# NDArrayBase

### Related Doc: package mxnet

#### abstract class NDArrayBase extends AnyRef

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### Abstract Value Members

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

Applies an activation function element-wise to the input.

The following activation functions are supported:

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

Defined in src/operator/nn/activation.cc:L165
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies an activation function element-wise to the input.

The following activation functions are supported:

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

Defined in src/operator/nn/activation.cc:L165
returns

org.apache.mxnet.NDArrayFuncReturn

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

Batch normalization.

Normalizes a data batch by mean and variance, and applies a scale gamma as
well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:

.. math::

data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])

Then compute the normalized output, which has the same shape as input, as following:

.. math::

out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]

Both *mean* and *var* returns a scalar by treating the input as a vector.

Assume the input has size *k* on axis 1, then both gamma and beta
have shape *(k,)*. If output_mean_var is set to be true, then outputs both data_mean and
the inverse of data_var, which are needed for the backward pass. Note that gradient of these
two outputs are blocked.

Besides the inputs and the outputs, this operator accepts two auxiliary
states, moving_mean and moving_var, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)

If use_global_stats is set to be true, then moving_mean and
moving_var are used instead of data_mean and data_var to compute
the output. It is often used during inference.

The parameter axis specifies which axis of the input shape denotes
the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
axis to be the last item in the input shape.

Both gamma and beta are learnable parameters. But if fix_gamma is true,
then set gamma to 1 and its gradient to 0.

.. Note::
When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False,
the sparse tensors will fallback.

Defined in src/operator/nn/batch_norm.cc:L607
returns

org.apache.mxnet.NDArrayFuncReturn

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

Batch normalization.

Normalizes a data batch by mean and variance, and applies a scale gamma as
well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:

.. math::

data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])

Then compute the normalized output, which has the same shape as input, as following:

.. math::

out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]

Both *mean* and *var* returns a scalar by treating the input as a vector.

Assume the input has size *k* on axis 1, then both gamma and beta
have shape *(k,)*. If output_mean_var is set to be true, then outputs both data_mean and
the inverse of data_var, which are needed for the backward pass. Note that gradient of these
two outputs are blocked.

Besides the inputs and the outputs, this operator accepts two auxiliary
states, moving_mean and moving_var, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)

If use_global_stats is set to be true, then moving_mean and
moving_var are used instead of data_mean and data_var to compute
the output. It is often used during inference.

The parameter axis specifies which axis of the input shape denotes
the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
axis to be the last item in the input shape.

Both gamma and beta are learnable parameters. But if fix_gamma is true,
then set gamma to 1 and its gradient to 0.

.. Note::
When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False,
the sparse tensors will fallback.

Defined in src/operator/nn/batch_norm.cc:L607
returns

org.apache.mxnet.NDArrayFuncReturn

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

Batch normalization.

This operator is DEPRECATED. Perform BatchNorm on the input.

Normalizes a data batch by mean and variance, and applies a scale gamma as
well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:

.. math::

data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])

Then compute the normalized output, which has the same shape as input, as following:

.. math::

out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]

Both *mean* and *var* returns a scalar by treating the input as a vector.

Assume the input has size *k* on axis 1, then both gamma and beta
have shape *(k,)*. If output_mean_var is set to be true, then outputs both data_mean and
data_var as well, which are needed for the backward pass.

Besides the inputs and the outputs, this operator accepts two auxiliary
states, moving_mean and moving_var, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)

If use_global_stats is set to be true, then moving_mean and
moving_var are used instead of data_mean and data_var to compute
the output. It is often used during inference.

Both gamma and beta are learnable parameters. But if fix_gamma is true,
then set gamma to 1 and its gradient to 0.

There's no sparse support for this operator, and it will exhibit problematic behavior if used with
sparse tensors.

Defined in src/operator/batch_norm_v1.cc:L95
returns

org.apache.mxnet.NDArrayFuncReturn

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

Batch normalization.

This operator is DEPRECATED. Perform BatchNorm on the input.

Normalizes a data batch by mean and variance, and applies a scale gamma as
well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis:

.. math::

data\_mean[i] = mean(data[:,i,:,...]) \\
data\_var[i] = var(data[:,i,:,...])

Then compute the normalized output, which has the same shape as input, as following:

.. math::

out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]

Both *mean* and *var* returns a scalar by treating the input as a vector.

Assume the input has size *k* on axis 1, then both gamma and beta
have shape *(k,)*. If output_mean_var is set to be true, then outputs both data_mean and
data_var as well, which are needed for the backward pass.

Besides the inputs and the outputs, this operator accepts two auxiliary
states, moving_mean and moving_var, which are *k*-length
vectors. They are global statistics for the whole dataset, which are updated
by::

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)

If use_global_stats is set to be true, then moving_mean and
moving_var are used instead of data_mean and data_var to compute
the output. It is often used during inference.

Both gamma and beta are learnable parameters. But if fix_gamma is true,
then set gamma to 1 and its gradient to 0.

There's no sparse support for this operator, and it will exhibit problematic behavior if used with
sparse tensors.

Defined in src/operator/batch_norm_v1.cc:L95
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies bilinear sampling to input feature map.

Bilinear Sampling is the key of  [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
except that the operator has the backward pass.

Given :math:data and :math:grid, then the output is computed by

.. math::
x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})

:math:x_{dst}, :math:y_{dst} enumerate all spatial locations in :math:output, and :math:G() denotes the bilinear interpolation kernel.
The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).

The operator assumes that :math:data has 'NCHW' layout and :math:grid has been normalized to [-1, 1].

BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
GridGenerator supports two kinds of transformation: affine and warp.
If users want to design a CustomOp to manipulate :math:grid, please firstly refer to the code of GridGenerator.

Example 1::

## Zoom out data two times
data = array([ [[ [1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3] ] ] ])

affine_matrix = array([ [2, 0, 0],
[0, 2, 0] ])

affine_matrix = reshape(affine_matrix, shape=(1, 6))

grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))

out = BilinearSampler(data, grid)

out
[ [[ [ 0,   0,     0,   0],
[ 0,   3.5,   6.5, 0],
[ 0,   1.25,  2.5, 0],
[ 0,   0,     0,   0] ] ]

Example 2::

## shift data horizontally by -1 pixel

data = array([ [[ [1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3] ] ] ])

warp_maxtrix = array([ [[ [1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1] ],
[ [0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0] ] ] ])

grid = GridGenerator(data=warp_matrix, transform_type='warp')
out = BilinearSampler(data, grid)

out
[ [[ [ 4,  3,  6,  0],
[ 8,  8,  9,  0],
[ 4,  1,  5,  0],
[ 0,  1,  3,  0] ] ]

Defined in src/operator/bilinear_sampler.cc:L256
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies bilinear sampling to input feature map.

Bilinear Sampling is the key of  [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
except that the operator has the backward pass.

Given :math:data and :math:grid, then the output is computed by

.. math::
x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})

:math:x_{dst}, :math:y_{dst} enumerate all spatial locations in :math:output, and :math:G() denotes the bilinear interpolation kernel.
The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).

The operator assumes that :math:data has 'NCHW' layout and :math:grid has been normalized to [-1, 1].

BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
GridGenerator supports two kinds of transformation: affine and warp.
If users want to design a CustomOp to manipulate :math:grid, please firstly refer to the code of GridGenerator.

Example 1::

## Zoom out data two times
data = array([ [[ [1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3] ] ] ])

affine_matrix = array([ [2, 0, 0],
[0, 2, 0] ])

affine_matrix = reshape(affine_matrix, shape=(1, 6))

grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))

out = BilinearSampler(data, grid)

out
[ [[ [ 0,   0,     0,   0],
[ 0,   3.5,   6.5, 0],
[ 0,   1.25,  2.5, 0],
[ 0,   0,     0,   0] ] ]

Example 2::

## shift data horizontally by -1 pixel

data = array([ [[ [1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3] ] ] ])

warp_maxtrix = array([ [[ [1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1] ],
[ [0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0] ] ] ])

grid = GridGenerator(data=warp_matrix, transform_type='warp')
out = BilinearSampler(data, grid)

out
[ [[ [ 4,  3,  6,  0],
[ 8,  8,  9,  0],
[ 4,  1,  5,  0],
[ 0,  1,  3,  0] ] ]

Defined in src/operator/bilinear_sampler.cc:L256
returns

org.apache.mxnet.NDArrayFuncReturn

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

Stops gradient computation.

Stops the accumulated gradient of the inputs from flowing through this operator
in the backward direction. In other words, this operator prevents the contribution
of its inputs to be taken into account for computing gradients.

Example::

v1 = [1, 2]
v2 = [0, 1]
a = Variable('a')
b = Variable('b')

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()
[ 0.  0.]
[ 1.  1.]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L325
returns

org.apache.mxnet.NDArrayFuncReturn

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

Stops gradient computation.

Stops the accumulated gradient of the inputs from flowing through this operator
in the backward direction. In other words, this operator prevents the contribution
of its inputs to be taken into account for computing gradients.

Example::

v1 = [1, 2]
v2 = [0, 1]
a = Variable('a')
b = Variable('b')

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()
[ 0.  0.]
[ 1.  1.]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L325
returns

org.apache.mxnet.NDArrayFuncReturn

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

Connectionist Temporal Classification Loss.

.. note:: The existing alias contrib_CTCLoss is deprecated.

The shapes of the inputs and outputs:

- **data**: (sequence_length, batch_size, alphabet_size)
- **label**: (batch_size, label_sequence_length)
- **out**: (batch_size)

The data tensor consists of sequences of activation vectors (without applying softmax),
with i-th channel in the last dimension corresponding to i-th label
for i between 0 and alphabet_size-1 (i.e always 0-indexed).
Alphabet size should include one additional value reserved for blank label.
When blank_label is "first", the 0-th channel is be reserved for
activation of blank label, or otherwise if it is "last", (alphabet_size-1)-th channel should be
reserved for blank label.

label is an index matrix of integers. When blank_label is "first",
the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
when blank_label is "last", the value (alphabet_size-1) is reserved for blank label.

If a sequence of labels is shorter than *label_sequence_length*, use the special
padding value at the end of the sequence to conform it to the correct
length. The padding value is 0 when blank_label is "first", and -1 otherwise.

For example, suppose the vocabulary is [a, b, c], and in one batch we have three sequences
'ba', 'cbb', and 'abac'. When blank_label is "first", we can index the labels as
{'a': 1, 'b': 2, 'c': 3}, and we reserve the 0-th channel for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]

When blank_label is "last", we can index the labels as
{'a': 0, 'b': 1, 'c': 2}, and we reserve the channel index 3 for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]

out is a list of CTC loss values, one per example in the batch.

See *Connectionist Temporal Classification: Labelling Unsegmented
Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
information on the definition and the algorithm.

Defined in src/operator/nn/ctc_loss.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

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

Connectionist Temporal Classification Loss.

.. note:: The existing alias contrib_CTCLoss is deprecated.

The shapes of the inputs and outputs:

- **data**: (sequence_length, batch_size, alphabet_size)
- **label**: (batch_size, label_sequence_length)
- **out**: (batch_size)

The data tensor consists of sequences of activation vectors (without applying softmax),
with i-th channel in the last dimension corresponding to i-th label
for i between 0 and alphabet_size-1 (i.e always 0-indexed).
Alphabet size should include one additional value reserved for blank label.
When blank_label is "first", the 0-th channel is be reserved for
activation of blank label, or otherwise if it is "last", (alphabet_size-1)-th channel should be
reserved for blank label.

label is an index matrix of integers. When blank_label is "first",
the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
when blank_label is "last", the value (alphabet_size-1) is reserved for blank label.

If a sequence of labels is shorter than *label_sequence_length*, use the special
padding value at the end of the sequence to conform it to the correct
length. The padding value is 0 when blank_label is "first", and -1 otherwise.

For example, suppose the vocabulary is [a, b, c], and in one batch we have three sequences
'ba', 'cbb', and 'abac'. When blank_label is "first", we can index the labels as
{'a': 1, 'b': 2, 'c': 3}, and we reserve the 0-th channel for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]

When blank_label is "last", we can index the labels as
{'a': 0, 'b': 1, 'c': 2}, and we reserve the channel index 3 for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]

out is a list of CTC loss values, one per example in the batch.

See *Connectionist Temporal Classification: Labelling Unsegmented
Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
information on the definition and the algorithm.

Defined in src/operator/nn/ctc_loss.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

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

Casts all elements of the input to a new type.

.. note:: Cast is deprecated. Use cast instead.

Example::

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L664
returns

org.apache.mxnet.NDArrayFuncReturn

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

Casts all elements of the input to a new type.

.. note:: Cast is deprecated. Use cast instead.

Example::

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L664
returns

org.apache.mxnet.NDArrayFuncReturn

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

Joins input arrays along a given axis.

.. note:: Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along
which they will be concatenated.
The dimension of the output array along the concatenated axis will be equal
to the sum of the corresponding dimensions of the input arrays.

The storage type of concat output depends on storage types of inputs

- concat(csr, csr, ..., csr, dim=0) = csr
- otherwise, concat generates output with default storage

Example::

x = [ [1,1],[2,2] ]
y = [ [3,3],[4,4],[5,5] ]
z = [ [6,6], [7,7],[8,8] ]

concat(x,y,z,dim=0) = [ [ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.] ]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [ [ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.] ]

Defined in src/operator/nn/concat.cc:L385
returns

org.apache.mxnet.NDArrayFuncReturn

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

Joins input arrays along a given axis.

.. note:: Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along
which they will be concatenated.
The dimension of the output array along the concatenated axis will be equal
to the sum of the corresponding dimensions of the input arrays.

The storage type of concat output depends on storage types of inputs

- concat(csr, csr, ..., csr, dim=0) = csr
- otherwise, concat generates output with default storage

Example::

x = [ [1,1],[2,2] ]
y = [ [3,3],[4,4],[5,5] ]
z = [ [6,6], [7,7],[8,8] ]

concat(x,y,z,dim=0) = [ [ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.] ]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [ [ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.] ]

Defined in src/operator/nn/concat.cc:L385
returns

org.apache.mxnet.NDArrayFuncReturn

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

Compute *N*-D convolution on *(N+2)*-D input.

In the 2-D convolution, given input data with shape *(batch_size,
channel, height, width)*, the output is computed by

.. math::

out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
weight[i,j,:,:]

where :math:\star is the 2-D cross-correlation operator.

For general 2-D convolution, the shapes are

- **data**: *(batch_size, channel, height, width)*
- **weight**: *(num_filter, channel, kernel[0], kernel[1])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_height, out_width)*.

Define::

f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1

then we have::

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)*.

*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:L476
returns

org.apache.mxnet.NDArrayFuncReturn

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

Compute *N*-D convolution on *(N+2)*-D input.

In the 2-D convolution, given input data with shape *(batch_size,
channel, height, width)*, the output is computed by

.. math::

out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star
weight[i,j,:,:]

where :math:\star is the 2-D cross-correlation operator.

For general 2-D convolution, the shapes are

- **data**: *(batch_size, channel, height, width)*
- **weight**: *(num_filter, channel, kernel[0], kernel[1])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_height, out_width)*.

Define::

f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1

then we have::

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)*.

*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:L476
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

org.apache.mxnet.NDArrayFuncReturn

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

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

org.apache.mxnet.NDArrayFuncReturn

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

Applies correlation to inputs.

The correlation layer performs multiplicative patch comparisons between two feature maps.

Given two multi-channel feature maps :math:f_{1}, f_{2}, with :math:w, :math:h, and :math:c being their width, height, and number of channels,
the correlation layer lets the network compare each patch from :math:f_{1} with each patch from :math:f_{2}.

For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:x_{1} in the first map and
:math:x_{2} in the second map is then defined as:

.. math::

c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o), f_{2}(x_{2} + o)>

for a square patch of size :math:K:=2k+1.

Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other
data. For this reason, it has no training weights.

Computing :math:c(x_{1}, x_{2}) involves :math:c * K^{2} multiplications. Comparing all patch combinations involves :math:w^{2}*h^{2} such computations.

Given a maximum displacement :math:d, for each location :math:x_{1} it computes correlations :math:c(x_{1}, x_{2}) only in a neighborhood of size :math:D:=2d+1,
by limiting the range of :math:x_{2}. We use strides :math:s_{1}, s_{2}, to quantize :math:x_{1} globally and to quantize :math:x_{2} within the neighborhood
centered around :math:x_{1}.

The final output is defined by the following expression:

.. math::
out[n, q, i, j] = c(x_{i, j}, x_{q})

where :math:i and :math:j enumerate spatial locations in :math:f_{1}, and :math:q denotes the :math:q^{th} neighborhood of :math:x_{i,j}.

Defined in src/operator/correlation.cc:L198
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies correlation to inputs.

The correlation layer performs multiplicative patch comparisons between two feature maps.

Given two multi-channel feature maps :math:f_{1}, f_{2}, with :math:w, :math:h, and :math:c being their width, height, and number of channels,
the correlation layer lets the network compare each patch from :math:f_{1} with each patch from :math:f_{2}.

For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:x_{1} in the first map and
:math:x_{2} in the second map is then defined as:

.. math::

c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o), f_{2}(x_{2} + o)>

for a square patch of size :math:K:=2k+1.

Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other
data. For this reason, it has no training weights.

Computing :math:c(x_{1}, x_{2}) involves :math:c * K^{2} multiplications. Comparing all patch combinations involves :math:w^{2}*h^{2} such computations.

Given a maximum displacement :math:d, for each location :math:x_{1} it computes correlations :math:c(x_{1}, x_{2}) only in a neighborhood of size :math:D:=2d+1,
by limiting the range of :math:x_{2}. We use strides :math:s_{1}, s_{2}, to quantize :math:x_{1} globally and to quantize :math:x_{2} within the neighborhood
centered around :math:x_{1}.

The final output is defined by the following expression:

.. math::
out[n, q, i, j] = c(x_{i, j}, x_{q})

where :math:i and :math:j enumerate spatial locations in :math:f_{1}, and :math:q denotes the :math:q^{th} neighborhood of :math:x_{i,j}.

Defined in src/operator/correlation.cc:L198
returns

org.apache.mxnet.NDArrayFuncReturn

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

.. note:: Crop is deprecated. Use slice instead.

Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or
with width and height of the second input symbol, i.e., with one input, we need h_w to
specify the crop height and width, otherwise the second input symbol's size will be used

Defined in src/operator/crop.cc:L50
returns

org.apache.mxnet.NDArrayFuncReturn

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

.. note:: Crop is deprecated. Use slice instead.

Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or
with width and height of the second input symbol, i.e., with one input, we need h_w to
specify the crop height and width, otherwise the second input symbol's size will be used

Defined in src/operator/crop.cc:L50
returns

org.apache.mxnet.NDArrayFuncReturn

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

Apply a custom operator implemented in a frontend language (like Python).

Custom operators should override required methods like forward and backward.
The custom operator must be registered before it can be used.
Please check the tutorial here: https://mxnet.incubator.apache.org/api/faq/new_op

Defined in src/operator/custom/custom.cc:L547
returns

org.apache.mxnet.NDArrayFuncReturn

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

Apply a custom operator implemented in a frontend language (like Python).

Custom operators should override required methods like forward and backward.
The custom operator must be registered before it can be used.
Please check the tutorial here: https://mxnet.incubator.apache.org/api/faq/new_op

Defined in src/operator/custom/custom.cc:L547
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

org.apache.mxnet.NDArrayFuncReturn

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

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

org.apache.mxnet.NDArrayFuncReturn

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

Applies dropout operation to input array.

- During training, each element of the input is set to zero with probability p.
The whole array is rescaled by :math:1/(1-p) to keep the expected
sum of the input unchanged.

- During testing, this operator does not change the input if mode is 'training'.
If mode is 'always', the same computaion as during training will be applied.

Example::

random.seed(998)
input_array = array([ [3., 0.5,  -0.5,  2., 7.],
[2., -0.4,   7.,  3., 0.2] ])
a = symbol.Variable('a')
dropout = symbol.Dropout(a, p = 0.2)
executor = dropout.simple_bind(a = input_array.shape)

## If training
executor.forward(is_train = True, a = input_array)
executor.outputs
[ [ 3.75   0.625 -0.     2.5    8.75 ]
[ 2.5   -0.5    8.75   3.75   0.   ] ]

## If testing
executor.forward(is_train = False, a = input_array)
executor.outputs
[ [ 3.     0.5   -0.5    2.     7.   ]
[ 2.    -0.4    7.     3.     0.2  ] ]

Defined in src/operator/nn/dropout.cc:L96
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies dropout operation to input array.

- During training, each element of the input is set to zero with probability p.
The whole array is rescaled by :math:1/(1-p) to keep the expected
sum of the input unchanged.

- During testing, this operator does not change the input if mode is 'training'.
If mode is 'always', the same computaion as during training will be applied.

Example::

random.seed(998)
input_array = array([ [3., 0.5,  -0.5,  2., 7.],
[2., -0.4,   7.,  3., 0.2] ])
a = symbol.Variable('a')
dropout = symbol.Dropout(a, p = 0.2)
executor = dropout.simple_bind(a = input_array.shape)

## If training
executor.forward(is_train = True, a = input_array)
executor.outputs
[ [ 3.75   0.625 -0.     2.5    8.75 ]
[ 2.5   -0.5    8.75   3.75   0.   ] ]

## If testing
executor.forward(is_train = False, a = input_array)
executor.outputs
[ [ 3.     0.5   -0.5    2.     7.   ]
[ 2.    -0.4    7.     3.     0.2  ] ]

Defined in src/operator/nn/dropout.cc:L96
returns

org.apache.mxnet.NDArrayFuncReturn

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

Adds all input arguments element-wise.

.. math::
add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n

add_n is potentially more efficient than calling add by n times.

The storage type of add_n output depends on storage types of inputs

- add_n(row_sparse, row_sparse, ..) = row_sparse
- add_n(default, csr, default) = default
- add_n(any input combinations longer than 4 (>4) with at least one default type) = default
- otherwise, add_n falls all inputs back to default storage and generates default storage

Defined in src/operator/tensor/elemwise_sum.cc:L156
returns

org.apache.mxnet.NDArrayFuncReturn

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

Adds all input arguments element-wise.

.. math::
add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n

add_n is potentially more efficient than calling add by n times.

The storage type of add_n output depends on storage types of inputs

- add_n(row_sparse, row_sparse, ..) = row_sparse
- add_n(default, csr, default) = default
- add_n(any input combinations longer than 4 (>4) with at least one default type) = default
- otherwise, add_n falls all inputs back to default storage and generates default storage

Defined in src/operator/tensor/elemwise_sum.cc:L156
returns

org.apache.mxnet.NDArrayFuncReturn

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

Maps integer indices to vector representations (embeddings).

This operator maps words to real-valued vectors in a high-dimensional space,
called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
For example, it has been noted that in the learned embedding spaces, similar words tend
to be close to each other and dissimilar words far apart.

For an input array of shape (d1, ..., dK),
the shape of an output array is (d1, ..., dK, output_dim).
All the input values should be integers in the range [0, input_dim).

If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
(ip0, op0).

When "sparse_grad" is False, if any index mentioned is too large, it is replaced by the index that
addresses the last vector in an embedding matrix.
When "sparse_grad" is True, an error will be raised if invalid indices are found.

Examples::

input_dim = 4
output_dim = 5

// Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
y = [ [  0.,   1.,   2.,   3.,   4.],
[  5.,   6.,   7.,   8.,   9.],
[ 10.,  11.,  12.,  13.,  14.],
[ 15.,  16.,  17.,  18.,  19.] ]

// Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
x = [ [ 1.,  3.],
[ 0.,  2.] ]

// Mapped input x to its vector representation y.
Embedding(x, y, 4, 5) = [ [ [  5.,   6.,   7.,   8.,   9.],
[ 15.,  16.,  17.,  18.,  19.] ],

[ [  0.,   1.,   2.,   3.,   4.],
[ 10.,  11.,  12.,  13.,  14.] ] ]

The storage type of weight can be either row_sparse or default.

