# SymbolBase

### Related Doc: package mxnet

#### abstract class SymbolBase extends AnyRef

Linear Supertypes
AnyRef, Any
Known Subclasses
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. SymbolBase
2. AnyRef
3. Any
1. Hide All
2. Show all
Visibility
1. Public
2. All

### Abstract Value Members

1. #### abstract def Activation(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies an activation function element-wise to the input.

The following activation functions are supported:

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

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

org.apache.mxnet.Symbol

2. #### abstract def BatchNorm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Batch normalization.

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

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

.. math::

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

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

.. math::

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

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

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

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

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

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

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

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

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

Defined in src/operator/nn/batch_norm.cc:L591
returns

org.apache.mxnet.Symbol

3. #### abstract def BatchNorm_v1(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Batch normalization.

This operator is DEPRECATED. Perform BatchNorm on the input.

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

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

.. math::

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

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

.. math::

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

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

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

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

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

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

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

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

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

org.apache.mxnet.Symbol

4. #### abstract def BilinearSampler(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies bilinear sampling to input feature map.

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

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

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

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

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

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

Example 1::

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

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

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

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

out = BilinearSampler(data, grid)

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

Example 2::

## shift data horizontally by -1 pixel

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

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

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

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

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

org.apache.mxnet.Symbol

5. #### abstract def BlockGrad(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

6. #### abstract def CTCLoss(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

7. #### abstract def Cast(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Casts all elements of the input to a new type.

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

Example::

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

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

org.apache.mxnet.Symbol

8. #### abstract def Concat(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Joins input arrays along a given axis.

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

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

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

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

Example::

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

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

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

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

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

org.apache.mxnet.Symbol

9. #### abstract def Convolution(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

.. math::

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

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

For general 2-D convolution, the shapes are

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

Define::

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

then we have::

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:L469
returns

org.apache.mxnet.Symbol

10. #### abstract def Convolution_v1(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

org.apache.mxnet.Symbol

11. #### abstract def Correlation(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies correlation to inputs.

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

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

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

.. math::

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

12. #### abstract def Crop(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

org.apache.mxnet.Symbol

13. #### abstract def Custom(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

14. #### abstract def Deconvolution(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

org.apache.mxnet.Symbol

15. #### abstract def Dropout(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies dropout operation to input array.

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

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

Example::

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

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

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

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

org.apache.mxnet.Symbol

16. #### abstract def ElementWiseSum(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

.. 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.Symbol

17. #### abstract def Embedding(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Maps integer indices to vector representations (embeddings).

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

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

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

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.Symbol

18. #### abstract def Flatten(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

19. #### abstract def FullyConnected(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

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

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

The learnable parameters include both weight and bias.

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

.. Note::

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

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

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

org.apache.mxnet.Symbol

20. #### abstract def GridGenerator(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Generates 2D sampling grid for bilinear sampling.
returns

org.apache.mxnet.Symbol

21. #### abstract def GroupNorm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

22. #### abstract def IdentityAttachKLSparseReg(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

org.apache.mxnet.Symbol

23. #### abstract def InstanceNorm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies instance normalization to the n-dimensional input array.

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

.. math::

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

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

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

This implementation is based on 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.Symbol

24. #### abstract def L2Normalization(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Normalize the input array using the L2 norm.

For 1-D NDArray, it computes::

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

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

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

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

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

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

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

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

Example::

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

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

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

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

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

org.apache.mxnet.Symbol

25. #### abstract def LRN(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies local response normalization to the input.

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

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

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

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

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

org.apache.mxnet.Symbol

26. #### abstract def LayerNorm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Layer normalization.

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

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

.. math::

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

Both gamma and beta are learnable parameters.

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

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

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

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

org.apache.mxnet.Symbol

27. #### abstract def LeakyReLU(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

The following modified ReLU Activation functions are supported:

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

Defined in src/operator/leaky_relu.cc:L161
returns

org.apache.mxnet.Symbol

28. #### abstract def LinearRegressionOutput(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

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

The storage type of label can be default or csr

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

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

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

org.apache.mxnet.Symbol

29. #### abstract def LogisticRegressionOutput(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies a logistic function to the input.

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

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

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

The storage type of label can be default or csr

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

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.Symbol

30. #### abstract def MAERegressionOutput(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes mean absolute error of the input.

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

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

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

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

The storage type of label can be default or csr

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

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

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

org.apache.mxnet.Symbol

31. #### abstract def MakeLoss(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Make your own loss function in network construction.

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

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

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

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

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

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

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

org.apache.mxnet.Symbol

32. #### abstract def Pad(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

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

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

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

Example::

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

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

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

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

[ [[ [  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.] ] ] ]

returns

org.apache.mxnet.Symbol

33. #### abstract def Pooling(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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:L414
returns

org.apache.mxnet.Symbol

34. #### abstract def Pooling_v1(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

This operator is DEPRECATED.
Perform pooling on the input.

The shapes for 2-D pooling is

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

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

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

- **valid** (default)::

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

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

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

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

Three pooling options are supported by pool_type:

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

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

*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.Symbol

35. #### abstract def RNN(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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:L368
returns

org.apache.mxnet.Symbol

36. #### abstract def ROIPooling(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

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

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

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

Example::

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

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

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

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

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

org.apache.mxnet.Symbol

37. #### abstract def Reshape(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

org.apache.mxnet.Symbol

38. #### abstract def SVMOutput(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes support vector machine based transformation of the input.

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

org.apache.mxnet.Symbol

39. #### abstract def SequenceLast(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Takes the last element of a sequence.

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

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

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

Example::

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

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

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

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

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

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

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

org.apache.mxnet.Symbol

40. #### abstract def SequenceMask(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Sets all elements outside the sequence to a constant value.

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

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

Example::

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

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

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

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

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

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

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

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

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

returns

org.apache.mxnet.Symbol

41. #### abstract def SequenceReverse(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Reverses the elements of each sequence.

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

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

Example::

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

org.apache.mxnet.Symbol

42. #### abstract def SliceChannel(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

Example::

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

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

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

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

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

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

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

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

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

Example::

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

[ [ 3.]
[ 4.] ]

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

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

org.apache.mxnet.Symbol

43. #### abstract def Softmax(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

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

- Softmax Function:

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

- Cross Entropy Function:

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

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

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

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

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

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

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

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

Example::

data = [ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ] ]
[ [ 0.    0.    0.    0.  ]
[-0.75  0.25  0.25  0.25]
[ 0.25  0.25 -0.75  0.25]
[ 0.25  0.25  0.25 -0.75] ]
## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.

- The parameter grad_scale can be used to rescale the gradient, which is often used to
give each loss function different weights.

- This operator also supports various ways to normalize the gradient by normalization,
The normalization is applied if softmax output has different shape than the labels.
The normalization mode can be set to the followings:

- 'null': do nothing.
- 'batch': divide the gradient by the batch size.
- 'valid': divide the gradient by the number of instances which are not ignored.

Defined in src/operator/softmax_output.cc:L231
returns

org.apache.mxnet.Symbol

44. #### abstract def SoftmaxActivation(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

.. note::

This operator has been deprecated, please use softmax.

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

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

Example::

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

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

org.apache.mxnet.Symbol

45. #### abstract def SoftmaxOutput(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

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

- Softmax Function:

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

- Cross Entropy Function:

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

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

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

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

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

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

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

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

Example::

data = [ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[ [ 0.0320586   0.08714432  0.23688284  0.64391428]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ] ]
[ [ 0.    0.    0.    0.  ]
[-0.75  0.25  0.25  0.25]
[ 0.25  0.25 -0.75  0.25]
[ 0.25  0.25  0.25 -0.75] ]
## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.

- The parameter grad_scale can be used to rescale the gradient, which is often used to
give each loss function different weights.

- This operator also supports various ways to normalize the gradient by normalization,
The normalization is applied if softmax output has different shape than the labels.
The normalization mode can be set to the followings:

- 'null': do nothing.
- 'batch': divide the gradient by the batch size.
- 'valid': divide the gradient by the number of instances which are not ignored.

Defined in src/operator/softmax_output.cc:L231
returns

org.apache.mxnet.Symbol

46. #### abstract def SpatialTransformer(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies a spatial transformer to input feature map.
returns

org.apache.mxnet.Symbol

47. #### abstract def SwapAxis(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Interchanges two axes of an array.

Examples::

x = [ [1, 2, 3] ])
swapaxes(x, 0, 1) = [ [ 1],
[ 2],
[ 3] ]

x = [ [ [ 0, 1],
[ 2, 3] ],
[ [ 4, 5],
[ 6, 7] ] ]  // (2,2,2) array

swapaxes(x, 0, 2) = [ [ [ 0, 4],
[ 2, 6] ],
[ [ 1, 5],
[ 3, 7] ] ]

Defined in src/operator/swapaxis.cc:L70
returns

org.apache.mxnet.Symbol

48. #### abstract def UpSampling(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

49. #### abstract def abs(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise absolute value of the input.

Example::

abs([-2, 0, 3]) = [2, 0, 3]

The storage type of abs output depends upon the input storage type:

- abs(default) = default
- abs(row_sparse) = row_sparse
- abs(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L720
returns

org.apache.mxnet.Symbol

50. #### abstract def adam_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

51. #### abstract def add_n(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

.. 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.Symbol

52. #### abstract def all_finite(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

53. #### abstract def amp_cast(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

54. #### abstract def amp_multicast(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

55. #### abstract def arccos(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise inverse cosine of the input array.

The input should be in range [-1, 1].
The output is in the closed interval :math:[0, \pi]

.. math::
arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]

The storage type of arccos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L233
returns

org.apache.mxnet.Symbol

56. #### abstract def arccosh(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the element-wise inverse hyperbolic cosine of the input array, \
computed element-wise.

The storage type of arccosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L535
returns

org.apache.mxnet.Symbol

57. #### abstract def arcsin(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise inverse sine of the input array.

The input should be in the range [-1, 1].
The output is in the closed interval of [:math:-\pi/2, :math:\pi/2].

.. math::
arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]

The storage type of arcsin output depends upon the input storage type:

- arcsin(default) = default
- arcsin(row_sparse) = row_sparse
- arcsin(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L187
returns

org.apache.mxnet.Symbol

58. #### abstract def arcsinh(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the element-wise inverse hyperbolic sine of the input array, \
computed element-wise.

The storage type of arcsinh output depends upon the input storage type:

- arcsinh(default) = default
- arcsinh(row_sparse) = row_sparse
- arcsinh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L494
returns

org.apache.mxnet.Symbol

59. #### abstract def arctan(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise inverse tangent of the input array.

The output is in the closed interval :math:[-\pi/2, \pi/2]

.. math::
arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]

The storage type of arctan output depends upon the input storage type:

- arctan(default) = default
- arctan(row_sparse) = row_sparse
- arctan(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L282
returns

org.apache.mxnet.Symbol

60. #### abstract def arctanh(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the element-wise inverse hyperbolic tangent of the input array, \
computed element-wise.

