trtrs

Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides.

trtrs supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

Description

The routine solves for X the following systems of linear equations with a triangular matrix A, with multiple right-hand sides stored in B:

A*X = B

if transa =transpose::nontrans,

AT*X = B

if transa =transpose::trans,

AH*X = B

if transa =transpose::conjtrans (for complex matrices only).

trtrs (BUFFER Version)

Syntax

void onemkl::lapack::trtrs(cl::sycl::queue &queue, onemkl::uplo upper_lower, onemkl::transpose transa, onemkl::diag unit_diag, std::int64_t n, std::int64_t nrhs, cl::sycl::buffer<T, 1> &a, std::int64_t lda, cl::sycl::buffer<T, 1> &b, std::int64_t ldb, cl::sycl::buffer<T, 1> &scratchpad, std::int64_t scratchpad_size)

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Indicates whether A is upper or lower triangular:

If upper_lower = uplo::upper, then A is upper triangular.

If upper_lower = uplo::lower, then A is lower triangular.

transa

If transa = transpose::nontrans, then A*X = B is solved for X.

If transa = transpose::trans, then AT*X = B is solved for X.

If transa = transpose::conjtrans, then AH*X = B is solved for X.

unit_diag

If unit_diag = diag::nonunit, then A is not a unit triangular matrix.

If unit_diag = diag::unit, then A is unit triangular: diagonal elements of A are assumed to be 1 and not referenced in the array a.

n

The order of A; the number of rows in B; n≥ 0.

nrhs

The number of right-hand sides; nrhs≥ 0.

a

Buffer containing the matrix A. The second dimension of a must be at least max(1,n).

lda

The leading dimension of a; lda≥ max(1, n).

b

Buffer containing the matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b at least max(1,nrhs).

ldb

The leading dimension of b; ldb≥ max(1, n).

scratchpad_size

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by trtrs_scratchpad_size function.

Output Parameters

b

Overwritten by the solution matrix X.

scratchpad

Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

If info=-i, the i-th parameter had an illegal value.

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

trtrs (USM Version)

Syntax

cl::sycl::event onemkl::lapack::trtrs(cl::sycl::queue &queue, onemkl::uplo upper_lower, onemkl::transpose transa, onemkl::diag unit_diag, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, T *b, std::int64_t ldb, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<cl::sycl::event> &events = {})

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Indicates whether A is upper or lower triangular:

If upper_lower = uplo::upper, then A is upper triangular.

If upper_lower = uplo::lower, then A is lower triangular.

transa

If transa = transpose::nontrans, then A*X = B is solved for X.

If transa = transpose::trans, then AT*X = B is solved for X.

If transa = transpose::conjtrans, then AH*X = B is solved for X.

unit_diag

If unit_diag = diag::nonunit, then A is not a unit triangular matrix.

If unit_diag = diag::unit, then A is unit triangular: diagonal elements of A are assumed to be 1 and not referenced in the array a.

n

The order of A; the number of rows in B; n≥ 0.

nrhs

The number of right-hand sides; nrhs≥ 0.

a

Array containing the matrix A. The second dimension of a must be at least max(1,n).

lda

The leading dimension of a; lda≥ max(1, n).

b

Array containing the matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b at least max(1,nrhs).

ldb

The leading dimension of b; ldb≥ max(1, n).

scratchpad_size

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by trtrs_scratchpad_size function.

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

b

Overwritten by the solution matrix X.

scratchpad

Pointer toscratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

If info=-i, the i-th parameter had an illegal value.

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Linear Equation Routines