0.60192931  0.72231513] ] ]
    
      L2Normalization(x, mode='channel')
      =`[ `[ [ 0.31622776  0.44721359]
         [ 0.94868326  0.89442718] ]
        `[ [ 0.37139067  0.31622776]
         [ 0.92847669  0.94868326] ] ]
    
      L2Normalization(x, mode='spatial')
      =`[ `[ [ 0.44721359  0.89442718]
         [ 0.60000002  0.80000001] ]
        `[ [ 0.70710677  0.70710677]
         [ 0.6401844   0.76822126] ] ]
    
    
    
    Defined in src/operator/l2_normalization.cc:L196
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Normalize the input array using the L2 norm.
    
    For 1-D NDArray, it computes::
    
      out = data / sqrt(sum(data ** 2) + eps)
    
    For N-D NDArray, if the input array has shape (N, N, ..., N),
    
    with ``mode`` = ``instance``, it normalizes each instance in the multidimensional
    array by its L2 norm.::
    
      for i in 0...N
        out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.::
    
      for i in 0...N
        out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)
    
    with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position
    in the array by its L2 norm.::
    
      for dim in 2...N
        for i in 0...N
          out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
              -dim-
    
    Example::
    
      x = `[ `[ [1,2],
            [3,4] ],
           `[ [2,2],
            [5,6] ] ]
    
      L2Normalization(x, mode='instance')
      =`[ `[ [ 0.18257418  0.36514837]
         [ 0.54772252  0.73029673] ]
        `[ [ 0.24077171  0.24077171]
         [ 0.60192931  0.72231513] ] ]
    
      L2Normalization(x, mode='channel')
      =`[ `[ [ 0.31622776  0.44721359]
         [ 0.94868326  0.89442718] ]
        `[ [ 0.37139067  0.31622776]
         [ 0.92847669  0.94868326] ] ]
    
      L2Normalization(x, mode='spatial')
      =`[ `[ [ 0.44721359  0.89442718]
         [ 0.60000002  0.80000001] ]
        `[ [ 0.70710677  0.70710677]
         [ 0.6401844   0.76822126] ] ]
    
    
    
    Defined in src/operator/l2_normalization.cc:L196
    returns

    org.apache.mxnet.NDArrayFuncReturn

  49. abstract def LRN(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  51. abstract def LayerNorm(args: Any*): NDArrayFuncReturn

    Layer normalization.
    
    Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis and then
    compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_std``. Note that no gradient will be passed through these two outputs.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is -1, which sets the channel
    axis to be the last item in the input shape.
    
    
    
    Defined in src/operator/nn/layer_norm.cc:L156
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Layer normalization.
    
    Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as
    well as offset ``beta``.
    
    Assume the input has more than one dimension and we normalize along axis 1.
    We first compute the mean and variance along this axis and then
    compute the normalized output, which has the same shape as input, as following:
    
    .. math::
    
      out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta
    
    Both ``gamma`` and ``beta`` are learnable parameters.
    
    Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.
    
    Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta``
    have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and
    ``data_std``. Note that no gradient will be passed through these two outputs.
    
    The parameter ``axis`` specifies which axis of the input shape denotes
    the 'channel' (separately normalized groups).  The default is -1, which sets the channel
    axis to be the last item in the input shape.
    
    
    
    Defined in src/operator/nn/layer_norm.cc:L156
    returns

    org.apache.mxnet.NDArrayFuncReturn

  53. abstract def LeakyReLU(args: Any*): NDArrayFuncReturn

    Applies Leaky rectified linear unit activation element-wise to the input.
    
    Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope`
    when the input is negative and has a slope of one when input is positive.
    
    The following modified ReLU Activation functions are supported:
    
    - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)`
    - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where
      *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
    - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x`
    - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training.
    - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from
      *[lower_bound, upper_bound)* for training, while fixed to be
      *(lower_bound+upper_bound)/2* for inference.
    
    
    
    Defined in src/operator/leaky_relu.cc:L161
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Applies Leaky rectified linear unit activation element-wise to the input.
    
    Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope`
    when the input is negative and has a slope of one when input is positive.
    
    The following modified ReLU Activation functions are supported:
    
    - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)`
    - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where
      *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
    - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x`
    - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training.
    - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from
      *[lower_bound, upper_bound)* for training, while fixed to be
      *(lower_bound+upper_bound)/2* for inference.
    
    
    
    Defined in src/operator/leaky_relu.cc:L161
    returns

    org.apache.mxnet.NDArrayFuncReturn

  55. abstract def LinearRegressionOutput(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  57. abstract def LogisticRegressionOutput(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  59. abstract def MAERegressionOutput(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  61. abstract def MakeLoss(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  63. abstract def Pad(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  65. abstract def Pooling(args: Any*): NDArrayFuncReturn

    Performs pooling on the input.
    
    The shapes for 1-D pooling are
    
    - **data** and **out**: *(batch_size, channel, width)* (NCW layout) or
      *(batch_size, width, channel)* (NWC layout),
    
    The shapes for 2-D pooling are
    
    - **data** and **out**: *(batch_size, channel, height, width)* (NCHW layout) or
      *(batch_size, height, width, channel)* (NHWC layout),
    
        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
    
    When ``global_pool`` is set to be true, then global pooling is performed. It will reset
    ``kernel=(height, width)`` and set the appropiate padding to 0.
    
    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 and output will have shape *(batch_size, channel, depth,
    height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout).
    
    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:L417
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Performs pooling on the input.
    
    The shapes for 1-D pooling are
    
    - **data** and **out**: *(batch_size, channel, width)* (NCW layout) or
      *(batch_size, width, channel)* (NWC layout),
    
    The shapes for 2-D pooling are
    
    - **data** and **out**: *(batch_size, channel, height, width)* (NCHW layout) or
      *(batch_size, height, width, channel)* (NHWC layout),
    
        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
    
    When ``global_pool`` is set to be true, then global pooling is performed. It will reset
    ``kernel=(height, width)`` and set the appropiate padding to 0.
    
    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 and output will have shape *(batch_size, channel, depth,
    height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout).
    
    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:L417
    returns

    org.apache.mxnet.NDArrayFuncReturn

  67. abstract def Pooling_v1(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  69. abstract def RNN(args: Any*): NDArrayFuncReturn

    Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
    implemented, with both multi-layer and bidirectional support.
    
    When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
    and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
    pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
    Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.
    
    **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}
    
    
    Defined in src/operator/rnn.cc:L354
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
    implemented, with both multi-layer and bidirectional support.
    
    When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
    and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
    pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
    Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.
    
    **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}
    
    
    Defined in src/operator/rnn.cc:L354
    returns

    org.apache.mxnet.NDArrayFuncReturn

  71. abstract def ROIPooling(args: Any*): NDArrayFuncReturn

    Performs region of interest(ROI) pooling on the input array.
    
    ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
    region of interest is a parameter. Its purpose is to perform max pooling on the inputs
    of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
    layer mostly used in training a `Fast R-CNN` network for object detection.
    
    This operator takes a 4D feature map as an input array and region proposals as `rois`,
    then it pools over sub-regions of input and produces a fixed-sized output array
    regardless of the ROI size.
    
    To crop the feature map accordingly, you can resize the bounding box coordinates
    by changing the parameters `rois` and `spatial_scale`.
    
    The cropped feature maps are pooled by standard max pooling operation to a fixed size output
    indicated by a `pooled_size` parameter. batch_size will change to the number of region
    bounding boxes after `ROIPooling`.
    
    The size of each region of interest doesn't have to be perfectly divisible by
    the number of pooling sections(`pooled_size`).
    
    Example::
    
      x = `[ [`[ [  0.,   1.,   2.,   3.,   4.,   5.],
             [  6.,   7.,   8.,   9.,  10.,  11.],
             [ 12.,  13.,  14.,  15.,  16.,  17.],
             [ 18.,  19.,  20.,  21.,  22.,  23.],
             [ 24.,  25.,  26.,  27.,  28.,  29.],
             [ 30.,  31.,  32.,  33.,  34.,  35.],
             [ 36.,  37.,  38.,  39.,  40.,  41.],
             [ 42.,  43.,  44.,  45.,  46.,  47.] ] ] ]
    
      // region of interest i.e. bounding box coordinates.
      y = `[ [0,0,0,4,4] ]
    
      // returns array of shape (2,2) according to the given roi with max pooling.
      ROIPooling(x, y, (2,2), 1.0) = `[ [`[ [ 14.,  16.],
                                        [ 26.,  28.] ] ] ]
    
      // region of interest is changed due to the change in `spacial_scale` parameter.
      ROIPooling(x, y, (2,2), 0.7) = `[ [`[ [  7.,   9.],
                                        [ 19.,  21.] ] ] ]
    
    
    
    Defined in src/operator/roi_pooling.cc:L225
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Performs region of interest(ROI) pooling on the input array.
    
    ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
    region of interest is a parameter. Its purpose is to perform max pooling on the inputs
    of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
    layer mostly used in training a `Fast R-CNN` network for object detection.
    
    This operator takes a 4D feature map as an input array and region proposals as `rois`,
    then it pools over sub-regions of input and produces a fixed-sized output array
    regardless of the ROI size.
    
    To crop the feature map accordingly, you can resize the bounding box coordinates
    by changing the parameters `rois` and `spatial_scale`.
    
    The cropped feature maps are pooled by standard max pooling operation to a fixed size output
    indicated by a `pooled_size` parameter. batch_size will change to the number of region
    bounding boxes after `ROIPooling`.
    
    The size of each region of interest doesn't have to be perfectly divisible by
    the number of pooling sections(`pooled_size`).
    
    Example::
    
      x = `[ [`[ [  0.,   1.,   2.,   3.,   4.,   5.],
             [  6.,   7.,   8.,   9.,  10.,  11.],
             [ 12.,  13.,  14.,  15.,  16.,  17.],
             [ 18.,  19.,  20.,  21.,  22.,  23.],
             [ 24.,  25.,  26.,  27.,  28.,  29.],
             [ 30.,  31.,  32.,  33.,  34.,  35.],
             [ 36.,  37.,  38.,  39.,  40.,  41.],
             [ 42.,  43.,  44.,  45.,  46.,  47.] ] ] ]
    
      // region of interest i.e. bounding box coordinates.
      y = `[ [0,0,0,4,4] ]
    
      // returns array of shape (2,2) according to the given roi with max pooling.
      ROIPooling(x, y, (2,2), 1.0) = `[ [`[ [ 14.,  16.],
                                        [ 26.,  28.] ] ] ]
    
      // region of interest is changed due to the change in `spacial_scale` parameter.
      ROIPooling(x, y, (2,2), 0.7) = `[ [`[ [  7.,   9.],
                                        [ 19.,  21.] ] ] ]
    
    
    
    Defined in src/operator/roi_pooling.cc:L225
    returns

    org.apache.mxnet.NDArrayFuncReturn

  73. abstract def Reshape(args: Any*): NDArrayFuncReturn

    Reshapes the input array.
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    Example::
      reshape([1,2,3,4], shape=(2,2)) = `[ [1,2], [3,4] ]
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    - ``0``  copy this dimension from the input to the output shape.
      Example::
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
      Example::
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
      Example::
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
      Example::
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
      Example::
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
      Example::
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    Defined in src/operator/tensor/matrix_op.cc:L175
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Reshapes the input array.
    .. note:: ``Reshape`` is deprecated, use ``reshape``
    Given an array and a shape, this function returns a copy of the array in the new shape.
    The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.
    Example::
      reshape([1,2,3,4], shape=(2,2)) = `[ [1,2], [3,4] ]
    Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:
    - ``0``  copy this dimension from the input to the output shape.
      Example::
      - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
      - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)
    - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
      keeping the size of the new array same as that of the input array.
      At most one dimension of shape can be -1.
      Example::
      - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
      - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
      - input shape = (2,3,4), shape=(-1,), output shape = (24,)
    - ``-2`` copy all/remainder of the input dimensions to the output shape.
      Example::
      - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
      - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)
    - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.
      Example::
      - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
      - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
      - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
      - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)
    - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).
      Example::
      - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
      - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)
    If the argument `reverse` is set to 1, then the special values are inferred from right to left.
      Example::
      - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
      - with reverse=1, output shape will be (50,4).
    
    
    Defined in src/operator/tensor/matrix_op.cc:L175
    returns

    org.apache.mxnet.NDArrayFuncReturn

  75. abstract def SVMOutput(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  77. abstract def SequenceLast(args: Any*): NDArrayFuncReturn

    Takes the last element of a sequence.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
    of the form [batch_size, other_feature_dims].
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be
    an input array of positive ints of dimension [batch_size]. To use this parameter,
    set `use_sequence_length` to `True`, otherwise each example in the batch is assumed
    to have the max sequence length.
    
    .. note:: Alternatively, you can also use `take` operator.
    
    Example::
    
       x = `[ `[ [  1.,   2.,   3.],
             [  4.,   5.,   6.],
             [  7.,   8.,   9.] ],
    
            `[ [ 10.,   11.,   12.],
             [ 13.,   14.,   15.],
             [ 16.,   17.,   18.] ],
    
            `[ [  19.,   20.,   21.],
             [  22.,   23.,   24.],
             [  25.,   26.,   27.] ] ]
    
       // returns last sequence when sequence_length parameter is not used
       SequenceLast(x) = `[ [  19.,   20.,   21.],
                          [  22.,   23.,   24.],
                          [  25.,   26.,   27.] ]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
                `[ [  1.,   2.,   3.],
                 [  4.,   5.,   6.],
                 [  7.,   8.,   9.] ]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
                `[ [  1.,    2.,   3.],
                 [  13.,  14.,  15.],
                 [  25.,  26.,  27.] ]
    
    
    
    Defined in src/operator/sequence_last.cc:L106
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Takes the last element of a sequence.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
    of the form [batch_size, other_feature_dims].
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be
    an input array of positive ints of dimension [batch_size]. To use this parameter,
    set `use_sequence_length` to `True`, otherwise each example in the batch is assumed
    to have the max sequence length.
    
    .. note:: Alternatively, you can also use `take` operator.
    
    Example::
    
       x = `[ `[ [  1.,   2.,   3.],
             [  4.,   5.,   6.],
             [  7.,   8.,   9.] ],
    
            `[ [ 10.,   11.,   12.],
             [ 13.,   14.,   15.],
             [ 16.,   17.,   18.] ],
    
            `[ [  19.,   20.,   21.],
             [  22.,   23.,   24.],
             [  25.,   26.,   27.] ] ]
    
       // returns last sequence when sequence_length parameter is not used
       SequenceLast(x) = `[ [  19.,   20.,   21.],
                          [  22.,   23.,   24.],
                          [  25.,   26.,   27.] ]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
                `[ [  1.,   2.,   3.],
                 [  4.,   5.,   6.],
                 [  7.,   8.,   9.] ]
    
       // sequence_length is used
       SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
                `[ [  1.,    2.,   3.],
                 [  13.,  14.,  15.],
                 [  25.,  26.,  27.] ]
    
    
    
    Defined in src/operator/sequence_last.cc:L106
    returns

    org.apache.mxnet.NDArrayFuncReturn

  79. abstract def SequenceMask(args: Any*): NDArrayFuncReturn

    Sets all elements outside the sequence to a constant value.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length`
    should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length and
    this operator works as the `identity` operator.
    