The storage type of arctanh output depends upon the input storage type:

- arctanh(default) = default
- arctanh(row_sparse) = row_sparse
- arctanh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L579
returns

org.apache.mxnet.Symbol

61. #### abstract def argmax(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns indices of the maximum values along an axis.

In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

// argmax along axis 0
argmax(x, axis=0) = [ 1.,  1.,  1.]

// argmax along axis 1
argmax(x, axis=1) = [ 2.,  2.]

// argmax along axis 1 keeping same dims as an input array
argmax(x, axis=1, keepdims=True) = [ [ 2.],
[ 2.] ]

returns

org.apache.mxnet.Symbol

62. #### abstract def argmax_channel(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns argmax indices of each channel from the input array.

The result will be an NDArray of shape (num_channel,).

In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

argmax_channel(x) = [ 2.,  2.]

returns

org.apache.mxnet.Symbol

63. #### abstract def argmin(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns indices of the minimum values along an axis.

In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence
are returned.

Examples::

x = [ [ 0.,  1.,  2.],
[ 3.,  4.,  5.] ]

// argmin along axis 0
argmin(x, axis=0) = [ 0.,  0.,  0.]

// argmin along axis 1
argmin(x, axis=1) = [ 0.,  0.]

// argmin along axis 1 keeping same dims as an input array
argmin(x, axis=1, keepdims=True) = [ [ 0.],
[ 0.] ]

returns

org.apache.mxnet.Symbol

64. #### abstract def argsort(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the indices that would sort an input array along the given axis.

This function performs sorting along the given axis and returns an array of indices having same shape
as an input array that index data in sorted order.

Examples::

x = [ [ 0.3,  0.2,  0.4],
[ 0.1,  0.3,  0.2] ]

// sort along axis -1
argsort(x) = [ [ 1.,  0.,  2.],
[ 0.,  2.,  1.] ]

// sort along axis 0
argsort(x, axis=0) = [ [ 1.,  0.,  1.]
[ 0.,  1.,  0.] ]

// flatten and then sort
argsort(x, axis=None) = [ 3.,  1.,  5.,  0.,  4.,  2.]

Defined in src/operator/tensor/ordering_op.cc:L185
returns

org.apache.mxnet.Symbol

65. #### abstract def batch_dot(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Batchwise dot product.

batch_dot is used to compute dot product of x and y when x and
y are data in batch, namely 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.Symbol

66. #### abstract def batch_take(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Takes elements from a data batch.

.. note::
batch_take is deprecated. Use pick instead.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

Examples::

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

// takes elements with specified indices
batch_take(x, [0,1,0]) = [ 1.  4.  5.]

Defined in src/operator/tensor/indexing_op.cc:L836
returns

org.apache.mxnet.Symbol

67. #### abstract def broadcast_add(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise sum of the input arrays with broadcasting.

broadcast_plus is an alias to the function broadcast_add.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_add(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

broadcast_plus(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

returns

org.apache.mxnet.Symbol

68. #### abstract def broadcast_axes(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

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.] ] ]

returns

org.apache.mxnet.Symbol

69. #### abstract def broadcast_axis(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to
(2,8,3,9). Elements will be duplicated on the broadcasted axes.

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.] ] ]

returns

org.apache.mxnet.Symbol

70. #### abstract def broadcast_div(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise division of the input arrays with broadcasting.

Example::

x = [ [ 6.,  6.,  6.],
[ 6.,  6.,  6.] ]

y = [ [ 2.],
[ 3.] ]

broadcast_div(x, y) = [ [ 3.,  3.,  3.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

returns

org.apache.mxnet.Symbol

71. #### abstract def broadcast_equal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **equal to** (==) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_equal(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

returns

org.apache.mxnet.Symbol

72. #### abstract def broadcast_greater(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **greater than** (>) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_greater(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

returns

org.apache.mxnet.Symbol

73. #### abstract def broadcast_greater_equal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_greater_equal(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

returns

org.apache.mxnet.Symbol

74. #### abstract def broadcast_hypot(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.] ]

returns

org.apache.mxnet.Symbol

75. #### abstract def broadcast_lesser(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_lesser(x, y) = [ [ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

returns

org.apache.mxnet.Symbol

76. #### abstract def broadcast_lesser_equal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_lesser_equal(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

returns

org.apache.mxnet.Symbol

77. #### abstract def broadcast_like(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Broadcasts lhs to have the same shape as rhs.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, Broadcasting <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]

returns

org.apache.mxnet.Symbol

78. #### abstract def broadcast_logical_and(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **logical and** with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_logical_and(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

returns

org.apache.mxnet.Symbol

79. #### abstract def broadcast_logical_or(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **logical or** with broadcasting.

Example::

x = [ [ 1.,  1.,  0.],
[ 1.,  1.,  0.] ]

y = [ [ 1.],
[ 0.] ]

broadcast_logical_or(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  0.] ]

returns

org.apache.mxnet.Symbol

80. #### abstract def broadcast_logical_xor(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **logical xor** with broadcasting.

Example::

x = [ [ 1.,  1.,  0.],
[ 1.,  1.,  0.] ]

y = [ [ 1.],
[ 0.] ]

broadcast_logical_xor(x, y) = [ [ 0.,  0.,  1.],
[ 1.,  1.,  0.] ]

returns

org.apache.mxnet.Symbol

81. #### abstract def broadcast_maximum(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise maximum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise maxima.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_maximum(x, y) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

returns

org.apache.mxnet.Symbol

82. #### abstract def broadcast_minimum(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise minimum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise minima.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_maximum(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

returns

org.apache.mxnet.Symbol

83. #### abstract def broadcast_minus(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise difference of the input arrays with broadcasting.

broadcast_minus is an alias to the function broadcast_sub.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_sub(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

broadcast_minus(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Supported sparse operations:

returns

org.apache.mxnet.Symbol

84. #### abstract def broadcast_mod(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise modulo of the input arrays with broadcasting.

Example::

x = [ [ 8.,  8.,  8.],
[ 8.,  8.,  8.] ]

y = [ [ 2.],
[ 3.] ]

broadcast_mod(x, y) = [ [ 0.,  0.,  0.],
[ 2.,  2.,  2.] ]

returns

org.apache.mxnet.Symbol

85. #### abstract def broadcast_mul(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise product of the input arrays with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_mul(x, y) = [ [ 0.,  0.,  0.],
[ 1.,  1.,  1.] ]

Supported sparse operations:

returns

org.apache.mxnet.Symbol

86. #### abstract def broadcast_not_equal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_not_equal(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

returns

org.apache.mxnet.Symbol

87. #### abstract def broadcast_plus(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise sum of the input arrays with broadcasting.

broadcast_plus is an alias to the function broadcast_add.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_add(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

broadcast_plus(x, y) = [ [ 1.,  1.,  1.],
[ 2.,  2.,  2.] ]

Supported sparse operations:

returns

org.apache.mxnet.Symbol

88. #### abstract def broadcast_power(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns result of first array elements raised to powers from second array, element-wise with broadcasting.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_power(x, y) = [ [ 2.,  2.,  2.],
[ 4.,  4.,  4.] ]

returns

org.apache.mxnet.Symbol

89. #### abstract def broadcast_sub(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise difference of the input arrays with broadcasting.

broadcast_minus is an alias to the function broadcast_sub.

Example::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

y = [ [ 0.],
[ 1.] ]

broadcast_sub(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

broadcast_minus(x, y) = [ [ 1.,  1.,  1.],
[ 0.,  0.,  0.] ]

Supported sparse operations:

returns

org.apache.mxnet.Symbol

90. #### abstract def broadcast_to(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Broadcasts the input array to a new shape.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, Broadcasting <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.

returns

org.apache.mxnet.Symbol

91. #### abstract def cast(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Casts all elements of the input to a new type.

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

Example::

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

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

org.apache.mxnet.Symbol

92. #### abstract def cast_storage(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Casts tensor storage type to the new type.

When an NDArray with default storage type is cast to csr or row_sparse storage,
the result is compact, which means:

- for csr, zero values will not be retained
- for row_sparse, row slices of all zeros will not be retained

The storage type of cast_storage output depends on stype parameter:

- cast_storage(csr, 'default') = default
- cast_storage(row_sparse, 'default') = default
- cast_storage(default, 'csr') = csr
- cast_storage(default, 'row_sparse') = row_sparse
- cast_storage(csr, 'csr') = csr
- cast_storage(row_sparse, 'row_sparse') = row_sparse

Example::

dense = [ [ 0.,  1.,  0.],
[ 2.,  0.,  3.],
[ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

# cast to row_sparse storage type
rsp = cast_storage(dense, 'row_sparse')
rsp.indices = [0, 1]
rsp.values = [ [ 0.,  1.,  0.],
[ 2.,  0.,  3.] ]

# cast to csr storage type
csr = cast_storage(dense, 'csr')
csr.indices = [1, 0, 2]
csr.values = [ 1.,  2.,  3.]
csr.indptr = [0, 1, 3, 3, 3]

Defined in src/operator/tensor/cast_storage.cc:L71
returns

org.apache.mxnet.Symbol

93. #### abstract def cbrt(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise cube-root value of the input.

.. math::
cbrt(x) = \sqrt[3]{x}

Example::

cbrt([1, 8, -125]) = [1, 2, -5]

The storage type of cbrt output depends upon the input storage type:

- cbrt(default) = default
- cbrt(row_sparse) = row_sparse
- cbrt(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L270
returns

org.apache.mxnet.Symbol

94. #### abstract def ceil(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise ceiling of the input.

The ceil of the scalar x is the smallest integer i, such that i >= x.

Example::

ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]

The storage type of ceil output depends upon the input storage type:

- ceil(default) = default
- ceil(row_sparse) = row_sparse
- ceil(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L817
returns

org.apache.mxnet.Symbol

95. #### abstract def choose_element_0index(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Picks elements from an input array according to the input indices along the given axis.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

By default, if any index mentioned is too large, it is replaced by the index that addresses
the last element along an axis (the clip mode).

This function supports n-dimensional input and (n-1)-dimensional indices arrays.

Examples::

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

// picks elements with specified indices along axis 0
pick(x, y=[0,1], 0) = [ 1.,  4.]

// picks elements with specified indices along axis 1
pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]

// 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.] ]

returns

org.apache.mxnet.Symbol

96. #### abstract def clip(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Clips (limits) the values in an array.
Given an interval, values outside the interval are clipped to the interval edges.
Clipping x between a_min and a_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.Symbol

97. #### abstract def col2im(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

98. #### abstract def concat(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Joins input arrays along a given axis.

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

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

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

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

Example::

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

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

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

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

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

org.apache.mxnet.Symbol

99. #### abstract def cos(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the element-wise cosine of the input array.

The input should be in radians (:math:2\pi rad equals 360 degrees).

