org.apache.mxnet

NDArrayAPI

Related Doc: package mxnet

object NDArrayAPI extends NDArrayAPIBase

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

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  1. abstract def Activation(data: NDArray, act_type: String, out: Option[NDArray] = None): 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:L167
    data

    The input array.

    act_type

    Activation function to be applied.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  2. abstract def BatchNorm(data: NDArray, gamma: NDArray, beta: NDArray, moving_mean: NDArray, moving_var: NDArray, eps: Option[Double] = None, momentum: Option[Float] = None, fix_gamma: Option[Boolean] = None, use_global_stats: Option[Boolean] = None, output_mean_var: Option[Boolean] = None, axis: Option[Int] = None, cudnn_off: Option[Boolean] = None, out: Option[NDArray] = None): 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:L572
    data

    Input data to batch normalization

    gamma

    gamma array

    beta

    beta array

    moving_mean

    running mean of input

    moving_var

    running variance of input

    eps

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

    momentum

    Momentum for moving average

    fix_gamma

    Fix gamma while training

    use_global_stats

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

    output_mean_var

    Output the mean and inverse std

    axis

    Specify which shape axis the channel is specified

    cudnn_off

    Do not select CUDNN operator, if available

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  3. abstract def BatchNorm_v1(data: NDArray, gamma: NDArray, beta: NDArray, eps: Option[Float] = None, momentum: Option[Float] = None, fix_gamma: Option[Boolean] = None, use_global_stats: Option[Boolean] = None, output_mean_var: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    Input data to batch normalization

    gamma

    gamma array

    beta

    beta array

    eps

    Epsilon to prevent div 0

    momentum

    Momentum for moving average

    fix_gamma

    Fix gamma while training

    use_global_stats

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

    output_mean_var

    Output All,normal mean and var

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  4. abstract def BilinearSampler(data: NDArray, grid: NDArray, cudnn_off: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    Input data to the BilinearsamplerOp.

    grid

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

    cudnn_off

    whether to turn cudnn off

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  5. abstract def BlockGrad(data: NDArray, out: Option[NDArray] = None): 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:L299
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  6. abstract def CTCLoss(data: NDArray, label: NDArray, data_lengths: NDArray, label_lengths: NDArray, use_data_lengths: Option[Boolean] = None, use_label_lengths: Option[Boolean] = None, blank_label: Option[String] = None, out: Option[NDArray] = None): 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
    data

    Input ndarray

    label

    Ground-truth labels for the loss.

    data_lengths

    Lengths of data for each of the samples. Only required when use_data_lengths is true.

    label_lengths

    Lengths of labels for each of the samples. Only required when use_label_lengths is true.

    use_data_lengths

    Whether the data lenghts are decided by data_lengths. If false, the lengths are equal to the max sequence length.

    use_label_lengths

    Whether the label lenghts are decided by label_lengths, or derived from padding_mask. If false, the lengths are derived from the first occurrence of the value of padding_mask. The value of padding_mask is 0 when first CTC label is reserved for blank, and -1 when last label is reserved for blank. See blank_label.

    blank_label

    Set the label that is reserved for blank label.If "first", 0-th label is reserved, and label values for tokens in the vocabulary are between 1 and alphabet_size-1, and the padding mask is -1. If "last", last label value alphabet_size-1 is reserved for blank label instead, and label values for tokens in the vocabulary are between 0 and alphabet_size-2, and the padding mask is 0.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  7. abstract def Cast(data: NDArray, dtype: String, out: Option[NDArray] = None): 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:L634
    data

    The input.

    dtype

    Output data type.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  8. abstract def Concat(data: Array[NDArray], num_args: Int, dim: Option[Int] = None, out: Option[NDArray] = None): 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:L371
    data

    List of arrays to concatenate

    num_args

    Number of inputs to be concated.

    dim

    the dimension to be concated.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  9. abstract def Convolution(data: NDArray, weight: NDArray, bias: NDArray, kernel: Shape, stride: Option[Shape] = None, dilate: Option[Shape] = None, pad: Option[Shape] = None, num_filter: Int, num_group: Option[Int] = None, workspace: Option[Long] = None, no_bias: Option[Boolean] = None, cudnn_tune: Option[String] = None, cudnn_off: Option[Boolean] = None, layout: Option[String] = None, out: Option[NDArray] = None): 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:L472
    data

    Input data to the ConvolutionOp.

    weight

    Weight matrix.

    bias

    Bias parameter.

    kernel

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

    stride

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

    dilate

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

    pad

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

    num_filter

    Convolution filter(channel) number

    num_group

    Number of group partitions.

    workspace

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

    no_bias

    Whether to disable bias parameter.

    cudnn_tune

    Whether to pick convolution algo by running performance test.

    cudnn_off

    Turn off cudnn for this layer.

    layout

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  10. abstract def Convolution_v1(data: NDArray, weight: NDArray, bias: NDArray, kernel: Shape, stride: Option[Shape] = None, dilate: Option[Shape] = None, pad: Option[Shape] = None, num_filter: Int, num_group: Option[Int] = None, workspace: Option[Long] = None, no_bias: Option[Boolean] = None, cudnn_tune: Option[String] = None, cudnn_off: Option[Boolean] = None, layout: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    Input data to the ConvolutionV1Op.

    weight

    Weight matrix.

    bias

    Bias parameter.

    kernel

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

    stride

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

    dilate

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

    pad

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

    num_filter

    convolution filter(channel) number

    num_group

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

    workspace

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

    no_bias

    Whether to disable bias parameter.

    cudnn_tune

    Whether to pick convolution algo by running performance test. Leads to higher startup time but may give faster speed. Options are: 'off': no tuning 'limited_workspace': run test and pick the fastest algorithm that doesn't exceed workspace limit. 'fastest': pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest.

    cudnn_off

    Turn off cudnn for this layer.

    layout

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  11. abstract def Correlation(data1: NDArray, data2: NDArray, kernel_size: Option[Int] = None, max_displacement: Option[Int] = None, stride1: Option[Int] = None, stride2: Option[Int] = None, pad_size: Option[Int] = None, is_multiply: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data1

    Input data1 to the correlation.

    data2

    Input data2 to the correlation.

    kernel_size

    kernel size for Correlation must be an odd number

    max_displacement

    Max displacement of Correlation

    stride1

    stride1 quantize data1 globally

    stride2

    stride2 quantize data2 within the neighborhood centered around data1

    pad_size

    pad for Correlation

    is_multiply

    operation type is either multiplication or subduction

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  12. abstract def Crop(data: Array[NDArray], num_args: Int, offset: Option[Shape] = None, h_w: Option[Shape] = None, center_crop: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

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

    num_args

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

    offset

    crop offset coordinate: (y, x)

    h_w

    crop height and width: (h, w)

    center_crop

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  13. abstract def Deconvolution(data: NDArray, weight: NDArray, bias: NDArray, kernel: Shape, stride: Option[Shape] = None, dilate: Option[Shape] = None, pad: Option[Shape] = None, adj: Option[Shape] = None, target_shape: Option[Shape] = None, num_filter: Int, num_group: Option[Int] = None, workspace: Option[Long] = None, no_bias: Option[Boolean] = None, cudnn_tune: Option[String] = None, cudnn_off: Option[Boolean] = None, layout: Option[String] = None, out: Option[NDArray] = None): 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.
    data

    Input tensor to the deconvolution operation.

    weight

    Weights representing the kernel.

    bias

    Bias added to the result after the deconvolution operation.

    kernel

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

    stride

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

    dilate

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

    pad

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

    adj

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

    target_shape

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

    num_filter

    Number of output filters.

    num_group

    Number of groups partition.

    workspace

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

    no_bias

    Whether to disable bias parameter.

    cudnn_tune

    Whether to pick convolution algorithm by running performance test.

    cudnn_off

    Turn off cudnn for this layer.

    layout

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  14. abstract def Dropout(data: NDArray, p: Option[Float] = None, mode: Option[String] = None, axes: Option[Shape] = None, cudnn_off: Option[Boolean] = None, out: Option[NDArray] = None): 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:L95
    data

    Input array to which dropout will be applied.

    p

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

    mode

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

    axes

    Axes for variational dropout kernel.

    cudnn_off

    Whether to turn off cudnn in dropout operator. This option is ignored if axes is specified.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  15. abstract def ElementWiseSum(args: Array[NDArray], out: Option[NDArray] = None): 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
    args

    Positional input arguments

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  16. abstract def Embedding(data: NDArray, weight: NDArray, input_dim: Int, output_dim: Int, dtype: Option[String] = None, sparse_grad: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Maps integer indices to vector representations (embeddings).
    
    This operator maps words to real-valued vectors in a high-dimensional space,
    called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
    For example, it has been noted that in the learned embedding spaces, similar words tend
    to be close to each other and dissimilar words far apart.
    
    For an input array of shape (d1, ..., dK),
    the shape of an output array is (d1, ..., dK, output_dim).
    All the input values should be integers in the range [0, input_dim).
    
    If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
    (ip0, op0).
    
    By default, if any index mentioned is too large, it is replaced by the index that addresses
    the last vector in an embedding matrix.
    
    Examples::
    
      input_dim = 4
      output_dim = 5
    
      // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
      y = `[ [  0.,   1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.,   9.],
           [ 10.,  11.,  12.,  13.,  14.],
           [ 15.,  16.,  17.,  18.,  19.] ]
    
      // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
      x = `[ [ 1.,  3.],
           [ 0.,  2.] ]
    
      // Mapped input x to its vector representation y.
      Embedding(x, y, 4, 5) = `[ `[ [  5.,   6.,   7.,   8.,   9.],
                                [ 15.,  16.,  17.,  18.,  19.] ],
    
                               `[ [  0.,   1.,   2.,   3.,   4.],
                                [ 10.,  11.,  12.,  13.,  14.] ] ]
    
    
    The storage type of weight can be either row_sparse or default.
    
    .. Note::
    
        If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
        "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
        and Adam. Note that by default lazy updates is turned on, which may perform differently
        from standard updates. For more details, please check the Optimization API at:
        https://mxnet.incubator.apache.org/api/python/optimization/optimization.html
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L519
    data

    The input array to the embedding operator.

    weight

    The embedding weight matrix.

    input_dim

    Vocabulary size of the input indices.

    output_dim

    Dimension of the embedding vectors.

    dtype

    Data type of weight.

    sparse_grad

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  17. abstract def Flatten(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = `[ [
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ] ],
    
        flatten(x) = `[ [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.] ]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L291
    data

    Input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  18. abstract def FullyConnected(data: NDArray, weight: NDArray, bias: NDArray, num_hidden: Int, no_bias: Option[Boolean] = None, flatten: Option[Boolean] = None, out: Option[NDArray] = None): 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:L277
    data

    Input data.

    weight

    Weight matrix.

    bias

    Bias parameter.

    num_hidden

    Number of hidden nodes of the output.

    no_bias

    Whether to disable bias parameter.

    flatten

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  19. abstract def GridGenerator(data: NDArray, transform_type: String, target_shape: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Generates 2D sampling grid for bilinear sampling.
    data

    Input data to the function.

    transform_type

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

    target_shape

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  20. abstract def IdentityAttachKLSparseReg(data: NDArray, sparseness_target: Option[Float] = None, penalty: Option[Float] = None, momentum: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    Input data.

    sparseness_target

    The sparseness target

    penalty

    The tradeoff parameter for the sparseness penalty

    momentum

    The momentum for running average

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  21. abstract def InstanceNorm(data: NDArray, gamma: NDArray, beta: NDArray, eps: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

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

    gamma

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

    beta

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

    eps

    An epsilon parameter to prevent division by 0.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  22. abstract def L2Normalization(data: NDArray, eps: Option[Float] = None, mode: Option[String] = None, out: Option[NDArray] = None): 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
    data

