Returns a copy of the input.

From:src/operator/tensor/elemwise_unary_op_basic.cc:218

`data`: The input array.
`out`: Output array. (optional)

Extracts the diagonal entries of a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, then *A* represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor.

If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an *n-1*-dimensional tensor.

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

Examples::

    // Single matrix diagonal extraction
    A = [[1.0, 2.0],
         [3.0, 4.0]]

    extractdiag(A) = [1.0, 4.0]

    extractdiag(A, 1) = [2.0]

    // Batch matrix diagonal extraction
    A = [[[1.0, 2.0],
          [3.0, 4.0]],
         [[5.0, 6.0],
          [7.0, 8.0]]]

    extractdiag(A) = [[1.0, 4.0],
                      [5.0, 8.0]]


Defined in src/operator/tensor/la_op.cc:L495

`a`: Tensor of square matrices
`offset`: Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal. (optional)
`out`: Output array. (optional)

Extracts a triangular sub-matrix from a square matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, then *A* represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor.

If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an *n-1*-dimensional tensor.

The *offset* and *lower* parameters determine the triangle to be extracted:

- When *offset = 0* either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter *lower*.
- When *offset = k > 0* the upper triangle with respect to the k-th diagonal above the main diagonal is extracted. 
- When *offset = k < 0* the lower triangle with respect to the k-th diagonal below the main diagonal is extracted. 

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

Examples::

    // Single triagonal extraction
    A = [[1.0, 2.0],
         [3.0, 4.0]]

    extracttrian(A) = [1.0, 3.0, 4.0]
    extracttrian(A, lower=False) = [1.0, 2.0, 4.0]
    extracttrian(A, 1) = [2.0]
    extracttrian(A, -1) = [3.0]

    // Batch triagonal extraction
    A = [[[1.0, 2.0],
          [3.0, 4.0]],
         [[5.0, 6.0],
          [7.0, 8.0]]]

    extracttrian(A) = [[1.0, 3.0, 4.0],
                       [5.0, 7.0, 8.0]]


Defined in src/operator/tensor/la_op.cc:L605

`a`: Tensor of square matrices
`offset`: Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal. (optional)
`lower`: Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0 (optional)
`out`: Output array. (optional)

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

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

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

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

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

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

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

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

Examples::

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

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


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

`a`: Tensor of input matrices to be factorized
`out`: Output array. (optional)

Performs general matrix multiplication and accumulation.
Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape
on the leading *n-2* dimensions.

If *n=2*, the BLAS3 function *gemm* is performed:

   *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C*

Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or
matrix transposition (depending on *transpose_a*, *transpose_b*).

If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
parameter. By default, the trailing two dimensions will be used for matrix encoding.

For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent
to the following without the overhead of the additional swapaxis operations::

    A1 = swapaxes(A, dim1=1, dim2=3)
    B1 = swapaxes(B, dim1=1, dim2=3)
    C = swapaxes(C, dim1=1, dim2=3)
    C = gemm(A1, B1, C)
    C = swapaxis(C, dim1=1, dim2=3)

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

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

Examples::

   // Single matrix multiply-add
   A = [[1.0, 1.0], [1.0, 1.0]]
   B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
   C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
   gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
           = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]

   // Batch matrix multiply-add
   A = [[[1.0, 1.0]], [[0.1, 0.1]]]
   B = [[[1.0, 1.0]], [[0.1, 0.1]]]
   C = [[[10.0]], [[0.01]]]
   gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
           = [[[104.0]], [[0.14]]]


Defined in src/operator/tensor/la_op.cc:L89

`a`: Tensor of input matrices
`b`: Tensor of input matrices
`c`: Tensor of input matrices
`transpose-a`: Multiply with transposed of first input (A). (optional)
`transpose-b`: Multiply with transposed of second input (B). (optional)
`alpha`: Scalar factor multiplied with A*B. (optional)
`beta`: Scalar factor multiplied with C. (optional)
`axis`: Axis corresponding to the matrix rows. (optional)
`out`: Output array. (optional)

Performs general matrix multiplication.
Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape
on the leading *n-2* dimensions.

If *n=2*, the BLAS3 function *gemm* is performed:

   *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*)

Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix
transposition (depending on *transpose_a*, *transpose_b*).

If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices
are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis*
parameter. By default, the trailing two dimensions will be used for matrix encoding.

For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes
calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to
the following without the overhead of the additional swapaxis operations::

    A1 = swapaxes(A, dim1=1, dim2=3)
    B1 = swapaxes(B, dim1=1, dim2=3)
    C = gemm2(A1, B1)
    C = swapaxis(C, dim1=1, dim2=3)

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

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

Examples::

   // Single matrix multiply
   A = [[1.0, 1.0], [1.0, 1.0]]
   B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
   gemm2(A, B, transpose_b=True, alpha=2.0)
            = [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]

   // Batch matrix multiply
   A = [[[1.0, 1.0]], [[0.1, 0.1]]]
   B = [[[1.0, 1.0]], [[0.1, 0.1]]]
   gemm2(A, B, transpose_b=True, alpha=2.0)
           = [[[4.0]], [[0.04 ]]]


Defined in src/operator/tensor/la_op.cc:L163

`a`: Tensor of input matrices
`b`: Tensor of input matrices
`transpose-a`: Multiply with transposed of first input (A). (optional)
`transpose-b`: Multiply with transposed of second input (B). (optional)
`alpha`: Scalar factor multiplied with A*B. (optional)
`axis`: Axis corresponding to the matrix row indices. (optional)
`out`: Output array. (optional)

Compute the inverse of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a square matrix. We compute:

  *out* = *A*\ :sup:`-1`

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

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

Examples::

   // Single matrix inversion
   A = [[1., 4.], [2., 3.]]
   inverse(A) = [[-0.6, 0.8], [0.4, -0.2]]

   // Batch matrix inversion
   A = [[[1., 4.], [2., 3.]],
        [[1., 3.], [2., 4.]]]
   inverse(A) = [[[-0.6, 0.8], [0.4, -0.2]],
                 [[-2., 1.5], [1., -0.5]]]


Defined in src/operator/tensor/la_op.cc:L917

`a`: Tensor of square matrix
`out`: Output array. (optional)

Constructs a square matrix with the input as diagonal.
Input is a tensor *A* of dimension *n >= 1*.

If *n=1*, then *A* represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor.
If *n>1*, then *A* represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an *n+1*-dimensional tensor.

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

Examples::

    // Single diagonal matrix construction
    A = [1.0, 2.0]

    makediag(A)    = [[1.0, 0.0],
                      [0.0, 2.0]]

    makediag(A, 1) = [[0.0, 1.0, 0.0],
                      [0.0, 0.0, 2.0],
                      [0.0, 0.0, 0.0]]

    // Batch diagonal matrix construction
    A = [[1.0, 2.0],
         [3.0, 4.0]]

    makediag(A) = [[[1.0, 0.0],
                    [0.0, 2.0]],
                   [[3.0, 0.0],
                    [0.0, 4.0]]]


Defined in src/operator/tensor/la_op.cc:L547

`a`: Tensor of diagonal entries
`offset`: Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal. (optional)
`out`: Output array. (optional)

Constructs a square matrix with the input representing a specific triangular sub-matrix.
This is basically the inverse of *linalg.extracttrian*. Input is a tensor *A* of dimension *n >= 1*.

If *n=1*, then *A* represents the entries of a triangular matrix which is lower triangular if *offset<0* or *offset=0*, *lower=true*. The resulting matrix is derived by first constructing the square
matrix with the entries outside the triangle set to zero and then adding *offset*-times an additional 
diagonal with zero entries to the square matrix. 

If *n>1*, then *A* represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an *n+1*-dimensional tensor.

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

Examples::

    // Single  matrix construction
    A = [1.0, 2.0, 3.0]

    maketrian(A)              = [[1.0, 0.0],
                                 [2.0, 3.0]]

    maketrian(A, lower=false) = [[1.0, 2.0],
                                 [0.0, 3.0]]

    maketrian(A, offset=1)    = [[0.0, 1.0, 2.0],
                                 [0.0, 0.0, 3.0],
                                 [0.0, 0.0, 0.0]]
    maketrian(A, offset=-1)   = [[0.0, 0.0, 0.0],
                                 [1.0, 0.0, 0.0],
                                 [2.0, 3.0, 0.0]]

    // Batch matrix construction
    A = [[1.0, 2.0, 3.0],
         [4.0, 5.0, 6.0]]

    maketrian(A)           = [[[1.0, 0.0],
                               [2.0, 3.0]],
                              [[4.0, 0.0],
                               [5.0, 6.0]]]

    maketrian(A, offset=1) = [[[0.0, 1.0, 2.0],
                               [0.0, 0.0, 3.0],
                               [0.0, 0.0, 0.0]],
                              [[0.0, 4.0, 5.0],
                               [0.0, 0.0, 6.0],
                               [0.0, 0.0, 0.0]]]


Defined in src/operator/tensor/la_op.cc:L673

`a`: Tensor of triangular matrices stored as vectors
`offset`: Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal. (optional)
`lower`: Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0 (optional)
`out`: Output array. (optional)

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

If *n=2*, the Cholesky factor *B* of the symmetric, positive definite matrix *A* is
computed. *B* is triangular (entries of upper or lower triangle are all zero), has
positive diagonal entries, and:

  *A* = *B* \* *B*\ :sup:`T`  if *lower* = *true*
  *A* = *B*\ :sup:`T` \* *B*  if *lower* = *false*

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

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

Examples::

   // Single matrix factorization
   A = [[4.0, 1.0], [1.0, 4.25]]
   potrf(A) = [[2.0, 0], [0.5, 2.0]]

   // Batch matrix factorization
   A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
   potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]


Defined in src/operator/tensor/la_op.cc:L214

`a`: Tensor of input matrices to be decomposed
`out`: Output array. (optional)

Performs matrix inversion from a Cholesky factorization.
Input is a tensor *A* of dimension *n >= 2*.

If *n=2*, *A* is a triangular matrix (entries of upper or lower triangle are all zero)
with positive diagonal. We compute:

  *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1` if *lower* = *true*
  *out* = *A*\ :sup:`-1` \* *A*\ :sup:`-T` if *lower* = *false*

In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix
*B* (obtained by *potrf*), then

  *out* = *B*\ :sup:`-1`

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

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

.. note:: Use this operator only if you are certain you need the inverse of *B*, and
          cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution
          (*trsm*). The latter is numerically much safer, and also cheaper.

Examples::

   // Single matrix inverse
   A = [[2.0, 0], [0.5, 2.0]]
   potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]

   // Batch matrix inverse
   A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
   potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
               [[0.06641, -0.01562], [-0.01562, 0,0625]]]


Defined in src/operator/tensor/la_op.cc:L275

`a`: Tensor of lower triangular matrices
`out`: Output array. (optional)

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

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

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

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

Examples::

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

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


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

`a`: Tensor of square matrices
`out`: Output array. (optional)

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

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

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

if *transpose=False*, or

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

if *transpose=True*.

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

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

Examples::

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

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


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

`a`: Tensor of input matrices
`transpose`: Use transpose of input matrix. (optional)
`alpha`: Scalar factor to be applied to the result. (optional)
`out`: Output array. (optional)

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

If *n=2*, *A* must be triangular. The operator performs the BLAS3 function
*trmm*:

   *out* = *alpha* \* *op*\ (*A*) \* *B*

if *rightside=False*, or

   *out* = *alpha* \* *B* \* *op*\ (*A*)

if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
identity or the matrix transposition (depending on *transpose*).

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

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

Examples::

   // Single triangular matrix multiply
   A = [[1.0, 0], [1.0, 1.0]]
   B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
   trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]

   // Batch triangular matrix multiply
   A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
   B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
   trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
                            [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]


Defined in src/operator/tensor/la_op.cc:L333

`a`: Tensor of lower triangular matrices
`b`: Tensor of matrices
`transpose`: Use transposed of the triangular matrix (optional)
`rightside`: Multiply triangular matrix from the right to non-triangular one. (optional)
`lower`: True if the triangular matrix is lower triangular, false if it is upper triangular. (optional)
`alpha`: Scalar factor to be applied to the result. (optional)
`out`: Output array. (optional)

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

If *n=2*, *A* must be triangular. The operator performs the BLAS3 function
*trsm*, solving for *out* in:

   *op*\ (*A*) \* *out* = *alpha* \* *B*

if *rightside=False*, or

   *out* \* *op*\ (*A*) = *alpha* \* *B*

if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the
identity or the matrix transposition (depending on *transpose*).