.. math::
cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]

The storage type of cos output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L90
returns

org.apache.mxnet.Symbol

100. #### abstract def cosh(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the hyperbolic cosine  of the input array, computed element-wise.

.. math::
cosh(x) = 0.5\times(exp(x) + exp(-x))

The storage type of cosh output is always dense

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L409
returns

org.apache.mxnet.Symbol

101. #### abstract def crop(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L482
returns

org.apache.mxnet.Symbol

102. #### abstract def ctc_loss(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

103. #### abstract def cumsum(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Return the cumulative sum of the elements along a given axis.

Defined in src/operator/numpy/np_cumsum.cc:L70
returns

org.apache.mxnet.Symbol

104. #### abstract def degrees(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Converts each element of the input array from radians to degrees.

.. math::
degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]

The storage type of degrees output depends upon the input storage type:

- degrees(default) = default
- degrees(row_sparse) = row_sparse
- degrees(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L332
returns

org.apache.mxnet.Symbol

105. #### abstract def depth_to_space(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L972
returns

org.apache.mxnet.Symbol

106. #### abstract def diag(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Extracts a diagonal or constructs a diagonal array.

diag's behavior depends on the input array dimensions:

- 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
- 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.Symbol

107. #### abstract def dot(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Dot product of two arrays.

dot's behavior depends on the input array dimensions:

- 1-D arrays: inner product of vectors
- 2-D arrays: matrix multiplication
- N-D arrays: a sum product over the last axis of the first input and the first
axis of the second input

For example, given 3-D x with shape (n,m,k) and y with shape (k,r,s), the
result array will have shape (n,m,r,s). It is computed by::

dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])

Example::

x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
dot(x,y)[0,0,1,1] = 0
sum(x[0,0,:]*y[:,1,1]) = 0

The storage type of dot output depends on storage types of inputs, transpose option and
forward_stype option for output storage type. Implemented sparse operations include:

- dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
- dot(csr, default, transpose_a=True) = default
- dot(csr, default, transpose_a=True) = row_sparse
- dot(csr, default) = default
- dot(csr, row_sparse) = default
- dot(default, csr) = csr (CPU only)
- dot(default, csr, forward_stype='default') = default
- dot(default, csr, transpose_b=True, forward_stype='default') = default

If the combination of input storage types and forward_stype does not match any of the
above patterns, dot will fallback and generate output with default storage.

.. Note::

If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
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.Symbol

108. #### abstract def elemwise_add(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

109. #### abstract def elemwise_div(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Divides arguments element-wise.

The storage type of elemwise_div output is always dense
returns

org.apache.mxnet.Symbol

110. #### abstract def elemwise_mul(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Multiplies arguments element-wise.

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

- elemwise_mul(default, default) = default
- elemwise_mul(row_sparse, row_sparse) = row_sparse
- elemwise_mul(default, row_sparse) = row_sparse
- elemwise_mul(row_sparse, default) = row_sparse
- elemwise_mul(csr, csr) = csr
- otherwise, elemwise_mul generates output with default storage
returns

org.apache.mxnet.Symbol

111. #### abstract def elemwise_sub(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Subtracts arguments element-wise.

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

- elemwise_sub(row_sparse, row_sparse) = row_sparse
- elemwise_sub(csr, csr) = csr
- elemwise_sub(default, csr) = default
- elemwise_sub(csr, default) = default
- elemwise_sub(default, rsp) = default
- elemwise_sub(rsp, default) = default
- otherwise, elemwise_sub generates output with default storage
returns

org.apache.mxnet.Symbol

112. #### abstract def erf(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

113. #### abstract def erfinv(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

114. #### abstract def exp(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise exponential value of the input.

.. math::
exp(x) = e^x \approx 2.718^x

Example::

exp([0, 1, 2]) = [1., 2.71828175, 7.38905621]

The storage type of exp output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L64
returns

org.apache.mxnet.Symbol

115. #### abstract def expand_dims(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Inserts a new axis of size 1 into the array shape
For example, given x with shape (2,3,4), then expand_dims(x, axis=1)
will return a new array with shape (2,1,3,4).

Defined in src/operator/tensor/matrix_op.cc:L395
returns

org.apache.mxnet.Symbol

116. #### abstract def expm1(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns exp(x) - 1 computed element-wise on the input.

This function provides greater precision than exp(x) - 1 for small values of x.

The storage type of expm1 output depends upon the input storage type:

- expm1(default) = default
- expm1(row_sparse) = row_sparse
- expm1(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L244
returns

org.apache.mxnet.Symbol

117. #### abstract def fill_element_0index(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

org.apache.mxnet.Symbol

118. #### abstract def fix(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise rounded value to the nearest \
integer towards zero of the input.

Example::

fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]

The storage type of fix output depends upon the input storage type:

- fix(default) = default
- fix(row_sparse) = row_sparse
- fix(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L874
returns

org.apache.mxnet.Symbol

119. #### abstract def flatten(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

120. #### abstract def flip(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L832
returns

org.apache.mxnet.Symbol

121. #### abstract def floor(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise floor of the input.

The floor of the scalar x is the largest integer i, such that i <= x.

Example::

floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]

The storage type of floor output depends upon the input storage type:

- floor(default) = default
- floor(row_sparse) = row_sparse
- floor(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L836
returns

org.apache.mxnet.Symbol

122. #### abstract def ftml_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

123. #### abstract def ftrl_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for Ftrl optimizer.
Referenced from *Ad Click Prediction: a View from the Trenches*, available at
http://dl.acm.org/citation.cfm?id=2488200.

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.Symbol

124. #### abstract def gamma(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the gamma function (extension of the factorial function \
to the reals), computed element-wise on the input array.

The storage type of gamma output is always dense
returns

org.apache.mxnet.Symbol

125. #### abstract def gammaln(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise log of the absolute value of the gamma function \
of the input.

The storage type of gammaln output is always dense
returns

org.apache.mxnet.Symbol

126. #### abstract def gather_nd(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Gather elements or slices from data and store to a tensor whose
shape is defined by indices.

Given data with shape (X_0, X_1, ..., X_{N-1}) and indices with shape
(M, Y_0, ..., Y_{K-1}), the output will have shape (Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1}),
where M <= N. If M == N, output shape will simply be (Y_0, ..., Y_{K-1}).

The elements in output is defined as follows::

output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}],
...,
indices[M-1, y_0, ..., y_{K-1}],
x_M, ..., x_{N-1}]

Examples::

data = [ [0, 1], [2, 3] ]
indices = [ [1, 1, 0], [0, 1, 0] ]
gather_nd(data, indices) = [2, 3, 0]

data = [ [ [1, 2], [3, 4] ], [ [5, 6], [7, 8] ] ]
indices = [ [0, 1], [1, 0] ]
gather_nd(data, indices) = [ [3, 4], [5, 6] ]
returns

org.apache.mxnet.Symbol

127. #### abstract def hard_sigmoid(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes hard sigmoid of x element-wise.

.. math::
y = max(0, min(1, alpha * x + beta))

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L161
returns

org.apache.mxnet.Symbol

128. #### abstract def identity(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns a copy of the input.

From:src/operator/tensor/elemwise_unary_op_basic.cc:244
returns

org.apache.mxnet.Symbol

129. #### abstract def im2col(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

130. #### abstract def khatri_rao(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the Khatri-Rao product of the input matrices.

Given a collection of :math:n input matrices,

.. math::
A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N},

the (column-wise) Khatri-Rao product is defined as the matrix,

.. math::
X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N},

where the :math:k th column is equal to the column-wise outer product
:math:{A_1}_k \otimes \cdots \otimes {A_n}_k where :math:{A_i}_k is the kth
column of the ith matrix.

Example::

>>> A = mx.nd.array([ [1, -1],
>>>                  [2, -3] ])
>>> B = mx.nd.array([ [1, 4],
>>>                  [2, 5],
>>>                  [3, 6] ])
>>> C = mx.nd.khatri_rao(A, B)
>>> print(C.asnumpy())
[ [  1.  -4.]
[  2.  -5.]
[  3.  -6.]
[  2. -12.]
[  4. -15.]
[  6. -18.] ]

Defined in src/operator/contrib/krprod.cc:L108
returns

org.apache.mxnet.Symbol

131. #### abstract def lamb_update_phase1(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

132. #### abstract def lamb_update_phase2(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

133. #### abstract def linalg_det(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

134. #### abstract def linalg_extractdiag(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

135. #### abstract def linalg_extracttrian(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

136. #### abstract def linalg_gelqf(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

LQ factorization for general matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A*
must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ
factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so
that:

*A* = *L* \* *Q*

Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal,
and *Q* is row-orthonormal, meaning that

*Q* \* *Q*\ :sup:T

is equal to the identity matrix of shape *(x, x)*.

If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single LQ factorization
A = [ [1., 2., 3.], [4., 5., 6.] ]
Q, L = gelqf(A)
Q = [ [-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578] ]
L = [ [-3.74165739, 0.],
[-8.55235974, 1.96396101] ]

Batch LQ factorization
A = [ [ [1., 2., 3.], [4., 5., 6.] ],
[ [7., 8., 9.], [10., 11., 12.] ] ]
Q, L = gelqf(A)
Q = [ [ [-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578] ],
[ [-0.50257071, -0.57436653, -0.64616234],
[0.7620735, 0.05862104, -0.64483142] ] ]
L = [ [ [-3.74165739, 0.],
[-8.55235974, 1.96396101] ],
[ [-13.92838828, 0.],
[-19.09768702, 0.52758934] ] ]

Defined in src/operator/tensor/la_op.cc:L798
returns

org.apache.mxnet.Symbol

137. #### abstract def linalg_gemm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

138. #### abstract def linalg_gemm2(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

139. #### abstract def linalg_inverse(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

140. #### abstract def linalg_makediag(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

141. #### abstract def linalg_maketrian(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

142. #### abstract def linalg_potrf(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Performs Cholesky factorization of a symmetric positive-definite matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, the Cholesky factor *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.Symbol

143. #### abstract def linalg_potri(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

144. #### abstract def linalg_slogdet(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

145. #### abstract def linalg_sumlogdiag(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the sum of the logarithms of the diagonal elements of a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* must be square with positive diagonal entries. We sum the natural
logarithms of the diagonal elements, the result has shape (1,).

If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix reduction
A = [ [1.0, 1.0], [1.0, 7.0] ]
sumlogdiag(A) = [1.9459]

Batch matrix reduction
A = [ [ [1.0, 1.0], [1.0, 7.0] ], [ [3.0, 0], [0, 17.0] ] ]
sumlogdiag(A) = [1.9459, 3.9318]

Defined in src/operator/tensor/la_op.cc:L445
returns

org.apache.mxnet.Symbol

146. #### abstract def linalg_syrk(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Multiplication of matrix with its transpose.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, the operator performs the BLAS3 function *syrk*:

*out* = *alpha* \* *A* \* *A*\ :sup:T

if *transpose=False*, or

*out* = *alpha* \* *A*\ :sup:T \ \* *A*

if *transpose=True*.