    Example::
    
       x = `[ `[ [  1.,   2.,   3.],
             [  4.,   5.,   6.] ],
    
            `[ [  7.,   8.,   9.],
             [ 10.,  11.,  12.] ],
    
            `[ [ 13.,  14.,   15.],
             [ 16.,  17.,   18.] ] ]
    
       // Batch 1
       B1 = `[ [  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.] ]
    
       // Batch 2
       B2 = `[ [  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.] ]
    
       // works as identity operator when sequence_length parameter is not used
       SequenceMask(x) = `[ `[ [  1.,   2.,   3.],
                           [  4.,   5.,   6.] ],
    
                          `[ [  7.,   8.,   9.],
                           [ 10.,  11.,  12.] ],
    
                          `[ [ 13.,  14.,   15.],
                           [ 16.,  17.,   18.] ] ]
    
       // sequence_length [1,1] means 1 of each batch will be kept
       // and other rows are masked with default mask value = 0
       SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) =
                    `[ `[ [  1.,   2.,   3.],
                      [  4.,   5.,   6.] ],
    
                     `[ [  0.,   0.,   0.],
                      [  0.,   0.,   0.] ],
    
                     `[ [  0.,   0.,   0.],
                      [  0.,   0.,   0.] ] ]
    
       // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
       // and other rows are masked with value = 1
       SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) =
                    `[ `[ [  1.,   2.,   3.],
                      [  4.,   5.,   6.] ],
    
                     `[ [  7.,   8.,   9.],
                      [  10.,  11.,  12.] ],
    
                     `[ [   1.,   1.,   1.],
                      [  16.,  17.,  18.] ] ]
    
    
    
    Defined in src/operator/sequence_mask.cc:L186
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Sets all elements outside the sequence to a constant value.
    
    This function takes an n-dimensional input array of the form
    [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length`
    should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length and
    this operator works as the `identity` operator.
    
    Example::
    
       x = `[ `[ [  1.,   2.,   3.],
             [  4.,   5.,   6.] ],
    
            `[ [  7.,   8.,   9.],
             [ 10.,  11.,  12.] ],
    
            `[ [ 13.,  14.,   15.],
             [ 16.,  17.,   18.] ] ]
    
       // Batch 1
       B1 = `[ [  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.] ]
    
       // Batch 2
       B2 = `[ [  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.] ]
    
       // works as identity operator when sequence_length parameter is not used
       SequenceMask(x) = `[ `[ [  1.,   2.,   3.],
                           [  4.,   5.,   6.] ],
    
                          `[ [  7.,   8.,   9.],
                           [ 10.,  11.,  12.] ],
    
                          `[ [ 13.,  14.,   15.],
                           [ 16.,  17.,   18.] ] ]
    
       // sequence_length [1,1] means 1 of each batch will be kept
       // and other rows are masked with default mask value = 0
       SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) =
                    `[ `[ [  1.,   2.,   3.],
                      [  4.,   5.,   6.] ],
    
                     `[ [  0.,   0.,   0.],
                      [  0.,   0.,   0.] ],
    
                     `[ [  0.,   0.,   0.],
                      [  0.,   0.,   0.] ] ]
    
       // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
       // and other rows are masked with value = 1
       SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) =
                    `[ `[ [  1.,   2.,   3.],
                      [  4.,   5.,   6.] ],
    
                     `[ [  7.,   8.,   9.],
                      [  10.,  11.,  12.] ],
    
                     `[ [   1.,   1.,   1.],
                      [  16.,  17.,  18.] ] ]
    
    
    
    Defined in src/operator/sequence_mask.cc:L186
    returns

    org.apache.mxnet.NDArrayFuncReturn

  81. abstract def SequenceReverse(args: Any*): NDArrayFuncReturn

    Reverses the elements of each sequence.
    
    This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
    and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences.
    `sequence_length` should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length.
    
    Example::
    
       x = `[ `[ [  1.,   2.,   3.],
             [  4.,   5.,   6.] ],
    
            `[ [  7.,   8.,   9.],
             [ 10.,  11.,  12.] ],
    
            `[ [ 13.,  14.,   15.],
             [ 16.,  17.,   18.] ] ]
    
       // Batch 1
       B1 = `[ [  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.] ]
    
       // Batch 2
       B2 = `[ [  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.] ]
    
       // returns reverse sequence when sequence_length parameter is not used
       SequenceReverse(x) = `[ `[ [ 13.,  14.,   15.],
                              [ 16.,  17.,   18.] ],
    
                             `[ [  7.,   8.,   9.],
                              [ 10.,  11.,  12.] ],
    
                             `[ [  1.,   2.,   3.],
                              [  4.,   5.,   6.] ] ]
    
       // sequence_length [2,2] means 2 rows of
       // both batch B1 and B2 will be reversed.
       SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
                         `[ `[ [  7.,   8.,   9.],
                           [ 10.,  11.,  12.] ],
    
                          `[ [  1.,   2.,   3.],
                           [  4.,   5.,   6.] ],
    
                          `[ [ 13.,  14.,   15.],
                           [ 16.,  17.,   18.] ] ]
    
       // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
       // will be reversed.
       SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
                        `[ `[ [  7.,   8.,   9.],
                          [ 16.,  17.,  18.] ],
    
                         `[ [  1.,   2.,   3.],
                          [ 10.,  11.,  12.] ],
    
                         `[ [ 13.,  14,   15.],
                          [  4.,   5.,   6.] ] ]
    
    
    
    Defined in src/operator/sequence_reverse.cc:L122
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Reverses the elements of each sequence.
    
    This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
    and returns an array of the same shape.
    
    Parameter `sequence_length` is used to handle variable-length sequences.
    `sequence_length` should be an input array of positive ints of dimension [batch_size].
    To use this parameter, set `use_sequence_length` to `True`,
    otherwise each example in the batch is assumed to have the max sequence length.
    
    Example::
    
       x = `[ `[ [  1.,   2.,   3.],
             [  4.,   5.,   6.] ],
    
            `[ [  7.,   8.,   9.],
             [ 10.,  11.,  12.] ],
    
            `[ [ 13.,  14.,   15.],
             [ 16.,  17.,   18.] ] ]
    
       // Batch 1
       B1 = `[ [  1.,   2.,   3.],
             [  7.,   8.,   9.],
             [ 13.,  14.,  15.] ]
    
       // Batch 2
       B2 = `[ [  4.,   5.,   6.],
             [ 10.,  11.,  12.],
             [ 16.,  17.,  18.] ]
    
       // returns reverse sequence when sequence_length parameter is not used
       SequenceReverse(x) = `[ `[ [ 13.,  14.,   15.],
                              [ 16.,  17.,   18.] ],
    
                             `[ [  7.,   8.,   9.],
                              [ 10.,  11.,  12.] ],
    
                             `[ [  1.,   2.,   3.],
                              [  4.,   5.,   6.] ] ]
    
       // sequence_length [2,2] means 2 rows of
       // both batch B1 and B2 will be reversed.
       SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
                         `[ `[ [  7.,   8.,   9.],
                           [ 10.,  11.,  12.] ],
    
                          `[ [  1.,   2.,   3.],
                           [  4.,   5.,   6.] ],
    
                          `[ [ 13.,  14.,   15.],
                           [ 16.,  17.,   18.] ] ]
    
       // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
       // will be reversed.
       SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
                        `[ `[ [  7.,   8.,   9.],
                          [ 16.,  17.,  18.] ],
    
                         `[ [  1.,   2.,   3.],
                          [ 10.,  11.,  12.] ],
    
                         `[ [ 13.,  14,   15.],
                          [  4.,   5.,   6.] ] ]
    
    
    
    Defined in src/operator/sequence_reverse.cc:L122
    returns

    org.apache.mxnet.NDArrayFuncReturn

  83. abstract def SliceChannel(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  85. abstract def Softmax(args: Any*): NDArrayFuncReturn

    Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = `[ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          `[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ] ]
          ## backward gradient output
          `[ [ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75] ]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L231
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = `[ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          `[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ] ]
          ## backward gradient output
          `[ [ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75] ]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L231
    returns

    org.apache.mxnet.NDArrayFuncReturn

  87. abstract def SoftmaxActivation(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  89. abstract def SoftmaxOutput(args: Any*): NDArrayFuncReturn

    Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = `[ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          `[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ] ]
          ## backward gradient output
          `[ [ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75] ]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L231
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Computes the gradient of cross entropy loss with respect to softmax output.
    
    - This operator computes the gradient in two steps.
      The cross entropy loss does not actually need to be computed.
    
      - Applies softmax function on the input array.
      - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
    
    - The softmax function, cross entropy loss and gradient is given by:
    
      - Softmax Function:
    
        .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
        .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
      - The gradient of cross entropy loss w.r.t softmax output:
    
        .. math:: \text{gradient} = \text{output} - \text{label}
    
    - During forward propagation, the softmax function is computed for each instance in the input array.
    
      For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is
      :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape`
      and `multi_output` to specify the way to compute softmax:
    
      - By default, `preserve_shape` is ``false``. This operator will reshape the input array
        into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for
        each row in the reshaped array, and afterwards reshape it back to the original shape
        :math:`(d_1, d_2, ..., d_n)`.
      - If `preserve_shape` is ``true``, the softmax function will be computed along
        the last axis (`axis` = ``-1``).
      - If `multi_output` is ``true``, the softmax function will be computed along
        the second axis (`axis` = ``1``).
    
    - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
      The provided label can be a one-hot label array or a probability label array.
    
      - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances
        with a particular label to be ignored during backward propagation. **This has no effect when
        softmax `output` has same shape as `label`**.
    
        Example::
    
          data = `[ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
          label = [1,0,2,3]
          ignore_label = 1
          SoftmaxOutput(data=data, label = label,\
                        multi_output=true, use_ignore=true,\
                        ignore_label=ignore_label)
          ## forward softmax output
          `[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ]
           [ 0.25        0.25        0.25        0.25      ] ]
          ## backward gradient output
          `[ [ 0.    0.    0.    0.  ]
           [-0.75  0.25  0.25  0.25]
           [ 0.25  0.25 -0.75  0.25]
           [ 0.25  0.25  0.25 -0.75] ]
          ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.
    
      - The parameter `grad_scale` can be used to rescale the gradient, which is often used to
        give each loss function different weights.
    
      - This operator also supports various ways to normalize the gradient by `normalization`,
        The `normalization` is applied if softmax output has different shape than the labels.
        The `normalization` mode can be set to the followings:
    
        - ``'null'``: do nothing.
        - ``'batch'``: divide the gradient by the batch size.
        - ``'valid'``: divide the gradient by the number of instances which are not ignored.
    
    
    
    Defined in src/operator/softmax_output.cc:L231
    returns

    org.apache.mxnet.NDArrayFuncReturn

  91. abstract def SpatialTransformer(args: Any*): NDArrayFuncReturn

    Applies a spatial transformer to input feature map.
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Applies a spatial transformer to input feature map.
    returns

    org.apache.mxnet.NDArrayFuncReturn

  93. abstract def SwapAxis(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  95. abstract def UpSampling(args: Any*): NDArrayFuncReturn

    Upsamples the given input data.
    
    Two algorithms (``sample_type``) are available for upsampling:
    
    - Nearest Neighbor
    - Bilinear
    
    **Nearest Neighbor Upsampling**
    
    Input data is expected to be NCHW.
    
    Example::
    
      x = `[ [`[ [1. 1. 1.]
             [1. 1. 1.]
             [1. 1. 1.] ] ] ]
    
      UpSampling(x, scale=2, sample_type='nearest') = `[ [`[ [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.] ] ] ]
    
    **Bilinear Upsampling**
    
    Uses `deconvolution` algorithm under the hood. You need provide both input data and the kernel.
    
    Input data is expected to be NCHW.
    
    `num_filter` is expected to be same as the number of channels.
    
    Example::
    
      x = `[ [`[ [1. 1. 1.]
             [1. 1. 1.]
             [1. 1. 1.] ] ] ]
    
      w = `[ [`[ [1. 1. 1. 1.]
             [1. 1. 1. 1.]
             [1. 1. 1. 1.]
             [1. 1. 1. 1.] ] ] ]
    
      UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = `[ [`[ [1. 2. 2. 2. 2. 1.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [1. 2. 2. 2. 2. 1.] ] ] ]
    
    
    Defined in src/operator/nn/upsampling.cc:L173
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Upsamples the given input data.
    
    Two algorithms (``sample_type``) are available for upsampling:
    
    - Nearest Neighbor
    - Bilinear
    
    **Nearest Neighbor Upsampling**
    
    Input data is expected to be NCHW.
    
    Example::
    
      x = `[ [`[ [1. 1. 1.]
             [1. 1. 1.]
             [1. 1. 1.] ] ] ]
    
      UpSampling(x, scale=2, sample_type='nearest') = `[ [`[ [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.]
                                                         [1. 1. 1. 1. 1. 1.] ] ] ]
    
    **Bilinear Upsampling**
    
    Uses `deconvolution` algorithm under the hood. You need provide both input data and the kernel.
    
    Input data is expected to be NCHW.
    
    `num_filter` is expected to be same as the number of channels.
    
    Example::
    
      x = `[ [`[ [1. 1. 1.]
             [1. 1. 1.]
             [1. 1. 1.] ] ] ]
    
      w = `[ [`[ [1. 1. 1. 1.]
             [1. 1. 1. 1.]
             [1. 1. 1. 1.]
             [1. 1. 1. 1.] ] ] ]
    
      UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = `[ [`[ [1. 2. 2. 2. 2. 1.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [2. 4. 4. 4. 4. 2.]
                                                                           [1. 2. 2. 2. 2. 1.] ] ] ]
    
    
    Defined in src/operator/nn/upsampling.cc:L173
    returns

    org.apache.mxnet.NDArrayFuncReturn

  97. abstract def abs(args: Any*): NDArrayFuncReturn

    Returns element-wise absolute value of the input.
    
    Example::
    
       abs([-2, 0, 3]) = [2, 0, 3]
    
    The storage type of ``abs`` output depends upon the input storage type:
    
       - abs(default) = default
       - abs(row_sparse) = row_sparse
       - abs(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L721
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise absolute value of the input.
    
    Example::
    
       abs([-2, 0, 3]) = [2, 0, 3]
    
    The storage type of ``abs`` output depends upon the input storage type:
    
       - abs(default) = default
       - abs(row_sparse) = row_sparse
       - abs(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L721
    returns

    org.apache.mxnet.NDArrayFuncReturn

  99. abstract def adam_update(args: Any*): NDArrayFuncReturn

    Update function for Adam optimizer. Adam is seen as a generalization
    of AdaGrad.
    
    Adam update consists of the following steps, where g represents gradient and m, v
    are 1st and 2nd order moment estimates (mean and variance).
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }
    
    It updates the weights using::
    
     m = beta1*m + (1-beta1)*grad
     v = beta2*v + (1-beta2)*(grad**2)
     w += - learning_rate * m / (sqrt(v) + epsilon)
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage
    type of weight is the same as those of m and v,
    only the row slices whose indices appear in grad.indices are updated (for w, m and v)::
    
     for row in grad.indices:
         m[row] = beta1*m[row] + (1-beta1)*grad[row]
         v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
         w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
    
    
    
    Defined in src/operator/optimizer_op.cc:L688
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Update function for Adam optimizer. Adam is seen as a generalization
    of AdaGrad.
    
    Adam update consists of the following steps, where g represents gradient and m, v
    are 1st and 2nd order moment estimates (mean and variance).
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }
    
    It updates the weights using::
    
     m = beta1*m + (1-beta1)*grad
     v = beta2*v + (1-beta2)*(grad**2)
     w += - learning_rate * m / (sqrt(v) + epsilon)
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage
    type of weight is the same as those of m and v,
    only the row slices whose indices appear in grad.indices are updated (for w, m and v)::
    
     for row in grad.indices:
         m[row] = beta1*m[row] + (1-beta1)*grad[row]
         v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
         w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
    
    
    
    Defined in src/operator/optimizer_op.cc:L688
    returns

    org.apache.mxnet.NDArrayFuncReturn

  101. abstract def add_n(args: Any*): NDArrayFuncReturn

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Adds all input arguments element-wise.
    
