trsm

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 7/13/2023

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trsm

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

Description

The trsm routines solve triangular matrix equations where one of the matrices in the multiplication is triangular. The argument left_right determines if the triangular matrix, A, is on the left of the multiplication (left_right = side::left) or on the right (left_right = side::right). The operation is defined as:

If (left_right = side::left),

If (left_right = side::right),

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 either m x m or n x n triangular matrix
B and X are m x n general matrices

On return, matrix B is overwritten by 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,
              oneapi::mkl::side left_right,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::transpose transa,
              oneapi::mkl::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,
              compute_mode mode = compute_mode::unset)
}

namespace oneapi::mkl::blas::row_major {
    void trsm(sycl::queue &queue,
              oneapi::mkl::side left_right,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::transpose trans,
              oneapi::mkl::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,
              compute_mode mode = compute_mode::unset)
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether matrix A is on the left side or right side of the multiplication. See Data Types for more details.
upper_lower: Specifies whether matrix A is upper or lower triangular. See Data Types for more details.
trans: Specifies op(A), the transposition operation applied to matrix A. See Data Types for more details.
unit_diag: Specifies whether matrix A is unit triangular or not. See Data Types for more details.
m: Number of rows of matrix B. Must be at least zero.
n: Number of columns of matrix B. Must be at least zero.
alpha: Scaling factor for the solution.
a: Buffer holding input matrix A. Size of the buffer must be 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 matrix A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.
b: Buffer holding input matrix B. Size of the buffer must be at least ldb * n if column major layout or at least ldb * m if row major layout is used. See Matrix Storage for more details.
ldb: Leading dimension of matrix B. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.
mode: Optional. Compute mode settings. See Compute Modes for more details.

Output Parameters

b: Output buffer overwritten by solution matrix X.

NOTE:

If alpha = 0, matrix B is set to zero, and A and B do not need to be initialized before calling trsm.

trsm (USM Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event trsm(sycl::queue &queue,
                     oneapi::mkl::side left_right,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     oneapi::mkl::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,
                     compute_mode mode = compute_mode::unset,
                     const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
    sycl::event trsm(sycl::queue &queue,
                     oneapi::mkl::side left_right,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     oneapi::mkl::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,
                     compute_mode mode = compute_mode::unset,
                     const std::vector<sycl::event> &dependencies = {})
}

Input Parameters

queue

The queue where the routine should be executed.

left_right

Specifies whether matrix A is on the left side or right side of the multiplication. See Data Types for more details.

upper_lower

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

trans

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

unit_diag

Specifies whether matrix A is unit triangular or not. See Data Types for more details.

m

Number of rows of matrix B. Must be at least zero.

n

Number of columns of matrix B. Must be at least zero.

alpha

Scaling factor for the solution.

a

Pointer to input matrix A. Size of the array must be 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 matrix A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.

b

Pointer to input matrix B. Size of the array must be at least ldb * n if column major layout or at least ldb * m if row major layout is used. See Matrix Storage for more details.

ldb

Leading dimension of matrix B. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.

mode

Optional. Compute mode settings. See Compute Modes for more details.

dependencies

Optional. List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

mode and dependencies may be omitted independently; it is not necessary to specify mode in order to provide dependencies.

Output Parameters

b: Pointer to output matrix overwritten by solution matrix X.

NOTE:

If alpha = 0, matrix B is set to zero, and A and B do not need to be initialized before calling trsm.

Return Values

Output event to wait on to ensure computation is complete.

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