trsm#

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

Description

The trsm routines solve one of the following matrix equations:

\[op(A)*X = alpha*B\]

\[X*op(A) = alpha*B\]

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 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>

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::host_bad_alloc

oneapi::mkl::device_bad_alloc

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.