    .. math::
       add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n
    
    ``add_n`` is potentially more efficient than calling ``add`` by `n` times.
    
    The storage type of ``add_n`` output depends on storage types of inputs
    
    - add_n(row_sparse, row_sparse, ..) = row_sparse
    - add_n(default, csr, default) = default
    - add_n(any input combinations longer than 4 (>4) with at least one default type) = default
    - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage
    
    
    
    Defined in src/operator/tensor/elemwise_sum.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

  103. abstract def all_finite(args: Any*): NDArrayFuncReturn

    Check if all the float numbers in the array are finite (used for AMP)
    
    
    Defined in src/operator/contrib/all_finite.cc:L101
    returns

    org.apache.mxnet.NDArrayFuncReturn

  104. abstract def all_finite(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Check if all the float numbers in the array are finite (used for AMP)
    
    
    Defined in src/operator/contrib/all_finite.cc:L101
    returns

    org.apache.mxnet.NDArrayFuncReturn

  105. abstract def amp_cast(args: Any*): NDArrayFuncReturn

    Cast function between low precision float/FP32 used by AMP.
    
    It casts only between low precision float/FP32 and does not do anything for other types.
    
    
    Defined in src/operator/tensor/amp_cast.cc:L37
    returns

    org.apache.mxnet.NDArrayFuncReturn

  106. abstract def amp_cast(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Cast function between low precision float/FP32 used by AMP.
    
    It casts only between low precision float/FP32 and does not do anything for other types.
    
    
    Defined in src/operator/tensor/amp_cast.cc:L37
    returns

    org.apache.mxnet.NDArrayFuncReturn

  107. abstract def amp_multicast(args: Any*): NDArrayFuncReturn

    Cast function used by AMP, that casts its inputs to the common widest type.
    
    It casts only between low precision float/FP32 and does not do anything for other types.
    
    
    
    Defined in src/operator/tensor/amp_cast.cc:L71
    returns

    org.apache.mxnet.NDArrayFuncReturn

  108. abstract def amp_multicast(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Cast function used by AMP, that casts its inputs to the common widest type.
    
    It casts only between low precision float/FP32 and does not do anything for other types.
    
    
    
    Defined in src/operator/tensor/amp_cast.cc:L71
    returns

    org.apache.mxnet.NDArrayFuncReturn

  109. abstract def arccos(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse cosine of the input array.
    
    The input should be in range `[-1, 1]`.
    The output is in the closed interval :math:`[0, \pi]`
    
    .. math::
       arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]
    
    The storage type of ``arccos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L206
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise inverse cosine of the input array.
    
    The input should be in range `[-1, 1]`.
    The output is in the closed interval :math:`[0, \pi]`
    
    .. math::
       arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]
    
    The storage type of ``arccos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L206
    returns

    org.apache.mxnet.NDArrayFuncReturn

  111. abstract def arccosh(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic cosine of the input array, \
    computed element-wise.
    
    The storage type of ``arccosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L474
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns the element-wise inverse hyperbolic cosine of the input array, \
    computed element-wise.
    
    The storage type of ``arccosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L474
    returns

    org.apache.mxnet.NDArrayFuncReturn

  113. abstract def arcsin(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse sine of the input array.
    
    The input should be in the range `[-1, 1]`.
    The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`].
    
    .. math::
       arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]
    
    The storage type of ``arcsin`` output depends upon the input storage type:
    
       - arcsin(default) = default
       - arcsin(row_sparse) = row_sparse
       - arcsin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L187
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise inverse sine of the input array.
    
    The input should be in the range `[-1, 1]`.
    The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`].
    
    .. math::
       arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]
    
    The storage type of ``arcsin`` output depends upon the input storage type:
    
       - arcsin(default) = default
       - arcsin(row_sparse) = row_sparse
       - arcsin(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L187
    returns

    org.apache.mxnet.NDArrayFuncReturn

  115. abstract def arcsinh(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic sine of the input array, \
    computed element-wise.
    
    The storage type of ``arcsinh`` output depends upon the input storage type:
    
       - arcsinh(default) = default
       - arcsinh(row_sparse) = row_sparse
       - arcsinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L436
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns the element-wise inverse hyperbolic sine of the input array, \
    computed element-wise.
    
    The storage type of ``arcsinh`` output depends upon the input storage type:
    
       - arcsinh(default) = default
       - arcsinh(row_sparse) = row_sparse
       - arcsinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L436
    returns

    org.apache.mxnet.NDArrayFuncReturn

  117. abstract def arctan(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse tangent of the input array.
    
    The output is in the closed interval :math:`[-\pi/2, \pi/2]`
    
    .. math::
       arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]
    
    The storage type of ``arctan`` output depends upon the input storage type:
    
       - arctan(default) = default
       - arctan(row_sparse) = row_sparse
       - arctan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L227
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise inverse tangent of the input array.
    
    The output is in the closed interval :math:`[-\pi/2, \pi/2]`
    
    .. math::
       arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]
    
    The storage type of ``arctan`` output depends upon the input storage type:
    
       - arctan(default) = default
       - arctan(row_sparse) = row_sparse
       - arctan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L227
    returns

    org.apache.mxnet.NDArrayFuncReturn

  119. abstract def arctanh(args: Any*): NDArrayFuncReturn

    Returns the element-wise inverse hyperbolic tangent of the input array, \
    computed element-wise.
    
    The storage type of ``arctanh`` output depends upon the input storage type:
    
       - arctanh(default) = default
       - arctanh(row_sparse) = row_sparse
       - arctanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L515
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns the element-wise inverse hyperbolic tangent of the input array, \
    computed element-wise.
    
    The storage type of ``arctanh`` output depends upon the input storage type:
    
       - arctanh(default) = default
       - arctanh(row_sparse) = row_sparse
       - arctanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L515
    returns

    org.apache.mxnet.NDArrayFuncReturn

  121. abstract def argmax(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  123. abstract def argmax_channel(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  125. abstract def argmin(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  127. abstract def argsort(args: Any*): NDArrayFuncReturn

    Returns the indices that would sort an input array along the given axis.
    
    This function performs sorting along the given axis and returns an array of indices having same shape
    as an input array that index data in sorted order.
    
    Examples::
    
      x = `[ [ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2] ]
    
      // sort along axis -1
      argsort(x) = `[ [ 1.,  0.,  2.],
                    [ 0.,  2.,  1.] ]
    
      // sort along axis 0
      argsort(x, axis=0) = `[ [ 1.,  0.,  1.]
                            [ 0.,  1.,  0.] ]
    
      // flatten and then sort
      argsort(x, axis=None) = [ 3.,  1.,  5.,  0.,  4.,  2.]
    
    
    Defined in src/operator/tensor/ordering_op.cc:L183
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns the indices that would sort an input array along the given axis.
    
    This function performs sorting along the given axis and returns an array of indices having same shape
    as an input array that index data in sorted order.
    
    Examples::
    
      x = `[ [ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2] ]
    
      // sort along axis -1
      argsort(x) = `[ [ 1.,  0.,  2.],
                    [ 0.,  2.,  1.] ]
    
      // sort along axis 0
      argsort(x, axis=0) = `[ [ 1.,  0.,  1.]
                            [ 0.,  1.,  0.] ]
    
      // flatten and then sort
      argsort(x, axis=None) = [ 3.,  1.,  5.,  0.,  4.,  2.]
    
    
    Defined in src/operator/tensor/ordering_op.cc:L183
    returns

    org.apache.mxnet.NDArrayFuncReturn

  129. abstract def batch_dot(args: Any*): NDArrayFuncReturn

    Batchwise dot product.
    
    ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and
    ``y`` are data in batch, namely N-D (N >= 3) arrays in shape of `(B0, ..., B_i, :, :)`.
    
    For example, given ``x`` with shape `(B_0, ..., B_i, N, M)` and ``y`` with shape
    `(B_0, ..., B_i, M, K)`, the result array will have shape `(B_0, ..., B_i, N, K)`,
    which is computed by::
    
       batch_dot(x,y)[b_0, ..., b_i, :, :] = dot(x[b_0, ..., b_i, :, :], y[b_0, ..., b_i, :, :])
    
    
    
    Defined in src/operator/tensor/dot.cc:L127
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Batchwise dot product.
    
    ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and
    ``y`` are data in batch, namely N-D (N >= 3) arrays in shape of `(B0, ..., B_i, :, :)`.
    
    For example, given ``x`` with shape `(B_0, ..., B_i, N, M)` and ``y`` with shape
    `(B_0, ..., B_i, M, K)`, the result array will have shape `(B_0, ..., B_i, N, K)`,
    which is computed by::
    
       batch_dot(x,y)[b_0, ..., b_i, :, :] = dot(x[b_0, ..., b_i, :, :], y[b_0, ..., b_i, :, :])
    
    
    
    Defined in src/operator/tensor/dot.cc:L127
    returns

    org.apache.mxnet.NDArrayFuncReturn

  131. abstract def batch_take(args: Any*): NDArrayFuncReturn

    Takes elements from a data batch.
    
    .. note::
      `batch_take` is deprecated. Use `pick` instead.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i] ]
    
    Examples::
    
      x = `[ [ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.] ]
    
      // takes elements with specified indices
      batch_take(x, [0,1,0]) = [ 1.  4.  5.]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L777
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Takes elements from a data batch.
    
    .. note::
      `batch_take` is deprecated. Use `pick` instead.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i] ]
    
    Examples::
    
      x = `[ [ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.] ]
    
      // takes elements with specified indices
      batch_take(x, [0,1,0]) = [ 1.  4.  5.]
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L777
    returns

    org.apache.mxnet.NDArrayFuncReturn

  133. abstract def broadcast_add(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  135. abstract def broadcast_axes(args: Any*): NDArrayFuncReturn

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    `broadcast_axes` is an alias to the function `broadcast_axis`.
    
    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:L58
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    `broadcast_axes` is an alias to the function `broadcast_axis`.
    
    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:L58
    returns

    org.apache.mxnet.NDArrayFuncReturn

  137. abstract def broadcast_axis(args: Any*): NDArrayFuncReturn

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    `broadcast_axes` is an alias to the function `broadcast_axis`.
    
    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:L58
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Broadcasts the input array over particular axes.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    `broadcast_axes` is an alias to the function `broadcast_axis`.
    
    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:L58
    returns

    org.apache.mxnet.NDArrayFuncReturn

  139. abstract def broadcast_div(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  141. abstract def broadcast_equal(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  143. abstract def broadcast_greater(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  145. abstract def broadcast_greater_equal(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  147. abstract def broadcast_hypot(args: Any*): NDArrayFuncReturn

     Returns the hypotenuse of a right angled triangle, given its "legs"
    with broadcasting.
    
    It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`.
    
    Example::
    
       x = `[ [ 3.,  3.,  3.] ]
    
       y = `[ [ 4.],
            [ 4.] ]
    
       broadcast_hypot(x, y) = `[ [ 5.,  5.,  5.],
                                [ 5.,  5.,  5.] ]
    
       z = `[ [ 0.],
            [ 4.] ]
    
       broadcast_hypot(x, z) = `[ [ 3.,  3.,  3.],
                                [ 5.,  5.,  5.] ]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L158
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

     Returns the hypotenuse of a right angled triangle, given its "legs"
    with broadcasting.
    
    It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`.
    
    Example::
    
       x = `[ [ 3.,  3.,  3.] ]
    
       y = `[ [ 4.],
            [ 4.] ]
    
       broadcast_hypot(x, y) = `[ [ 5.,  5.,  5.],
                                [ 5.,  5.,  5.] ]
    
       z = `[ [ 0.],
            [ 4.] ]
    
       broadcast_hypot(x, z) = `[ [ 3.,  3.,  3.],
                                [ 5.,  5.,  5.] ]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L158
    returns

    org.apache.mxnet.NDArrayFuncReturn

  149. abstract def broadcast_lesser(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  151. abstract def broadcast_lesser_equal(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  153. abstract def broadcast_like(args: Any*): NDArrayFuncReturn

    Broadcasts lhs to have the same shape as rhs.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_like(`[ [1,2,3] ], `[ [5,6,7],[7,8,9] ]) = `[ [ 1.,  2.,  3.],
                                                       [ 1.,  2.,  3.] ])
    
       broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L135
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Broadcasts lhs to have the same shape as rhs.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more explanation.
    
    Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to
    `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes.
    
    For example::
    
       broadcast_like(`[ [1,2,3] ], `[ [5,6,7],[7,8,9] ]) = `[ [ 1.,  2.,  3.],
                                                       [ 1.,  2.,  3.] ])
    
       broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L135
    returns

    org.apache.mxnet.NDArrayFuncReturn

  155. abstract def broadcast_logical_and(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  157. abstract def broadcast_logical_or(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  159. abstract def broadcast_logical_xor(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  161. abstract def broadcast_maximum(args: Any*): NDArrayFuncReturn

    Returns element-wise maximum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise maxima.
    
    Example::
    
       x = `[ [ 1.,  1.,  1.],
            [ 1.,  1.,  1.] ]
    
       y = `[ [ 0.],
            [ 1.] ]
    
       broadcast_maximum(x, y) = `[ [ 1.,  1.,  1.],
                                  [ 1.,  1.,  1.] ]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L81
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise maximum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise maxima.
    
    Example::
    
       x = `[ [ 1.,  1.,  1.],
            [ 1.,  1.,  1.] ]
    
       y = `[ [ 0.],
            [ 1.] ]
    
       broadcast_maximum(x, y) = `[ [ 1.,  1.,  1.],
                                  [ 1.,  1.,  1.] ]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L81
    returns

    org.apache.mxnet.NDArrayFuncReturn

  163. abstract def broadcast_minimum(args: Any*): NDArrayFuncReturn

    Returns element-wise minimum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise minima.
    
    Example::
    
       x = `[ [ 1.,  1.,  1.],
            [ 1.,  1.,  1.] ]
    
       y = `[ [ 0.],
            [ 1.] ]
    
       broadcast_maximum(x, y) = `[ [ 0.,  0.,  0.],
                                  [ 1.,  1.,  1.] ]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L117
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise minimum of the input arrays with broadcasting.
    
    This function compares two input arrays and returns a new array having the element-wise minima.
    
    Example::
    
       x = `[ [ 1.,  1.,  1.],
            [ 1.,  1.,  1.] ]
    
       y = `[ [ 0.],
            [ 1.] ]
    
       broadcast_maximum(x, y) = `[ [ 0.,  0.,  0.],
                                  [ 1.,  1.,  1.] ]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L117
    returns

    org.apache.mxnet.NDArrayFuncReturn

  165. abstract def broadcast_minus(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  167. abstract def broadcast_mod(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  169. abstract def broadcast_mul(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  171. abstract def broadcast_not_equal(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  173. abstract def broadcast_plus(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  175. abstract def broadcast_power(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  177. abstract def broadcast_sub(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  179. abstract def broadcast_to(args: Any*): NDArrayFuncReturn

    Broadcasts the input array to a new shape.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ 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:L82
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Broadcasts the input array to a new shape.
    
    Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
    with arrays of different shapes efficiently without creating multiple copies of arrays.
    Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ 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:L82
    returns

    org.apache.mxnet.NDArrayFuncReturn

  181. abstract def cast(args: Any*): NDArrayFuncReturn

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L665
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Casts all elements of the input to a new type.
    
    .. note:: ``Cast`` is deprecated. Use ``cast`` instead.
    
