# 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.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::unimplemented

## 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.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::invalid_argument

oneapi::mkl::unsupported_device