.. Note::

If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
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:L598
returns

org.apache.mxnet.NDArrayFuncReturn

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

Maps integer indices to vector representations (embeddings).

This operator maps words to real-valued vectors in a high-dimensional space,
called word embeddings. These embeddings can capture semantic and syntactic properties of the words.
For example, it has been noted that in the learned embedding spaces, similar words tend
to be close to each other and dissimilar words far apart.

For an input array of shape (d1, ..., dK),
the shape of an output array is (d1, ..., dK, output_dim).
All the input values should be integers in the range [0, input_dim).

If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be
(ip0, op0).

When "sparse_grad" is False, if any index mentioned is too large, it is replaced by the index that
addresses the last vector in an embedding matrix.
When "sparse_grad" is True, an error will be raised if invalid indices are found.

Examples::

input_dim = 4
output_dim = 5

// Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
y = [ [  0.,   1.,   2.,   3.,   4.],
[  5.,   6.,   7.,   8.,   9.],
[ 10.,  11.,  12.,  13.,  14.],
[ 15.,  16.,  17.,  18.,  19.] ]

// Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
x = [ [ 1.,  3.],
[ 0.,  2.] ]

// Mapped input x to its vector representation y.
Embedding(x, y, 4, 5) = [ [ [  5.,   6.,   7.,   8.,   9.],
[ 15.,  16.,  17.,  18.,  19.] ],

[ [  0.,   1.,   2.,   3.,   4.],
[ 10.,  11.,  12.,  13.,  14.] ] ]

The storage type of weight can be either row_sparse or default.

.. Note::

If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
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:L598
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L250
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L250
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies a linear transformation: :math:Y = XW^T + b.

If flatten is set to be true, then the shapes are:

- **data**: (batch_size, x1, x2, ..., xn)
- **weight**: (num_hidden, x1 * x2 * ... * xn)
- **bias**: (num_hidden,)
- **out**: (batch_size, num_hidden)

If flatten is set to be false, then the shapes are:

- **data**: (x1, x2, ..., xn, input_dim)
- **weight**: (num_hidden, input_dim)
- **bias**: (num_hidden,)
- **out**: (x1, x2, ..., xn, num_hidden)

The learnable parameters include both weight and bias.

If no_bias is set to be true, then the bias term is ignored.

.. Note::

The sparse support for FullyConnected is limited to forward evaluation with row_sparse
weight and bias, where the length of weight.indices and bias.indices must be equal
to num_hidden. This could be useful for model inference with row_sparse weights
trained with importance sampling or noise contrastive estimation.

To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
of sparse.FullyConnected.

Defined in src/operator/nn/fully_connected.cc:L287
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies a linear transformation: :math:Y = XW^T + b.

If flatten is set to be true, then the shapes are:

- **data**: (batch_size, x1, x2, ..., xn)
- **weight**: (num_hidden, x1 * x2 * ... * xn)
- **bias**: (num_hidden,)
- **out**: (batch_size, num_hidden)

If flatten is set to be false, then the shapes are:

- **data**: (x1, x2, ..., xn, input_dim)
- **weight**: (num_hidden, input_dim)
- **bias**: (num_hidden,)
- **out**: (x1, x2, ..., xn, num_hidden)

The learnable parameters include both weight and bias.

If no_bias is set to be true, then the bias term is ignored.

.. Note::

The sparse support for FullyConnected is limited to forward evaluation with row_sparse
weight and bias, where the length of weight.indices and bias.indices must be equal
to num_hidden. This could be useful for model inference with row_sparse weights
trained with importance sampling or noise contrastive estimation.

To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead
of sparse.FullyConnected.

Defined in src/operator/nn/fully_connected.cc:L287
returns

org.apache.mxnet.NDArrayFuncReturn

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

Generates 2D sampling grid for bilinear sampling.
returns

org.apache.mxnet.NDArrayFuncReturn

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

Generates 2D sampling grid for bilinear sampling.
returns

org.apache.mxnet.NDArrayFuncReturn

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

Group normalization.

The input channels are separated into num_groups groups, each containing num_channels / num_groups channels.
The mean and standard-deviation are calculated separately over the each group.

.. math::

data = data.reshape((N, num_groups, C // num_groups, ...))
out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta

Both gamma and beta are learnable parameters.

Defined in src/operator/nn/group_norm.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

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

Group normalization.

The input channels are separated into num_groups groups, each containing num_channels / num_groups channels.
The mean and standard-deviation are calculated separately over the each group.

.. math::

data = data.reshape((N, num_groups, C // num_groups, ...))
out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta

Both gamma and beta are learnable parameters.

Defined in src/operator/nn/group_norm.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

org.apache.mxnet.NDArrayFuncReturn

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

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

org.apache.mxnet.NDArrayFuncReturn

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

Applies instance normalization to the n-dimensional input array.

This operator takes an n-dimensional input array where (n>2) and normalizes
the input using the following formula:

.. math::

out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta

This layer is similar to batch normalization layer (BatchNorm)
with two differences: first, the normalization is
carried out per example (instance), not over a batch. Second, the
same normalization is applied both at test and train time. This
operation is also known as contrast normalization.

If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
gamma and beta parameters must be vectors of shape [channel].

This implementation is based on this paper [1]_

.. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).

Examples::

// Input of shape (2,1,2)
x = [ [ [ 1.1,  2.2] ],
[ [ 3.3,  4.4] ] ]

// gamma parameter of length 1
gamma = [1.5]

// beta parameter of length 1
beta = [0.5]

// Instance normalization is calculated with the above formula
InstanceNorm(x,gamma,beta) = [ [ [-0.997527  ,  1.99752665] ],
[ [-0.99752653,  1.99752724] ] ]

Defined in src/operator/instance_norm.cc:L95
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies instance normalization to the n-dimensional input array.

This operator takes an n-dimensional input array where (n>2) and normalizes
the input using the following formula:

.. math::

out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta

This layer is similar to batch normalization layer (BatchNorm)
with two differences: first, the normalization is
carried out per example (instance), not over a batch. Second, the
same normalization is applied both at test and train time. This
operation is also known as contrast normalization.

If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...],
gamma and beta parameters must be vectors of shape [channel].

This implementation is based on this paper [1]_

.. [1] Instance Normalization: The Missing Ingredient for Fast Stylization,
D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).

Examples::

// Input of shape (2,1,2)
x = [ [ [ 1.1,  2.2] ],
[ [ 3.3,  4.4] ] ]

// gamma parameter of length 1
gamma = [1.5]

// beta parameter of length 1
beta = [0.5]

// Instance normalization is calculated with the above formula
InstanceNorm(x,gamma,beta) = [ [ [-0.997527  ,  1.99752665] ],
[ [-0.99752653,  1.99752724] ] ]

Defined in src/operator/instance_norm.cc:L95
returns

org.apache.mxnet.NDArrayFuncReturn

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

Normalize the input array using the L2 norm.

For 1-D NDArray, it computes::

out = data / sqrt(sum(data ** 2) + eps)

For N-D NDArray, if the input array has shape (N, N, ..., N),

with mode = instance, it normalizes each instance in the multidimensional
array by its L2 norm.::

for i in 0...N
out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)

with mode = channel, it normalizes each channel in the array by its L2 norm.::

for i in 0...N
out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)

with mode = spatial, it normalizes the cross channel norm for each position
in the array by its L2 norm.::

for dim in 2...N
for i in 0...N
out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
-dim-

Example::

x = [ [ [1,2],
[3,4] ],
[ [2,2],
[5,6] ] ]

L2Normalization(x, mode='instance')
=[ [ [ 0.18257418  0.36514837]
[ 0.54772252  0.73029673] ]
[ [ 0.24077171  0.24077171]
[ 0.60192931  0.72231513] ] ]

L2Normalization(x, mode='channel')
=[ [ [ 0.31622776  0.44721359]
[ 0.94868326  0.89442718] ]
[ [ 0.37139067  0.31622776]
[ 0.92847669  0.94868326] ] ]

L2Normalization(x, mode='spatial')
=[ [ [ 0.44721359  0.89442718]
[ 0.60000002  0.80000001] ]
[ [ 0.70710677  0.70710677]
[ 0.6401844   0.76822126] ] ]

Defined in src/operator/l2_normalization.cc:L196
returns

org.apache.mxnet.NDArrayFuncReturn

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

Normalize the input array using the L2 norm.

For 1-D NDArray, it computes::

out = data / sqrt(sum(data ** 2) + eps)

For N-D NDArray, if the input array has shape (N, N, ..., N),

with mode = instance, it normalizes each instance in the multidimensional
array by its L2 norm.::

for i in 0...N
out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)

with mode = channel, it normalizes each channel in the array by its L2 norm.::

for i in 0...N
out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)

with mode = spatial, it normalizes the cross channel norm for each position
in the array by its L2 norm.::

for dim in 2...N
for i in 0...N
out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
-dim-

Example::

x = [ [ [1,2],
[3,4] ],
[ [2,2],
[5,6] ] ]

L2Normalization(x, mode='instance')
=[ [ [ 0.18257418  0.36514837]
[ 0.54772252  0.73029673] ]
[ [ 0.24077171  0.24077171]
[ 0.60192931  0.72231513] ] ]

L2Normalization(x, mode='channel')
=[ [ [ 0.31622776  0.44721359]
[ 0.94868326  0.89442718] ]
[ [ 0.37139067  0.31622776]
[ 0.92847669  0.94868326] ] ]

L2Normalization(x, mode='spatial')
=[ [ [ 0.44721359  0.89442718]
[ 0.60000002  0.80000001] ]
[ [ 0.70710677  0.70710677]
[ 0.6401844   0.76822126] ] ]

Defined in src/operator/l2_normalization.cc:L196
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies local response normalization to the input.

The local response normalization layer performs "lateral inhibition" by normalizing
over local input regions.

If :math:a_{x,y}^{i} is the activity of a neuron computed by applying kernel :math:i at position
:math:(x, y) and then applying the ReLU nonlinearity, the response-normalized
activity :math:b_{x,y}^{i} is given by the expression:

.. math::
b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}

where the sum runs over :math:n "adjacent" kernel maps at the same spatial position, and :math:N is the total
number of kernels in the layer.

Defined in src/operator/nn/lrn.cc:L158
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies local response normalization to the input.

The local response normalization layer performs "lateral inhibition" by normalizing
over local input regions.

If :math:a_{x,y}^{i} is the activity of a neuron computed by applying kernel :math:i at position
:math:(x, y) and then applying the ReLU nonlinearity, the response-normalized
activity :math:b_{x,y}^{i} is given by the expression:

.. math::
b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}

where the sum runs over :math:n "adjacent" kernel maps at the same spatial position, and :math:N is the total
number of kernels in the layer.

Defined in src/operator/nn/lrn.cc:L158
returns

org.apache.mxnet.NDArrayFuncReturn

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

Layer normalization.

Normalizes the channels of the input tensor by mean and variance, and applies a scale gamma as
well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis and then
compute the normalized output, which has the same shape as input, as following:

.. math::

out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta

Both gamma and beta are learnable parameters.

Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.

Assume the input has size *k* on axis 1, then both gamma and beta
have shape *(k,)*. If output_mean_var is set to be true, then outputs both data_mean and
data_std. Note that no gradient will be passed through these two outputs.

The parameter axis specifies which axis of the input shape denotes
the 'channel' (separately normalized groups).  The default is -1, which sets the channel
axis to be the last item in the input shape.

Defined in src/operator/nn/layer_norm.cc:L159
returns

org.apache.mxnet.NDArrayFuncReturn

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

Layer normalization.

Normalizes the channels of the input tensor by mean and variance, and applies a scale gamma as
well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1.
We first compute the mean and variance along this axis and then
compute the normalized output, which has the same shape as input, as following:

.. math::

out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta

Both gamma and beta are learnable parameters.

Unlike BatchNorm and InstanceNorm,  the *mean* and *var* are computed along the channel dimension.

Assume the input has size *k* on axis 1, then both gamma and beta
have shape *(k,)*. If output_mean_var is set to be true, then outputs both data_mean and
data_std. Note that no gradient will be passed through these two outputs.

The parameter axis specifies which axis of the input shape denotes
the 'channel' (separately normalized groups).  The default is -1, which sets the channel
axis to be the last item in the input shape.

Defined in src/operator/nn/layer_norm.cc:L159
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies Leaky rectified linear unit activation element-wise to the input.

Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small slope
when the input is negative and has a slope of one when input is positive.

The following modified ReLU Activation functions are supported:

- *elu*: Exponential Linear Unit. y = x > 0 ? x : slope * (exp(x)-1)
- *selu*: Scaled Exponential Linear Unit. y = lambda * (x > 0 ? x : alpha * (exp(x) - 1)) where
*lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
- *leaky*: Leaky ReLU. y = x > 0 ? x : slope * x
- *prelu*: Parametric ReLU. This is same as *leaky* except that slope is learnt during training.
- *rrelu*: Randomized ReLU. same as *leaky* but the slope is uniformly and randomly chosen from
*[lower_bound, upper_bound)* for training, while fixed to be
*(lower_bound+upper_bound)/2* for inference.

Defined in src/operator/leaky_relu.cc:L163
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies Leaky rectified linear unit activation element-wise to the input.

Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small slope
when the input is negative and has a slope of one when input is positive.

The following modified ReLU Activation functions are supported:

- *elu*: Exponential Linear Unit. y = x > 0 ? x : slope * (exp(x)-1)
- *selu*: Scaled Exponential Linear Unit. y = lambda * (x > 0 ? x : alpha * (exp(x) - 1)) where
*lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*.
- *leaky*: Leaky ReLU. y = x > 0 ? x : slope * x
- *prelu*: Parametric ReLU. This is same as *leaky* except that slope is learnt during training.
- *rrelu*: Randomized ReLU. same as *leaky* but the slope is uniformly and randomly chosen from
*[lower_bound, upper_bound)* for training, while fixed to be
*(lower_bound+upper_bound)/2* for inference.

Defined in src/operator/leaky_relu.cc:L163
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes and optimizes for squared loss during backward propagation.
Just outputs data during forward propagation.

If :math:\hat{y}_i is the predicted value of the i-th sample, and :math:y_i is the corresponding target value,
then the squared loss estimated over :math:n samples is defined as

:math:\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert  \textbf{y}_i - \hat{\textbf{y}}_i  \rVert_2

.. note::
Use the LinearRegressionOutput as the final output layer of a net.

The storage type of label can be default or csr

- LinearRegressionOutput(default, default) = default
- LinearRegressionOutput(default, csr) = default

By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example.
The parameter grad_scale can be used to change this scale to grad_scale/m.

Defined in src/operator/regression_output.cc:L92
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes and optimizes for squared loss during backward propagation.
Just outputs data during forward propagation.

If :math:\hat{y}_i is the predicted value of the i-th sample, and :math:y_i is the corresponding target value,
then the squared loss estimated over :math:n samples is defined as

:math:\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert  \textbf{y}_i - \hat{\textbf{y}}_i  \rVert_2

.. note::
Use the LinearRegressionOutput as the final output layer of a net.

The storage type of label can be default or csr

- LinearRegressionOutput(default, default) = default
- LinearRegressionOutput(default, csr) = default

By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example.
The parameter grad_scale can be used to change this scale to grad_scale/m.

Defined in src/operator/regression_output.cc:L92
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies a logistic function to the input.

The logistic function, also known as the sigmoid function, is computed as
:math:\frac{1}{1+exp(-\textbf{x})}.

Commonly, the sigmoid is used to squash the real-valued output of a linear model
:math:wTx+b into the [0,1] range so that it can be interpreted as a probability.
It is suitable for binary classification or probability prediction tasks.

.. note::
Use the LogisticRegressionOutput as the final output layer of a net.

The storage type of label can be default or csr

- LogisticRegressionOutput(default, default) = default
- LogisticRegressionOutput(default, csr) = default

The loss function used is the Binary Cross Entropy Loss:

:math:-{(y\log(p) + (1 - y)\log(1 - p))}

Where y is the ground truth probability of positive outcome for a given example, and p the probability predicted by the model. By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example.
The parameter grad_scale can be used to change this scale to grad_scale/m.

Defined in src/operator/regression_output.cc:L152
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies a logistic function to the input.

The logistic function, also known as the sigmoid function, is computed as
:math:\frac{1}{1+exp(-\textbf{x})}.

Commonly, the sigmoid is used to squash the real-valued output of a linear model
:math:wTx+b into the [0,1] range so that it can be interpreted as a probability.
It is suitable for binary classification or probability prediction tasks.

.. note::
Use the LogisticRegressionOutput as the final output layer of a net.

The storage type of label can be default or csr

- LogisticRegressionOutput(default, default) = default
- LogisticRegressionOutput(default, csr) = default

The loss function used is the Binary Cross Entropy Loss:

:math:-{(y\log(p) + (1 - y)\log(1 - p))}

Where y is the ground truth probability of positive outcome for a given example, and p the probability predicted by the model. By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example.
The parameter grad_scale can be used to change this scale to grad_scale/m.

Defined in src/operator/regression_output.cc:L152
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes mean absolute error of the input.

MAE is a risk metric corresponding to the expected value of the absolute error.

If :math:\hat{y}_i is the predicted value of the i-th sample, and :math:y_i is the corresponding target value,
then the mean absolute error (MAE) estimated over :math:n samples is defined as

:math:\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1

.. note::
Use the MAERegressionOutput as the final output layer of a net.

The storage type of label can be default or csr

- MAERegressionOutput(default, default) = default
- MAERegressionOutput(default, csr) = default

By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example.
The parameter grad_scale can be used to change this scale to grad_scale/m.

Defined in src/operator/regression_output.cc:L120
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes mean absolute error of the input.

MAE is a risk metric corresponding to the expected value of the absolute error.

If :math:\hat{y}_i is the predicted value of the i-th sample, and :math:y_i is the corresponding target value,
then the mean absolute error (MAE) estimated over :math:n samples is defined as

:math:\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1

.. note::
Use the MAERegressionOutput as the final output layer of a net.

The storage type of label can be default or csr

- MAERegressionOutput(default, default) = default
- MAERegressionOutput(default, csr) = default

By default, gradients of this loss function are scaled by factor 1/m, where m is the number of regression outputs of a training example.
The parameter grad_scale can be used to change this scale to grad_scale/m.

Defined in src/operator/regression_output.cc:L120
returns

org.apache.mxnet.NDArrayFuncReturn

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

Make your own loss function in network construction.

This operator accepts a customized loss function symbol as a terminal loss and
the symbol should be an operator with no backward dependency.
The output of this function is the gradient of loss with respect to the input data.

For example, if you are a making a cross entropy loss function. Assume out is the
predicted output and label is the true label, then the cross entropy can be defined as::

cross_entropy = label * log(out) + (1 - label) * log(1 - out)
loss = MakeLoss(cross_entropy)

We will need to use MakeLoss when we are creating our own loss function or we want to
combine multiple loss functions. Also we may want to stop some variables' gradients
from backpropagation. See more detail in BlockGrad or stop_gradient.

In addition, we can give a scale to the loss by setting grad_scale,
so that the gradient of the loss will be rescaled in the backpropagation.

.. note:: This operator should be used as a Symbol instead of NDArray.

Defined in src/operator/make_loss.cc:L71
returns

org.apache.mxnet.NDArrayFuncReturn

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

Make your own loss function in network construction.

This operator accepts a customized loss function symbol as a terminal loss and
the symbol should be an operator with no backward dependency.
The output of this function is the gradient of loss with respect to the input data.

For example, if you are a making a cross entropy loss function. Assume out is the
predicted output and label is the true label, then the cross entropy can be defined as::

cross_entropy = label * log(out) + (1 - label) * log(1 - out)
loss = MakeLoss(cross_entropy)

We will need to use MakeLoss when we are creating our own loss function or we want to
combine multiple loss functions. Also we may want to stop some variables' gradients
from backpropagation. See more detail in BlockGrad or stop_gradient.

In addition, we can give a scale to the loss by setting grad_scale,
so that the gradient of the loss will be rescaled in the backpropagation.

.. note:: This operator should be used as a Symbol instead of NDArray.

Defined in src/operator/make_loss.cc:L71
returns

org.apache.mxnet.NDArrayFuncReturn

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

Pads an input array with a constant or edge values of the array.

.. note:: Pad is deprecated. Use pad instead.

.. note:: Current implementation only supports 4D and 5D input arrays with padding applied
only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.

This operation pads an input array with either a constant_value or edge values
along each axis of the input array. The amount of padding is specified by pad_width.

pad_width is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N). The pad_width should be of length 2*N
where N is the number of dimensions of the array.

For dimension N of the input array, before_N and after_N indicates how many values
to add before and after the elements of the array along dimension N.
The widths of the higher two dimensions before_1, after_1, before_2,
after_2 must be 0.

Example::

x = [ [[ [  1.   2.   3.]
[  4.   5.   6.] ]

[ [  7.   8.   9.]
[ 10.  11.  12.] ] ]

[ [ [ 11.  12.  13.]
[ 14.  15.  16.] ]

[ [ 17.  18.  19.]
[ 20.  21.  22.] ] ] ]

[ [[ [  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.] ] ] ]

[ [[ [  0.   0.   0.   0.   0.]
[  0.   1.   2.   3.   0.]
[  0.   4.   5.   6.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.   7.   8.   9.   0.]
[  0.  10.  11.  12.   0.]
[  0.   0.   0.   0.   0.] ] ]

[ [ [  0.   0.   0.   0.   0.]
[  0.  11.  12.  13.   0.]
[  0.  14.  15.  16.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.  17.  18.  19.   0.]
[  0.  20.  21.  22.   0.]
[  0.   0.   0.   0.   0.] ] ] ]

Defined in src/operator/pad.cc:L766
returns

org.apache.mxnet.NDArrayFuncReturn

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

Pads an input array with a constant or edge values of the array.

.. note:: Pad is deprecated. Use pad instead.

.. note:: Current implementation only supports 4D and 5D input arrays with padding applied
only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.

This operation pads an input array with either a constant_value or edge values
along each axis of the input array. The amount of padding is specified by pad_width.

pad_width is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N). The pad_width should be of length 2*N
where N is the number of dimensions of the array.

For dimension N of the input array, before_N and after_N indicates how many values
to add before and after the elements of the array along dimension N.
The widths of the higher two dimensions before_1, after_1, before_2,
after_2 must be 0.

Example::

x = [ [[ [  1.   2.   3.]
[  4.   5.   6.] ]

[ [  7.   8.   9.]
[ 10.  11.  12.] ] ]

[ [ [ 11.  12.  13.]
[ 14.  15.  16.] ]

[ [ 17.  18.  19.]
[ 20.  21.  22.] ] ] ]

[ [[ [  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.] ] ] ]

[ [[ [  0.   0.   0.   0.   0.]
[  0.   1.   2.   3.   0.]
[  0.   4.   5.   6.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.   7.   8.   9.   0.]
[  0.  10.  11.  12.   0.]
[  0.   0.   0.   0.   0.] ] ]

[ [ [  0.   0.   0.   0.   0.]
[  0.  11.  12.  13.   0.]
[  0.  14.  15.  16.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.  17.  18.  19.   0.]
[  0.  20.  21.  22.   0.]
[  0.   0.   0.   0.   0.] ] ] ]

Defined in src/operator/pad.cc:L766
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs pooling on the input.

The shapes for 1-D pooling are

- **data** and **out**: *(batch_size, channel, width)* (NCW layout) or
*(batch_size, width, channel)* (NWC layout),

The shapes for 2-D pooling are

- **data** and **out**: *(batch_size, channel, height, width)* (NCHW layout) or
*(batch_size, height, width, channel)* (NHWC layout),

out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])

The definition of *f* depends on pooling_convention, which has two options:

- **valid** (default)::

f(x, k, p, s) = floor((x+2*p-k)/s)+1

- **full**, which is compatible with Caffe::

f(x, k, p, s) = ceil((x+2*p-k)/s)+1

When global_pool is set to be true, then global pooling is performed. It will reset
kernel=(height, width) and set the appropiate padding to 0.

