# Linear Algebra Symbol API¶

## Overview¶

This document lists the linear algebra routines of the symbolic expression package:

 mxnet.symbol.linalg Linear Algebra Symbol API of MXNet.

The Linear Algebra Symbol API, defined in the symbol.linalg package, provides symbolic expressions for linear algebra routines.

In the rest of this document, we list routines provided by the symbol.linalg package.

## Linear Algebra¶

 gemm Performs general matrix multiplication and accumulation. gemm2 Performs general matrix multiplication. potrf Performs Cholesky factorization of a symmetric positive-definite matrix. potri Performs matrix inversion from a Cholesky factorization. trmm Performs multiplication with a lower triangular matrix. trsm Solves matrix equation involving a lower triangular matrix. syrk Multiplication of matrix with its transpose. gelqf LQ factorization for general matrix. syevd Eigendecomposition for symmetric matrix. sumlogdiag Computes the sum of the logarithms of the diagonal elements of a square matrix. extractdiag Extracts the diagonal entries of a square matrix. makediag Constructs a square matrix with the input as diagonal. extracttrian Extracts a triangular sub-matrix from a square matrix. maketrian Constructs a square matrix with the input representing a specific triangular sub-matrix. inverse Compute the inverse of a matrix.

## API Reference¶

Linear Algebra Symbol API of MXNet.

mxnet.symbol.linalg.extractdiag(A=None, offset=_Null, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of square matrices offset (int, optional, default='0') – 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. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.extracttrian(A=None, offset=_Null, lower=_Null, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of square matrices offset (int, optional, default='0') – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal. lower (boolean, optional, default=1) – Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0 name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.gelqf(A=None, name=None, attr=None, out=None, **kwargs)

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 * QT

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

Parameters: A (Symbol) – Tensor of input matrices to be factorized name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.gemm(A=None, B=None, C=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, beta=_Null, axis=_Null, name=None, attr=None, out=None, **kwargs)

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

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

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

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

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

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

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


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

Note

The operator supports float32 and float64 data types only.

Examples:

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

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

Parameters: A (Symbol) – Tensor of input matrices B (Symbol) – Tensor of input matrices C (Symbol) – Tensor of input matrices transpose_a (boolean, optional, default=0) – Multiply with transposed of first input (A). transpose_b (boolean, optional, default=0) – Multiply with transposed of second input (B). alpha (double, optional, default=1) – Scalar factor multiplied with A*B. beta (double, optional, default=1) – Scalar factor multiplied with C. axis (int, optional, default='-2') – Axis corresponding to the matrix rows. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.gemm2(A=None, B=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, axis=_Null, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of input matrices B (Symbol) – Tensor of input matrices transpose_a (boolean, optional, default=0) – Multiply with transposed of first input (A). transpose_b (boolean, optional, default=0) – Multiply with transposed of second input (B). alpha (double, optional, default=1) – Scalar factor multiplied with A*B. axis (int, optional, default='-2') – Axis corresponding to the matrix row indices. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.inverse(A=None, name=None, attr=None, out=None, **kwargs)

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-1

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

Note

The operator supports float32 and float64 data types only.

Examples:

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

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


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

Parameters: A (Symbol) – Tensor of square matrix name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.makediag(A=None, offset=_Null, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of diagonal entries offset (int, optional, default='0') – 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. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.maketrian(A=None, offset=_Null, lower=_Null, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of triangular matrices stored as vectors offset (int, optional, default='0') – Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal. lower (boolean, optional, default=1) – Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0 name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.potrf(A=None, name=None, attr=None, out=None, **kwargs)

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 * BT if lower = true A = BT * 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

Parameters: A (Symbol) – Tensor of input matrices to be decomposed name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.potri(A=None, name=None, attr=None, out=None, **kwargs)

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-T * A-1 if lower = true out = A-1 * A-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-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

Parameters: A (Symbol) – Tensor of lower triangular matrices name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.sumlogdiag(A=None, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of square matrices name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.syevd(A=None, name=None, attr=None, out=None, **kwargs)

Eigendecomposition for symmetric matrix. Input is a tensor A of dimension n >= 2.

If n=2, A must be symmetric, of shape (x, x). We compute the eigendecomposition, resulting in the orthonormal matrix U of eigenvectors, shape (x, x), and the vector L of eigenvalues, shape (x,), so that:

U * A = diag(L) * U

Here:

U * UT = UT * U = I

where I is the identity matrix. Also, L(0) <= L(1) <= L(2) <= ... (ascending order).

If n>2, syevd is performed separately on the trailing two dimensions of A (batch mode). In this case, U has n dimensions like A, and L has n-1 dimensions.

Note

The operator supports float32 and float64 data types only.

Note

Derivatives for this operator are defined only if A is such that all its eigenvalues are distinct, and the eigengaps are not too small. If you need gradients, do not apply this operator to matrices with multiple eigenvalues.

Examples:

// Single symmetric eigendecomposition
A = [[1., 2.], [2., 4.]]
U, L = syevd(A)
U = [[0.89442719, -0.4472136],
[0.4472136, 0.89442719]]
L = [0., 5.]

// Batch symmetric eigendecomposition
A = [[[1., 2.], [2., 4.]],
[[1., 2.], [2., 5.]]]
U, L = syevd(A)
U = [[[0.89442719, -0.4472136],
[0.4472136, 0.89442719]],
[[0.92387953, -0.38268343],
[0.38268343, 0.92387953]]]
L = [[0., 5.],
[0.17157288, 5.82842712]]


Defined in src/operator/tensor/la_op.cc:L867

Parameters: A (Symbol) – Tensor of input matrices to be factorized name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.syrk(A=None, transpose=_Null, alpha=_Null, name=None, attr=None, out=None, **kwargs)

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 * AT

if transpose=False, or

out = alpha * AT * 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

Parameters: A (Symbol) – Tensor of input matrices transpose (boolean, optional, default=0) – Use transpose of input matrix. alpha (double, optional, default=1) – Scalar factor to be applied to the result. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.trmm(A=None, B=None, transpose=_Null, rightside=_Null, lower=_Null, alpha=_Null, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of lower triangular matrices B (Symbol) – Tensor of matrices transpose (boolean, optional, default=0) – Use transposed of the triangular matrix rightside (boolean, optional, default=0) – Multiply triangular matrix from the right to non-triangular one. lower (boolean, optional, default=1) – True if the triangular matrix is lower triangular, false if it is upper triangular. alpha (double, optional, default=1) – Scalar factor to be applied to the result. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg.trsm(A=None, B=None, transpose=_Null, rightside=_Null, lower=_Null, alpha=_Null, name=None, attr=None, out=None, **kwargs)

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

Parameters: A (Symbol) – Tensor of lower triangular matrices B (Symbol) – Tensor of matrices transpose (boolean, optional, default=0) – Use transposed of the triangular matrix rightside (boolean, optional, default=0) – Multiply triangular matrix from the right to non-triangular one. lower (boolean, optional, default=1) – True if the triangular matrix is lower triangular, false if it is upper triangular. alpha (double, optional, default=1) – Scalar factor to be applied to the result. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol