# org.apache.clojure-mxnet.ndarray-api

Experimental


### -copy

(-copy {:keys [data out], :or {out nil}, :as opts})
Returns a copy of the input.

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

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

### -linalg-det

(-linalg-det {:keys [a out], :or {out nil}, :as opts})
Compute the determinant of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

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

*out* = *det(A)*

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

.. note:: The operator supports float32 and float64 data types only.
.. note:: There is no gradient backwarded when A is non-invertible (which is
equivalent to det(A) = 0) because zero is rarely hit upon in float
point computation and the Jacobi's formula on determinant gradient
is not computationally efficient when A is non-invertible.

Examples::

Single matrix determinant
A = [[1., 4.], [2., 3.]]
det(A) = [-5.]

Batch matrix determinant
A = [[[1., 4.], [2., 3.]],
[[2., 3.], [1., 4.]]]
det(A) = [-5., 5.]

Defined in src/operator/tensor/la_op.cc:L975

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

### -linalg-extractdiag

(-linalg-extractdiag {:keys [a offset out], :or {offset nil, out nil}, :as opts})
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)

### -linalg-extracttrian

(-linalg-extracttrian {:keys [a offset lower out], :or {offset nil, lower nil, out nil}, :as opts})
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)

### -linalg-gelqf

(-linalg-gelqf {:keys [a out], :or {out nil}, :as opts})
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)

### -linalg-gemm

(-linalg-gemm a b c)(-linalg-gemm {:keys [a b c transpose-a transpose-b alpha beta axis out], :or {transpose-a nil, transpose-b nil, alpha nil, beta nil, axis nil, out nil}, :as opts})
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::

A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
= [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]

A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
C = [[[10.0]], [[0.01]]]
gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
= [[[104.0]], [[0.14]]]

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

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)

### -linalg-gemm2

(-linalg-gemm2 a b)(-linalg-gemm2 {:keys [a b transpose-a transpose-b alpha axis out], :or {transpose-a nil, transpose-b nil, alpha nil, axis nil, out nil}, :as opts})
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)

### -linalg-inverse

(-linalg-inverse {:keys [a out], :or {out nil}, :as opts})
Compute the inverse of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

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

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

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

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

Examples::

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

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

Defined in src/operator/tensor/la_op.cc:L920

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

### -linalg-makediag

(-linalg-makediag {:keys [a offset out], :or {offset nil, out nil}, :as opts})
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)

### -linalg-maketrian

(-linalg-maketrian {:keys [a offset lower out], :or {offset nil, lower nil, out nil}, :as opts})
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)

### -linalg-potrf

(-linalg-potrf {:keys [a out], :or {out nil}, :as opts})
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)

### -linalg-potri

(-linalg-potri {:keys [a out], :or {out nil}, :as opts})
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)

### -linalg-slogdet

(-linalg-slogdet {:keys [a out], :or {out nil}, :as opts})
Compute the sign and log of the determinant of a matrix.
Input is a tensor *A* of dimension *n >= 2*.

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

*sign* = *sign(det(A))*
*logabsdet* = *log(abs(det(A)))*

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

.. note:: The operator supports float32 and float64 data types only.
.. note:: The gradient is not properly defined on sign, so the gradient of
it is not backwarded.
.. note:: No gradient is backwarded when A is non-invertible. Please see
the docs of operator det for detail.

Examples::

Single matrix signed log determinant
A = [[2., 3.], [1., 4.]]
sign, logabsdet = slogdet(A)
sign = [1.]
logabsdet = [1.609438]

Batch matrix signed log determinant
A = [[[2., 3.], [1., 4.]],
[[1., 2.], [2., 4.]],
[[1., 2.], [4., 3.]]]
sign, logabsdet = slogdet(A)
sign = [1., 0., -1.]
logabsdet = [1.609438, -inf, 1.609438]

Defined in src/operator/tensor/la_op.cc:L1034

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

### -linalg-sumlogdiag

(-linalg-sumlogdiag {:keys [a out], :or {out nil}, :as opts})
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)

### -linalg-syrk

(-linalg-syrk {:keys [a transpose alpha out], :or {transpose nil, alpha nil, out nil}, :as opts})
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)

### -linalg-trmm

(-linalg-trmm a b)(-linalg-trmm {:keys [a b transpose rightside lower alpha out], :or {transpose nil, rightside nil, lower nil, alpha nil, out nil}, :as opts})
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)

### -linalg-trsm

(-linalg-trsm a b)(-linalg-trsm {:keys [a b transpose rightside lower alpha out], :or {transpose nil, rightside nil, lower nil, alpha nil, out nil}, :as opts})
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)

### -np-cumsum

(-np-cumsum {:keys [a axis dtype out], :or {axis nil, dtype nil, out nil}, :as opts})
Return the cumulative sum of the elements along a given axis.

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

a: Input ndarray
axis: Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array. (optional)
dtype: Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used. (optional)
out: Output array. (optional)

### -ravel-multi-index

(-ravel-multi-index {:keys [data shape out], :or {shape nil, out nil}, :as opts})
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)

### -shuffle

(-shuffle {:keys [data out], :or {out nil}, :as opts})
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)

### -unravel-index

(-unravel-index {:keys [data shape out], :or {shape nil, out nil}, :as opts})
Converts an array of flat indices into a batch of index arrays. The operator follows numpy conventions so a single multi index is given by a column of the output matrix. The leading dimension may be left unspecified by using -1 as placeholder.

Examples::

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

Defined in src/operator/tensor/ravel.cc:L68

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

### abs

(abs {:keys [data out], :or {out nil}, :as opts})
Returns element-wise absolute value of the input.

Example::

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

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

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

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

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

### activation

(activation data act-type)(activation {:keys [data act-type out], :or {out nil}, :as opts})
Applies an activation function element-wise to the input.

The following activation functions are supported:

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

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

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

(adam-update weight grad mean var lr)(adam-update {:keys [weight grad mean var lr beta1 beta2 epsilon wd rescale-grad clip-gradient lazy-update out], :or {beta1 nil, beta2 nil, epsilon nil, wd nil, rescale-grad nil, clip-gradient nil, lazy-update nil, out nil}, :as opts})
Update function for Adam optimizer. Adam is seen as a generalization

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

.. math::

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

It updates the weights using::

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

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

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

Defined in src/operator/optimizer_op.cc:L688

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)

(add-n {:keys [args out], :or {out nil}, :as opts})
Adds all input arguments element-wise.

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

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

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

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

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

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

### all-finite

(all-finite {:keys [data init-output out], :or {init-output nil, out nil}, :as opts})
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)

### amp-cast

(amp-cast data dtype)(amp-cast {:keys [data dtype out], :or {out nil}, :as opts})
Cast function between low precision float/FP32 used by AMP.

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

Defined in src/operator/tensor/amp_cast.cc:L121

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

### amp-multicast

(amp-multicast data num-outputs)(amp-multicast {:keys [data num-outputs cast-narrow out], :or {cast-narrow nil, out nil}, :as opts})
Cast function used by AMP, that casts its inputs to the common widest type.

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

Defined in src/operator/tensor/amp_cast.cc:L165

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

### arccos

(arccos {:keys [data out], :or {out nil}, :as opts})
Returns element-wise inverse cosine of the input array.

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

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

The storage type of arccos output is always dense

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

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

### arccosh

(arccosh {:keys [data out], :or {out nil}, :as opts})
Returns the element-wise inverse hyperbolic cosine of the input array, \
computed element-wise.

The storage type of arccosh output is always dense

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

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

### arcsin

(arcsin {:keys [data out], :or {out nil}, :as opts})
Returns element-wise inverse sine of the input array.

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

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

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

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

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

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

### arcsinh

(arcsinh {:keys [data out], :or {out nil}, :as opts})
Returns the element-wise inverse hyperbolic sine of the input array, \
computed element-wise.

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

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

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

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

### arctan

(arctan {:keys [data out], :or {out nil}, :as opts})
Returns element-wise inverse tangent of the input array.

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

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

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

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

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

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

### arctanh

(arctanh {:keys [data out], :or {out nil}, :as opts})
Returns the element-wise inverse hyperbolic tangent of the input array, \
computed element-wise.

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

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

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

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

### argmax

(argmax {:keys [data axis keepdims out], :or {axis nil, keepdims nil, out nil}, :as opts})
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.]]