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

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

Examples::

   // Single matrix solve
   A = [[1.0, 0], [1.0, 1.0]]
   B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
   trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]

   // Batch matrix solve
   A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
   B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
        [[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
   trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
                            [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]


Defined in src/operator/tensor/la_op.cc:L396

`a`: Tensor of lower triangular matrices
`b`: Tensor of matrices
`transpose`: Use transposed of the triangular matrix (optional)
`rightside`: Multiply triangular matrix from the right to non-triangular one. (optional)
`lower`: True if the triangular matrix is lower triangular, false if it is upper triangular. (optional)
`alpha`: Scalar factor to be applied to the result. (optional)
`out`: Output array. (optional)

Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix. The leading dimension may be left unspecified by using -1 as placeholder.  

Examples::
   
   A = [[3,6,6],[4,5,1]]
   ravel(A, shape=(7,6)) = [22,41,37]
   ravel(A, shape=(-1,6)) = [22,41,37]



Defined in src/operator/tensor/ravel.cc:L42

`data`: Batch of multi-indices
`shape`: Shape of the array into which the multi-indices apply. (optional)
`out`: Output array. (optional)

Randomly shuffle the elements.

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


`data`: Data to be shuffled.
`out`: Output array. (optional)

Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix. The leading dimension may be left unspecified by using -1 as placeholder.  

Examples::

   A = [22,41,37]
   unravel(A, shape=(7,6)) = [[3,6,6],[4,5,1]]
   unravel(A, shape=(-1,6)) = [[3,6,6],[4,5,1]]



Defined in src/operator/tensor/ravel.cc:L67

`data`: Array of flat indices
`shape`: Shape of the array into which the multi-indices apply. (optional)
`out`: Output array. (optional)

Returns element-wise absolute value of the input.

Example::

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L708

`data`: The input array.
`out`: Output array. (optional)

Applies an activation function element-wise to the input.

The following activation functions are supported:

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



Defined in src/operator/nn/activation.cc:L167

`data`: The input array.
`act-type`: Activation function to be applied.
`out`: Output array. (optional)

Update function for Adam optimizer. Adam is seen as a generalization
of AdaGrad.

Adam update consists of the following steps, where g represents gradient and m, v
are 1st and 2nd order moment estimates (mean and variance).

.. math::

 g_t = \nabla J(W_{t-1})\\
 m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\
 v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
 W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }

It updates the weights using::

 m = beta1*m + (1-beta1)*grad
 v = beta2*v + (1-beta2)*(grad**2)
 w += - learning_rate * m / (sqrt(v) + epsilon)

However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage
type of weight is the same as those of m and v,
only the row slices whose indices appear in grad.indices are updated (for w, m and v)::

 for row in grad.indices:
     m[row] = beta1*m[row] + (1-beta1)*grad[row]
     v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2)
     w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon)



Defined in src/operator/optimizer_op.cc:L686

`weight`: Weight
`grad`: Gradient
`mean`: Moving mean
`var`: Moving variance
`lr`: Learning rate
`beta1`: The decay rate for the 1st moment estimates. (optional)
`beta2`: The decay rate for the 2nd moment estimates. (optional)
`epsilon`: A small constant for numerical stability. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`lazy-update`: If true, lazy updates are applied if gradient's stype is row_sparse and all of w, m and v have the same stype (optional)
`out`: Output array. (optional)

Adds all input arguments element-wise.

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

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

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

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



Defined in src/operator/tensor/elemwise_sum.cc:L155

`args`: Positional input arguments
`out`: Output array. (optional)

Check if all the float numbers in the array are finite (used for AMP)


Defined in src/operator/contrib/all_finite.cc:L101

`data`: Array
`init-output`: Initialize output to 1. (optional)
`out`: Output array. (optional)

Cast function between low precision float/FP32 used by AMP.

It casts only between low precision float/FP32 and does not do anything for other types.


Defined in src/operator/tensor/amp_cast.cc:L37

`data`: The input.
`dtype`: Output data type.
`out`: Output array. (optional)

Cast function used by AMP, that casts its inputs to the common widest type.

It casts only between low precision float/FP32 and does not do anything for other types.



Defined in src/operator/tensor/amp_cast.cc:L71

`data`: Weights
`num-outputs`: Number of input/output pairs to be casted to the widest type.
`out`: Output array. (optional)

Returns element-wise inverse cosine of the input array.

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

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

The storage type of ``arccos`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L179

`data`: The input array.
`out`: Output array. (optional)

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

The storage type of ``arccosh`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L320

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise inverse sine of the input array.

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

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L160

`data`: The input array.
`out`: Output array. (optional)

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L306

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise inverse tangent of the input array.

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

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L200

`data`: The input array.
`out`: Output array. (optional)

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L337

`data`: The input array.
`out`: Output array. (optional)

Returns indices of the maximum values along an axis.

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

Examples::

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

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

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

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



Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52

`data`: The input
`axis`: The axis along which to perform the reduction. Negative values means indexing from right to left. ``Requires axis to be set as int, because global reduction is not supported yet.`` (optional)
`keepdims`: If this is set to `True`, the reduced axis is left in the result as dimension with size one. (optional)
`out`: Output array. (optional)

Returns argmax indices of each channel from the input array.

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

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

Examples::

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

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



Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97

`data`: The input array
`out`: Output array. (optional)

Returns indices of the minimum values along an axis.

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

Examples::

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

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

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

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



Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77

`data`: The input
`axis`: The axis along which to perform the reduction. Negative values means indexing from right to left. ``Requires axis to be set as int, because global reduction is not supported yet.`` (optional)
`keepdims`: If this is set to `True`, the reduced axis is left in the result as dimension with size one. (optional)
`out`: Output array. (optional)

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

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

Examples::

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

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

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

  // flatten and then sort
  argsort(x) = [ 3.,  1.,  5.,  0.,  4.,  2.]


Defined in src/operator/tensor/ordering_op.cc:L177

`data`: The input array
`axis`: Axis along which to sort the input tensor. If not given, the flattened array is used. Default is -1. (optional)
`is-ascend`: Whether to sort in ascending or descending order. (optional)
`dtype`: DType of the output indices. It is only valid when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely represent the indices. (optional)
`out`: Output array. (optional)

Batchwise dot product.

``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and
``y`` are data in batch, namely 3D arrays in shape of `(batch_size, :, :)`.

For example, given ``x`` with shape `(batch_size, n, m)` and ``y`` with shape
`(batch_size, m, k)`, the result array will have shape `(batch_size, n, k)`,
which is computed by::

   batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:])



Defined in src/operator/tensor/dot.cc:L125

`lhs`: The first input
`rhs`: The second input
`transpose-a`: If true then transpose the first input before dot. (optional)
`transpose-b`: If true then transpose the second input before dot. (optional)
`forward-stype`: The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type. (optional)
`out`: Output array. (optional)

Batch normalization.

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

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

.. math::

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

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

.. math::

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

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

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

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

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

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

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

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

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



Defined in src/operator/nn/batch_norm.cc:L572

`data`: Input data to batch normalization
`gamma`: gamma array
`beta`: beta array
`moving-mean`: running mean of input
`moving-var`: running variance of input
`eps`: Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5) (optional)
`momentum`: Momentum for moving average (optional)
`fix-gamma`: Fix gamma while training (optional)
`use-global-stats`: Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator. (optional)
`output-mean-var`: Output the mean and inverse std  (optional)
`axis`: Specify which shape axis the channel is specified (optional)
`cudnn-off`: Do not select CUDNN operator, if available (optional)
`out`: Output array. (optional)

Batch normalization.

This operator is DEPRECATED. Perform BatchNorm on the input.

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

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

.. math::

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

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

.. math::

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

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

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

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

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

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

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

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



Defined in src/operator/batch_norm_v1.cc:L95

`data`: Input data to batch normalization
`gamma`: gamma array
`beta`: beta array
`eps`: Epsilon to prevent div 0 (optional)
`momentum`: Momentum for moving average (optional)
`fix-gamma`: Fix gamma while training (optional)
`use-global-stats`: Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator. (optional)
`output-mean-var`: Output All,normal mean and var (optional)
`out`: Output array. (optional)

Takes elements from a data batch.

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

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

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

Examples::

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

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



Defined in src/operator/tensor/indexing_op.cc:L753

`a`: The input array
`indices`: The index array
`out`: Output array. (optional)

Applies bilinear sampling to input feature map.

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

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

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

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

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

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

Example 1::

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

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

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

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

  out = BilinearSampler(data, grid)

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


Example 2::

  ## shift data horizontally by -1 pixel

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

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

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

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


Defined in src/operator/bilinear_sampler.cc:L256

`data`: Input data to the BilinearsamplerOp.
`grid`: Input grid to the BilinearsamplerOp.grid has two channels: x_src, y_src
`cudnn-off`: whether to turn cudnn off (optional)
`out`: Output array. (optional)

Stops gradient computation.

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

Example::

  v1 = [1, 2]
  v2 = [0, 1]
  a = Variable('a')
  b = Variable('b')
  b_stop_grad = stop_gradient(3 * b)
  loss = MakeLoss(b_stop_grad + a)

  executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
  executor.forward(is_train=True, a=v1, b=v2)
  executor.outputs
  [ 1.  5.]

  executor.backward()
  executor.grad_arrays
  [ 0.  0.]
  [ 1.  1.]



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L299

`data`: The input array.
`out`: Output array. (optional)

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

`broadcast_plus` is an alias to the function `broadcast_add`.

Example::

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

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

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

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

Supported sparse operations:

   broadcast_add(csr, dense(1D)) = dense
   broadcast_add(dense(1D), csr) = dense



Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

Broadcasts the input array over particular axes.

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

Example::

   // given x of shape (1,2,1)
   x = [[[ 1.],
         [ 2.]]]

   // broadcast x on on axis 2
   broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
                                         [ 2.,  2.,  2.]]]
   // broadcast x on on axes 0 and 2
   broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
                                                 [ 2.,  2.,  2.]],
                                                [[ 1.,  1.,  1.],
                                                 [ 2.,  2.,  2.]]]


Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L238

`data`: The input
`axis`: The axes to perform the broadcasting. (optional)
`size`: Target sizes of the broadcasting axes. (optional)
`out`: Output array. (optional)

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

Example::

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

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

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

Supported sparse operations:

   broadcast_div(csr, dense(1D)) = csr



Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

 Returns the hypotenuse of a right angled triangle, given its "legs"
with broadcasting.

It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`.

Example::

   x = [[ 3.,  3.,  3.]]

   y = [[ 4.],
        [ 4.]]

   broadcast_hypot(x, y) = [[ 5.,  5.,  5.],
                            [ 5.,  5.,  5.]]

   z = [[ 0.],
        [ 4.]]

   broadcast_hypot(x, z) = [[ 3.,  3.,  3.],
                            [ 5.,  5.,  5.]]



Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L156

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

Broadcasts lhs to have the same shape as rhs.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>;`_ for more explanation.

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

For example::

   broadcast_like([[1,2,3]], [[5,6,7],[7,8,9]]) = [[ 1.,  2.,  3.],
                                                   [ 1.,  2.,  3.]])

   broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9]



Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L315

`lhs`: First input.
`rhs`: Second input.
`lhs-axes`: Axes to perform broadcast on in the first input array (optional)
`rhs-axes`: Axes to copy from the second input array (optional)
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L80

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L115

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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

Supported sparse operations:

   broadcast_mul(csr, dense(1D)) = csr



Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

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

`broadcast_minus` is an alias to the function `broadcast_sub`.

Example::

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

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

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

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

Supported sparse operations:

   broadcast_sub/minus(csr, dense(1D)) = dense
   broadcast_sub/minus(dense(1D), csr) = dense



Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106

`lhs`: First input to the function
`rhs`: Second input to the function
`out`: Output array. (optional)

Broadcasts the input array to a new shape.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations
with arrays of different shapes efficiently without creating multiple copies of arrays.
Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>;`_ for more explanation.

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

For example::

   broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1.,  2.,  3.],
                                           [ 1.,  2.,  3.]])

The dimension which you do not want to change can also be kept as `0` which means copy the original value.
So with `shape=(2,0)`, we will obtain the same result as in the above example.



Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L262

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

Casts all elements of the input to a new type.

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

Example::

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L634

`data`: The input.
`dtype`: Output data type.
`out`: Output array. (optional)

Casts tensor storage type to the new type.

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

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

The storage type of ``cast_storage`` output depends on stype parameter:

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

Example::

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

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

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



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

`data`: The input.
`stype`: Output storage type.
`out`: Output array. (optional)

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

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L950

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise ceiling of the input.

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L786

`data`: The input array.
`out`: Output array. (optional)

Clips (limits) the values in an array.

Given an interval, values outside the interval are clipped to the interval edges.
Clipping ``x`` between `a_min` and `a_x` would be::

   clip(x, a_min, a_max) = max(min(x, a_max), a_min))

Example::

    x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

    clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]

The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \
parameter values:

   - clip(default) = default
   - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
   - clip(csr, a_min <= 0, a_max >= 0) = csr
   - clip(row_sparse, a_min < 0, a_max < 0) = default
   - clip(row_sparse, a_min > 0, a_max > 0) = default
   - clip(csr, a_min < 0, a_max < 0) = csr
   - clip(csr, a_min > 0, a_max > 0) = csr



Defined in src/operator/tensor/matrix_op.cc:L723

`data`: Input array.
`a-min`: Minimum value
`a-max`: Maximum value
`out`: Output array. (optional)

Joins input arrays along a given axis.