Three pooling options are supported by pool_type:

- **avg**: average pooling
- **max**: max pooling
- **sum**: sum pooling
- **lp**: Lp pooling

*height*. Namely the input data and output will have shape *(batch_size, channel, depth,
height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout).

Notes on Lp pooling:

Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf.
L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
We can see that Lp pooling stands between those two, in practice the most common value for p is 2.

For each window X, the mathematical expression for Lp pooling is:

:math:f(X) = \sqrt[p]{\sum_{x}^{X} x^p}

Defined in src/operator/nn/pooling.cc:L417
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs pooling on the input.

The shapes for 1-D pooling are

- **data** and **out**: *(batch_size, channel, width)* (NCW layout) or
*(batch_size, width, channel)* (NWC layout),

The shapes for 2-D pooling are

- **data** and **out**: *(batch_size, channel, height, width)* (NCHW layout) or
*(batch_size, height, width, channel)* (NHWC layout),

out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])

The definition of *f* depends on pooling_convention, which has two options:

- **valid** (default)::

f(x, k, p, s) = floor((x+2*p-k)/s)+1

- **full**, which is compatible with Caffe::

f(x, k, p, s) = ceil((x+2*p-k)/s)+1

When global_pool is set to be true, then global pooling is performed. It will reset
kernel=(height, width) and set the appropiate padding to 0.

Three pooling options are supported by pool_type:

- **avg**: average pooling
- **max**: max pooling
- **sum**: sum pooling
- **lp**: Lp pooling

*height*. Namely the input data and output will have shape *(batch_size, channel, depth,
height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout).

Notes on Lp pooling:

Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf.
L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling.
We can see that Lp pooling stands between those two, in practice the most common value for p is 2.

For each window X, the mathematical expression for Lp pooling is:

:math:f(X) = \sqrt[p]{\sum_{x}^{X} x^p}

Defined in src/operator/nn/pooling.cc:L417
returns

org.apache.mxnet.NDArrayFuncReturn

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

This operator is DEPRECATED.
Perform pooling on the input.

The shapes for 2-D pooling is

- **data**: *(batch_size, channel, height, width)*
- **out**: *(batch_size, num_filter, out_height, out_width)*, with::

out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])

The definition of *f* depends on pooling_convention, which has two options:

- **valid** (default)::

f(x, k, p, s) = floor((x+2*p-k)/s)+1

- **full**, which is compatible with Caffe::

f(x, k, p, s) = ceil((x+2*p-k)/s)+1

But global_pool is set to be true, then do a global pooling, namely reset
kernel=(height, width).

Three pooling options are supported by pool_type:

- **avg**: average pooling
- **max**: max pooling
- **sum**: sum pooling

1-D pooling is special case of 2-D pooling with *weight=1* and
*kernel[1]=1*.

*height*. Namely the input data will have shape *(batch_size, channel, depth,
height, width)*.

Defined in src/operator/pooling_v1.cc:L104
returns

org.apache.mxnet.NDArrayFuncReturn

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

This operator is DEPRECATED.
Perform pooling on the input.

The shapes for 2-D pooling is

- **data**: *(batch_size, channel, height, width)*
- **out**: *(batch_size, num_filter, out_height, out_width)*, with::

out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])

The definition of *f* depends on pooling_convention, which has two options:

- **valid** (default)::

f(x, k, p, s) = floor((x+2*p-k)/s)+1

- **full**, which is compatible with Caffe::

f(x, k, p, s) = ceil((x+2*p-k)/s)+1

But global_pool is set to be true, then do a global pooling, namely reset
kernel=(height, width).

Three pooling options are supported by pool_type:

- **avg**: average pooling
- **max**: max pooling
- **sum**: sum pooling

1-D pooling is special case of 2-D pooling with *weight=1* and
*kernel[1]=1*.

*height*. Namely the input data will have shape *(batch_size, channel, depth,
height, width)*.

Defined in src/operator/pooling_v1.cc:L104
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
implemented, with both multi-layer and bidirectional support.

When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

**Vanilla RNN**

Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported:
ReLU and Tanh.

With ReLU activation function:

.. math::
h_t = relu(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})

With Tanh activtion function:

.. math::
h_t = \tanh(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})

Reference paper: Finding structure in time - Elman, 1988.
https://crl.ucsd.edu/~elman/Papers/fsit.pdf

**LSTM**

Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf

.. math::
\begin{array}{ll}
i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\
f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\
g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\
o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\
c_t = f_t * c_{(t-1)} + i_t * g_t \\
h_t = o_t * \tanh(c_t)
\end{array}

With the projection size being set, LSTM could use the projection feature to reduce the parameters
size and give some speedups without significant damage to the accuracy.

Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech
Recognition - Sak et al. 2014. https://arxiv.org/abs/1402.1128

.. math::
\begin{array}{ll}
i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{ri} r_{(t-1)} + b_{ri}) \\
f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{rf} r_{(t-1)} + b_{rf}) \\
g_t = \tanh(W_{ig} x_t + b_{ig} + W_{rc} r_{(t-1)} + b_{rg}) \\
o_t = \mathrm{sigmoid}(W_{io} x_t + b_{o} + W_{ro} r_{(t-1)} + b_{ro}) \\
c_t = f_t * c_{(t-1)} + i_t * g_t \\
h_t = o_t * \tanh(c_t)
r_t = W_{hr} h_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:L369
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
implemented, with both multi-layer and bidirectional support.

When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

**Vanilla RNN**

Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported:
ReLU and Tanh.

With ReLU activation function:

.. math::
h_t = relu(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})

With Tanh activtion function:

.. math::
h_t = \tanh(W_{ih} * x_t + b_{ih}  +  W_{hh} * h_{(t-1)} + b_{hh})

Reference paper: Finding structure in time - Elman, 1988.
https://crl.ucsd.edu/~elman/Papers/fsit.pdf

**LSTM**

Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf

.. math::
\begin{array}{ll}
i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\
f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\
g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\
o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\
c_t = f_t * c_{(t-1)} + i_t * g_t \\
h_t = o_t * \tanh(c_t)
\end{array}

With the projection size being set, LSTM could use the projection feature to reduce the parameters
size and give some speedups without significant damage to the accuracy.

Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech
Recognition - Sak et al. 2014. https://arxiv.org/abs/1402.1128

.. math::
\begin{array}{ll}
i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{ri} r_{(t-1)} + b_{ri}) \\
f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{rf} r_{(t-1)} + b_{rf}) \\
g_t = \tanh(W_{ig} x_t + b_{ig} + W_{rc} r_{(t-1)} + b_{rg}) \\
o_t = \mathrm{sigmoid}(W_{io} x_t + b_{o} + W_{ro} r_{(t-1)} + b_{ro}) \\
c_t = f_t * c_{(t-1)} + i_t * g_t \\
h_t = o_t * \tanh(c_t)
r_t = W_{hr} h_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:L369
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs region of interest(ROI) pooling on the input array.

ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
region of interest is a parameter. Its purpose is to perform max pooling on the inputs
of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
layer mostly used in training a Fast R-CNN network for object detection.

This operator takes a 4D feature map as an input array and region proposals as rois,
then it pools over sub-regions of input and produces a fixed-sized output array
regardless of the ROI size.

To crop the feature map accordingly, you can resize the bounding box coordinates
by changing the parameters rois and spatial_scale.

The cropped feature maps are pooled by standard max pooling operation to a fixed size output
indicated by a pooled_size parameter. batch_size will change to the number of region
bounding boxes after ROIPooling.

The size of each region of interest doesn't have to be perfectly divisible by
the number of pooling sections(pooled_size).

Example::

x = [ [[ [  0.,   1.,   2.,   3.,   4.,   5.],
[  6.,   7.,   8.,   9.,  10.,  11.],
[ 12.,  13.,  14.,  15.,  16.,  17.],
[ 18.,  19.,  20.,  21.,  22.,  23.],
[ 24.,  25.,  26.,  27.,  28.,  29.],
[ 30.,  31.,  32.,  33.,  34.,  35.],
[ 36.,  37.,  38.,  39.,  40.,  41.],
[ 42.,  43.,  44.,  45.,  46.,  47.] ] ] ]

// region of interest i.e. bounding box coordinates.
y = [ [0,0,0,4,4] ]

// returns array of shape (2,2) according to the given roi with max pooling.
ROIPooling(x, y, (2,2), 1.0) = [ [[ [ 14.,  16.],
[ 26.,  28.] ] ] ]

// region of interest is changed due to the change in spacial_scale parameter.
ROIPooling(x, y, (2,2), 0.7) = [ [[ [  7.,   9.],
[ 19.,  21.] ] ] ]

Defined in src/operator/roi_pooling.cc:L225
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs region of interest(ROI) pooling on the input array.

ROI pooling is a variant of a max pooling layer, in which the output size is fixed and
region of interest is a parameter. Its purpose is to perform max pooling on the inputs
of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net
layer mostly used in training a Fast R-CNN network for object detection.

This operator takes a 4D feature map as an input array and region proposals as rois,
then it pools over sub-regions of input and produces a fixed-sized output array
regardless of the ROI size.

To crop the feature map accordingly, you can resize the bounding box coordinates
by changing the parameters rois and spatial_scale.

The cropped feature maps are pooled by standard max pooling operation to a fixed size output
indicated by a pooled_size parameter. batch_size will change to the number of region
bounding boxes after ROIPooling.

The size of each region of interest doesn't have to be perfectly divisible by
the number of pooling sections(pooled_size).

Example::

x = [ [[ [  0.,   1.,   2.,   3.,   4.,   5.],
[  6.,   7.,   8.,   9.,  10.,  11.],
[ 12.,  13.,  14.,  15.,  16.,  17.],
[ 18.,  19.,  20.,  21.,  22.,  23.],
[ 24.,  25.,  26.,  27.,  28.,  29.],
[ 30.,  31.,  32.,  33.,  34.,  35.],
[ 36.,  37.,  38.,  39.,  40.,  41.],
[ 42.,  43.,  44.,  45.,  46.,  47.] ] ] ]

// region of interest i.e. bounding box coordinates.
y = [ [0,0,0,4,4] ]

// returns array of shape (2,2) according to the given roi with max pooling.
ROIPooling(x, y, (2,2), 1.0) = [ [[ [ 14.,  16.],
[ 26.,  28.] ] ] ]

// region of interest is changed due to the change in spacial_scale parameter.
ROIPooling(x, y, (2,2), 0.7) = [ [[ [  7.,   9.],
[ 19.,  21.] ] ] ]

Defined in src/operator/roi_pooling.cc:L225
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L175
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L175
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes support vector machine based transformation of the input.

This tutorial demonstrates using SVM as output layer for classification instead of softmax:
https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes support vector machine based transformation of the input.

This tutorial demonstrates using SVM as output layer for classification instead of softmax:
https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
returns

org.apache.mxnet.NDArrayFuncReturn

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

Takes the last element of a sequence.

This function takes an n-dimensional input array of the form
[max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
of the form [batch_size, other_feature_dims].

Parameter sequence_length is used to handle variable-length sequences. sequence_length should be
an input array of positive ints of dimension [batch_size]. To use this parameter,
set use_sequence_length to True, otherwise each example in the batch is assumed
to have the max sequence length.

.. note:: Alternatively, you can also use take operator.

Example::

x = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.],
[  7.,   8.,   9.] ],

[ [ 10.,   11.,   12.],
[ 13.,   14.,   15.],
[ 16.,   17.,   18.] ],

[ [  19.,   20.,   21.],
[  22.,   23.,   24.],
[  25.,   26.,   27.] ] ]

// returns last sequence when sequence_length parameter is not used
SequenceLast(x) = [ [  19.,   20.,   21.],
[  22.,   23.,   24.],
[  25.,   26.,   27.] ]

// sequence_length is used
SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
[ [  1.,   2.,   3.],
[  4.,   5.,   6.],
[  7.,   8.,   9.] ]

// sequence_length is used
SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
[ [  1.,    2.,   3.],
[  13.,  14.,  15.],
[  25.,  26.,  27.] ]

Defined in src/operator/sequence_last.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

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

Takes the last element of a sequence.

This function takes an n-dimensional input array of the form
[max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array
of the form [batch_size, other_feature_dims].

Parameter sequence_length is used to handle variable-length sequences. sequence_length should be
an input array of positive ints of dimension [batch_size]. To use this parameter,
set use_sequence_length to True, otherwise each example in the batch is assumed
to have the max sequence length.

.. note:: Alternatively, you can also use take operator.

Example::

x = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.],
[  7.,   8.,   9.] ],

[ [ 10.,   11.,   12.],
[ 13.,   14.,   15.],
[ 16.,   17.,   18.] ],

[ [  19.,   20.,   21.],
[  22.,   23.,   24.],
[  25.,   26.,   27.] ] ]

// returns last sequence when sequence_length parameter is not used
SequenceLast(x) = [ [  19.,   20.,   21.],
[  22.,   23.,   24.],
[  25.,   26.,   27.] ]

// sequence_length is used
SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) =
[ [  1.,   2.,   3.],
[  4.,   5.,   6.],
[  7.,   8.,   9.] ]

// sequence_length is used
SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) =
[ [  1.,    2.,   3.],
[  13.,  14.,  15.],
[  25.,  26.,  27.] ]

Defined in src/operator/sequence_last.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

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

Sets all elements outside the sequence to a constant value.

This function takes an n-dimensional input array of the form
[max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.

Parameter sequence_length is used to handle variable-length sequences. sequence_length
should be an input array of positive ints of dimension [batch_size].
To use this parameter, set use_sequence_length to True,
otherwise each example in the batch is assumed to have the max sequence length and
this operator works as the identity operator.

Example::

x = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// Batch 1
B1 = [ [  1.,   2.,   3.],
[  7.,   8.,   9.],
[ 13.,  14.,  15.] ]

// Batch 2
B2 = [ [  4.,   5.,   6.],
[ 10.,  11.,  12.],
[ 16.,  17.,  18.] ]

// works as identity operator when sequence_length parameter is not used
SequenceMask(x) = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// sequence_length [1,1] means 1 of each batch will be kept
// and other rows are masked with default mask value = 0
[ [ [  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
[ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[  10.,  11.,  12.] ],

[ [   1.,   1.,   1.],
[  16.,  17.,  18.] ] ]

Defined in src/operator/sequence_mask.cc:L186
returns

org.apache.mxnet.NDArrayFuncReturn

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

Sets all elements outside the sequence to a constant value.

This function takes an n-dimensional input array of the form
[max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.

Parameter sequence_length is used to handle variable-length sequences. sequence_length
should be an input array of positive ints of dimension [batch_size].
To use this parameter, set use_sequence_length to True,
otherwise each example in the batch is assumed to have the max sequence length and
this operator works as the identity operator.

Example::

x = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// Batch 1
B1 = [ [  1.,   2.,   3.],
[  7.,   8.,   9.],
[ 13.,  14.,  15.] ]

// Batch 2
B2 = [ [  4.,   5.,   6.],
[ 10.,  11.,  12.],
[ 16.,  17.,  18.] ]

// works as identity operator when sequence_length parameter is not used
SequenceMask(x) = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// sequence_length [1,1] means 1 of each batch will be kept
// and other rows are masked with default mask value = 0
[ [ [  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
[ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[  10.,  11.,  12.] ],

[ [   1.,   1.,   1.],
[  16.,  17.,  18.] ] ]

Defined in src/operator/sequence_mask.cc:L186
returns

org.apache.mxnet.NDArrayFuncReturn

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

Reverses the elements of each sequence.

This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
and returns an array of the same shape.

Parameter sequence_length is used to handle variable-length sequences.
sequence_length should be an input array of positive ints of dimension [batch_size].
To use this parameter, set use_sequence_length to True,
otherwise each example in the batch is assumed to have the max sequence length.

Example::

x = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// Batch 1
B1 = [ [  1.,   2.,   3.],
[  7.,   8.,   9.],
[ 13.,  14.,  15.] ]

// Batch 2
B2 = [ [  4.,   5.,   6.],
[ 10.,  11.,  12.],
[ 16.,  17.,  18.] ]

// returns reverse sequence when sequence_length parameter is not used
SequenceReverse(x) = [ [ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [  1.,   2.,   3.],
[  4.,   5.,   6.] ] ]

// sequence_length [2,2] means 2 rows of
// both batch B1 and B2 will be reversed.
SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
[ [ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
// will be reversed.
SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
[ [ [  7.,   8.,   9.],
[ 16.,  17.,  18.] ],

[ [  1.,   2.,   3.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14,   15.],
[  4.,   5.,   6.] ] ]

Defined in src/operator/sequence_reverse.cc:L122
returns

org.apache.mxnet.NDArrayFuncReturn

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

Reverses the elements of each sequence.

This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims]
and returns an array of the same shape.

Parameter sequence_length is used to handle variable-length sequences.
sequence_length should be an input array of positive ints of dimension [batch_size].
To use this parameter, set use_sequence_length to True,
otherwise each example in the batch is assumed to have the max sequence length.

Example::

x = [ [ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// Batch 1
B1 = [ [  1.,   2.,   3.],
[  7.,   8.,   9.],
[ 13.,  14.,  15.] ]

// Batch 2
B2 = [ [  4.,   5.,   6.],
[ 10.,  11.,  12.],
[ 16.,  17.,  18.] ]

// returns reverse sequence when sequence_length parameter is not used
SequenceReverse(x) = [ [ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ],

[ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [  1.,   2.,   3.],
[  4.,   5.,   6.] ] ]

// sequence_length [2,2] means 2 rows of
// both batch B1 and B2 will be reversed.
SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) =
[ [ [  7.,   8.,   9.],
[ 10.,  11.,  12.] ],

[ [  1.,   2.,   3.],
[  4.,   5.,   6.] ],

[ [ 13.,  14.,   15.],
[ 16.,  17.,   18.] ] ]

// sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
// will be reversed.
SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) =
[ [ [  7.,   8.,   9.],
[ 16.,  17.,  18.] ],

[ [  1.,   2.,   3.],
[ 10.,  11.,  12.] ],

[ [ 13.,  14,   15.],
[  4.,   5.,   6.] ] ]

Defined in src/operator/sequence_reverse.cc:L122
returns

org.apache.mxnet.NDArrayFuncReturn

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

Splits an array along a particular axis into multiple sub-arrays.

.. note:: SliceChannel is deprecated. Use split instead.

**Note** that num_outputs should evenly divide the length of the axis
along which to split the array.

Example::

x  = [ [ [ 1.]
[ 2.] ]
[ [ 3.]
[ 4.] ]
[ [ 5.]
[ 6.] ] ]
x.shape = (3, 2, 1)

y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
y = [ [ [ 1.] ]
[ [ 3.] ]
[ [ 5.] ] ]

[ [ [ 2.] ]
[ [ 4.] ]
[ [ 6.] ] ]

y[0].shape = (3, 1, 1)

z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
z = [ [ [ 1.]
[ 2.] ] ]

[ [ [ 3.]
[ 4.] ] ]

[ [ [ 5.]
[ 6.] ] ]

z[0].shape = (1, 2, 1)

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

Example::

z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
z = [ [ 1.]
[ 2.] ]

[ [ 3.]
[ 4.] ]

[ [ 5.]
[ 6.] ]
z[0].shape = (2 ,1 )

Defined in src/operator/slice_channel.cc:L107
returns

org.apache.mxnet.NDArrayFuncReturn

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

Splits an array along a particular axis into multiple sub-arrays.

.. note:: SliceChannel is deprecated. Use split instead.

**Note** that num_outputs should evenly divide the length of the axis
along which to split the array.

Example::

x  = [ [ [ 1.]
[ 2.] ]
[ [ 3.]
[ 4.] ]
[ [ 5.]
[ 6.] ] ]
x.shape = (3, 2, 1)

y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
y = [ [ [ 1.] ]
[ [ 3.] ]
[ [ 5.] ] ]

[ [ [ 2.] ]
[ [ 4.] ]
[ [ 6.] ] ]

y[0].shape = (3, 1, 1)

z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
z = [ [ [ 1.]
[ 2.] ] ]

[ [ [ 3.]
[ 4.] ] ]

[ [ [ 5.]
[ 6.] ] ]

z[0].shape = (1, 2, 1)

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

Example::

z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
z = [ [ 1.]
[ 2.] ]

[ [ 3.]
[ 4.] ]

[ [ 5.]
[ 6.] ]
z[0].shape = (2 ,1 )

Defined in src/operator/slice_channel.cc:L107
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the gradient of cross entropy loss with respect to softmax output.

- This operator computes the gradient in two steps.
The cross entropy loss does not actually need to be computed.

- Applies softmax function on the input array.
- Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.

- The softmax function, cross entropy loss and gradient is given by:

- Softmax Function:

.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}

- Cross Entropy Function:

.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)

- The gradient of cross entropy loss w.r.t softmax output:

.. math:: \text{gradient} = \text{output} - \text{label}

- During forward propagation, the softmax function is computed for each instance in the input array.

For general *N*-D input arrays with shape :math:(d_1, d_2, ..., d_n). The size is
:math:s=d_1 \cdot d_2 \cdot \cdot \cdot d_n. We can use the parameters preserve_shape
and multi_output to specify the way to compute softmax:

- By default, preserve_shape is false. This operator will reshape the input array
into a 2-D array with shape :math:(d_1, \frac{s}{d_1}) and then compute the softmax function for
each row in the reshaped array, and afterwards reshape it back to the original shape
:math:(d_1, d_2, ..., d_n).
- If preserve_shape is true, the softmax function will be computed along
the last axis (axis = -1).
- If multi_output is true, the softmax function will be computed along
the second axis (axis = 1).

- During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
The provided label can be a one-hot label array or a probability label array.

- If the parameter use_ignore is true, ignore_label can specify input instances
with a particular label to be ignored during backward propagation. **This has no effect when
softmax output has same shape as label**.

Example::

data = [ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ] ]
[ [ 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:L243
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the gradient of cross entropy loss with respect to softmax output.

- This operator computes the gradient in two steps.
The cross entropy loss does not actually need to be computed.

- Applies softmax function on the input array.
- Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.

- The softmax function, cross entropy loss and gradient is given by:

- Softmax Function:

.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}

- Cross Entropy Function:

.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)

- The gradient of cross entropy loss w.r.t softmax output:

.. math:: \text{gradient} = \text{output} - \text{label}

- During forward propagation, the softmax function is computed for each instance in the input array.

For general *N*-D input arrays with shape :math:(d_1, d_2, ..., d_n). The size is
:math:s=d_1 \cdot d_2 \cdot \cdot \cdot d_n. We can use the parameters preserve_shape
and multi_output to specify the way to compute softmax:

- By default, preserve_shape is false. This operator will reshape the input array
into a 2-D array with shape :math:(d_1, \frac{s}{d_1}) and then compute the softmax function for
each row in the reshaped array, and afterwards reshape it back to the original shape
:math:(d_1, d_2, ..., d_n).
- If preserve_shape is true, the softmax function will be computed along
the last axis (axis = -1).
- If multi_output is true, the softmax function will be computed along
the second axis (axis = 1).

- During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
The provided label can be a one-hot label array or a probability label array.

- If the parameter use_ignore is true, ignore_label can specify input instances
with a particular label to be ignored during backward propagation. **This has no effect when
softmax output has same shape as label**.

Example::

data = [ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ] ]
[ [ 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:L243
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies softmax activation to input. This is intended for internal layers.

.. note::

This operator has been deprecated, please use softmax.

If mode = instance, this operator will compute a softmax for each instance in the batch.
This is the default mode.

If mode = channel, this operator will compute a k-class softmax at each position
of each instance, where k = num_channel. This mode can only be used when the input array
has at least 3 dimensions.
This can be used for fully convolutional network, image segmentation, etc.

Example::

>>> input_array = mx.nd.array([ [3., 0.5, -0.5, 2., 7.],
>>>                            [2., -.4, 7.,   3., 0.2] ])
>>> softmax_act = mx.nd.SoftmaxActivation(input_array)
>>> print softmax_act.asnumpy()
[ [  1.78322066e-02   1.46375655e-03   5.38485940e-04   6.56010211e-03   9.73605454e-01]
[  6.56221947e-03   5.95310994e-04   9.73919690e-01   1.78379621e-02   1.08472735e-03] ]

Defined in src/operator/nn/softmax_activation.cc:L59
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies softmax activation to input. This is intended for internal layers.

