mkl_sparse_?

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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mkl_sparse_?_trsv

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

Syntax

sparse_status_t mkl_sparse_s_trsv (const sparse_operation_t operation, const float alpha, const sparse_matrix_t A, const struct matrix_descr descr, const float *x, float *y);

sparse_status_t mkl_sparse_d_trsv (const sparse_operation_t operation, const double alpha, const sparse_matrix_t A, const struct matrix_descr descr, const double *x, double *y);

sparse_status_t mkl_sparse_c_trsv (const sparse_operation_t operation, const MKL_Complex8 alpha, const sparse_matrix_t A, const struct matrix_descr descr, const MKL_Complex8 *x, MKL_Complex8 *y);

sparse_status_t mkl_sparse_z_trsv (const sparse_operation_t operation, const MKL_Complex16 alpha, const sparse_matrix_t A, const struct matrix_descr descr, const MKL_Complex16 *x, MKL_Complex16 *y);

Include Files

mkl_spblas.h

Description

The mkl_sparse_?_trsv routine solves a system of linear equations for a matrix:

op(A)*y = alpha * x

where A is a triangular sparse matrix , op is a matrix modifier for matrix A, alpha is a scalar, and x and y are vectors .

NOTE:

For sparse matrices in the BSR format, the supported combinations of (indexing,block_layout) are:

(SPARSE_INDEX_BASE_ZERO, SPARSE_LAYOUT_ROW_MAJOR)
(SPARSE_INDEX_BASE_ONE, SPARSE_LAYOUT_COLUMN_MAJOR)

Input Parameters

operation

Specifies operation op() on input matrix.

`SPARSE_OPERATION_NON_TRANSPOSE`	Non-transpose, `op(A) = A`.
`SPARSE_OPERATION_TRANSPOSE`	Transpose, `op(A) = A^T`.
`SPARSE_OPERATION_CONJUGATE_TRANSPOSE`	Conjugate transpose, `op(A) = A^H`.

alpha

Specifies the scalar alpha.

A

Handle which contains the input matrix A.

descr

Structure specifying sparse matrix properties.

sparse_matrix_type_t type - Specifies the type of a sparse matrix:

`SPARSE_MATRIX_TYPE_GENERAL`	The matrix is processed as is.
`SPARSE_MATRIX_TYPE_SYMMETRIC`	The matrix is symmetric (only the requested triangle is processed).
`SPARSE_MATRIX_TYPE_HERMITIAN`	The matrix is Hermitian (only the requested triangle is processed).
`SPARSE_MATRIX_TYPE_TRIANGULAR`	The matrix is triangular (only the requested triangle is processed).
`SPARSE_MATRIX_TYPE_DIAGONAL`	The matrix is diagonal (only diagonal elements are processed).
`SPARSE_MATRIX_TYPE_BLOCK_TRIANGULAR`	The matrix is block-triangular (only requested triangle is processed). Applies to BSR format only.
`SPARSE_MATRIX_TYPE_BLOCK_DIAGONAL`	The matrix is block-diagonal (only diagonal blocks are processed). Applies to BSR format only.

sparse_fill_mode_t mode - Specifies the triangular matrix part for symmetric, Hermitian, triangular, and block-triangular matrices:

`SPARSE_FILL_MODE_LOWER`	The lower triangular matrix part is processed.
`SPARSE_FILL_MODE_UPPER`	The upper triangular matrix part is processed.

sparse_diag_type_t diag - Specifies diagonal type for non-general matrices:

`SPARSE_DIAG_NON_UNIT`	Diagonal elements might not be equal to one.
`SPARSE_DIAG_UNIT`	Diagonal elements are equal to one.

x

Array of size at least m, where m is the number of rows of matrix A. On entry, the array must contain the vector x.

Output Parameters

y: Array of size at least m containing the solution to the system of linear equations.

Return Values

The function returns a value indicating whether the operation was successful or not, and why.

`SPARSE_STATUS_SUCCESS`	The operation was successful.
`SPARSE_STATUS_NOT_INITIALIZED`	The routine encountered an empty handle or matrix array.
`SPARSE_STATUS_ALLOC_FAILED`	Internal memory allocation failed.
`SPARSE_STATUS_INVALID_VALUE`	The input parameters contain an invalid value.
`SPARSE_STATUS_EXECUTION_FAILED`	Execution failed.
`SPARSE_STATUS_INTERNAL_ERROR`	An error in algorithm implementation occurred.
`SPARSE_STATUS_NOT_SUPPORTED`	The requested operation is not supported.

Parent topic: Inspector-Executor Sparse BLAS Execution Routines

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