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

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

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

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

Example::

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

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

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

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



Defined in src/operator/nn/concat.cc:L371

`data`: List of arrays to concatenate
`num-args`: Number of inputs to be concated.
`dim`: the dimension to be concated. (optional)
`out`: Output array. (optional)

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

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

.. math::

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

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

For general 2-D convolution, the shapes are

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

Define::

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

then we have::

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

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

The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height,
width)*. We can choose other layouts such as *NWC*.

If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data``
evenly into *g* parts along the channel axis, and also evenly split ``weight``
along the first dimension. Next compute the convolution on the *i*-th part of
the data with the *i*-th weight part. The output is obtained by concatenating all
the *g* results.

1-D convolution does not have *height* dimension but only *width* in space.

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

3-D convolution adds an additional *depth* dimension besides *height* and
*width*. The shapes are

- **data**: *(batch_size, channel, depth, height, width)*
- **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])*
- **bias**: *(num_filter,)*
- **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*.

Both ``weight`` and ``bias`` are learnable parameters.

There are other options to tune the performance.

- **cudnn_tune**: enable this option leads to higher startup time but may give
  faster speed. Options are

  - **off**: no tuning
  - **limited_workspace**:run test and pick the fastest algorithm that doesn't
    exceed workspace limit.
  - **fastest**: pick the fastest algorithm and ignore workspace limit.
  - **None** (default): the behavior is determined by environment variable
    ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace
    (default), 2 for fastest.

- **workspace**: A large number leads to more (GPU) memory usage but may improve
  the performance.



Defined in src/operator/nn/convolution.cc:L472

`data`: Input data to the ConvolutionOp.
`weight`: Weight matrix.
`bias`: Bias parameter.
`kernel`: Convolution kernel size: (w,), (h, w) or (d, h, w)
`stride`: Convolution stride: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
`dilate`: Convolution dilate: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
`pad`: Zero pad for convolution: (w,), (h, w) or (d, h, w). Defaults to no padding. (optional)
`num-filter`: Convolution filter(channel) number
`num-group`: Number of group partitions. (optional)
`workspace`: Maximum temporary workspace allowed (MB) in convolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the convolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when `limited_workspace` strategy is used. (optional)
`no-bias`: Whether to disable bias parameter. (optional)
`cudnn-tune`: Whether to pick convolution algo by running performance test. (optional)
`cudnn-off`: Turn off cudnn for this layer. (optional)
`layout`: Set layout for input, output and weight. Empty for
    default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU. (optional)
`out`: Output array. (optional)

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

`data`: Input data to the ConvolutionV1Op.
`weight`: Weight matrix.
`bias`: Bias parameter.
`kernel`: convolution kernel size: (h, w) or (d, h, w)
`stride`: convolution stride: (h, w) or (d, h, w) (optional)
`dilate`: convolution dilate: (h, w) or (d, h, w) (optional)
`pad`: pad for convolution: (h, w) or (d, h, w) (optional)
`num-filter`: convolution filter(channel) number
`num-group`: Number of group partitions. Equivalent to slicing input into num_group
    partitions, apply convolution on each, then concatenate the results (optional)
`workspace`: Maximum temporary workspace allowed for convolution (MB).This parameter determines the effective batch size of the convolution kernel, which may be smaller than the given batch size. Also, the workspace will be automatically enlarged to make sure that we can run the kernel with batch_size=1 (optional)
`no-bias`: Whether to disable bias parameter. (optional)
`cudnn-tune`: Whether to pick convolution algo by running performance test.
    Leads to higher startup time but may give faster speed. Options are:
    'off': no tuning
    'limited_workspace': run test and pick the fastest algorithm that doesn't exceed workspace limit.
    'fastest': pick the fastest algorithm and ignore workspace limit.
    If set to None (default), behavior is determined by environment
    variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off,
    1 for limited workspace (default), 2 for fastest. (optional)
`cudnn-off`: Turn off cudnn for this layer. (optional)
`layout`: Set layout for input, output and weight. Empty for
    default layout: NCHW for 2d and NCDHW for 3d. (optional)
`out`: Output array. (optional)

Applies correlation to inputs.

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

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

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

.. math::

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

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

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

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

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

The final output is defined by the following expression:

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

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


Defined in src/operator/correlation.cc:L198

`data1`: Input data1 to the correlation.
`data2`: Input data2 to the correlation.
`kernel-size`: kernel size for Correlation must be an odd number (optional)
`max-displacement`: Max displacement of Correlation  (optional)
`stride1`: stride1 quantize data1 globally (optional)
`stride2`: stride2 quantize data2 within the neighborhood centered around data1 (optional)
`pad-size`: pad for Correlation (optional)
`is-multiply`: operation type is either multiplication or subduction (optional)
`out`: Output array. (optional)

Computes the element-wise cosine of the input array.

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

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

The storage type of ``cos`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L89

`data`: The input array.
`out`: Output array. (optional)

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

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

The storage type of ``cosh`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L272

`data`: The input array.
`out`: Output array. (optional)

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

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


Defined in src/operator/crop.cc:L50

`data`: Tensor or List of Tensors, the second input will be used as crop_like shape reference
`num-args`: Number of inputs for crop, if equals one, then we will use the h_wfor crop height and width, else if equals two, then we will use the heightand width of the second input symbol, we name crop_like here
`offset`: crop offset coordinate: (y, x) (optional)
`h-w`: crop height and width: (h, w) (optional)
`center-crop`: If set to true, then it will use be the center_crop,or it will crop using the shape of crop_like (optional)
`out`: Output array. (optional)

Connectionist Temporal Classification Loss.

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

The shapes of the inputs and outputs:

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

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

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

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

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

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

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

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

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

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



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

`data`: Input ndarray
`label`: Ground-truth labels for the loss.
`data-lengths`: Lengths of data for each of the samples. Only required when use_data_lengths is true.
`label-lengths`: Lengths of labels for each of the samples. Only required when use_label_lengths is true.
`use-data-lengths`: Whether the data lenghts are decided by `data_lengths`. If false, the lengths are equal to the max sequence length. (optional)
`use-label-lengths`: Whether the label lenghts are decided by `label_lengths`, or derived from `padding_mask`. If false, the lengths are derived from the first occurrence of the value of `padding_mask`. The value of `padding_mask` is ``0`` when first CTC label is reserved for blank, and ``-1`` when last label is reserved for blank. See `blank_label`. (optional)
`blank-label`: Set the label that is reserved for blank label.If "first", 0-th label is reserved, and label values for tokens in the vocabulary are between ``1`` and ``alphabet_size-1``, and the padding mask is ``-1``. If "last", last label value ``alphabet_size-1`` is reserved for blank label instead, and label values for tokens in the vocabulary are between ``0`` and ``alphabet_size-2``, and the padding mask is ``0``. (optional)
`out`: Output array. (optional)

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

`data`: Input tensor to the deconvolution operation.
`weight`: Weights representing the kernel.
`bias`: Bias added to the result after the deconvolution operation.
`kernel`: Deconvolution kernel size: (w,), (h, w) or (d, h, w). This is same as the kernel size used for the corresponding convolution
`stride`: The stride used for the corresponding convolution: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
`dilate`: Dilation factor for each dimension of the input: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
`pad`: The amount of implicit zero padding added during convolution for each dimension of the input: (w,), (h, w) or (d, h, w). ``(kernel-1)/2`` is usually a good choice. If `target_shape` is set, `pad` will be ignored and a padding that will generate the target shape will be used. Defaults to no padding. (optional)
`adj`: Adjustment for output shape: (w,), (h, w) or (d, h, w). If `target_shape` is set, `adj` will be ignored and computed accordingly. (optional)
`target-shape`: Shape of the output tensor: (w,), (h, w) or (d, h, w). (optional)
`num-filter`: Number of output filters.
`num-group`: Number of groups partition. (optional)
`workspace`: Maximum temporary workspace allowed (MB) in deconvolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the deconvolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when `limited_workspace` strategy is used. (optional)
`no-bias`: Whether to disable bias parameter. (optional)
`cudnn-tune`: Whether to pick convolution algorithm by running performance test. (optional)
`cudnn-off`: Turn off cudnn for this layer. (optional)
`layout`: Set layout for input, output and weight. Empty for default layout, NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU. (optional)
`out`: Output array. (optional)

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

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L219

`data`: The input array.
`out`: Output array. (optional)

Rearranges(permutes) data from depth into blocks of spatial data.
Similar to ONNX DepthToSpace operator:
https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace.
The output is a new tensor where the values from depth dimension are moved in spatial blocks 
to height and width dimension. The reverse of this operation is ``space_to_depth``.

.. math::

    \begin{gather*}
    x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\
    x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\
    y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size])
    \end{gather*}

where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width] 
and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]`

Example::

  x = [[[[0, 1, 2],
         [3, 4, 5]],
        [[6, 7, 8],
         [9, 10, 11]],
        [[12, 13, 14],
         [15, 16, 17]],
        [[18, 19, 20],
         [21, 22, 23]]]]

  depth_to_space(x, 2) = [[[[0, 6, 1, 7, 2, 8],
                            [12, 18, 13, 19, 14, 20],
                            [3, 9, 4, 10, 5, 11],
                            [15, 21, 16, 22, 17, 23]]]]


Defined in src/operator/tensor/matrix_op.cc:L1050

`data`: Input ndarray
`block-size`: Blocks of [block_size. block_size] are moved
`out`: Output array. (optional)

Extracts a diagonal or constructs a diagonal array.

``diag``'s behavior depends on the input array dimensions:

- 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero.
- N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``.
  The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the
  input shape and appending to the result a new axis with the size of the diagonals in question.

  For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2
  respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`.

Examples::

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

  diag(x) = [1, 5]

  diag(x, k=1) = [2, 6]

  diag(x, k=-1) = [4]

  x = [1, 2, 3]

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

  diag(x, k=1) = [[0, 1, 0],
                  [0, 0, 2],
                  [0, 0, 0]]

  diag(x, k=-1) = [[0, 0, 0],
                   [1, 0, 0],
                   [0, 2, 0]]

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

       [[5, 6],
        [7, 8]]]

  diag(x) = [[1, 7],
             [2, 8]]

  diag(x, k=1) = [[3],
                  [4]]

  diag(x, axis1=-2, axis2=-1) = [[1, 4],
                                 [5, 8]]



Defined in src/operator/tensor/diag_op.cc:L87

`data`: Input ndarray
`k`: Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. If input has shape (S0 S1) k must be between -S0 and S1 (optional)
`axis1`: The first axis of the sub-arrays of interest. Ignored when the input is a 1-D array. (optional)
`axis2`: The second axis of the sub-arrays of interest. Ignored when the input is a 1-D array. (optional)
`out`: Output array. (optional)

Dot product of two arrays.

``dot``'s behavior depends on the input array dimensions:

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

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

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

  Example::

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

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

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

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

.. Note::

    If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be
    "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
    and Adam. Note that by default lazy updates is turned on, which may perform differently
    from standard updates. For more details, please check the Optimization API at:
    /api/python/optimization/optimization.html



Defined in src/operator/tensor/dot.cc:L77

`lhs`: The first input
`rhs`: The second input
`transpose-a`: If true then transpose the first input before dot. (optional)
`transpose-b`: If true then transpose the second input before dot. (optional)
`forward-stype`: The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type. (optional)
`out`: Output array. (optional)

Applies dropout operation to input array.

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

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

Example::

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

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

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


Defined in src/operator/nn/dropout.cc:L95

`data`: Input array to which dropout will be applied.
`p`: Fraction of the input that gets dropped out during training time. (optional)
`mode`: Whether to only turn on dropout during training or to also turn on for inference. (optional)
`axes`: Axes for variational dropout kernel. (optional)
`cudnn-off`: Whether to turn off cudnn in dropout operator. This option is ignored if axes is specified. (optional)
`out`: Output array. (optional)

Adds arguments element-wise.

The storage type of ``elemwise_add`` output depends on storage types of inputs

   - elemwise_add(row_sparse, row_sparse) = row_sparse
   - elemwise_add(csr, csr) = csr
   - elemwise_add(default, csr) = default
   - elemwise_add(csr, default) = default
   - elemwise_add(default, rsp) = default
   - elemwise_add(rsp, default) = default
   - otherwise, ``elemwise_add`` generates output with default storage



`lhs`: first input
`rhs`: second input
`out`: Output array. (optional)

Divides arguments element-wise.

The storage type of ``elemwise_div`` output is always dense



`lhs`: first input
`rhs`: second input
`out`: Output array. (optional)

Multiplies arguments element-wise.

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

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



`lhs`: first input
`rhs`: second input
`out`: Output array. (optional)

Subtracts arguments element-wise.