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)

### argmax-channel

(argmax-channel {:keys [data out], :or {out nil}, :as opts})
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.]

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

### argmin

(argmin {:keys [data axis keepdims out], :or {axis nil, keepdims nil, out nil}, :as opts})
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.]]

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)

### argsort

(argsort {:keys [data axis is-ascend dtype out], :or {axis nil, is-ascend nil, dtype nil, out nil}, :as opts})
Returns the indices that would sort an input array along the given axis.

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

Examples::

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

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

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

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

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

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)

### batch-dot

(batch-dot lhs rhs)(batch-dot {:keys [lhs rhs transpose-a transpose-b forward-stype out], :or {transpose-a nil, transpose-b nil, forward-stype nil, out nil}, :as opts})
Batchwise dot product.

batch_dot is used to compute dot product of x and y when x and
y are data in batch, namely N-D (N >= 3) arrays in shape of (B0, ..., B_i, :, :).

For example, given x with shape (B_0, ..., B_i, N, M) and y with shape
(B_0, ..., B_i, M, K), the result array will have shape (B_0, ..., B_i, N, K),
which is computed by::

batch_dot(x,y)[b_0, ..., b_i, :, :] = dot(x[b_0, ..., b_i, :, :], y[b_0, ..., b_i, :, :])

Defined in src/operator/tensor/dot.cc:L127

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-norm

(batch-norm data gamma beta moving-mean moving-var)(batch-norm {:keys [data gamma beta moving-mean moving-var eps momentum fix-gamma use-global-stats output-mean-var axis cudnn-off min-calib-range max-calib-range out], :or {output-mean-var nil, axis nil, cudnn-off nil, fix-gamma nil, eps nil, max-calib-range nil, use-global-stats nil, out nil, min-calib-range nil, momentum nil}, :as opts})
Batch normalization.

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

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

.. math::

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

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

.. math::

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

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

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

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

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

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

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

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

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

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

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)
min-calib-range: The minimum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output. (optional)
max-calib-range: The maximum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output. (optional)
out: Output array. (optional)

### batch-norm-v1

(batch-norm-v1 data gamma beta)(batch-norm-v1 {:keys [data gamma beta eps momentum fix-gamma use-global-stats output-mean-var out], :or {eps nil, momentum nil, fix-gamma nil, use-global-stats nil, output-mean-var nil, out nil}, :as opts})
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)

### batch-take

(batch-take a indices)(batch-take {:keys [a indices out], :or {out nil}, :as opts})
Takes elements from a data batch.

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

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

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

Examples::

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

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

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

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

### bilinear-sampler

(bilinear-sampler data grid)(bilinear-sampler {:keys [data grid cudnn-off out], :or {cudnn-off nil, out nil}, :as opts})
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)

(block-grad {:keys [data out], :or {out nil}, :as opts})
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')
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()
[ 0.  0.]
[ 1.  1.]

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

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

(broadcast-add lhs rhs)(broadcast-add {:keys [lhs rhs out], :or {out nil}, :as opts})
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:

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

(broadcast-axis {:keys [data axis size out], :or {axis nil, size nil, out nil}, :as opts})
Broadcasts the input array over particular axes.

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

broadcast_axes is an alias to the function broadcast_axis.

Example::

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

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

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

(broadcast-div lhs rhs)(broadcast-div {:keys [lhs rhs out], :or {out nil}, :as opts})
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

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

(broadcast-equal lhs rhs)(broadcast-equal {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-greater lhs rhs)(broadcast-greater {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-greater-equal lhs rhs)(broadcast-greater-equal {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-hypot lhs rhs)(broadcast-hypot {:keys [lhs rhs out], :or {out nil}, :as opts})
 Returns the hypotenuse of a right angled triangle, given its "legs"

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

Example::

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

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

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

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

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

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

(broadcast-lesser lhs rhs)(broadcast-lesser {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-lesser-equal lhs rhs)(broadcast-lesser-equal {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-like lhs rhs)(broadcast-like {:keys [lhs rhs lhs-axes rhs-axes out], :or {lhs-axes nil, rhs-axes nil, out nil}, :as opts})
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]

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)

(broadcast-logical-and lhs rhs)(broadcast-logical-and {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-logical-or lhs rhs)(broadcast-logical-or {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-logical-xor lhs rhs)(broadcast-logical-xor {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-maximum lhs rhs)(broadcast-maximum {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-minimum lhs rhs)(broadcast-minimum {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-mod lhs rhs)(broadcast-mod {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-mul lhs rhs)(broadcast-mul {:keys [lhs rhs out], :or {out nil}, :as opts})
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

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

(broadcast-not-equal lhs rhs)(broadcast-not-equal {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-power lhs rhs)(broadcast-power {:keys [lhs rhs out], :or {out nil}, :as opts})
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.]]

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

(broadcast-sub lhs rhs)(broadcast-sub {:keys [lhs rhs out], :or {out nil}, :as opts})
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

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

(broadcast-to {:keys [data shape out], :or {shape nil, out nil}, :as opts})
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.

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)

### cast

(cast data dtype)(cast {:keys [data dtype out], :or {out nil}, :as opts})
Casts all elements of the input to a new type.

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

Example::

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

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

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

### cast-storage

(cast-storage data stype)(cast-storage {:keys [data stype out], :or {out nil}, :as opts})
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)

### cbrt

(cbrt {:keys [data out], :or {out nil}, :as opts})
Returns element-wise cube-root value of the input.

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

Example::

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

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

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

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

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

### ceil

(ceil {:keys [data out], :or {out nil}, :as opts})
Returns element-wise ceiling of the input.

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

Example::

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

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

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

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

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

### clip

(clip data a-min a-max)(clip {:keys [data a-min a-max out], :or {out nil}, :as opts})
Clips (limits) the values in an array.
Given an interval, values outside the interval are clipped to the interval edges.
Clipping x between a_min and a_max would be::
.. math::
clip(x, a_min, a_max) = \max(\min(x, a_max), a_min))
Example::
x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]
The storage type of clip output depends on storage types of inputs and the a_min, a_max \
parameter values:
- clip(default) = default
- clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse
- clip(csr, a_min <= 0, a_max >= 0) = csr
- clip(row_sparse, a_min < 0, a_max < 0) = default
- clip(row_sparse, a_min > 0, a_max > 0) = default
- clip(csr, a_min < 0, a_max < 0) = csr
- clip(csr, a_min > 0, a_max > 0) = csr

Defined in src/operator/tensor/matrix_op.cc:L677

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

### col2im

(col2im data output-size kernel)(col2im {:keys [data output-size kernel stride dilate pad out], :or {stride nil, dilate nil, pad nil, out nil}, :as opts})
Combining the output column matrix of im2col back to image array.

Like :class:~mxnet.ndarray.im2col, this operator is also used in the vanilla convolution
implementation. Despite the name, col2im is not the reverse operation of im2col. Since there
may be overlaps between neighbouring sliding blocks, the column elements cannot be directly
put back into image. Instead, they are accumulated (i.e., summed) in the input image
just like the gradient computation, so col2im is the gradient of im2col and vice versa.

Using the notation in im2col, given an input column array of shape
:math:(N, C \times  \prod(\text{kernel}), W), this operator accumulates the column elements
into output array of shape :math:(N, C, \text{output_size}[0], \text{output_size}[1], \dots).
Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L182

data: Input array to combine sliding blocks.
output-size: The spatial dimension of image array: (w,), (h, w) or (d, h, w).
kernel: Sliding kernel size: (w,), (h, w) or (d, h, w).
stride: The stride between adjacent sliding blocks in spatial dimension: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
dilate: The spacing between adjacent kernel points: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
pad: The zero-value padding size on both sides of spatial dimension: (w,), (h, w) or (d, h, w). Defaults to no padding. (optional)
out: Output array. (optional)

### concat

(concat data num-args)(concat {:keys [data num-args dim out], :or {dim nil, out nil}, :as opts})
Joins input arrays along a given axis.