    Input array to normalize.

    eps

    A small constant for numerical stability.

    mode

    Specify the dimension along which to compute L2 norm.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  23. abstract def LRN(data: NDArray, alpha: Option[Float] = None, beta: Option[Float] = None, knorm: Option[Float] = None, nsize: Int, out: Option[NDArray] = None): 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
    data

    Input data to LRN

    alpha

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

    beta

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

    knorm

    The parameter :math:k in the LRN expression.

    nsize

    normalization window width in elements.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  24. abstract def LayerNorm(data: NDArray, gamma: NDArray, beta: NDArray, axis: Option[Int] = None, eps: Option[Float] = None, output_mean_var: Option[Boolean] = None, out: Option[NDArray] = None): 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:L155
    data

    Input data to layer normalization

    gamma

    gamma array

    beta

    beta array

    axis

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

    eps

    An epsilon parameter to prevent division by 0.

    output_mean_var

    Output the mean and std calculated along the given axis.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  25. abstract def LeakyReLU(data: NDArray, gamma: NDArray, act_type: Option[String] = None, slope: Option[Float] = None, lower_bound: Option[Float] = None, upper_bound: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    Input data to activation function.

    gamma

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

    act_type

    Activation function to be applied.

    slope

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

    lower_bound

    Lower bound of random slope. (For rrelu only)

    upper_bound

    Upper bound of random slope. (For rrelu only)

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  26. abstract def LinearRegressionOutput(data: NDArray, label: NDArray, grad_scale: Option[Float] = None, out: Option[NDArray] = None): 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
    data

    Input data to the function.

    label

    Input label to the function.

    grad_scale

    Scale the gradient by a float factor

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  27. abstract def LogisticRegressionOutput(data: NDArray, label: NDArray, grad_scale: Option[Float] = None, out: Option[NDArray] = None): 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
    data

    Input data to the function.

    label

    Input label to the function.

    grad_scale

    Scale the gradient by a float factor

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  28. abstract def MAERegressionOutput(data: NDArray, label: NDArray, grad_scale: Option[Float] = None, out: Option[NDArray] = None): 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
    data

    Input data to the function.

    label

    Input label to the function.

    grad_scale

    Scale the gradient by a float factor

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  29. abstract def MakeLoss(data: NDArray, grad_scale: Option[Float] = None, valid_thresh: Option[Float] = None, normalization: Option[String] = None, out: Option[NDArray] = None): 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
    data

    Input array.

    grad_scale

    Gradient scale as a supplement to unary and binary operators

    valid_thresh

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

    normalization

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  30. abstract def Pad(data: NDArray, mode: String, pad_width: Shape, constant_value: Option[Double] = None, out: Option[NDArray] = None): 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
    data

    An n-dimensional input array.

    mode

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

    pad_width

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

    constant_value

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  31. abstract def Pooling(data: NDArray, kernel: Option[Shape] = None, pool_type: Option[String] = None, global_pool: Option[Boolean] = None, cudnn_off: Option[Boolean] = None, pooling_convention: Option[String] = None, stride: Option[Shape] = None, pad: Option[Shape] = None, p_value: Option[Int] = None, count_include_pad: Option[Boolean] = None, layout: Option[String] = None, out: Option[NDArray] = None): 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
    
    But ``global_pool`` is set to be true, then do a global pooling, namely reset
    ``kernel=(height, width)``.
    
    Three pooling options are supported by ``pool_type``:
    
    - **avg**: average pooling
    - **max**: max pooling
    - **sum**: sum pooling
    - **lp**: Lp pooling
    
    For 3-D pooling, an additional *depth* dimension is added before
    *height*. Namely the input data 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:L416
    data

    Input data to the pooling operator.

    kernel

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

    pool_type

    Pooling type to be applied.

    global_pool

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

    cudnn_off

    Turn off cudnn pooling and use MXNet pooling operator.

    pooling_convention

    Pooling convention to be applied.

    stride

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

    pad

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

    p_value

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

    count_include_pad

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

    layout

    Set layout for input and output. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  32. abstract def Pooling_v1(data: NDArray, kernel: Option[Shape] = None, pool_type: Option[String] = None, global_pool: Option[Boolean] = None, pooling_convention: Option[String] = None, stride: Option[Shape] = None, pad: Option[Shape] = None, out: Option[NDArray] = None): 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
    data

    Input data to the pooling operator.

    kernel

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

    pool_type

    Pooling type to be applied.

    global_pool

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

    pooling_convention

    Pooling convention to be applied.

    stride

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

    pad

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  33. abstract def RNN(data: NDArray, parameters: NDArray, state: NDArray, state_cell: NDArray, sequence_length: NDArray, state_size: Int, num_layers: Int, bidirectional: Option[Boolean] = None, mode: String, p: Option[Float] = None, state_outputs: Option[Boolean] = None, projection_size: Option[Int] = None, lstm_state_clip_min: Option[Double] = None, lstm_state_clip_max: Option[Double] = None, lstm_state_clip_nan: Option[Boolean] = None, use_sequence_length: Option[Boolean] = None, out: Option[NDArray] = None): 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:L690
    data

    Input data to RNN

    parameters

    Vector of all RNN trainable parameters concatenated

    state

    initial hidden state of the RNN

    state_cell

    initial cell state for LSTM networks (only for LSTM)

    sequence_length

    Vector of valid sequence lengths for each element in batch. (Only used if use_sequence_length kwarg is True)

    state_size

    size of the state for each layer

    num_layers

    number of stacked layers

    bidirectional

    whether to use bidirectional recurrent layers

    mode

    the type of RNN to compute

    p

    drop rate of the dropout on the outputs of each RNN layer, except the last layer.

    state_outputs

    Whether to have the states as symbol outputs.

    projection_size

    size of project size

    lstm_state_clip_min

    Minimum clip value of LSTM states. This option must be used together with lstm_state_clip_max.

    lstm_state_clip_max

    Maximum clip value of LSTM states. This option must be used together with lstm_state_clip_min.

    lstm_state_clip_nan

    Whether to stop NaN from propagating in state by clipping it to min/max. If clipping range is not specified, this option is ignored.

    use_sequence_length

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  34. abstract def ROIPooling(data: NDArray, rois: NDArray, pooled_size: Shape, spatial_scale: Float, out: Option[NDArray] = None): NDArrayFuncReturn

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

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

    rois

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

    pooled_size

    ROI pooling output shape (h,w)

    spatial_scale

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  35. abstract def Reshape(data: NDArray, shape: Option[Shape] = None, reverse: Option[Boolean] = None, target_shape: Option[Shape] = None, keep_highest: Option[Boolean] = None, out: Option[NDArray] = None): 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:L202
    data

    Input data to reshape.

    shape

    The target shape

    reverse

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

    target_shape

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

    keep_highest

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  36. abstract def SVMOutput(data: NDArray, label: NDArray, margin: Option[Float] = None, regularization_coefficient: Option[Float] = None, use_linear: Option[Boolean] = None, out: Option[NDArray] = None): 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.
    data

    Input data for SVM transformation.

    label

    Class label for the input data.

    margin

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

    regularization_coefficient

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

    use_linear

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  37. abstract def SequenceLast(data: NDArray, sequence_length: NDArray, use_sequence_length: Option[Boolean] = None, axis: Option[Int] = None, out: Option[NDArray] = None): 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:L100
    data

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

    sequence_length

    vector of sequence lengths of the form [batch_size]

    use_sequence_length

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

    axis

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  38. abstract def SequenceMask(data: NDArray, sequence_length: NDArray, use_sequence_length: Option[Boolean] = None, value: Option[Float] = None, axis: Option[Int] = None, out: Option[NDArray] = None): 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
    data

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

    sequence_length

    vector of sequence lengths of the form [batch_size]

    use_sequence_length

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

    value

    The value to be used as a mask.

    axis

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  39. abstract def SequenceReverse(data: NDArray, sequence_length: NDArray, use_sequence_length: Option[Boolean] = None, axis: Option[Int] = None, out: Option[NDArray] = None): 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
    data

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

    sequence_length

    vector of sequence lengths of the form [batch_size]

    use_sequence_length

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

    axis

    The sequence axis. Only 0 is currently supported.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  40. abstract def SliceChannel(data: NDArray, num_outputs: Int, axis: Option[Int] = None, squeeze_axis: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    The input

    num_outputs

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

    axis

    Axis along which to split.

    squeeze_axis

    If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting squeeze_axis to true removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only if input.shape[axis] == num_outputs.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  41. abstract def Softmax(data: NDArray, label: NDArray, grad_scale: Option[Float] = None, ignore_label: Option[Float] = None, multi_output: Option[Boolean] = None, use_ignore: Option[Boolean] = None, preserve_shape: Option[Boolean] = None, normalization: Option[String] = None, out_grad: Option[Boolean] = None, smooth_alpha: Option[Float] = None, out: Option[NDArray] = None): 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:L230
    data

    Input array.

    label

    Ground truth label.

    grad_scale

    Scales the gradient by a float factor.

    ignore_label

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

    multi_output

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

    use_ignore

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

    preserve_shape

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

    normalization

    Normalizes the gradient.

    out_grad

    Multiplies gradient with output gradient element-wise.

    smooth_alpha

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  42. abstract def SoftmaxActivation(data: NDArray, mode: Option[String] = None, out: Option[NDArray] = None): 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
    data

    The input array.

    mode

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  43. abstract def SoftmaxOutput(data: NDArray, label: NDArray, grad_scale: Option[Float] = None, ignore_label: Option[Float] = None, multi_output: Option[Boolean] = None, use_ignore: Option[Boolean] = None, preserve_shape: Option[Boolean] = None, normalization: Option[String] = None, out_grad: Option[Boolean] = None, smooth_alpha: Option[Float] = None, out: Option[NDArray] = None): 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:L230
    data

    Input array.

    label

    Ground truth label.

    grad_scale

    Scales the gradient by a float factor.

    ignore_label

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

    multi_output

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

    use_ignore

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

    preserve_shape

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

    normalization

    Normalizes the gradient.

    out_grad

    Multiplies gradient with output gradient element-wise.

    smooth_alpha

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  44. abstract def SpatialTransformer(data: NDArray, loc: NDArray, target_shape: Option[Shape] = None, transform_type: String, sampler_type: String, cudnn_off: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Applies a spatial transformer to input feature map.
    data

    Input data to the SpatialTransformerOp.

    loc

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

    target_shape

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

    transform_type

    transformation type

    sampler_type

    sampling type

    cudnn_off

    whether to turn cudnn off

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  45. abstract def SwapAxis(data: NDArray, dim1: Option[Int] = None, dim2: Option[Int] = None, out: Option[NDArray] = None): 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
    data

    Input array.

    dim1

    the first axis to be swapped.

    dim2

    the second axis to be swapped.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  46. abstract def UpSampling(data: Array[NDArray], scale: Int, num_filter: Option[Int] = None, sample_type: String, multi_input_mode: Option[String] = None, num_args: Int, workspace: Option[Long] = None, out: Option[NDArray] = None): 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
    data

    Array of tensors to upsample. For bilinear upsampling, there should be 2 inputs - 1 data and 1 weight.

    scale

    Up sampling scale

    num_filter

    Input filter. Only used by bilinear sample_type.Since bilinear upsampling uses deconvolution, num_filters is set to the number of channels.

    sample_type

    upsampling method

    multi_input_mode

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

    num_args

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

    workspace

    Tmp workspace for deconvolution (MB)

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  47. abstract def abs(data: NDArray, out: Option[NDArray] = None): 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:L708
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  48. abstract def adam_update(weight: NDArray, grad: NDArray, mean: NDArray, vari: NDArray, lr: Float, beta1: Option[Float] = None, beta2: Option[Float] = None, epsilon: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, lazy_update: Option[Boolean] = None, out: Option[NDArray] = None): 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:L686
    weight