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

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



`lhs`: first input
`rhs`: second input
`out`: Output array. (optional)

Maps integer indices to vector representations (embeddings).

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

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

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

By default, if any index mentioned is too large, it is replaced by the index that addresses
the last vector in an embedding matrix.

Examples::

  input_dim = 4
  output_dim = 5

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

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

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

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


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

.. Note::

    If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be
    "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad
    and Adam. Note that by default lazy updates is turned on, which may perform differently
    from standard updates. For more details, please check the Optimization API at:
    /api/python/optimization/optimization.html



Defined in src/operator/tensor/indexing_op.cc:L519

`data`: The input array to the embedding operator.
`weight`: The embedding weight matrix.
`input-dim`: Vocabulary size of the input indices.
`output-dim`: Dimension of the embedding vectors.
`dtype`: Data type of weight. (optional)
`sparse-grad`: Compute row sparse gradient in the backward calculation. If set to True, the grad's storage type is row_sparse. (optional)
`out`: Output array. (optional)

Returns element-wise gauss error function of the input.

Example::

   erf([0, -1., 10.]) = [0., -0.8427, 1.]



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L964

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise inverse gauss error function of the input.

Example::

   erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf]



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L985

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise exponential value of the input.

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

Example::

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

The storage type of ``exp`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1044

`data`: The input array.
`out`: Output array. (optional)

Inserts a new axis of size 1 into the array shape

For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)``
will return a new array with shape ``(2,1,3,4)``.



Defined in src/operator/tensor/matrix_op.cc:L416

`data`: Source input
`axis`: Position where new axis is to be inserted. Suppose that the input `NDArray`'s dimension is `ndim`, the range of the inserted axis is `[-ndim, ndim]`
`out`: Output array. (optional)

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

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1189

`data`: The input array.
`out`: Output array. (optional)

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

`lhs`: Left operand to the function.
`mhs`: Middle operand to the function.
`rhs`: Right operand to the function.
`out`: Output array. (optional)

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L843

`data`: The input array.
`out`: Output array. (optional)

Flattens the input array into a 2-D array by collapsing the higher dimensions.

.. note:: `Flatten` is deprecated. Use `flatten` instead.

For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes
the input array into an output array of shape ``(d1, d2*...*dk)``.

Note that the bahavior of this function is different from numpy.ndarray.flatten,
which behaves similar to mxnet.ndarray.reshape((-1,)).

Example::

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

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



Defined in src/operator/tensor/matrix_op.cc:L291

`data`: Input array.
`out`: Output array. (optional)

Returns element-wise floor of the input.

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

Example::

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L805

`data`: The input array.
`out`: Output array. (optional)

The FTML optimizer described in
*FTML - Follow the Moving Leader in Deep Learning*,
available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.

.. math::

 g_t = \nabla J(W_{t-1})\\
 v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\
 d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon)
 \sigma_t = d_t - \beta_1 d_{t-1}
 z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1}
 W_t = - \frac{ z_t }{ d_t }



Defined in src/operator/optimizer_op.cc:L638

`weight`: Weight
`grad`: Gradient
`d`: Internal state ``d_t``
`v`: Internal state ``v_t``
`z`: Internal state ``z_t``
`lr`: Learning rate.
`beta1`: Generally close to 0.5. (optional)
`beta2`: Generally close to 1. (optional)
`epsilon`: Epsilon to prevent div 0. (optional)
`t`: Number of update.
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-grad`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`out`: Output array. (optional)

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

It updates the weights using::

 rescaled_grad = clip(grad * rescale_grad, clip_gradient)
 z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
 n += rescaled_grad**2
 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)

If w, z and n are all of ``row_sparse`` storage type,
only the row slices whose indices appear in grad.indices are updated (for w, z and n)::

 for row in grad.indices:
     rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
     z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
     n[row] += rescaled_grad[row]**2
     w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)



Defined in src/operator/optimizer_op.cc:L874

`weight`: Weight
`grad`: Gradient
`z`: z
`n`: Square of grad
`lr`: Learning rate
`lamda1`: The L1 regularization coefficient. (optional)
`beta`: Per-Coordinate Learning Rate beta. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`out`: Output array. (optional)

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

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

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

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

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

The learnable parameters include both ``weight`` and ``bias``.

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

.. Note::

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

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



Defined in src/operator/nn/fully_connected.cc:L277

`data`: Input data.
`weight`: Weight matrix.
`bias`: Bias parameter.
`num-hidden`: Number of hidden nodes of the output.
`no-bias`: Whether to disable bias parameter. (optional)
`flatten`: Whether to collapse all but the first axis of the input data tensor. (optional)
`out`: Output array. (optional)

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

The storage type of ``gamma`` output is always dense



`data`: The input array.
`out`: Output array. (optional)

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

The storage type of ``gammaln`` output is always dense



`data`: The input array.
`out`: Output array. (optional)

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

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

The elements in output is defined as follows::

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

Examples::

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

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



`data`: data
`indices`: indices
`out`: Output array. (optional)

Generates 2D sampling grid for bilinear sampling.

`data`: Input data to the function.
`transform-type`: The type of transformation. For `affine`, input data should be an affine matrix of size (batch, 6). For `warp`, input data should be an optical flow of size (batch, 2, h, w).
`target-shape`: Specifies the output shape (H, W). This is required if transformation type is `affine`. If transformation type is `warp`, this parameter is ignored. (optional)
`out`: Output array. (optional)

Computes hard sigmoid of x element-wise.

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L133

`data`: The input array.
`alpha`: Slope of hard sigmoid (optional)
`beta`: Bias of hard sigmoid. (optional)
`out`: Output array. (optional)

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

`data`: Input data.
`sparseness-target`: The sparseness target (optional)
`penalty`: The tradeoff parameter for the sparseness penalty (optional)
`momentum`: The momentum for running average (optional)
`out`: Output array. (optional)

Applies instance normalization to the n-dimensional input array.

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

.. math::

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

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

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

This implementation is based on paper:

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

Examples::

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

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

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

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



Defined in src/operator/instance_norm.cc:L95

`data`: An n-dimensional input array (n > 2) of the form [batch, channel, spatial_dim1, spatial_dim2, ...].
`gamma`: A vector of length 'channel', which multiplies the normalized input.
`beta`: A vector of length 'channel', which is added to the product of the normalized input and the weight.
`eps`: An `epsilon` parameter to prevent division by 0. (optional)
`out`: Output array. (optional)

Computes the Khatri-Rao product of the input matrices.

Given a collection of :math:`n` input matrices,

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

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

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

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

Example::

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



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

`args`: Positional input matrices
`out`: Output array. (optional)

Normalize the input array using the L2 norm.

For 1-D NDArray, it computes::

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

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

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

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

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

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

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

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

Example::

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

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

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

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



Defined in src/operator/l2_normalization.cc:L196

`data`: Input array to normalize.
`eps`: A small constant for numerical stability. (optional)
`mode`: Specify the dimension along which to compute L2 norm. (optional)
`out`: Output array. (optional)

Layer normalization.

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

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

.. math::

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

Both ``gamma`` and ``beta`` are learnable parameters.

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

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

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



Defined in src/operator/nn/layer_norm.cc:L155

`data`: Input data to layer normalization
`gamma`: gamma array
`beta`: beta array
`axis`: The axis to perform layer normalization. Usually, this should be be axis of the channel dimension. Negative values means indexing from right to left. (optional)
`eps`: An `epsilon` parameter to prevent division by 0. (optional)
`output-mean-var`: Output the mean and std calculated along the given axis. (optional)
`out`: Output array. (optional)

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

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

The following modified ReLU Activation functions are supported:

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



Defined in src/operator/leaky_relu.cc:L65

`data`: Input data to activation function.
`gamma`: Slope parameter for PReLU. Only required when act_type is 'prelu'. It should be either a vector of size 1, or the same size as the second dimension of data.
`act-type`: Activation function to be applied. (optional)
`slope`: Init slope for the activation. (For leaky and elu only) (optional)
`lower-bound`: Lower bound of random slope. (For rrelu only) (optional)
`upper-bound`: Upper bound of random slope. (For rrelu only) (optional)
`out`: Output array. (optional)

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

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

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

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

The storage type of ``label`` can be ``default`` or ``csr``

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

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



Defined in src/operator/regression_output.cc:L92

`data`: Input data to the function.
`label`: Input label to the function.
`grad-scale`: Scale the gradient by a float factor (optional)
`out`: Output array. (optional)

Returns element-wise Natural logarithmic value of the input.

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

The storage type of ``log`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1057

`data`: The input array.
`out`: Output array. (optional)

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

Examples::

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

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




`data`: The input array.
`axis`: The axis along which to compute softmax. (optional)
`temperature`: Temperature parameter in softmax (optional)
`dtype`: DType of the output in case this can't be inferred. Defaults to the same as input's dtype if not defined (dtype=None). (optional)
`out`: Output array. (optional)

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

``10**log10(x) = x``

The storage type of ``log10`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1074

`data`: The input array.
`out`: Output array. (optional)

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

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1171

`data`: The input array.
`out`: Output array. (optional)

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

``2**log2(x) = x``

The storage type of ``log2`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1086

`data`: The input array.
`out`: Output array. (optional)

Returns the result of logical NOT (!) function

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



`data`: The input array.
`out`: Output array. (optional)

Applies a logistic function to the input.

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

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

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

The storage type of ``label`` can be ``default`` or ``csr``

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

The loss function used is the Binary Cross Entropy Loss:

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

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



Defined in src/operator/regression_output.cc:L152

`data`: Input data to the function.
`label`: Input label to the function.
`grad-scale`: Scale the gradient by a float factor (optional)
`out`: Output array. (optional)

Applies local response normalization to the input.

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

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

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

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



Defined in src/operator/nn/lrn.cc:L164

`data`: Input data to LRN
`alpha`: The variance scaling parameter :math:`lpha` in the LRN expression. (optional)
`beta`: The power parameter :math:`eta` in the LRN expression. (optional)
`knorm`: The parameter :math:`k` in the LRN expression. (optional)
`nsize`: normalization window width in elements.
`out`: Output array. (optional)

Computes mean absolute error of the input.

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

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

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

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

The storage type of ``label`` can be ``default`` or ``csr``

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

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



Defined in src/operator/regression_output.cc:L120

`data`: Input data to the function.
`label`: Input label to the function.
`grad-scale`: Scale the gradient by a float factor (optional)
`out`: Output array. (optional)

Make your own loss function in network construction.

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

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

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

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

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

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



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L332

`data`: The input array.
`out`: Output array. (optional)

Computes the max of array elements over given axes.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L191

`data`: The input
`axis`: The axis or axes along which to perform the reduction.

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

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

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

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

      Negative values means indexing from right to left. (optional)
`keepdims`: If this is set to `True`, the reduced axes are left in the result as dimension with size one. (optional)
`exclude`: Whether to perform reduction on axis that are NOT in axis instead. (optional)
`out`: Output array. (optional)

Computes the mean of array elements over given axes.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L132

`data`: The input
`axis`: The axis or axes along which to perform the reduction.

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

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

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

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

      Negative values means indexing from right to left. (optional)
`keepdims`: If this is set to `True`, the reduced axes are left in the result as dimension with size one. (optional)
`exclude`: Whether to perform reduction on axis that are NOT in axis instead. (optional)
`out`: Output array. (optional)

Computes the min of array elements over given axes.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L205

`data`: The input
`axis`: The axis or axes along which to perform the reduction.

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

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

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

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

      Negative values means indexing from right to left. (optional)
`keepdims`: If this is set to `True`, the reduced axes are left in the result as dimension with size one. (optional)
`exclude`: Whether to perform reduction on axis that are NOT in axis instead. (optional)
`out`: Output array. (optional)

Calculate the mean and variance of `data`.

The mean and variance are calculated by aggregating the contents of data across axes.
If x is 1-D and axes = [0] this is just the mean and variance of a vector.