.. note::

This operator has been deprecated, please use softmax.

If mode = instance, this operator will compute a softmax for each instance in the batch.
This is the default mode.

If mode = channel, this operator will compute a k-class softmax at each position
of each instance, where k = num_channel. This mode can only be used when the input array
has at least 3 dimensions.
This can be used for fully convolutional network, image segmentation, etc.

Example::

>>> input_array = mx.nd.array([ [3., 0.5, -0.5, 2., 7.],
>>>                            [2., -.4, 7.,   3., 0.2] ])
>>> softmax_act = mx.nd.SoftmaxActivation(input_array)
>>> print softmax_act.asnumpy()
[ [  1.78322066e-02   1.46375655e-03   5.38485940e-04   6.56010211e-03   9.73605454e-01]
[  6.56221947e-03   5.95310994e-04   9.73919690e-01   1.78379621e-02   1.08472735e-03] ]

Defined in src/operator/nn/softmax_activation.cc:L59
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the gradient of cross entropy loss with respect to softmax output.

- This operator computes the gradient in two steps.
The cross entropy loss does not actually need to be computed.

- Applies softmax function on the input array.
- Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.

- The softmax function, cross entropy loss and gradient is given by:

- Softmax Function:

.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}

- Cross Entropy Function:

.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)

- The gradient of cross entropy loss w.r.t softmax output:

.. math:: \text{gradient} = \text{output} - \text{label}

- During forward propagation, the softmax function is computed for each instance in the input array.

For general *N*-D input arrays with shape :math:(d_1, d_2, ..., d_n). The size is
:math:s=d_1 \cdot d_2 \cdot \cdot \cdot d_n. We can use the parameters preserve_shape
and multi_output to specify the way to compute softmax:

- By default, preserve_shape is false. This operator will reshape the input array
into a 2-D array with shape :math:(d_1, \frac{s}{d_1}) and then compute the softmax function for
each row in the reshaped array, and afterwards reshape it back to the original shape
:math:(d_1, d_2, ..., d_n).
- If preserve_shape is true, the softmax function will be computed along
the last axis (axis = -1).
- If multi_output is true, the softmax function will be computed along
the second axis (axis = 1).

- During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
The provided label can be a one-hot label array or a probability label array.

- If the parameter use_ignore is true, ignore_label can specify input instances
with a particular label to be ignored during backward propagation. **This has no effect when
softmax output has same shape as label**.

Example::

data = [ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ] ]
[ [ 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:L243
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the gradient of cross entropy loss with respect to softmax output.

- This operator computes the gradient in two steps.
The cross entropy loss does not actually need to be computed.

- Applies softmax function on the input array.
- Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.

- The softmax function, cross entropy loss and gradient is given by:

- Softmax Function:

.. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}

- Cross Entropy Function:

.. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)

- The gradient of cross entropy loss w.r.t softmax output:

.. math:: \text{gradient} = \text{output} - \text{label}

- During forward propagation, the softmax function is computed for each instance in the input array.

For general *N*-D input arrays with shape :math:(d_1, d_2, ..., d_n). The size is
:math:s=d_1 \cdot d_2 \cdot \cdot \cdot d_n. We can use the parameters preserve_shape
and multi_output to specify the way to compute softmax:

- By default, preserve_shape is false. This operator will reshape the input array
into a 2-D array with shape :math:(d_1, \frac{s}{d_1}) and then compute the softmax function for
each row in the reshaped array, and afterwards reshape it back to the original shape
:math:(d_1, d_2, ..., d_n).
- If preserve_shape is true, the softmax function will be computed along
the last axis (axis = -1).
- If multi_output is true, the softmax function will be computed along
the second axis (axis = 1).

- During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed.
The provided label can be a one-hot label array or a probability label array.

- If the parameter use_ignore is true, ignore_label can specify input instances
with a particular label to be ignored during backward propagation. **This has no effect when
softmax output has same shape as label**.

Example::

data = [ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ] ]
[ [ 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:L243
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies a spatial transformer to input feature map.
returns

org.apache.mxnet.NDArrayFuncReturn

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

Applies a spatial transformer to input feature map.
returns

org.apache.mxnet.NDArrayFuncReturn

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

Interchanges two axes of an array.

Examples::

x = [ [1, 2, 3] ])
swapaxes(x, 0, 1) = [ [ 1],
[ 2],
[ 3] ]

x = [ [ [ 0, 1],
[ 2, 3] ],
[ [ 4, 5],
[ 6, 7] ] ]  // (2,2,2) array

swapaxes(x, 0, 2) = [ [ [ 0, 4],
[ 2, 6] ],
[ [ 1, 5],
[ 3, 7] ] ]

Defined in src/operator/swapaxis.cc:L70
returns

org.apache.mxnet.NDArrayFuncReturn

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

Interchanges two axes of an array.

Examples::

x = [ [1, 2, 3] ])
swapaxes(x, 0, 1) = [ [ 1],
[ 2],
[ 3] ]

x = [ [ [ 0, 1],
[ 2, 3] ],
[ [ 4, 5],
[ 6, 7] ] ]  // (2,2,2) array

swapaxes(x, 0, 2) = [ [ [ 0, 4],
[ 2, 6] ],
[ [ 1, 5],
[ 3, 7] ] ]

Defined in src/operator/swapaxis.cc:L70
returns

org.apache.mxnet.NDArrayFuncReturn

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

Upsamples the given input data.

Two algorithms (sample_type) are available for upsampling:

- Nearest Neighbor
- Bilinear

**Nearest Neighbor Upsampling**

Input data is expected to be NCHW.

Example::

x = [ [[ [1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.] ] ] ]

UpSampling(x, scale=2, sample_type='nearest') = [ [[ [1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.] ] ] ]

**Bilinear Upsampling**

Uses deconvolution algorithm under the hood. You need provide both input data and the kernel.

Input data is expected to be NCHW.

num_filter is expected to be same as the number of channels.

Example::

x = [ [[ [1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.] ] ] ]

w = [ [[ [1. 1. 1. 1.]
[1. 1. 1. 1.]
[1. 1. 1. 1.]
[1. 1. 1. 1.] ] ] ]

UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = [ [[ [1. 2. 2. 2. 2. 1.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[1. 2. 2. 2. 2. 1.] ] ] ]

Defined in src/operator/nn/upsampling.cc:L173
returns

org.apache.mxnet.NDArrayFuncReturn

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

Upsamples the given input data.

Two algorithms (sample_type) are available for upsampling:

- Nearest Neighbor
- Bilinear

**Nearest Neighbor Upsampling**

Input data is expected to be NCHW.

Example::

x = [ [[ [1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.] ] ] ]

UpSampling(x, scale=2, sample_type='nearest') = [ [[ [1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.]
[1. 1. 1. 1. 1. 1.] ] ] ]

**Bilinear Upsampling**

Uses deconvolution algorithm under the hood. You need provide both input data and the kernel.

Input data is expected to be NCHW.

num_filter is expected to be same as the number of channels.

Example::

x = [ [[ [1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.] ] ] ]

w = [ [[ [1. 1. 1. 1.]
[1. 1. 1. 1.]
[1. 1. 1. 1.]
[1. 1. 1. 1.] ] ] ]

UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = [ [[ [1. 2. 2. 2. 2. 1.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[2. 4. 4. 4. 4. 2.]
[1. 2. 2. 2. 2. 1.] ] ] ]

Defined in src/operator/nn/upsampling.cc:L173
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise absolute value of the input.

Example::

abs([-2, 0, 3]) = [2, 0, 3]

The storage type of abs output depends upon the input storage type:

- abs(default) = default
- abs(row_sparse) = row_sparse
- abs(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L720
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise absolute value of the input.

Example::

abs([-2, 0, 3]) = [2, 0, 3]

The storage type of abs output depends upon the input storage type:

- abs(default) = default
- abs(row_sparse) = row_sparse
- abs(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L720
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for Adam optimizer. Adam is seen as a generalization

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 }

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)::

w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)

Defined in src/operator/optimizer_op.cc:L688
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for Adam optimizer. Adam is seen as a generalization

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 }

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)::

w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)

Defined in src/operator/optimizer_op.cc:L688
returns

org.apache.mxnet.NDArrayFuncReturn

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

Adds all input arguments element-wise.

.. math::
add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n

add_n is potentially more efficient than calling add by n times.

The storage type of add_n output depends on storage types of inputs

- add_n(row_sparse, row_sparse, ..) = row_sparse
- add_n(default, csr, default) = default
- add_n(any input combinations longer than 4 (>4) with at least one default type) = default
- otherwise, add_n falls all inputs back to default storage and generates default storage

Defined in src/operator/tensor/elemwise_sum.cc:L156
returns

org.apache.mxnet.NDArrayFuncReturn

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

Adds all input arguments element-wise.

.. math::
add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n

add_n is potentially more efficient than calling add by n times.

The storage type of add_n output depends on storage types of inputs

- add_n(row_sparse, row_sparse, ..) = row_sparse
- add_n(default, csr, default) = default
- add_n(any input combinations longer than 4 (>4) with at least one default type) = default
- otherwise, add_n falls all inputs back to default storage and generates default storage

Defined in src/operator/tensor/elemwise_sum.cc:L156
returns

org.apache.mxnet.NDArrayFuncReturn

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

Check if all the float numbers in the array are finite (used for AMP)

Defined in src/operator/contrib/all_finite.cc:L101
returns

org.apache.mxnet.NDArrayFuncReturn

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

Check if all the float numbers in the array are finite (used for AMP)

Defined in src/operator/contrib/all_finite.cc:L101
returns

org.apache.mxnet.NDArrayFuncReturn

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

Cast function between low precision float/FP32 used by AMP.

It casts only between low precision float/FP32 and does not do anything for other types.

Defined in src/operator/tensor/amp_cast.cc:L121
returns

org.apache.mxnet.NDArrayFuncReturn

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

Cast function between low precision float/FP32 used by AMP.

It casts only between low precision float/FP32 and does not do anything for other types.

Defined in src/operator/tensor/amp_cast.cc:L121
returns

org.apache.mxnet.NDArrayFuncReturn

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

Cast function used by AMP, that casts its inputs to the common widest type.

It casts only between low precision float/FP32 and does not do anything for other types.

Defined in src/operator/tensor/amp_cast.cc:L165
returns

org.apache.mxnet.NDArrayFuncReturn

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

Cast function used by AMP, that casts its inputs to the common widest type.

It casts only between low precision float/FP32 and does not do anything for other types.

Defined in src/operator/tensor/amp_cast.cc:L165
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise inverse cosine of the input array.

The input should be in range [-1, 1].
The output is in the closed interval :math:[0, \pi]

.. math::
arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]

The storage type of arccos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L233
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise inverse cosine of the input array.

The input should be in range [-1, 1].
The output is in the closed interval :math:[0, \pi]

.. math::
arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]

The storage type of arccos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L233
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the element-wise inverse hyperbolic cosine of the input array, \
computed element-wise.

The storage type of arccosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L535
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the element-wise inverse hyperbolic cosine of the input array, \
computed element-wise.

The storage type of arccosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L535
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise inverse sine of the input array.

The input should be in the range [-1, 1].
The output is in the closed interval of [:math:-\pi/2, :math:\pi/2].

.. math::
arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]

The storage type of arcsin output depends upon the input storage type:

- arcsin(default) = default
- arcsin(row_sparse) = row_sparse
- arcsin(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L187
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise inverse sine of the input array.

The input should be in the range [-1, 1].
The output is in the closed interval of [:math:-\pi/2, :math:\pi/2].

.. math::
arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]

The storage type of arcsin output depends upon the input storage type:

- arcsin(default) = default
- arcsin(row_sparse) = row_sparse
- arcsin(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L187
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the element-wise inverse hyperbolic sine of the input array, \
computed element-wise.

The storage type of arcsinh output depends upon the input storage type:

- arcsinh(default) = default
- arcsinh(row_sparse) = row_sparse
- arcsinh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L494
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the element-wise inverse hyperbolic sine of the input array, \
computed element-wise.

The storage type of arcsinh output depends upon the input storage type:

- arcsinh(default) = default
- arcsinh(row_sparse) = row_sparse
- arcsinh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L494
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise inverse tangent of the input array.

The output is in the closed interval :math:[-\pi/2, \pi/2]

.. math::
arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]

The storage type of arctan output depends upon the input storage type:

- arctan(default) = default
- arctan(row_sparse) = row_sparse
- arctan(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L282
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise inverse tangent of the input array.

The output is in the closed interval :math:[-\pi/2, \pi/2]

.. math::
arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]

The storage type of arctan output depends upon the input storage type:

- arctan(default) = default
- arctan(row_sparse) = row_sparse
- arctan(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L282
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the element-wise inverse hyperbolic tangent of the input array, \
computed element-wise.

The storage type of arctanh output depends upon the input storage type:

- arctanh(default) = default
- arctanh(row_sparse) = row_sparse
- arctanh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L579
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the element-wise inverse hyperbolic tangent of the input array, \
computed element-wise.

The storage type of arctanh output depends upon the input storage type:

- arctanh(default) = default
- arctanh(row_sparse) = row_sparse
- arctanh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L579
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns indices of the maximum values along an axis.

In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

// argmax along axis 0
argmax(x, axis=0) = [ 1.,  1.,  1.]

// argmax along axis 1
argmax(x, axis=1) = [ 2.,  2.]

// argmax along axis 1 keeping same dims as an input array
argmax(x, axis=1, keepdims=True) = [ [ 2.],
[ 2.] ]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns indices of the maximum values along an axis.

In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

// argmax along axis 0
argmax(x, axis=0) = [ 1.,  1.,  1.]

// argmax along axis 1
argmax(x, axis=1) = [ 2.,  2.]

// argmax along axis 1 keeping same dims as an input array
argmax(x, axis=1, keepdims=True) = [ [ 2.],
[ 2.] ]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns argmax indices of each channel from the input array.

The result will be an NDArray of shape (num_channel,).

In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

argmax_channel(x) = [ 2.,  2.]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns argmax indices of each channel from the input array.

The result will be an NDArray of shape (num_channel,).

In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

argmax_channel(x) = [ 2.,  2.]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns indices of the minimum values along an axis.

In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

// argmin along axis 0
argmin(x, axis=0) = [ 0.,  0.,  0.]

// argmin along axis 1
argmin(x, axis=1) = [ 0.,  0.]

// argmin along axis 1 keeping same dims as an input array
argmin(x, axis=1, keepdims=True) = [ [ 0.],
[ 0.] ]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns indices of the minimum values along an axis.

In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

// argmin along axis 0
argmin(x, axis=0) = [ 0.,  0.,  0.]

// argmin along axis 1
argmin(x, axis=1) = [ 0.,  0.]

// argmin along axis 1 keeping same dims as an input array
argmin(x, axis=1, keepdims=True) = [ [ 0.],
[ 0.] ]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the indices that would sort an input array along the given axis.

This function performs sorting along the given axis and returns an array of indices having same shape
as an input array that index data in sorted order.

Examples::

x = [ [ 0.3,  0.2,  0.4],
[ 0.1,  0.3,  0.2] ]

// sort along axis -1
argsort(x) = [ [ 1.,  0.,  2.],
[ 0.,  2.,  1.] ]

// sort along axis 0
argsort(x, axis=0) = [ [ 1.,  0.,  1.]
[ 0.,  1.,  0.] ]

// flatten and then sort
argsort(x, axis=None) = [ 3.,  1.,  5.,  0.,  4.,  2.]

Defined in src/operator/tensor/ordering_op.cc:L185
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the indices that would sort an input array along the given axis.

This function performs sorting along the given axis and returns an array of indices having same shape
as an input array that index data in sorted order.

Examples::

x = [ [ 0.3,  0.2,  0.4],
[ 0.1,  0.3,  0.2] ]

// sort along axis -1
argsort(x) = [ [ 1.,  0.,  2.],
[ 0.,  2.,  1.] ]

// sort along axis 0
argsort(x, axis=0) = [ [ 1.,  0.,  1.]
[ 0.,  1.,  0.] ]

// flatten and then sort
argsort(x, axis=None) = [ 3.,  1.,  5.,  0.,  4.,  2.]

Defined in src/operator/tensor/ordering_op.cc:L185
returns

org.apache.mxnet.NDArrayFuncReturn

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

Batchwise dot product.

batch_dot is used to compute dot product of x and y when x and
y are data in batch, namely N-D (N >= 3) arrays in shape of (B0, ..., B_i, :, :).

For example, given x with shape (B_0, ..., B_i, N, M) and y with shape
(B_0, ..., B_i, M, K), the result array will have shape (B_0, ..., B_i, N, K),
which is computed by::

batch_dot(x,y)[b_0, ..., b_i, :, :] = dot(x[b_0, ..., b_i, :, :], y[b_0, ..., b_i, :, :])

Defined in src/operator/tensor/dot.cc:L127
returns

org.apache.mxnet.NDArrayFuncReturn

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

Batchwise dot product.

batch_dot is used to compute dot product of x and y when x and
y are data in batch, namely N-D (N >= 3) arrays in shape of (B0, ..., B_i, :, :).

For example, given x with shape (B_0, ..., B_i, N, M) and y with shape
(B_0, ..., B_i, M, K), the result array will have shape (B_0, ..., B_i, N, K),
which is computed by::

batch_dot(x,y)[b_0, ..., b_i, :, :] = dot(x[b_0, ..., b_i, :, :], y[b_0, ..., b_i, :, :])

Defined in src/operator/tensor/dot.cc:L127
returns

org.apache.mxnet.NDArrayFuncReturn

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

Takes elements from a data batch.

.. note::
batch_take is deprecated. Use pick instead.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

Examples::

x = [ [ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.] ]

// takes elements with specified indices
batch_take(x, [0,1,0]) = [ 1.  4.  5.]

Defined in src/operator/tensor/indexing_op.cc:L836
returns

org.apache.mxnet.NDArrayFuncReturn

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

Takes elements from a data batch.

.. note::
batch_take is deprecated. Use pick instead.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

Examples::

x = [ [ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.] ]

// takes elements with specified indices
batch_take(x, [0,1,0]) = [ 1.  4.  5.]

Defined in src/operator/tensor/indexing_op.cc:L836
returns

org.apache.mxnet.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.] ]

[ 2.,  2.,  2.] ]

broadcast_plus(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
returns

org.apache.mxnet.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.] ]

[ 2.,  2.,  2.] ]

broadcast_plus(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

broadcast_axes is an alias to the function broadcast_axis.

Example::

// given x of shape (1,2,1)
x = [ [ [ 1.],
[ 2.] ] ]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ],
[ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L93
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

broadcast_axes is an alias to the function broadcast_axis.

Example::

// given x of shape (1,2,1)
x = [ [ [ 1.],
[ 2.] ] ]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ],
[ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L93
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

broadcast_axes is an alias to the function broadcast_axis.

Example::

// given x of shape (1,2,1)
x = [ [ [ 1.],
[ 2.] ] ]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ],
[ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L93
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

broadcast_axes is an alias to the function broadcast_axis.

Example::

// given x of shape (1,2,1)
x = [ [ [ 1.],
[ 2.] ] ]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [ [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ],
[ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ] ]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L93
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise division of the input arrays with broadcasting.

Example::

x = [ [ 6.,  6.,  6.],
[ 6.,  6.,  6.] ]

y = [ [ 2.],
[ 3.] ]

broadcast_div(x, y) = [ [ 3.,  3.,  3.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise division of the input arrays with broadcasting.

Example::

x = [ [ 6.,  6.,  6.],
[ 6.,  6.,  6.] ]

y = [ [ 2.],
[ 3.] ]

broadcast_div(x, y) = [ [ 3.,  3.,  3.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **equal to** (==) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_equal(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **equal to** (==) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_equal(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **greater than** (>) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_greater(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **greater than** (>) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_greater(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_greater_equal(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_greater_equal(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

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

 Returns the hypotenuse of a right angled triangle, given its "legs"

It is equivalent to doing :math:sqrt(x_1^2 + x_2^2).

Example::

x = [ [ 3.,  3.,  3.] ]

y = [ [ 4.],
[ 4.] ]

broadcast_hypot(x, y) = [ [ 5.,  5.,  5.],
[ 5.,  5.,  5.] ]

z = [ [ 0.],
[ 4.] ]

broadcast_hypot(x, z) = [ [ 3.,  3.,  3.],
[ 5.,  5.,  5.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L158
returns

org.apache.mxnet.NDArrayFuncReturn

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

 Returns the hypotenuse of a right angled triangle, given its "legs"

It is equivalent to doing :math:sqrt(x_1^2 + x_2^2).

Example::

x = [ [ 3.,  3.,  3.] ]

y = [ [ 4.],
[ 4.] ]

broadcast_hypot(x, y) = [ [ 5.,  5.,  5.],
[ 5.,  5.,  5.] ]

z = [ [ 0.],
[ 4.] ]

broadcast_hypot(x, z) = [ [ 3.,  3.,  3.],
[ 5.,  5.,  5.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L158
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_lesser(x, y) = [ [ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_lesser(x, y) = [ [ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_lesser_equal(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_lesser_equal(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts lhs to have the same shape as rhs.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>_ for more explanation.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

For example::

broadcast_like([ [1,2,3] ], [ [5,6,7],[7,8,9] ]) = [ [ 1.,  2.,  3.],
[ 1.,  2.,  3.] ])

broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L179
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts lhs to have the same shape as rhs.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>_ for more explanation.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

For example::

broadcast_like([ [1,2,3] ], [ [5,6,7],[7,8,9] ]) = [ [ 1.,  2.,  3.],
[ 1.,  2.,  3.] ])

broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L179
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **logical and** with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_logical_and(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **logical and** with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_logical_and(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **logical or** with broadcasting.

Example::

x = [ [ 1.,  1.,  0.],
[ 1.,  1.,  0.] ]

y = [ [ 1.],
[ 0.] ]

broadcast_logical_or(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **logical or** with broadcasting.

Example::

x = [ [ 1.,  1.,  0.],
[ 1.,  1.,  0.] ]

y = [ [ 1.],
[ 0.] ]

broadcast_logical_or(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **logical xor** with broadcasting.

Example::

x = [ [ 1.,  1.,  0.],
[ 1.,  1.,  0.] ]

y = [ [ 1.],
[ 0.] ]

broadcast_logical_xor(x, y) = [ [ 0.,  0.,  1.],
[ 1.,  1.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **logical xor** with broadcasting.

Example::

x = [ [ 1.,  1.,  0.],
[ 1.,  1.,  0.] ]

y = [ [ 1.],
[ 0.] ]

broadcast_logical_xor(x, y) = [ [ 0.,  0.,  1.],
[ 1.,  1.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise maximum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise maxima.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_maximum(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L81
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise maximum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise maxima.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_maximum(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L81
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise minimum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise minima.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_maximum(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L117
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise minimum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise minima.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_maximum(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L117
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise difference of the input arrays with broadcasting.

broadcast_minus is an alias to the function broadcast_sub.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_sub(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

broadcast_minus(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise difference of the input arrays with broadcasting.

broadcast_minus is an alias to the function broadcast_sub.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_sub(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

broadcast_minus(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise modulo of the input arrays with broadcasting.

Example::

x = [ [ 8.,  8.,  8.],
[ 8.,  8.,  8.] ]

y = [ [ 2.],
[ 3.] ]

broadcast_mod(x, y) = [ [ 0.,  0.,  0.],
[ 2.,  2.,  2.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise modulo of the input arrays with broadcasting.