If *n>2*, *syrk* is performed separately on the trailing two dimensions for all
inputs (batch mode).

.. note:: The operator supports float32 and float64 data types only.

Examples::

Single matrix multiply
A = [ [1., 2., 3.], [4., 5., 6.] ]
syrk(A, alpha=1., transpose=False)
= [ [14., 32.],
[32., 77.] ]
syrk(A, alpha=1., transpose=True)
= [ [17., 22., 27.],
[22., 29., 36.],
[27., 36., 45.] ]

Batch matrix multiply
A = [ [ [1., 1.] ], [ [0.1, 0.1] ] ]
syrk(A, alpha=2., transpose=False) = [ [ [4.] ], [ [0.04] ] ]

Defined in src/operator/tensor/la_op.cc:L730
returns

org.apache.mxnet.Symbol

147. #### abstract def linalg_trmm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

148. #### abstract def linalg_trsm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Solves matrix equation involving a lower triangular matrix.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape

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.Symbol

149. #### abstract def log(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise Natural logarithmic value of the input.

The natural logarithm is logarithm in base *e*, so that log(exp(x)) = x

The storage type of log output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L77
returns

org.apache.mxnet.Symbol

150. #### abstract def log10(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise Base-10 logarithmic value of the input.

10**log10(x) = x

The storage type of log10 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L94
returns

org.apache.mxnet.Symbol

151. #### abstract def log1p(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise log(1 + x) value of the input.

This function is more accurate than log(1 + x)  for small x so that
:math:1+x\approx 1

The storage type of log1p output depends upon the input storage type:

- log1p(default) = default
- log1p(row_sparse) = row_sparse
- log1p(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L199
returns

org.apache.mxnet.Symbol

152. #### abstract def log2(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise Base-2 logarithmic value of the input.

2**log2(x) = x

The storage type of log2 output is always dense

Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L106
returns

org.apache.mxnet.Symbol

153. #### abstract def log_softmax(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the log softmax of the input.
This is equivalent to computing softmax followed by log.

Examples::

>>> x = mx.nd.array([1, 2, .1])
>>> mx.nd.log_softmax(x).asnumpy()
array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)

>>> x = mx.nd.array( [ [1, 2, .1],[.1, 2, 1] ] )
>>> mx.nd.log_softmax(x, axis=0).asnumpy()
array([ [-0.34115392, -0.69314718, -1.24115396],
[-1.24115396, -0.69314718, -0.34115392] ], dtype=float32)
returns

org.apache.mxnet.Symbol

154. #### abstract def logical_not(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the result of logical NOT (!) function

Example:
logical_not([-2., 0., 1.]) = [0., 1., 0.]
returns

org.apache.mxnet.Symbol

155. #### abstract def make_loss(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Make your own loss function in network construction.

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

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

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

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

The storage type of make_loss output depends upon the input storage type:

- make_loss(default) = default
- make_loss(row_sparse) = row_sparse

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L358
returns

org.apache.mxnet.Symbol

156. #### abstract def max(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the max of array elements over given axes.

returns

org.apache.mxnet.Symbol

157. #### abstract def max_axis(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the max of array elements over given axes.

returns

org.apache.mxnet.Symbol

158. #### abstract def mean(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the mean of array elements over given axes.

returns

org.apache.mxnet.Symbol

159. #### abstract def min(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the min of array elements over given axes.

returns

org.apache.mxnet.Symbol

160. #### abstract def min_axis(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the min of array elements over given axes.

returns

org.apache.mxnet.Symbol

161. #### abstract def moments(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

162. #### abstract def mp_lamb_update_phase1(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

163. #### abstract def mp_lamb_update_phase2(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

164. #### abstract def mp_nag_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.

Defined in src/operator/optimizer_op.cc:L745
returns

org.apache.mxnet.Symbol

165. #### abstract def mp_sgd_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Updater function for multi-precision sgd optimizer
returns

org.apache.mxnet.Symbol

166. #### abstract def mp_sgd_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Updater function for multi-precision sgd optimizer
returns

org.apache.mxnet.Symbol

167. #### abstract def multi_all_finite(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

168. #### abstract def multi_lars(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

169. #### abstract def multi_mp_sgd_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

170. #### abstract def multi_mp_sgd_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

171. #### abstract def multi_sgd_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

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.Symbol

172. #### abstract def multi_sgd_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

173. #### abstract def multi_sum_sq(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Compute the sums of squares of multiple arrays

Defined in src/operator/contrib/multi_sum_sq.cc:L36
returns

org.apache.mxnet.Symbol

174. #### abstract def nag_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

175. #### abstract def nanprod(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the product of array elements over given axes treating Not a Numbers (NaN) as one.

returns

org.apache.mxnet.Symbol

176. #### abstract def nansum(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero.

returns

org.apache.mxnet.Symbol

177. #### abstract def negative(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Numerical negative of the argument, element-wise.

The storage type of negative output depends upon the input storage type:

- negative(default) = default
- negative(row_sparse) = row_sparse
- negative(csr) = csr
returns

org.apache.mxnet.Symbol

178. #### abstract def norm(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the norm on an NDArray.

This operator computes the norm on an NDArray with the specified axis, depending
on the value of the ord parameter. By default, it computes the L2 norm on the entire
array. Currently only ord=2 supports sparse ndarrays.

Examples::

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

norm(x, ord=2, axis=1) = [ [3.1622777 4.472136 ]
[5.3851647 6.3245554] ]

norm(x, ord=1, axis=1) = [ [4., 6.],
[7., 8.] ]

rsp = x.cast_storage('row_sparse')

norm(rsp) = [5.47722578]

csr = x.cast_storage('csr')

norm(csr) = [5.47722578]

returns

org.apache.mxnet.Symbol

179. #### abstract def normal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a normal (Gaussian) distribution.

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

Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale*
(standard deviation).

Example::

normal(loc=0, scale=1, shape=(2,2)) = [ [ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114] ]

Defined in src/operator/random/sample_op.cc:L113
returns

org.apache.mxnet.Symbol

180. #### abstract def one_hot(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns a one-hot array.

The locations represented by indices take value on_value, while all
other locations take value off_value.

one_hot operation with indices of shape (i0, i1) and depth  of d would result
in an output array of shape (i0, i1, d) with::

output[i,j,:] = off_value
output[i,j,indices[i,j] ] = on_value

Examples::

one_hot([1,0,2,0], 3) = [ [ 0.  1.  0.]
[ 1.  0.  0.]
[ 0.  0.  1.]
[ 1.  0.  0.] ]

one_hot([1,0,2,0], 3, on_value=8, off_value=1,
dtype='int32') = [ [1 8 1]
[8 1 1]
[1 1 8]
[8 1 1] ]

one_hot([ [1,0],[1,0],[2,0] ], 3) = [ [ [ 0.  1.  0.]
[ 1.  0.  0.] ]

[ [ 0.  1.  0.]
[ 1.  0.  0.] ]

[ [ 0.  0.  1.]
[ 1.  0.  0.] ] ]

Defined in src/operator/tensor/indexing_op.cc:L883
returns

org.apache.mxnet.Symbol

181. #### abstract def ones_like(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Return an array of ones with the same shape and type
as the input array.

Examples::

x = [ [ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]

ones_like(x) = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]
returns

org.apache.mxnet.Symbol

182. #### abstract def pad(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

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

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

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

Example::

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

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

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

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

[ [[ [  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.] ] ] ]

returns

org.apache.mxnet.Symbol

183. #### abstract def pick(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Picks elements from an input array according to the input indices along the given axis.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be
an output array of shape (i0,) with::

output[i] = input[i, indices[i] ]

By default, if any index mentioned is too large, it is replaced by the index that addresses
the last element along an axis (the clip mode).

This function supports n-dimensional input and (n-1)-dimensional indices arrays.

Examples::

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

// picks elements with specified indices along axis 0
pick(x, y=[0,1], 0) = [ 1.,  4.]

// picks elements with specified indices along axis 1
pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]

// 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.] ]

returns

org.apache.mxnet.Symbol

184. #### abstract def preloaded_multi_mp_sgd_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.

returns

org.apache.mxnet.Symbol

185. #### abstract def preloaded_multi_mp_sgd_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

returns

org.apache.mxnet.Symbol

186. #### abstract def preloaded_multi_sgd_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

returns

org.apache.mxnet.Symbol

187. #### abstract def preloaded_multi_sgd_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

returns

org.apache.mxnet.Symbol

188. #### abstract def prod(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the product of array elements over given axes.

returns

org.apache.mxnet.Symbol

189. #### abstract def radians(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Converts each element of the input array from degrees to radians.

.. math::
radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]

The storage type of radians output depends upon the input storage type:

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L351
returns

org.apache.mxnet.Symbol

190. #### abstract def random_exponential(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from an exponential distribution.

Samples are distributed according to an exponential distribution parametrized by *lambda* (rate).

Example::

exponential(lam=4, shape=(2,2)) = [ [ 0.0097189 ,  0.08999364],
[ 0.04146638,  0.31715935] ]

Defined in src/operator/random/sample_op.cc:L137
returns

org.apache.mxnet.Symbol

191. #### abstract def random_gamma(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a gamma distribution.

Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale).

Example::

gamma(alpha=9, beta=0.5, shape=(2,2)) = [ [ 7.10486984,  3.37695289],
[ 3.91697288,  3.65933681] ]

Defined in src/operator/random/sample_op.cc:L125
returns

org.apache.mxnet.Symbol

192. #### abstract def random_generalized_negative_binomial(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a generalized negative binomial distribution.

Samples are distributed according to a generalized negative binomial distribution parametrized by
*mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the
number of unsuccessful experiments (generalized to real numbers).
Samples will always be returned as a floating point data type.

Example::

generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [ [ 2.,  1.],
[ 6.,  4.] ]

Defined in src/operator/random/sample_op.cc:L179
returns

org.apache.mxnet.Symbol

193. #### abstract def random_negative_binomial(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a negative binomial distribution.

Samples are distributed according to a negative binomial distribution parametrized by
*k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment).
Samples will always be returned as a floating point data type.

Example::

negative_binomial(k=3, p=0.4, shape=(2,2)) = [ [ 4.,  7.],
[ 2.,  5.] ]

Defined in src/operator/random/sample_op.cc:L164
returns

org.apache.mxnet.Symbol

194. #### abstract def random_normal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a normal (Gaussian) distribution.

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

Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale*
(standard deviation).

Example::

normal(loc=0, scale=1, shape=(2,2)) = [ [ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114] ]

Defined in src/operator/random/sample_op.cc:L113
returns

org.apache.mxnet.Symbol

195. #### abstract def random_pdf_dirichlet(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of *sample* of
Dirichlet distributions with parameter *alpha*.