    Weight

    grad

    Gradient

    mean

    Moving mean

    vari

    Moving variance

    lr

    Learning rate

    beta1

    The decay rate for the 1st moment estimates.

    beta2

    The decay rate for the 2nd moment estimates.

    epsilon

    A small constant for numerical stability.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    lazy_update

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  49. abstract def add_n(args: Array[NDArray], out: Option[NDArray] = None): 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
    args

    Positional input arguments

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  50. abstract def all_finite(data: NDArray, init_output: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    Array

    init_output

    Initialize output to 1.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  51. abstract def amp_cast(data: NDArray, dtype: String, out: Option[NDArray] = None): 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
    data

    The input.

    dtype

    Output data type.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  52. abstract def amp_multicast(data: Array[NDArray], num_outputs: Int, out: Option[NDArray] = None): 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
    data

    Weights

    num_outputs

    Number of input/output pairs to be casted to the widest type.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  53. abstract def arccos(data: NDArray, out: Option[NDArray] = None): 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:L179
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  54. abstract def arccosh(data: NDArray, out: Option[NDArray] = None): 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:L320
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  55. abstract def arcsin(data: NDArray, out: Option[NDArray] = None): 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:L160
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  56. abstract def arcsinh(data: NDArray, out: Option[NDArray] = None): 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:L306
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  57. abstract def arctan(data: NDArray, out: Option[NDArray] = None): 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:L200
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  58. abstract def arctanh(data: NDArray, out: Option[NDArray] = None): 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:L337
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  59. abstract def argmax(data: NDArray, axis: Option[Int] = None, keepdims: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    The input

    axis

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

    keepdims

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  60. abstract def argmax_channel(data: NDArray, out: Option[NDArray] = None): 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
    data

    The input array

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  61. abstract def argmin(data: NDArray, axis: Option[Int] = None, keepdims: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    The input

    axis

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

    keepdims

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  62. abstract def argsort(data: NDArray, axis: Option[Int] = None, is_ascend: Option[Boolean] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    The input array

    axis

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

    is_ascend

    Whether to sort in ascending or descending order.

    dtype

    DType of the output indices. It is only valid when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely represent the indices.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  63. abstract def batch_dot(lhs: NDArray, rhs: NDArray, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, forward_stype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    The first input

    rhs

    The second input

    transpose_a

    If true then transpose the first input before dot.

    transpose_b

    If true then transpose the second input before dot.

    forward_stype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  64. abstract def batch_take(a: NDArray, indices: NDArray, out: Option[NDArray] = None): 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:L753
    a

    The input array

    indices

    The index array

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  65. abstract def broadcast_add(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  66. abstract def broadcast_axes(data: NDArray, axis: Option[Shape] = None, size: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    The input

    axis

    The axes to perform the broadcasting.

    size

    Target sizes of the broadcasting axes.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  67. abstract def broadcast_axis(data: NDArray, axis: Option[Shape] = None, size: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    The input

    axis

    The axes to perform the broadcasting.

    size

    Target sizes of the broadcasting axes.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  68. abstract def broadcast_div(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  69. abstract def broadcast_equal(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  70. abstract def broadcast_greater(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  71. abstract def broadcast_greater_equal(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  72. abstract def broadcast_hypot(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  73. abstract def broadcast_lesser(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  74. abstract def broadcast_lesser_equal(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  75. abstract def broadcast_like(lhs: NDArray, rhs: NDArray, lhs_axes: Option[Shape] = None, rhs_axes: Option[Shape] = None, out: Option[NDArray] = None): 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:L315
    lhs

    First input.

    rhs

    Second input.

    lhs_axes

    Axes to perform broadcast on in the first input array

    rhs_axes

    Axes to copy from the second input array

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  76. abstract def broadcast_logical_and(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  77. abstract def broadcast_logical_or(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  78. abstract def broadcast_logical_xor(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  79. abstract def broadcast_maximum(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  80. abstract def broadcast_minimum(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  81. abstract def broadcast_minus(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  82. abstract def broadcast_mod(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  83. abstract def broadcast_mul(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  84. abstract def broadcast_not_equal(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  85. abstract def broadcast_plus(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  86. abstract def broadcast_power(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  87. abstract def broadcast_sub(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    First input to the function

    rhs

    Second input to the function

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  88. abstract def broadcast_to(data: NDArray, shape: Option[Shape] = None, out: Option[NDArray] = None): 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:L262
    data

    The input

    shape

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  89. abstract def cast(data: NDArray, dtype: String, out: Option[NDArray] = None): 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:L634
    data

    The input.

    dtype

    Output data type.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  90. abstract def cast_storage(data: NDArray, stype: String, out: Option[NDArray] = None): 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
    data

    The input.

    stype

    Output storage type.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  91. abstract def cbrt(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise cube-root value of the input.
    
    .. math::
       cbrt(x) = \sqrt[3]{x}
    
    Example::
    
       cbrt([1, 8, -125]) = [1, 2, -5]
    
    The storage type of ``cbrt`` output depends upon the input storage type:
    
       - cbrt(default) = default
       - cbrt(row_sparse) = row_sparse
       - cbrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L950
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  92. abstract def ceil(data: NDArray, out: Option[NDArray] = None): 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:L786
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  93. abstract def choose_element_0index(data: NDArray, index: NDArray, axis: Option[Int] = None, keepdims: Option[Boolean] = None, mode: Option[String] = None, out: Option[NDArray] = None): 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:L154
    data

    The input array

    index

    The index array

    axis

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

    keepdims

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

    mode

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  94. abstract def clip(data: NDArray, a_min: Float, a_max: Float, out: Option[NDArray] = None): NDArrayFuncReturn

    Clips (limits) the values in an array.
    
    Given an interval, values outside the interval are clipped to the interval edges.
    Clipping ``x`` between `a_min` and `a_x` would be::
    
       clip(x, a_min, a_max) = max(min(x, a_max), a_min))
    
    Example::
    
        x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    
        clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]
    
    The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \
    parameter values:
    
       - clip(default) = default
       - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
       - clip(csr, a_min <= 0, a_max >= 0) = csr
       - clip(row_sparse, a_min < 0, a_max < 0) = default
       - clip(row_sparse, a_min > 0, a_max > 0) = default
       - clip(csr, a_min < 0, a_max < 0) = csr
       - clip(csr, a_min > 0, a_max > 0) = csr
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L723
    data

    Input array.

    a_min

    Minimum value

    a_max

    Maximum value

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  95. abstract def concat(data: Array[NDArray], num_args: Int, dim: Option[Int] = None, out: Option[NDArray] = None): 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:L371
    data

    List of arrays to concatenate

    num_args

    Number of inputs to be concated.

    dim

    the dimension to be concated.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  96. abstract def cos(data: NDArray, out: Option[NDArray] = None): 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:L89
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  97. abstract def cosh(data: NDArray, out: Option[NDArray] = None): 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:L272
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  98. abstract def crop(data: NDArray, begin: Shape, end: Shape, step: Option[Shape] = None, out: Option[NDArray] = None): 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:L506
    data

    Source input

    begin

    starting indices for the slice operation, supports negative indices.

    end

    ending indices for the slice operation, supports negative indices.

    step

    step for the slice operation, supports negative values.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  99. abstract def ctc_loss(data: NDArray, label: NDArray, data_lengths: NDArray, label_lengths: NDArray, use_data_lengths: Option[Boolean] = None, use_label_lengths: Option[Boolean] = None, blank_label: Option[String] = None, out: Option[NDArray] = None): 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
    data

    Input ndarray

    label

    Ground-truth labels for the loss.

    data_lengths

    Lengths of data for each of the samples. Only required when use_data_lengths is true.

    label_lengths

    Lengths of labels for each of the samples. Only required when use_label_lengths is true.

    use_data_lengths

    Whether the data lenghts are decided by data_lengths. If false, the lengths are equal to the max sequence length.

    use_label_lengths

    Whether the label lenghts are decided by label_lengths, or derived from padding_mask. If false, the lengths are derived from the first occurrence of the value of padding_mask. The value of padding_mask is 0 when first CTC label is reserved for blank, and -1 when last label is reserved for blank. See blank_label.

    blank_label

    Set the label that is reserved for blank label.If "first", 0-th label is reserved, and label values for tokens in the vocabulary are between 1 and alphabet_size-1, and the padding mask is -1. If "last", last label value alphabet_size-1 is reserved for blank label instead, and label values for tokens in the vocabulary are between 0 and alphabet_size-2, and the padding mask is 0.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  100. abstract def degrees(data: NDArray, out: Option[NDArray] = None): 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:L219
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  101. abstract def depth_to_space(data: NDArray, block_size: Int, out: Option[NDArray] = None): 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:L1050
    data

    Input ndarray

    block_size

    Blocks of [block_size. block_size] are moved

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  102. abstract def diag(data: NDArray, k: Option[Int] = None, axis1: Option[Int] = None, axis2: Option[Int] = None, out: Option[NDArray] = None): 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
    data

    Input ndarray

    k

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

    axis1

    The first axis of the sub-arrays of interest. Ignored when the input is a 1-D array.

    axis2

    The second axis of the sub-arrays of interest. Ignored when the input is a 1-D array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  103. abstract def dot(lhs: NDArray, rhs: NDArray, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, forward_stype: Option[String] = None, out: Option[NDArray] = None): 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
    lhs

    The first input

    rhs

    The second input

    transpose_a

    If true then transpose the first input before dot.

    transpose_b

    If true then transpose the second input before dot.

    forward_stype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  104. abstract def elemwise_add(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    first input

    rhs

    second input

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  105. abstract def elemwise_div(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    first input

    rhs

    second input

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  106. abstract def elemwise_mul(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    first input

    rhs

    second input

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  107. abstract def elemwise_sub(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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
    lhs

    first input

    rhs

    second input

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  108. abstract def erf(data: NDArray, out: Option[NDArray] = None): 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:L964
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  109. abstract def erfinv(data: NDArray, out: Option[NDArray] = None): 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:L985
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  110. abstract def exp(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise exponential value of the input.
    
    .. math::
       exp(x) = e^x \approx 2.718^x
    
    Example::
    
       exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]
    
    The storage type of ``exp`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1044
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  111. abstract def expand_dims(data: NDArray, axis: Int, out: Option[NDArray] = None): 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:L416
    data

    Source input

    axis

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  112. abstract def expm1(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns ``exp(x) - 1`` computed element-wise on the input.
    
    This function provides greater precision than ``exp(x) - 1`` for small values of ``x``.
    
    The storage type of ``expm1`` output depends upon the input storage type:
    
       - expm1(default) = default
       - expm1(row_sparse) = row_sparse
       - expm1(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1189
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  113. abstract def fill_element_0index(lhs: NDArray, mhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): 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.
    lhs

    Left operand to the function.

    mhs

    Middle operand to the function.

    rhs

    Right operand to the function.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  114. abstract def fix(data: NDArray, out: Option[NDArray] = None): 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:L843
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  115. abstract def flatten(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Flattens the input array into a 2-D array by collapsing the higher dimensions.
    
    .. note:: `Flatten` is deprecated. Use `flatten` instead.
    
    For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
    the input array into an output array of shape ``(d1, d2*...*dk)``.
    
    Note that the bahavior of this function is different from numpy.ndarray.flatten,
    which behaves similar to mxnet.ndarray.reshape((-1,)).
    