Example::

x = [ [ 8.,  8.,  8.],
[ 8.,  8.,  8.] ]

y = [ [ 2.],
[ 3.] ]

broadcast_mod(x, y) = [ [ 0.,  0.,  0.],
[ 2.,  2.,  2.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise product of the input arrays with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_mul(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise product of the input arrays with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_mul(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_not_equal(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_not_equal(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise sum of the input arrays with broadcasting.

broadcast_plus is an alias to the function broadcast_add.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

[ 2.,  2.,  2.] ]

broadcast_plus(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise sum of the input arrays with broadcasting.

broadcast_plus is an alias to the function broadcast_add.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

[ 2.,  2.,  2.] ]

broadcast_plus(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns result of first array elements raised to powers from second array, element-wise with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_power(x, y) = [ [ 2.,  2.,  2.],
[ 4.,  4.,  4.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns result of first array elements raised to powers from second array, element-wise with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_power(x, y) = [ [ 2.,  2.,  2.],
[ 4.,  4.,  4.] ]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise difference of the input arrays with broadcasting.

broadcast_minus is an alias to the function broadcast_sub.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_sub(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

broadcast_minus(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise difference of the input arrays with broadcasting.

broadcast_minus is an alias to the function broadcast_sub.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_sub(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

broadcast_minus(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Supported sparse operations:

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts the input array to a new shape.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>_ for more explanation.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

For example::

broadcast_to([ [1,2,3] ], shape=(2,3)) = [ [ 1.,  2.,  3.],
[ 1.,  2.,  3.] ])

The dimension which you do not want to change can also be kept as 0 which means copy the original value.
So with shape=(2,0), we will obtain the same result as in the above example.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L117
returns

org.apache.mxnet.NDArrayFuncReturn

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

Broadcasts the input array to a new shape.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>_ for more explanation.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

For example::

broadcast_to([ [1,2,3] ], shape=(2,3)) = [ [ 1.,  2.,  3.],
[ 1.,  2.,  3.] ])

The dimension which you do not want to change can also be kept as 0 which means copy the original value.
So with shape=(2,0), we will obtain the same result as in the above example.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L117
returns

org.apache.mxnet.NDArrayFuncReturn

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

Casts all elements of the input to a new type.

.. note:: Cast is deprecated. Use cast instead.

Example::

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L664
returns

org.apache.mxnet.NDArrayFuncReturn

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

Casts all elements of the input to a new type.

.. note:: Cast is deprecated. Use cast instead.

Example::

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L664
returns

org.apache.mxnet.NDArrayFuncReturn

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

Casts tensor storage type to the new type.

When an NDArray with default storage type is cast to csr or row_sparse storage,
the result is compact, which means:

- for csr, zero values will not be retained
- for row_sparse, row slices of all zeros will not be retained

The storage type of cast_storage output depends on stype parameter:

- cast_storage(csr, 'default') = default
- cast_storage(row_sparse, 'default') = default
- cast_storage(default, 'csr') = csr
- cast_storage(default, 'row_sparse') = row_sparse
- cast_storage(csr, 'csr') = csr
- cast_storage(row_sparse, 'row_sparse') = row_sparse

Example::

dense = [ [ 0.,  1.,  0.],
[ 2.,  0.,  3.],
[ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

# cast to row_sparse storage type
rsp = cast_storage(dense, 'row_sparse')
rsp.indices = [0, 1]
rsp.values = [ [ 0.,  1.,  0.],
[ 2.,  0.,  3.] ]

# cast to csr storage type
csr = cast_storage(dense, 'csr')
csr.indices = [1, 0, 2]
csr.values = [ 1.,  2.,  3.]
csr.indptr = [0, 1, 3, 3, 3]

Defined in src/operator/tensor/cast_storage.cc:L71
returns

org.apache.mxnet.NDArrayFuncReturn

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

Casts tensor storage type to the new type.

When an NDArray with default storage type is cast to csr or row_sparse storage,
the result is compact, which means:

- for csr, zero values will not be retained
- for row_sparse, row slices of all zeros will not be retained

The storage type of cast_storage output depends on stype parameter:

- cast_storage(csr, 'default') = default
- cast_storage(row_sparse, 'default') = default
- cast_storage(default, 'csr') = csr
- cast_storage(default, 'row_sparse') = row_sparse
- cast_storage(csr, 'csr') = csr
- cast_storage(row_sparse, 'row_sparse') = row_sparse

Example::

dense = [ [ 0.,  1.,  0.],
[ 2.,  0.,  3.],
[ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

# cast to row_sparse storage type
rsp = cast_storage(dense, 'row_sparse')
rsp.indices = [0, 1]
rsp.values = [ [ 0.,  1.,  0.],
[ 2.,  0.,  3.] ]

# cast to csr storage type
csr = cast_storage(dense, 'csr')
csr.indices = [1, 0, 2]
csr.values = [ 1.,  2.,  3.]
csr.indptr = [0, 1, 3, 3, 3]

Defined in src/operator/tensor/cast_storage.cc:L71
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise cube-root value of the input.

.. math::
cbrt(x) = \sqrt[3]{x}

Example::

cbrt([1, 8, -125]) = [1, 2, -5]

The storage type of cbrt output depends upon the input storage type:

- cbrt(default) = default
- cbrt(row_sparse) = row_sparse
- cbrt(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L270
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise cube-root value of the input.

.. math::
cbrt(x) = \sqrt[3]{x}

Example::

cbrt([1, 8, -125]) = [1, 2, -5]

The storage type of cbrt output depends upon the input storage type:

- cbrt(default) = default
- cbrt(row_sparse) = row_sparse
- cbrt(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L270
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise ceiling of the input.

The ceil of the scalar x is the smallest integer i, such that i >= x.

Example::

ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]

The storage type of ceil output depends upon the input storage type:

- ceil(default) = default
- ceil(row_sparse) = row_sparse
- ceil(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L817
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise ceiling of the input.

The ceil of the scalar x is the smallest integer i, such that i >= x.

Example::

ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]

The storage type of ceil output depends upon the input storage type:

- ceil(default) = default
- ceil(row_sparse) = row_sparse
- ceil(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L817
returns

org.apache.mxnet.NDArrayFuncReturn

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

Picks elements from an input array according to the input indices along the given axis.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

By default, if any index mentioned is too large, it is replaced by the index that addresses
the last element along an axis (the clip mode).

This function supports n-dimensional input and (n-1)-dimensional indices arrays.

Examples::

x = [ [ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.] ]

// picks elements with specified indices along axis 0
pick(x, y=[0,1], 0) = [ 1.,  4.]

// picks elements with specified indices along axis 1
pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]

// 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:L151
returns

org.apache.mxnet.NDArrayFuncReturn

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

Picks elements from an input array according to the input indices along the given axis.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

By default, if any index mentioned is too large, it is replaced by the index that addresses
the last element along an axis (the clip mode).

This function supports n-dimensional input and (n-1)-dimensional indices arrays.

Examples::

x = [ [ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.] ]

// picks elements with specified indices along axis 0
pick(x, y=[0,1], 0) = [ 1.,  4.]

// picks elements with specified indices along axis 1
pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]

// 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:L151
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L677
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L677
returns

org.apache.mxnet.NDArrayFuncReturn

193. #### abstract def col2im(args: Any*): NDArrayFuncReturn

Combining the output column matrix of im2col back to image array.

Like :class:~mxnet.ndarray.im2col, this operator is also used in the vanilla convolution
implementation. Despite the name, col2im is not the reverse operation of im2col. Since there
may be overlaps between neighbouring sliding blocks, the column elements cannot be directly
put back into image. Instead, they are accumulated (i.e., summed) in the input image
just like the gradient computation, so col2im is the gradient of im2col and vice versa.

Using the notation in im2col, given an input column array of shape
:math:(N, C \times  \prod(\text{kernel}), W), this operator accumulates the column elements
into output array of shape :math:(N, C, \text{output_size}[0], \text{output_size}[1], \dots).
Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L182
returns

org.apache.mxnet.NDArrayFuncReturn

194. #### abstract def col2im(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

Combining the output column matrix of im2col back to image array.

Like :class:~mxnet.ndarray.im2col, this operator is also used in the vanilla convolution
implementation. Despite the name, col2im is not the reverse operation of im2col. Since there
may be overlaps between neighbouring sliding blocks, the column elements cannot be directly
put back into image. Instead, they are accumulated (i.e., summed) in the input image
just like the gradient computation, so col2im is the gradient of im2col and vice versa.

Using the notation in im2col, given an input column array of shape
:math:(N, C \times  \prod(\text{kernel}), W), this operator accumulates the column elements
into output array of shape :math:(N, C, \text{output_size}[0], \text{output_size}[1], \dots).
Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L182
returns

org.apache.mxnet.NDArrayFuncReturn

195. #### abstract def concat(args: Any*): NDArrayFuncReturn

Joins input arrays along a given axis.

.. note:: Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along
which they will be concatenated.
The dimension of the output array along the concatenated axis will be equal
to the sum of the corresponding dimensions of the input arrays.

The storage type of concat output depends on storage types of inputs

- concat(csr, csr, ..., csr, dim=0) = csr
- otherwise, concat generates output with default storage

Example::

x = [ [1,1],[2,2] ]
y = [ [3,3],[4,4],[5,5] ]
z = [ [6,6], [7,7],[8,8] ]

concat(x,y,z,dim=0) = [ [ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.] ]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [ [ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.] ]

Defined in src/operator/nn/concat.cc:L385
returns

org.apache.mxnet.NDArrayFuncReturn

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

Joins input arrays along a given axis.

.. note:: Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along
which they will be concatenated.
The dimension of the output array along the concatenated axis will be equal
to the sum of the corresponding dimensions of the input arrays.

The storage type of concat output depends on storage types of inputs

- concat(csr, csr, ..., csr, dim=0) = csr
- otherwise, concat generates output with default storage

Example::

x = [ [1,1],[2,2] ]
y = [ [3,3],[4,4],[5,5] ]
z = [ [6,6], [7,7],[8,8] ]

concat(x,y,z,dim=0) = [ [ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.] ]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [ [ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.] ]

Defined in src/operator/nn/concat.cc:L385
returns

org.apache.mxnet.NDArrayFuncReturn

197. #### abstract def cos(args: Any*): NDArrayFuncReturn

Computes the element-wise cosine of the input array.

The input should be in radians (:math:2\pi rad equals 360 degrees).

.. math::
cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]

The storage type of cos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L90
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the element-wise cosine of the input array.

The input should be in radians (:math:2\pi rad equals 360 degrees).

.. math::
cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]

The storage type of cos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L90
returns

org.apache.mxnet.NDArrayFuncReturn

199. #### abstract def cosh(args: Any*): NDArrayFuncReturn

Returns the hyperbolic cosine  of the input array, computed element-wise.

.. math::
cosh(x) = 0.5\times(exp(x) + exp(-x))

The storage type of cosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L409
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the hyperbolic cosine  of the input array, computed element-wise.

.. math::
cosh(x) = 0.5\times(exp(x) + exp(-x))

The storage type of cosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L409
returns

org.apache.mxnet.NDArrayFuncReturn

201. #### abstract def crop(args: Any*): NDArrayFuncReturn

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

Defined in src/operator/tensor/matrix_op.cc:L482
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L482
returns

org.apache.mxnet.NDArrayFuncReturn

203. #### abstract def ctc_loss(args: Any*): NDArrayFuncReturn

Connectionist Temporal Classification Loss.

.. note:: The existing alias contrib_CTCLoss is deprecated.

The shapes of the inputs and outputs:

- **data**: (sequence_length, batch_size, alphabet_size)
- **label**: (batch_size, label_sequence_length)
- **out**: (batch_size)

The data tensor consists of sequences of activation vectors (without applying softmax),
with i-th channel in the last dimension corresponding to i-th label
for i between 0 and alphabet_size-1 (i.e always 0-indexed).
Alphabet size should include one additional value reserved for blank label.
When blank_label is "first", the 0-th channel is be reserved for
activation of blank label, or otherwise if it is "last", (alphabet_size-1)-th channel should be
reserved for blank label.

label is an index matrix of integers. When blank_label is "first",
the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
when blank_label is "last", the value (alphabet_size-1) is reserved for blank label.

If a sequence of labels is shorter than *label_sequence_length*, use the special
padding value at the end of the sequence to conform it to the correct
length. The padding value is 0 when blank_label is "first", and -1 otherwise.

For example, suppose the vocabulary is [a, b, c], and in one batch we have three sequences
'ba', 'cbb', and 'abac'. When blank_label is "first", we can index the labels as
{'a': 1, 'b': 2, 'c': 3}, and we reserve the 0-th channel for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]

When blank_label is "last", we can index the labels as
{'a': 0, 'b': 1, 'c': 2}, and we reserve the channel index 3 for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]

out is a list of CTC loss values, one per example in the batch.

See *Connectionist Temporal Classification: Labelling Unsegmented
Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
information on the definition and the algorithm.

Defined in src/operator/nn/ctc_loss.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

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

Connectionist Temporal Classification Loss.

.. note:: The existing alias contrib_CTCLoss is deprecated.

The shapes of the inputs and outputs:

- **data**: (sequence_length, batch_size, alphabet_size)
- **label**: (batch_size, label_sequence_length)
- **out**: (batch_size)

The data tensor consists of sequences of activation vectors (without applying softmax),
with i-th channel in the last dimension corresponding to i-th label
for i between 0 and alphabet_size-1 (i.e always 0-indexed).
Alphabet size should include one additional value reserved for blank label.
When blank_label is "first", the 0-th channel is be reserved for
activation of blank label, or otherwise if it is "last", (alphabet_size-1)-th channel should be
reserved for blank label.

label is an index matrix of integers. When blank_label is "first",
the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise,
when blank_label is "last", the value (alphabet_size-1) is reserved for blank label.

If a sequence of labels is shorter than *label_sequence_length*, use the special
padding value at the end of the sequence to conform it to the correct
length. The padding value is 0 when blank_label is "first", and -1 otherwise.

For example, suppose the vocabulary is [a, b, c], and in one batch we have three sequences
'ba', 'cbb', and 'abac'. When blank_label is "first", we can index the labels as
{'a': 1, 'b': 2, 'c': 3}, and we reserve the 0-th channel for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ]

When blank_label is "last", we can index the labels as
{'a': 0, 'b': 1, 'c': 2}, and we reserve the channel index 3 for blank label in data tensor.
The resulting label tensor should be padded to be::

[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ]

out is a list of CTC loss values, one per example in the batch.

See *Connectionist Temporal Classification: Labelling Unsegmented
Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more
information on the definition and the algorithm.

Defined in src/operator/nn/ctc_loss.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

205. #### abstract def cumsum(args: Any*): NDArrayFuncReturn

Return the cumulative sum of the elements along a given axis.

Defined in src/operator/numpy/np_cumsum.cc:L70
returns

org.apache.mxnet.NDArrayFuncReturn

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

Return the cumulative sum of the elements along a given axis.

Defined in src/operator/numpy/np_cumsum.cc:L70
returns

org.apache.mxnet.NDArrayFuncReturn

207. #### abstract def degrees(args: Any*): NDArrayFuncReturn

Converts each element of the input array from radians to degrees.

.. math::
degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]

The storage type of degrees output depends upon the input storage type:

- degrees(default) = default
- degrees(row_sparse) = row_sparse
- degrees(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L332
returns

org.apache.mxnet.NDArrayFuncReturn

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

Converts each element of the input array from radians to degrees.

.. math::
degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]

The storage type of degrees output depends upon the input storage type:

- degrees(default) = default
- degrees(row_sparse) = row_sparse
- degrees(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L332
returns

org.apache.mxnet.NDArrayFuncReturn

209. #### abstract def depth_to_space(args: Any*): NDArrayFuncReturn

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

Defined in src/operator/tensor/matrix_op.cc:L972
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L972
returns

org.apache.mxnet.NDArrayFuncReturn

211. #### abstract def diag(args: Any*): NDArrayFuncReturn

Extracts a diagonal or constructs a diagonal array.

diag's behavior depends on the input array dimensions:

- 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
- N-D arrays: extracts the diagonals of the sub-arrays with axes specified by axis1 and axis2.
The output shape would be decided by removing the axes numbered axis1 and axis2 from the
input shape and appending to the result a new axis with the size of the diagonals in question.

For example, when the input shape is (2, 3, 4, 5), axis1 and axis2 are 0 and 2
respectively and k is 0, the resulting shape would be (3, 5, 2).

Examples::

x = [ [1, 2, 3],
[4, 5, 6] ]

diag(x) = [1, 5]

diag(x, k=1) = [2, 6]

diag(x, k=-1) = [4]

x = [1, 2, 3]

diag(x) = [ [1, 0, 0],
[0, 2, 0],
[0, 0, 3] ]

diag(x, k=1) = [ [0, 1, 0],
[0, 0, 2],
[0, 0, 0] ]

diag(x, k=-1) = [ [0, 0, 0],
[1, 0, 0],
[0, 2, 0] ]

x = [ [ [1, 2],
[3, 4] ],

[ [5, 6],
[7, 8] ] ]

diag(x) = [ [1, 7],
[2, 8] ]

diag(x, k=1) = [ [3],
[4] ]

diag(x, axis1=-2, axis2=-1) = [ [1, 4],
[5, 8] ]

Defined in src/operator/tensor/diag_op.cc:L87
returns

org.apache.mxnet.NDArrayFuncReturn

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

Extracts a diagonal or constructs a diagonal array.

diag's behavior depends on the input array dimensions:

- 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
- N-D arrays: extracts the diagonals of the sub-arrays with axes specified by axis1 and axis2.
The output shape would be decided by removing the axes numbered axis1 and axis2 from the
input shape and appending to the result a new axis with the size of the diagonals in question.

For example, when the input shape is (2, 3, 4, 5), axis1 and axis2 are 0 and 2
respectively and k is 0, the resulting shape would be (3, 5, 2).

Examples::

x = [ [1, 2, 3],
[4, 5, 6] ]

diag(x) = [1, 5]

diag(x, k=1) = [2, 6]

diag(x, k=-1) = [4]

x = [1, 2, 3]

diag(x) = [ [1, 0, 0],
[0, 2, 0],
[0, 0, 3] ]

diag(x, k=1) = [ [0, 1, 0],
[0, 0, 2],
[0, 0, 0] ]

diag(x, k=-1) = [ [0, 0, 0],
[1, 0, 0],
[0, 2, 0] ]

x = [ [ [1, 2],
[3, 4] ],

[ [5, 6],
[7, 8] ] ]

diag(x) = [ [1, 7],
[2, 8] ]

diag(x, k=1) = [ [3],
[4] ]

diag(x, axis1=-2, axis2=-1) = [ [1, 4],
[5, 8] ]

Defined in src/operator/tensor/diag_op.cc:L87
returns

org.apache.mxnet.NDArrayFuncReturn

213. #### abstract def dot(args: Any*): NDArrayFuncReturn

Dot product of two arrays.

dot's behavior depends on the input array dimensions:

- 1-D arrays: inner product of vectors
- 2-D arrays: matrix multiplication
- N-D arrays: a sum product over the last axis of the first input and the first
axis of the second input

For example, given 3-D x with shape (n,m,k) and y with shape (k,r,s), the
result array will have shape (n,m,r,s). It is computed by::

dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])

Example::

x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
dot(x,y)[0,0,1,1] = 0
sum(x[0,0,:]*y[:,1,1]) = 0

The storage type of dot output depends on storage types of inputs, transpose option and
forward_stype option for output storage type. Implemented sparse operations include:

- dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
- dot(csr, default, transpose_a=True) = default
- dot(csr, default, transpose_a=True) = row_sparse
- dot(csr, default) = default
- dot(csr, row_sparse) = default
- dot(default, csr) = csr (CPU only)
- dot(default, csr, forward_stype='default') = default
- dot(default, csr, transpose_b=True, forward_stype='default') = default

If the combination of input storage types and forward_stype does not match any of the
above patterns, dot will fallback and generate output with default storage.

.. Note::

If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
and Adam. Note that by default lazy updates is turned on, which may perform differently
from standard updates. For more details, please check the Optimization API at:
https://mxnet.incubator.apache.org/api/python/optimization/optimization.html

Defined in src/operator/tensor/dot.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

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

Dot product of two arrays.

dot's behavior depends on the input array dimensions:

- 1-D arrays: inner product of vectors
- 2-D arrays: matrix multiplication
- N-D arrays: a sum product over the last axis of the first input and the first
axis of the second input

For example, given 3-D x with shape (n,m,k) and y with shape (k,r,s), the
result array will have shape (n,m,r,s). It is computed by::

dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])

Example::

x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
dot(x,y)[0,0,1,1] = 0
sum(x[0,0,:]*y[:,1,1]) = 0

The storage type of dot output depends on storage types of inputs, transpose option and
forward_stype option for output storage type. Implemented sparse operations include:

- dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
- dot(csr, default, transpose_a=True) = default
- dot(csr, default, transpose_a=True) = row_sparse
- dot(csr, default) = default
- dot(csr, row_sparse) = default
- dot(default, csr) = csr (CPU only)
- dot(default, csr, forward_stype='default') = default
- dot(default, csr, transpose_b=True, forward_stype='default') = default

If the combination of input storage types and forward_stype does not match any of the
above patterns, dot will fallback and generate output with default storage.

.. Note::

If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
and Adam. Note that by default lazy updates is turned on, which may perform differently
from standard updates. For more details, please check the Optimization API at:
https://mxnet.incubator.apache.org/api/python/optimization/optimization.html

Defined in src/operator/tensor/dot.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

215. #### abstract def elemwise_add(args: Any*): NDArrayFuncReturn

Adds arguments element-wise.

The storage type of elemwise_add output depends on storage types of inputs

- otherwise, elemwise_add generates output with default storage
returns

org.apache.mxnet.NDArrayFuncReturn

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

Adds arguments element-wise.

The storage type of elemwise_add output depends on storage types of inputs

- otherwise, elemwise_add generates output with default storage
returns

org.apache.mxnet.NDArrayFuncReturn

217. #### abstract def elemwise_div(args: Any*): NDArrayFuncReturn

Divides arguments element-wise.

The storage type of elemwise_div output is always dense
returns

org.apache.mxnet.NDArrayFuncReturn

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

Divides arguments element-wise.

The storage type of elemwise_div output is always dense
returns

org.apache.mxnet.NDArrayFuncReturn

219. #### abstract def elemwise_mul(args: Any*): NDArrayFuncReturn

Multiplies arguments element-wise.

The storage type of elemwise_mul output depends on storage types of inputs

- elemwise_mul(default, default) = default
- elemwise_mul(row_sparse, row_sparse) = row_sparse
- elemwise_mul(default, row_sparse) = row_sparse
- elemwise_mul(row_sparse, default) = row_sparse
- elemwise_mul(csr, csr) = csr
- otherwise, elemwise_mul generates output with default storage
returns

org.apache.mxnet.NDArrayFuncReturn

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

Multiplies arguments element-wise.

The storage type of elemwise_mul output depends on storage types of inputs

- elemwise_mul(default, default) = default
- elemwise_mul(row_sparse, row_sparse) = row_sparse
- elemwise_mul(default, row_sparse) = row_sparse
- elemwise_mul(row_sparse, default) = row_sparse
- elemwise_mul(csr, csr) = csr
- otherwise, elemwise_mul generates output with default storage
returns

org.apache.mxnet.NDArrayFuncReturn

221. #### abstract def elemwise_sub(args: Any*): NDArrayFuncReturn

Subtracts arguments element-wise.

The storage type of elemwise_sub output depends on storage types of inputs

- elemwise_sub(row_sparse, row_sparse) = row_sparse
- elemwise_sub(csr, csr) = csr
- elemwise_sub(default, csr) = default
- elemwise_sub(csr, default) = default
- elemwise_sub(default, rsp) = default
- elemwise_sub(rsp, default) = default
- otherwise, elemwise_sub generates output with default storage
returns

org.apache.mxnet.NDArrayFuncReturn

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

Subtracts arguments element-wise.

The storage type of elemwise_sub output depends on storage types of inputs

- elemwise_sub(row_sparse, row_sparse) = row_sparse
- elemwise_sub(csr, csr) = csr
- elemwise_sub(default, csr) = default
- elemwise_sub(csr, default) = default
- elemwise_sub(default, rsp) = default
- elemwise_sub(rsp, default) = default
- otherwise, elemwise_sub generates output with default storage
returns

org.apache.mxnet.NDArrayFuncReturn

223. #### abstract def erf(args: Any*): NDArrayFuncReturn

Returns element-wise gauss error function of the input.

