mxnet.ndarray.linalg.trsm¶

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 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 (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 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.
out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays