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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)
}

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)
}

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.

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 (Buffer 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,
                     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,
                     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.

dependencies

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

trmm BLAS-like Extensions