    Example::
    
       cast([0.9, 1.3], dtype='int32') = [0, 1]
       cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
       cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L665
    returns

    org.apache.mxnet.NDArrayFuncReturn

  183. abstract def cast_storage(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  185. abstract def cbrt(args: Any*): NDArrayFuncReturn

    Returns element-wise cube-root value of the input.
    
    .. math::
       cbrt(x) = \sqrt[3]{x}
    
    Example::
    
       cbrt([1, 8, -125]) = [1, 2, -5]
    
    The storage type of ``cbrt`` output depends upon the input storage type:
    
       - cbrt(default) = default
       - cbrt(row_sparse) = row_sparse
       - cbrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L216
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise cube-root value of the input.
    
    .. math::
       cbrt(x) = \sqrt[3]{x}
    
    Example::
    
       cbrt([1, 8, -125]) = [1, 2, -5]
    
    The storage type of ``cbrt`` output depends upon the input storage type:
    
       - cbrt(default) = default
       - cbrt(row_sparse) = row_sparse
       - cbrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L216
    returns

    org.apache.mxnet.NDArrayFuncReturn

  187. abstract def ceil(args: Any*): NDArrayFuncReturn

    Returns element-wise ceiling of the input.
    
    The ceil of the scalar x is the smallest integer i, such that i >= x.
    
    Example::
    
       ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]
    
    The storage type of ``ceil`` output depends upon the input storage type:
    
       - ceil(default) = default
       - ceil(row_sparse) = row_sparse
       - ceil(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L818
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise ceiling of the input.
    
    The ceil of the scalar x is the smallest integer i, such that i >= x.
    
    Example::
    
       ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]
    
    The storage type of ``ceil`` output depends upon the input storage type:
    
       - ceil(default) = default
       - ceil(row_sparse) = row_sparse
       - ceil(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L818
    returns

    org.apache.mxnet.NDArrayFuncReturn

  189. abstract def choose_element_0index(args: Any*): NDArrayFuncReturn

    Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i] ]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = `[ [ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.] ]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = `[ [ 2.],
                                     [ 3.],
                                     [ 6.] ]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i] ]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = `[ [ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.] ]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = `[ [ 2.],
                                     [ 3.],
                                     [ 6.] ]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

  191. abstract def clip(args: Any*): NDArrayFuncReturn

    Clips (limits) the values in an array.
    Given an interval, values outside the interval are clipped to the interval edges.
    Clipping ``x`` between `a_min` and `a_max` would be::
    .. math::
       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:L677
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Clips (limits) the values in an array.
    Given an interval, values outside the interval are clipped to the interval edges.
    Clipping ``x`` between `a_min` and `a_max` would be::
    .. math::
       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:L677
    returns

    org.apache.mxnet.NDArrayFuncReturn

  193. abstract def concat(args: Any*): NDArrayFuncReturn

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = `[ [1,1],[2,2] ]
       y = `[ [3,3],[4,4],[5,5] ]
       z = `[ [6,6], [7,7],[8,8] ]
    
       concat(x,y,z,dim=0) = `[ [ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.] ]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = `[ [ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.] ]
    
    
    
    Defined in src/operator/nn/concat.cc:L383
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Joins input arrays along a given axis.
    
    .. note:: `Concat` is deprecated. Use `concat` instead.
    
    The dimensions of the input arrays should be the same except the axis along
    which they will be concatenated.
    The dimension of the output array along the concatenated axis will be equal
    to the sum of the corresponding dimensions of the input arrays.
    
    The storage type of ``concat`` output depends on storage types of inputs
    
    - concat(csr, csr, ..., csr, dim=0) = csr
    - otherwise, ``concat`` generates output with default storage
    
    Example::
    
       x = `[ [1,1],[2,2] ]
       y = `[ [3,3],[4,4],[5,5] ]
       z = `[ [6,6], [7,7],[8,8] ]
    
       concat(x,y,z,dim=0) = `[ [ 1.,  1.],
                              [ 2.,  2.],
                              [ 3.,  3.],
                              [ 4.,  4.],
                              [ 5.,  5.],
                              [ 6.,  6.],
                              [ 7.,  7.],
                              [ 8.,  8.] ]
    
       Note that you cannot concat x,y,z along dimension 1 since dimension
       0 is not the same for all the input arrays.
    
       concat(y,z,dim=1) = `[ [ 3.,  3.,  6.,  6.],
                             [ 4.,  4.,  7.,  7.],
                             [ 5.,  5.,  8.,  8.] ]
    
    
    
    Defined in src/operator/nn/concat.cc:L383
    returns

    org.apache.mxnet.NDArrayFuncReturn

  195. abstract def cos(args: Any*): NDArrayFuncReturn

    Computes the element-wise cosine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]
    
    The storage type of ``cos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L90
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Computes the element-wise cosine of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]
    
    The storage type of ``cos`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L90
    returns

    org.apache.mxnet.NDArrayFuncReturn

  197. abstract def cosh(args: Any*): NDArrayFuncReturn

    Returns the hyperbolic cosine  of the input array, computed element-wise.
    
    .. math::
       cosh(x) = 0.5\times(exp(x) + exp(-x))
    
    The storage type of ``cosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L351
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns the hyperbolic cosine  of the input array, computed element-wise.
    
    .. math::
       cosh(x) = 0.5\times(exp(x) + exp(-x))
    
    The storage type of ``cosh`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L351
    returns

    org.apache.mxnet.NDArrayFuncReturn

  199. abstract def crop(args: Any*): NDArrayFuncReturn

    Slices a region of the array.
    .. note:: ``crop`` is deprecated. Use ``slice`` instead.
    This function returns a sliced array between the indices given
    by `begin` and `end` with the corresponding `step`.
    For an input array of ``shape=(d_0, d_1, ..., d_n-1)``,
    slice operation with ``begin=(b_0, b_1...b_m-1)``,
    ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``,
    where m <= n, results in an array with the shape
    ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``.
    The resulting array's *k*-th dimension contains elements
    from the *k*-th dimension of the input array starting
    from index ``b_k`` (inclusive) with step ``s_k``
    until reaching ``e_k`` (exclusive).
    If the *k*-th elements are `None` in the sequence of `begin`, `end`,
    and `step`, the following rule will be used to set default values.
    If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`;
    else, set `b_k=d_k-1`, `e_k=-1`.
    The storage type of ``slice`` output depends on storage types of inputs
    - slice(csr) = csr
    - otherwise, ``slice`` generates output with default storage
    .. note:: When input data storage type is csr, it only supports
       step=(), or step=(None,), or step=(1,) to generate a csr output.
       For other step parameter values, it falls back to slicing
       a dense tensor.
    Example::
      x = `[ [  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.] ]
      slice(x, begin=(0,1), end=(2,4)) = `[ [ 2.,  3.,  4.],
                                         [ 6.,  7.,  8.] ]
      slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = `[ [9., 11.],
                                                                [5.,  7.],
                                                                [1.,  3.] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L482
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Slices a region of the array.
    .. note:: ``crop`` is deprecated. Use ``slice`` instead.
    This function returns a sliced array between the indices given
    by `begin` and `end` with the corresponding `step`.
    For an input array of ``shape=(d_0, d_1, ..., d_n-1)``,
    slice operation with ``begin=(b_0, b_1...b_m-1)``,
    ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``,
    where m <= n, results in an array with the shape
    ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``.
    The resulting array's *k*-th dimension contains elements
    from the *k*-th dimension of the input array starting
    from index ``b_k`` (inclusive) with step ``s_k``
    until reaching ``e_k`` (exclusive).
    If the *k*-th elements are `None` in the sequence of `begin`, `end`,
    and `step`, the following rule will be used to set default values.
    If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`;
    else, set `b_k=d_k-1`, `e_k=-1`.
    The storage type of ``slice`` output depends on storage types of inputs
    - slice(csr) = csr
    - otherwise, ``slice`` generates output with default storage
    .. note:: When input data storage type is csr, it only supports
       step=(), or step=(None,), or step=(1,) to generate a csr output.
       For other step parameter values, it falls back to slicing
       a dense tensor.
    Example::
      x = `[ [  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.] ]
      slice(x, begin=(0,1), end=(2,4)) = `[ [ 2.,  3.,  4.],
                                         [ 6.,  7.,  8.] ]
      slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = `[ [9., 11.],
                                                                [5.,  7.],
                                                                [1.,  3.] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L482
    returns

    org.apache.mxnet.NDArrayFuncReturn

  201. abstract def ctc_loss(args: Any*): NDArrayFuncReturn

    Connectionist Temporal Classification Loss.
    
    .. note:: The existing alias ``contrib_CTCLoss`` is deprecated.
    
    The shapes of the inputs and outputs:
    
    - **data**: `(sequence_length, batch_size, alphabet_size)`
    - **label**: `(batch_size, label_sequence_length)`
    - **out**: `(batch_size)`
    
    The `data` tensor consists of sequences of activation vectors (without applying softmax),
    with i-th channel in the last dimension corresponding to i-th label
    for i between 0 and alphabet_size-1 (i.e always 0-indexed).
    Alphabet size should include one additional value reserved for blank label.
    When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for
    activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be
    reserved for blank label.
    
    ``label`` is an index matrix of integers. When `blank_label` is ``"first"``,
    the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
    when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label.
    
    If a sequence of labels is shorter than *label_sequence_length*, use the special
    padding value at the end of the sequence to conform it to the correct
    length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise.
    
    For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences
    'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as
    `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]
    
    When `blank_label` is ``"last"``, we can index the labels as
    `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]
    
    ``out`` is a list of CTC loss values, one per example in the batch.
    
    See *Connectionist Temporal Classification: Labelling Unsegmented
    Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
    information on the definition and the algorithm.
    
    
    
    Defined in src/operator/nn/ctc_loss.cc:L100
    returns

    org.apache.mxnet.NDArrayFuncReturn

  202. abstract def ctc_loss(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Connectionist Temporal Classification Loss.
    
    .. note:: The existing alias ``contrib_CTCLoss`` is deprecated.
    
    The shapes of the inputs and outputs:
    
    - **data**: `(sequence_length, batch_size, alphabet_size)`
    - **label**: `(batch_size, label_sequence_length)`
    - **out**: `(batch_size)`
    
    The `data` tensor consists of sequences of activation vectors (without applying softmax),
    with i-th channel in the last dimension corresponding to i-th label
    for i between 0 and alphabet_size-1 (i.e always 0-indexed).
    Alphabet size should include one additional value reserved for blank label.
    When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for
    activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be
    reserved for blank label.
    
    ``label`` is an index matrix of integers. When `blank_label` is ``"first"``,
    the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
    when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label.
    
    If a sequence of labels is shorter than *label_sequence_length*, use the special
    padding value at the end of the sequence to conform it to the correct
    length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise.
    
    For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences
    'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as
    `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]
    
    When `blank_label` is ``"last"``, we can index the labels as
    `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor.
    The resulting `label` tensor should be padded to be::
    
      `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]
    
    ``out`` is a list of CTC loss values, one per example in the batch.
    
    See *Connectionist Temporal Classification: Labelling Unsegmented
    Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
    information on the definition and the algorithm.
    
    
    
    Defined in src/operator/nn/ctc_loss.cc:L100
    returns

    org.apache.mxnet.NDArrayFuncReturn

  203. abstract def cumsum(args: Any*): NDArrayFuncReturn

    Return the cumulative sum of the elements along a given axis.
    
    Defined in src/operator/numpy/np_cumsum.cc:L70
    returns

    org.apache.mxnet.NDArrayFuncReturn

  204. abstract def cumsum(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Return the cumulative sum of the elements along a given axis.
    
    Defined in src/operator/numpy/np_cumsum.cc:L70
    returns

    org.apache.mxnet.NDArrayFuncReturn

  205. abstract def degrees(args: Any*): NDArrayFuncReturn

    Converts each element of the input array from radians to degrees.
    
    .. math::
       degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]
    
    The storage type of ``degrees`` output depends upon the input storage type:
    
       - degrees(default) = default
       - degrees(row_sparse) = row_sparse
       - degrees(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L274
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Converts each element of the input array from radians to degrees.
    
    .. math::
       degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]
    
    The storage type of ``degrees`` output depends upon the input storage type:
    
       - degrees(default) = default
       - degrees(row_sparse) = row_sparse
       - degrees(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L274
    returns

    org.apache.mxnet.NDArrayFuncReturn

  207. abstract def depth_to_space(args: Any*): NDArrayFuncReturn

    Rearranges(permutes) data from depth into blocks of spatial data.
    Similar to ONNX DepthToSpace operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace.
    The output is a new tensor where the values from depth dimension are moved in spatial blocks
    to height and width dimension. The reverse of this operation is ``space_to_depth``.
    .. math::
        \begin{gather*}
        x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\
        y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size])
        \end{gather*}
    where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width]
    and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]`
    Example::
      x = `[ [`[ [0, 1, 2],
             [3, 4, 5] ],
            `[ [6, 7, 8],
             [9, 10, 11] ],
            `[ [12, 13, 14],
             [15, 16, 17] ],
            `[ [18, 19, 20],
             [21, 22, 23] ] ] ]
      depth_to_space(x, 2) = `[ [`[ [0, 6, 1, 7, 2, 8],
                                [12, 18, 13, 19, 14, 20],
                                [3, 9, 4, 10, 5, 11],
                                [15, 21, 16, 22, 17, 23] ] ] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L972
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Rearranges(permutes) data from depth into blocks of spatial data.
    Similar to ONNX DepthToSpace operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace.
    The output is a new tensor where the values from depth dimension are moved in spatial blocks
    to height and width dimension. The reverse of this operation is ``space_to_depth``.
    .. math::
        \begin{gather*}
        x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\
        y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size])
        \end{gather*}
    where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width]
    and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]`
    Example::
      x = `[ [`[ [0, 1, 2],
             [3, 4, 5] ],
            `[ [6, 7, 8],
             [9, 10, 11] ],
            `[ [12, 13, 14],
             [15, 16, 17] ],
            `[ [18, 19, 20],
             [21, 22, 23] ] ] ]
      depth_to_space(x, 2) = `[ [`[ [0, 6, 1, 7, 2, 8],
                                [12, 18, 13, 19, 14, 20],
                                [3, 9, 4, 10, 5, 11],
                                [15, 21, 16, 22, 17, 23] ] ] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L972
    returns

    org.apache.mxnet.NDArrayFuncReturn

  209. abstract def diag(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  211. abstract def dot(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  213. abstract def elemwise_add(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  215. abstract def elemwise_div(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  217. abstract def elemwise_mul(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  219. abstract def elemwise_sub(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  221. abstract def erf(args: Any*): NDArrayFuncReturn

    Returns element-wise gauss error function of the input.
    
    Example::
    
       erf([0, -1., 10.]) = [0., -0.8427, 1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L886
    returns

    org.apache.mxnet.NDArrayFuncReturn

  222. abstract def erf(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise gauss error function of the input.
    
    Example::
    
       erf([0, -1., 10.]) = [0., -0.8427, 1.]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L886
    returns

    org.apache.mxnet.NDArrayFuncReturn

  223. abstract def erfinv(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse gauss error function of the input.
    
    Example::
    
       erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L907
    returns

    org.apache.mxnet.NDArrayFuncReturn

  224. abstract def erfinv(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns element-wise inverse gauss error function of the input.
    
    Example::
    
       erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L907
    returns

    org.apache.mxnet.NDArrayFuncReturn

  225. abstract def exp(args: Any*): NDArrayFuncReturn

    Returns element-wise exponential value of the input.
    
    .. math::
       exp(x) = e^x \approx 2.718^x
    
    Example::
    
       exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
    
    The storage type of ``exp`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L63
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise exponential value of the input.
    