    Example::
    
        x = `[ [
            [1,2,3],
            [4,5,6],
            [7,8,9]
        ],
        [    [1,2,3],
            [4,5,6],
            [7,8,9]
        ] ],
    
        flatten(x) = `[ [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
           [ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.] ]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L291
    data

    Input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  116. abstract def flip(data: NDArray, axis: Shape, out: Option[NDArray] = None): 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:L898
    data

    Input data array

    axis

    The axis which to reverse elements.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  117. abstract def floor(data: NDArray, out: Option[NDArray] = None): 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:L805
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  118. abstract def ftml_update(weight: NDArray, grad: NDArray, d: NDArray, v: NDArray, z: NDArray, lr: Float, beta1: Option[Float] = None, beta2: Option[Float] = None, epsilon: Option[Double] = None, t: Int, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_grad: Option[Float] = None, out: Option[NDArray] = None): 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:L638
    weight

    Weight

    grad

    Gradient

    d

    Internal state d_t

    v

    Internal state v_t

    z

    Internal state z_t

    lr

    Learning rate.

    beta1

    Generally close to 0.5.

    beta2

    Generally close to 1.

    epsilon

    Epsilon to prevent div 0.

    t

    Number of update.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_grad

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  119. abstract def ftrl_update(weight: NDArray, grad: NDArray, z: NDArray, n: NDArray, lr: Float, lamda1: Option[Float] = None, beta: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, out: Option[NDArray] = None): 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:L874
    weight

    Weight

    grad

    Gradient

    z

    z

    n

    Square of grad

    lr

    Learning rate

    lamda1

    The L1 regularization coefficient.

    beta

    Per-Coordinate Learning Rate beta.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  120. abstract def gamma(data: NDArray, out: Option[NDArray] = None): 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
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  121. abstract def gammaln(data: NDArray, out: Option[NDArray] = None): 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
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  122. abstract def gather_nd(data: NDArray, indices: NDArray, out: Option[NDArray] = None): 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] ]
    data

    data

    indices

    indices

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  123. abstract def hard_sigmoid(data: NDArray, alpha: Option[Float] = None, beta: Option[Float] = None, out: Option[NDArray] = None): 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:L133
    data

    The input array.

    alpha

    Slope of hard sigmoid

    beta

    Bias of hard sigmoid.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  124. abstract def identity(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns a copy of the input.
    
    From:src/operator/tensor/elemwise_unary_op_basic.cc:218
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  125. abstract def khatri_rao(args: Array[NDArray], out: Option[NDArray] = None): 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
    args

    Positional input matrices

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  126. abstract def linalg_extractdiag(A: NDArray, offset: Option[Int] = None, out: Option[NDArray] = None): 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
    A

    Tensor of square matrices

    offset

    Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  127. abstract def linalg_extracttrian(A: NDArray, offset: Option[Int] = None, lower: Option[Boolean] = None, out: Option[NDArray] = None): 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
    A

    Tensor of square matrices

    offset

    Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

    lower

    Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  128. abstract def linalg_gelqf(A: NDArray, out: Option[NDArray] = None): 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
    A

    Tensor of input matrices to be factorized

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  129. abstract def linalg_gemm(A: NDArray, B: NDArray, C: NDArray, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, alpha: Option[Double] = None, beta: Option[Double] = None, axis: Option[Int] = None, out: Option[NDArray] = None): 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
    A

    Tensor of input matrices

    B

    Tensor of input matrices

    C

    Tensor of input matrices

    transpose_a

    Multiply with transposed of first input (A).

    transpose_b

    Multiply with transposed of second input (B).

    alpha

    Scalar factor multiplied with A*B.

    beta

    Scalar factor multiplied with C.

    axis

    Axis corresponding to the matrix rows.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  130. abstract def linalg_gemm2(A: NDArray, B: NDArray, transpose_a: Option[Boolean] = None, transpose_b: Option[Boolean] = None, alpha: Option[Double] = None, axis: Option[Int] = None, out: Option[NDArray] = None): 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
    A

    Tensor of input matrices

    B

    Tensor of input matrices

    transpose_a

    Multiply with transposed of first input (A).

    transpose_b

    Multiply with transposed of second input (B).

    alpha

    Scalar factor multiplied with A*B.

    axis

    Axis corresponding to the matrix row indices.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  131. abstract def linalg_inverse(A: NDArray, out: Option[NDArray] = None): 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 inversion
       A = `[ [1., 4.], [2., 3.] ]
       inverse(A) = `[ [-0.6, 0.8], [0.4, -0.2] ]
    
       // Batch matrix inversion
       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:L917
    A

    Tensor of square matrix

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  132. abstract def linalg_makediag(A: NDArray, offset: Option[Int] = None, out: Option[NDArray] = None): 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
    A

    Tensor of diagonal entries

    offset

    Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  133. abstract def linalg_maketrian(A: NDArray, offset: Option[Int] = None, lower: Option[Boolean] = None, out: Option[NDArray] = None): 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
    A

    Tensor of triangular matrices stored as vectors

    offset

    Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.

    lower

    Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  134. abstract def linalg_potrf(A: NDArray, out: Option[NDArray] = None): 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
    A

    Tensor of input matrices to be decomposed

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  135. abstract def linalg_potri(A: NDArray, out: Option[NDArray] = None): 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
    A

    Tensor of lower triangular matrices

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  136. abstract def linalg_sumlogdiag(A: NDArray, out: Option[NDArray] = None): 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
    A

    Tensor of square matrices

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  137. abstract def linalg_syrk(A: NDArray, transpose: Option[Boolean] = None, alpha: Option[Double] = None, out: Option[NDArray] = None): 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
    A

    Tensor of input matrices

    transpose

    Use transpose of input matrix.

    alpha

    Scalar factor to be applied to the result.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  138. abstract def linalg_trmm(A: NDArray, B: NDArray, transpose: Option[Boolean] = None, rightside: Option[Boolean] = None, lower: Option[Boolean] = None, alpha: Option[Double] = None, out: Option[NDArray] = None): 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
    A

    Tensor of lower triangular matrices

    B

    Tensor of matrices

    transpose

    Use transposed of the triangular matrix

    rightside

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

    lower

    True if the triangular matrix is lower triangular, false if it is upper triangular.

    alpha

    Scalar factor to be applied to the result.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  139. abstract def linalg_trsm(A: NDArray, B: NDArray, transpose: Option[Boolean] = None, rightside: Option[Boolean] = None, lower: Option[Boolean] = None, alpha: Option[Double] = None, out: Option[NDArray] = None): 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
    A

    Tensor of lower triangular matrices

    B

    Tensor of matrices

    transpose

    Use transposed of the triangular matrix

    rightside

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

    lower

    True if the triangular matrix is lower triangular, false if it is upper triangular.

    alpha

    Scalar factor to be applied to the result.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  140. abstract def log(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise Natural logarithmic value of the input.
    
    The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
    
    The storage type of ``log`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1057
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  141. abstract def log10(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise Base-10 logarithmic value of the input.
    
    ``10**log10(x) = x``
    
    The storage type of ``log10`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1074
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  142. abstract def log1p(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise ``log(1 + x)`` value of the input.
    
    This function is more accurate than ``log(1 + x)``  for small ``x`` so that
    :math:`1+x\approx 1`
    
    The storage type of ``log1p`` output depends upon the input storage type:
    
       - log1p(default) = default
       - log1p(row_sparse) = row_sparse
       - log1p(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1171
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  143. abstract def log2(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise Base-2 logarithmic value of the input.
    
    ``2**log2(x) = x``
    
    The storage type of ``log2`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1086
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  144. abstract def log_softmax(data: NDArray, axis: Option[Int] = None, temperature: Option[Double] = None, dtype: Option[String] = None, out: Option[NDArray] = None): 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)
    data

    The input array.

    axis

    The axis along which to compute softmax.

    temperature

    Temperature parameter in softmax

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  145. abstract def logical_not(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  146. abstract def make_loss(data: NDArray, out: Option[NDArray] = None): 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:L332
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  147. abstract def max(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  148. abstract def max_axis(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the max of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  149. abstract def mean(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the mean of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  150. abstract def min(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  151. abstract def min_axis(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the min of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  152. abstract def moments(data: NDArray, axes: Option[Shape] = None, keepdims: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    Input ndarray

    axes

    Array of ints. Axes along which to compute mean and variance.

    keepdims

    produce moments with the same dimensionality as the input.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  153. abstract def mp_nag_mom_update(weight: NDArray, grad: NDArray, mom: NDArray, weight32: NDArray, lr: Float, momentum: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.
    
    
    Defined in src/operator/optimizer_op.cc:L743
    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    weight32

    Weight32

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  154. abstract def mp_sgd_mom_update(weight: NDArray, grad: NDArray, mom: NDArray, weight32: NDArray, lr: Float, momentum: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, lazy_update: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    weight32

    Weight32

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    lazy_update

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  155. abstract def mp_sgd_update(weight: NDArray, grad: NDArray, weight32: NDArray, lr: Float, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, lazy_update: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Updater function for multi-precision sgd optimizer
    weight

    Weight

    grad

    gradient

    weight32

    Weight32

    lr

    Learning rate

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    lazy_update

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  156. abstract def multi_all_finite(data: Array[NDArray], num_arrays: Option[Int] = None, init_output: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    Arrays

    num_arrays

    Number of arrays.

    init_output

    Initialize output to 1.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  157. abstract def multi_mp_sgd_mom_update(data: Array[NDArray], lrs: Any, wds: Any, momentum: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, num_weights: Option[Int] = None, out: Option[NDArray] = None): 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:L470
    data

    Weights

    lrs

    Learning rates.

    wds

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

    momentum

    The decay rate of momentum estimates at each epoch.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    num_weights

    Number of updated weights.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  158. abstract def multi_mp_sgd_update(data: Array[NDArray], lrs: Any, wds: Any, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, num_weights: Option[Int] = None, out: Option[NDArray] = None): 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:L415
    data

    Weights

    lrs

    Learning rates.

    wds

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    num_weights

    Number of updated weights.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  159. abstract def multi_sgd_mom_update(data: Array[NDArray], lrs: Any, wds: Any, momentum: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, num_weights: Option[Int] = None, out: Option[NDArray] = None): 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:L372
    data

    Weights, gradients and momentum

    lrs

    Learning rates.

    wds

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

    momentum

    The decay rate of momentum estimates at each epoch.

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    num_weights

    Number of updated weights.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  160. abstract def multi_sgd_update(data: Array[NDArray], lrs: Any, wds: Any, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, num_weights: Option[Int] = None, out: Option[NDArray] = None): 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:L327
    data

    Weights

    lrs

    Learning rates.

    wds

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    num_weights

    Number of updated weights.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  161. abstract def nag_mom_update(weight: NDArray, grad: NDArray, mom: NDArray, lr: Float, momentum: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, out: Option[NDArray] = None): 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:L724
    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  162. abstract def nanprod(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  163. abstract def nansum(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero.
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  164. abstract def negative(data: NDArray, out: Option[NDArray] = None): 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
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  165. abstract def norm(data: NDArray, ord: Option[Int] = None, axis: Option[Shape] = None, out_dtype: Option[String] = None, keepdims: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the norm on an NDArray.
    
    This operator computes the norm on an NDArray with the specified axis, depending
    on the value of the ord parameter. By default, it computes the L2 norm on the entire
    array. Currently only ord=2 supports sparse ndarrays.
    