The shape of *alpha* must match the leftmost subshape of *sample*.  That is, *sample*
can have the same shape as *alpha*, in which case the output contains one density per
distribution, or *sample* can be a tensor of tensors with that shape, in which case
the output is a tensor of densities such that the densities at index *i* in the output
are given by the samples at index *i* in *sample* parameterized by the value of *alpha*
at index *i*.

Examples::

random_pdf_dirichlet(sample=[ [1,2],[2,3],[3,4] ], alpha=[2.5, 2.5]) =
[38.413498, 199.60245, 564.56085]

sample = [ [ [1, 2, 3], [10, 20, 30], [100, 200, 300] ],
[ [0.1, 0.2, 0.3], [0.01, 0.02, 0.03], [0.001, 0.002, 0.003] ] ]

random_pdf_dirichlet(sample=sample, alpha=[0.1, 0.4, 0.9]) =
[ [2.3257459e-02, 5.8420084e-04, 1.4674458e-05],
[9.2589635e-01, 3.6860607e+01, 1.4674468e+03] ]

Defined in src/operator/random/pdf_op.cc:L316
returns

org.apache.mxnet.Symbol

196. #### abstract def random_pdf_exponential(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of *sample* of
exponential distributions with parameters *lam* (rate).

The shape of *lam* must match the leftmost subshape of *sample*.  That is, *sample*
can have the same shape as *lam*, in which case the output contains one density per
distribution, or *sample* can be a tensor of tensors with that shape, in which case
the output is a tensor of densities such that the densities at index *i* in the output
are given by the samples at index *i* in *sample* parameterized by the value of *lam*
at index *i*.

Examples::

random_pdf_exponential(sample=[ [1, 2, 3] ], lam=[1]) =
[ [0.36787945, 0.13533528, 0.04978707] ]

sample = [ [1,2,3],
[1,2,3],
[1,2,3] ]

random_pdf_exponential(sample=sample, lam=[1,0.5,0.25]) =
[ [0.36787945, 0.13533528, 0.04978707],
[0.30326533, 0.18393973, 0.11156508],
[0.1947002,  0.15163267, 0.11809164] ]

Defined in src/operator/random/pdf_op.cc:L305
returns

org.apache.mxnet.Symbol

197. #### abstract def random_pdf_gamma(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of *sample* of
gamma distributions with parameters *alpha* (shape) and *beta* (rate).

*alpha* and *beta* must have the same shape, which must match the leftmost subshape
of *sample*.  That is, *sample* can have the same shape as *alpha* and *beta*, in which
case the output contains one density per distribution, or *sample* can be a tensor
of tensors with that shape, in which case the output is a tensor of densities such that
the densities at index *i* in the output are given by the samples at index *i* in *sample*
parameterized by the values of *alpha* and *beta* at index *i*.

Examples::

random_pdf_gamma(sample=[ [1,2,3,4,5] ], alpha=[5], beta=[1]) =
[ [0.01532831, 0.09022352, 0.16803136, 0.19536681, 0.17546739] ]

sample = [ [1, 2, 3, 4, 5],
[2, 3, 4, 5, 6],
[3, 4, 5, 6, 7] ]

random_pdf_gamma(sample=sample, alpha=[5,6,7], beta=[1,1,1]) =
[ [0.01532831, 0.09022352, 0.16803136, 0.19536681, 0.17546739],
[0.03608941, 0.10081882, 0.15629345, 0.17546739, 0.16062315],
[0.05040941, 0.10419563, 0.14622283, 0.16062315, 0.14900276] ]

Defined in src/operator/random/pdf_op.cc:L303
returns

org.apache.mxnet.Symbol

198. #### abstract def random_pdf_generalized_negative_binomial(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of *sample* of
generalized negative binomial distributions with parameters *mu* (mean)
and *alpha* (dispersion).  This can be understood as a reparameterization of
the negative binomial, where *k* = *1 / alpha* and *p* = *1 / (mu \* alpha + 1)*.

*mu* and *alpha* must have the same shape, which must match the leftmost subshape
of *sample*.  That is, *sample* can have the same shape as *mu* and *alpha*, in which
case the output contains one density per distribution, or *sample* can be a tensor
of tensors with that shape, in which case the output is a tensor of densities such that
the densities at index *i* in the output are given by the samples at index *i* in *sample*
parameterized by the values of *mu* and *alpha* at index *i*.

Examples::

random_pdf_generalized_negative_binomial(sample=[ [1, 2, 3, 4] ], alpha=[1], mu=[1]) =
[ [0.25, 0.125, 0.0625, 0.03125] ]

sample = [ [1,2,3,4],
[1,2,3,4] ]
random_pdf_generalized_negative_binomial(sample=sample, alpha=[1, 0.6666], mu=[1, 1.5]) =
[ [0.25,       0.125,      0.0625,     0.03125   ],
[0.26517063, 0.16573331, 0.09667706, 0.05437994] ]

Defined in src/operator/random/pdf_op.cc:L314
returns

org.apache.mxnet.Symbol

199. #### abstract def random_pdf_negative_binomial(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of samples of
negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).

*k* and *p* must have the same shape, which must match the leftmost subshape
of *sample*.  That is, *sample* can have the same shape as *k* and *p*, in which
case the output contains one density per distribution, or *sample* can be a tensor
of tensors with that shape, in which case the output is a tensor of densities such that
the densities at index *i* in the output are given by the samples at index *i* in *sample*
parameterized by the values of *k* and *p* at index *i*.

Examples::

random_pdf_negative_binomial(sample=[ [1,2,3,4] ], k=[1], p=a[0.5]) =
[ [0.25, 0.125, 0.0625, 0.03125] ]

# Note that k may be real-valued
sample = [ [1,2,3,4],
[1,2,3,4] ]
random_pdf_negative_binomial(sample=sample, k=[1, 1.5], p=[0.5, 0.5]) =
[ [0.25,       0.125,      0.0625,     0.03125   ],
[0.26516506, 0.16572815, 0.09667476, 0.05437956] ]

Defined in src/operator/random/pdf_op.cc:L310
returns

org.apache.mxnet.Symbol

200. #### abstract def random_pdf_normal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of *sample* of
normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).

*mu* and *sigma* must have the same shape, which must match the leftmost subshape
of *sample*.  That is, *sample* can have the same shape as *mu* and *sigma*, in which
case the output contains one density per distribution, or *sample* can be a tensor
of tensors with that shape, in which case the output is a tensor of densities such that
the densities at index *i* in the output are given by the samples at index *i* in *sample*
parameterized by the values of *mu* and *sigma* at index *i*.

Examples::

sample = [ [-2, -1, 0, 1, 2] ]
random_pdf_normal(sample=sample, mu=[0], sigma=[1]) =
[ [0.05399097, 0.24197073, 0.3989423, 0.24197073, 0.05399097] ]

random_pdf_normal(sample=sample*2, mu=[0,0], sigma=[1,2]) =
[ [0.05399097, 0.24197073, 0.3989423,  0.24197073, 0.05399097],
[0.12098537, 0.17603266, 0.19947115, 0.17603266, 0.12098537] ]

Defined in src/operator/random/pdf_op.cc:L300
returns

org.apache.mxnet.Symbol

201. #### abstract def random_pdf_poisson(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of *sample* of
Poisson distributions with parameters *lam* (rate).

The shape of *lam* must match the leftmost subshape of *sample*.  That is, *sample*
can have the same shape as *lam*, in which case the output contains one density per
distribution, or *sample* can be a tensor of tensors with that shape, in which case
the output is a tensor of densities such that the densities at index *i* in the output
are given by the samples at index *i* in *sample* parameterized by the value of *lam*
at index *i*.

Examples::

random_pdf_poisson(sample=[ [0,1,2,3] ], lam=[1]) =
[ [0.36787945, 0.36787945, 0.18393973, 0.06131324] ]

sample = [ [0,1,2,3],
[0,1,2,3],
[0,1,2,3] ]

random_pdf_poisson(sample=sample, lam=[1,2,3]) =
[ [0.36787945, 0.36787945, 0.18393973, 0.06131324],
[0.13533528, 0.27067056, 0.27067056, 0.18044704],
[0.04978707, 0.14936121, 0.22404182, 0.22404182] ]

Defined in src/operator/random/pdf_op.cc:L307
returns

org.apache.mxnet.Symbol

202. #### abstract def random_pdf_uniform(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the value of the PDF of *sample* of
uniform distributions on the intervals given by *[low,high)*.

*low* and *high* must have the same shape, which must match the leftmost subshape
of *sample*.  That is, *sample* can have the same shape as *low* and *high*, in which
case the output contains one density per distribution, or *sample* can be a tensor
of tensors with that shape, in which case the output is a tensor of densities such that
the densities at index *i* in the output are given by the samples at index *i* in *sample*
parameterized by the values of *low* and *high* at index *i*.

Examples::

random_pdf_uniform(sample=[ [1,2,3,4] ], low=[0], high=[10]) = [0.1, 0.1, 0.1, 0.1]

sample = [ [ [1, 2, 3],
[1, 2, 3] ],
[ [1, 2, 3],
[1, 2, 3] ] ]
low  = [ [0, 0],
[0, 0] ]
high = [ [ 5, 10],
[15, 20] ]
random_pdf_uniform(sample=sample, low=low, high=high) =
[ [ [0.2,        0.2,        0.2    ],
[0.1,        0.1,        0.1    ] ],
[ [0.06667,    0.06667,    0.06667],
[0.05,       0.05,       0.05   ] ] ]

Defined in src/operator/random/pdf_op.cc:L298
returns

org.apache.mxnet.Symbol

203. #### abstract def random_poisson(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a Poisson distribution.

Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate).
Samples will always be returned as a floating point data type.

Example::

poisson(lam=4, shape=(2,2)) = [ [ 5.,  2.],
[ 4.,  6.] ]

Defined in src/operator/random/sample_op.cc:L150
returns

org.apache.mxnet.Symbol

204. #### abstract def random_randint(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a discrete uniform distribution.

Samples are uniformly distributed over the half-open interval *[low, high)*
(includes *low*, but excludes *high*).

Example::

randint(low=0, high=5, shape=(2,2)) = [ [ 0,  2],
[ 3,  1] ]

Defined in src/operator/random/sample_op.cc:L194
returns

org.apache.mxnet.Symbol

205. #### abstract def random_uniform(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a uniform distribution.

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

Samples are uniformly distributed over the half-open interval *[low, high)*
(includes *low*, but excludes *high*).

Example::

uniform(low=0, high=1, shape=(2,2)) = [ [ 0.60276335,  0.85794562],
[ 0.54488319,  0.84725171] ]

Defined in src/operator/random/sample_op.cc:L96
returns

org.apache.mxnet.Symbol

206. #### abstract def ravel_multi_index(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix. The leading dimension may be left unspecified by using -1 as placeholder.

Examples::

A = [ [3,6,6],[4,5,1] ]
ravel(A, shape=(7,6)) = [22,41,37]
ravel(A, shape=(-1,6)) = [22,41,37]

Defined in src/operator/tensor/ravel.cc:L42
returns

org.apache.mxnet.Symbol

207. #### abstract def rcbrt(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise inverse cube-root value of the input.