    .. math::
       exp(x) = e^x \approx 2.718^x
    
    Example::
    
       exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
    
    The storage type of ``exp`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L63
    returns

    org.apache.mxnet.NDArrayFuncReturn

  227. abstract def expand_dims(args: Any*): NDArrayFuncReturn

    Inserts a new axis of size 1 into the array shape
    For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)``
    will return a new array with shape ``(2,1,3,4)``.
    
    
    Defined in src/operator/tensor/matrix_op.cc:L395
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Inserts a new axis of size 1 into the array shape
    For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)``
    will return a new array with shape ``(2,1,3,4)``.
    
    
    Defined in src/operator/tensor/matrix_op.cc:L395
    returns

    org.apache.mxnet.NDArrayFuncReturn

  229. abstract def expm1(args: Any*): NDArrayFuncReturn

    Returns ``exp(x) - 1`` computed element-wise on the input.
    
    This function provides greater precision than ``exp(x) - 1`` for small values of ``x``.
    
    The storage type of ``expm1`` output depends upon the input storage type:
    
       - expm1(default) = default
       - expm1(row_sparse) = row_sparse
       - expm1(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L224
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns ``exp(x) - 1`` computed element-wise on the input.
    
    This function provides greater precision than ``exp(x) - 1`` for small values of ``x``.
    
    The storage type of ``expm1`` output depends upon the input storage type:
    
       - expm1(default) = default
       - expm1(row_sparse) = row_sparse
       - expm1(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L224
    returns

    org.apache.mxnet.NDArrayFuncReturn

  231. abstract def fill_element_0index(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  233. abstract def fix(args: Any*): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest \
    integer towards zero of the input.
    
    Example::
    
       fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]
    
    The storage type of ``fix`` output depends upon the input storage type:
    
       - fix(default) = default
       - fix(row_sparse) = row_sparse
       - fix(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L875
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise rounded value to the nearest \
    integer towards zero of the input.
    
    Example::
    
       fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]
    
    The storage type of ``fix`` output depends upon the input storage type:
    
       - fix(default) = default
       - fix(row_sparse) = row_sparse
       - fix(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L875
    returns

    org.apache.mxnet.NDArrayFuncReturn

  235. abstract def flatten(args: Any*): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    Note that the behavior 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:L250
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    Note that the behavior 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:L250
    returns

    org.apache.mxnet.NDArrayFuncReturn

  237. abstract def flip(args: Any*): NDArrayFuncReturn

    Reverses the order of elements along given axis while preserving array shape.
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    Examples::
      x = `[ [ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.] ]
      reverse(x, axis=0) = `[ [ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.] ]
      reverse(x, axis=1) = `[ [ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L832
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Reverses the order of elements along given axis while preserving array shape.
    Note: reverse and flip are equivalent. We use reverse in the following examples.
    Examples::
      x = `[ [ 0.,  1.,  2.,  3.,  4.],
           [ 5.,  6.,  7.,  8.,  9.] ]
      reverse(x, axis=0) = `[ [ 5.,  6.,  7.,  8.,  9.],
                            [ 0.,  1.,  2.,  3.,  4.] ]
      reverse(x, axis=1) = `[ [ 4.,  3.,  2.,  1.,  0.],
                            [ 9.,  8.,  7.,  6.,  5.] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L832
    returns

    org.apache.mxnet.NDArrayFuncReturn

  239. abstract def floor(args: Any*): NDArrayFuncReturn

    Returns element-wise floor of the input.
    
    The floor of the scalar x is the largest integer i, such that i <= x.
    
    Example::
    
       floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]
    
    The storage type of ``floor`` output depends upon the input storage type:
    
       - floor(default) = default
       - floor(row_sparse) = row_sparse
       - floor(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L837
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise floor of the input.
    
    The floor of the scalar x is the largest integer i, such that i <= x.
    
    Example::
    
       floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]
    
    The storage type of ``floor`` output depends upon the input storage type:
    
       - floor(default) = default
       - floor(row_sparse) = row_sparse
       - floor(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L837
    returns

    org.apache.mxnet.NDArrayFuncReturn

  241. abstract def ftml_update(args: Any*): NDArrayFuncReturn

    The FTML optimizer described in
    *FTML - Follow the Moving Leader in Deep Learning*,
    available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
     \sigma_t = d_t - \beta_1 d_{t-1}
     z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
     W_t = - \frac{ z_t }{ d_t }
    
    
    
    Defined in src/operator/optimizer_op.cc:L640
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    The FTML optimizer described in
    *FTML - Follow the Moving Leader in Deep Learning*,
    available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
     d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
     \sigma_t = d_t - \beta_1 d_{t-1}
     z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
     W_t = - \frac{ z_t }{ d_t }
    
    
    
    Defined in src/operator/optimizer_op.cc:L640
    returns

    org.apache.mxnet.NDArrayFuncReturn

  243. abstract def ftrl_update(args: Any*): NDArrayFuncReturn

    Update function for Ftrl optimizer.
    Referenced from *Ad Click Prediction: a View from the Trenches*, available at
    http://dl.acm.org/citation.cfm?id=2488200.
    
    It updates the weights using::
    
     rescaled_grad = clip(grad * rescale_grad, clip_gradient)
     z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
     n += rescaled_grad**2
     w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
    
    If w, z and n are all of ``row_sparse`` storage type,
    only the row slices whose indices appear in grad.indices are updated (for w, z and n)::
    
     for row in grad.indices:
         rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
         z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
         n[row] += rescaled_grad[row]**2
         w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
    
    
    
    Defined in src/operator/optimizer_op.cc:L876
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Update function for Ftrl optimizer.
    Referenced from *Ad Click Prediction: a View from the Trenches*, available at
    http://dl.acm.org/citation.cfm?id=2488200.
    
    It updates the weights using::
    
     rescaled_grad = clip(grad * rescale_grad, clip_gradient)
     z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
     n += rescaled_grad**2
     w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
    
    If w, z and n are all of ``row_sparse`` storage type,
    only the row slices whose indices appear in grad.indices are updated (for w, z and n)::
    
     for row in grad.indices:
         rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
         z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
         n[row] += rescaled_grad[row]**2
         w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
    
    
    
    Defined in src/operator/optimizer_op.cc:L876
    returns

    org.apache.mxnet.NDArrayFuncReturn

  245. abstract def gamma(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  247. abstract def gammaln(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  249. abstract def gather_nd(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  251. abstract def hard_sigmoid(args: Any*): NDArrayFuncReturn

    Computes hard sigmoid of x element-wise.
    
    .. math::
       y = max(0, min(1, alpha * x + beta))
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L161
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Computes hard sigmoid of x element-wise.
    
    .. math::
       y = max(0, min(1, alpha * x + beta))
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L161
    returns

    org.apache.mxnet.NDArrayFuncReturn

  253. abstract def identity(args: Any*): NDArrayFuncReturn

    Returns a copy of the input.
    
    From:src/operator/tensor/elemwise_unary_op_basic.cc:246
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns a copy of the input.
    
    From:src/operator/tensor/elemwise_unary_op_basic.cc:246
    returns

    org.apache.mxnet.NDArrayFuncReturn

  255. abstract def khatri_rao(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  257. abstract def lamb_update_phase1(args: Any*): NDArrayFuncReturn

    Phase I of lamb update it performs the following operations and returns g:.
    
    Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
    .. math::
        \begin{gather*}
        grad = grad * rescale_grad
        if (grad < -clip_gradient)
        then
             grad = -clip_gradient
        if (grad > clip_gradient)
        then
             grad = clip_gradient
    
        mean = beta1 * mean + (1 - beta1) * grad;
        variance = beta2 * variance + (1. - beta2) * grad ^ 2;
    
        if (bias_correction)
        then
             mean_hat = mean / (1. - beta1^t);
             var_hat = var / (1 - beta2^t);
             g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight;
        else
             g = mean / (var_data^(1/2) + epsilon) + wd * weight;
        \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L953
    returns

    org.apache.mxnet.NDArrayFuncReturn

  258. abstract def lamb_update_phase1(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Phase I of lamb update it performs the following operations and returns g:.
    
    Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
    .. math::
        \begin{gather*}
        grad = grad * rescale_grad
        if (grad < -clip_gradient)
        then
             grad = -clip_gradient
        if (grad > clip_gradient)
        then
             grad = clip_gradient
    
        mean = beta1 * mean + (1 - beta1) * grad;
        variance = beta2 * variance + (1. - beta2) * grad ^ 2;
    
        if (bias_correction)
        then
             mean_hat = mean / (1. - beta1^t);
             var_hat = var / (1 - beta2^t);
             g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight;
        else
             g = mean / (var_data^(1/2) + epsilon) + wd * weight;
        \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L953
    returns

    org.apache.mxnet.NDArrayFuncReturn

  259. abstract def lamb_update_phase2(args: Any*): NDArrayFuncReturn

    Phase II of lamb update it performs the following operations and updates grad.
    
    Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
    .. math::
        \begin{gather*}
        if (lower_bound >= 0)
        then
             r1 = max(r1, lower_bound)
        if (upper_bound >= 0)
        then
             r1 = max(r1, upper_bound)
    
        if (r1 == 0 or r2 == 0)
        then
             lr = lr
        else
             lr = lr * (r1/r2)
        weight = weight - lr * g
        \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L992
    returns

    org.apache.mxnet.NDArrayFuncReturn

  260. abstract def lamb_update_phase2(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Phase II of lamb update it performs the following operations and updates grad.
    
    Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
    .. math::
        \begin{gather*}
        if (lower_bound >= 0)
        then
             r1 = max(r1, lower_bound)
        if (upper_bound >= 0)
        then
             r1 = max(r1, upper_bound)
    
        if (r1 == 0 or r2 == 0)
        then
             lr = lr
        else
             lr = lr * (r1/r2)
        weight = weight - lr * g
        \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L992
    returns

    org.apache.mxnet.NDArrayFuncReturn

  261. abstract def linalg_det(args: Any*): NDArrayFuncReturn

    Compute the determinant of a matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a square matrix. We compute:
    
      *out* = *det(A)*
    
    If *n>2*, *det* is performed separately on the trailing two dimensions
    for all inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    .. note:: There is no gradient backwarded when A is non-invertible (which is
              equivalent to det(A) = 0) because zero is rarely hit upon in float
              point computation and the Jacobi's formula on determinant gradient
              is not computationally efficient when A is non-invertible.
    
    Examples::
    
       Single matrix determinant
       A = `[ [1., 4.], [2., 3.] ]
       det(A) = [-5.]
    
       Batch matrix determinant
       A = `[ `[ [1., 4.], [2., 3.] ],
            `[ [2., 3.], [1., 4.] ] ]
       det(A) = [-5., 5.]
    
    
    Defined in src/operator/tensor/la_op.cc:L973
    returns

    org.apache.mxnet.NDArrayFuncReturn

  262. abstract def linalg_det(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Compute the determinant of a matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a square matrix. We compute:
    
      *out* = *det(A)*
    
    If *n>2*, *det* is performed separately on the trailing two dimensions
    for all inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    .. note:: There is no gradient backwarded when A is non-invertible (which is
              equivalent to det(A) = 0) because zero is rarely hit upon in float
              point computation and the Jacobi's formula on determinant gradient
              is not computationally efficient when A is non-invertible.
    
    Examples::
    
       Single matrix determinant
       A = `[ [1., 4.], [2., 3.] ]
       det(A) = [-5.]
    
       Batch matrix determinant
       A = `[ `[ [1., 4.], [2., 3.] ],
            `[ [2., 3.], [1., 4.] ] ]
       det(A) = [-5., 5.]
    
    
    Defined in src/operator/tensor/la_op.cc:L973
    returns

    org.apache.mxnet.NDArrayFuncReturn

  263. abstract def linalg_extractdiag(args: Any*): NDArrayFuncReturn

    Extracts the diagonal entries of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, then *A* represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor.
    
    If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an *n-1*-dimensional tensor.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single matrix diagonal extraction
        A = `[ [1.0, 2.0],
             [3.0, 4.0] ]
    
        extractdiag(A) = [1.0, 4.0]
    
        extractdiag(A, 1) = [2.0]
    
        Batch matrix diagonal extraction
        A = `[ `[ [1.0, 2.0],
              [3.0, 4.0] ],
             `[ [5.0, 6.0],
              [7.0, 8.0] ] ]
    
        extractdiag(A) = `[ [1.0, 4.0],
                          [5.0, 8.0] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L495
    returns

    org.apache.mxnet.NDArrayFuncReturn

  264. abstract def linalg_extractdiag(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Extracts the diagonal entries of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, then *A* represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor.
    
    If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an *n-1*-dimensional tensor.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single matrix diagonal extraction
        A = `[ [1.0, 2.0],
             [3.0, 4.0] ]
    
        extractdiag(A) = [1.0, 4.0]
    
        extractdiag(A, 1) = [2.0]
    
        Batch matrix diagonal extraction
        A = `[ `[ [1.0, 2.0],
              [3.0, 4.0] ],
             `[ [5.0, 6.0],
              [7.0, 8.0] ] ]
    
        extractdiag(A) = `[ [1.0, 4.0],
                          [5.0, 8.0] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L495
    returns

    org.apache.mxnet.NDArrayFuncReturn

  265. abstract def linalg_extracttrian(args: Any*): NDArrayFuncReturn

    Extracts a triangular sub-matrix from a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, then *A* represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor.
    
    If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an *n-1*-dimensional tensor.
    
    The *offset* and *lower* parameters determine the triangle to be extracted:
    
    - When *offset = 0* either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter *lower*.
    - When *offset = k > 0* the upper triangle with respect to the k-th diagonal above the main diagonal is extracted.
    - When *offset = k < 0* the lower triangle with respect to the k-th diagonal below the main diagonal is extracted.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single triagonal extraction
        A = `[ [1.0, 2.0],
             [3.0, 4.0] ]
    
        extracttrian(A) = [1.0, 3.0, 4.0]
        extracttrian(A, lower=False) = [1.0, 2.0, 4.0]
        extracttrian(A, 1) = [2.0]
        extracttrian(A, -1) = [3.0]
    
        Batch triagonal extraction
        A = `[ `[ [1.0, 2.0],
              [3.0, 4.0] ],
             `[ [5.0, 6.0],
              [7.0, 8.0] ] ]
    
        extracttrian(A) = `[ [1.0, 3.0, 4.0],
                           [5.0, 7.0, 8.0] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L605
    returns

    org.apache.mxnet.NDArrayFuncReturn

  266. abstract def linalg_extracttrian(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Extracts a triangular sub-matrix from a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, then *A* represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor.
    
    If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an *n-1*-dimensional tensor.
    
    The *offset* and *lower* parameters determine the triangle to be extracted:
    
    - When *offset = 0* either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter *lower*.
    - When *offset = k > 0* the upper triangle with respect to the k-th diagonal above the main diagonal is extracted.
    - When *offset = k < 0* the lower triangle with respect to the k-th diagonal below the main diagonal is extracted.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single triagonal extraction
        A = `[ [1.0, 2.0],
             [3.0, 4.0] ]
    
        extracttrian(A) = [1.0, 3.0, 4.0]
        extracttrian(A, lower=False) = [1.0, 2.0, 4.0]
        extracttrian(A, 1) = [2.0]
        extracttrian(A, -1) = [3.0]
    
        Batch triagonal extraction
        A = `[ `[ [1.0, 2.0],
              [3.0, 4.0] ],
             `[ [5.0, 6.0],
              [7.0, 8.0] ] ]
    
        extracttrian(A) = `[ [1.0, 3.0, 4.0],
                           [5.0, 7.0, 8.0] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L605
    returns

    org.apache.mxnet.NDArrayFuncReturn

  267. abstract def linalg_gelqf(args: Any*): NDArrayFuncReturn

    LQ factorization for general matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
    must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
    factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
    that:
    
       *A* = *L* \* *Q*
    
    Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
    and *Q* is row-orthonormal, meaning that
    
       *Q* \* *Q*\ :sup:`T`
    
    is equal to the identity matrix of shape *(x, x)*.
    
