# trsm¶

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

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.

trsm supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## trsm (Buffer Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
void 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)
}

namespace oneapi::mkl::blas::row_major {
void 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 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 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 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 row major layout is used to store matrices.

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

namespace oneapi::mkl::blas::column_major {
sycl::event 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 std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event 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 std::vector<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 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 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 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 row 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.

Parent topic: BLAS Level 3 Routines