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

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

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

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

Example::

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

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

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

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

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

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)

### convolution

(convolution data weight bias kernel num-filter)(convolution {:keys [data weight bias kernel stride dilate pad num-filter num-group workspace no-bias cudnn-tune cudnn-off layout out], :or {no-bias nil, cudnn-off nil, stride nil, dilate nil, workspace nil, layout nil, out nil, pad nil, num-group nil, cudnn-tune nil}, :as opts})
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:L469

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)

### convolution-v1

(convolution-v1 data weight bias kernel num-filter)(convolution-v1 {:keys [data weight bias kernel stride dilate pad num-filter num-group workspace no-bias cudnn-tune cudnn-off layout out], :or {no-bias nil, cudnn-off nil, stride nil, dilate nil, workspace nil, layout nil, out nil, pad nil, num-group nil, cudnn-tune nil}, :as opts})
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)

### correlation

(correlation data1 data2)(correlation {:keys [data1 data2 kernel-size max-displacement stride1 stride2 pad-size is-multiply out], :or {kernel-size nil, max-displacement nil, stride1 nil, stride2 nil, pad-size nil, is-multiply nil, out nil}, :as opts})
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)

### cos

(cos {:keys [data out], :or {out nil}, :as opts})
Computes the element-wise cosine of the input array.

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

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

The storage type of cos output is always dense

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

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

### cosh

(cosh {:keys [data out], :or {out nil}, :as opts})
Returns the hyperbolic cosine  of the input array, computed element-wise.

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

The storage type of cosh output is always dense

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

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

### crop

(crop data num-args)(crop {:keys [data num-args offset h-w center-crop out], :or {offset nil, h-w nil, center-crop nil, out nil}, :as opts})

.. 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)

### ctc-loss

(ctc-loss data label data-lengths label-lengths)(ctc-loss {:keys [data label data-lengths label-lengths use-data-lengths use-label-lengths blank-label out], :or {use-data-lengths nil, use-label-lengths nil, blank-label nil, out nil}, :as opts})
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)

### deconvolution

(deconvolution data weight bias kernel num-filter)(deconvolution {:keys [data weight bias kernel stride dilate pad adj target-shape num-filter num-group workspace no-bias cudnn-tune cudnn-off layout out], :or {target-shape nil, no-bias nil, cudnn-off nil, stride nil, dilate nil, workspace nil, layout nil, adj nil, out nil, pad nil, num-group nil, cudnn-tune nil}, :as opts})
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)

### degrees

(degrees {:keys [data out], :or {out nil}, :as opts})
Converts each element of the input array from radians to degrees.

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

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

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

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

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

### depth-to-space

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

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

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

### diag

(diag {:keys [data k axis1 axis2 out], :or {k nil, axis1 nil, axis2 nil, out nil}, :as opts})
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

(dot lhs rhs)(dot {:keys [lhs rhs transpose-a transpose-b forward-stype out], :or {transpose-a nil, transpose-b nil, forward-stype nil, out nil}, :as opts})
Dot product of two arrays.

dot's behavior depends on the input array dimensions:

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

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

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

Example::

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

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

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

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

.. Note::

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

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

lhs: The first input
rhs: The second input
transpose-a: If true then transpose the first input before dot. (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)

### dropout

(dropout {:keys [data p mode axes cudnn-off out], :or {p nil, mode nil, axes nil, cudnn-off nil, out nil}, :as opts})
Applies dropout operation to input array.

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

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

Example::

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

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

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

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

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)

(elemwise-add lhs rhs)(elemwise-add {:keys [lhs rhs out], :or {out nil}, :as opts})
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)

### elemwise-div

(elemwise-div lhs rhs)(elemwise-div {:keys [lhs rhs out], :or {out nil}, :as opts})
Divides arguments element-wise.

The storage type of elemwise_div output is always dense

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

### elemwise-mul

(elemwise-mul lhs rhs)(elemwise-mul {:keys [lhs rhs out], :or {out nil}, :as opts})
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)

### elemwise-sub

(elemwise-sub lhs rhs)(elemwise-sub {:keys [lhs rhs out], :or {out nil}, :as opts})
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)

### embedding

(embedding data weight input-dim output-dim)(embedding {:keys [data weight input-dim output-dim dtype sparse-grad out], :or {dtype nil, sparse-grad nil, out nil}, :as opts})
Maps integer indices to vector representations (embeddings).

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

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

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

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

Examples::

input_dim = 4
output_dim = 5

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

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

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

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

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

.. Note::

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

Defined in src/operator/tensor/indexing_op.cc:L598

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)

### erf

(erf {:keys [data out], :or {out nil}, :as opts})
Returns element-wise gauss error function of the input.

Example::

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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L886

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

### erfinv

(erfinv {:keys [data out], :or {out nil}, :as opts})
Returns element-wise inverse gauss error function of the input.

Example::

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

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L908

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

### exp

(exp {:keys [data out], :or {out nil}, :as opts})
Returns element-wise exponential value of the input.

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

Example::

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

The storage type of exp output is always dense

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

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

### expand-dims

(expand-dims data axis)(expand-dims {:keys [data axis out], :or {out nil}, :as opts})
Inserts a new axis of size 1 into the array shape
For example, given x with shape (2,3,4), then expand_dims(x, axis=1)
will return a new array with shape (2,1,3,4).

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

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)

### expm1

(expm1 {:keys [data out], :or {out nil}, :as opts})
Returns exp(x) - 1 computed element-wise on the input.

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

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

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

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

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

### fill-element-0index

(fill-element-0index lhs mhs rhs)(fill-element-0index {:keys [lhs mhs rhs out], :or {out nil}, :as opts})
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)

### fix

(fix {:keys [data out], :or {out nil}, :as opts})
Returns element-wise rounded value to the nearest \
integer towards zero of the input.

Example::

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

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

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

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

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

### flatten

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

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

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

### floor

(floor {:keys [data out], :or {out nil}, :as opts})
Returns element-wise floor of the input.

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

Example::

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

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

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

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

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

### ftml-update

(ftml-update weight grad d v z lr t)(ftml-update {:keys [weight grad d v z lr beta1 beta2 epsilon t wd rescale-grad clip-grad out], :or {beta1 nil, beta2 nil, epsilon nil, wd nil, rescale-grad nil, clip-grad nil, out nil}, :as opts})
The FTML optimizer described in
*FTML - Follow the Moving Leader in Deep Learning*,
available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.

.. math::

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

Defined in src/operator/optimizer_op.cc:L640

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)

### ftrl-update

(ftrl-update weight grad z n lr)(ftrl-update {:keys [weight grad z n lr lamda1 beta wd rescale-grad clip-gradient out], :or {lamda1 nil, beta nil, wd nil, rescale-grad nil, clip-gradient nil, out nil}, :as opts})
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::

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

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

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

Defined in src/operator/optimizer_op.cc:L876

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)

### fully-connected

(fully-connected data weight bias num-hidden)(fully-connected {:keys [data weight bias num-hidden no-bias flatten out], :or {no-bias nil, flatten nil, out nil}, :as opts})
Applies a linear transformation: :math:Y = XW^T + b.

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

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

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

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

The learnable parameters include both weight and bias.

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

.. Note::

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

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

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

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)

### gamma

(gamma {:keys [data out], :or {out nil}, :as opts})
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)

### gammaln

(gammaln {:keys [data out], :or {out nil}, :as opts})
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-nd

(gather-nd data indices)(gather-nd {:keys [data indices out], :or {out nil}, :as opts})
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)

### grid-generator

(grid-generator data transform-type)(grid-generator {:keys [data transform-type target-shape out], :or {target-shape nil, out nil}, :as opts})
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)

### group-norm

(group-norm data gamma beta)(group-norm {:keys [data gamma beta num-groups eps output-mean-var out], :or {num-groups nil, eps nil, output-mean-var nil, out nil}, :as opts})
Group normalization.

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

.. math::

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

Both gamma and beta are learnable parameters.

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

data: Input data
gamma: gamma array
beta: beta array
num-groups: Total number of groups. (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)

### hard-sigmoid

(hard-sigmoid {:keys [data alpha beta out], :or {alpha nil, beta nil, out nil}, :as opts})
Computes hard sigmoid of x element-wise.

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

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

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

### identity-attach-kl-sparse-reg

(identity-attach-kl-sparse-reg {:keys [data sparseness-target penalty momentum out], :or {sparseness-target nil, penalty nil, momentum nil, out nil}, :as opts})
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)

### im2col

(im2col data kernel)(im2col {:keys [data kernel stride dilate pad out], :or {stride nil, dilate nil, pad nil, out nil}, :as opts})
Extract sliding blocks from input array.

This operator is used in vanilla convolution implementation to transform the sliding
blocks on image to column matrix, then the convolution operation can be computed
by matrix multiplication between column and convolution weight. Due to the close
relation between im2col and convolution, the concept of **kernel**, **stride**,
**dilate** and **pad** in this operator are inherited from convolution operation.

Given the input data of shape :math:(N, C, *), where :math:N is the batch size,
:math:C is the channel size, and :math:* is the arbitrary spatial dimension,
the output column array is always with shape :math:(N, C \times \prod(\text{kernel}), W),
where :math:C \times \prod(\text{kernel}) is the block size, and :math:W is the
block number which is the spatial size of the convolution output with same input parameters.
Only 1-D, 2-D and 3-D of spatial dimension is supported in this operator.

Defined in src/operator/nn/im2col.cc:L100

data: Input array to extract sliding blocks.
kernel: Sliding kernel size: (w,), (h, w) or (d, h, w).
stride: The stride between adjacent sliding blocks in spatial dimension: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
dilate: The spacing between adjacent kernel points: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension. (optional)
pad: The zero-value padding size on both sides of spatial dimension: (w,), (h, w) or (d, h, w). Defaults to no padding. (optional)
out: Output array. (optional)

### instance-norm

(instance-norm data gamma beta)(instance-norm {:keys [data gamma beta eps out], :or {eps nil, out nil}, :as opts})
Applies instance normalization to the n-dimensional input array.

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

.. math::

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

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

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

This implementation is based on this paper [1]_

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

Examples::

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

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

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

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

Defined in src/operator/instance_norm.cc:L95

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)

### khatri-rao

(khatri-rao {:keys [args out], :or {out nil}, :as opts})
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)

### l2-normalization

(l2-normalization {:keys [data eps mode out], :or {eps nil, mode nil, out nil}, :as opts})
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)

### lamb-update-phase1

(lamb-update-phase1 weight grad mean var t wd)(lamb-update-phase1 {:keys [weight grad mean var beta1 beta2 epsilon t bias-correction wd rescale-grad clip-gradient out], :or {beta1 nil, beta2 nil, epsilon nil, bias-correction nil, rescale-grad nil, clip-gradient nil, out nil}, :as opts})
Phase I of lamb update it performs the following operations and returns g:.

Link to paper: https://arxiv.org/pdf/1904.00962.pdf

.. math::
\begin{gather*}
then
then

mean = beta1 * mean + (1 - beta1) * grad;
variance = beta2 * variance + (1. - beta2) * grad ^ 2;

if (bias_correction)
then
mean_hat = mean / (1. - beta1^t);
var_hat = var / (1 - beta2^t);
g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight;
else
g = mean / (var_data^(1/2) + epsilon) + wd * weight;
\end{gather*}

Defined in src/operator/optimizer_op.cc:L953

weight: Weight
grad: Gradient
mean: Moving mean
var: Moving variance
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)
t: Index update count.
bias-correction: Whether to use bias correction. (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.
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)

### lamb-update-phase2

(lamb-update-phase2 weight g r1 r2 lr)(lamb-update-phase2 {:keys [weight g r1 r2 lr lower-bound upper-bound out], :or {lower-bound nil, upper-bound nil, out nil}, :as opts})
Phase II of lamb update it performs the following operations and updates grad.

Link to paper: https://arxiv.org/pdf/1904.00962.pdf

.. math::
\begin{gather*}
if (lower_bound >= 0)
then
r1 = max(r1, lower_bound)
if (upper_bound >= 0)
then
r1 = max(r1, upper_bound)

if (r1 == 0 or r2 == 0)
then
lr = lr
else
lr = lr * (r1/r2)
weight = weight - lr * g
\end{gather*}

Defined in src/operator/optimizer_op.cc:L992

weight: Weight
g: Output of lamb_update_phase 1
r1: r1
r2: r2
lr: Learning rate
lower-bound: Lower limit of norm of weight. If lower_bound <= 0, Lower limit is not set (optional)
upper-bound: Upper limit of norm of weight. If upper_bound <= 0, Upper limit is not set (optional)
out: Output array. (optional)

### layer-norm

(layer-norm data gamma beta)(layer-norm {:keys [data gamma beta axis eps output-mean-var out], :or {axis nil, eps nil, output-mean-var nil, out nil}, :as opts})
Layer normalization.

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

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

.. math::

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

Both gamma and beta are learnable parameters.

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

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

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

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

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)

### leaky-re-lu

(leaky-re-lu data gamma)(leaky-re-lu {:keys [data gamma act-type slope lower-bound upper-bound out], :or {act-type nil, slope nil, lower-bound nil, upper-bound nil, out nil}, :as opts})
Applies Leaky rectified linear unit activation element-wise to the input.

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

The following modified ReLU Activation functions are supported:

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

Defined in src/operator/leaky_relu.cc:L161

data: Input data to activation function.
gamma: Input data to activation function.
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)

### linear-regression-output

(linear-regression-output data label)(linear-regression-output {:keys [data label grad-scale out], :or {grad-scale nil, out nil}, :as opts})
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)

### log

(log {:keys [data out], :or {out nil}, :as opts})
Returns element-wise Natural logarithmic value of the input.

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

The storage type of log output is always dense

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

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

### log-softmax

(log-softmax {:keys [data axis temperature dtype use-length out], :or {axis nil, temperature nil, dtype nil, use-length nil, out nil}, :as opts})
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)
use-length: Whether to use the length input as a mask over the data input. (optional)
out: Output array. (optional)

### log10

(log10 {:keys [data out], :or {out nil}, :as opts})
Returns element-wise Base-10 logarithmic value of the input.

10**log10(x) = x

The storage type of log10 output is always dense

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

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

### log1p

(log1p {:keys [data out], :or {out nil}, :as opts})
Returns element-wise log(1 + x) value of the input.

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

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

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

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

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

### log2

(log2 {:keys [data out], :or {out nil}, :as opts})
Returns element-wise Base-2 logarithmic value of the input.

2**log2(x) = x

The storage type of log2 output is always dense

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

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

### logical-not

(logical-not {:keys [data out], :or {out nil}, :as opts})
Returns the result of logical NOT (!) function

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

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

### logistic-regression-output

(logistic-regression-output data label)(logistic-regression-output {:keys [data label grad-scale out], :or {grad-scale nil, out nil}, :as opts})
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)

### lrn

(lrn data nsize)(lrn {:keys [data alpha beta knorm nsize out], :or {alpha nil, beta nil, knorm nil, out nil}, :as opts})
Applies local response normalization to the input.

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

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

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

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

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

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)

### mae-regression-output

(mae-regression-output data label)(mae-regression-output {:keys [data label grad-scale out], :or {grad-scale nil, out nil}, :as opts})
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-loss

(make-loss {:keys [data out], :or {out nil}, :as opts})
Make your own loss function in network construction.

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

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

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

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

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

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

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

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

### max

(max {:keys [data axis keepdims exclude out], :or {axis nil, keepdims nil, exclude nil, out nil}, :as opts})
Computes the max of array elements over given axes.

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)

### mean

(mean {:keys [data axis keepdims exclude out], :or {axis nil, keepdims nil, exclude nil, out nil}, :as opts})
Computes the mean of array elements over given axes.

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)

### min

(min {:keys [data axis keepdims exclude out], :or {axis nil, keepdims nil, exclude nil, out nil}, :as opts})
Computes the min of array elements over given axes.

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)

### moments

(moments {:keys [data axes keepdims out], :or {axes nil, keepdims nil, out nil}, :as opts})
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)

### mp-lamb-update-phase1

(mp-lamb-update-phase1 weight grad mean var weight32 t wd)(mp-lamb-update-phase1 {:keys [weight grad mean var weight32 beta1 beta2 epsilon t bias-correction wd rescale-grad clip-gradient out], :or {beta1 nil, beta2 nil, epsilon nil, bias-correction nil, rescale-grad nil, clip-gradient nil, out nil}, :as opts})
Mixed Precision version of Phase I of lamb update
it performs the following operations and returns g:.