    Examples::
    
      x = `[ `[ [1, 2],
            [3, 4] ],
           `[ [2, 2],
            [5, 6] ] ]
    
      norm(x, ord=2, axis=1) = `[ [3.1622777 4.472136 ]
                                [5.3851647 6.3245554] ]
    
      norm(x, ord=1, axis=1) = `[ [4., 6.],
                                [7., 8.] ]
    
      rsp = x.cast_storage('row_sparse')
    
      norm(rsp) = [5.47722578]
    
      csr = x.cast_storage('csr')
    
      norm(csr) = [5.47722578]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L350
    data

    The input

    ord

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

    axis

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

    out_dtype

    The data type of the output.

    keepdims

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  166. abstract def normal(loc: Option[Float] = None, scale: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): 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
    loc

    Mean of the distribution.

    scale

    Standard deviation of the distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  167. abstract def one_hot(indices: NDArray, depth: Int, on_value: Option[Double] = None, off_value: Option[Double] = None, dtype: Option[String] = None, out: Option[NDArray] = None): 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:L799
    indices

    array of locations where to set on_value

    depth

    Depth of the one hot dimension.

    on_value

    The value assigned to the locations represented by indices.

    off_value

    The value assigned to the locations not represented by indices.

    dtype

    DType of the output

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  168. abstract def ones_like(data: NDArray, out: Option[NDArray] = None): 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.] ]
    data

    The input

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  169. abstract def pad(data: NDArray, mode: String, pad_width: Shape, constant_value: Option[Double] = None, out: Option[NDArray] = None): 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
    data

    An n-dimensional input array.

    mode

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

    pad_width

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

    constant_value

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  170. abstract def pick(data: NDArray, index: NDArray, axis: Option[Int] = None, keepdims: Option[Boolean] = None, mode: Option[String] = None, out: Option[NDArray] = None): 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:L154
    data

    The input array

    index

    The index array

    axis

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

    keepdims

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

    mode

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  171. abstract def prod(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the product of array elements over given axes.
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  172. abstract def radians(data: NDArray, out: Option[NDArray] = None): 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:L238
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  173. abstract def random_exponential(lam: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): 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
    lam

    Lambda parameter (rate) of the exponential distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  174. abstract def random_gamma(alpha: Option[Float] = None, beta: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): 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
    alpha

    Alpha parameter (shape) of the gamma distribution.

    beta

    Beta parameter (scale) of the gamma distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  175. abstract def random_generalized_negative_binomial(mu: Option[Float] = None, alpha: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Draw random samples from a generalized negative binomial distribution.
    
    Samples are distributed according to a generalized negative binomial distribution parametrized by
    *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the
    number of unsuccessful experiments (generalized to real numbers).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = `[ [ 2.,  1.],
                                                                        [ 6.,  4.] ]
    
    
    Defined in src/operator/random/sample_op.cc:L179
    mu

    Mean of the negative binomial distribution.

    alpha

    Alpha (dispersion) parameter of the negative binomial distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  176. abstract def random_negative_binomial(k: Option[Int] = None, p: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Draw random samples from a negative binomial distribution.
    
    Samples are distributed according to a negative binomial distribution parametrized by
    *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       negative_binomial(k=3, p=0.4, shape=(2,2)) = `[ [ 4.,  7.],
                                                     [ 2.,  5.] ]
    
    
    Defined in src/operator/random/sample_op.cc:L164
    k

    Limit of unsuccessful experiments.

    p

    Failure probability in each experiment.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  177. abstract def random_normal(loc: Option[Float] = None, scale: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): 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
    loc

    Mean of the distribution.

    scale

    Standard deviation of the distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  178. abstract def random_poisson(lam: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Draw random samples from a Poisson distribution.
    
    Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate).
    Samples will always be returned as a floating point data type.
    
    Example::
    
       poisson(lam=4, shape=(2,2)) = `[ [ 5.,  2.],
                                      [ 4.,  6.] ]
    
    
    Defined in src/operator/random/sample_op.cc:L150
    lam

    Lambda parameter (rate) of the Poisson distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  179. abstract def random_randint(low: Any, high: Any, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Draw random samples from a discrete uniform distribution.
    
    Samples are uniformly distributed over the half-open interval *[low, high)*
    (includes *low*, but excludes *high*).
    
    Example::
    
       randint(low=0, high=5, shape=(2,2)) = `[ [ 0,  2],
                                              [ 3,  1] ]
    
    
    
    Defined in src/operator/random/sample_op.cc:L193
    low

    Lower bound of the distribution.

    high

    Upper bound of the distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

    DType of the output in case this can't be inferred. Defaults to int32 if not defined (dtype=None).

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  180. abstract def random_uniform(low: Option[Float] = None, high: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Draw random samples from a uniform distribution.
    
    .. note:: The existing alias ``uniform`` is deprecated.
    
    Samples are uniformly distributed over the half-open interval *[low, high)*
    (includes *low*, but excludes *high*).
    
    Example::
    
       uniform(low=0, high=1, shape=(2,2)) = `[ [ 0.60276335,  0.85794562],
                                              [ 0.54488319,  0.84725171] ]
    
    
    
    Defined in src/operator/random/sample_op.cc:L96
    low

    Lower bound of the distribution.

    high

    Upper bound of the distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  181. abstract def ravel_multi_index(data: NDArray, shape: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix. The leading dimension may be left unspecified by using -1 as placeholder.
    
    Examples::
    
       A = `[ [3,6,6],[4,5,1] ]
       ravel(A, shape=(7,6)) = [22,41,37]
       ravel(A, shape=(-1,6)) = [22,41,37]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L42
    data

    Batch of multi-indices

    shape

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  182. abstract def rcbrt(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise inverse cube-root value of the input.
    
    .. math::
       rcbrt(x) = 1/\sqrt[3]{x}
    
    Example::
    
       rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1004
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  183. abstract def reciprocal(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns the reciprocal of the argument, element-wise.
    
    Calculates 1/x.
    
    Example::
    
        reciprocal([-2, 1, 3, 1.6.0, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L686
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  184. abstract def relu(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes rectified linear activation.
    
    .. math::
       max(features, 0)
    
    The storage type of ``relu`` output depends upon the input storage type:
    
       - relu(default) = default
       - relu(row_sparse) = row_sparse
       - relu(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  185. abstract def repeat(data: NDArray, repeats: Int, axis: Option[Int] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Repeats elements of an array.
    
    By default, ``repeat`` flattens the input array into 1-D and then repeats the
    elements::
    
      x = `[ [ 1, 2],
           [ 3, 4] ]
    
      repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]
    
    The parameter ``axis`` specifies the axis along which to perform repeat::
    
      repeat(x, repeats=2, axis=1) = `[ [ 1.,  1.,  2.,  2.],
                                      [ 3.,  3.,  4.,  4.] ]
    
      repeat(x, repeats=2, axis=0) = `[ [ 1.,  2.],
                                      [ 1.,  2.],
                                      [ 3.,  4.],
                                      [ 3.,  4.] ]
    
      repeat(x, repeats=2, axis=-1) = `[ [ 1.,  1.,  2.,  2.],
                                       [ 3.,  3.,  4.,  4.] ]
    
    
    
    Defined in src/operator/tensor/matrix_op.cc:L796
    data

    Input data array

    repeats

    The number of repetitions for each element.

    axis

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  186. abstract def reshape(data: NDArray, shape: Option[Shape] = None, reverse: Option[Boolean] = None, target_shape: Option[Shape] = None, keep_highest: Option[Boolean] = None, out: Option[NDArray] = None): 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:L202
    data

    Input data to reshape.

    shape

    The target shape

    reverse

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

    target_shape

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

    keep_highest

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  187. abstract def reshape_like(lhs: NDArray, rhs: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`.
    
    Returns a **view** of the `lhs` array with a new shape without altering any data.
    
    Example::
    
      x = [1, 2, 3, 4, 5, 6]
      y = `[ [0, -4], [3, 2], [2, 2] ]
      reshape_like(x, y) = `[ [1, 2], [3, 4], [5, 6] ]
    
    More precise control over how dimensions are inherited is achieved by specifying \
    slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \
    are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same.
    
      Examples::
    
      - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
      - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)
    
    Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range.
    
      Example::
    
      - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L485
    lhs

    First input.

    rhs

    Second input.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  188. abstract def reverse(data: NDArray, axis: Shape, out: Option[NDArray] = None): 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:L898
    data

    Input data array

    axis

    The axis which to reverse elements.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  189. abstract def rint(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest integer of the input.
    
    .. note::
       - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``.
       - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``.
    
    Example::
    
       rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  1., -2.,  2.,  2.]
    
    The storage type of ``rint`` output depends upon the input storage type:
    
       - rint(default) = default
       - rint(row_sparse) = row_sparse
       - rint(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L767
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  190. abstract def rmsprop_update(weight: NDArray, grad: NDArray, n: NDArray, lr: Float, gamma1: Option[Float] = None, epsilon: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, clip_weights: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Update function for `RMSProp` optimizer.
    
    `RMSprop` is a variant of stochastic gradient descent where the gradients are
    divided by a cache which grows with the sum of squares of recent gradients?
    
    `RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
    tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for
    each parameter monotonically over the course of training.
    While this is analytically motivated for convex optimizations, it may not be ideal
    for non-convex problems. `RMSProp` deals with this heuristically by allowing the
    learning rates to rebound as the denominator decays over time.
    
    Define the Root Mean Square (RMS) error criterion of the gradient as
    :math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
    gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient.
    
    The :math:`E[g^2]_t` is given by:
    
    .. math::
      E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t
    
    The RMSProp code follows the version in
    http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
    Tieleman & Hinton, 2012.
    
    Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
    :math:`\eta` to be 0.001.
    
    
    
    Defined in src/operator/optimizer_op.cc:L795
    weight

    Weight

    grad

    Gradient

    n

    n

    lr

    Learning rate

    gamma1

    The decay rate of momentum estimates.

    epsilon

    A small constant for numerical stability.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    clip_weights

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  191. abstract def rmspropalex_update(weight: NDArray, grad: NDArray, n: NDArray, g: NDArray, delta: NDArray, lr: Float, gamma1: Option[Float] = None, gamma2: Option[Float] = None, epsilon: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, clip_weights: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Update function for RMSPropAlex optimizer.
    
    `RMSPropAlex` is non-centered version of `RMSProp`.
    
    Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
    :math:`E[g]_t` is the decaying average over past gradient.
    
    .. math::
      E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
      E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
      \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\
    
    The update step is
    
    .. math::
      \theta_{t+1} = \theta_t + \Delta_t
    
    The RMSPropAlex code follows the version in
    http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
    
    Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
    to be 0.9 and the learning rate :math:`\eta` to be 0.0001.
    
    
    Defined in src/operator/optimizer_op.cc:L834
    weight

    Weight

    grad

    Gradient

    n

    n

    g

    g

    delta

    delta

    lr

    Learning rate

    gamma1

    Decay rate.

    gamma2

    Decay rate.

    epsilon

    A small constant for numerical stability.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    clip_weights

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  192. abstract def round(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise rounded value to the nearest integer of the input.
    
    Example::
    
       round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]
    
    The storage type of ``round`` output depends upon the input storage type:
    
      - round(default) = default
      - round(row_sparse) = row_sparse
      - round(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  193. abstract def rsqrt(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise inverse square-root value of the input.
    
    .. math::
       rsqrt(x) = 1/\sqrt{x}
    
    Example::
    
       rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]
    
    The storage type of ``rsqrt`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L927
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  194. abstract def sample_exponential(lam: NDArray, shape: Option[Shape] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple
    exponential distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_exponential(lam) = [ 0.51837951,  0.09994757]
    
       // Draw a vector containing two samples for each distribution
       sample_exponential(lam, shape=(2)) = `[ [ 0.51837951,  0.19866663],
                                             [ 0.09994757,  0.50447971] ]
    
    
    Defined in src/operator/random/multisample_op.cc:L284
    lam

    Lambda (rate) parameters of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  195. abstract def sample_gamma(alpha: NDArray, shape: Option[Shape] = None, dtype: Option[String] = None, beta: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple
    gamma distributions with parameters *alpha* (shape) and *beta* (scale).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       alpha = [ 0.0, 2.5 ]
       beta = [ 1.0, 0.7 ]
    
       // Draw a single sample for each distribution
       sample_gamma(alpha, beta) = [ 0.        ,  2.25797319]
    
       // Draw a vector containing two samples for each distribution
       sample_gamma(alpha, beta, shape=(2)) = `[ [ 0.        ,  0.        ],
                                               [ 2.25797319,  1.70734084] ]
    
    
    Defined in src/operator/random/multisample_op.cc:L282
    alpha

    Alpha (shape) parameters of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

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

    beta

    Beta (scale) parameters of the distributions.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  196. abstract def sample_generalized_negative_binomial(mu: NDArray, shape: Option[Shape] = None, dtype: Option[String] = None, alpha: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple
    generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       mu = [ 2.0, 2.5 ]
       alpha = [ 1.0, 0.1 ]
    
       // Draw a single sample for each distribution
       sample_generalized_negative_binomial(mu, alpha) = [ 0.,  3.]
    
       // Draw a vector containing two samples for each distribution
       sample_generalized_negative_binomial(mu, alpha, shape=(2)) = `[ [ 0.,  3.],
                                                                     [ 3.,  1.] ]
    
    
    Defined in src/operator/random/multisample_op.cc:L293
    mu

    Means of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

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

    alpha

    Alpha (dispersion) parameters of the distributions.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  197. abstract def sample_multinomial(data: NDArray, shape: Option[Shape] = None, get_prob: Option[Boolean] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple multinomial distributions.
    
    *data* is an *n* dimensional array whose last dimension has length *k*, where
    *k* is the number of possible outcomes of each multinomial distribution. This
    operator will draw *shape* samples from each distribution. If shape is empty
    one sample will be drawn from each distribution.
    
    If *get_prob* is true, a second array containing log likelihood of the drawn
    samples will also be returned. This is usually used for reinforcement learning
    where you can provide reward as head gradient for this array to estimate
    gradient.
    
    Note that the input distribution must be normalized, i.e. *data* must sum to
    1 along its last axis.
    
    Examples::
    
       probs = `[ [0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0] ]
    
       // Draw a single sample for each distribution
       sample_multinomial(probs) = [3, 0]
    
       // Draw a vector containing two samples for each distribution
       sample_multinomial(probs, shape=(2)) = `[ [4, 2],
                                               [0, 0] ]
    
       // requests log likelihood
       sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
    data

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

    shape

    Shape to be sampled from each random distribution.

    get_prob

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  198. abstract def sample_negative_binomial(k: NDArray, shape: Option[Shape] = None, dtype: Option[String] = None, p: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple
    negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       k = [ 20, 49 ]
       p = [ 0.4 , 0.77 ]
    
       // Draw a single sample for each distribution
       sample_negative_binomial(k, p) = [ 15.,  16.]
    
       // Draw a vector containing two samples for each distribution
       sample_negative_binomial(k, p, shape=(2)) = `[ [ 15.,  50.],
                                                    [ 16.,  12.] ]
    
    
    Defined in src/operator/random/multisample_op.cc:L289
    k

    Limits of unsuccessful experiments.

    shape

    Shape to be sampled from each random distribution.

    dtype

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

    p

    Failure probabilities in each experiment.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  199. abstract def sample_normal(mu: NDArray, shape: Option[Shape] = None, dtype: Option[String] = None, sigma: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple
    normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       mu = [ 0.0, 2.5 ]
       sigma = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_normal(mu, sigma) = [-0.56410581,  0.95934606]
    
       // Draw a vector containing two samples for each distribution
       sample_normal(mu, sigma, shape=(2)) = `[ [-0.56410581,  0.2928229 ],
                                              [ 0.95934606,  4.48287058] ]
    
    
    Defined in src/operator/random/multisample_op.cc:L279
    mu

    Means of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

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

    sigma

    Standard deviations of the distributions.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  200. abstract def sample_poisson(lam: NDArray, shape: Option[Shape] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple
    Poisson distributions with parameters lambda (rate).
    
    The parameters of the distributions are provided as an input array.
    Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input value at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input array.
    
    Samples will always be returned as a floating point data type.
    
    Examples::
    
       lam = [ 1.0, 8.5 ]
    
       // Draw a single sample for each distribution
       sample_poisson(lam) = [  0.,  13.]
    
       // Draw a vector containing two samples for each distribution
       sample_poisson(lam, shape=(2)) = `[ [  0.,   4.],
                                         [ 13.,   8.] ]
    
    
    Defined in src/operator/random/multisample_op.cc:L286
    lam

    Lambda (rate) parameters of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  201. abstract def sample_uniform(low: NDArray, shape: Option[Shape] = None, dtype: Option[String] = None, high: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Concurrent sampling from multiple
    uniform distributions on the intervals given by *[low,high)*.
    
    The parameters of the distributions are provided as input arrays.
    Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
    be the shape specified as the parameter of the operator, and *m* be the dimension
    of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.
    
    For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
    will be an *m*-dimensional array that holds randomly drawn samples from the distribution
    which is parameterized by the input values at index *i*. If the shape parameter of the
    operator is not set, then one sample will be drawn per distribution and the output array
    has the same shape as the input arrays.
    
    Examples::
    
       low = [ 0.0, 2.5 ]
       high = [ 1.0, 3.7 ]
    
       // Draw a single sample for each distribution
       sample_uniform(low, high) = [ 0.40451524,  3.18687344]
    
       // Draw a vector containing two samples for each distribution
       sample_uniform(low, high, shape=(2)) = `[ [ 0.40451524,  0.18017688],
                                               [ 3.18687344,  3.68352246] ]
    
    
    Defined in src/operator/random/multisample_op.cc:L277
    low

    Lower bounds of the distributions.

    shape

    Shape to be sampled from each random distribution.

    dtype

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

    high

    Upper bounds of the distributions.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  202. abstract def scatter_nd(data: NDArray, indices: NDArray, shape: Shape, out: Option[NDArray] = None): NDArrayFuncReturn

    Scatters data into a new tensor according to indices.
    
    Given `data` with shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})` and indices with shape
    `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(X_0, X_1, ..., X_{N-1})`,
    where `M <= N`. If `M == N`, data shape should simply be `(Y_0, ..., Y_{K-1})`.
    
    The elements in output is defined as follows::
    
      output[indices[0, y_0, ..., y_{K-1}],
             ...,
             indices[M-1, y_0, ..., y_{K-1}],
             x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]
    
    all other entries in output are 0.
    
    .. warning::
    
        If the indices have duplicates, the result will be non-deterministic and
        the gradient of `scatter_nd` will not be correct!!
    
    
    Examples::
    
      data = [2, 3, 0]
      indices = `[ [1, 1, 0], [0, 1, 0] ]
      shape = (2, 2)
      scatter_nd(data, indices, shape) = `[ [0, 0], [2, 3] ]
    
      data = `[ `[ [1, 2], [3, 4] ], `[ [5, 6], [7, 8] ] ]
      indices = `[ [0, 1], [1, 1] ]
      shape = (2, 2, 2, 2)
      scatter_nd(data, indices, shape) = `[ [`[ [0, 0],
                                            [0, 0] ],
    
                                           `[ [1, 2],
                                            [3, 4] ] ],
    
                                          `[ `[ [0, 0],
                                            [0, 0] ],
    
                                           `[ [5, 6],
                                            [7, 8] ] ] ]
    data

    data

    indices

    indices

    shape

    Shape of output.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  203. abstract def sgd_mom_update(weight: NDArray, grad: NDArray, mom: NDArray, lr: Float, momentum: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, lazy_update: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Momentum update function for Stochastic Gradient Descent (SGD) optimizer.
    
    Momentum update has better convergence rates on neural networks. Mathematically it looks
    like below:
    
    .. math::
    
      v_1 = \alpha * \nabla J(W_0)\\
      v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
      W_t = W_{t-1} + v_t
    
    It updates the weights using::
    
      v = momentum * v - learning_rate * gradient
      weight += v
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage
    type is the same as momentum's storage type,
    only the row slices whose indices appear in grad.indices are updated (for both weight and momentum)::
    
      for row in gradient.indices:
          v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
          weight[row] += v[row]
    
    
    
    Defined in src/operator/optimizer_op.cc:L563
    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    lazy_update

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  204. abstract def sgd_update(weight: NDArray, grad: NDArray, lr: Float, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, lazy_update: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Update function for Stochastic Gradient Descent (SGD) optimizer.
    
    It updates the weights using::
    
     weight = weight - learning_rate * (gradient + wd * weight)
    
    However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is True,
    only the row slices whose indices appear in grad.indices are updated::
    
     for row in gradient.indices:
         weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])
    
    
    
    Defined in src/operator/optimizer_op.cc:L522
    weight

    Weight

    grad

    Gradient

    lr

    Learning rate

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    lazy_update

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  205. abstract def shape_array(data: NDArray, lhs_begin: Option[Int] = None, lhs_end: Option[Int] = None, rhs_begin: Option[Int] = None, rhs_end: Option[Int] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns a 1D int64 array containing the shape of data.
    
    Example::
    
      shape_array(`[ [1,2,3,4], [5,6,7,8] ]) = [2,4]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L544
    data

    Input Array.

    lhs_begin

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

    lhs_end

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

    rhs_begin

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

    rhs_end

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  206. abstract def shuffle(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Randomly shuffle the elements.
    
    This shuffles the array along the first axis.
    The order of the elements in each subarray does not change.
    For example, if a 2D array is given, the order of the rows randomly changes,
    but the order of the elements in each row does not change.
    data

    Data to be shuffled.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  207. abstract def sigmoid(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes sigmoid of x element-wise.
    
    .. math::
       y = 1 / (1 + exp(-x))
    
    The storage type of ``sigmoid`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L119
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  208. abstract def sign(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise sign of the input.
    
    Example::
    
       sign([-2, 0, 3]) = [-1, 0, 1]
    
    The storage type of ``sign`` output depends upon the input storage type:
    
       - sign(default) = default
       - sign(row_sparse) = row_sparse
       - sign(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  209. abstract def signsgd_update(weight: NDArray, grad: NDArray, lr: Float, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Update function for SignSGD optimizer.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     W_t = W_{t-1} - \eta_t \text{sign}(g_t)
    
    It updates the weights using::
    
     weight = weight - learning_rate * sign(gradient)
    
    .. note::
       - sparse ndarray not supported for this optimizer yet.
    
    
    Defined in src/operator/optimizer_op.cc:L61
    weight

    Weight

    grad

    Gradient

    lr

    Learning rate

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  210. abstract def signum_update(weight: NDArray, grad: NDArray, mom: NDArray, lr: Float, momentum: Option[Float] = None, wd: Option[Float] = None, rescale_grad: Option[Float] = None, clip_gradient: Option[Float] = None, wd_lh: Option[Float] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    SIGN momentUM (Signum) optimizer.
    
    .. math::
    
     g_t = \nabla J(W_{t-1})\\
     m_t = \beta m_{t-1} + (1 - \beta) g_t\\
     W_t = W_{t-1} - \eta_t \text{sign}(m_t)
    
    It updates the weights using::
     state = momentum * state + (1-momentum) * gradient
     weight = weight - learning_rate * sign(state)
    
    Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.
    
    .. note::
       - sparse ndarray not supported for this optimizer yet.
    
    
    Defined in src/operator/optimizer_op.cc:L90
    weight

    Weight

    grad

    Gradient

    mom

    Momentum

    lr

    Learning rate

    momentum

    The decay rate of momentum estimates at each epoch.

    wd

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

    rescale_grad

    Rescale gradient to grad = rescale_grad*grad.

    clip_gradient

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

    wd_lh

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  211. abstract def sin(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  212. abstract def sinh(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns the hyperbolic sine of the input array, computed element-wise.
    