    If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       Single LQ factorization
       A = `[ [1., 2., 3.], [4., 5., 6.] ]
       Q, L = gelqf(A)
       Q = `[ [-0.26726124, -0.53452248, -0.80178373],
            [0.87287156, 0.21821789, -0.43643578] ]
       L = `[ [-3.74165739, 0.],
            [-8.55235974, 1.96396101] ]
    
       Batch LQ factorization
       A = `[ `[ [1., 2., 3.], [4., 5., 6.] ],
            `[ [7., 8., 9.], [10., 11., 12.] ] ]
       Q, L = gelqf(A)
       Q = `[ `[ [-0.26726124, -0.53452248, -0.80178373],
             [0.87287156, 0.21821789, -0.43643578] ],
            `[ [-0.50257071, -0.57436653, -0.64616234],
             [0.7620735, 0.05862104, -0.64483142] ] ]
       L = `[ `[ [-3.74165739, 0.],
             [-8.55235974, 1.96396101] ],
            `[ [-13.92838828, 0.],
             [-19.09768702, 0.52758934] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L798
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    LQ factorization for general matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
    must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
    factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
    that:
    
       *A* = *L* \* *Q*
    
    Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
    and *Q* is row-orthonormal, meaning that
    
       *Q* \* *Q*\ :sup:`T`
    
    is equal to the identity matrix of shape *(x, x)*.
    
    If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       Single LQ factorization
       A = `[ [1., 2., 3.], [4., 5., 6.] ]
       Q, L = gelqf(A)
       Q = `[ [-0.26726124, -0.53452248, -0.80178373],
            [0.87287156, 0.21821789, -0.43643578] ]
       L = `[ [-3.74165739, 0.],
            [-8.55235974, 1.96396101] ]
    
       Batch LQ factorization
       A = `[ `[ [1., 2., 3.], [4., 5., 6.] ],
            `[ [7., 8., 9.], [10., 11., 12.] ] ]
       Q, L = gelqf(A)
       Q = `[ `[ [-0.26726124, -0.53452248, -0.80178373],
             [0.87287156, 0.21821789, -0.43643578] ],
            `[ [-0.50257071, -0.57436653, -0.64616234],
             [0.7620735, 0.05862104, -0.64483142] ] ]
       L = `[ `[ [-3.74165739, 0.],
             [-8.55235974, 1.96396101] ],
            `[ [-13.92838828, 0.],
             [-19.09768702, 0.52758934] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L798
    returns

    org.apache.mxnet.NDArrayFuncReturn

  269. abstract def linalg_gemm(args: Any*): NDArrayFuncReturn

    Performs general matrix multiplication and accumulation.
    Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C*
    
    Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or
    matrix transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent
    to the following without the overhead of the additional swapaxis operations::
    
        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)
    
    When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
    and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
    pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
    Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.
    
    .. 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:L89
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Performs general matrix multiplication and accumulation.
    Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C*
    
    Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or
    matrix transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent
    to the following without the overhead of the additional swapaxis operations::
    
        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)
    
    When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
    and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
    pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
    Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.
    
    .. 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:L89
    returns

    org.apache.mxnet.NDArrayFuncReturn

  271. abstract def linalg_gemm2(args: Any*): NDArrayFuncReturn

    Performs general matrix multiplication.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)
    
    Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
    transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to
    the following without the overhead of the additional swapaxis operations::
    
        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)
    
    When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
    and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
    pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
    Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.
    
    .. 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:L163
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Performs general matrix multiplication.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, the BLAS3 function *gemm* is performed:
    
       *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)
    
    Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
    transposition (depending on *transpose_a*, *transpose_b*).
    
    If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
    are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
    parameter. By default, the trailing two dimensions will be used for matrix encoding.
    
    For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
    calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to
    the following without the overhead of the additional swapaxis operations::
    
        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)
    
    When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
    and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
    pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
    Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.
    
    .. 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:L163
    returns

    org.apache.mxnet.NDArrayFuncReturn

  273. abstract def linalg_inverse(args: Any*): NDArrayFuncReturn

    Compute the inverse of a matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a square matrix. We compute:
    
      *out* = *A*\ :sup:`-1`
    
    If *n>2*, *inverse* 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 inverse
       A = `[ [1., 4.], [2., 3.] ]
       inverse(A) = `[ [-0.6, 0.8], [0.4, -0.2] ]
    
       Batch matrix inverse
       A = `[ `[ [1., 4.], [2., 3.] ],
            `[ [1., 3.], [2., 4.] ] ]
       inverse(A) = `[ `[ [-0.6, 0.8], [0.4, -0.2] ],
                     `[ [-2., 1.5], [1., -0.5] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L919
    returns

    org.apache.mxnet.NDArrayFuncReturn

  274. abstract def linalg_inverse(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Compute the inverse of a matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a square matrix. We compute:
    
      *out* = *A*\ :sup:`-1`
    
    If *n>2*, *inverse* 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 inverse
       A = `[ [1., 4.], [2., 3.] ]
       inverse(A) = `[ [-0.6, 0.8], [0.4, -0.2] ]
    
       Batch matrix inverse
       A = `[ `[ [1., 4.], [2., 3.] ],
            `[ [1., 3.], [2., 4.] ] ]
       inverse(A) = `[ `[ [-0.6, 0.8], [0.4, -0.2] ],
                     `[ [-2., 1.5], [1., -0.5] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L919
    returns

    org.apache.mxnet.NDArrayFuncReturn

  275. abstract def linalg_makediag(args: Any*): NDArrayFuncReturn

    Constructs a square matrix with the input as diagonal.
    Input is a tensor *A* of dimension *n >= 1*.
    
    If *n=1*, then *A* represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor.
    If *n>1*, then *A* represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an *n+1*-dimensional tensor.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single diagonal matrix construction
        A = [1.0, 2.0]
    
        makediag(A)    = `[ [1.0, 0.0],
                          [0.0, 2.0] ]
    
        makediag(A, 1) = `[ [0.0, 1.0, 0.0],
                          [0.0, 0.0, 2.0],
                          [0.0, 0.0, 0.0] ]
    
        Batch diagonal matrix construction
        A = `[ [1.0, 2.0],
             [3.0, 4.0] ]
    
        makediag(A) = `[ `[ [1.0, 0.0],
                        [0.0, 2.0] ],
                       `[ [3.0, 0.0],
                        [0.0, 4.0] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L547
    returns

    org.apache.mxnet.NDArrayFuncReturn

  276. abstract def linalg_makediag(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Constructs a square matrix with the input as diagonal.
    Input is a tensor *A* of dimension *n >= 1*.
    
    If *n=1*, then *A* represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor.
    If *n>1*, then *A* represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an *n+1*-dimensional tensor.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single diagonal matrix construction
        A = [1.0, 2.0]
    
        makediag(A)    = `[ [1.0, 0.0],
                          [0.0, 2.0] ]
    
        makediag(A, 1) = `[ [0.0, 1.0, 0.0],
                          [0.0, 0.0, 2.0],
                          [0.0, 0.0, 0.0] ]
    
        Batch diagonal matrix construction
        A = `[ [1.0, 2.0],
             [3.0, 4.0] ]
    
        makediag(A) = `[ `[ [1.0, 0.0],
                        [0.0, 2.0] ],
                       `[ [3.0, 0.0],
                        [0.0, 4.0] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L547
    returns

    org.apache.mxnet.NDArrayFuncReturn

  277. abstract def linalg_maketrian(args: Any*): NDArrayFuncReturn

    Constructs a square matrix with the input representing a specific triangular sub-matrix.
    This is basically the inverse of *linalg.extracttrian*. Input is a tensor *A* of dimension *n >= 1*.
    
    If *n=1*, then *A* represents the entries of a triangular matrix which is lower triangular if *offset<0* or *offset=0*, *lower=true*. The resulting matrix is derived by first constructing the square
    matrix with the entries outside the triangle set to zero and then adding *offset*-times an additional
    diagonal with zero entries to the square matrix.
    
    If *n>1*, then *A* represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an *n+1*-dimensional tensor.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single  matrix construction
        A = [1.0, 2.0, 3.0]
    
        maketrian(A)              = `[ [1.0, 0.0],
                                     [2.0, 3.0] ]
    
        maketrian(A, lower=false) = `[ [1.0, 2.0],
                                     [0.0, 3.0] ]
    
        maketrian(A, offset=1)    = `[ [0.0, 1.0, 2.0],
                                     [0.0, 0.0, 3.0],
                                     [0.0, 0.0, 0.0] ]
        maketrian(A, offset=-1)   = `[ [0.0, 0.0, 0.0],
                                     [1.0, 0.0, 0.0],
                                     [2.0, 3.0, 0.0] ]
    
        Batch matrix construction
        A = `[ [1.0, 2.0, 3.0],
             [4.0, 5.0, 6.0] ]
    
        maketrian(A)           = `[ `[ [1.0, 0.0],
                                   [2.0, 3.0] ],
                                  `[ [4.0, 0.0],
                                   [5.0, 6.0] ] ]
    
        maketrian(A, offset=1) = `[ `[ [0.0, 1.0, 2.0],
                                   [0.0, 0.0, 3.0],
                                   [0.0, 0.0, 0.0] ],
                                  `[ [0.0, 4.0, 5.0],
                                   [0.0, 0.0, 6.0],
                                   [0.0, 0.0, 0.0] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L673
    returns

    org.apache.mxnet.NDArrayFuncReturn

  278. abstract def linalg_maketrian(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Constructs a square matrix with the input representing a specific triangular sub-matrix.
    This is basically the inverse of *linalg.extracttrian*. Input is a tensor *A* of dimension *n >= 1*.
    
    If *n=1*, then *A* represents the entries of a triangular matrix which is lower triangular if *offset<0* or *offset=0*, *lower=true*. The resulting matrix is derived by first constructing the square
    matrix with the entries outside the triangle set to zero and then adding *offset*-times an additional
    diagonal with zero entries to the square matrix.
    
    If *n>1*, then *A* represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an *n+1*-dimensional tensor.
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
        Single  matrix construction
        A = [1.0, 2.0, 3.0]
    
        maketrian(A)              = `[ [1.0, 0.0],
                                     [2.0, 3.0] ]
    
        maketrian(A, lower=false) = `[ [1.0, 2.0],
                                     [0.0, 3.0] ]
    
        maketrian(A, offset=1)    = `[ [0.0, 1.0, 2.0],
                                     [0.0, 0.0, 3.0],
                                     [0.0, 0.0, 0.0] ]
        maketrian(A, offset=-1)   = `[ [0.0, 0.0, 0.0],
                                     [1.0, 0.0, 0.0],
                                     [2.0, 3.0, 0.0] ]
    
        Batch matrix construction
        A = `[ [1.0, 2.0, 3.0],
             [4.0, 5.0, 6.0] ]
    
        maketrian(A)           = `[ `[ [1.0, 0.0],
                                   [2.0, 3.0] ],
                                  `[ [4.0, 0.0],
                                   [5.0, 6.0] ] ]
    
        maketrian(A, offset=1) = `[ `[ [0.0, 1.0, 2.0],
                                   [0.0, 0.0, 3.0],
                                   [0.0, 0.0, 0.0] ],
                                  `[ [0.0, 4.0, 5.0],
                                   [0.0, 0.0, 6.0],
                                   [0.0, 0.0, 0.0] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L673
    returns

    org.apache.mxnet.NDArrayFuncReturn

  279. abstract def linalg_potrf(args: Any*): NDArrayFuncReturn

    Performs Cholesky factorization of a symmetric positive-definite matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the Cholesky factor *B* of the symmetric, positive definite matrix *A* is
    computed. *B* is triangular (entries of upper or lower triangle are all zero), has
    positive diagonal entries, and:
    
      *A* = *B* \* *B*\ :sup:`T`  if *lower* = *true*
      *A* = *B*\ :sup:`T` \* *B*  if *lower* = *false*
    
    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:L214
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Performs Cholesky factorization of a symmetric positive-definite matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the Cholesky factor *B* of the symmetric, positive definite matrix *A* is
    computed. *B* is triangular (entries of upper or lower triangle are all zero), has
    positive diagonal entries, and:
    
      *A* = *B* \* *B*\ :sup:`T`  if *lower* = *true*
      *A* = *B*\ :sup:`T` \* *B*  if *lower* = *false*
    
    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:L214
    returns

    org.apache.mxnet.NDArrayFuncReturn

  281. abstract def linalg_potri(args: Any*): NDArrayFuncReturn

    Performs matrix inversion from a Cholesky factorization.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a triangular matrix (entries of upper or lower triangle are all zero)
    with positive diagonal. We compute:
    
      *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1` if *lower* = *true*
      *out* = *A*\ :sup:`-1` \* *A*\ :sup:`-T` if *lower* = *false*
    
    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:L275
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Performs matrix inversion from a Cholesky factorization.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a triangular matrix (entries of upper or lower triangle are all zero)
    with positive diagonal. We compute:
    
      *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1` if *lower* = *true*
      *out* = *A*\ :sup:`-1` \* *A*\ :sup:`-T` if *lower* = *false*
    
    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:L275
    returns

    org.apache.mxnet.NDArrayFuncReturn

  283. abstract def linalg_slogdet(args: Any*): NDArrayFuncReturn

    Compute the sign and log of the determinant of a matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a square matrix. We compute:
    
      *sign* = *sign(det(A))*
      *logabsdet* = *log(abs(det(A)))*
    
    If *n>2*, *slogdet* is performed separately on the trailing two dimensions
    for all inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    .. note:: The gradient is not properly defined on sign, so the gradient of
              it is not backwarded.
    .. note:: No gradient is backwarded when A is non-invertible. Please see
              the docs of operator det for detail.
    
    Examples::
    
       Single matrix signed log determinant
       A = `[ [2., 3.], [1., 4.] ]
       sign, logabsdet = slogdet(A)
       sign = [1.]
       logabsdet = [1.609438]
    
       Batch matrix signed log determinant
       A = `[ `[ [2., 3.], [1., 4.] ],
            `[ [1., 2.], [2., 4.] ],
            `[ [1., 2.], [4., 3.] ] ]
       sign, logabsdet = slogdet(A)
       sign = [1., 0., -1.]
       logabsdet = [1.609438, -inf, 1.609438]
    
    
    Defined in src/operator/tensor/la_op.cc:L1031
    returns

    org.apache.mxnet.NDArrayFuncReturn

  284. abstract def linalg_slogdet(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Compute the sign and log of the determinant of a matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* is a square matrix. We compute:
    
      *sign* = *sign(det(A))*
      *logabsdet* = *log(abs(det(A)))*
    
    If *n>2*, *slogdet* is performed separately on the trailing two dimensions
    for all inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    .. note:: The gradient is not properly defined on sign, so the gradient of
              it is not backwarded.
    .. note:: No gradient is backwarded when A is non-invertible. Please see
              the docs of operator det for detail.
    
    Examples::
    
       Single matrix signed log determinant
       A = `[ [2., 3.], [1., 4.] ]
       sign, logabsdet = slogdet(A)
       sign = [1.]
       logabsdet = [1.609438]
    
       Batch matrix signed log determinant
       A = `[ `[ [2., 3.], [1., 4.] ],
            `[ [1., 2.], [2., 4.] ],
            `[ [1., 2.], [4., 3.] ] ]
       sign, logabsdet = slogdet(A)
       sign = [1., 0., -1.]
       logabsdet = [1.609438, -inf, 1.609438]
    
    
    Defined in src/operator/tensor/la_op.cc:L1031
    returns

    org.apache.mxnet.NDArrayFuncReturn

  285. abstract def linalg_sumlogdiag(args: Any*): NDArrayFuncReturn

    Computes the sum of the logarithms of the diagonal elements of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
    logarithms of the diagonal elements, the result has shape (1,).
    