Example::

erf([0, -1., 10.]) = [0., -0.8427, 1.]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L886
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise gauss error function of the input.

Example::

erf([0, -1., 10.]) = [0., -0.8427, 1.]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L886
returns

org.apache.mxnet.NDArrayFuncReturn

225. #### abstract def erfinv(args: Any*): NDArrayFuncReturn

Returns element-wise inverse gauss error function of the input.

Example::

erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L908
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise inverse gauss error function of the input.

Example::

erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L908
returns

org.apache.mxnet.NDArrayFuncReturn

227. #### abstract def exp(args: Any*): NDArrayFuncReturn

Returns element-wise exponential value of the input.

.. math::
exp(x) = e^x \approx 2.718^x

Example::

exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]

The storage type of exp output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L64
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise exponential value of the input.

.. math::
exp(x) = e^x \approx 2.718^x

Example::

exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]

The storage type of exp output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L64
returns

org.apache.mxnet.NDArrayFuncReturn

229. #### abstract def expand_dims(args: Any*): NDArrayFuncReturn

Inserts a new axis of size 1 into the array shape
For example, given x with shape (2,3,4), then expand_dims(x, axis=1)
will return a new array with shape (2,1,3,4).

Defined in src/operator/tensor/matrix_op.cc:L395
returns

org.apache.mxnet.NDArrayFuncReturn

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

Inserts a new axis of size 1 into the array shape
For example, given x with shape (2,3,4), then expand_dims(x, axis=1)
will return a new array with shape (2,1,3,4).

Defined in src/operator/tensor/matrix_op.cc:L395
returns

org.apache.mxnet.NDArrayFuncReturn

231. #### abstract def expm1(args: Any*): NDArrayFuncReturn

Returns exp(x) - 1 computed element-wise on the input.

This function provides greater precision than exp(x) - 1 for small values of x.

The storage type of expm1 output depends upon the input storage type:

- expm1(default) = default
- expm1(row_sparse) = row_sparse
- expm1(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L244
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns exp(x) - 1 computed element-wise on the input.

This function provides greater precision than exp(x) - 1 for small values of x.

The storage type of expm1 output depends upon the input storage type:

- expm1(default) = default
- expm1(row_sparse) = row_sparse
- expm1(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L244
returns

org.apache.mxnet.NDArrayFuncReturn

233. #### abstract def fill_element_0index(args: Any*): NDArrayFuncReturn

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

org.apache.mxnet.NDArrayFuncReturn

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

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

org.apache.mxnet.NDArrayFuncReturn

235. #### abstract def fix(args: Any*): NDArrayFuncReturn

Returns element-wise rounded value to the nearest \
integer towards zero of the input.

Example::

fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]

The storage type of fix output depends upon the input storage type:

- fix(default) = default
- fix(row_sparse) = row_sparse
- fix(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L874
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise rounded value to the nearest \
integer towards zero of the input.

Example::

fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]

The storage type of fix output depends upon the input storage type:

- fix(default) = default
- fix(row_sparse) = row_sparse
- fix(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L874
returns

org.apache.mxnet.NDArrayFuncReturn

237. #### abstract def flatten(args: Any*): NDArrayFuncReturn

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

Defined in src/operator/tensor/matrix_op.cc:L250
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L250
returns

org.apache.mxnet.NDArrayFuncReturn

239. #### abstract def flip(args: Any*): NDArrayFuncReturn

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

Defined in src/operator/tensor/matrix_op.cc:L832
returns

org.apache.mxnet.NDArrayFuncReturn

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

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

Defined in src/operator/tensor/matrix_op.cc:L832
returns

org.apache.mxnet.NDArrayFuncReturn

241. #### abstract def floor(args: Any*): NDArrayFuncReturn

Returns element-wise floor of the input.

The floor of the scalar x is the largest integer i, such that i <= x.

Example::

floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]

The storage type of floor output depends upon the input storage type:

- floor(default) = default
- floor(row_sparse) = row_sparse
- floor(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L836
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise floor of the input.

The floor of the scalar x is the largest integer i, such that i <= x.

Example::

floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]

The storage type of floor output depends upon the input storage type:

- floor(default) = default
- floor(row_sparse) = row_sparse
- floor(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L836
returns

org.apache.mxnet.NDArrayFuncReturn

243. #### abstract def ftml_update(args: Any*): NDArrayFuncReturn

The FTML optimizer described in
available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.

.. math::

g_t = \nabla J(W_{t-1})\\
v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
\sigma_t = d_t - \beta_1 d_{t-1}
z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
W_t = - \frac{ z_t }{ d_t }

Defined in src/operator/optimizer_op.cc:L640
returns

org.apache.mxnet.NDArrayFuncReturn

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

The FTML optimizer described in
available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.

.. math::

g_t = \nabla J(W_{t-1})\\
v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
\sigma_t = d_t - \beta_1 d_{t-1}
z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
W_t = - \frac{ z_t }{ d_t }

Defined in src/operator/optimizer_op.cc:L640
returns

org.apache.mxnet.NDArrayFuncReturn

245. #### abstract def ftrl_update(args: Any*): NDArrayFuncReturn

Update function for Ftrl optimizer.
Referenced from *Ad Click Prediction: a View from the Trenches*, available at
http://dl.acm.org/citation.cfm?id=2488200.

z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
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)::

z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)

Defined in src/operator/optimizer_op.cc:L876
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for Ftrl optimizer.
Referenced from *Ad Click Prediction: a View from the Trenches*, available at
http://dl.acm.org/citation.cfm?id=2488200.

z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
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)::

z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)

Defined in src/operator/optimizer_op.cc:L876
returns

org.apache.mxnet.NDArrayFuncReturn

247. #### abstract def gamma(args: Any*): NDArrayFuncReturn

Returns the gamma function (extension of the factorial function \
to the reals), computed element-wise on the input array.

The storage type of gamma output is always dense
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the gamma function (extension of the factorial function \
to the reals), computed element-wise on the input array.

The storage type of gamma output is always dense
returns

org.apache.mxnet.NDArrayFuncReturn

249. #### abstract def gammaln(args: Any*): NDArrayFuncReturn

Returns element-wise log of the absolute value of the gamma function \
of the input.

The storage type of gammaln output is always dense
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise log of the absolute value of the gamma function \
of the input.

The storage type of gammaln output is always dense
returns

org.apache.mxnet.NDArrayFuncReturn

251. #### abstract def gather_nd(args: Any*): NDArrayFuncReturn

Gather elements or slices from data and store to a tensor whose
shape is defined by indices.

Given data with shape (X_0, X_1, ..., X_{N-1}) and indices with shape
(M, Y_0, ..., Y_{K-1}), the output will have shape (Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1}),
where M <= N. If M == N, output shape will simply be (Y_0, ..., Y_{K-1}).

The elements in output is defined as follows::

output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
...,
indices[M-1, y_0, ..., y_{K-1}],
x_M, ..., x_{N-1}]

Examples::

data = [ [0, 1], [2, 3] ]
indices = [ [1, 1, 0], [0, 1, 0] ]
gather_nd(data, indices) = [2, 3, 0]

data = [ [ [1, 2], [3, 4] ], [ [5, 6], [7, 8] ] ]
indices = [ [0, 1], [1, 0] ]
gather_nd(data, indices) = [ [3, 4], [5, 6] ]
returns

org.apache.mxnet.NDArrayFuncReturn

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

Gather elements or slices from data and store to a tensor whose
shape is defined by indices.

Given data with shape (X_0, X_1, ..., X_{N-1}) and indices with shape
(M, Y_0, ..., Y_{K-1}), the output will have shape (Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1}),
where M <= N. If M == N, output shape will simply be (Y_0, ..., Y_{K-1}).

The elements in output is defined as follows::

output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
...,
indices[M-1, y_0, ..., y_{K-1}],
x_M, ..., x_{N-1}]

Examples::

data = [ [0, 1], [2, 3] ]
indices = [ [1, 1, 0], [0, 1, 0] ]
gather_nd(data, indices) = [2, 3, 0]

data = [ [ [1, 2], [3, 4] ], [ [5, 6], [7, 8] ] ]
indices = [ [0, 1], [1, 0] ]
gather_nd(data, indices) = [ [3, 4], [5, 6] ]
returns

org.apache.mxnet.NDArrayFuncReturn

253. #### abstract def hard_sigmoid(args: Any*): NDArrayFuncReturn

Computes hard sigmoid of x element-wise.

.. math::
y = max(0, min(1, alpha * x + beta))

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L161
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes hard sigmoid of x element-wise.

.. math::
y = max(0, min(1, alpha * x + beta))

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L161
returns

org.apache.mxnet.NDArrayFuncReturn

255. #### abstract def identity(args: Any*): NDArrayFuncReturn

Returns a copy of the input.

From:src/operator/tensor/elemwise_unary_op_basic.cc:244
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns a copy of the input.

From:src/operator/tensor/elemwise_unary_op_basic.cc:244
returns

org.apache.mxnet.NDArrayFuncReturn

257. #### abstract def im2col(args: Any*): NDArrayFuncReturn

Extract sliding blocks from input array.

This operator is used in vanilla convolution implementation to transform the sliding
blocks on image to column matrix, then the convolution operation can be computed
by matrix multiplication between column and convolution weight. Due to the close
relation between im2col and convolution, the concept of **kernel**, **stride**,
**dilate** and **pad** in this operator are inherited from convolution operation.

Given the input data of shape :math:(N, C, *), where :math:N is the batch size,
:math:C is the channel size, and :math:* is the arbitrary spatial dimension,
the output column array is always with shape :math:(N, C \times \prod(\text{kernel}), W),
where :math:C \times \prod(\text{kernel}) is the block size, and :math:W is the
block number which is the spatial size of the convolution output with same input parameters.
Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

258. #### abstract def im2col(kwargs: Map[String, Any] = null)(args: Any*): NDArrayFuncReturn

Extract sliding blocks from input array.

This operator is used in vanilla convolution implementation to transform the sliding
blocks on image to column matrix, then the convolution operation can be computed
by matrix multiplication between column and convolution weight. Due to the close
relation between im2col and convolution, the concept of **kernel**, **stride**,
**dilate** and **pad** in this operator are inherited from convolution operation.

Given the input data of shape :math:(N, C, *), where :math:N is the batch size,
:math:C is the channel size, and :math:* is the arbitrary spatial dimension,
the output column array is always with shape :math:(N, C \times \prod(\text{kernel}), W),
where :math:C \times \prod(\text{kernel}) is the block size, and :math:W is the
block number which is the spatial size of the convolution output with same input parameters.
Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L100
returns

org.apache.mxnet.NDArrayFuncReturn

259. #### abstract def khatri_rao(args: Any*): NDArrayFuncReturn

Computes the Khatri-Rao product of the input matrices.

Given a collection of :math:n input matrices,

.. math::
A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},

the (column-wise) Khatri-Rao product is defined as the matrix,

.. math::
X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},

where the :math:k th column is equal to the column-wise outer product
:math:{A_1}_k \otimes \cdots \otimes {A_n}_k where :math:{A_i}_k is the kth
column of the ith matrix.

Example::

>>> A = mx.nd.array([ [1, -1],
>>>                  [2, -3] ])
>>> B = mx.nd.array([ [1, 4],
>>>                  [2, 5],
>>>                  [3, 6] ])
>>> C = mx.nd.khatri_rao(A, B)
>>> print(C.asnumpy())
[ [  1.  -4.]
[  2.  -5.]
[  3.  -6.]
[  2. -12.]
[  4. -15.]
[  6. -18.] ]

Defined in src/operator/contrib/krprod.cc:L108
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the Khatri-Rao product of the input matrices.

Given a collection of :math:n input matrices,

.. math::
A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},

the (column-wise) Khatri-Rao product is defined as the matrix,

.. math::
X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},

where the :math:k th column is equal to the column-wise outer product
:math:{A_1}_k \otimes \cdots \otimes {A_n}_k where :math:{A_i}_k is the kth
column of the ith matrix.

Example::

>>> A = mx.nd.array([ [1, -1],
>>>                  [2, -3] ])
>>> B = mx.nd.array([ [1, 4],
>>>                  [2, 5],
>>>                  [3, 6] ])
>>> C = mx.nd.khatri_rao(A, B)
>>> print(C.asnumpy())
[ [  1.  -4.]
[  2.  -5.]
[  3.  -6.]
[  2. -12.]
[  4. -15.]
[  6. -18.] ]

Defined in src/operator/contrib/krprod.cc:L108
returns

org.apache.mxnet.NDArrayFuncReturn

261. #### abstract def lamb_update_phase1(args: Any*): NDArrayFuncReturn

Phase I of lamb update it performs the following operations and returns g:.

.. math::
\begin{gather*}
then
then

mean = beta1 * mean + (1 - beta1) * grad;
variance = beta2 * variance + (1. - beta2) * grad ^ 2;

if (bias_correction)
then
mean_hat = mean / (1. - beta1^t);
var_hat = var / (1 - beta2^t);
g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight;
else
g = mean / (var_data^(1/2) + epsilon) + wd * weight;
\end{gather*}

Defined in src/operator/optimizer_op.cc:L953
returns

org.apache.mxnet.NDArrayFuncReturn

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

Phase I of lamb update it performs the following operations and returns g:.

.. math::
\begin{gather*}
then
then

mean = beta1 * mean + (1 - beta1) * grad;
variance = beta2 * variance + (1. - beta2) * grad ^ 2;

if (bias_correction)
then
mean_hat = mean / (1. - beta1^t);
var_hat = var / (1 - beta2^t);
g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight;
else
g = mean / (var_data^(1/2) + epsilon) + wd * weight;
\end{gather*}

Defined in src/operator/optimizer_op.cc:L953
returns

org.apache.mxnet.NDArrayFuncReturn

263. #### abstract def lamb_update_phase2(args: Any*): NDArrayFuncReturn

Phase II of lamb update it performs the following operations and updates grad.

.. math::
\begin{gather*}
if (lower_bound >= 0)
then
r1 = max(r1, lower_bound)
if (upper_bound >= 0)
then
r1 = max(r1, upper_bound)

if (r1 == 0 or r2 == 0)
then
lr = lr
else
lr = lr * (r1/r2)
weight = weight - lr * g
\end{gather*}

Defined in src/operator/optimizer_op.cc:L992
returns

org.apache.mxnet.NDArrayFuncReturn

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

Phase II of lamb update it performs the following operations and updates grad.

.. math::
\begin{gather*}
if (lower_bound >= 0)
then
r1 = max(r1, lower_bound)
if (upper_bound >= 0)
then
r1 = max(r1, upper_bound)

if (r1 == 0 or r2 == 0)
then
lr = lr
else
lr = lr * (r1/r2)
weight = weight - lr * g
\end{gather*}

Defined in src/operator/optimizer_op.cc:L992
returns

org.apache.mxnet.NDArrayFuncReturn

265. #### abstract def linalg_det(args: Any*): NDArrayFuncReturn

Compute the determinant of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a square matrix. We compute:

*out* = *det(A)*

If *n>2*, *det* is performed separately on the trailing two dimensions
for all inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.
.. note:: There is no gradient backwarded when A is non-invertible (which is
equivalent to det(A) = 0) because zero is rarely hit upon in float
point computation and the Jacobi's formula on determinant gradient
is not computationally efficient when A is non-invertible.

Examples::

Single matrix determinant
A = [ [1., 4.], [2., 3.] ]
det(A) = [-5.]

Batch matrix determinant
A = [ [ [1., 4.], [2., 3.] ],
[ [2., 3.], [1., 4.] ] ]
det(A) = [-5., 5.]

Defined in src/operator/tensor/la_op.cc:L975
returns

org.apache.mxnet.NDArrayFuncReturn

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

Compute the determinant of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a square matrix. We compute:

*out* = *det(A)*

If *n>2*, *det* is performed separately on the trailing two dimensions
for all inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.
.. note:: There is no gradient backwarded when A is non-invertible (which is
equivalent to det(A) = 0) because zero is rarely hit upon in float
point computation and the Jacobi's formula on determinant gradient
is not computationally efficient when A is non-invertible.

Examples::

Single matrix determinant
A = [ [1., 4.], [2., 3.] ]
det(A) = [-5.]

Batch matrix determinant
A = [ [ [1., 4.], [2., 3.] ],
[ [2., 3.], [1., 4.] ] ]
det(A) = [-5., 5.]

Defined in src/operator/tensor/la_op.cc:L975
returns

org.apache.mxnet.NDArrayFuncReturn

267. #### abstract def linalg_extractdiag(args: Any*): NDArrayFuncReturn

Extracts the diagonal entries of a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, then *A* represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor.

If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an *n-1*-dimensional tensor.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix diagonal extraction
A = [ [1.0, 2.0],
[3.0, 4.0] ]

extractdiag(A) = [1.0, 4.0]

extractdiag(A, 1) = [2.0]

Batch matrix diagonal extraction
A = [ [ [1.0, 2.0],
[3.0, 4.0] ],
[ [5.0, 6.0],
[7.0, 8.0] ] ]

extractdiag(A) = [ [1.0, 4.0],
[5.0, 8.0] ]

Defined in src/operator/tensor/la_op.cc:L495
returns

org.apache.mxnet.NDArrayFuncReturn

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

Extracts the diagonal entries of a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, then *A* represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor.

If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an *n-1*-dimensional tensor.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix diagonal extraction
A = [ [1.0, 2.0],
[3.0, 4.0] ]

extractdiag(A) = [1.0, 4.0]

extractdiag(A, 1) = [2.0]

Batch matrix diagonal extraction
A = [ [ [1.0, 2.0],
[3.0, 4.0] ],
[ [5.0, 6.0],
[7.0, 8.0] ] ]

extractdiag(A) = [ [1.0, 4.0],
[5.0, 8.0] ]

Defined in src/operator/tensor/la_op.cc:L495
returns

org.apache.mxnet.NDArrayFuncReturn

269. #### abstract def linalg_extracttrian(args: Any*): NDArrayFuncReturn

Extracts a triangular sub-matrix from a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, then *A* represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor.

If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an *n-1*-dimensional tensor.

The *offset* and *lower* parameters determine the triangle to be extracted:

- When *offset = 0* either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter *lower*.
- When *offset = k > 0* the upper triangle with respect to the k-th diagonal above the main diagonal is extracted.
- When *offset = k < 0* the lower triangle with respect to the k-th diagonal below the main diagonal is extracted.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single triagonal extraction
A = [ [1.0, 2.0],
[3.0, 4.0] ]

extracttrian(A) = [1.0, 3.0, 4.0]
extracttrian(A, lower=False) = [1.0, 2.0, 4.0]
extracttrian(A, 1) = [2.0]
extracttrian(A, -1) = [3.0]

Batch triagonal extraction
A = [ [ [1.0, 2.0],
[3.0, 4.0] ],
[ [5.0, 6.0],
[7.0, 8.0] ] ]

extracttrian(A) = [ [1.0, 3.0, 4.0],
[5.0, 7.0, 8.0] ]

Defined in src/operator/tensor/la_op.cc:L605
returns

org.apache.mxnet.NDArrayFuncReturn

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

Extracts a triangular sub-matrix from a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, then *A* represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor.

If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an *n-1*-dimensional tensor.

The *offset* and *lower* parameters determine the triangle to be extracted:

- When *offset = 0* either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter *lower*.
- When *offset = k > 0* the upper triangle with respect to the k-th diagonal above the main diagonal is extracted.
- When *offset = k < 0* the lower triangle with respect to the k-th diagonal below the main diagonal is extracted.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single triagonal extraction
A = [ [1.0, 2.0],
[3.0, 4.0] ]

extracttrian(A) = [1.0, 3.0, 4.0]
extracttrian(A, lower=False) = [1.0, 2.0, 4.0]
extracttrian(A, 1) = [2.0]
extracttrian(A, -1) = [3.0]

Batch triagonal extraction
A = [ [ [1.0, 2.0],
[3.0, 4.0] ],
[ [5.0, 6.0],
[7.0, 8.0] ] ]

extracttrian(A) = [ [1.0, 3.0, 4.0],
[5.0, 7.0, 8.0] ]

Defined in src/operator/tensor/la_op.cc:L605
returns

org.apache.mxnet.NDArrayFuncReturn

271. #### abstract def linalg_gelqf(args: Any*): NDArrayFuncReturn

LQ factorization for general matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
that:

*A* = *L* \* *Q*

Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
and *Q* is row-orthonormal, meaning that

*Q* \* *Q*\ :sup:T

is equal to the identity matrix of shape *(x, x)*.

If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single LQ factorization
A = [ [1., 2., 3.], [4., 5., 6.] ]
Q, L = gelqf(A)
Q = [ [-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578] ]
L = [ [-3.74165739, 0.],
[-8.55235974, 1.96396101] ]

Batch LQ factorization
A = [ [ [1., 2., 3.], [4., 5., 6.] ],
[ [7., 8., 9.], [10., 11., 12.] ] ]
Q, L = gelqf(A)
Q = [ [ [-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578] ],
[ [-0.50257071, -0.57436653, -0.64616234],
[0.7620735, 0.05862104, -0.64483142] ] ]
L = [ [ [-3.74165739, 0.],
[-8.55235974, 1.96396101] ],
[ [-13.92838828, 0.],
[-19.09768702, 0.52758934] ] ]

Defined in src/operator/tensor/la_op.cc:L798
returns

org.apache.mxnet.NDArrayFuncReturn

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

LQ factorization for general matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
that:

*A* = *L* \* *Q*

Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
and *Q* is row-orthonormal, meaning that

*Q* \* *Q*\ :sup:T

is equal to the identity matrix of shape *(x, x)*.

If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single LQ factorization
A = [ [1., 2., 3.], [4., 5., 6.] ]
Q, L = gelqf(A)
Q = [ [-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578] ]
L = [ [-3.74165739, 0.],
[-8.55235974, 1.96396101] ]

Batch LQ factorization
A = [ [ [1., 2., 3.], [4., 5., 6.] ],
[ [7., 8., 9.], [10., 11., 12.] ] ]
Q, L = gelqf(A)
Q = [ [ [-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578] ],
[ [-0.50257071, -0.57436653, -0.64616234],
[0.7620735, 0.05862104, -0.64483142] ] ]
L = [ [ [-3.74165739, 0.],
[-8.55235974, 1.96396101] ],
[ [-13.92838828, 0.],
[-19.09768702, 0.52758934] ] ]

Defined in src/operator/tensor/la_op.cc:L798
returns

org.apache.mxnet.NDArrayFuncReturn

273. #### abstract def linalg_gemm(args: Any*): NDArrayFuncReturn

Performs general matrix multiplication and accumulation.
Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape

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

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::

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] ]

A = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
B = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
C = [ [ [10.0] ], [ [0.01] ] ]
gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
= [ [ [104.0] ], [ [0.14] ] ]

Defined in src/operator/tensor/la_op.cc:L89
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs general matrix multiplication and accumulation.
Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape

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

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::

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] ]

A = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
B = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
C = [ [ [10.0] ], [ [0.01] ] ]
gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
= [ [ [104.0] ], [ [0.14] ] ]

Defined in src/operator/tensor/la_op.cc:L89
returns

org.apache.mxnet.NDArrayFuncReturn

275. #### abstract def linalg_gemm2(args: Any*): NDArrayFuncReturn

Performs general matrix multiplication.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape

If *n=2*, the BLAS3 function *gemm* is performed:

*out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)

Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
transposition (depending on *transpose_a*, *transpose_b*).

If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
parameter. By default, the trailing two dimensions will be used for matrix encoding.