.. math::
rcbrt(x) = 1/\sqrt[3]{x}

Example::

rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L323
returns

org.apache.mxnet.Symbol

208. #### abstract def reciprocal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the reciprocal of the argument, element-wise.

Calculates 1/x.

Example::

reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L43
returns

org.apache.mxnet.Symbol

209. #### abstract def relu(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes rectified linear activation.

.. math::
max(features, 0)

The storage type of relu output depends upon the input storage type:

- relu(default) = default
- relu(row_sparse) = row_sparse
- relu(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
returns

org.apache.mxnet.Symbol

210. #### abstract def repeat(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Repeats elements of an array.
By default, repeat flattens the input array into 1-D and then repeats the
elements::
x = [ [ 1, 2],
[ 3, 4] ]
repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]
The parameter axis specifies the axis along which to perform repeat::
repeat(x, repeats=2, axis=1) = [ [ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.] ]
repeat(x, repeats=2, axis=0) = [ [ 1.,  2.],
[ 1.,  2.],
[ 3.,  4.],
[ 3.,  4.] ]
repeat(x, repeats=2, axis=-1) = [ [ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.] ]

Defined in src/operator/tensor/matrix_op.cc:L744
returns

org.apache.mxnet.Symbol

211. #### abstract def reset_arrays(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Set to zero multiple arrays

Defined in src/operator/contrib/reset_arrays.cc:L36
returns

org.apache.mxnet.Symbol

212. #### abstract def reshape(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

org.apache.mxnet.Symbol

213. #### abstract def reshape_like(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Reshape some or all dimensions of lhs to have the same shape as some or all dimensions of rhs.

Returns a **view** of the lhs array with a new shape without altering any data.

Example::

x = [1, 2, 3, 4, 5, 6]
y = [ [0, -4], [3, 2], [2, 2] ]
reshape_like(x, y) = [ [1, 2], [3, 4], [5, 6] ]

More precise control over how dimensions are inherited is achieved by specifying \
slices over the lhs and rhs array dimensions. Only the sliced lhs dimensions \
are reshaped to the rhs sliced dimensions, with the non-sliced lhs dimensions staying the same.

Examples::

- lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
- lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)

Negative indices are supported, and None can be used for either lhs_end or rhs_end to indicate the end of the range.

Example::

- lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L511
returns

org.apache.mxnet.Symbol

214. #### abstract def reverse(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L832
returns

org.apache.mxnet.Symbol

215. #### abstract def rint(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise rounded value to the nearest integer of the input.

.. note::
- For input n.5 rint returns n while round returns n+1.
- For input -n.5 both rint and round returns -n-1.

Example::

rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  1., -2.,  2.,  2.]

The storage type of rint output depends upon the input storage type:

- rint(default) = default
- rint(row_sparse) = row_sparse
- rint(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L798
returns

org.apache.mxnet.Symbol

216. #### abstract def rmsprop_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for RMSProp optimizer.

RMSprop is a variant of stochastic gradient descent where the gradients are
divided by a cache which grows with the sum of squares of recent gradients?

RMSProp is similar to AdaGrad, a popular variant of SGD which adaptively
tunes the learning rate of each parameter. AdaGrad lowers the learning rate for
each parameter monotonically over the course of training.
While this is analytically motivated for convex optimizations, it may not be ideal
for non-convex problems. RMSProp deals with this heuristically by allowing the
learning rates to rebound as the denominator decays over time.

Define the Root Mean Square (RMS) error criterion of the gradient as
:math:RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}, where :math:g represents
gradient and :math:E[g^2]_t is the decaying average over past squared gradient.

The :math:E[g^2]_t is given by:

.. math::
E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2

The update step is

.. math::
\theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t

The RMSProp code follows the version in
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
Tieleman & Hinton, 2012.

Hinton suggests the momentum term :math:\gamma to be 0.9 and the learning rate
:math:\eta to be 0.001.

Defined in src/operator/optimizer_op.cc:L797
returns

org.apache.mxnet.Symbol

217. #### abstract def rmspropalex_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for RMSPropAlex optimizer.

RMSPropAlex is non-centered version of RMSProp.

Define :math:E[g^2]_t is the decaying average over past squared gradient and
:math:E[g]_t is the decaying average over past gradient.

.. math::
E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
\Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\

The update step is

.. math::
\theta_{t+1} = \theta_t + \Delta_t

The RMSPropAlex code follows the version in
http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.

Graves suggests the momentum term :math:\gamma_1 to be 0.95, :math:\gamma_2
to be 0.9 and the learning rate :math:\eta to be 0.0001.

Defined in src/operator/optimizer_op.cc:L836
returns

org.apache.mxnet.Symbol

218. #### abstract def round(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise rounded value to the nearest integer of the input.

Example::

round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]

The storage type of round output depends upon the input storage type:

- round(default) = default
- round(row_sparse) = row_sparse
- round(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L777
returns

org.apache.mxnet.Symbol

219. #### abstract def rsqrt(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise inverse square-root value of the input.

.. math::
rsqrt(x) = 1/\sqrt{x}

Example::

rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]

The storage type of rsqrt output is always dense

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L221
returns

org.apache.mxnet.Symbol

220. #### abstract def sample_exponential(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple
exponential distributions with parameters lambda (rate).

The parameters of the distributions are provided as an input array.
Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
be the shape specified as the parameter of the operator, and *m* be the dimension
of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.

For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
will be an *m*-dimensional array that holds randomly drawn samples from the distribution
which is parameterized by the input value at index *i*. If the shape parameter of the
operator is not set, then one sample will be drawn per distribution and the output array
has the same shape as the input array.

Examples::

lam = [ 1.0, 8.5 ]

// Draw a single sample for each distribution
sample_exponential(lam) = [ 0.51837951,  0.09994757]

// Draw a vector containing two samples for each distribution
sample_exponential(lam, shape=(2)) = [ [ 0.51837951,  0.19866663],
[ 0.09994757,  0.50447971] ]

Defined in src/operator/random/multisample_op.cc:L284
returns

org.apache.mxnet.Symbol

221. #### abstract def sample_gamma(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple
gamma distributions with parameters *alpha* (shape) and *beta* (scale).

The parameters of the distributions are provided as input arrays.
Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
be the shape specified as the parameter of the operator, and *m* be the dimension
of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.

For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
will be an *m*-dimensional array that holds randomly drawn samples from the distribution
which is parameterized by the input values at index *i*. If the shape parameter of the
operator is not set, then one sample will be drawn per distribution and the output array
has the same shape as the input arrays.

Examples::

alpha = [ 0.0, 2.5 ]
beta = [ 1.0, 0.7 ]

// Draw a single sample for each distribution
sample_gamma(alpha, beta) = [ 0.        ,  2.25797319]

// Draw a vector containing two samples for each distribution
sample_gamma(alpha, beta, shape=(2)) = [ [ 0.        ,  0.        ],
[ 2.25797319,  1.70734084] ]

Defined in src/operator/random/multisample_op.cc:L282
returns

org.apache.mxnet.Symbol

222. #### abstract def sample_generalized_negative_binomial(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple
generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion).

The parameters of the distributions are provided as input arrays.
Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
be the shape specified as the parameter of the operator, and *m* be the dimension
of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.

For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
will be an *m*-dimensional array that holds randomly drawn samples from the distribution
which is parameterized by the input values at index *i*. If the shape parameter of the
operator is not set, then one sample will be drawn per distribution and the output array
has the same shape as the input arrays.

Samples will always be returned as a floating point data type.

Examples::

mu = [ 2.0, 2.5 ]
alpha = [ 1.0, 0.1 ]

// Draw a single sample for each distribution
sample_generalized_negative_binomial(mu, alpha) = [ 0.,  3.]

// Draw a vector containing two samples for each distribution
sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [ [ 0.,  3.],
[ 3.,  1.] ]

Defined in src/operator/random/multisample_op.cc:L293
returns

org.apache.mxnet.Symbol

223. #### abstract def sample_multinomial(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple multinomial distributions.

*data* is an *n* dimensional array whose last dimension has length *k*, where
*k* is the number of possible outcomes of each multinomial distribution. This
operator will draw *shape* samples from each distribution. If shape is empty
one sample will be drawn from each distribution.

If *get_prob* is true, a second array containing log likelihood of the drawn
samples will also be returned. This is usually used for reinforcement learning
where you can provide reward as head gradient for this array to estimate

Note that the input distribution must be normalized, i.e. *data* must sum to
1 along its last axis.

Examples::

probs = [ [0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0] ]

// Draw a single sample for each distribution
sample_multinomial(probs) = [3, 0]

// Draw a vector containing two samples for each distribution
sample_multinomial(probs, shape=(2)) = [ [4, 2],
[0, 0] ]

// requests log likelihood
sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]
returns

org.apache.mxnet.Symbol

224. #### abstract def sample_negative_binomial(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple
negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability).

The parameters of the distributions are provided as input arrays.
Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
be the shape specified as the parameter of the operator, and *m* be the dimension
of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.

For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
will be an *m*-dimensional array that holds randomly drawn samples from the distribution
which is parameterized by the input values at index *i*. If the shape parameter of the
operator is not set, then one sample will be drawn per distribution and the output array
has the same shape as the input arrays.

Samples will always be returned as a floating point data type.

Examples::

k = [ 20, 49 ]
p = [ 0.4 , 0.77 ]

// Draw a single sample for each distribution
sample_negative_binomial(k, p) = [ 15.,  16.]

// Draw a vector containing two samples for each distribution
sample_negative_binomial(k, p, shape=(2)) = [ [ 15.,  50.],
[ 16.,  12.] ]

Defined in src/operator/random/multisample_op.cc:L289
returns

org.apache.mxnet.Symbol

225. #### abstract def sample_normal(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple
normal distributions with parameters *mu* (mean) and *sigma* (standard deviation).

The parameters of the distributions are provided as input arrays.
Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
be the shape specified as the parameter of the operator, and *m* be the dimension
of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.

For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
will be an *m*-dimensional array that holds randomly drawn samples from the distribution
which is parameterized by the input values at index *i*. If the shape parameter of the
operator is not set, then one sample will be drawn per distribution and the output array
has the same shape as the input arrays.

Examples::

mu = [ 0.0, 2.5 ]
sigma = [ 1.0, 3.7 ]

// Draw a single sample for each distribution
sample_normal(mu, sigma) = [-0.56410581,  0.95934606]

// Draw a vector containing two samples for each distribution
sample_normal(mu, sigma, shape=(2)) = [ [-0.56410581,  0.2928229 ],
[ 0.95934606,  4.48287058] ]

Defined in src/operator/random/multisample_op.cc:L279
returns

org.apache.mxnet.Symbol

226. #### abstract def sample_poisson(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple
Poisson distributions with parameters lambda (rate).