Example:

     x = [[1, 2, 3], [4, 5, 6]]
     mean, var = moments(data=x, axes=[0])
     mean = [2.5, 3.5, 4.5]
     var = [2.25, 2.25, 2.25]
     mean, var = moments(data=x, axes=[1])
     mean = [2.0, 5.0]
     var = [0.66666667, 0.66666667]
     mean, var = moments(data=x, axis=[0, 1])
     mean = [3.5]
     var = [2.9166667]



Defined in src/operator/nn/moments.cc:L54

`data`: Input ndarray
`axes`: Array of ints. Axes along which to compute mean and variance. (optional)
`keepdims`: produce moments with the same dimensionality as the input. (optional)
`out`: Output array. (optional)

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


Defined in src/operator/optimizer_op.cc:L743

`weight`: Weight
`grad`: Gradient
`mom`: Momentum
`weight32`: Weight32
`lr`: Learning rate
`momentum`: The decay rate of momentum estimates at each epoch. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`out`: Output array. (optional)

Updater function for multi-precision sgd optimizer

`weight`: Weight
`grad`: Gradient
`mom`: Momentum
`weight32`: Weight32
`lr`: Learning rate
`momentum`: The decay rate of momentum estimates at each epoch. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`lazy-update`: If true, lazy updates are applied if gradient's stype is row_sparse and both weight and momentum have the same stype (optional)
`out`: Output array. (optional)

Updater function for multi-precision sgd optimizer

`weight`: Weight
`grad`: gradient
`weight32`: Weight32
`lr`: Learning rate
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`lazy-update`: If true, lazy updates are applied if gradient's stype is row_sparse. (optional)
`out`: Output array. (optional)

Check if all the float numbers in all the arrays are finite (used for AMP)


Defined in src/operator/contrib/all_finite.cc:L133

`data`: Arrays
`num-arrays`: Number of arrays. (optional)
`init-output`: Initialize output to 1. (optional)
`out`: Output array. (optional)

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

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

.. math::

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

It updates the weights using::

  v = momentum * v - learning_rate * gradient
  weight += v

Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.



Defined in src/operator/optimizer_op.cc:L470

`data`: Weights
`lrs`: Learning rates.
`wds`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
`momentum`: The decay rate of momentum estimates at each epoch. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`num-weights`: Number of updated weights. (optional)
`out`: Output array. (optional)

Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

It updates the weights using::

 weight = weight - learning_rate * (gradient + wd * weight)



Defined in src/operator/optimizer_op.cc:L415

`data`: Weights
`lrs`: Learning rates.
`wds`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`num-weights`: Number of updated weights. (optional)
`out`: Output array. (optional)

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

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

.. math::

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

It updates the weights using::

  v = momentum * v - learning_rate * gradient
  weight += v

Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.



Defined in src/operator/optimizer_op.cc:L372

`data`: Weights, gradients and momentum
`lrs`: Learning rates.
`wds`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
`momentum`: The decay rate of momentum estimates at each epoch. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`num-weights`: Number of updated weights. (optional)
`out`: Output array. (optional)

Update function for Stochastic Gradient Descent (SDG) optimizer.

It updates the weights using::

 weight = weight - learning_rate * (gradient + wd * weight)



Defined in src/operator/optimizer_op.cc:L327

`data`: Weights
`lrs`: Learning rates.
`wds`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`num-weights`: Number of updated weights. (optional)
`out`: Output array. (optional)

Update function for Nesterov Accelerated Gradient( NAG) optimizer.
It updates the weights using the following formula,

.. math::
  v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\
  W_t = W_{t-1} - v_t

Where 
:math:`\eta` is the learning rate of the optimizer
:math:`\gamma` is the decay rate of the momentum estimate
:math:`\v_t` is the update vector at time step `t`
:math:`\W_t` is the weight vector at time step `t`



Defined in src/operator/optimizer_op.cc:L724

`weight`: Weight
`grad`: Gradient
`mom`: Momentum
`lr`: Learning rate
`momentum`: The decay rate of momentum estimates at each epoch. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`out`: Output array. (optional)

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



Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L177

`data`: The input
`axis`: The axis or axes along which to perform the reduction.

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

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

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

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

      Negative values means indexing from right to left. (optional)
`keepdims`: If this is set to `True`, the reduced axes are left in the result as dimension with size one. (optional)
`exclude`: Whether to perform reduction on axis that are NOT in axis instead. (optional)
`out`: Output array. (optional)

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



Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L162

`data`: The input
`axis`: The axis or axes along which to perform the reduction.

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

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

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

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

      Negative values means indexing from right to left. (optional)
`keepdims`: If this is set to `True`, the reduced axes are left in the result as dimension with size one. (optional)
`exclude`: Whether to perform reduction on axis that are NOT in axis instead. (optional)
`out`: Output array. (optional)

Numerical negative of the argument, element-wise.

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

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



`data`: The input array.
`out`: Output array. (optional)

Computes the norm on an NDArray.

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

Examples::

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

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

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

  rsp = x.cast_storage('row_sparse')

  norm(rsp) = [5.47722578]

  csr = x.cast_storage('csr')

  norm(csr) = [5.47722578]



Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L350

`data`: The input
`ord`: Order of the norm. Currently ord=1 and ord=2 is supported. (optional)
`axis`: The axis or axes along which to perform the reduction.
      The default, `axis=()`, will compute over all elements into a
      scalar array with shape `(1,)`.
      If `axis` is int, a reduction is performed on a particular axis.
      If `axis` is a 2-tuple, it specifies the axes that hold 2-D matrices,
      and the matrix norms of these matrices are computed. (optional)
`out-dtype`: The data type of the output. (optional)
`keepdims`: If this is set to `True`, the reduced axis is left in the result as dimension with size one. (optional)
`out`: Output array. (optional)

Returns a one-hot array.

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

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

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

Examples::

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

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

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

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

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


Defined in src/operator/tensor/indexing_op.cc:L799

`indices`: array of locations where to set on_value
`depth`: Depth of the one hot dimension.
`on-value`: The value assigned to the locations represented by indices. (optional)
`off-value`: The value assigned to the locations not represented by indices. (optional)
`dtype`: DType of the output (optional)
`out`: Output array. (optional)

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

Examples::

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

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



`data`: The input
`out`: Output array. (optional)

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

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

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

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

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

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

Example::

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

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


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

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

   pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) =

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

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


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

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

   pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) =

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

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


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

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




Defined in src/operator/pad.cc:L766

`data`: An n-dimensional input array.
`mode`: Padding type to use. "constant" pads with `constant_value` "edge" pads using the edge values of the input array "reflect" pads by reflecting values with respect to the edges.
`pad-width`: Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. It should be of length ``2*N`` where ``N`` is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened.
`constant-value`: The value used for padding when `mode` is "constant". (optional)
`out`: Output array. (optional)

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

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

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

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

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

Examples::

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

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

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

  y = [[ 1.],
       [ 0.],
       [ 2.]]

  // picks elements with specified indices along axis 1 using 'wrap' mode
  // to place indicies that would normally be out of bounds
  pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]

  y = [[ 1.],
       [ 0.],
       [ 2.]]

  // picks elements with specified indices along axis 1 and dims are maintained
  pick(x,y, 1, keepdims=True) = [[ 2.],
                                 [ 3.],
                                 [ 6.]]



Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L154

`data`: The input array
`index`: The index array
`axis`: int or None. The axis to picking the elements. Negative values means indexing from right to left. If is `None`, the elements in the index w.r.t the flattened input will be picked. (optional)
`keepdims`: If true, the axis where we pick the elements is left in the result as dimension with size one. (optional)
`mode`: Specify how out-of-bound indices behave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis.  "wrap" means to wrap around. (optional)
`out`: Output array. (optional)

Performs pooling on the input.

The shapes for 1-D pooling are

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

The shapes for 2-D pooling are

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

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

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

- **valid** (default)::

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

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

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

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

Three pooling options are supported by ``pool_type``:

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

For 3-D pooling, an additional *depth* dimension is added before
*height*. Namely the input data and output will have shape *(batch_size, channel, depth,
height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout).

Notes on Lp pooling:

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

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

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



Defined in src/operator/nn/pooling.cc:L416

`data`: Input data to the pooling operator.
`kernel`: Pooling kernel size: (y, x) or (d, y, x) (optional)
`pool-type`: Pooling type to be applied. (optional)
`global-pool`: Ignore kernel size, do global pooling based on current input feature map.  (optional)
`cudnn-off`: Turn off cudnn pooling and use MXNet pooling operator.  (optional)
`pooling-convention`: Pooling convention to be applied. (optional)
`stride`: Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each dimension. (optional)
`pad`: Pad for pooling: (y, x) or (d, y, x). Defaults to no padding. (optional)
`p-value`: Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling. (optional)
`count-include-pad`: Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set to true,or it will be divided by 9 if this is set to false. Defaults to true. (optional)
`layout`: Set layout for input and output. Empty for
    default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d. (optional)
`out`: Output array. (optional)

This operator is DEPRECATED.
Perform pooling on the input.

The shapes for 2-D pooling is

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

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

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

- **valid** (default)::

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

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

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

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

Three pooling options are supported by ``pool_type``:

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

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

For 3-D pooling, an additional *depth* dimension is added before
*height*. Namely the input data will have shape *(batch_size, channel, depth,
height, width)*.



Defined in src/operator/pooling_v1.cc:L104

`data`: Input data to the pooling operator.
`kernel`: pooling kernel size: (y, x) or (d, y, x) (optional)
`pool-type`: Pooling type to be applied. (optional)
`global-pool`: Ignore kernel size, do global pooling based on current input feature map.  (optional)
`pooling-convention`: Pooling convention to be applied. (optional)
`stride`: stride: for pooling (y, x) or (d, y, x) (optional)
`pad`: pad for pooling: (y, x) or (d, y, x) (optional)
`out`: Output array. (optional)

Computes the product of array elements over given axes.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L147

`data`: The input
`axis`: The axis or axes along which to perform the reduction.

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

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

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

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

      Negative values means indexing from right to left. (optional)
`keepdims`: If this is set to `True`, the reduced axes are left in the result as dimension with size one. (optional)
`exclude`: Whether to perform reduction on axis that are NOT in axis instead. (optional)
`out`: Output array. (optional)

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

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

The storage type of ``radians`` output depends upon the input storage type:

   - radians(default) = default
   - radians(row_sparse) = row_sparse
   - radians(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L238

`data`: The input array.
`out`: Output array. (optional)

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

.. math::
   rcbrt(x) = 1/\sqrt[3]{x}

Example::

   rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L1004

`data`: The input array.
`out`: Output array. (optional)

Returns the reciprocal of the argument, element-wise.

Calculates 1/x.

Example::

    reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L686

`data`: The input array.
`out`: Output array. (optional)

Computes rectified linear activation.

.. math::
   max(features, 0)

The storage type of ``relu`` output depends upon the input storage type:

   - relu(default) = default
   - relu(row_sparse) = row_sparse
   - relu(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85

`data`: The input array.
`out`: Output array. (optional)

Repeats elements of an array.

By default, ``repeat`` flattens the input array into 1-D and then repeats the
elements::

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

  repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]

The parameter ``axis`` specifies the axis along which to perform repeat::

  repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
                                  [ 3.,  3.,  4.,  4.]]

  repeat(x, repeats=2, axis=0) = [[ 1.,  2.],
                                  [ 1.,  2.],
                                  [ 3.,  4.],
                                  [ 3.,  4.]]

  repeat(x, repeats=2, axis=-1) = [[ 1.,  1.,  2.,  2.],
                                   [ 3.,  3.,  4.,  4.]]



Defined in src/operator/tensor/matrix_op.cc:L796

`data`: Input data array
`repeats`: The number of repetitions for each element.
`axis`: The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input array, and return a flat output array. (optional)
`out`: Output array. (optional)

Reshapes the input array.

.. note:: ``Reshape`` is deprecated, use ``reshape``

Given an array and a shape, this function returns a copy of the array in the new shape.
The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array.

Example::

  reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]

Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:

- ``0``  copy this dimension from the input to the output shape.

  Example::

  - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
  - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)

- ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions
  keeping the size of the new array same as that of the input array.
  At most one dimension of shape can be -1.

  Example::

  - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
  - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
  - input shape = (2,3,4), shape=(-1,), output shape = (24,)

- ``-2`` copy all/remainder of the input dimensions to the output shape.

  Example::

  - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
  - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
  - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)

- ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension.

  Example::

  - input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
  - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
  - input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
  - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)

- ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).

  Example::

  - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
  - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)

If the argument `reverse` is set to 1, then the special values are inferred from right to left.

  Example::

  - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
  - with reverse=1, output shape will be (50,4).



Defined in src/operator/tensor/matrix_op.cc:L202

`data`: Input data to reshape.
`shape`: The target shape (optional)
`reverse`: If true then the special values are inferred from right to left (optional)
`target-shape`: (Deprecated! Use ``shape`` instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims (optional)
`keep-highest`: (Deprecated! Use ``shape`` instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input (optional)
`out`: Output array. (optional)

Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`.

Returns a **view** of the `lhs` array with a new shape without altering any data.

Example::

  x = [1, 2, 3, 4, 5, 6]
  y = [[0, -4], [3, 2], [2, 2]]
  reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]]

More precise control over how dimensions are inherited is achieved by specifying \
slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \
are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same.

  Examples::

  - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
  - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)

Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range.

  Example::

  - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L485

`lhs`: First input.
`rhs`: Second input.
`out`: Output array. (optional)

Reverses the order of elements along given axis while preserving array shape.

Note: reverse and flip are equivalent. We use reverse in the following examples.

Examples::

  x = [[ 0.,  1.,  2.,  3.,  4.],
       [ 5.,  6.,  7.,  8.,  9.]]

  reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
                        [ 0.,  1.,  2.,  3.,  4.]]

  reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
                        [ 9.,  8.,  7.,  6.,  5.]]