    .. math::
       sinh(x) = 0.5\times(exp(x) - exp(-x))
    
    The storage type of ``sinh`` output depends upon the input storage type:
    
       - sinh(default) = default
       - sinh(row_sparse) = row_sparse
       - sinh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L257
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  213. abstract def size_array(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns a 1D int64 array containing the size of data.
    
    Example::
    
      size_array(`[ [1,2,3,4], [5,6,7,8] ]) = [8]
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L596
    data

    Input Array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  214. abstract def slice(data: NDArray, begin: Shape, end: Shape, step: Option[Shape] = None, out: Option[NDArray] = None): 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:L506
    data

    Source input

    begin

    starting indices for the slice operation, supports negative indices.

    end

    ending indices for the slice operation, supports negative indices.

    step

    step for the slice operation, supports negative values.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  215. abstract def slice_axis(data: NDArray, axis: Int, begin: Int, end: Int, out: Option[NDArray] = None): NDArrayFuncReturn

    Slices along a given axis.
    
    Returns an array slice along a given `axis` starting from the `begin` index
    to the `end` index.
    
    Examples::
    
      x = `[ [  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.] ]
    
      slice_axis(x, axis=0, begin=1, end=3) = `[ [  5.,   6.,   7.,   8.],
                                               [  9.,  10.,  11.,  12.] ]
    
      slice_axis(x, axis=1, begin=0, end=2) = `[ [  1.,   2.],
                                               [  5.,   6.],
                                               [  9.,  10.] ]
    
      slice_axis(x, axis=1, begin=-3, end=-1) = `[ [  2.,   3.],
                                                 [  6.,   7.],
                                                 [ 10.,  11.] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L596
    data

    Source input

    axis

    Axis along which to be sliced, supports negative indexes.

    begin

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

    end

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  216. abstract def slice_like(data: NDArray, shape_like: NDArray, axes: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Slices a region of the array like the shape of another array.
    
    This function is similar to ``slice``, however, the `begin` are always `0`s
    and `end` of specific axes are inferred from the second input `shape_like`.
    
    Given the second `shape_like` input of ``shape=(d_0, d_1, ..., d_n-1)``,
    a ``slice_like`` operator with default empty `axes`, it performs the
    following operation:
    
    `` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``.
    
    When `axes` is not empty, it is used to speficy which axes are being sliced.
    
    Given a 4-d input data, ``slice_like`` operator with ``axes=(0, 2, -1)``
    will perform the following operation:
    
    `` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``.
    
    Note that it is allowed to have first and second input with different dimensions,
    however, you have to make sure the `axes` are specified and not exceeding the
    dimension limits.
    
    For example, given `input_1` with ``shape=(2,3,4,5)`` and `input_2` with
    ``shape=(1,2,3)``, it is not allowed to use:
    
    `` out = slice_like(a, b)`` because ndim of `input_1` is 4, and ndim of `input_2`
    is 3.
    
    The following is allowed in this situation:
    
    `` out = slice_like(a, b, axes=(0, 2))``
    
    Example::
    
      x = `[ [  1.,   2.,   3.,   4.],
           [  5.,   6.,   7.,   8.],
           [  9.,  10.,  11.,  12.] ]
    
      y = `[ [  0.,   0.,   0.],
           [  0.,   0.,   0.] ]
    
      slice_like(x, y) = `[ [ 1.,  2.,  3.]
                          [ 5.,  6.,  7.] ]
      slice_like(x, y, axes=(0, 1)) = `[ [ 1.,  2.,  3.]
                                       [ 5.,  6.,  7.] ]
      slice_like(x, y, axes=(0)) = `[ [ 1.,  2.,  3.,  4.]
                                    [ 5.,  6.,  7.,  8.] ]
      slice_like(x, y, axes=(-1)) = `[ [  1.,   2.,   3.]
                                     [  5.,   6.,   7.]
                                     [  9.,  10.,  11.] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L665
    data

    Source input

    shape_like

    Shape like input

    axes

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  217. abstract def smooth_l1(data: NDArray, scalar: Float, out: Option[NDArray] = None): NDArrayFuncReturn

    Calculate Smooth L1 Loss(lhs, scalar) by summing
    
    .. math::
    
        f(x) =
        \begin{cases}
        (\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
        |x|-0.5/\sigma^2,& \text{otherwise}
        \end{cases}
    
    where :math:`x` is an element of the tensor *lhs* and :math:`\sigma` is the scalar.
    
    Example::
    
      smooth_l1([1, 2, 3, 4]) = [0.5, 1.5, 2.5, 3.5]
      smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]
    
    
    
    Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L104
    data

    source input

    scalar

    scalar input

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  218. abstract def softmax(data: NDArray, axis: Option[Int] = None, temperature: Option[Double] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Applies the softmax function.
    
    The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.
    
    .. math::
       softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}
    
    for :math:`j = 1, ..., K`
    
    t is the temperature parameter in softmax function. By default, t equals 1.0
    
    Example::
    
      x = `[ [ 1.  1.  1.]
           [ 1.  1.  1.] ]
    
      softmax(x,axis=0) = `[ [ 0.5  0.5  0.5]
                           [ 0.5  0.5  0.5] ]
    
      softmax(x,axis=1) = `[ [ 0.33333334,  0.33333334,  0.33333334],
                           [ 0.33333334,  0.33333334,  0.33333334] ]
    
    
    
    Defined in src/operator/nn/softmax.cc:L93
    data

    The input array.

    axis

    The axis along which to compute softmax.

    temperature

    Temperature parameter in softmax

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  219. abstract def softmax_cross_entropy(data: NDArray, label: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Calculate cross entropy of softmax output and one-hot label.
    
    - This operator computes the cross entropy in two steps:
      - Applies softmax function on the input array.
      - Computes and returns the cross entropy loss between the softmax output and the labels.
    
    - The softmax function and cross entropy loss is given by:
    
      - Softmax Function:
    
      .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}
    
      - Cross Entropy Function:
    
      .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)
    
    Example::
    
      x = `[ [1, 2, 3],
           [11, 7, 5] ]
    
      label = [2, 0]
    
      softmax(x) = `[ [0.09003057, 0.24472848, 0.66524094],
                    [0.97962922, 0.01794253, 0.00242826] ]
    
      softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871
    
    
    
    Defined in src/operator/loss_binary_op.cc:L59
    data

    Input data

    label

    Input label

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  220. abstract def softmin(data: NDArray, axis: Option[Int] = None, temperature: Option[Double] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Applies the softmin function.
    
    The resulting array contains elements in the range (0,1) and the elements along the given axis sum
    up to 1.
    
    .. math::
       softmin(\mathbf{z/t})_j = \frac{e^{-z_j/t}}{\sum_{k=1}^K e^{-z_k/t}}
    
    for :math:`j = 1, ..., K`
    
    t is the temperature parameter in softmax function. By default, t equals 1.0
    
    Example::
    
      x = `[ [ 1.  2.  3.]
           [ 3.  2.  1.] ]
    
      softmin(x,axis=0) = `[ [ 0.88079703,  0.5,  0.11920292],
                           [ 0.11920292,  0.5,  0.88079703] ]
    
      softmin(x,axis=1) = `[ [ 0.66524094,  0.24472848,  0.09003057],
                           [ 0.09003057,  0.24472848,  0.66524094] ]
    
    
    
    Defined in src/operator/nn/softmax.cc:L153
    data

    The input array.

    axis

    The axis along which to compute softmax.

    temperature

    Temperature parameter in softmax

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  221. abstract def softsign(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes softsign of x element-wise.
    
    .. math::
       y = x / (1 + abs(x))
    
    The storage type of ``softsign`` output is always dense
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L163
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  222. abstract def sort(data: NDArray, axis: Option[Int] = None, is_ascend: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns a sorted copy of an input array along the given axis.
    
    Examples::
    
      x = `[ [ 1, 4],
           [ 3, 1] ]
    
      // sorts along the last axis
      sort(x) = `[ [ 1.,  4.],
                 [ 1.,  3.] ]
    
      // flattens and then sorts
      sort(x) = [ 1.,  1.,  3.,  4.]
    
      // sorts along the first axis
      sort(x, axis=0) = `[ [ 1.,  1.],
                         [ 3.,  4.] ]
    
      // in a descend order
      sort(x, is_ascend=0) = `[ [ 4.,  1.],
                              [ 3.,  1.] ]
    
    
    
    Defined in src/operator/tensor/ordering_op.cc:L127
    data

    The input array

    axis

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

    is_ascend

    Whether to sort in ascending or descending order.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  223. abstract def space_to_depth(data: NDArray, block_size: Int, out: Option[NDArray] = None): NDArrayFuncReturn

    Rearranges(permutes) blocks of spatial data into depth.
    Similar to ONNX SpaceToDepth operator:
    https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth
    
    The output is a new tensor where the values from height and width dimension are
    moved to the depth dimension. The reverse of this operation is ``depth_to_space``.
    
    .. math::
    
        \begin{gather*}
        x \prime = reshape(x, [N, C, H / block\_size, block\_size, W / block\_size, block\_size]) \\
        x \prime \prime = transpose(x \prime, [0, 3, 5, 1, 2, 4]) \\
        y = reshape(x \prime \prime, [N, C * (block\_size ^ 2), H / block\_size, W / block\_size])
        \end{gather*}
    
    where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width]
    and :math:`y` is the output tensor of layout :math:`[N, C * (block\_size ^ 2), H / block\_size, W / block\_size]`
    
    Example::
    
      x = `[ [`[ [0, 6, 1, 7, 2, 8],
             [12, 18, 13, 19, 14, 20],
             [3, 9, 4, 10, 5, 11],
             [15, 21, 16, 22, 17, 23] ] ] ]
    
    
      space_to_depth(x, 2) = `[ [`[ [0, 1, 2],
                                [3, 4, 5] ],
                               `[ [6, 7, 8],
                                [9, 10, 11] ],
                               `[ [12, 13, 14],
                                [15, 16, 17] ],
                               `[ [18, 19, 20],
                                [21, 22, 23] ] ] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L1104
    data

    Input ndarray

    block_size

    Blocks of [block_size. block_size] are moved

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  224. abstract def split(data: NDArray, num_outputs: Int, axis: Option[Int] = None, squeeze_axis: Option[Boolean] = None, out: Option[NDArray] = None): 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
    data

    The input

    num_outputs

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

    axis

    Axis along which to split.

    squeeze_axis

    If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting squeeze_axis to true removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only if input.shape[axis] == num_outputs.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  225. abstract def sqrt(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise square-root value of the input.
    
    .. math::
       \textrm{sqrt}(x) = \sqrt{x}
    
    Example::
    
       sqrt([4, 9, 16]) = [2, 3, 4]
    
    The storage type of ``sqrt`` output depends upon the input storage type:
    
       - sqrt(default) = default
       - sqrt(row_sparse) = row_sparse
       - sqrt(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L907
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  226. abstract def square(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns element-wise squared value of the input.
    
    .. math::
       square(x) = x^2
    
    Example::
    
       square([2, 3, 4]) = [4, 9, 16]
    
    The storage type of ``square`` output depends upon the input storage type:
    
       - square(default) = default
       - square(row_sparse) = row_sparse
       - square(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L883
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  227. abstract def squeeze(data: Array[NDArray], axis: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

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

    data to squeeze

    axis

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  228. abstract def stack(data: Array[NDArray], axis: Option[Int] = None, num_args: Int, out: Option[NDArray] = None): NDArrayFuncReturn

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

    List of arrays to stack

    axis

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

    num_args

    Number of inputs to be stacked.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  229. abstract def stop_gradient(data: NDArray, out: Option[NDArray] = None): 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:L299
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  230. abstract def sum(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the sum of array elements over given axes.
    