Link to paper: https://arxiv.org/pdf/1904.00962.pdf

.. math::
\begin{gather*}
then
then

mean = beta1 * mean + (1 - beta1) * grad;
variance = beta2 * variance + (1. - beta2) * grad ^ 2;

if (bias_correction)
then
mean_hat = mean / (1. - beta1^t);
var_hat = var / (1 - beta2^t);
g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight32;
else
g = mean / (var_data^(1/2) + epsilon) + wd * weight32;
\end{gather*}

Defined in src/operator/optimizer_op.cc:L1033

weight: Weight
grad: Gradient
mean: Moving mean
var: Moving variance
weight32: Weight32
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)
t: Index update count.
bias-correction: Whether to use bias correction. (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.
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)

### mp-lamb-update-phase2

(mp-lamb-update-phase2 weight g r1 r2 weight32 lr)(mp-lamb-update-phase2 {:keys [weight g r1 r2 weight32 lr lower-bound upper-bound out], :or {lower-bound nil, upper-bound nil, out nil}, :as opts})
Mixed Precision version Phase II of lamb update
it performs the following operations and updates grad.

Link to paper: https://arxiv.org/pdf/1904.00962.pdf

.. math::
\begin{gather*}
if (lower_bound >= 0)
then
r1 = max(r1, lower_bound)
if (upper_bound >= 0)
then
r1 = max(r1, upper_bound)

if (r1 == 0 or r2 == 0)
then
lr = lr
else
lr = lr * (r1/r2)
weight32 = weight32 - lr * g
weight(float16) = weight32
\end{gather*}

Defined in src/operator/optimizer_op.cc:L1075

weight: Weight
g: Output of mp_lamb_update_phase 1
r1: r1
r2: r2
weight32: Weight32
lr: Learning rate
lower-bound: Lower limit of norm of weight. If lower_bound <= 0, Lower limit is not set (optional)
upper-bound: Upper limit of norm of weight. If upper_bound <= 0, Upper limit is not set (optional)
out: Output array. (optional)

### mp-nag-mom-update

(mp-nag-mom-update weight grad mom weight32 lr)(mp-nag-mom-update {:keys [weight grad mom weight32 lr momentum wd rescale-grad clip-gradient out], :or {momentum nil, wd nil, rescale-grad nil, clip-gradient nil, out nil}, :as opts})
Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.

Defined in src/operator/optimizer_op.cc:L745

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)

### mp-sgd-mom-update

(mp-sgd-mom-update weight grad mom weight32 lr)(mp-sgd-mom-update {:keys [weight grad mom weight32 lr momentum wd rescale-grad clip-gradient lazy-update out], :or {momentum nil, wd nil, rescale-grad nil, clip-gradient nil, lazy-update nil, out nil}, :as opts})
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)

### mp-sgd-update

(mp-sgd-update weight grad weight32 lr)(mp-sgd-update {:keys [weight grad weight32 lr wd rescale-grad clip-gradient lazy-update out], :or {wd nil, rescale-grad nil, clip-gradient nil, lazy-update nil, out nil}, :as opts})
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)

### multi-all-finite

(multi-all-finite {:keys [data num-arrays init-output out], :or {num-arrays nil, init-output nil, out nil}, :as opts})
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)

### multi-lars

(multi-lars lrs weights-sum-sq grads-sum-sq wds eta eps)(multi-lars {:keys [lrs weights-sum-sq grads-sum-sq wds eta eps rescale-grad out], :or {rescale-grad nil, out nil}, :as opts})
Compute the LARS coefficients of multiple weights and grads from their sums of square"

Defined in src/operator/contrib/multi_lars.cc:L37

lrs: Learning rates to scale by LARS coefficient
weights-sum-sq: sum of square of weights arrays
grads-sum-sq: sum of square of gradients arrays
wds: weight decays
eta: LARS eta
eps: LARS eps
rescale-grad: Gradient rescaling factor (optional)
out: Output array. (optional)

### multi-mp-sgd-mom-update

(multi-mp-sgd-mom-update data lrs wds)(multi-mp-sgd-mom-update {:keys [data lrs wds momentum rescale-grad clip-gradient num-weights out], :or {momentum nil, rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer.

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

.. math::

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

It updates the weights using::

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L472

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)

### multi-mp-sgd-update

(multi-mp-sgd-update data lrs wds)(multi-mp-sgd-update {:keys [data lrs wds rescale-grad clip-gradient num-weights out], :or {rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

It updates the weights using::

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/optimizer_op.cc:L417

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)

### multi-sgd-mom-update

(multi-sgd-mom-update data lrs wds)(multi-sgd-mom-update {:keys [data lrs wds momentum rescale-grad clip-gradient num-weights out], :or {momentum nil, rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
Momentum update function for Stochastic Gradient Descent (SGD) optimizer.

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

.. math::

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

It updates the weights using::

v = momentum * v - learning_rate * gradient
weight += v

Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L374

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)

### multi-sgd-update

(multi-sgd-update data lrs wds)(multi-sgd-update {:keys [data lrs wds rescale-grad clip-gradient num-weights out], :or {rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
Update function for Stochastic Gradient Descent (SDG) optimizer.

It updates the weights using::

weight = weight - learning_rate * (gradient + wd * weight)

Defined in src/operator/optimizer_op.cc:L329

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)

### multi-sum-sq

(multi-sum-sq data num-arrays)(multi-sum-sq {:keys [data num-arrays out], :or {out nil}, :as opts})
Compute the sums of squares of multiple arrays

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

data: Arrays
num-arrays: number of input arrays.
out: Output array. (optional)

### nag-mom-update

(nag-mom-update weight grad mom lr)(nag-mom-update {:keys [weight grad mom lr momentum wd rescale-grad clip-gradient out], :or {momentum nil, wd nil, rescale-grad nil, clip-gradient nil, out nil}, :as opts})
Update function for Nesterov Accelerated Gradient( NAG) optimizer.
It updates the weights using the following formula,

.. math::
v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\
W_t = W_{t-1} - v_t

Where
:math:\eta is the learning rate of the optimizer
:math:\gamma is the decay rate of the momentum estimate
:math:\v_t is the update vector at time step t
:math:\W_t is the weight vector at time step t

Defined in src/operator/optimizer_op.cc:L726

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)

### nanprod

(nanprod {:keys [data axis keepdims exclude out], :or {axis nil, keepdims nil, exclude nil, out nil}, :as opts})
Computes the product of array elements over given axes treating Not a Numbers (NaN) as one.

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)

### nansum

(nansum {:keys [data axis keepdims exclude out], :or {axis nil, keepdims nil, exclude nil, out nil}, :as opts})
Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero.

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)

### negative

(negative {:keys [data out], :or {out nil}, :as opts})
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)

### norm

(norm {:keys [data ord axis out-dtype keepdims out], :or {ord nil, axis nil, out-dtype nil, keepdims nil, out nil}, :as opts})
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]

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)

### one-hot

(one-hot indices depth)(one-hot {:keys [indices depth on-value off-value dtype out], :or {on-value nil, off-value nil, dtype nil, out nil}, :as opts})
Returns a one-hot array.

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

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

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

Examples::

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

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

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

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

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

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

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)

### ones-like

(ones-like {:keys [data out], :or {out nil}, :as opts})
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)

(pad data mode pad-width)(pad {:keys [data mode pad-width constant-value out], :or {constant-value nil, out nil}, :as opts})
Pads an input array with a constant or edge values of the array.

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

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

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

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

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

Example::

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

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

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

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

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

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

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

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

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

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

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

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

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)

### pick

(pick data index)(pick {:keys [data index axis keepdims mode out], :or {axis nil, keepdims nil, mode nil, out nil}, :as opts})
Picks elements from an input array according to the input indices along the given axis.

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

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

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

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

Examples::

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

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

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

// picks elements with specified indices along axis 1 using 'wrap' mode
// to place indicies that would normally be out of bounds
pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1.,  4.,  5.]

y = [[ 1.],
[ 0.],
[ 2.]]

// picks elements with specified indices along axis 1 and dims are maintained
pick(x, y, 1, keepdims=True) = [[ 2.],
[ 3.],
[ 6.]]

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)

### pooling

(pooling {:keys [data kernel pool-type global-pool cudnn-off pooling-convention stride pad p-value count-include-pad layout out], :or {cudnn-off nil, stride nil, layout nil, p-value nil, pooling-convention nil, count-include-pad nil, pool-type nil, out nil, pad nil, global-pool nil, kernel nil}, :as opts})
Performs pooling on the input.

