mkl_sparse_?

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

mkl_sparse_?_trsv

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

Syntax

stat = mkl_sparse_s_trsv ( operation, alpha, A, descr, x, y )

stat = mkl_sparse_d_trsv ( operation, alpha, A, descr, x, y )

stat = mkl_sparse_c_trsv ( operation, alpha, A, descr, x, y )

stat = mkl_sparse_z_trsv ( operation, alpha, A, descr, x, y )

Include Files

mkl_spblas.f90

Description

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

\[op(A)\cdot y = \alpha \cdot x\]

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

C_INT .

Specifies operation op() on input matrix:

`operation`	Description
`SPARSE_OPERATION_NON_TRANSPOSE`	`\(op(A) = A\)`
`SPARSE_OPERATION_TRANSPOSE`	`\(op(A) = A^{T}\)`
`SPARSE_OPERATION_CONJUGATE_TRANSPOSE`	`\(op(A) = A^{H}\)`

alpha

`C_FLOAT`	for `mkl_sparse_s_trsv`
`C_DOUBLE`	for `mkl_sparse_d_trsv`
`C_FLOAT_COMPLEX`	for `mkl_sparse_c_trsv`
`C_DOUBLE_COMPLEX`	for `mkl_sparse_z_trsv`

Specifies the scalar, \(\alpha\) .

A

SPARSE_MATRIX_T.

Handle which contains the sparse matrix A .

descr

MATRIX_DESCR .

Descriptor 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 requested 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

`C_FLOAT`	for `mkl_sparse_s_trsv`
`C_DOUBLE`	for `mkl_sparse_d_trsv`
`C_FLOAT_COMPLEX`	for `mkl_sparse_c_trsv`
`C_DOUBLE_COMPLEX`	for `mkl_sparse_z_trsv`

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

`C_FLOAT`	for `mkl_sparse_s_trsv`
`C_DOUBLE`	for `mkl_sparse_d_trsv`
`C_FLOAT_COMPLEX`	for `mkl_sparse_c_trsv`
`C_DOUBLE_COMPLEX`	for `mkl_sparse_z_trsv`

Array of size at least \(m\) containing the solution to the system of linear equations.

stat

INTEGER

Value indicating whether the operation was successful, and if not, 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.

Return Values

See Output Parameter, stat.

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