Defined in src/operator/tensor/matrix_op.cc:L898

`data`: Input data array
`axis`: The axis which to reverse elements.
`out`: Output array. (optional)

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

.. note::
   - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``.
   - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``.

Example::

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

The storage type of ``rint`` output depends upon the input storage type:

   - rint(default) = default
   - rint(row_sparse) = row_sparse
   - rint(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L767

`data`: The input array.
`out`: Output array. (optional)

Update function for `RMSProp` optimizer.

`RMSprop` is a variant of stochastic gradient descent where the gradients are
divided by a cache which grows with the sum of squares of recent gradients?

`RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively
tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for
each parameter monotonically over the course of training.
While this is analytically motivated for convex optimizations, it may not be ideal
for non-convex problems. `RMSProp` deals with this heuristically by allowing the
learning rates to rebound as the denominator decays over time.

Define the Root Mean Square (RMS) error criterion of the gradient as
:math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents
gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient.

The :math:`E[g^2]_t` is given by:

.. math::
  E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2

The update step is

.. math::
  \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t

The RMSProp code follows the version in
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
Tieleman & Hinton, 2012.

Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate
:math:`\eta` to be 0.001.



Defined in src/operator/optimizer_op.cc:L795

`weight`: Weight
`grad`: Gradient
`n`: n
`lr`: Learning rate
`gamma1`: The decay rate of momentum estimates. (optional)
`epsilon`: A small constant for numerical stability. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`clip-weights`: Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights). (optional)
`out`: Output array. (optional)

Update function for RMSPropAlex optimizer.

`RMSPropAlex` is non-centered version of `RMSProp`.

Define :math:`E[g^2]_t` is the decaying average over past squared gradient and
:math:`E[g]_t` is the decaying average over past gradient.

.. math::
  E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
  E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
  \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\

The update step is

.. math::
  \theta_{t+1} = \theta_t + \Delta_t

The RMSPropAlex code follows the version in
http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.

Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2`
to be 0.9 and the learning rate :math:`\eta` to be 0.0001.


Defined in src/operator/optimizer_op.cc:L834

`weight`: Weight
`grad`: Gradient
`n`: n
`g`: g
`delta`: delta
`lr`: Learning rate
`gamma1`: Decay rate. (optional)
`gamma2`: Decay rate. (optional)
`epsilon`: A small constant for numerical stability. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`clip-weights`: Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights). (optional)
`out`: Output array. (optional)

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

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

**Vanilla RNN**

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

With ReLU activation function:

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

With Tanh activtion function:

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

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

**LSTM**

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

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

**GRU**

Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078

The definition of GRU here is slightly different from paper but compatible with CUDNN.

.. math::
  \begin{array}{ll}
            r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
            z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
            n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
            h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\
            \end{array}


Defined in src/operator/rnn.cc:L690

`data`: Input data to RNN
`parameters`: Vector of all RNN trainable parameters concatenated
`state`: initial hidden state of the RNN
`state-cell`: initial cell state for LSTM networks (only for LSTM)
`sequence-length`: Vector of valid sequence lengths for each element in batch. (Only used if use_sequence_length kwarg is True)
`state-size`: size of the state for each layer
`num-layers`: number of stacked layers
`bidirectional`: whether to use bidirectional recurrent layers (optional)
`mode`: the type of RNN to compute
`p`: drop rate of the dropout on the outputs of each RNN layer, except the last layer. (optional)
`state-outputs`: Whether to have the states as symbol outputs. (optional)
`projection-size`: size of project size (optional)
`lstm-state-clip-min`: Minimum clip value of LSTM states. This option must be used together with lstm_state_clip_max. (optional)
`lstm-state-clip-max`: Maximum clip value of LSTM states. This option must be used together with lstm_state_clip_min. (optional)
`lstm-state-clip-nan`: Whether to stop NaN from propagating in state by clipping it to min/max. If clipping range is not specified, this option is ignored. (optional)
`use-sequence-length`: If set to true, this layer takes in an extra input parameter `sequence_length` to specify variable length sequence (optional)
`out`: Output array. (optional)

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

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

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

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

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

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

Example::

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

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

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

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



Defined in src/operator/roi_pooling.cc:L295

`data`: The input array to the pooling operator,  a 4D Feature maps 
`rois`: Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]], where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest. `batch_index` indicates the index of corresponding image in the input array
`pooled-size`: ROI pooling output shape (h,w) 
`spatial-scale`: Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers
`out`: Output array. (optional)

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

Example::

   round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]

The storage type of ``round`` output depends upon the input storage type:

  - round(default) = default
  - round(row_sparse) = row_sparse
  - round(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L746

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise inverse square-root value of the input.

.. math::
   rsqrt(x) = 1/\sqrt{x}

Example::

   rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]

The storage type of ``rsqrt`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L927

`data`: The input array.
`out`: Output array. (optional)

Scatters data into a new tensor according to indices.

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

The elements in output is defined as follows::

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

all other entries in output are 0.

.. warning::

    If the indices have duplicates, the result will be non-deterministic and
    the gradient of `scatter_nd` will not be correct!!


Examples::

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

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

                                       [[1, 2],
                                        [3, 4]]],

                                      [[[0, 0],
                                        [0, 0]],

                                       [[5, 6],
                                        [7, 8]]]]



`data`: data
`indices`: indices
`shape`: Shape of output.
`out`: Output array. (optional)

Takes the last element of a sequence.

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

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

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

Example::

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

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

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

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

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

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



Defined in src/operator/sequence_last.cc:L100

`data`: n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2
`sequence-length`: vector of sequence lengths of the form [batch_size]
`use-sequence-length`: If set to true, this layer takes in an extra input parameter `sequence_length` to specify variable length sequence (optional)
`axis`: The sequence axis. Only values of 0 and 1 are currently supported. (optional)
`out`: Output array. (optional)

Sets all elements outside the sequence to a constant value.

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

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

Example::

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

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

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

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

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

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

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

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

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

                 [[  0.,   0.,   0.],
                  [  0.,   0.,   0.]],

                 [[  0.,   0.,   0.],
                  [  0.,   0.,   0.]]]

   // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
   // and other rows are masked with value = 1
   SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) =
                [[[  1.,   2.,   3.],
                  [  4.,   5.,   6.]],

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

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



Defined in src/operator/sequence_mask.cc:L186

`data`: n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2
`sequence-length`: vector of sequence lengths of the form [batch_size]
`use-sequence-length`: If set to true, this layer takes in an extra input parameter `sequence_length` to specify variable length sequence (optional)
`value`: The value to be used as a mask. (optional)
`axis`: The sequence axis. Only values of 0 and 1 are currently supported. (optional)
`out`: Output array. (optional)

Reverses the elements of each sequence.

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

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

Example::

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

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

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

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

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

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

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

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

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

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

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

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

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

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



Defined in src/operator/sequence_reverse.cc:L122

`data`: n-dimensional input array of the form [max_sequence_length, batch_size, other dims] where n>2 
`sequence-length`: vector of sequence lengths of the form [batch_size]
`use-sequence-length`: If set to true, this layer takes in an extra input parameter `sequence_length` to specify variable length sequence (optional)
`axis`: The sequence axis. Only 0 is currently supported. (optional)
`out`: Output array. (optional)

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

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

.. math::

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

It updates the weights using::

  v = momentum * v - learning_rate * gradient
  weight += v

Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.

However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and weight's storage
type is the same as momentum's storage type,
only the row slices whose indices appear in grad.indices are updated (for both weight and momentum)::

  for row in gradient.indices:
      v[row] = momentum[row] * v[row] - learning_rate * gradient[row]
      weight[row] += v[row]



Defined in src/operator/optimizer_op.cc:L563

`weight`: Weight
`grad`: Gradient
`mom`: Momentum
`lr`: Learning rate
`momentum`: The decay rate of momentum estimates at each epoch. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`lazy-update`: If true, lazy updates are applied if gradient's stype is row_sparse and both weight and momentum have the same stype (optional)
`out`: Output array. (optional)

Update function for Stochastic Gradient Descent (SGD) optimizer.

It updates the weights using::

 weight = weight - learning_rate * (gradient + wd * weight)

However, if gradient is of ``row_sparse`` storage type and ``lazy_update`` is True,
only the row slices whose indices appear in grad.indices are updated::

 for row in gradient.indices:
     weight[row] = weight[row] - learning_rate * (gradient[row] + wd * weight[row])



Defined in src/operator/optimizer_op.cc:L522

`weight`: Weight
`grad`: Gradient
`lr`: Learning rate
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`lazy-update`: If true, lazy updates are applied if gradient's stype is row_sparse. (optional)
`out`: Output array. (optional)

Returns a 1D int64 array containing the shape of data.

Example::

  shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4]



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L544

`data`: Input Array.
`lhs-begin`: Defaults to 0. The beginning index along which the lhs dimensions are to be reshaped. Supports negative indices. (optional)
`lhs-end`: Defaults to None. The ending index along which the lhs dimensions are to be used for reshaping. Supports negative indices. (optional)
`rhs-begin`: Defaults to 0. The beginning index along which the rhs dimensions are to be used for reshaping. Supports negative indices. (optional)
`rhs-end`: Defaults to None. The ending index along which the rhs dimensions are to be used for reshaping. Supports negative indices. (optional)
`out`: Output array. (optional)

Computes sigmoid of x element-wise.

.. math::
   y = 1 / (1 + exp(-x))

The storage type of ``sigmoid`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L119

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise sign of the input.

Example::

   sign([-2, 0, 3]) = [-1, 0, 1]

The storage type of ``sign`` output depends upon the input storage type:

   - sign(default) = default
   - sign(row_sparse) = row_sparse
   - sign(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L727

`data`: The input array.
`out`: Output array. (optional)

Update function for SignSGD optimizer.

.. math::

 g_t = \nabla J(W_{t-1})\\
 W_t = W_{t-1} - \eta_t \text{sign}(g_t)

It updates the weights using::

 weight = weight - learning_rate * sign(gradient)

.. note::
   - sparse ndarray not supported for this optimizer yet.


Defined in src/operator/optimizer_op.cc:L61

`weight`: Weight
`grad`: Gradient
`lr`: Learning rate
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`out`: Output array. (optional)

SIGN momentUM (Signum) optimizer.

.. math::

 g_t = \nabla J(W_{t-1})\\
 m_t = \beta m_{t-1} + (1 - \beta) g_t\\
 W_t = W_{t-1} - \eta_t \text{sign}(m_t)

It updates the weights using::
 state = momentum * state + (1-momentum) * gradient
 weight = weight - learning_rate * sign(state)

Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch.

.. note::
   - sparse ndarray not supported for this optimizer yet.


Defined in src/operator/optimizer_op.cc:L90

`weight`: Weight
`grad`: Gradient
`mom`: Momentum
`lr`: Learning rate
`momentum`: The decay rate of momentum estimates at each epoch. (optional)
`wd`: Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight. (optional)
`rescale-grad`: Rescale gradient to grad = rescale_grad*grad. (optional)
`clip-gradient`: Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient). (optional)
`wd-lh`: The amount of weight decay that does not go into gradient/momentum calculationsotherwise do weight decay algorithmically only. (optional)
`out`: Output array. (optional)

Computes the element-wise sine of the input array.

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

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

The storage type of ``sin`` output depends upon the input storage type:

   - sin(default) = default
   - sin(row_sparse) = row_sparse
   - sin(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L46

`data`: The input array.
`out`: Output array. (optional)

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

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

The storage type of ``sinh`` output depends upon the input storage type:

   - sinh(default) = default
   - sinh(row_sparse) = row_sparse
   - sinh(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L257

`data`: The input array.
`out`: Output array. (optional)

Returns a 1D int64 array containing the size of data.

Example::

  size_array([[1,2,3,4], [5,6,7,8]]) = [8]



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L596

`data`: Input Array.
`out`: Output array. (optional)

Slices a region of the array.

.. note:: ``crop`` is deprecated. Use ``slice`` instead.

This function returns a sliced array between the indices given
by `begin` and `end` with the corresponding `step`.

For an input array of ``shape=(d_0, d_1, ..., d_n-1)``,
slice operation with ``begin=(b_0, b_1...b_m-1)``,
``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``,
where m <= n, results in an array with the shape
``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``.

The resulting array's *k*-th dimension contains elements
from the *k*-th dimension of the input array starting
from index ``b_k`` (inclusive) with step ``s_k``
until reaching ``e_k`` (exclusive).

If the *k*-th elements are `None` in the sequence of `begin`, `end`,
and `step`, the following rule will be used to set default values.
If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`;
else, set `b_k=d_k-1`, `e_k=-1`.

The storage type of ``slice`` output depends on storage types of inputs

- slice(csr) = csr
- otherwise, ``slice`` generates output with default storage

.. note:: When input data storage type is csr, it only supports
   step=(), or step=(None,), or step=(1,) to generate a csr output.
   For other step parameter values, it falls back to slicing
   a dense tensor.

