Linear Algebra NDArray API¶
Overview¶
This document lists the linear algebra routines of the ndimensional array package:
mxnet.ndarray.linalg 
Linear Algebra NDArray API of MXNet. 
The Linear Algebra NDArray
API, defined in the ndarray.linalg
package, provides
imperative linear algebra tensor operations on CPU/GPU.
In the rest of this document, we list routines provided by the ndarray.linalg
package.
Linear Algebra¶
gemm 
Performs general matrix multiplication and accumulation. 
gemm2 
Performs general matrix multiplication. 
potrf 
Performs Cholesky factorization of a symmetric positivedefinite 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 submatrix from a square matrix. 
maketrian 
Constructs a square matrix with the input representing a specific triangular submatrix. 
API Reference¶
Linear Algebra NDArray API of MXNet.

mxnet.ndarray.linalg.
extractdiag
(A=None, offset=_Null, out=None, name=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 1dimensional tensor.
If n>2, then A represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an n1dimensional 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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
extracttrian
(A=None, offset=_Null, lower=_Null, out=None, name=None, **kwargs)¶ Extracts a triangular submatrix 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 submatrix is extracted as a 1dimensional tensor.
If n>2, then A represents a batch of square matrices on the trailing two dimensions. The extracted triangular submatrices are returned as an n1dimensional 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 kth diagonal above the main diagonal is extracted.
 When offset = k < 0 the lower triangle with respect to the kth 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 (NDArray) – 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
 out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
gelqf
(A=None, out=None, name=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 * QHere, L is lower triangular (upper triangle equal to zero) with nonzero diagonal, and Q is roworthonormal, meaning that
Q * Q^{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
Parameters: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
gemm
(A=None, B=None, C=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, beta=_Null, axis=_Null, out=None, name=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 n2 dimensions.
If n=2, the BLAS3 function gemm is performed:
out = alpha * op(A) * op(B) + beta * CHere, 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 nondefault 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 pseudofloat16 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 multiplyadd A = [[1.0, 1.0], [1.0, 1.0]] B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]] C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]] gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0) = [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]] // Batch matrix multiplyadd 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 (NDArray) – Tensor of input matrices
 B (NDArray) – Tensor of input matrices
 C (NDArray) – 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.
 out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
gemm2
(A=None, B=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, axis=_Null, out=None, name=None, **kwargs)¶ Performs general matrix multiplication. Input are tensors A, B, each of dimension n >= 2 and having the same shape on the leading n2 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 nondefault 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 pseudofloat16 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 (NDArray) – Tensor of input matrices
 B (NDArray) – 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.
 out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
inverse
(A=None, out=None, name=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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
makediag
(A=None, offset=_Null, out=None, name=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 2dimensional 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+1dimensional 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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
maketrian
(A=None, offset=_Null, lower=_Null, out=None, name=None, **kwargs)¶ Constructs a square matrix with the input representing a specific triangular submatrix. 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 offsettimes an additional diagonal with zero entries to the square matrix.
If n>1, then A represents a batch of triangular submatrices. The batch of corresponding square matrices is returned as an n+1dimensional 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 (NDArray) – 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
 out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
potrf
(A=None, out=None, name=None, **kwargs)¶ Performs Cholesky factorization of a symmetric positivedefinite 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^{T} if lower = true A = B^{T} * B if lower = falseIf 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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
potri
(A=None, out=None, name=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 = falseIn 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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
sumlogdiag
(A=None, out=None, name=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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
syevd
(A=None, out=None, name=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) * UHere:
U * U^{T} = U^{T} * U = Iwhere 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 n1 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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
syrk
(A=None, transpose=_Null, alpha=_Null, out=None, name=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 * A^{T}if transpose=False, or
out = alpha * A^{T} * Aif 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: Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
trmm
(A=None, B=None, transpose=_Null, rightside=_Null, lower=_Null, alpha=_Null, out=None, name=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 n2 dimensions.
If n=2, A must be triangular. The operator performs the BLAS3 function trmm:
out = alpha * op(A) * Bif 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 (NDArray) – Tensor of lower triangular matrices
 B (NDArray) – 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 nontriangular 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.
 out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays

mxnet.ndarray.linalg.
trsm
(A=None, B=None, transpose=_Null, rightside=_Null, lower=_Null, alpha=_Null, out=None, name=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 n2 dimensions.
If n=2, A must be triangular. The operator performs the BLAS3 function trsm, solving for out in:
op(A) * out = alpha * Bif rightside=False, or
out * op(A) = alpha * Bif 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 (NDArray) – Tensor of lower triangular matrices
 B (NDArray) – 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 nontriangular 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.
 out (NDArray, optional) – The output NDArray to hold the result.
Returns: out – The output of this function.
Return type: NDArray or list of NDArrays