For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to

A1 = swapaxes(A, dim1=1, dim2=3)
B1 = swapaxes(B, dim1=1, dim2=3)
C = gemm2(A1, B1)
C = swapaxis(C, dim1=1, dim2=3)

When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix multiply
A = [ [1.0, 1.0], [1.0, 1.0] ]
B = [ [1.0, 1.0], [1.0, 1.0], [1.0, 1.0] ]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [ [4.0, 4.0, 4.0], [4.0, 4.0, 4.0] ]

Batch matrix multiply
A = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
B = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [ [ [4.0] ], [ [0.04 ] ] ]

Defined in src/operator/tensor/la_op.cc:L163
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs general matrix multiplication.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape

If *n=2*, the BLAS3 function *gemm* is performed:

*out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)

Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
transposition (depending on *transpose_a*, *transpose_b*).

If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
parameter. By default, the trailing two dimensions will be used for matrix encoding.

For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to

A1 = swapaxes(A, dim1=1, dim2=3)
B1 = swapaxes(B, dim1=1, dim2=3)
C = gemm2(A1, B1)
C = swapaxis(C, dim1=1, dim2=3)

When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE
and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use
pseudo-float16 precision (float32 math with float16 I/O) precision in order to use
Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix multiply
A = [ [1.0, 1.0], [1.0, 1.0] ]
B = [ [1.0, 1.0], [1.0, 1.0], [1.0, 1.0] ]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [ [4.0, 4.0, 4.0], [4.0, 4.0, 4.0] ]

Batch matrix multiply
A = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
B = [ [ [1.0, 1.0] ], [ [0.1, 0.1] ] ]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [ [ [4.0] ], [ [0.04 ] ] ]

Defined in src/operator/tensor/la_op.cc:L163
returns

org.apache.mxnet.NDArrayFuncReturn

277. #### abstract def linalg_inverse(args: Any*): NDArrayFuncReturn

Compute the inverse of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a square matrix. We compute:

*out* = *A*\ :sup:-1

If *n>2*, *inverse* is performed separately on the trailing two dimensions
for all inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix inverse
A = [ [1., 4.], [2., 3.] ]
inverse(A) = [ [-0.6, 0.8], [0.4, -0.2] ]

Batch matrix inverse
A = [ [ [1., 4.], [2., 3.] ],
[ [1., 3.], [2., 4.] ] ]
inverse(A) = [ [ [-0.6, 0.8], [0.4, -0.2] ],
[ [-2., 1.5], [1., -0.5] ] ]

Defined in src/operator/tensor/la_op.cc:L920
returns

org.apache.mxnet.NDArrayFuncReturn

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

Compute the inverse of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a square matrix. We compute:

*out* = *A*\ :sup:-1

If *n>2*, *inverse* is performed separately on the trailing two dimensions
for all inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix inverse
A = [ [1., 4.], [2., 3.] ]
inverse(A) = [ [-0.6, 0.8], [0.4, -0.2] ]

Batch matrix inverse
A = [ [ [1., 4.], [2., 3.] ],
[ [1., 3.], [2., 4.] ] ]
inverse(A) = [ [ [-0.6, 0.8], [0.4, -0.2] ],
[ [-2., 1.5], [1., -0.5] ] ]

Defined in src/operator/tensor/la_op.cc:L920
returns

org.apache.mxnet.NDArrayFuncReturn

279. #### abstract def linalg_makediag(args: Any*): NDArrayFuncReturn

Constructs a square matrix with the input as diagonal.
Input is a tensor *A* of dimension *n >= 1*.

If *n=1*, then *A* represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor.
If *n>1*, then *A* represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an *n+1*-dimensional tensor.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single diagonal matrix construction
A = [1.0, 2.0]

makediag(A)    = [ [1.0, 0.0],
[0.0, 2.0] ]

makediag(A, 1) = [ [0.0, 1.0, 0.0],
[0.0, 0.0, 2.0],
[0.0, 0.0, 0.0] ]

Batch diagonal matrix construction
A = [ [1.0, 2.0],
[3.0, 4.0] ]

makediag(A) = [ [ [1.0, 0.0],
[0.0, 2.0] ],
[ [3.0, 0.0],
[0.0, 4.0] ] ]

Defined in src/operator/tensor/la_op.cc:L547
returns

org.apache.mxnet.NDArrayFuncReturn

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

Constructs a square matrix with the input as diagonal.
Input is a tensor *A* of dimension *n >= 1*.

If *n=1*, then *A* represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor.
If *n>1*, then *A* represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an *n+1*-dimensional tensor.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single diagonal matrix construction
A = [1.0, 2.0]

makediag(A)    = [ [1.0, 0.0],
[0.0, 2.0] ]

makediag(A, 1) = [ [0.0, 1.0, 0.0],
[0.0, 0.0, 2.0],
[0.0, 0.0, 0.0] ]

Batch diagonal matrix construction
A = [ [1.0, 2.0],
[3.0, 4.0] ]

makediag(A) = [ [ [1.0, 0.0],
[0.0, 2.0] ],
[ [3.0, 0.0],
[0.0, 4.0] ] ]

Defined in src/operator/tensor/la_op.cc:L547
returns

org.apache.mxnet.NDArrayFuncReturn

281. #### abstract def linalg_maketrian(args: Any*): NDArrayFuncReturn

Constructs a square matrix with the input representing a specific triangular sub-matrix.
This is basically the inverse of *linalg.extracttrian*. Input is a tensor *A* of dimension *n >= 1*.

If *n=1*, then *A* represents the entries of a triangular matrix which is lower triangular if *offset<0* or *offset=0*, *lower=true*. The resulting matrix is derived by first constructing the square
matrix with the entries outside the triangle set to zero and then adding *offset*-times an additional
diagonal with zero entries to the square matrix.

If *n>1*, then *A* represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an *n+1*-dimensional tensor.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single  matrix construction
A = [1.0, 2.0, 3.0]

maketrian(A)              = [ [1.0, 0.0],
[2.0, 3.0] ]

maketrian(A, lower=false) = [ [1.0, 2.0],
[0.0, 3.0] ]

maketrian(A, offset=1)    = [ [0.0, 1.0, 2.0],
[0.0, 0.0, 3.0],
[0.0, 0.0, 0.0] ]
maketrian(A, offset=-1)   = [ [0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[2.0, 3.0, 0.0] ]

Batch matrix construction
A = [ [1.0, 2.0, 3.0],
[4.0, 5.0, 6.0] ]

maketrian(A)           = [ [ [1.0, 0.0],
[2.0, 3.0] ],
[ [4.0, 0.0],
[5.0, 6.0] ] ]

maketrian(A, offset=1) = [ [ [0.0, 1.0, 2.0],
[0.0, 0.0, 3.0],
[0.0, 0.0, 0.0] ],
[ [0.0, 4.0, 5.0],
[0.0, 0.0, 6.0],
[0.0, 0.0, 0.0] ] ]

Defined in src/operator/tensor/la_op.cc:L673
returns

org.apache.mxnet.NDArrayFuncReturn

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

Constructs a square matrix with the input representing a specific triangular sub-matrix.
This is basically the inverse of *linalg.extracttrian*. Input is a tensor *A* of dimension *n >= 1*.

If *n=1*, then *A* represents the entries of a triangular matrix which is lower triangular if *offset<0* or *offset=0*, *lower=true*. The resulting matrix is derived by first constructing the square
matrix with the entries outside the triangle set to zero and then adding *offset*-times an additional
diagonal with zero entries to the square matrix.

If *n>1*, then *A* represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an *n+1*-dimensional tensor.

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single  matrix construction
A = [1.0, 2.0, 3.0]

maketrian(A)              = [ [1.0, 0.0],
[2.0, 3.0] ]

maketrian(A, lower=false) = [ [1.0, 2.0],
[0.0, 3.0] ]

maketrian(A, offset=1)    = [ [0.0, 1.0, 2.0],
[0.0, 0.0, 3.0],
[0.0, 0.0, 0.0] ]
maketrian(A, offset=-1)   = [ [0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[2.0, 3.0, 0.0] ]

Batch matrix construction
A = [ [1.0, 2.0, 3.0],
[4.0, 5.0, 6.0] ]

maketrian(A)           = [ [ [1.0, 0.0],
[2.0, 3.0] ],
[ [4.0, 0.0],
[5.0, 6.0] ] ]

maketrian(A, offset=1) = [ [ [0.0, 1.0, 2.0],
[0.0, 0.0, 3.0],
[0.0, 0.0, 0.0] ],
[ [0.0, 4.0, 5.0],
[0.0, 0.0, 6.0],
[0.0, 0.0, 0.0] ] ]

Defined in src/operator/tensor/la_op.cc:L673
returns

org.apache.mxnet.NDArrayFuncReturn

283. #### abstract def linalg_potrf(args: Any*): NDArrayFuncReturn

Performs Cholesky factorization of a symmetric positive-definite matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, the Cholesky factor *B* of the symmetric, positive definite matrix *A* is
computed. *B* is triangular (entries of upper or lower triangle are all zero), has
positive diagonal entries, and:

*A* = *B* \* *B*\ :sup:T  if *lower* = *true*
*A* = *B*\ :sup:T \* *B*  if *lower* = *false*

If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix factorization
A = [ [4.0, 1.0], [1.0, 4.25] ]
potrf(A) = [ [2.0, 0], [0.5, 2.0] ]

Batch matrix factorization
A = [ [ [4.0, 1.0], [1.0, 4.25] ], [ [16.0, 4.0], [4.0, 17.0] ] ]
potrf(A) = [ [ [2.0, 0], [0.5, 2.0] ], [ [4.0, 0], [1.0, 4.0] ] ]

Defined in src/operator/tensor/la_op.cc:L214
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs Cholesky factorization of a symmetric positive-definite matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, the Cholesky factor *B* of the symmetric, positive definite matrix *A* is
computed. *B* is triangular (entries of upper or lower triangle are all zero), has
positive diagonal entries, and:

*A* = *B* \* *B*\ :sup:T  if *lower* = *true*
*A* = *B*\ :sup:T \* *B*  if *lower* = *false*

If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix factorization
A = [ [4.0, 1.0], [1.0, 4.25] ]
potrf(A) = [ [2.0, 0], [0.5, 2.0] ]

Batch matrix factorization
A = [ [ [4.0, 1.0], [1.0, 4.25] ], [ [16.0, 4.0], [4.0, 17.0] ] ]
potrf(A) = [ [ [2.0, 0], [0.5, 2.0] ], [ [4.0, 0], [1.0, 4.0] ] ]

Defined in src/operator/tensor/la_op.cc:L214
returns

org.apache.mxnet.NDArrayFuncReturn

285. #### abstract def linalg_potri(args: Any*): NDArrayFuncReturn

Performs matrix inversion from a Cholesky factorization.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a triangular matrix (entries of upper or lower triangle are all zero)
with positive diagonal. We compute:

*out* = *A*\ :sup:-T \* *A*\ :sup:-1 if *lower* = *true*
*out* = *A*\ :sup:-1 \* *A*\ :sup:-T if *lower* = *false*

In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix
*B* (obtained by *potrf*), then

*out* = *B*\ :sup:-1

If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

.. note:: Use this operator only if you are certain you need the inverse of *B*, and
cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution
(*trsm*). The latter is numerically much safer, and also cheaper.

Examples::

Single matrix inverse
A = [ [2.0, 0], [0.5, 2.0] ]
potri(A) = [ [0.26563, -0.0625], [-0.0625, 0.25] ]

Batch matrix inverse
A = [ [ [2.0, 0], [0.5, 2.0] ], [ [4.0, 0], [1.0, 4.0] ] ]
potri(A) = [ [ [0.26563, -0.0625], [-0.0625, 0.25] ],
[ [0.06641, -0.01562], [-0.01562, 0,0625] ] ]

Defined in src/operator/tensor/la_op.cc:L275
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs matrix inversion from a Cholesky factorization.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a triangular matrix (entries of upper or lower triangle are all zero)
with positive diagonal. We compute:

*out* = *A*\ :sup:-T \* *A*\ :sup:-1 if *lower* = *true*
*out* = *A*\ :sup:-1 \* *A*\ :sup:-T if *lower* = *false*

In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix
*B* (obtained by *potrf*), then

*out* = *B*\ :sup:-1

If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

.. note:: Use this operator only if you are certain you need the inverse of *B*, and
cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution
(*trsm*). The latter is numerically much safer, and also cheaper.

Examples::

Single matrix inverse
A = [ [2.0, 0], [0.5, 2.0] ]
potri(A) = [ [0.26563, -0.0625], [-0.0625, 0.25] ]

Batch matrix inverse
A = [ [ [2.0, 0], [0.5, 2.0] ], [ [4.0, 0], [1.0, 4.0] ] ]
potri(A) = [ [ [0.26563, -0.0625], [-0.0625, 0.25] ],
[ [0.06641, -0.01562], [-0.01562, 0,0625] ] ]

Defined in src/operator/tensor/la_op.cc:L275
returns

org.apache.mxnet.NDArrayFuncReturn

287. #### abstract def linalg_slogdet(args: Any*): NDArrayFuncReturn

Compute the sign and log of the determinant of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a square matrix. We compute:

*sign* = *sign(det(A))*
*logabsdet* = *log(abs(det(A)))*

If *n>2*, *slogdet* is performed separately on the trailing two dimensions
for all inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.
.. note:: The gradient is not properly defined on sign, so the gradient of
it is not backwarded.
.. note:: No gradient is backwarded when A is non-invertible. Please see
the docs of operator det for detail.

Examples::

Single matrix signed log determinant
A = [ [2., 3.], [1., 4.] ]
sign, logabsdet = slogdet(A)
sign = [1.]
logabsdet = [1.609438]

Batch matrix signed log determinant
A = [ [ [2., 3.], [1., 4.] ],
[ [1., 2.], [2., 4.] ],
[ [1., 2.], [4., 3.] ] ]
sign, logabsdet = slogdet(A)
sign = [1., 0., -1.]
logabsdet = [1.609438, -inf, 1.609438]

Defined in src/operator/tensor/la_op.cc:L1034
returns

org.apache.mxnet.NDArrayFuncReturn

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

Compute the sign and log of the determinant of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a square matrix. We compute:

*sign* = *sign(det(A))*
*logabsdet* = *log(abs(det(A)))*

If *n>2*, *slogdet* is performed separately on the trailing two dimensions
for all inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.
.. note:: The gradient is not properly defined on sign, so the gradient of
it is not backwarded.
.. note:: No gradient is backwarded when A is non-invertible. Please see
the docs of operator det for detail.

Examples::

Single matrix signed log determinant
A = [ [2., 3.], [1., 4.] ]
sign, logabsdet = slogdet(A)
sign = [1.]
logabsdet = [1.609438]

Batch matrix signed log determinant
A = [ [ [2., 3.], [1., 4.] ],
[ [1., 2.], [2., 4.] ],
[ [1., 2.], [4., 3.] ] ]
sign, logabsdet = slogdet(A)
sign = [1., 0., -1.]
logabsdet = [1.609438, -inf, 1.609438]

Defined in src/operator/tensor/la_op.cc:L1034
returns

org.apache.mxnet.NDArrayFuncReturn

289. #### abstract def linalg_sumlogdiag(args: Any*): NDArrayFuncReturn

Computes the sum of the logarithms of the diagonal elements of a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
logarithms of the diagonal elements, the result has shape (1,).

If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix reduction
A = [ [1.0, 1.0], [1.0, 7.0] ]
sumlogdiag(A) = [1.9459]

Batch matrix reduction
A = [ [ [1.0, 1.0], [1.0, 7.0] ], [ [3.0, 0], [0, 17.0] ] ]
sumlogdiag(A) = [1.9459, 3.9318]

Defined in src/operator/tensor/la_op.cc:L445
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the sum of the logarithms of the diagonal elements of a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
logarithms of the diagonal elements, the result has shape (1,).

If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix reduction
A = [ [1.0, 1.0], [1.0, 7.0] ]
sumlogdiag(A) = [1.9459]

Batch matrix reduction
A = [ [ [1.0, 1.0], [1.0, 7.0] ], [ [3.0, 0], [0, 17.0] ] ]
sumlogdiag(A) = [1.9459, 3.9318]

Defined in src/operator/tensor/la_op.cc:L445
returns

org.apache.mxnet.NDArrayFuncReturn

291. #### abstract def linalg_syrk(args: Any*): NDArrayFuncReturn

Multiplication of matrix with its transpose.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, the operator performs the BLAS3 function *syrk*:

*out* = *alpha* \* *A* \* *A*\ :sup:T

if *transpose=False*, or

*out* = *alpha* \* *A*\ :sup:T \ \* *A*

if *transpose=True*.

If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix multiply
A = [ [1., 2., 3.], [4., 5., 6.] ]
syrk(A, alpha=1., transpose=False)
= [ [14., 32.],
[32., 77.] ]
syrk(A, alpha=1., transpose=True)
= [ [17., 22., 27.],
[22., 29., 36.],
[27., 36., 45.] ]

Batch matrix multiply
A = [ [ [1., 1.] ], [ [0.1, 0.1] ] ]
syrk(A, alpha=2., transpose=False) = [ [ [4.] ], [ [0.04] ] ]

Defined in src/operator/tensor/la_op.cc:L730
returns

org.apache.mxnet.NDArrayFuncReturn

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

Multiplication of matrix with its transpose.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, the operator performs the BLAS3 function *syrk*:

*out* = *alpha* \* *A* \* *A*\ :sup:T

if *transpose=False*, or

*out* = *alpha* \* *A*\ :sup:T \ \* *A*

if *transpose=True*.

If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix multiply
A = [ [1., 2., 3.], [4., 5., 6.] ]
syrk(A, alpha=1., transpose=False)
= [ [14., 32.],
[32., 77.] ]
syrk(A, alpha=1., transpose=True)
= [ [17., 22., 27.],
[22., 29., 36.],
[27., 36., 45.] ]

Batch matrix multiply
A = [ [ [1., 1.] ], [ [0.1, 0.1] ] ]
syrk(A, alpha=2., transpose=False) = [ [ [4.] ], [ [0.04] ] ]

Defined in src/operator/tensor/la_op.cc:L730
returns

org.apache.mxnet.NDArrayFuncReturn

293. #### abstract def linalg_trmm(args: Any*): NDArrayFuncReturn

Performs multiplication with a lower triangular matrix.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape

If *n=2*, *A* must be triangular. The operator performs the BLAS3 function
*trmm*:

*out* = *alpha* \* *op*\ (*A*) \* *B*

if *rightside=False*, or

*out* = *alpha* \* *B* \* *op*\ (*A*)

if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
identity or the matrix transposition (depending on *transpose*).

If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single triangular matrix multiply
A = [ [1.0, 0], [1.0, 1.0] ]
B = [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ]
trmm(A, B, alpha=2.0) = [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ]

Batch triangular matrix multiply
A = [ [ [1.0, 0], [1.0, 1.0] ], [ [1.0, 0], [1.0, 1.0] ] ]
B = [ [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ], [ [0.5, 0.5, 0.5], [0.5, 0.5, 0.5] ] ]
trmm(A, B, alpha=2.0) = [ [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ],
[ [1.0, 1.0, 1.0], [2.0, 2.0, 2.0] ] ]

Defined in src/operator/tensor/la_op.cc:L333
returns

org.apache.mxnet.NDArrayFuncReturn

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

Performs multiplication with a lower triangular matrix.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape

If *n=2*, *A* must be triangular. The operator performs the BLAS3 function
*trmm*:

*out* = *alpha* \* *op*\ (*A*) \* *B*

if *rightside=False*, or

*out* = *alpha* \* *B* \* *op*\ (*A*)

if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
identity or the matrix transposition (depending on *transpose*).

If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single triangular matrix multiply
A = [ [1.0, 0], [1.0, 1.0] ]
B = [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ]
trmm(A, B, alpha=2.0) = [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ]

Batch triangular matrix multiply
A = [ [ [1.0, 0], [1.0, 1.0] ], [ [1.0, 0], [1.0, 1.0] ] ]
B = [ [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ], [ [0.5, 0.5, 0.5], [0.5, 0.5, 0.5] ] ]
trmm(A, B, alpha=2.0) = [ [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ],
[ [1.0, 1.0, 1.0], [2.0, 2.0, 2.0] ] ]

Defined in src/operator/tensor/la_op.cc:L333
returns

org.apache.mxnet.NDArrayFuncReturn

295. #### abstract def linalg_trsm(args: Any*): NDArrayFuncReturn

Solves matrix equation involving a lower triangular matrix.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape

If *n=2*, *A* must be triangular. The operator performs the BLAS3 function
*trsm*, solving for *out* in:

*op*\ (*A*) \* *out* = *alpha* \* *B*

if *rightside=False*, or

*out* \* *op*\ (*A*) = *alpha* \* *B*

if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
identity or the matrix transposition (depending on *transpose*).

If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix solve
A = [ [1.0, 0], [1.0, 1.0] ]
B = [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ]
trsm(A, B, alpha=0.5) = [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ]

Batch matrix solve
A = [ [ [1.0, 0], [1.0, 1.0] ], [ [1.0, 0], [1.0, 1.0] ] ]
B = [ [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ],
[ [4.0, 4.0, 4.0], [8.0, 8.0, 8.0] ] ]
trsm(A, B, alpha=0.5) = [ [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ],
[ [2.0, 2.0, 2.0], [2.0, 2.0, 2.0] ] ]

Defined in src/operator/tensor/la_op.cc:L396
returns

org.apache.mxnet.NDArrayFuncReturn

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

Solves matrix equation involving a lower triangular matrix.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape

If *n=2*, *A* must be triangular. The operator performs the BLAS3 function
*trsm*, solving for *out* in:

*op*\ (*A*) \* *out* = *alpha* \* *B*

if *rightside=False*, or

*out* \* *op*\ (*A*) = *alpha* \* *B*

if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
identity or the matrix transposition (depending on *transpose*).

If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs
(batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix solve
A = [ [1.0, 0], [1.0, 1.0] ]
B = [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ]
trsm(A, B, alpha=0.5) = [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ]

Batch matrix solve
A = [ [ [1.0, 0], [1.0, 1.0] ], [ [1.0, 0], [1.0, 1.0] ] ]
B = [ [ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ],
[ [4.0, 4.0, 4.0], [8.0, 8.0, 8.0] ] ]
trsm(A, B, alpha=0.5) = [ [ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ],
[ [2.0, 2.0, 2.0], [2.0, 2.0, 2.0] ] ]

Defined in src/operator/tensor/la_op.cc:L396
returns

org.apache.mxnet.NDArrayFuncReturn

297. #### abstract def log(args: Any*): NDArrayFuncReturn

Returns element-wise Natural logarithmic value of the input.

The natural logarithm is logarithm in base *e*, so that log(exp(x)) = x

The storage type of log output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise Natural logarithmic value of the input.

The natural logarithm is logarithm in base *e*, so that log(exp(x)) = x

The storage type of log output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L77
returns

org.apache.mxnet.NDArrayFuncReturn

299. #### abstract def log10(args: Any*): NDArrayFuncReturn

Returns element-wise Base-10 logarithmic value of the input.

10**log10(x) = x

The storage type of log10 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L94
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise Base-10 logarithmic value of the input.

10**log10(x) = x

The storage type of log10 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L94
returns

org.apache.mxnet.NDArrayFuncReturn

301. #### abstract def log1p(args: Any*): NDArrayFuncReturn

Returns element-wise log(1 + x) value of the input.

This function is more accurate than log(1 + x)  for small x so that
:math:1+x\approx 1

The storage type of log1p output depends upon the input storage type:

- log1p(default) = default
- log1p(row_sparse) = row_sparse
- log1p(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L199
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise log(1 + x) value of the input.

This function is more accurate than log(1 + x)  for small x so that
:math:1+x\approx 1

The storage type of log1p output depends upon the input storage type:

- log1p(default) = default
- log1p(row_sparse) = row_sparse
- log1p(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L199
returns

org.apache.mxnet.NDArrayFuncReturn

303. #### abstract def log2(args: Any*): NDArrayFuncReturn

Returns element-wise Base-2 logarithmic value of the input.

2**log2(x) = x

The storage type of log2 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns element-wise Base-2 logarithmic value of the input.