The shapes for 1-D pooling are

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

The shapes for 2-D pooling are

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

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

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

- **valid** (default)::

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

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

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

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

Three pooling options are supported by pool_type:

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

For 3-D pooling, an additional *depth* dimension is added before
*height*. Namely the input data and output will have shape *(batch_size, channel, depth,
height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout).

Notes on Lp pooling:

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

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

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

Defined in src/operator/nn/pooling.cc:L414

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)

### pooling-v1

(pooling-v1 {:keys [data kernel pool-type global-pool pooling-convention stride pad out], :or {kernel nil, pool-type nil, global-pool nil, pooling-convention nil, stride nil, pad nil, out nil}, :as opts})
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)

(preloaded-multi-mp-sgd-mom-update {:keys [data momentum rescale-grad clip-gradient num-weights out], :or {momentum nil, rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
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.

data: Weights, gradients, momentums, learning rates and weight decays
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)

(preloaded-multi-mp-sgd-update {:keys [data rescale-grad clip-gradient num-weights out], :or {rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.

It updates the weights using::

weight = weight - learning_rate * (gradient + wd * weight)

data: Weights, gradients, learning rates and weight decays
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)

(preloaded-multi-sgd-mom-update {:keys [data momentum rescale-grad clip-gradient num-weights out], :or {momentum nil, rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
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.

data: Weights, gradients, momentum, learning rates and weight decays
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)

(preloaded-multi-sgd-update {:keys [data rescale-grad clip-gradient num-weights out], :or {rescale-grad nil, clip-gradient nil, num-weights nil, out nil}, :as opts})
Update function for Stochastic Gradient Descent (SDG) optimizer.

It updates the weights using::

weight = weight - learning_rate * (gradient + wd * weight)

data: Weights, gradients, learning rates and weight decays
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)

### prod

(prod {:keys [data axis keepdims exclude out], :or {axis nil, keepdims nil, exclude nil, out nil}, :as opts})
Computes the product of array elements over given axes.

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)

(radians {:keys [data out], :or {out nil}, :as opts})
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:L351

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

### rcbrt

(rcbrt {:keys [data out], :or {out nil}, :as opts})
Returns element-wise inverse cube-root value of the input.

.. math::
rcbrt(x) = 1/\sqrt[3]{x}

Example::

rcbrt([1,8,-125]) = [1.0, 0.5, -0.2]

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L323

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

### reciprocal

(reciprocal {:keys [data out], :or {out nil}, :as opts})
Returns the reciprocal of the argument, element-wise.

Calculates 1/x.

Example::

reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L43

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

### relu

(relu {:keys [data out], :or {out nil}, :as opts})
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)

### repeat

(repeat data repeats)(repeat {:keys [data repeats axis out], :or {axis nil, out nil}, :as opts})
Repeats elements of an array.
By default, repeat flattens the input array into 1-D and then repeats the
elements::
x = [[ 1, 2],
[ 3, 4]]
repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]
The parameter axis specifies the axis along which to perform repeat::
repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.]]
repeat(x, repeats=2, axis=0) = [[ 1.,  2.],
[ 1.,  2.],
[ 3.,  4.],
[ 3.,  4.]]
repeat(x, repeats=2, axis=-1) = [[ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.]]

Defined in src/operator/tensor/matrix_op.cc:L744

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)

### reset-arrays

(reset-arrays data num-arrays)(reset-arrays {:keys [data num-arrays out], :or {out nil}, :as opts})
Set to zero multiple arrays

Defined in src/operator/contrib/reset_arrays.cc:L36

data: Arrays
num-arrays: number of input arrays.
out: Output array. (optional)

### reshape

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

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

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-like

(reshape-like lhs rhs)(reshape-like {:keys [lhs rhs lhs-begin lhs-end rhs-begin rhs-end out], :or {lhs-begin nil, lhs-end nil, rhs-begin nil, rhs-end nil, out nil}, :as opts})
Reshape some or all dimensions of lhs to have the same shape as some or all dimensions of rhs.

Returns a **view** of the lhs array with a new shape without altering any data.

Example::

x = [1, 2, 3, 4, 5, 6]
y = [[0, -4], [3, 2], [2, 2]]
reshape_like(x, y) = [[1, 2], [3, 4], [5, 6]]

More precise control over how dimensions are inherited is achieved by specifying \
slices over the lhs and rhs array dimensions. Only the sliced lhs dimensions \
are reshaped to the rhs sliced dimensions, with the non-sliced lhs dimensions staying the same.

Examples::

- lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7)
- lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15)

Negative indices are supported, and None can be used for either lhs_end or rhs_end to indicate the end of the range.

Example::

- lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3)

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L511

lhs: First input.
rhs: Second input.
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)

### reverse

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

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

data: Input data array
axis: The axis which to reverse elements.
out: Output array. (optional)

### rint

(rint {:keys [data out], :or {out nil}, :as opts})
Returns element-wise rounded value to the nearest integer of the input.

.. note::
- For input n.5 rint returns n while round returns n+1.
- For input -n.5 both rint and round returns -n-1.

Example::

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

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

- rint(default) = default
- rint(row_sparse) = row_sparse
- rint(csr) = csr

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

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

### rmsprop-update

(rmsprop-update weight grad n lr)(rmsprop-update {:keys [weight grad n lr gamma1 epsilon wd rescale-grad clip-gradient clip-weights out], :or {gamma1 nil, epsilon nil, wd nil, rescale-grad nil, clip-gradient nil, clip-weights nil, out nil}, :as opts})
Update function for RMSProp optimizer.

RMSprop is a variant of stochastic gradient descent where the gradients are
divided by a cache which grows with the sum of squares of recent gradients?

RMSProp is similar to AdaGrad, a popular variant of SGD which adaptively
tunes the learning rate of each parameter. AdaGrad lowers the learning rate for
each parameter monotonically over the course of training.
While this is analytically motivated for convex optimizations, it may not be ideal
for non-convex problems. RMSProp deals with this heuristically by allowing the
learning rates to rebound as the denominator decays over time.

Define the Root Mean Square (RMS) error criterion of the gradient as
:math:RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}, where :math:g represents
gradient and :math:E[g^2]_t is the decaying average over past squared gradient.

The :math:E[g^2]_t is given by:

.. math::
E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2

The update step is

.. math::
\theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t

The RMSProp code follows the version in
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf
Tieleman & Hinton, 2012.

Hinton suggests the momentum term :math:\gamma to be 0.9 and the learning rate
:math:\eta to be 0.001.

Defined in src/operator/optimizer_op.cc:L797

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)

### rmspropalex-update

(rmspropalex-update weight grad n g delta lr)(rmspropalex-update {:keys [weight grad n g delta lr gamma1 gamma2 epsilon wd rescale-grad clip-gradient clip-weights out], :or {gamma1 nil, gamma2 nil, epsilon nil, wd nil, rescale-grad nil, clip-gradient nil, clip-weights nil, out nil}, :as opts})
Update function for RMSPropAlex optimizer.

RMSPropAlex is non-centered version of RMSProp.

Define :math:E[g^2]_t is the decaying average over past squared gradient and
:math:E[g]_t is the decaying average over past gradient.

.. math::
E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\
E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\
\Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\

The update step is

.. math::
\theta_{t+1} = \theta_t + \Delta_t

The RMSPropAlex code follows the version in
http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.

Graves suggests the momentum term :math:\gamma_1 to be 0.95, :math:\gamma_2
to be 0.9 and the learning rate :math:\eta to be 0.0001.

Defined in src/operator/optimizer_op.cc:L836

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)

### rnn

(rnn data parameters state state-cell sequence-length state-size num-layers mode)(rnn {:keys [data parameters state state-cell sequence-length state-size num-layers bidirectional mode p state-outputs projection-size lstm-state-clip-min lstm-state-clip-max lstm-state-clip-nan use-sequence-length out], :or {projection-size nil, p nil, lstm-state-clip-min nil, state-outputs nil, lstm-state-clip-max nil, use-sequence-length nil, lstm-state-clip-nan nil, out nil, bidirectional nil}, :as opts})
Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are
implemented, with both multi-layer and bidirectional support.

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

**Vanilla RNN**

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

With ReLU activation function:

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

With Tanh activtion function:

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

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

**LSTM**

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

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

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

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

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

**GRU**

Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078

The definition of GRU here is slightly different from paper but compatible with CUDNN.