    .. Note::
    
      `sum` and `sum_axis` are equivalent.
      For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
      Setting keepdims or exclude to True will cause a fallback to dense operator.
    
    Example::
    
      data = `[ `[ [1, 2], [2, 3], [1, 3] ],
              `[ [1, 4], [4, 3], [5, 2] ],
              `[ [7, 1], [7, 2], [7, 3] ] ]
    
      sum(data, axis=1)
      `[ [  4.   8.]
       [ 10.   9.]
       [ 21.   6.] ]
    
      sum(data, axis=[1,2])
      [ 12.  19.  27.]
    
      data = `[ [1, 2, 0],
              [3, 0, 1],
              [4, 1, 0] ]
    
      csr = cast_storage(data, 'csr')
    
      sum(csr, axis=0)
      [ 8.  3.  1.]
    
      sum(csr, axis=1)
      [ 3.  4.  5.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L116
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  231. abstract def sum_axis(data: NDArray, axis: Option[Shape] = None, keepdims: Option[Boolean] = None, exclude: Option[Boolean] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the sum of array elements over given axes.
    
    .. Note::
    
      `sum` and `sum_axis` are equivalent.
      For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
      Setting keepdims or exclude to True will cause a fallback to dense operator.
    
    Example::
    
      data = `[ `[ [1, 2], [2, 3], [1, 3] ],
              `[ [1, 4], [4, 3], [5, 2] ],
              `[ [7, 1], [7, 2], [7, 3] ] ]
    
      sum(data, axis=1)
      `[ [  4.   8.]
       [ 10.   9.]
       [ 21.   6.] ]
    
      sum(data, axis=[1,2])
      [ 12.  19.  27.]
    
      data = `[ [1, 2, 0],
              [3, 0, 1],
              [4, 1, 0] ]
    
      csr = cast_storage(data, 'csr')
    
      sum(csr, axis=0)
      [ 8.  3.  1.]
    
      sum(csr, axis=1)
      [ 3.  4.  5.]
    
    
    
    Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L116
    data

    The input

    axis

    The axis or axes along which to perform the reduction.

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

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

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

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

    Negative values means indexing from right to left.

    keepdims

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

    exclude

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  232. abstract def swapaxes(data: NDArray, dim1: Option[Int] = None, dim2: Option[Int] = None, out: Option[NDArray] = None): 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
    data

    Input array.

    dim1

    the first axis to be swapped.

    dim2

    the second axis to be swapped.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  233. abstract def take(a: NDArray, indices: NDArray, axis: Option[Int] = None, mode: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Takes elements from an input array along the given axis.
    
    This function slices the input array along a particular axis with the provided indices.
    
    Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis
    dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them
    in an output tensor of rank q + (r - 1).
    
    Examples::
    
      x = [4.  5.  6.]
    
      // Trivial case, take the second element along the first axis.
    
      take(x, [1]) = [ 5. ]
    
      // The other trivial case, axis=-1, take the third element along the first axis
    
      take(x, [3], axis=-1, mode='clip') = [ 6. ]
    
      x = `[ [ 1.,  2.],
           [ 3.,  4.],
           [ 5.,  6.] ]
    
      // In this case we will get rows 0 and 1, then 1 and 2. Along axis 0
    
      take(x, `[ [0,1],[1,2] ]) = `[ `[ [ 1.,  2.],
                                 [ 3.,  4.] ],
    
                                `[ [ 3.,  4.],
                                 [ 5.,  6.] ] ]
    
      // In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around).
      // Along axis 1
    
      take(x, `[ [0, 3], [-1, -2] ], axis=1, mode='wrap') = `[ `[ [ 1.  2.]
                                                           [ 2.  1.] ]
    
                                                          `[ [ 3.  4.]
                                                           [ 4.  3.] ]
    
                                                          `[ [ 5.  6.]
                                                           [ 6.  5.] ] ]
    
    The storage type of ``take`` output depends upon the input storage type:
    
       - take(default, default) = default
       - take(csr, default, axis=0) = csr
    
    
    
    Defined in src/operator/tensor/indexing_op.cc:L695
    a

    The input array.

    indices

    The indices of the values to be extracted.

    axis

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

    mode

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  234. abstract def tan(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Computes the element-wise tangent of the input array.
    
    The input should be in radians (:math:`2\pi` rad equals 360 degrees).
    
    .. math::
       tan([0, \pi/4, \pi/2]) = [0, 1, -inf]
    
    The storage type of ``tan`` output depends upon the input storage type:
    
       - tan(default) = default
       - tan(row_sparse) = row_sparse
       - tan(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L139
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  235. abstract def tanh(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns the hyperbolic tangent of the input array, computed element-wise.
    
    .. math::
       tanh(x) = sinh(x) / cosh(x)
    
    The storage type of ``tanh`` output depends upon the input storage type:
    
       - tanh(default) = default
       - tanh(row_sparse) = row_sparse
       - tanh(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L290
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  236. abstract def tile(data: NDArray, reps: Shape, out: Option[NDArray] = None): NDArrayFuncReturn

    Repeats the whole array multiple times.
    
    If ``reps`` has length *d*, and input array has dimension of *n*. There are
    three cases:
    
    - **n=d**. Repeat *i*-th dimension of the input by ``reps[i]`` times::
    
        x = `[ [1, 2],
             [3, 4] ]
    
        tile(x, reps=(2,3)) = `[ [ 1.,  2.,  1.,  2.,  1.,  2.],
                               [ 3.,  4.,  3.,  4.,  3.,  4.],
                               [ 1.,  2.,  1.,  2.,  1.,  2.],
                               [ 3.,  4.,  3.,  4.,  3.,  4.] ]
    
    - **n>d**. ``reps`` is promoted to length *n* by pre-pending 1's to it. Thus for
      an input shape ``(2,3)``, ``repos=(2,)`` is treated as ``(1,2)``::
    
    
        tile(x, reps=(2,)) = `[ [ 1.,  2.,  1.,  2.],
                              [ 3.,  4.,  3.,  4.] ]
    
    - **n<d**. The input is promoted to be d-dimensional by prepending new axes. So a
      shape ``(2,2)`` array is promoted to ``(1,2,2)`` for 3-D replication::
    
        tile(x, reps=(2,2,3)) = `[ `[ [ 1.,  2.,  1.,  2.,  1.,  2.],
                                  [ 3.,  4.,  3.,  4.,  3.,  4.],
                                  [ 1.,  2.,  1.,  2.,  1.,  2.],
                                  [ 3.,  4.,  3.,  4.,  3.,  4.] ],
    
                                 `[ [ 1.,  2.,  1.,  2.,  1.,  2.],
                                  [ 3.,  4.,  3.,  4.,  3.,  4.],
                                  [ 1.,  2.,  1.,  2.,  1.,  2.],
                                  [ 3.,  4.,  3.,  4.,  3.,  4.] ] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L857
    data

    Input data array

    reps

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  237. abstract def topk(data: NDArray, axis: Option[Int] = None, k: Option[Int] = None, ret_typ: Option[String] = None, is_ascend: Option[Boolean] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Returns the top *k* elements in an input array along the given axis.
     The returned elements will be sorted.
    
    Examples::
    
      x = `[ [ 0.3,  0.2,  0.4],
           [ 0.1,  0.3,  0.2] ]
    
      // returns an index of the largest element on last axis
      topk(x) = `[ [ 2.],
                 [ 1.] ]
    
      // returns the value of top-2 largest elements on last axis
      topk(x, ret_typ='value', k=2) = `[ [ 0.4,  0.3],
                                       [ 0.3,  0.2] ]
    
      // returns the value of top-2 smallest elements on last axis
      topk(x, ret_typ='value', k=2, is_ascend=1) = `[ [ 0.2 ,  0.3],
                                                   [ 0.1 ,  0.2] ]
    
      // returns the value of top-2 largest elements on axis 0
      topk(x, axis=0, ret_typ='value', k=2) = `[ [ 0.3,  0.3,  0.4],
                                               [ 0.1,  0.2,  0.2] ]
    
      // flattens and then returns list of both values and indices
      topk(x, ret_typ='both', k=2) = `[ `[ [ 0.4,  0.3], [ 0.3,  0.2] ] ,  `[ [ 2.,  0.], [ 1.,  2.] ] ]
    
    
    
    Defined in src/operator/tensor/ordering_op.cc:L64
    data

    The input array

    axis

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

    k

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

    ret_typ

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

    is_ascend

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

    dtype

    DType of the output indices when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely represent the indices.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  238. abstract def transpose(data: NDArray, axes: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Permutes the dimensions of an array.
    
    Examples::
    
      x = `[ [ 1, 2],
           [ 3, 4] ]
    
      transpose(x) = `[ [ 1.,  3.],
                      [ 2.,  4.] ]
    
      x = `[ `[ [ 1.,  2.],
            [ 3.,  4.] ],
    
           `[ [ 5.,  6.],
            [ 7.,  8.] ] ]
    
      transpose(x) = `[ `[ [ 1.,  5.],
                       [ 3.,  7.] ],
    
                      `[ [ 2.,  6.],
                       [ 4.,  8.] ] ]
    
      transpose(x, axes=(1,0,2)) = `[ `[ [ 1.,  2.],
                                     [ 5.,  6.] ],
    
                                    `[ [ 3.,  4.],
                                     [ 7.,  8.] ] ]
    
    
    Defined in src/operator/tensor/matrix_op.cc:L375
    data

    Source input

    axes

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  239. abstract def trunc(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

    Return the element-wise truncated value of the input.
    
    The truncated value of the scalar x is the nearest integer i which is closer to
    zero than x is. In short, the fractional part of the signed number x is discarded.
    
    Example::
    
       trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  1.,  1.,  2.]
    
    The storage type of ``trunc`` output depends upon the input storage type:
    
       - trunc(default) = default
       - trunc(row_sparse) = row_sparse
       - trunc(csr) = csr
    
    
    
    Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L825
    data

    The input array.

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  240. abstract def uniform(low: Option[Float] = None, high: Option[Float] = None, shape: Option[Shape] = None, ctx: Option[String] = None, dtype: Option[String] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Draw random samples from a uniform distribution.
    
    .. note:: The existing alias ``uniform`` is deprecated.
    
    Samples are uniformly distributed over the half-open interval *[low, high)*
    (includes *low*, but excludes *high*).
    
    Example::
    
       uniform(low=0, high=1, shape=(2,2)) = `[ [ 0.60276335,  0.85794562],
                                              [ 0.54488319,  0.84725171] ]
    
    
    
    Defined in src/operator/random/sample_op.cc:L96
    low

    Lower bound of the distribution.

    high

    Upper bound of the distribution.

    shape

    Shape of the output.

    ctx

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

    dtype

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  241. abstract def unravel_index(data: NDArray, shape: Option[Shape] = None, out: Option[NDArray] = None): NDArrayFuncReturn

    Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix. The leading dimension may be left unspecified by using -1 as placeholder.
    
    Examples::
    
       A = [22,41,37]
       unravel(A, shape=(7,6)) = `[ [3,6,6],[4,5,1] ]
       unravel(A, shape=(-1,6)) = `[ [3,6,6],[4,5,1] ]
    
    
    
    Defined in src/operator/tensor/ravel.cc:L67
    data

    Array of flat indices

    shape

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

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  242. abstract def where(condition: NDArray, x: NDArray, y: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    condition array

    x
    y
    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()
  243. abstract def zeros_like(data: NDArray, out: Option[NDArray] = None): NDArrayFuncReturn

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

    The input

    returns

    org.apache.mxnet.NDArrayFuncReturn

    Definition Classes
    NDArrayAPIBase
    Annotations
    @Experimental()

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