oneapi::mkl::sparse::trsv

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 11/07/2023

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oneapi::mkl::sparse::trsv

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

Description
API
Examples

Description

NOTE:

Refer to Sparse BLAS Supported Data and Integer Types for a list of supported <DATA_TYPE> and <INT_TYPE> data and integer types and refer to Error Handling for a detailed description of the possible exceptions thrown.

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

where is a sparse triangular matrix of size rows by columns and is a matrix modifier:

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

NOTE:

While it can make sense to pass the same array in for both rhs,

, and solution,

, to update the rhs in place, we currentlydo not guarantee that this will always work.

For a given matrix decomposition into lower, diagonal and upper parts , 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 or for oneapi::mkl::diag::nonunit or if using oneapi::mkl::diag::unit, will perform the appropriate forward or backward substitution for or where is the identity matrix.

API

Syntax

Using SYCL buffers:

namespace oneapi::mkl::sparse {
    void trsv (
        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,
        sycl::buffer<DATA_TYPE, 1> &x,
        sycl::buffer<DATA_TYPE, 1> &y)
}

Using USM pointers:

namespace oneapi::mkl::sparse {
    sycl::event trsv(
        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,
        DATA_TYPE *x,
        DATA_TYPE *y,
        const std::vector<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, .
`oneapi::mkl::transpose::trans`	Transpose, .
`oneapi::mkl::transpose::conjtrans`	Conjugate transpose, .

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 sparsity profile and must not be zero valued. This is not necessary for the oneapi::mkl::diag::unit case. An exception of type onemkl::invalid_value() will be thrown in case this is violated.

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<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)

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:

share/doc/mkl/examples/sycl/sparse_blas/source/sparse_trsv.cpp

share/doc/mkl/examples/sycl/sparse_blas/source/sparse_trsv_usm.cpp

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oneapi::mkl::sparse::trsv

Description

API

Examples