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trsv

Solves a system of linear equations whose coefficients are in a triangular matrix.

Description

The trsv routines solve a system of linear equations whose coefficients are in a triangular matrix. The operation is defined as:

op(A)*x = b

where:

  • op(A) is one of op(A) = A, or op(A) = AT, or op(A) = AH

  • A is n x n unit or non-unit, upper or lower triangular matrix

  • b and x are vectors of length n

trsv supports the following precisions:

T

float

double

std::complex<float>

std::complex<double>

trsv (Buffer Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    void trsv(sycl::queue &queue,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::transpose trans,
              oneapi::mkl::diag unit_diag,
              std::int64_t n,
              std::int64_t k,
              sycl::buffer<T,1> &a,
              std::int64_t lda,
              sycl::buffer<T,1> &x,
              std::int64_t incx)
}

namespace oneapi::mkl::blas::row_major {
    void trsv(sycl::queue &queue,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::transpose trans,
              oneapi::mkl::diag unit_diag,
              std::int64_t n,
              std::int64_t k,
              sycl::buffer<T,1> &a,
              std::int64_t lda,
              sycl::buffer<T,1> &x,
              std::int64_t incx)
}

Input Parameters

queue

The queue where the routine should be executed.

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.

n

Number of rows and columns of matrix A. Must be at least zero.

a

Buffer holding input matrix A. Size of the buffer must be at least lda * n. See Matrix Storage for more details.

lda

Leading dimension of matrix A. Must be at least n and positive.

x

Buffer holding the n-element right-hand side vector b. Size of the buffer must be at least (1 + (n - 1)*abs(incx)). See Matrix Storage for more details.

incx

Stride of vector x.

Output Parameters

x

Buffer holding solution vector x.

trsv (USM Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event trsv(sycl::queue &queue,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     oneapi::mkl::diag unit_diag,
                     std::int64_t n,
                     std::int64_t k,
                     const T *a,
                     std::int64_t lda,
                     T *x,
                     std::int64_t incx,
                     const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
    sycl::event trsv(sycl::queue &queue,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     oneapi::mkl::diag unit_diag,
                     std::int64_t n,
                     std::int64_t k,
                     const T *a,
                     std::int64_t lda,
                     T *x,
                     std::int64_t incx,
                     const std::vector<sycl::event> &dependencies = {})
}

Input Parameters

queue

The queue where the routine should be executed.

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.

n

Number of rows and columns of matrix A. Must be at least zero.

a

Pointer to input matrix A. Size of the array holding input matrix A must be at least lda * n. See Matrix Storage for more details.

lda

Leading dimension of matrix A. Must be at least n and positive.

x

Pointer to the n-element right-hand side vector b. Size of the array holding the n-element right-hand side vector b must be at least (1 + (n - 1)*abs(incx)). See Matrix Storage for more details.

incx

Stride of vector x.

dependencies

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

Output Parameters

x

Pointer to solution vector x.

Return Values

Output event to wait on to ensure computation is complete.

trmv BLAS Level 3 Routines