The parameters of the distributions are provided as an input array.
Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]*
be the shape specified as the parameter of the operator, and *m* be the dimension
of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.

For any valid *n*-dimensional index *i* with respect to the input array, *output[i]*
will be an *m*-dimensional array that holds randomly drawn samples from the distribution
which is parameterized by the input value at index *i*. If the shape parameter of the
operator is not set, then one sample will be drawn per distribution and the output array
has the same shape as the input array.

Samples will always be returned as a floating point data type.

Examples::

lam = [ 1.0, 8.5 ]

// Draw a single sample for each distribution
sample_poisson(lam) = [  0.,  13.]

// Draw a vector containing two samples for each distribution
sample_poisson(lam, shape=(2)) = [ [  0.,   4.],
[ 13.,   8.] ]

Defined in src/operator/random/multisample_op.cc:L286
returns

org.apache.mxnet.Symbol

227. #### abstract def sample_uniform(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Concurrent sampling from multiple
uniform distributions on the intervals given by *[low,high)*.

The parameters of the distributions are provided as input arrays.
Let *[s]* be the shape of the input arrays, *n* be the dimension of *[s]*, *[t]*
be the shape specified as the parameter of the operator, and *m* be the dimension
of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*.

For any valid *n*-dimensional index *i* with respect to the input arrays, *output[i]*
will be an *m*-dimensional array that holds randomly drawn samples from the distribution
which is parameterized by the input values at index *i*. If the shape parameter of the
operator is not set, then one sample will be drawn per distribution and the output array
has the same shape as the input arrays.

Examples::

low = [ 0.0, 2.5 ]
high = [ 1.0, 3.7 ]

// Draw a single sample for each distribution
sample_uniform(low, high) = [ 0.40451524,  3.18687344]

// Draw a vector containing two samples for each distribution
sample_uniform(low, high, shape=(2)) = [ [ 0.40451524,  0.18017688],
[ 3.18687344,  3.68352246] ]

Defined in src/operator/random/multisample_op.cc:L277
returns

org.apache.mxnet.Symbol

228. #### abstract def scatter_nd(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Scatters data into a new tensor according to indices.

Given data with shape (Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1}) and indices with shape
(M, Y_0, ..., Y_{K-1}), the output will have shape (X_0, X_1, ..., X_{N-1}),
where M <= N. If M == N, data shape should simply be (Y_0, ..., Y_{K-1}).

The elements in output is defined as follows::

output[indices[0, y_0, ..., y_{K-1}],
...,
indices[M-1, y_0, ..., y_{K-1}],
x_M, ..., x_{N-1}] = data[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}]

all other entries in output are 0.

.. warning::

If the indices have duplicates, the result will be non-deterministic and
the gradient of scatter_nd will not be correct!!

Examples::

data = [2, 3, 0]
indices = [ [1, 1, 0], [0, 1, 0] ]
shape = (2, 2)
scatter_nd(data, indices, shape) = [ [0, 0], [2, 3] ]

data = [ [ [1, 2], [3, 4] ], [ [5, 6], [7, 8] ] ]
indices = [ [0, 1], [1, 1] ]
shape = (2, 2, 2, 2)
scatter_nd(data, indices, shape) = [ [[ [0, 0],
[0, 0] ],

[ [1, 2],
[3, 4] ] ],

[ [ [0, 0],
[0, 0] ],

[ [5, 6],
[7, 8] ] ] ]
returns

org.apache.mxnet.Symbol

229. #### abstract def sgd_mom_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks
like below:

.. math::

v_1 = \alpha * \nabla J(W_0)\\
v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\
W_t = W_{t-1} + v_t

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

However, if grad's storage type is row_sparse, lazy_update is True and weight's storage
type is the same as momentum's storage type,
only the row slices whose indices appear in grad.indices are updated (for both weight and momentum)::

v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
weight[row] += v[row]

Defined in src/operator/optimizer_op.cc:L565
returns

org.apache.mxnet.Symbol

230. #### abstract def sgd_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for Stochastic Gradient Descent (SGD) optimizer.

weight = weight - learning_rate * (gradient + wd * weight)

However, if gradient is of row_sparse storage type and lazy_update is True,
only the row slices whose indices appear in grad.indices are updated::

weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])

Defined in src/operator/optimizer_op.cc:L524
returns

org.apache.mxnet.Symbol

231. #### abstract def shape_array(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns a 1D int64 array containing the shape of data.

Example::

shape_array([ [1,2,3,4], [5,6,7,8] ]) = [2,4]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L573
returns

org.apache.mxnet.Symbol

232. #### abstract def shuffle(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Randomly shuffle the elements.

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

org.apache.mxnet.Symbol

233. #### abstract def sigmoid(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes sigmoid of x element-wise.

.. math::
y = 1 / (1 + exp(-x))

The storage type of sigmoid output is always dense

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L119
returns

org.apache.mxnet.Symbol

234. #### abstract def sign(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise sign of the input.

Example::

sign([-2, 0, 3]) = [-1, 0, 1]

The storage type of sign output depends upon the input storage type:

- sign(default) = default
- sign(row_sparse) = row_sparse
- sign(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L758
returns

org.apache.mxnet.Symbol

235. #### abstract def signsgd_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Update function for SignSGD optimizer.

.. math::

g_t = \nabla J(W_{t-1})\\
W_t = W_{t-1} - \eta_t \text{sign}(g_t)

weight = weight - learning_rate * sign(gradient)

.. note::
- sparse ndarray not supported for this optimizer yet.

Defined in src/operator/optimizer_op.cc:L63
returns

org.apache.mxnet.Symbol

236. #### abstract def signum_update(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

SIGN momentUM (Signum) optimizer.

.. math::

g_t = \nabla J(W_{t-1})\\
m_t = \beta m_{t-1} + (1 - \beta) g_t\\
W_t = W_{t-1} - \eta_t \text{sign}(m_t)

state = momentum * state + (1-momentum) * gradient
weight = weight - learning_rate * sign(state)

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

.. note::
- sparse ndarray not supported for this optimizer yet.

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

org.apache.mxnet.Symbol

237. #### abstract def sin(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the element-wise sine of the input array.

The input should be in radians (:math:2\pi rad equals 360 degrees).

.. math::
sin([0, \pi/4, \pi/2]) = [0, 0.707, 1]

The storage type of sin output depends upon the input storage type:

- sin(default) = default
- sin(row_sparse) = row_sparse
- sin(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L47
returns

org.apache.mxnet.Symbol

238. #### abstract def sinh(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the hyperbolic sine of the input array, computed element-wise.

.. math::
sinh(x) = 0.5\times(exp(x) - exp(-x))

The storage type of sinh output depends upon the input storage type:

- sinh(default) = default
- sinh(row_sparse) = row_sparse
- sinh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L371
returns

org.apache.mxnet.Symbol

239. #### abstract def size_array(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns a 1D int64 array containing the size of data.

Example::

size_array([ [1,2,3,4], [5,6,7,8] ]) = [8]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L624
returns

org.apache.mxnet.Symbol

240. #### abstract def slice(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L482
returns

org.apache.mxnet.Symbol

241. #### abstract def slice_axis(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L571
returns

org.apache.mxnet.Symbol

242. #### abstract def slice_like(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L625
returns

org.apache.mxnet.Symbol

243. #### abstract def smooth_l1(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Calculate Smooth L1 Loss(lhs, scalar) by summing

.. math::

f(x) =
\begin{cases}
(\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
|x|-0.5/\sigma^2,& \text{otherwise}
\end{cases}

where :math:x is an element of the tensor *lhs* and :math:\sigma is the scalar.

Example::

smooth_l1([1, 2, 3, 4]) = [0.5, 1.5, 2.5, 3.5]
smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]

Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L109
returns

org.apache.mxnet.Symbol

244. #### abstract def softmax(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies the softmax function.

The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.

.. math::
softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}

for :math:j = 1, ..., K

t is the temperature parameter in softmax function. By default, t equals 1.0

Example::

x = [ [ 1.  1.  1.]
[ 1.  1.  1.] ]

softmax(x,axis=0) = [ [ 0.5  0.5  0.5]
[ 0.5  0.5  0.5] ]

softmax(x,axis=1) = [ [ 0.33333334,  0.33333334,  0.33333334],
[ 0.33333334,  0.33333334,  0.33333334] ]

Defined in src/operator/nn/softmax.cc:L134
returns

org.apache.mxnet.Symbol

245. #### abstract def softmax_cross_entropy(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Calculate cross entropy of softmax output and one-hot label.

- This operator computes the cross entropy in two steps:
- Applies softmax function on the input array.
- Computes and returns the cross entropy loss between the softmax output and the labels.

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

- Softmax Function:

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

- Cross Entropy Function:

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

Example::

x = [ [1, 2, 3],
[11, 7, 5] ]

label = [2, 0]

softmax(x) = [ [0.09003057, 0.24472848, 0.66524094],
[0.97962922, 0.01794253, 0.00242826] ]

softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871

Defined in src/operator/loss_binary_op.cc:L59
returns

org.apache.mxnet.Symbol

246. #### abstract def softmin(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Applies the softmin function.

The resulting array contains elements in the range (0,1) and the elements along the given axis sum
up to 1.

.. math::
softmin(\mathbf{z/t})_j = \frac{e^{-z_j/t}}{\sum_{k=1}^K e^{-z_k/t}}

for :math:j = 1, ..., K

t is the temperature parameter in softmax function. By default, t equals 1.0

Example::

x = [ [ 1.  2.  3.]
[ 3.  2.  1.] ]

softmin(x,axis=0) = [ [ 0.88079703,  0.5,  0.11920292],
[ 0.11920292,  0.5,  0.88079703] ]

softmin(x,axis=1) = [ [ 0.66524094,  0.24472848,  0.09003057],
[ 0.09003057,  0.24472848,  0.66524094] ]

Defined in src/operator/nn/softmin.cc:L57
returns

org.apache.mxnet.Symbol

247. #### abstract def softsign(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes softsign of x element-wise.

.. math::
y = x / (1 + abs(x))

The storage type of softsign output is always dense

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L191
returns

org.apache.mxnet.Symbol

248. #### abstract def sort(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns a sorted copy of an input array along the given axis.

Examples::

x = [ [ 1, 4],
[ 3, 1] ]

// sorts along the last axis
sort(x) = [ [ 1.,  4.],
[ 1.,  3.] ]

// flattens and then sorts
sort(x, axis=None) = [ 1.,  1.,  3.,  4.]

// sorts along the first axis
sort(x, axis=0) = [ [ 1.,  1.],
[ 3.,  4.] ]

// in a descend order
sort(x, is_ascend=0) = [ [ 4.,  1.],
[ 3.,  1.] ]

Defined in src/operator/tensor/ordering_op.cc:L133
returns

org.apache.mxnet.Symbol

249. #### abstract def space_to_depth(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L1019
returns

org.apache.mxnet.Symbol

250. #### abstract def split(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

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

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

Example::

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

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

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

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

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

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

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

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

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

Example::

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

[ [ 3.]
[ 4.] ]

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

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

org.apache.mxnet.Symbol

251. #### abstract def sqrt(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise square-root value of the input.