    If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       Single matrix reduction
       A = `[ [1.0, 1.0], [1.0, 7.0] ]
       sumlogdiag(A) = [1.9459]
    
       Batch matrix reduction
       A = `[ `[ [1.0, 1.0], [1.0, 7.0] ], `[ [3.0, 0], [0, 17.0] ] ]
       sumlogdiag(A) = [1.9459, 3.9318]
    
    
    Defined in src/operator/tensor/la_op.cc:L445
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Computes the sum of the logarithms of the diagonal elements of a square matrix.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
    logarithms of the diagonal elements, the result has shape (1,).
    
    If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       Single matrix reduction
       A = `[ [1.0, 1.0], [1.0, 7.0] ]
       sumlogdiag(A) = [1.9459]
    
       Batch matrix reduction
       A = `[ `[ [1.0, 1.0], [1.0, 7.0] ], `[ [3.0, 0], [0, 17.0] ] ]
       sumlogdiag(A) = [1.9459, 3.9318]
    
    
    Defined in src/operator/tensor/la_op.cc:L445
    returns

    org.apache.mxnet.NDArrayFuncReturn

  287. abstract def linalg_syrk(args: Any*): NDArrayFuncReturn

    Multiplication of matrix with its transpose.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the operator performs the BLAS3 function *syrk*:
    
      *out* = *alpha* \* *A* \* *A*\ :sup:`T`
    
    if *transpose=False*, or
    
      *out* = *alpha* \* *A*\ :sup:`T` \ \* *A*
    
    if *transpose=True*.
    
    If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       Single matrix multiply
       A = `[ [1., 2., 3.], [4., 5., 6.] ]
       syrk(A, alpha=1., transpose=False)
                = `[ [14., 32.],
                   [32., 77.] ]
       syrk(A, alpha=1., transpose=True)
                = `[ [17., 22., 27.],
                   [22., 29., 36.],
                   [27., 36., 45.] ]
    
       Batch matrix multiply
       A = `[ `[ [1., 1.] ], `[ [0.1, 0.1] ] ]
       syrk(A, alpha=2., transpose=False) = `[ `[ [4.] ], `[ [0.04] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L730
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Multiplication of matrix with its transpose.
    Input is a tensor *A* of dimension *n >= 2*.
    
    If *n=2*, the operator performs the BLAS3 function *syrk*:
    
      *out* = *alpha* \* *A* \* *A*\ :sup:`T`
    
    if *transpose=False*, or
    
      *out* = *alpha* \* *A*\ :sup:`T` \ \* *A*
    
    if *transpose=True*.
    
    If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
    inputs (batch mode).
    
    .. note:: The operator supports float32 and float64 data types only.
    
    Examples::
    
       Single matrix multiply
       A = `[ [1., 2., 3.], [4., 5., 6.] ]
       syrk(A, alpha=1., transpose=False)
                = `[ [14., 32.],
                   [32., 77.] ]
       syrk(A, alpha=1., transpose=True)
                = `[ [17., 22., 27.],
                   [22., 29., 36.],
                   [27., 36., 45.] ]
    
       Batch matrix multiply
       A = `[ `[ [1., 1.] ], `[ [0.1, 0.1] ] ]
       syrk(A, alpha=2., transpose=False) = `[ `[ [4.] ], `[ [0.04] ] ]
    
    
    Defined in src/operator/tensor/la_op.cc:L730
    returns

    org.apache.mxnet.NDArrayFuncReturn

  289. abstract def linalg_trmm(args: Any*): NDArrayFuncReturn

    Performs multiplication with a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be 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:L333
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Performs multiplication with a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be 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:L333
    returns

    org.apache.mxnet.NDArrayFuncReturn

  291. abstract def linalg_trsm(args: Any*): NDArrayFuncReturn

    Solves matrix equation involving a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be 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:L396
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Solves matrix equation involving a lower triangular matrix.
    Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
    on the leading *n-2* dimensions.
    
    If *n=2*, *A* must be 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:L396
    returns

    org.apache.mxnet.NDArrayFuncReturn

  293. abstract def log(args: Any*): NDArrayFuncReturn

    Returns element-wise Natural logarithmic value of the input.
    
    The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
    
    The storage type of ``log`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L76
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise Natural logarithmic value of the input.
    
    The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
    
    The storage type of ``log`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L76
    returns

    org.apache.mxnet.NDArrayFuncReturn

  295. abstract def log10(args: Any*): NDArrayFuncReturn

    Returns element-wise Base-10 logarithmic value of the input.
    
    ``10**log10(x) = x``
    
    The storage type of ``log10`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L93
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise Base-10 logarithmic value of the input.
    
    ``10**log10(x) = x``
    
    The storage type of ``log10`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L93
    returns

    org.apache.mxnet.NDArrayFuncReturn

  297. abstract def log1p(args: Any*): NDArrayFuncReturn

    Returns element-wise ``log(1 + x)`` value of the input.
    
    This function is more accurate than ``log(1 + x)``  for small ``x`` so that
    :math:`1+x\approx 1`
    
    The storage type of ``log1p`` output depends upon the input storage type:
    
       - log1p(default) = default
       - log1p(row_sparse) = row_sparse
       - log1p(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L206
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise ``log(1 + x)`` value of the input.
    
    This function is more accurate than ``log(1 + x)``  for small ``x`` so that
    :math:`1+x\approx 1`
    
    The storage type of ``log1p`` output depends upon the input storage type:
    
       - log1p(default) = default
       - log1p(row_sparse) = row_sparse
       - log1p(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L206
    returns

    org.apache.mxnet.NDArrayFuncReturn

  299. abstract def log2(args: Any*): NDArrayFuncReturn

    Returns element-wise Base-2 logarithmic value of the input.
    
    ``2**log2(x) = x``
    
    The storage type of ``log2`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L105
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Returns element-wise Base-2 logarithmic value of the input.
    
    ``2**log2(x) = x``
    
    The storage type of ``log2`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L105
    returns

    org.apache.mxnet.NDArrayFuncReturn

  301. abstract def log_softmax(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  303. abstract def logical_not(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

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

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

    org.apache.mxnet.NDArrayFuncReturn

  305. abstract def make_loss(args: Any*): NDArrayFuncReturn

    Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = make_loss(cross_entropy)
    
    We will need to use ``make_loss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    The storage type of ``make_loss`` output depends upon the input storage type:
    
       - make_loss(default) = default
       - make_loss(row_sparse) = row_sparse
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L360
    returns

    org.apache.mxnet.NDArrayFuncReturn

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

    Make your own loss function in network construction.
    
    This operator accepts a customized loss function symbol as a terminal loss and
    the symbol should be an operator with no backward dependency.
    The output of this function is the gradient of loss with respect to the input data.
    
    For example, if you are a making a cross entropy loss function. Assume ``out`` is the
    predicted output and ``label`` is the true label, then the cross entropy can be defined as::
    
      cross_entropy = label * log(out) + (1 - label) * log(1 - out)
      loss = make_loss(cross_entropy)
    
    We will need to use ``make_loss`` when we are creating our own loss function or we want to
    combine multiple loss functions. Also we may want to stop some variables' gradients
    from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``.
    
    The storage type of ``make_loss`` output depends upon the input storage type:
    
       - make_loss(default) = default
       - make_loss(row_sparse) = row_sparse
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L360
    returns

    org.apache.mxnet.NDArrayFuncReturn

  307. abstract def max(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
    returns

    org.apache.mxnet.NDArrayFuncReturn

  308. abstract def max(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
    returns

    org.apache.mxnet.NDArrayFuncReturn

  309. abstract def max_axis(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
    returns

    org.apache.mxnet.NDArrayFuncReturn

  310. abstract def max_axis(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
    returns

    org.apache.mxnet.NDArrayFuncReturn

  311. abstract def mean(args: Any*): NDArrayFuncReturn

    Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L84
    returns

    org.apache.mxnet.NDArrayFuncReturn

  312. abstract def mean(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L84
    returns

    org.apache.mxnet.NDArrayFuncReturn

  313. abstract def min(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
    returns

    org.apache.mxnet.NDArrayFuncReturn

  314. abstract def min(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
    returns

    org.apache.mxnet.NDArrayFuncReturn

  315. abstract def min_axis(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
    returns

    org.apache.mxnet.NDArrayFuncReturn

  316. abstract def min_axis(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
    returns

    org.apache.mxnet.NDArrayFuncReturn

  317. abstract def moments(args: Any*): NDArrayFuncReturn

    Calculate the mean and variance of `data`.
    
    The mean and variance are calculated by aggregating the contents of data across axes.
    If x is 1-D and axes = [0] this is just the mean and variance of a vector.
    
    Example:
    
         x = `[ [1, 2, 3], [4, 5, 6] ]
         mean, var = moments(data=x, axes=[0])
         mean = [2.5, 3.5, 4.5]
         var = [2.25, 2.25, 2.25]
         mean, var = moments(data=x, axes=[1])
         mean = [2.0, 5.0]
         var = [0.66666667, 0.66666667]
         mean, var = moments(data=x, axis=[0, 1])
         mean = [3.5]
         var = [2.9166667]
    
    
    
    Defined in src/operator/nn/moments.cc:L54
    returns

    org.apache.mxnet.NDArrayFuncReturn

  318. abstract def moments(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Calculate the mean and variance of `data`.
    
    The mean and variance are calculated by aggregating the contents of data across axes.
    If x is 1-D and axes = [0] this is just the mean and variance of a vector.
    
    Example:
    
         x = `[ [1, 2, 3], [4, 5, 6] ]
         mean, var = moments(data=x, axes=[0])
         mean = [2.5, 3.5, 4.5]
         var = [2.25, 2.25, 2.25]
         mean, var = moments(data=x, axes=[1])
         mean = [2.0, 5.0]
         var = [0.66666667, 0.66666667]
         mean, var = moments(data=x, axis=[0, 1])
         mean = [3.5]
         var = [2.9166667]
    
    
    
    Defined in src/operator/nn/moments.cc:L54
    returns

    org.apache.mxnet.NDArrayFuncReturn

  319. abstract def mp_lamb_update_phase1(args: Any*): NDArrayFuncReturn

    Mixed Precision version of Phase I of lamb update
    it performs the following operations and returns g:.
    
              Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
              .. math::
                  \begin{gather*}
                  grad32 = grad(float16) * rescale_grad
                  if (grad < -clip_gradient)
                  then
                       grad = -clip_gradient
                  if (grad > clip_gradient)
                  then
                       grad = clip_gradient
    
                  mean = beta1 * mean + (1 - beta1) * grad;
                  variance = beta2 * variance + (1. - beta2) * grad ^ 2;
    
                  if (bias_correction)
                  then
                       mean_hat = mean / (1. - beta1^t);
                       var_hat = var / (1 - beta2^t);
                       g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight32;
                  else
                       g = mean / (var_data^(1/2) + epsilon) + wd * weight32;
                  \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L1033
    returns

    org.apache.mxnet.NDArrayFuncReturn

  320. abstract def mp_lamb_update_phase1(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Mixed Precision version of Phase I of lamb update
    it performs the following operations and returns g:.
    
              Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
              .. math::
                  \begin{gather*}
                  grad32 = grad(float16) * rescale_grad
                  if (grad < -clip_gradient)
                  then
                       grad = -clip_gradient
                  if (grad > clip_gradient)
                  then
                       grad = clip_gradient
    
                  mean = beta1 * mean + (1 - beta1) * grad;
                  variance = beta2 * variance + (1. - beta2) * grad ^ 2;
    
                  if (bias_correction)
                  then
                       mean_hat = mean / (1. - beta1^t);
                       var_hat = var / (1 - beta2^t);
                       g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight32;
                  else
                       g = mean / (var_data^(1/2) + epsilon) + wd * weight32;
                  \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L1033
    returns

    org.apache.mxnet.NDArrayFuncReturn

  321. abstract def mp_lamb_update_phase2(args: Any*): NDArrayFuncReturn

    Mixed Precision version Phase II of lamb update
    it performs the following operations and updates grad.
    
              Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
              .. math::
                  \begin{gather*}
                  if (lower_bound >= 0)
                  then
                       r1 = max(r1, lower_bound)
                  if (upper_bound >= 0)
                  then
                       r1 = max(r1, upper_bound)
    
                  if (r1 == 0 or r2 == 0)
                  then
                       lr = lr
                  else
                       lr = lr * (r1/r2)
                  weight32 = weight32 - lr * g
                  weight(float16) = weight32
                  \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L1075
    returns

    org.apache.mxnet.NDArrayFuncReturn

  322. abstract def mp_lamb_update_phase2(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Mixed Precision version Phase II of lamb update
    it performs the following operations and updates grad.
    
              Link to paper: https://arxiv.org/pdf/1904.00962.pdf
    
              .. math::
                  \begin{gather*}
                  if (lower_bound >= 0)
                  then
                       r1 = max(r1, lower_bound)
                  if (upper_bound >= 0)
                  then
                       r1 = max(r1, upper_bound)
    
                  if (r1 == 0 or r2 == 0)
                  then
                       lr = lr
                  else
                       lr = lr * (r1/r2)
                  weight32 = weight32 - lr * g
                  weight(float16) = weight32
                  \end{gather*}
    
    
    
    Defined in src/operator/optimizer_op.cc:L1075
    returns

    org.apache.mxnet.NDArrayFuncReturn

  323. abstract def mp_nag_mom_update(args: Any*): NDArrayFuncReturn

    Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.
    
    
    Defined in src/operator/optimizer_op.cc:L745
    returns

    org.apache.mxnet.NDArrayFuncReturn

  324. abstract def mp_nag_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.
    
    
    Defined in src/operator/optimizer_op.cc:L745
    returns

    org.apache.mxnet.NDArrayFuncReturn

  325. abstract def mp_sgd_mom_update(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    returns

    org.apache.mxnet.NDArrayFuncReturn

  326. abstract def mp_sgd_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    returns

    org.apache.mxnet.NDArrayFuncReturn

  327. abstract def mp_sgd_update(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    returns

    org.apache.mxnet.NDArrayFuncReturn

  328. abstract def mp_sgd_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    returns

    org.apache.mxnet.NDArrayFuncReturn

  329. abstract def multi_all_finite(args: Any*): NDArrayFuncReturn

    Check if all the float numbers in all the arrays are finite (used for AMP)
    
    
    Defined in src/operator/contrib/all_finite.cc:L133
    returns

    org.apache.mxnet.NDArrayFuncReturn

  330. abstract def multi_all_finite(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Check if all the float numbers in all the arrays are finite (used for AMP)
    
    
    Defined in src/operator/contrib/all_finite.cc:L133
    returns

    org.apache.mxnet.NDArrayFuncReturn

  331. abstract def multi_lars(args: Any*): NDArrayFuncReturn

    Compute the LARS coefficients of multiple weights and grads from their sums of square"
    
    
    Defined in src/operator/contrib/multi_lars.cc:L37
    returns

    org.apache.mxnet.NDArrayFuncReturn

  332. abstract def multi_lars(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Compute the LARS coefficients of multiple weights and grads from their sums of square"
    
    
    Defined in src/operator/contrib/multi_lars.cc:L37
    returns

    org.apache.mxnet.NDArrayFuncReturn

  333. abstract def multi_mp_sgd_mom_update(args: Any*): NDArrayFuncReturn

    Momentum update function for multi-precision 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.
    