Example::

  x = [[  1.,   2.,   3.,   4.],
       [  5.,   6.,   7.,   8.],
       [  9.,  10.,  11.,  12.]]

  slice(x, begin=(0,1), end=(2,4)) = [[ 2.,  3.,  4.],
                                     [ 6.,  7.,  8.]]
  slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = [[9., 11.],
                                                            [5.,  7.],
                                                            [1.,  3.]]


Defined in src/operator/tensor/matrix_op.cc:L506

`data`: Source input
`begin`: starting indices for the slice operation, supports negative indices.
`end`: ending indices for the slice operation, supports negative indices.
`step`: step for the slice operation, supports negative values. (optional)
`out`: Output array. (optional)

Slices along a given axis.

Returns an array slice along a given `axis` starting from the `begin` index
to the `end` index.

Examples::

  x = [[  1.,   2.,   3.,   4.],
       [  5.,   6.,   7.,   8.],
       [  9.,  10.,  11.,  12.]]

  slice_axis(x, axis=0, begin=1, end=3) = [[  5.,   6.,   7.,   8.],
                                           [  9.,  10.,  11.,  12.]]

  slice_axis(x, axis=1, begin=0, end=2) = [[  1.,   2.],
                                           [  5.,   6.],
                                           [  9.,  10.]]

  slice_axis(x, axis=1, begin=-3, end=-1) = [[  2.,   3.],
                                             [  6.,   7.],
                                             [ 10.,  11.]]


Defined in src/operator/tensor/matrix_op.cc:L596

`data`: Source input
`axis`: Axis along which to be sliced, supports negative indexes.
`begin`: The beginning index along the axis to be sliced,  supports negative indexes.
`end`: The ending index along the axis to be sliced,  supports negative indexes.
`out`: Output array. (optional)

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

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

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

Example::

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

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

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

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

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

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

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

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

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

Example::

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

       [[ 3.]
        [ 4.]]

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



Defined in src/operator/slice_channel.cc:L107

`data`: The input
`num-outputs`: Number of splits. Note that this should evenly divide the length of the `axis`.
`axis`: Axis along which to split. (optional)
`squeeze-axis`: If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting `squeeze_axis` to ``true`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to ``true`` only if ``input.shape[axis] == num_outputs``. (optional)
`out`: Output array. (optional)

Slices a region of the array like the shape of another array.

This function is similar to ``slice``, however, the `begin` are always `0`s
and `end` of specific axes are inferred from the second input `shape_like`.

Given the second `shape_like` input of ``shape=(d_0, d_1, ..., d_n-1)``,
a ``slice_like`` operator with default empty `axes`, it performs the
following operation:

`` out = slice(input, begin=(0, 0, ..., 0), end=(d_0, d_1, ..., d_n-1))``.

When `axes` is not empty, it is used to speficy which axes are being sliced.

Given a 4-d input data, ``slice_like`` operator with ``axes=(0, 2, -1)``
will perform the following operation:

`` out = slice(input, begin=(0, 0, 0, 0), end=(d_0, None, d_2, d_3))``.

Note that it is allowed to have first and second input with different dimensions,
however, you have to make sure the `axes` are specified and not exceeding the
dimension limits.

For example, given `input_1` with ``shape=(2,3,4,5)`` and `input_2` with
``shape=(1,2,3)``, it is not allowed to use:

`` out = slice_like(a, b)`` because ndim of `input_1` is 4, and ndim of `input_2`
is 3.

The following is allowed in this situation:

`` out = slice_like(a, b, axes=(0, 2))``

Example::

  x = [[  1.,   2.,   3.,   4.],
       [  5.,   6.,   7.,   8.],
       [  9.,  10.,  11.,  12.]]

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

  slice_like(x, y) = [[ 1.,  2.,  3.]
                      [ 5.,  6.,  7.]]
  slice_like(x, y, axes=(0, 1)) = [[ 1.,  2.,  3.]
                                   [ 5.,  6.,  7.]]
  slice_like(x, y, axes=(0)) = [[ 1.,  2.,  3.,  4.]
                                [ 5.,  6.,  7.,  8.]]
  slice_like(x, y, axes=(-1)) = [[  1.,   2.,   3.]
                                 [  5.,   6.,   7.]
                                 [  9.,  10.,  11.]]


Defined in src/operator/tensor/matrix_op.cc:L665

`data`: Source input
`shape-like`: Shape like input
`axes`: List of axes on which input data will be sliced according to the corresponding size of the second input. By default will slice on all axes. Negative axes are supported. (optional)
`out`: Output array. (optional)

Calculate Smooth L1 Loss(lhs, scalar) by summing

.. math::

    f(x) =
    \begin{cases}
    (\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
    |x|-0.5/\sigma^2,& \text{otherwise}
    \end{cases}

where :math:`x` is an element of the tensor *lhs* and :math:`\sigma` is the scalar.

Example::

  smooth_l1([1, 2, 3, 4]) = [0.5, 1.5, 2.5, 3.5]
  smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]



Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L104

`data`: source input
`scalar`: scalar input
`out`: Output array. (optional)

Applies the softmax function.

The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.

.. math::
   softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}

for :math:`j = 1, ..., K`

t is the temperature parameter in softmax function. By default, t equals 1.0

Example::

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

  softmax(x,axis=0) = [[ 0.5  0.5  0.5]
                       [ 0.5  0.5  0.5]]

  softmax(x,axis=1) = [[ 0.33333334,  0.33333334,  0.33333334],
                       [ 0.33333334,  0.33333334,  0.33333334]]



Defined in src/operator/nn/softmax.cc:L93

`data`: The input array.
`axis`: The axis along which to compute softmax. (optional)
`temperature`: Temperature parameter in softmax (optional)
`dtype`: DType of the output in case this can't be inferred. Defaults to the same as input's dtype if not defined (dtype=None). (optional)
`out`: Output array. (optional)

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

.. note::

  This operator has been deprecated, please use `softmax`.

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

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

Example::

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



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

`data`: The input array.
`mode`: Specifies how to compute the softmax. If set to ``instance``, it computes softmax for each instance. If set to ``channel``, It computes cross channel softmax for each position of each instance. (optional)
`out`: Output array. (optional)

Calculate cross entropy of softmax output and one-hot label.

- This operator computes the cross entropy in two steps:
  - Applies softmax function on the input array.
  - Computes and returns the cross entropy loss between the softmax output and the labels.

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

  - Softmax Function:

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

  - Cross Entropy Function:

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

Example::

  x = [[1, 2, 3],
       [11, 7, 5]]

  label = [2, 0]

  softmax(x) = [[0.09003057, 0.24472848, 0.66524094],
                [0.97962922, 0.01794253, 0.00242826]]

  softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871



Defined in src/operator/loss_binary_op.cc:L59

`data`: Input data
`label`: Input label
`out`: Output array. (optional)

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

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

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

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

  - Softmax Function:

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

  - Cross Entropy Function:

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

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

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

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

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

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

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

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

    Example::

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

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

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

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



Defined in src/operator/softmax_output.cc:L230

`data`: Input array.
`label`: Ground truth label.
`grad-scale`: Scales the gradient by a float factor. (optional)
`ignore-label`: The instances whose `labels` == `ignore_label` will be ignored during backward, if `use_ignore` is set to ``true``). (optional)
`multi-output`: If set to ``true``, the softmax function will be computed along axis ``1``. This is applied when the shape of input array differs from the shape of label array. (optional)
`use-ignore`: If set to ``true``, the `ignore_label` value will not contribute to the backward gradient. (optional)
`preserve-shape`: If set to ``true``, the softmax function will be computed along the last axis (``-1``). (optional)
`normalization`: Normalizes the gradient. (optional)
`out-grad`: Multiplies gradient with output gradient element-wise. (optional)
`smooth-alpha`: Constant for computing a label smoothed version of cross-entropyfor the backwards pass.  This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels. (optional)
`out`: Output array. (optional)

Applies the softmin function.

The resulting array contains elements in the range (0,1) and the elements along the given axis sum
up to 1.

.. math::
   softmin(\mathbf{z/t})_j = \frac{e^{-z_j/t}}{\sum_{k=1}^K e^{-z_k/t}}

for :math:`j = 1, ..., K`

t is the temperature parameter in softmax function. By default, t equals 1.0

Example::

  x = [[ 1.  2.  3.]
       [ 3.  2.  1.]]

  softmin(x,axis=0) = [[ 0.88079703,  0.5,  0.11920292],
                       [ 0.11920292,  0.5,  0.88079703]]

  softmin(x,axis=1) = [[ 0.66524094,  0.24472848,  0.09003057],
                       [ 0.09003057,  0.24472848,  0.66524094]]



Defined in src/operator/nn/softmax.cc:L153

`data`: The input array.
`axis`: The axis along which to compute softmax. (optional)
`temperature`: Temperature parameter in softmax (optional)
`dtype`: DType of the output in case this can't be inferred. Defaults to the same as input's dtype if not defined (dtype=None). (optional)
`out`: Output array. (optional)

Computes softsign of x element-wise.

.. math::
   y = x / (1 + abs(x))

The storage type of ``softsign`` output is always dense



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L163

`data`: The input array.
`out`: Output array. (optional)

Returns a sorted copy of an input array along the given axis.

Examples::

  x = [[ 1, 4],
       [ 3, 1]]

  // sorts along the last axis
  sort(x) = [[ 1.,  4.],
             [ 1.,  3.]]

  // flattens and then sorts
  sort(x) = [ 1.,  1.,  3.,  4.]

  // sorts along the first axis
  sort(x, axis=0) = [[ 1.,  1.],
                     [ 3.,  4.]]

  // in a descend order
  sort(x, is_ascend=0) = [[ 4.,  1.],
                          [ 3.,  1.]]



Defined in src/operator/tensor/ordering_op.cc:L127

`data`: The input array
`axis`: Axis along which to choose sort the input tensor. If not given, the flattened array is used. Default is -1. (optional)
`is-ascend`: Whether to sort in ascending or descending order. (optional)
`out`: Output array. (optional)

Rearranges(permutes) blocks of spatial data into depth.
Similar to ONNX SpaceToDepth operator:
https://github.com/onnx/onnx/blob/master/docs/Operators.md#SpaceToDepth 

The output is a new tensor where the values from height and width dimension are 
moved to the depth dimension. The reverse of this operation is ``depth_to_space``.

.. math::

    \begin{gather*}
    x \prime = reshape(x, [N, C, H / block\_size, block\_size, W / block\_size, block\_size]) \\
    x \prime \prime = transpose(x \prime, [0, 3, 5, 1, 2, 4]) \\
    y = reshape(x \prime \prime, [N, C * (block\_size ^ 2), H / block\_size, W / block\_size])
    \end{gather*}

where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width] 
and :math:`y` is the output tensor of layout :math:`[N, C * (block\_size ^ 2), H / block\_size, W / block\_size]`

Example::

  x = [[[[0, 6, 1, 7, 2, 8],
         [12, 18, 13, 19, 14, 20],
         [3, 9, 4, 10, 5, 11],
         [15, 21, 16, 22, 17, 23]]]]


  space_to_depth(x, 2) = [[[[0, 1, 2],
                            [3, 4, 5]],
                           [[6, 7, 8],
                            [9, 10, 11]],
                           [[12, 13, 14],
                            [15, 16, 17]],
                           [[18, 19, 20],
                            [21, 22, 23]]]]


Defined in src/operator/tensor/matrix_op.cc:L1104

`data`: Input ndarray
`block-size`: Blocks of [block_size. block_size] are moved
`out`: Output array. (optional)

Applies a spatial transformer to input feature map.

`data`: Input data to the SpatialTransformerOp.
`loc`: localisation net, the output dim should be 6 when transform_type is affine. You shold initialize the weight and bias with identity tranform.
`target-shape`: output shape(h, w) of spatial transformer: (y, x) (optional)
`transform-type`: transformation type
`sampler-type`: sampling type
`cudnn-off`: whether to turn cudnn off (optional)
`out`: Output array. (optional)

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

.. math::
   \textrm{sqrt}(x) = \sqrt{x}

Example::

   sqrt([4, 9, 16]) = [2, 3, 4]

The storage type of ``sqrt`` output depends upon the input storage type:

   - sqrt(default) = default
   - sqrt(row_sparse) = row_sparse
   - sqrt(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L907

`data`: The input array.
`out`: Output array. (optional)

Returns element-wise squared value of the input.

.. math::
   square(x) = x^2

Example::

   square([2, 3, 4]) = [4, 9, 16]

The storage type of ``square`` output depends upon the input storage type:

   - square(default) = default
   - square(row_sparse) = row_sparse
   - square(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L883

`data`: The input array.
`out`: Output array. (optional)

Remove single-dimensional entries from the shape of an array.
Same behavior of defining the output tensor shape as numpy.squeeze for the most of cases.
See the following note for exception.