.. math::
\textrm{sqrt}(x) = \sqrt{x}

Example::

sqrt([4, 9, 16]) = [2, 3, 4]

The storage type of sqrt output depends upon the input storage type:

- sqrt(default) = default
- sqrt(row_sparse) = row_sparse
- sqrt(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L170
returns

org.apache.mxnet.Symbol

252. #### abstract def square(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns element-wise squared value of the input.

.. math::
square(x) = x^2

Example::

square([2, 3, 4]) = [4, 9, 16]

The storage type of square output depends upon the input storage type:

- square(default) = default
- square(row_sparse) = row_sparse
- square(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L119
returns

org.apache.mxnet.Symbol

253. #### abstract def squeeze(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

org.apache.mxnet.Symbol

254. #### abstract def stack(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

org.apache.mxnet.Symbol

255. #### abstract def stop_gradient(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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.Symbol

256. #### abstract def sum(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the sum of array elements over given axes.

.. Note::

sum and sum_axis are equivalent.
For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
Setting keepdims or exclude to True will cause a fallback to dense operator.

Example::

data = [ [ [1, 2], [2, 3], [1, 3] ],
[ [1, 4], [4, 3], [5, 2] ],
[ [7, 1], [7, 2], [7, 3] ] ]

sum(data, axis=1)
[ [  4.   8.]
[ 10.   9.]
[ 21.   6.] ]

sum(data, axis=[1,2])
[ 12.  19.  27.]

data = [ [1, 2, 0],
[3, 0, 1],
[4, 1, 0] ]

csr = cast_storage(data, 'csr')

sum(csr, axis=0)
[ 8.  3.  1.]

sum(csr, axis=1)
[ 3.  4.  5.]

returns

org.apache.mxnet.Symbol

257. #### abstract def sum_axis(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the sum of array elements over given axes.

.. Note::

sum and sum_axis are equivalent.
For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
Setting keepdims or exclude to True will cause a fallback to dense operator.

Example::

data = [ [ [1, 2], [2, 3], [1, 3] ],
[ [1, 4], [4, 3], [5, 2] ],
[ [7, 1], [7, 2], [7, 3] ] ]

sum(data, axis=1)
[ [  4.   8.]
[ 10.   9.]
[ 21.   6.] ]

sum(data, axis=[1,2])
[ 12.  19.  27.]

data = [ [1, 2, 0],
[3, 0, 1],
[4, 1, 0] ]

csr = cast_storage(data, 'csr')

sum(csr, axis=0)
[ 8.  3.  1.]

sum(csr, axis=1)
[ 3.  4.  5.]

returns

org.apache.mxnet.Symbol

258. #### abstract def swapaxes(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Interchanges two axes of an array.

Examples::

x = [ [1, 2, 3] ])
swapaxes(x, 0, 1) = [ [ 1],
[ 2],
[ 3] ]

x = [ [ [ 0, 1],
[ 2, 3] ],
[ [ 4, 5],
[ 6, 7] ] ]  // (2,2,2) array

swapaxes(x, 0, 2) = [ [ [ 0, 4],
[ 2, 6] ],
[ [ 1, 5],
[ 3, 7] ] ]

Defined in src/operator/swapaxis.cc:L70
returns

org.apache.mxnet.Symbol

259. #### abstract def take(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Takes elements from an input array along the given axis.

This function slices the input array along a particular axis with the provided indices.

Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis
dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them
in an output tensor of rank q + (r - 1).

Examples::

x = [4.  5.  6.]

// Trivial case, take the second element along the first axis.

take(x, [1]) = [ 5. ]

// The other trivial case, axis=-1, take the third element along the first axis

take(x, [3], axis=-1, mode='clip') = [ 6. ]

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

// In this case we will get rows 0 and 1, then 1 and 2. Along axis 0

take(x, [ [0,1],[1,2] ]) = [ [ [ 1.,  2.],
[ 3.,  4.] ],

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

// In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around).
// Along axis 1

take(x, [ [0, 3], [-1, -2] ], axis=1, mode='wrap') = [ [ [ 1.  2.]
[ 2.  1.] ]

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

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

The storage type of take output depends upon the input storage type:

- take(default, default) = default
- take(csr, default, axis=0) = csr

Defined in src/operator/tensor/indexing_op.cc:L777
returns

org.apache.mxnet.Symbol

260. #### abstract def tan(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Computes the element-wise tangent of the input array.

The input should be in radians (:math:2\pi rad equals 360 degrees).

.. math::
tan([0, \pi/4, \pi/2]) = [0, 1, -inf]

The storage type of tan output depends upon the input storage type:

- tan(default) = default
- tan(row_sparse) = row_sparse
- tan(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L140
returns

org.apache.mxnet.Symbol

261. #### abstract def tanh(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the hyperbolic tangent of the input array, computed element-wise.

.. math::
tanh(x) = sinh(x) / cosh(x)

The storage type of tanh output depends upon the input storage type:

- tanh(default) = default
- tanh(row_sparse) = row_sparse
- tanh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L451
returns

org.apache.mxnet.Symbol

262. #### abstract def tile(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

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

Defined in src/operator/tensor/matrix_op.cc:L796
returns

org.apache.mxnet.Symbol

263. #### abstract def topk(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Returns the indices of the top *k* elements in an input array along the given
axis (by default).
If ret_type is set to 'value' returns the value of top *k* elements (instead of indices).
In case of ret_type = 'both', both value and index would be returned.
The returned elements will be sorted.

Examples::

x = [ [ 0.3,  0.2,  0.4],
[ 0.1,  0.3,  0.2] ]

// returns an index of the largest element on last axis
topk(x) = [ [ 2.],
[ 1.] ]

// returns the value of top-2 largest elements on last axis
topk(x, ret_typ='value', k=2) = [ [ 0.4,  0.3],
[ 0.3,  0.2] ]

// returns the value of top-2 smallest elements on last axis
topk(x, ret_typ='value', k=2, is_ascend=1) = [ [ 0.2 ,  0.3],
[ 0.1 ,  0.2] ]

// returns the value of top-2 largest elements on axis 0
topk(x, axis=0, ret_typ='value', k=2) = [ [ 0.3,  0.3,  0.4],
[ 0.1,  0.2,  0.2] ]

// flattens and then returns list of both values and indices
topk(x, ret_typ='both', k=2) = [ [ [ 0.4,  0.3], [ 0.3,  0.2] ] ,  [ [ 2.,  0.], [ 1.,  2.] ] ]

Defined in src/operator/tensor/ordering_op.cc:L68
returns

org.apache.mxnet.Symbol

264. #### abstract def transpose(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Permutes the dimensions of an array.
Examples::
x = [ [ 1, 2],
[ 3, 4] ]
transpose(x) = [ [ 1.,  3.],
[ 2.,  4.] ]
x = [ [ [ 1.,  2.],
[ 3.,  4.] ],
[ [ 5.,  6.],
[ 7.,  8.] ] ]
transpose(x) = [ [ [ 1.,  5.],
[ 3.,  7.] ],
[ [ 2.,  6.],
[ 4.,  8.] ] ]
transpose(x, axes=(1,0,2)) = [ [ [ 1.,  2.],
[ 5.,  6.] ],
[ [ 3.,  4.],
[ 7.,  8.] ] ]

Defined in src/operator/tensor/matrix_op.cc:L328
returns

org.apache.mxnet.Symbol

265. #### abstract def trunc(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Return the element-wise truncated value of the input.

The truncated value of the scalar x is the nearest integer i which is closer to
zero than x is. In short, the fractional part of the signed number x is discarded.

Example::

trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  1.,  1.,  2.]

The storage type of trunc output depends upon the input storage type:

- trunc(default) = default
- trunc(row_sparse) = row_sparse
- trunc(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L856
returns

org.apache.mxnet.Symbol

266. #### abstract def uniform(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Draw random samples from a uniform distribution.

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

Samples are uniformly distributed over the half-open interval *[low, high)*
(includes *low*, but excludes *high*).

Example::

uniform(low=0, high=1, shape=(2,2)) = [ [ 0.60276335,  0.85794562],
[ 0.54488319,  0.84725171] ]

Defined in src/operator/random/sample_op.cc:L96
returns

org.apache.mxnet.Symbol

267. #### abstract def unravel_index(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix. The leading dimension may be left unspecified by using -1 as placeholder.

Examples::

A = [22,41,37]
unravel(A, shape=(7,6)) = [ [3,6,6],[4,5,1] ]
unravel(A, shape=(-1,6)) = [ [3,6,6],[4,5,1] ]

Defined in src/operator/tensor/ravel.cc:L68
returns

org.apache.mxnet.Symbol

268. #### abstract def where(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Return the elements, either from x or y, depending on the condition.

Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y,
depending on the elements from condition are true or false. x and y must have the same shape.
If condition has the same shape as x, each element in the output array is from x if the
corresponding element in the condition is true, and from y if false.

If condition does not have the same shape as x, it must be a 1D array whose size is
the same as x's first dimension size. Each row of the output array is from x's row
if the corresponding element from condition is true, and from y's row if false.

Note that all non-zero values are interpreted as True in condition.

Examples::

x = [ [1, 2], [3, 4] ]
y = [ [5, 6], [7, 8] ]
cond = [ [0, 1], [-1, 0] ]

where(cond, x, y) = [ [5, 2], [3, 8] ]

csr_cond = cast_storage(cond, 'csr')

where(csr_cond, x, y) = [ [5, 2], [3, 8] ]

Defined in src/operator/tensor/control_flow_op.cc:L57
returns

org.apache.mxnet.Symbol

269. #### abstract def zeros_like(name: String = null, attr: Map[String, String] = null)(args: Symbol*)(kwargs: Map[String, Any] = null): Symbol

Return an array of zeros with the same shape, type and storage type
as the input array.

The storage type of zeros_like output depends on the storage type of the input

- zeros_like(row_sparse) = row_sparse
- zeros_like(csr) = csr
- zeros_like(default) = default

Examples::

x = [ [ 1.,  1.,  1.],
[ 1.,  1.,  1.] ]

zeros_like(x) = `[ [ 0.,  0.,  0.],
[ 0.,  0.,  0.] ]
returns

org.apache.mxnet.Symbol

### Concrete Value Members

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

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

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

Definition Classes
AnyRef → Any
4. #### final def asInstanceOf[T0]: T0

Definition Classes
Any
5. #### def clone(): AnyRef

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

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

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

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

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

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

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

Definition Classes
AnyRef
13. #### final def notify(): Unit

Definition Classes
AnyRef
14. #### final def notifyAll(): Unit

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

Definition Classes
AnyRef
16. #### def toString(): String

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

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

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

Definition Classes
AnyRef
Annotations
@throws( ... )