.. math::
\begin{array}{ll}
r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\
\end{array}

Defined in src/operator/rnn.cc:L368

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)

### roi-pooling

(roi-pooling data rois pooled-size spatial-scale)(roi-pooling {:keys [data rois pooled-size spatial-scale out], :or {out nil}, :as opts})
Performs region of interest(ROI) pooling on the input array.

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

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

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

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

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

Example::

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

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

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

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

Defined in src/operator/roi_pooling.cc:L225

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)

### round

(round {:keys [data out], :or {out nil}, :as opts})
Returns element-wise rounded value to the nearest integer of the input.

Example::

round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]

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

- round(default) = default
- round(row_sparse) = row_sparse
- round(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L777

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

### rsqrt

(rsqrt {:keys [data out], :or {out nil}, :as opts})
Returns element-wise inverse square-root value of the input.

.. math::
rsqrt(x) = 1/\sqrt{x}

Example::

rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]

The storage type of rsqrt output is always dense

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L221

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

### scatter-nd

(scatter-nd data indices shape)(scatter-nd {:keys [data indices shape out], :or {out nil}, :as opts})
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)

### sequence-last

(sequence-last data sequence-length)(sequence-last {:keys [data sequence-length use-sequence-length axis out], :or {use-sequence-length nil, axis nil, out nil}, :as opts})
Takes the last element of a sequence.

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

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

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

Example::

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

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

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

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

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

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

Defined in src/operator/sequence_last.cc:L106

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)

(sequence-mask data sequence-length)(sequence-mask {:keys [data sequence-length use-sequence-length value axis out], :or {use-sequence-length nil, value nil, axis nil, out nil}, :as opts})
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.]]]

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)

### sequence-reverse

(sequence-reverse data sequence-length)(sequence-reverse {:keys [data sequence-length use-sequence-length axis out], :or {use-sequence-length nil, axis nil, out nil}, :as opts})
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)

### sgd-mom-update

(sgd-mom-update weight grad mom lr)(sgd-mom-update {:keys [weight grad mom lr momentum wd rescale-grad clip-gradient lazy-update out], :or {momentum nil, wd nil, rescale-grad nil, clip-gradient nil, lazy-update nil, out nil}, :as opts})
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:L565

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)

### sgd-update

(sgd-update weight grad lr)(sgd-update {:keys [weight grad lr wd rescale-grad clip-gradient lazy-update out], :or {wd nil, rescale-grad nil, clip-gradient nil, lazy-update nil, out nil}, :as opts})
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:L524

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)

### shape-array

(shape-array {:keys [data out], :or {out nil}, :as opts})
Returns a 1D int64 array containing the shape of data.

Example::

shape_array([[1,2,3,4], [5,6,7,8]]) = [2,4]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L573

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

### sigmoid

(sigmoid {:keys [data out], :or {out nil}, :as opts})
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)

### sign

(sign {:keys [data out], :or {out nil}, :as opts})
Returns element-wise sign of the input.

Example::

sign([-2, 0, 3]) = [-1, 0, 1]

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

- sign(default) = default
- sign(row_sparse) = row_sparse
- sign(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L758

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

### signsgd-update

(signsgd-update weight grad lr)(signsgd-update {:keys [weight grad lr wd rescale-grad clip-gradient out], :or {wd nil, rescale-grad nil, clip-gradient nil, out nil}, :as opts})
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:L63

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)

### signum-update

(signum-update weight grad mom lr)(signum-update {:keys [weight grad mom lr momentum wd rescale-grad clip-gradient wd-lh out], :or {momentum nil, wd nil, rescale-grad nil, clip-gradient nil, wd-lh nil, out nil}, :as opts})
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:L92

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)

### sin

(sin {:keys [data out], :or {out nil}, :as opts})
Computes the element-wise sine of the input array.

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

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

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

- sin(default) = default
- sin(row_sparse) = row_sparse
- sin(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L47

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

### sinh

(sinh {:keys [data out], :or {out nil}, :as opts})
Returns the hyperbolic sine of the input array, computed element-wise.

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

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

- sinh(default) = default
- sinh(row_sparse) = row_sparse
- sinh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L371

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

### size-array

(size-array {:keys [data out], :or {out nil}, :as opts})
Returns a 1D int64 array containing the size of data.

Example::

size_array([[1,2,3,4], [5,6,7,8]]) = [8]

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L624

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

### slice

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

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

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)

### slice-axis

(slice-axis data axis begin end)(slice-axis {:keys [data axis begin end out], :or {out nil}, :as opts})
Slices along a given axis.
Returns an array slice along a given axis starting from the begin index
to the end index.
Examples::
x = [[  1.,   2.,   3.,   4.],
[  5.,   6.,   7.,   8.],
[  9.,  10.,  11.,  12.]]
slice_axis(x, axis=0, begin=1, end=3) = [[  5.,   6.,   7.,   8.],
[  9.,  10.,  11.,  12.]]
slice_axis(x, axis=1, begin=0, end=2) = [[  1.,   2.],
[  5.,   6.],
[  9.,  10.]]
slice_axis(x, axis=1, begin=-3, end=-1) = [[  2.,   3.],
[  6.,   7.],
[ 10.,  11.]]

Defined in src/operator/tensor/matrix_op.cc:L571

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)

### slice-channel

(slice-channel data num-outputs)(slice-channel {:keys [data num-outputs axis squeeze-axis out], :or {axis nil, squeeze-axis nil, out nil}, :as opts})
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)

### slice-like

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

Defined in src/operator/tensor/matrix_op.cc:L625

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)

### smooth-l1

(smooth-l1 data scalar)(smooth-l1 {:keys [data scalar out], :or {out nil}, :as opts})
Calculate Smooth L1 Loss(lhs, scalar) by summing

.. math::

f(x) =
\begin{cases}
(\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\
|x|-0.5/\sigma^2,& \text{otherwise}
\end{cases}

where :math:x is an element of the tensor *lhs* and :math:\sigma is the scalar.

Example::

smooth_l1([1, 2, 3, 4]) = [0.5, 1.5, 2.5, 3.5]
smooth_l1([1, 2, 3, 4], scalar=1) = [0.5, 1.5, 2.5, 3.5]

Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L109

data: source input
scalar: scalar input
out: Output array. (optional)

### softmax

(softmax data length)(softmax {:keys [data length axis temperature dtype use-length out], :or {axis nil, temperature nil, dtype nil, use-length nil, out nil}, :as opts})
Applies the softmax function.

The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.

.. math::
softmax(\mathbf{z/t})_j = \frac{e^{z_j/t}}{\sum_{k=1}^K e^{z_k/t}}

for :math:j = 1, ..., K

t is the temperature parameter in softmax function. By default, t equals 1.0

Example::

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

softmax(x,axis=0) = [[ 0.5  0.5  0.5]
[ 0.5  0.5  0.5]]

softmax(x,axis=1) = [[ 0.33333334,  0.33333334,  0.33333334],
[ 0.33333334,  0.33333334,  0.33333334]]

Defined in src/operator/nn/softmax.cc:L134

data: The input array.
length: The length 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)
use-length: Whether to use the length input as a mask over the data input. (optional)
out: Output array. (optional)

### softmax-activation

(softmax-activation {:keys [data mode out], :or {mode nil, out nil}, :as opts})
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)

### softmax-cross-entropy

(softmax-cross-entropy data label)(softmax-cross-entropy {:keys [data label out], :or {out nil}, :as opts})
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)

### softmax-output

(softmax-output data label)(softmax-output {:keys [data label grad-scale ignore-label multi-output use-ignore preserve-shape normalization out-grad smooth-alpha out], :or {use-ignore nil, normalization nil, smooth-alpha nil, grad-scale nil, ignore-label nil, preserve-shape nil, multi-output nil, out-grad nil, out nil}, :as opts})
Computes the gradient of cross entropy loss with respect to softmax output.

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

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

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

- Softmax Function:

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

- Cross Entropy Function:

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

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

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

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

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

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

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

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

Example::

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

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

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

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

Defined in src/operator/softmax_output.cc:L231

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)

### softmin

(softmin {:keys [data axis temperature dtype use-length out], :or {axis nil, temperature nil, dtype nil, use-length nil, out nil}, :as opts})
Applies the softmin function.