    
    
    Defined in src/operator/optimizer_op.cc:L472
    returns

    org.apache.mxnet.NDArrayFuncReturn

  334. abstract def multi_mp_sgd_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Momentum update function for multi-precision 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.
    
    
    
    Defined in src/operator/optimizer_op.cc:L472
    returns

    org.apache.mxnet.NDArrayFuncReturn

  335. abstract def multi_mp_sgd_update(args: Any*): NDArrayFuncReturn

    Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/optimizer_op.cc:L417
    returns

    org.apache.mxnet.NDArrayFuncReturn

  336. abstract def multi_mp_sgd_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/optimizer_op.cc:L417
    returns

    org.apache.mxnet.NDArrayFuncReturn

  337. abstract def multi_sgd_mom_update(args: Any*): NDArrayFuncReturn

    Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    
    
    Defined in src/operator/optimizer_op.cc:L374
    returns

    org.apache.mxnet.NDArrayFuncReturn

  338. abstract def multi_sgd_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    
    
    Defined in src/operator/optimizer_op.cc:L374
    returns

    org.apache.mxnet.NDArrayFuncReturn

  339. abstract def multi_sgd_update(args: Any*): NDArrayFuncReturn

    Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/optimizer_op.cc:L329
    returns

    org.apache.mxnet.NDArrayFuncReturn

  340. abstract def multi_sgd_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/optimizer_op.cc:L329
    returns

    org.apache.mxnet.NDArrayFuncReturn

  341. abstract def multi_sum_sq(args: Any*): NDArrayFuncReturn

    Compute the sums of squares of multiple arrays
    
    
    Defined in src/operator/contrib/multi_sum_sq.cc:L36
    returns

    org.apache.mxnet.NDArrayFuncReturn

  342. abstract def multi_sum_sq(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Compute the sums of squares of multiple arrays
    
    
    Defined in src/operator/contrib/multi_sum_sq.cc:L36
    returns

    org.apache.mxnet.NDArrayFuncReturn

  343. abstract def nag_mom_update(args: Any*): NDArrayFuncReturn

    Update function for Nesterov Accelerated Gradient( NAG) optimizer.
    It updates the weights using the following formula,
    
    .. math::
      v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\
      W_t = W_{t-1} - v_t
    
    Where
    :math:`\eta` is the learning rate of the optimizer
    :math:`\gamma` is the decay rate of the momentum estimate
    :math:`\v_t` is the update vector at time step `t`
    :math:`\W_t` is the weight vector at time step `t`
    
    
    
    Defined in src/operator/optimizer_op.cc:L726
    returns

    org.apache.mxnet.NDArrayFuncReturn

  344. abstract def nag_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for Nesterov Accelerated Gradient( NAG) optimizer.
    It updates the weights using the following formula,
    
    .. math::
      v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\
      W_t = W_{t-1} - v_t
    
    Where
    :math:`\eta` is the learning rate of the optimizer
    :math:`\gamma` is the decay rate of the momentum estimate
    :math:`\v_t` is the update vector at time step `t`
    :math:`\W_t` is the weight vector at time step `t`
    
    
    
    Defined in src/operator/optimizer_op.cc:L726
    returns

    org.apache.mxnet.NDArrayFuncReturn

  345. abstract def nanprod(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_prod_value.cc:L47
    returns

    org.apache.mxnet.NDArrayFuncReturn

  346. abstract def nanprod(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_prod_value.cc:L47
    returns

    org.apache.mxnet.NDArrayFuncReturn

  347. abstract def nansum(args: Any*): NDArrayFuncReturn

    Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_sum_value.cc:L102
    returns

    org.apache.mxnet.NDArrayFuncReturn

  348. abstract def nansum(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_sum_value.cc:L102
    returns

    org.apache.mxnet.NDArrayFuncReturn

  349. abstract def negative(args: Any*): NDArrayFuncReturn

    Numerical negative of the argument, element-wise.
    
    The storage type of ``negative`` output depends upon the input storage type:
    
       - negative(default) = default
       - negative(row_sparse) = row_sparse
       - negative(csr) = csr
    returns

    org.apache.mxnet.NDArrayFuncReturn

  350. abstract def negative(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Numerical negative of the argument, element-wise.
    
    The storage type of ``negative`` output depends upon the input storage type:
    
       - negative(default) = default
       - negative(row_sparse) = row_sparse
       - negative(csr) = csr
    returns

    org.apache.mxnet.NDArrayFuncReturn

  351. abstract def norm(args: Any*): NDArrayFuncReturn

    Computes the norm on an NDArray.
    
    This operator computes the norm on an NDArray with the specified axis, depending
    on the value of the ord parameter. By default, it computes the L2 norm on the entire
    array. Currently only ord=2 supports sparse ndarrays.
    
    Examples::
    
      x = `[ `[ [1, 2],
            [3, 4] ],
           `[ [2, 2],
            [5, 6] ] ]
    
      norm(x, ord=2, axis=1) = `[ [3.1622777 4.472136 ]
                                [5.3851647 6.3245554] ]
    
      norm(x, ord=1, axis=1) = `[ [4., 6.],
                                [7., 8.] ]
    
      rsp = x.cast_storage('row_sparse')
    
      norm(rsp) = [5.47722578]
    
      csr = x.cast_storage('csr')
    
      norm(csr) = [5.47722578]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_norm_value.cc:L89
    returns

    org.apache.mxnet.NDArrayFuncReturn

  352. abstract def norm(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the norm on an NDArray.
    
    This operator computes the norm on an NDArray with the specified axis, depending
    on the value of the ord parameter. By default, it computes the L2 norm on the entire
    array. Currently only ord=2 supports sparse ndarrays.
    
    Examples::
    
      x = `[ `[ [1, 2],
            [3, 4] ],
           `[ [2, 2],
            [5, 6] ] ]
    
      norm(x, ord=2, axis=1) = `[ [3.1622777 4.472136 ]
                                [5.3851647 6.3245554] ]
    
      norm(x, ord=1, axis=1) = `[ [4., 6.],
                                [7., 8.] ]
    
      rsp = x.cast_storage('row_sparse')
    
      norm(rsp) = [5.47722578]
    
      csr = x.cast_storage('csr')
    
      norm(csr) = [5.47722578]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_norm_value.cc:L89
    returns

    org.apache.mxnet.NDArrayFuncReturn

  353. abstract def normal(args: Any*): NDArrayFuncReturn

    Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale*
    (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = `[ [ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114] ]
    
    
    Defined in src/operator/random/sample_op.cc:L113
    returns

    org.apache.mxnet.NDArrayFuncReturn

  354. abstract def normal(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from a normal (Gaussian) distribution.
    
    .. note:: The existing alias ``normal`` is deprecated.
    
    Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale*
    (standard deviation).
    
    Example::
    
       normal(loc=0, scale=1, shape=(2,2)) = `[ [ 1.89171135, -1.16881478],
                                              [-1.23474145,  1.55807114] ]
    
    
    Defined in src/operator/random/sample_op.cc:L113
    returns

    org.apache.mxnet.NDArrayFuncReturn

  355. abstract def one_hot(args: Any*): NDArrayFuncReturn

    Returns a one-hot array.
    
    The locations represented by `indices` take value `on_value`, while all
    other locations take value `off_value`.
    
    `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth`  of ``d`` would result
    in an output array of shape ``(i0, i1, d)`` with::
    
      output[i,j,:] = off_value
      output[i,j,indices[i,j] ] = on_value
    
    Examples::
    
      one_hot([1,0,2,0], 3) = `[ [ 0.  1.  0.]
                               [ 1.  0.  0.]
                               [ 0.  0.  1.]
                               [ 1.  0.  0.] ]
    
      one_hot([1,0,2,0], 3, on_value=8, off_value=1,
              dtype='int32') = `[ [1 8 1]
                                [8 1 1]
                                [1 1 8]
                                [8 1 1] ]
    
      one_hot(`[ [1,0],[1,0],[2,0] ], 3) = `[ `[ [ 0.  1.  0.]
                                          [ 1.  0.  0.] ]
    
                                         `[ [ 0.  1.  0.]
                                          [ 1.  0.  0.] ]
    
                                         `[ [ 0.  0.  1.]
                                          [ 1.  0.  0.] ] ]
    
    
    Defined in src/operator/tensor/indexing_op.cc:L824
    returns

    org.apache.mxnet.NDArrayFuncReturn

  356. abstract def one_hot(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Returns a one-hot array.
    
    The locations represented by `indices` take value `on_value`, while all
    other locations take value `off_value`.
    
    `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth`  of ``d`` would result
    in an output array of shape ``(i0, i1, d)`` with::
    
      output[i,j,:] = off_value
      output[i,j,indices[i,j] ] = on_value
    
    Examples::
    
      one_hot([1,0,2,0], 3) = `[ [ 0.  1.  0.]
                               [ 1.  0.  0.]
                               [ 0.  0.  1.]
                               [ 1.  0.  0.] ]
    
      one_hot([1,0,2,0], 3, on_value=8, off_value=1,
              dtype='int32') = `[ [1 8 1]
                                [8 1 1]
                                [1 1 8]
                                [8 1 1] ]
    
      one_hot(`[ [1,0],[1,0],[2,0] ], 3) = `[ `[ [ 0.  1.  0.]
                                          [ 1.  0.  0.] ]
    
                                         `[ [ 0.  1.  0.]
                                          [ 1.  0.  0.] ]
    
                                         `[ [ 0.  0.  1.]
                                          [ 1.  0.  0.] ] ]
    
    
    Defined in src/operator/tensor/indexing_op.cc:L824
    returns

    org.apache.mxnet.NDArrayFuncReturn

  357. abstract def ones_like(args: Any*): NDArrayFuncReturn

    Return an array of ones with the same shape and type
    as the input array.
    
    Examples::
    
      x = `[ [ 0.,  0.,  0.],
           [ 0.,  0.,  0.] ]
    
      ones_like(x) = `[ [ 1.,  1.,  1.],
                      [ 1.,  1.,  1.] ]
    returns

    org.apache.mxnet.NDArrayFuncReturn

  358. abstract def ones_like(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Return an array of ones with the same shape and type
    as the input array.
    
    Examples::
    
      x = `[ [ 0.,  0.,  0.],
           [ 0.,  0.,  0.] ]
    
      ones_like(x) = `[ [ 1.,  1.,  1.],
                      [ 1.,  1.,  1.] ]
    returns

    org.apache.mxnet.NDArrayFuncReturn

  359. abstract def pad(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

  360. abstract def pad(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

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

    org.apache.mxnet.NDArrayFuncReturn

  361. abstract def pick(args: Any*): NDArrayFuncReturn

    Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i] ]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = `[ [ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.] ]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = `[ [ 2.],
                                     [ 3.],
                                     [ 6.] ]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

  362. abstract def pick(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Picks elements from an input array according to the input indices along the given axis.
    
    Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be
    an output array of shape ``(i0,)`` with::
    
      output[i] = input[i, indices[i] ]
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last element along an axis (the `clip` mode).
    
    This function supports n-dimensional input and (n-1)-dimensional indices arrays.
    
    Examples::
    
      x = `[ [ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.] ]
    
      // picks elements with specified indices along axis 0
      pick(x, y=[0,1], 0) = [ 1.,  4.]
    
      // picks elements with specified indices along axis 1
      pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 using 'wrap' mode
      // to place indicies that would normally be out of bounds
      pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]
    
      y = `[ [ 1.],
           [ 0.],
           [ 2.] ]
    
      // picks elements with specified indices along axis 1 and dims are maintained
      pick(x,y, 1, keepdims=True) = `[ [ 2.],
                                     [ 3.],
                                     [ 6.] ]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L155
    returns

    org.apache.mxnet.NDArrayFuncReturn

  363. abstract def preloaded_multi_mp_sgd_mom_update(args: Any*): NDArrayFuncReturn

    Momentum update function for multi-precision 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.
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L200
    returns

    org.apache.mxnet.NDArrayFuncReturn

  364. abstract def preloaded_multi_mp_sgd_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Momentum update function for multi-precision 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.
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L200
    returns

    org.apache.mxnet.NDArrayFuncReturn

  365. abstract def preloaded_multi_mp_sgd_update(args: Any*): NDArrayFuncReturn

    Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L140
    returns

    org.apache.mxnet.NDArrayFuncReturn

  366. abstract def preloaded_multi_mp_sgd_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L140
    returns

    org.apache.mxnet.NDArrayFuncReturn

  367. abstract def preloaded_multi_sgd_mom_update(args: Any*): NDArrayFuncReturn

    Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L91
    returns

    org.apache.mxnet.NDArrayFuncReturn

  368. abstract def preloaded_multi_sgd_mom_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L91
    returns

    org.apache.mxnet.NDArrayFuncReturn

  369. abstract def preloaded_multi_sgd_update(args: Any*): NDArrayFuncReturn

    Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L42
    returns

    org.apache.mxnet.NDArrayFuncReturn

  370. abstract def preloaded_multi_sgd_update(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Update function for Stochastic Gradient Descent (SDG) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    
    
    Defined in src/operator/contrib/preloaded_multi_sgd.cc:L42
    returns

    org.apache.mxnet.NDArrayFuncReturn

  371. abstract def prod(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L31
    returns

    org.apache.mxnet.NDArrayFuncReturn

  372. abstract def prod(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/./broadcast_reduce_op.h:L31
    returns

    org.apache.mxnet.NDArrayFuncReturn

  373. abstract def radians(args: Any*): NDArrayFuncReturn

    Converts each element of the input array from degrees to radians.
    
    .. math::
       radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]
    
    The storage type of ``radians`` output depends upon the input storage type:
    
       - radians(default) = default
       - radians(row_sparse) = row_sparse
       - radians(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L293
    returns

    org.apache.mxnet.NDArrayFuncReturn

  374. abstract def radians(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Converts each element of the input array from degrees to radians.
    
    .. math::
       radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]
    
    The storage type of ``radians`` output depends upon the input storage type:
    
       - radians(default) = default
       - radians(row_sparse) = row_sparse
       - radians(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L293
    returns

    org.apache.mxnet.NDArrayFuncReturn

  375. abstract def random_exponential(args: Any*): NDArrayFuncReturn

    Draw random samples from an exponential distribution.
    
    Samples are distributed according to an exponential distribution parametrized by *lambda* (rate).
    
    Example::
    
       exponential(lam=4, shape=(2,2)) = `[ [ 0.0097189 ,  0.08999364],
                                          [ 0.04146638,  0.31715935] ]
    
    
    Defined in src/operator/random/sample_op.cc:L137
    returns

    org.apache.mxnet.NDArrayFuncReturn

  376. abstract def random_exponential(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

    Draw random samples from an exponential distribution.
    
    Samples are distributed according to an exponential distribution parametrized by *lambda* (rate).
    
    Example::
    
       exponential(lam=4, shape=(2,2)) = `[ [ 0.0097189 ,  0.08999364],
                                          [ 0.04146638,  0.31715935] ]
    
    
    Defined in src/operator/random/sample_op.cc:L137
    returns

    org.apache.mxnet.NDArrayFuncReturn

  377. abstract def random_gamma(args: Any*): NDArrayFuncReturn

    Draw random samples from a gamma distribution.
    
    Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale).
    
    Example::
    
       gamma(alpha=9, beta=0.5, shape=(2,2)) = `[ [ 7.10486984,  3.37695289],
                                                [ 3.91697288,  3.65933681] ]
    
    
    Defined in src/operator/random/sample_op.cc:L125
    returns

    org.apache.mxnet.NDArrayFuncReturn

  378. abstract def random_gamma(kwargs: Map[String, Any] = null)(args: Any*</