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oneapi::mkl::sparse::trsv

Solves a system of linear equations for a triangular sparse matrix.

Description

Note

Refer to Supported Types for a list of supported <fp> and <intType>, and refer to Exceptions for a detailed description of the exceptions thrown.

The oneapi::mkl::sparse::trsv routine solves the sparse triangular system

\text{op}(A)\cdot y = x

where A is a sparse triangular matrix of size m rows by m columns and \text{op()} is a matrix modifier:

\text{op}(A) = \begin{cases} A,& \text{ oneapi::mkl::transpose::nontrans}\\ A^{T},& \text{ oneapi::mkl::transpose::trans}\\A^{H},& \text{ oneapi::mkl::transpose::conjtrans} \end{cases}

The dense vectors x and y should be of length at least m. The vector x is input right hand side data and math:y is the resulting output vector.

For a given matrix decomposition into lower, diagonal and upper parts A = L + D + U, the triangular solve with one of oneapi::mkl::uplo::lower or oneapi::mkl::uplo::upper selected will perform the appropriate forward or backward substitution using respectively \text{op}(L+D) or \text{op}(D+U) for oneapi::mkl::diag::nonunit or if using oneapi::mkl::diag::unit, will perform the appropriate forward or backward substitution for \text{op}(L+I) or \text{op}(I+U) where I is the identity matrix.

API

Syntax

Note

Currently, complex types are not supported.

Using SYCL buffers:

namespace oneapi::mkl::sparse {
    void trsv (
        cl::sycl::queue &queue,
        oneapi::mkl::uplo uplo_flag,
        oneapi::mkl::transpose transpose_flag,
        oneapi::mkl::diag diag_flag,
        oneapi::mkl::sparse::matrix_handle_t handle,
        cl::sycl::buffer<fp, 1> &x,
        cl::sycl::buffer<fp, 1> &y)
}

Using USM pointers:

namespace oneapi::mkl::sparse {
    cl::sycl::event trsv(
        cl::sycl::queue &queue,
        oneapi::mkl::uplo uplo_flag,
        oneapi::mkl::transpose transpose_flag,
        oneapi::mkl::diag diag_flag,
        oneapi::mkl::sparse::matrix_handle_t handle,
        fp *x,
        fp *y,
        const std::vector<cl::sycl::event> &dependencies = {})
}

Include Files

  • oneapi/mkl/spblas.hpp

Input Parameters

queue

Specifies the SYCL command queue which will be used for SYCL kernels execution.

uplo_flag

Specifies which part of the matrix is to be processed.

oneapi::mkl::uplo::lower

The lower triangular matrix part is processed.

oneapi::mkl::uplo::upper

The upper triangular matrix part is processed.
transpose_flag

Specifies operation op() on input matrix.

oneapi::mkl::transpose::nontrans

Non-transpose, \text{op}(A) = A.

oneapi::mkl::transpose::trans

Transpose, \text{op}(A) = A^{T}.

oneapi::mkl::transpose::conjtrans

Conjugate transpose, \text{op}(A) = A^{H}.

Note

Currently, the only supported case for operation is oneapi::mkl::transpose::nontrans.

diag_flag

Specifies if the diagonal used for computations is unit or based on provided matrix data.

oneapi::mkl::diag::nonunit

Diagonal elements are used as provided in the sparse matrix.

oneapi::mkl::diag::unit

The value of one is substituted for the diagonal elements in the triangular solve algorithm.

Note

If oneapi::mkl::diag::nonunit is selected, all diagonal values must be present in the sparse matrix. This is not necessary for the oneapi::mkl::diag::unit case.

handle

Handle to object containing sparse matrix and other internal data. Created using one of the oneapi::mkl::sparse::set_<sparse_matrix_type>_data routines.

Note

Currently, the only supported case for <sparse_matrix_type> is csr.

x

SYCL buffer or device-accessible USM pointer of size at least equal to the number of columns of input matrix if transpose_flag = oneapi::mkl::transpose::nontrans and at least the number of rows of input matrix otherwise. It is the input vector x

dependencies

A vector of type std::vector<cl::sycl::event> containing the list of events that the oneapi::mkl::sparse::trsv routine depends on.

Output Parameters

y

SYCL buffer or device-accessible USM pointer of size at least equal to the number of rows of the input matrix if transpose_flag = oneapi::mkl::transpose::nontrans and at least the number of columns of the input matrix otherwise. The solution of the triangular solve is filled into this array.

Return Values (USM Only)

cl::sycl::event

SYCL event which can be waited upon or added as a dependency for the completion of the trsv routine.

Examples

An example of how to use oneapi::mkl::sparse::trsv with SYCL buffers or USM can be found in the oneMKL installation directory, under:

examples/dpcpp/sparse_blas/source/sparse_trsv.cpp

examples/dpcpp/sparse_blas/source/sparse_trsv_usm.cpp
oneapi::mkl::sparse::trmv oneapi::mkl::sparse::gemm