trsm¶

Solves a triangular matrix equation (forward or backward solve).

trsm supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

Description

The trsm routines solve one of the following matrix equations:

op(A)*X = alpha*B,

or

X*op(A) = alpha*B,

where:

op(A) is one of op(A) = A, or op(A) = A^T, or op(A) = A^H,

alpha is a scalar,

A is a triangular matrix, and

B and X are m x n general matrices.

A is either m x m or n x n, depending on whether it multiplies X on the left or right. On return, the matrix B is overwritten by the solution matrix X.

trsm (Buffer Version)¶

Syntax

void onemkl::blas::trsm(sycl::queue &queue, onemkl::side left_right, onemkl::uplo upper_lower, onemkl::transpose transa, onemkl::diag unit_diag, std::int64_t m, std::int64_t n, T alpha, sycl::buffer<T, 1> &a, std::int64_t lda, sycl::buffer<T, 1> &b, std::int64_t ldb)¶

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether A multiplies X on the left (side::left) or on the right (side::right). See oneMKL defined datatypes for more details.
uplo: Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.
unit_diag: Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMKL defined datatypes for more details.
m: Specifies the number of rows of B. The value of m must be at least zero.
n: Specifies the number of columns of B. The value of n must be at least zero.
alpha: Scaling factor for the solution.
a: Buffer holding input matrix A. Must have size at least lda*m if left_right = side::left, or lda*n if left_right = side::right. See Matrix and Vector Storage for more details.
lda: Leading dimension of A. Must be at least m if left_right = side::left, and at least n if left_right = side::right. Must be positive.
b: Buffer holding input/output matrix B. Must have size at least ldb*n. See Matrix and Vector Storage for more details.
ldb: Leading dimension of B. Must be at least m and positive.

Output Parameters

b: Output buffer. Overwritten by the solution matrix X.

Notes

If alpha = 0, matrix B is set to zero, and A and B do not need to be initialized at entry.

trsm (USM Version)¶

Syntax

sycl::event onemkl::blas::trsm(sycl::queue &queue, onemkl::side left_right, onemkl::uplo upper_lower, onemkl::transpose transa, onemkl::diag unit_diag, std::int64_t m, std::int64_t n, T alpha, const T *a, std::int64_t lda, T *b, std::int64_t ldb, const sycl::vector_class<sycl::event> &dependencies = {})¶

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether A multiplies X on the left (side::left) or on the right (side::right). See oneMKL defined datatypes for more details.
uplo: Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.
transa: Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.
unit_diag: Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMKL defined datatypes for more details.
m: Specifies the number of rows of B. The value of m must be at least zero.
n: Specifies the number of columns of B. The value of n must be at least zero.
alpha: Scaling factor for the solution.
a: Pointer to input matrix A. Must have size at least lda*m if left_right = side::left, or lda*n if left_right = side::right. See Matrix and Vector Storage for more details.
lda: Leading dimension of A. Must be at least m if left_right = side::left, and at least n if left_right = side::right. Must be positive.
b: Pointer to input/output matrix B. Must have size at least ldb*n. See Matrix and Vector Storage for more details.
ldb: Leading dimension of B. Must be at least m and positive.
dependencies: List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters

b: Pointer to the output matrix. Overwritten by the solution matrix X.

Notes

If alpha = 0, matrix B is set to zero, and A and B do not need to be initialized at entry.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: BLAS Level 3 Routines