Examples::

  data = [[[0], [1], [2]]]
  squeeze(data) = [0, 1, 2]
  squeeze(data, axis=0) = [[0], [1], [2]]
  squeeze(data, axis=2) = [[0, 1, 2]]
  squeeze(data, axis=(0, 2)) = [0, 1, 2]

.. Note::
  The output of this operator will keep at least one dimension not removed. For example,
  squeeze([[[4]]]) = [4], while in numpy.squeeze, the output will become a scalar.


`data`: data to squeeze
`axis`: Selects a subset of the single-dimensional entries in the shape. If an axis is selected with shape entry greater than one, an error is raised. (optional)
`out`: Output array. (optional)

Join a sequence of arrays along a new axis.

The axis parameter specifies the index of the new axis in the dimensions of the
result. For example, if axis=0 it will be the first dimension and if axis=-1 it
will be the last dimension.

Examples::

  x = [1, 2]
  y = [3, 4]

  stack(x, y) = [[1, 2],
                 [3, 4]]
  stack(x, y, axis=1) = [[1, 3],
                         [2, 4]]


`data`: List of arrays to stack
`axis`: The axis in the result array along which the input arrays are stacked. (optional)
`num-args`: Number of inputs to be stacked.
`out`: Output array. (optional)

Computes the sum of array elements over given axes.

.. Note::

  `sum` and `sum_axis` are equivalent.
  For ndarray of csr storage type summation along axis 0 and axis 1 is supported.
  Setting keepdims or exclude to True will cause a fallback to dense operator.

Example::

  data = [[[1, 2], [2, 3], [1, 3]],
          [[1, 4], [4, 3], [5, 2]],
          [[7, 1], [7, 2], [7, 3]]]

  sum(data, axis=1)
  [[  4.   8.]
   [ 10.   9.]
   [ 21.   6.]]

  sum(data, axis=[1,2])
  [ 12.  19.  27.]

  data = [[1, 2, 0],
          [3, 0, 1],
          [4, 1, 0]]

  csr = cast_storage(data, 'csr')

  sum(csr, axis=0)
  [ 8.  3.  1.]

  sum(csr, axis=1)
  [ 3.  4.  5.]



Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L116

`data`: The input
`axis`: The axis or axes along which to perform the reduction.

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

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

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

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

      Negative values means indexing from right to left. (optional)
`keepdims`: If this is set to `True`, the reduced axes are left in the result as dimension with size one. (optional)
`exclude`: Whether to perform reduction on axis that are NOT in axis instead. (optional)
`out`: Output array. (optional)

Computes support vector machine based transformation of the input.

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



`data`: Input data for SVM transformation.
`label`: Class label for the input data.
`margin`: The loss function penalizes outputs that lie outside this margin. Default margin is 1. (optional)
`regularization-coefficient`: Regularization parameter for the SVM. This balances the tradeoff between coefficient size and error. (optional)
`use-linear`: Whether to use L1-SVM objective. L2-SVM objective is used by default. (optional)
`out`: Output array. (optional)

Interchanges two axes of an array.

Examples::

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

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

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


Defined in src/operator/swapaxis.cc:L70

`data`: Input array.
`dim1`: the first axis to be swapped. (optional)
`dim2`: the second axis to be swapped. (optional)
`out`: Output array. (optional)

Takes elements from an input array along the given axis.

This function slices the input array along a particular axis with the provided indices.

Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis
dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them
in an output tensor of rank q + (r - 1).

Examples::

  x = [4.  5.  6.]

  // Trivial case, take the second element along the first axis.

  take(x, [1]) = [ 5. ]

  // The other trivial case, axis=-1, take the third element along the first axis

  take(x, [3], axis=-1, mode='clip') = [ 6. ]

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

  // In this case we will get rows 0 and 1, then 1 and 2. Along axis 0

  take(x, [[0,1],[1,2]]) = [[[ 1.,  2.],
                             [ 3.,  4.]],

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

  // In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around).
  // Along axis 1

  take(x, [[0, 3], [-1, -2]], axis=1, mode='wrap') = [[[ 1.  2.]
                                                       [ 2.  1.]]

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

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

The storage type of ``take`` output depends upon the input storage type:

   - take(default, default) = default
   - take(csr, default, axis=0) = csr



Defined in src/operator/tensor/indexing_op.cc:L695

`a`: The input array.
`indices`: The indices of the values to be extracted.
`axis`: The axis of input array to be taken.For input tensor of rank r, it could be in the range of [-r, r-1] (optional)
`mode`: Specify how out-of-bound indices bahave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis.  "wrap" means to wrap around.  "raise" means to raise an error, not supported yet. (optional)
`out`: Output array. (optional)

Computes the element-wise tangent of the input array.

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

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

The storage type of ``tan`` output depends upon the input storage type:

   - tan(default) = default
   - tan(row_sparse) = row_sparse
   - tan(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L139

`data`: The input array.
`out`: Output array. (optional)

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

.. math::
   tanh(x) = sinh(x) / cosh(x)

The storage type of ``tanh`` output depends upon the input storage type:

   - tanh(default) = default
   - tanh(row_sparse) = row_sparse
   - tanh(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L290

`data`: The input array.
`out`: Output array. (optional)

Repeats the whole array multiple times.

If ``reps`` has length *d*, and input array has dimension of *n*. There are
three cases:

- **n=d**. Repeat *i*-th dimension of the input by ``reps[i]`` times::

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

    tile(x, reps=(2,3)) = [[ 1.,  2.,  1.,  2.,  1.,  2.],
                           [ 3.,  4.,  3.,  4.,  3.,  4.],
                           [ 1.,  2.,  1.,  2.,  1.,  2.],
                           [ 3.,  4.,  3.,  4.,  3.,  4.]]

- **n>d**. ``reps`` is promoted to length *n* by pre-pending 1's to it. Thus for
  an input shape ``(2,3)``, ``repos=(2,)`` is treated as ``(1,2)``::


    tile(x, reps=(2,)) = [[ 1.,  2.,  1.,  2.],
                          [ 3.,  4.,  3.,  4.]]

- **n<d**. The input is promoted to be d-dimensional by prepending new axes. So a
  shape ``(2,2)`` array is promoted to ``(1,2,2)`` for 3-D replication::

    tile(x, reps=(2,2,3)) = [[[ 1.,  2.,  1.,  2.,  1.,  2.],
                              [ 3.,  4.,  3.,  4.,  3.,  4.],
                              [ 1.,  2.,  1.,  2.,  1.,  2.],
                              [ 3.,  4.,  3.,  4.,  3.,  4.]],

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


Defined in src/operator/tensor/matrix_op.cc:L857

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

Returns the top *k* elements in an input array along the given axis.
 The returned elements will be sorted.

Examples::

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

  // returns an index of the largest element on last axis
  topk(x) = [[ 2.],
             [ 1.]]

  // returns the value of top-2 largest elements on last axis
  topk(x, ret_typ='value', k=2) = [[ 0.4,  0.3],
                                   [ 0.3,  0.2]]

  // returns the value of top-2 smallest elements on last axis
  topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 ,  0.3],
                                               [ 0.1 ,  0.2]]

  // returns the value of top-2 largest elements on axis 0
  topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3,  0.3,  0.4],
                                           [ 0.1,  0.2,  0.2]]

  // flattens and then returns list of both values and indices
  topk(x, ret_typ='both', k=2) = [[[ 0.4,  0.3], [ 0.3,  0.2]] ,  [[ 2.,  0.], [ 1.,  2.]]]



Defined in src/operator/tensor/ordering_op.cc:L64

`data`: The input array
`axis`: Axis along which to choose the top k indices. If not given, the flattened array is used. Default is -1. (optional)
`k`: Number of top elements to select, should be always smaller than or equal to the element number in the given axis. A global sort is performed if set k < 1. (optional)
`ret-typ`: The return type.
 "value" means to return the top k values, "indices" means to return the indices of the top k values, "mask" means to return a mask array containing 0 and 1. 1 means the top k values. "both" means to return a list of both values and indices of top k elements. (optional)
`is-ascend`: Whether to choose k largest or k smallest elements. Top K largest elements will be chosen if set to false. (optional)
`dtype`: DType of the output indices when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely represent the indices. (optional)
`out`: Output array. (optional)

Permutes the dimensions of an array.

Examples::

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

  transpose(x) = [[ 1.,  3.],
                  [ 2.,  4.]]

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

       [[ 5.,  6.],
        [ 7.,  8.]]]

  transpose(x) = [[[ 1.,  5.],
                   [ 3.,  7.]],

                  [[ 2.,  6.],
                   [ 4.,  8.]]]

  transpose(x, axes=(1,0,2)) = [[[ 1.,  2.],
                                 [ 5.,  6.]],

                                [[ 3.,  4.],
                                 [ 7.,  8.]]]


Defined in src/operator/tensor/matrix_op.cc:L375

`data`: Source input
`axes`: Target axis order. By default the axes will be inverted. (optional)
`out`: Output array. (optional)

Return the element-wise truncated value of the input.

The truncated value of the scalar x is the nearest integer i which is closer to
zero than x is. In short, the fractional part of the signed number x is discarded.

Example::

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

The storage type of ``trunc`` output depends upon the input storage type:

   - trunc(default) = default
   - trunc(row_sparse) = row_sparse
   - trunc(csr) = csr



Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L825

`data`: The input array.
`out`: Output array. (optional)

Upsamples the given input data.

Two algorithms (``sample_type``) are available for upsampling:

- Nearest Neighbor
- Bilinear

**Nearest Neighbor Upsampling**

Input data is expected to be NCHW.

Example::

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

  UpSampling(x, scale=2, sample_type='nearest') = [[[[1. 1. 1. 1. 1. 1.]
                                                     [1. 1. 1. 1. 1. 1.]
                                                     [1. 1. 1. 1. 1. 1.]
                                                     [1. 1. 1. 1. 1. 1.]
                                                     [1. 1. 1. 1. 1. 1.]
                                                     [1. 1. 1. 1. 1. 1.]]]]

**Bilinear Upsampling**

Uses `deconvolution` algorithm under the hood. You need provide both input data and the kernel.

Input data is expected to be NCHW.

`num_filter` is expected to be same as the number of channels.

Example::

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

  w = [[[[1. 1. 1. 1.]
         [1. 1. 1. 1.]
         [1. 1. 1. 1.]
         [1. 1. 1. 1.]]]]
  
  UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = [[[[1. 2. 2. 2. 2. 1.]
                                                                       [2. 4. 4. 4. 4. 2.]
                                                                       [2. 4. 4. 4. 4. 2.]
                                                                       [2. 4. 4. 4. 4. 2.]
                                                                       [2. 4. 4. 4. 4. 2.]
                                                                       [1. 2. 2. 2. 2. 1.]]]]


Defined in src/operator/nn/upsampling.cc:L173

`data`: Array of tensors to upsample. For bilinear upsampling, there should be 2 inputs - 1 data and 1 weight.
`scale`: Up sampling scale
`num-filter`: Input filter. Only used by bilinear sample_type.Since bilinear upsampling uses deconvolution, num_filters is set to the number of channels. (optional)
`sample-type`: upsampling method
`multi-input-mode`: How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images together, only available for nearest neighbor upsampling. (optional)
`num-args`: Number of inputs to be upsampled. For nearest neighbor upsampling, this can be 1-N; the size of output will be(scale*h_0,scale*w_0) and all other inputs will be upsampled to thesame size. For bilinear upsampling this must be 2; 1 input and 1 weight.
`workspace`: Tmp workspace for deconvolution (MB) (optional)
`out`: Output array. (optional)

Return the elements, either from x or y, depending on the condition.

Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y,
depending on the elements from condition are true or false. x and y must have the same shape.
If condition has the same shape as x, each element in the output array is from x if the
corresponding element in the condition is true, and from y if false.

If condition does not have the same shape as x, it must be a 1D array whose size is
the same as x's first dimension size. Each row of the output array is from x's row
if the corresponding element from condition is true, and from y's row if false.

Note that all non-zero values are interpreted as ``True`` in condition.

Examples::

  x = [[1, 2], [3, 4]]
  y = [[5, 6], [7, 8]]
  cond = [[0, 1], [-1, 0]]

  where(cond, x, y) = [[5, 2], [3, 8]]

  csr_cond = cast_storage(cond, 'csr')

  where(csr_cond, x, y) = [[5, 2], [3, 8]]



Defined in src/operator/tensor/control_flow_op.cc:L57

`condition`: condition array
`x`: 
`y`: 
`out`: Output array. (optional)

Return an array of zeros with the same shape, type and storage type
as the input array.

The storage type of ``zeros_like`` output depends on the storage type of the input

- zeros_like(row_sparse) = row_sparse
- zeros_like(csr) = csr
- zeros_like(default) = default

Examples::

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

  zeros_like(x) = [[ 0.,  0.,  0.],
                   [ 0.,  0.,  0.]]



`data`: The input
`out`: Output array. (optional)