2**log2(x) = x

The storage type of log2 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L106
returns

org.apache.mxnet.NDArrayFuncReturn

305. #### abstract def log_softmax(args: Any*): NDArrayFuncReturn

Computes the log softmax of the input.
This is equivalent to computing softmax followed by log.

Examples::

>>> x = mx.nd.array([1, 2, .1])
>>> mx.nd.log_softmax(x).asnumpy()
array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)

>>> x = mx.nd.array( [ [1, 2, .1],[.1, 2, 1] ] )
>>> mx.nd.log_softmax(x, axis=0).asnumpy()
array([ [-0.34115392, -0.69314718, -1.24115396],
[-1.24115396, -0.69314718, -0.34115392] ], dtype=float32)
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the log softmax of the input.
This is equivalent to computing softmax followed by log.

Examples::

>>> x = mx.nd.array([1, 2, .1])
>>> mx.nd.log_softmax(x).asnumpy()
array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)

>>> x = mx.nd.array( [ [1, 2, .1],[.1, 2, 1] ] )
>>> mx.nd.log_softmax(x, axis=0).asnumpy()
array([ [-0.34115392, -0.69314718, -1.24115396],
[-1.24115396, -0.69314718, -0.34115392] ], dtype=float32)
returns

org.apache.mxnet.NDArrayFuncReturn

307. #### abstract def logical_not(args: Any*): NDArrayFuncReturn

Returns the result of logical NOT (!) function

Example:
logical_not([-2., 0., 1.]) = [0., 1., 0.]
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns the result of logical NOT (!) function

Example:
logical_not([-2., 0., 1.]) = [0., 1., 0.]
returns

org.apache.mxnet.NDArrayFuncReturn

309. #### abstract def make_loss(args: Any*): NDArrayFuncReturn

Make your own loss function in network construction.

This operator accepts a customized loss function symbol as a terminal loss and
the symbol should be an operator with no backward dependency.
The output of this function is the gradient of loss with respect to the input data.

For example, if you are a making a cross entropy loss function. Assume out is the
predicted output and label is the true label, then the cross entropy can be defined as::

cross_entropy = label * log(out) + (1 - label) * log(1 - out)
loss = make_loss(cross_entropy)

We will need to use make_loss when we are creating our own loss function or we want to
combine multiple loss functions. Also we may want to stop some variables' gradients
from backpropagation. See more detail in BlockGrad or stop_gradient.

The storage type of make_loss output depends upon the input storage type:

- make_loss(default) = default
- make_loss(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L358
returns

org.apache.mxnet.NDArrayFuncReturn

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

Make your own loss function in network construction.

This operator accepts a customized loss function symbol as a terminal loss and
the symbol should be an operator with no backward dependency.
The output of this function is the gradient of loss with respect to the input data.

For example, if you are a making a cross entropy loss function. Assume out is the
predicted output and label is the true label, then the cross entropy can be defined as::

cross_entropy = label * log(out) + (1 - label) * log(1 - out)
loss = make_loss(cross_entropy)

We will need to use make_loss when we are creating our own loss function or we want to
combine multiple loss functions. Also we may want to stop some variables' gradients
from backpropagation. See more detail in BlockGrad or stop_gradient.

The storage type of make_loss output depends upon the input storage type:

- make_loss(default) = default
- make_loss(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L358
returns

org.apache.mxnet.NDArrayFuncReturn

311. #### abstract def max(args: Any*): NDArrayFuncReturn

Computes the max of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the max of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
returns

org.apache.mxnet.NDArrayFuncReturn

313. #### abstract def max_axis(args: Any*): NDArrayFuncReturn

Computes the max of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the max of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
returns

org.apache.mxnet.NDArrayFuncReturn

315. #### abstract def mean(args: Any*): NDArrayFuncReturn

Computes the mean of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L84
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the mean of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L84
returns

org.apache.mxnet.NDArrayFuncReturn

317. #### abstract def min(args: Any*): NDArrayFuncReturn

Computes the min of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the min of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
returns

org.apache.mxnet.NDArrayFuncReturn

319. #### abstract def min_axis(args: Any*): NDArrayFuncReturn

Computes the min of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the min of array elements over given axes.

Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
returns

org.apache.mxnet.NDArrayFuncReturn

321. #### abstract def moments(args: Any*): NDArrayFuncReturn

Calculate the mean and variance of data.

The mean and variance are calculated by aggregating the contents of data across axes.
If x is 1-D and axes = [0] this is just the mean and variance of a vector.

Example:

x = [ [1, 2, 3], [4, 5, 6] ]
mean, var = moments(data=x, axes=[0])
mean = [2.5, 3.5, 4.5]
var = [2.25, 2.25, 2.25]
mean, var = moments(data=x, axes=[1])
mean = [2.0, 5.0]
var = [0.66666667, 0.66666667]
mean, var = moments(data=x, axis=[0, 1])
mean = [3.5]
var = [2.9166667]

Defined in src/operator/nn/moments.cc:L54
returns

org.apache.mxnet.NDArrayFuncReturn

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

Calculate the mean and variance of data.

The mean and variance are calculated by aggregating the contents of data across axes.
If x is 1-D and axes = [0] this is just the mean and variance of a vector.

Example:

x = [ [1, 2, 3], [4, 5, 6] ]
mean, var = moments(data=x, axes=[0])
mean = [2.5, 3.5, 4.5]
var = [2.25, 2.25, 2.25]
mean, var = moments(data=x, axes=[1])
mean = [2.0, 5.0]
var = [0.66666667, 0.66666667]
mean, var = moments(data=x, axis=[0, 1])
mean = [3.5]
var = [2.9166667]

Defined in src/operator/nn/moments.cc:L54
returns

org.apache.mxnet.NDArrayFuncReturn

323. #### abstract def mp_lamb_update_phase1(args: Any*): NDArrayFuncReturn

Mixed Precision version of Phase I of lamb update
it performs the following operations and returns g:.

.. math::
\begin{gather*}
then
then

mean = beta1 * mean + (1 - beta1) * grad;
variance = beta2 * variance + (1. - beta2) * grad ^ 2;

if (bias_correction)
then
mean_hat = mean / (1. - beta1^t);
var_hat = var / (1 - beta2^t);
g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight32;
else
g = mean / (var_data^(1/2) + epsilon) + wd * weight32;
\end{gather*}

Defined in src/operator/optimizer_op.cc:L1033
returns

org.apache.mxnet.NDArrayFuncReturn

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

Mixed Precision version of Phase I of lamb update
it performs the following operations and returns g:.

.. math::
\begin{gather*}
then
then

mean = beta1 * mean + (1 - beta1) * grad;
variance = beta2 * variance + (1. - beta2) * grad ^ 2;

if (bias_correction)
then
mean_hat = mean / (1. - beta1^t);
var_hat = var / (1 - beta2^t);
g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight32;
else
g = mean / (var_data^(1/2) + epsilon) + wd * weight32;
\end{gather*}

Defined in src/operator/optimizer_op.cc:L1033
returns

org.apache.mxnet.NDArrayFuncReturn

325. #### abstract def mp_lamb_update_phase2(args: Any*): NDArrayFuncReturn

Mixed Precision version Phase II of lamb update

.. math::
\begin{gather*}
if (lower_bound >= 0)
then
r1 = max(r1, lower_bound)
if (upper_bound >= 0)
then
r1 = max(r1, upper_bound)

if (r1 == 0 or r2 == 0)
then
lr = lr
else
lr = lr * (r1/r2)
weight32 = weight32 - lr * g
weight(float16) = weight32
\end{gather*}

Defined in src/operator/optimizer_op.cc:L1075
returns

org.apache.mxnet.NDArrayFuncReturn

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

Mixed Precision version Phase II of lamb update

.. math::
\begin{gather*}
if (lower_bound >= 0)
then
r1 = max(r1, lower_bound)
if (upper_bound >= 0)
then
r1 = max(r1, upper_bound)

if (r1 == 0 or r2 == 0)
then
lr = lr
else
lr = lr * (r1/r2)
weight32 = weight32 - lr * g
weight(float16) = weight32
\end{gather*}

Defined in src/operator/optimizer_op.cc:L1075
returns

org.apache.mxnet.NDArrayFuncReturn

327. #### abstract def mp_nag_mom_update(args: Any*): NDArrayFuncReturn

Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.

Defined in src/operator/optimizer_op.cc:L745
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.

Defined in src/operator/optimizer_op.cc:L745
returns

org.apache.mxnet.NDArrayFuncReturn

329. #### abstract def mp_sgd_mom_update(args: Any*): NDArrayFuncReturn

Updater function for multi-precision sgd optimizer
returns

org.apache.mxnet.NDArrayFuncReturn

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

Updater function for multi-precision sgd optimizer
returns

org.apache.mxnet.NDArrayFuncReturn

331. #### abstract def mp_sgd_update(args: Any*): NDArrayFuncReturn

Updater function for multi-precision sgd optimizer
returns

org.apache.mxnet.NDArrayFuncReturn

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

Updater function for multi-precision sgd optimizer
returns

org.apache.mxnet.NDArrayFuncReturn

333. #### abstract def multi_all_finite(args: Any*): NDArrayFuncReturn

Check if all the float numbers in all the arrays are finite (used for AMP)

Defined in src/operator/contrib/all_finite.cc:L133
returns

org.apache.mxnet.NDArrayFuncReturn

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

Check if all the float numbers in all the arrays are finite (used for AMP)

Defined in src/operator/contrib/all_finite.cc:L133
returns

org.apache.mxnet.NDArrayFuncReturn

335. #### abstract def multi_lars(args: Any*): NDArrayFuncReturn

Compute the LARS coefficients of multiple weights and grads from their sums of square"

Defined in src/operator/contrib/multi_lars.cc:L37
returns

org.apache.mxnet.NDArrayFuncReturn

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

Compute the LARS coefficients of multiple weights and grads from their sums of square"

Defined in src/operator/contrib/multi_lars.cc:L37
returns

org.apache.mxnet.NDArrayFuncReturn

337. #### abstract def multi_mp_sgd_mom_update(args: Any*): NDArrayFuncReturn

Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L472
returns

org.apache.mxnet.NDArrayFuncReturn

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

Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L472
returns

org.apache.mxnet.NDArrayFuncReturn

339. #### abstract def multi_mp_sgd_update(args: Any*): NDArrayFuncReturn

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/optimizer_op.cc:L417
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/optimizer_op.cc:L417
returns

org.apache.mxnet.NDArrayFuncReturn

341. #### abstract def multi_sgd_mom_update(args: Any*): NDArrayFuncReturn

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L374
returns

org.apache.mxnet.NDArrayFuncReturn

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

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L374
returns

org.apache.mxnet.NDArrayFuncReturn

343. #### abstract def multi_sgd_update(args: Any*): NDArrayFuncReturn

Update function for Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/optimizer_op.cc:L329
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/optimizer_op.cc:L329
returns

org.apache.mxnet.NDArrayFuncReturn

345. #### abstract def multi_sum_sq(args: Any*): NDArrayFuncReturn

Compute the sums of squares of multiple arrays

Defined in src/operator/contrib/multi_sum_sq.cc:L36
returns

org.apache.mxnet.NDArrayFuncReturn

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

Compute the sums of squares of multiple arrays

Defined in src/operator/contrib/multi_sum_sq.cc:L36
returns

org.apache.mxnet.NDArrayFuncReturn

347. #### abstract def nag_mom_update(args: Any*): NDArrayFuncReturn

Update function for Nesterov Accelerated Gradient( NAG) optimizer.
It updates the weights using the following formula,

.. math::
v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\
W_t = W_{t-1} - v_t

Where
:math:\eta is the learning rate of the optimizer
:math:\gamma is the decay rate of the momentum estimate
:math:\v_t is the update vector at time step t
:math:\W_t is the weight vector at time step t

Defined in src/operator/optimizer_op.cc:L726
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for Nesterov Accelerated Gradient( NAG) optimizer.
It updates the weights using the following formula,

.. math::
v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\
W_t = W_{t-1} - v_t

Where
:math:\eta is the learning rate of the optimizer
:math:\gamma is the decay rate of the momentum estimate
:math:\v_t is the update vector at time step t
:math:\W_t is the weight vector at time step t

Defined in src/operator/optimizer_op.cc:L726
returns

org.apache.mxnet.NDArrayFuncReturn

349. #### abstract def nanprod(args: Any*): NDArrayFuncReturn

Computes the product of array elements over given axes treating Not a Numbers (NaN) as one.

Defined in src/operator/tensor/broadcast_reduce_prod_value.cc:L47
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the product of array elements over given axes treating Not a Numbers (NaN) as one.

Defined in src/operator/tensor/broadcast_reduce_prod_value.cc:L47
returns

org.apache.mxnet.NDArrayFuncReturn

351. #### abstract def nansum(args: Any*): NDArrayFuncReturn

Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero.

Defined in src/operator/tensor/broadcast_reduce_sum_value.cc:L102
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero.

Defined in src/operator/tensor/broadcast_reduce_sum_value.cc:L102
returns

org.apache.mxnet.NDArrayFuncReturn

353. #### abstract def negative(args: Any*): NDArrayFuncReturn

Numerical negative of the argument, element-wise.

The storage type of negative output depends upon the input storage type:

- negative(default) = default
- negative(row_sparse) = row_sparse
- negative(csr) = csr
returns

org.apache.mxnet.NDArrayFuncReturn

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

Numerical negative of the argument, element-wise.

The storage type of negative output depends upon the input storage type:

- negative(default) = default
- negative(row_sparse) = row_sparse
- negative(csr) = csr
returns

org.apache.mxnet.NDArrayFuncReturn

355. #### abstract def norm(args: Any*): NDArrayFuncReturn

Computes the norm on an NDArray.

This operator computes the norm on an NDArray with the specified axis, depending
on the value of the ord parameter. By default, it computes the L2 norm on the entire
array. Currently only ord=2 supports sparse ndarrays.

Examples::

x = [ [ [1, 2],
[3, 4] ],
[ [2, 2],
[5, 6] ] ]

norm(x, ord=2, axis=1) = [ [3.1622777 4.472136 ]
[5.3851647 6.3245554] ]

norm(x, ord=1, axis=1) = [ [4., 6.],
[7., 8.] ]

rsp = x.cast_storage('row_sparse')

norm(rsp) = [5.47722578]

csr = x.cast_storage('csr')

norm(csr) = [5.47722578]

Defined in src/operator/tensor/broadcast_reduce_norm_value.cc:L89
returns

org.apache.mxnet.NDArrayFuncReturn

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

Computes the norm on an NDArray.

This operator computes the norm on an NDArray with the specified axis, depending
on the value of the ord parameter. By default, it computes the L2 norm on the entire
array. Currently only ord=2 supports sparse ndarrays.

Examples::

x = [ [ [1, 2],
[3, 4] ],
[ [2, 2],
[5, 6] ] ]

norm(x, ord=2, axis=1) = [ [3.1622777 4.472136 ]
[5.3851647 6.3245554] ]

norm(x, ord=1, axis=1) = [ [4., 6.],
[7., 8.] ]

rsp = x.cast_storage('row_sparse')

norm(rsp) = [5.47722578]

csr = x.cast_storage('csr')

norm(csr) = [5.47722578]

Defined in src/operator/tensor/broadcast_reduce_norm_value.cc:L89
returns

org.apache.mxnet.NDArrayFuncReturn

357. #### abstract def normal(args: Any*): NDArrayFuncReturn

Draw random samples from a normal (Gaussian) distribution.

.. note:: The existing alias normal is deprecated.

Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale*
(standard deviation).

Example::

normal(loc=0, scale=1, shape=(2,2)) = [ [ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114] ]

Defined in src/operator/random/sample_op.cc:L113
returns

org.apache.mxnet.NDArrayFuncReturn

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

Draw random samples from a normal (Gaussian) distribution.

.. note:: The existing alias normal is deprecated.

Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale*
(standard deviation).

Example::

normal(loc=0, scale=1, shape=(2,2)) = [ [ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114] ]

Defined in src/operator/random/sample_op.cc:L113
returns

org.apache.mxnet.NDArrayFuncReturn

359. #### abstract def one_hot(args: Any*): NDArrayFuncReturn

Returns a one-hot array.

The locations represented by indices take value on_value, while all
other locations take value off_value.

one_hot operation with indices of shape (i0, i1) and depth  of d would result
in an output array of shape (i0, i1, d) with::

output[i,j,:] = off_value
output[i,j,indices[i,j] ] = on_value

Examples::

one_hot([1,0,2,0], 3) = [ [ 0.  1.  0.]
[ 1.  0.  0.]
[ 0.  0.  1.]
[ 1.  0.  0.] ]

one_hot([1,0,2,0], 3, on_value=8, off_value=1,
dtype='int32') = [ [1 8 1]
[8 1 1]
[1 1 8]
[8 1 1] ]

one_hot([ [1,0],[1,0],[2,0] ], 3) = [ [ [ 0.  1.  0.]
[ 1.  0.  0.] ]

[ [ 0.  1.  0.]
[ 1.  0.  0.] ]

[ [ 0.  0.  1.]
[ 1.  0.  0.] ] ]

Defined in src/operator/tensor/indexing_op.cc:L883
returns

org.apache.mxnet.NDArrayFuncReturn

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

Returns a one-hot array.

The locations represented by indices take value on_value, while all
other locations take value off_value.

one_hot operation with indices of shape (i0, i1) and depth  of d would result
in an output array of shape (i0, i1, d) with::

output[i,j,:] = off_value
output[i,j,indices[i,j] ] = on_value

Examples::

one_hot([1,0,2,0], 3) = [ [ 0.  1.  0.]
[ 1.  0.  0.]
[ 0.  0.  1.]
[ 1.  0.  0.] ]

one_hot([1,0,2,0], 3, on_value=8, off_value=1,
dtype='int32') = [ [1 8 1]
[8 1 1]
[1 1 8]
[8 1 1] ]

one_hot([ [1,0],[1,0],[2,0] ], 3) = [ [ [ 0.  1.  0.]
[ 1.  0.  0.] ]

[ [ 0.  1.  0.]
[ 1.  0.  0.] ]

[ [ 0.  0.  1.]
[ 1.  0.  0.] ] ]

Defined in src/operator/tensor/indexing_op.cc:L883
returns

org.apache.mxnet.NDArrayFuncReturn

361. #### abstract def ones_like(args: Any*): NDArrayFuncReturn

Return an array of ones with the same shape and type
as the input array.

Examples::

x = [ [ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

ones_like(x) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]
returns

org.apache.mxnet.NDArrayFuncReturn

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

Return an array of ones with the same shape and type
as the input array.

Examples::

x = [ [ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

ones_like(x) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]
returns

org.apache.mxnet.NDArrayFuncReturn

363. #### abstract def pad(args: Any*): NDArrayFuncReturn

Pads an input array with a constant or edge values of the array.

.. note:: Pad is deprecated. Use pad instead.

.. note:: Current implementation only supports 4D and 5D input arrays with padding applied
only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.

This operation pads an input array with either a constant_value or edge values
along each axis of the input array. The amount of padding is specified by pad_width.

pad_width is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N). The pad_width should be of length 2*N
where N is the number of dimensions of the array.

For dimension N of the input array, before_N and after_N indicates how many values
to add before and after the elements of the array along dimension N.
The widths of the higher two dimensions before_1, after_1, before_2,
after_2 must be 0.

Example::

x = [ [[ [  1.   2.   3.]
[  4.   5.   6.] ]

[ [  7.   8.   9.]
[ 10.  11.  12.] ] ]

[ [ [ 11.  12.  13.]
[ 14.  15.  16.] ]

[ [ 17.  18.  19.]
[ 20.  21.  22.] ] ] ]

[ [[ [  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.] ] ] ]

[ [[ [  0.   0.   0.   0.   0.]
[  0.   1.   2.   3.   0.]
[  0.   4.   5.   6.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.   7.   8.   9.   0.]
[  0.  10.  11.  12.   0.]
[  0.   0.   0.   0.   0.] ] ]

[ [ [  0.   0.   0.   0.   0.]
[  0.  11.  12.  13.   0.]
[  0.  14.  15.  16.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.  17.  18.  19.   0.]
[  0.  20.  21.  22.   0.]
[  0.   0.   0.   0.   0.] ] ] ]

Defined in src/operator/pad.cc:L766
returns

org.apache.mxnet.NDArrayFuncReturn

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

Pads an input array with a constant or edge values of the array.

.. note:: Pad is deprecated. Use pad instead.

.. note:: Current implementation only supports 4D and 5D input arrays with padding applied
only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.

This operation pads an input array with either a constant_value or edge values
along each axis of the input array. The amount of padding is specified by pad_width.

pad_width is a tuple of integer padding widths for each axis of the format
(before_1, after_1, ... , before_N, after_N). The pad_width should be of length 2*N
where N is the number of dimensions of the array.

For dimension N of the input array, before_N and after_N indicates how many values
to add before and after the elements of the array along dimension N.
The widths of the higher two dimensions before_1, after_1, before_2,
after_2 must be 0.

Example::

x = [ [[ [  1.   2.   3.]
[  4.   5.   6.] ]

[ [  7.   8.   9.]
[ 10.  11.  12.] ] ]

[ [ [ 11.  12.  13.]
[ 14.  15.  16.] ]

[ [ 17.  18.  19.]
[ 20.  21.  22.] ] ] ]

[ [[ [  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.] ] ] ]

[ [[ [  0.   0.   0.   0.   0.]
[  0.   1.   2.   3.   0.]
[  0.   4.   5.   6.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.   7.   8.   9.   0.]
[  0.  10.  11.  12.   0.]
[  0.   0.   0.   0.   0.] ] ]

[ [ [  0.   0.   0.   0.   0.]
[  0.  11.  12.  13.   0.]
[  0.  14.  15.  16.   0.]
[  0.   0.   0.   0.   0.] ]

[ [  0.   0.   0.   0.   0.]
[  0.  17.  18.  19.   0.]
[  0.  20.  21.  22.   0.]
[  0.   0.   0.   0.   0.] ] ] ]

Defined in src/operator/pad.cc:L766
returns

org.apache.mxnet.NDArrayFuncReturn

365. #### abstract def pick(args: Any*): NDArrayFuncReturn

Picks elements from an input array according to the input indices along the given axis.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

By default, if any index mentioned is too large, it is replaced by the index that addresses
the last element along an axis (the clip mode).

This function supports n-dimensional input and (n-1)-dimensional indices arrays.

Examples::

x = [ [ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.] ]

// picks elements with specified indices along axis 0
pick(x, y=[0,1], 0) = [ 1.,  4.]

// picks elements with specified indices along axis 1
pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]

// 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:L151
returns

org.apache.mxnet.NDArrayFuncReturn

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

Picks elements from an input array according to the input indices along the given axis.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

By default, if any index mentioned is too large, it is replaced by the index that addresses
the last element along an axis (the clip mode).

This function supports n-dimensional input and (n-1)-dimensional indices arrays.

Examples::

x = [ [ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.] ]

// picks elements with specified indices along axis 0
pick(x, y=[0,1], 0) = [ 1.,  4.]

// picks elements with specified indices along axis 1
pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]

// 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:L151
returns

org.apache.mxnet.NDArrayFuncReturn

367. #### abstract def preloaded_multi_mp_sgd_mom_update(args: Any*): NDArrayFuncReturn

Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/contrib/preloaded_multi_sgd.cc:L200
returns

org.apache.mxnet.NDArrayFuncReturn

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

Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/contrib/preloaded_multi_sgd.cc:L200
returns

org.apache.mxnet.NDArrayFuncReturn

369. #### abstract def preloaded_multi_mp_sgd_update(args: Any*): NDArrayFuncReturn

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/contrib/preloaded_multi_sgd.cc:L140
returns

org.apache.mxnet.NDArrayFuncReturn

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

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/contrib/preloaded_multi_sgd.cc:L140
returns

org.apache.mxnet.NDArrayFuncReturn

371. #### abstract def preloaded_multi_sgd_mom_update(args: Any*): NDArrayFuncReturn

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/contrib/preloaded_multi_sgd.cc:L91
returns

org.apache.mxnet.NDArrayFuncReturn

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

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

Where the parameter momentum is the decay rate of momentum estimates at