The resulting array contains elements in the range (0,1) and the elements along the given axis sum
up to 1.

.. math::
softmin(\mathbf{z/t})_j = \frac{e^{-z_j/t}}{\sum_{k=1}^K e^{-z_k/t}}

for :math:j = 1, ..., K

t is the temperature parameter in softmax function. By default, t equals 1.0

Example::

x = [[ 1.  2.  3.]
[ 3.  2.  1.]]

softmin(x,axis=0) = [[ 0.88079703,  0.5,  0.11920292],
[ 0.11920292,  0.5,  0.88079703]]

softmin(x,axis=1) = [[ 0.66524094,  0.24472848,  0.09003057],
[ 0.09003057,  0.24472848,  0.66524094]]

Defined in src/operator/nn/softmin.cc:L57

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)
use-length: Whether to use the length input as a mask over the data input. (optional)
out: Output array. (optional)

### softsign

(softsign {:keys [data out], :or {out nil}, :as opts})
Computes softsign of x element-wise.

.. math::
y = x / (1 + abs(x))

The storage type of softsign output is always dense

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L191

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

### sort

(sort {:keys [data axis is-ascend out], :or {axis nil, is-ascend nil, out nil}, :as opts})
Returns a sorted copy of an input array along the given axis.

Examples::

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

// sorts along the last axis
sort(x) = [[ 1.,  4.],
[ 1.,  3.]]

// flattens and then sorts
sort(x, axis=None) = [ 1.,  1.,  3.,  4.]

// sorts along the first axis
sort(x, axis=0) = [[ 1.,  1.],
[ 3.,  4.]]

// in a descend order
sort(x, is_ascend=0) = [[ 4.,  1.],
[ 3.,  1.]]

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

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)

### space-to-depth

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

Defined in src/operator/tensor/matrix_op.cc:L1019

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

### spatial-transformer

(spatial-transformer data loc transform-type sampler-type)(spatial-transformer {:keys [data loc target-shape transform-type sampler-type cudnn-off out], :or {target-shape nil, cudnn-off nil, out nil}, :as opts})
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)

### sqrt

(sqrt {:keys [data out], :or {out nil}, :as opts})
Returns element-wise square-root value of the input.

.. math::
\textrm{sqrt}(x) = \sqrt{x}

Example::

sqrt([4, 9, 16]) = [2, 3, 4]

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

- sqrt(default) = default
- sqrt(row_sparse) = row_sparse
- sqrt(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L170

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

### square

(square {:keys [data out], :or {out nil}, :as opts})
Returns element-wise squared value of the input.

.. math::
square(x) = x^2

Example::

square([2, 3, 4]) = [4, 9, 16]

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

- square(default) = default
- square(row_sparse) = row_sparse
- square(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L119

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

### squeeze

(squeeze {:keys [data axis out], :or {axis nil, out nil}, :as opts})
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)

### stack

(stack data num-args)(stack {:keys [data axis num-args out], :or {axis nil, out nil}, :as opts})
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)

### sum

(sum {:keys [data axis keepdims exclude out], :or {axis nil, keepdims nil, exclude nil, out nil}, :as opts})
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.]

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)

### svm-output

(svm-output data label)(svm-output {:keys [data label margin regularization-coefficient use-linear out], :or {margin nil, regularization-coefficient nil, use-linear nil, out nil}, :as opts})
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)

### swap-axis

(swap-axis {:keys [data dim1 dim2 out], :or {dim1 nil, dim2 nil, out nil}, :as opts})
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)

### take

(take a indices)(take {:keys [a indices axis mode out], :or {axis nil, mode nil, out nil}, :as opts})
Takes elements from an input array along the given axis.

This function slices the input array along a particular axis with the provided indices.

Given data tensor of rank r >= 1, and indices tensor of rank q, gather entries of the axis
dimension of data (by default outer-most one as axis=0) indexed by indices, and concatenates them
in an output tensor of rank q + (r - 1).

Examples::

x = [4.  5.  6.]

// Trivial case, take the second element along the first axis.

take(x, [1]) = [ 5. ]

// The other trivial case, axis=-1, take the third element along the first axis

take(x, [3], axis=-1, mode='clip') = [ 6. ]

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

// In this case we will get rows 0 and 1, then 1 and 2. Along axis 0

take(x, [[0,1],[1,2]]) = [[[ 1.,  2.],
[ 3.,  4.]],

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

// In this case we will get rows 0 and 1, then 1 and 2 (calculated by wrapping around).
// Along axis 1

take(x, [[0, 3], [-1, -2]], axis=1, mode='wrap') = [[[ 1.  2.]
[ 2.  1.]]

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

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

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

- take(default, default) = default
- take(csr, default, axis=0) = csr

Defined in src/operator/tensor/indexing_op.cc:L777

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 when index out of range. (optional)
out: Output array. (optional)

### tan

(tan {:keys [data out], :or {out nil}, :as opts})
Computes the element-wise tangent of the input array.

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

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

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

- tan(default) = default
- tan(row_sparse) = row_sparse
- tan(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L140

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

### tanh

(tanh {:keys [data out], :or {out nil}, :as opts})
Returns the hyperbolic tangent of the input array, computed element-wise.

.. math::
tanh(x) = sinh(x) / cosh(x)

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

- tanh(default) = default
- tanh(row_sparse) = row_sparse
- tanh(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L451

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

### tile

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

Defined in src/operator/tensor/matrix_op.cc:L796

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)

### topk

(topk {:keys [data axis k ret-typ is-ascend dtype out], :or {axis nil, k nil, ret-typ nil, is-ascend nil, dtype nil, out nil}, :as opts})
Returns the indices of the top *k* elements in an input array along the given
axis (by default).
If ret_type is set to 'value' returns the value of top *k* elements (instead of indices).
In case of ret_type = 'both', both value and index would be returned.
The returned elements will be sorted.

Examples::

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

// returns an index of the largest element on last axis
topk(x) = [[ 2.],
[ 1.]]

// returns the value of top-2 largest elements on last axis
topk(x, ret_typ='value', k=2) = [[ 0.4,  0.3],
[ 0.3,  0.2]]

// returns the value of top-2 smallest elements on last axis
topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 ,  0.3],
[ 0.1 ,  0.2]]

// returns the value of top-2 largest elements on axis 0
topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3,  0.3,  0.4],
[ 0.1,  0.2,  0.2]]

// flattens and then returns list of both values and indices
topk(x, ret_typ='both', k=2) = [[[ 0.4,  0.3], [ 0.3,  0.2]] ,  [[ 2.,  0.], [ 1.,  2.]]]

Defined in src/operator/tensor/ordering_op.cc:L68

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)

### transpose

(transpose {:keys [data axes out], :or {axes nil, out nil}, :as opts})
Permutes the dimensions of an array.
Examples::
x = [[ 1, 2],
[ 3, 4]]
transpose(x) = [[ 1.,  3.],
[ 2.,  4.]]
x = [[[ 1.,  2.],
[ 3.,  4.]],
[[ 5.,  6.],
[ 7.,  8.]]]
transpose(x) = [[[ 1.,  5.],
[ 3.,  7.]],
[[ 2.,  6.],
[ 4.,  8.]]]
transpose(x, axes=(1,0,2)) = [[[ 1.,  2.],
[ 5.,  6.]],
[[ 3.,  4.],
[ 7.,  8.]]]

Defined in src/operator/tensor/matrix_op.cc:L328

data: Source input
axes: Target axis order. By default the axes will be inverted. (optional)
out: Output array. (optional)

### trunc

(trunc {:keys [data out], :or {out nil}, :as opts})
Return the element-wise truncated value of the input.

The truncated value of the scalar x is the nearest integer i which is closer to
zero than x is. In short, the fractional part of the signed number x is discarded.

Example::

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

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

- trunc(default) = default
- trunc(row_sparse) = row_sparse
- trunc(csr) = csr

Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L856

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

### up-sampling

(up-sampling data scale sample-type num-args)(up-sampling {:keys [data scale num-filter sample-type multi-input-mode num-args workspace out], :or {num-filter nil, multi-input-mode nil, workspace nil, out nil}, :as opts})
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)

### where

(where condition x y)(where {:keys [condition x y out], :or {out nil}, :as opts})
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)

### zeros-like

(zeros-like {:keys [data out], :or {out nil}, :as opts})
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)