trsm (USM Version)

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

Syntax

event trsm(queue &exec_queue, side left_right, uplo upper_lower, transpose transa, 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 vector_class<event> &dependencies = {})

The USM version of trsm supports the following precisions and devices:

T

Devices Supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

std::complex<float>

Host, CPU, and GPU

std::complex<double>

Host, CPU, and GPU

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) = AT, or op(A) = AH,

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.

Input Parameters

exec_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 Data Types for more details.

uplo

Specifies whether the matrix A is upper or lower triangular. See Data Types for more details.

transa

Specifies op(A), the transposition operation applied to A. See Data Types for more details.

unit_diag

Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See Data Types 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. It must have size at least ldb*n if column major layout is used to store matrices or at least ldb*m if row major layout is used to store matrices. See Matrix and Vector Storage for more details.

ldb

Leading dimension of B. It must be positive and at least m if column major layout is used to store matrices or at least n if column major layout is used to store matrices.

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.