mkl_sparse_?

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

mkl_sparse_?_trsm

Solves a system of linear equations with multiple right hand sides for a triangular sparse matrix.

Syntax

sparse_status_t mkl_sparse_s_trsm (       sparse_operation_t operation,
                                    const sparse_matrix_t A,
                                          float alpha,
                                    const struct matrix_descr descr,
                                          sparse_layout_t layout,
                                    const float *x,
                                          MKL_INT columns,
                                          MKL_INT ldx,
                                          float *y,
                                          MKL_INT ldy );

sparse_status_t mkl_sparse_d_trsm (       sparse_operation_t operation,
                                    const sparse_matrix_t A,
                                          double alpha,
                                    const struct matrix_descr descr,
                                          sparse_layout_t layout,
                                    const double *x,
                                          MKL_INT columns,
                                          MKL_INT ldx,
                                          double *y,
                                          MKL_INT ldy );

sparse_status_t mkl_sparse_c_trsm (       sparse_operation_t operation,
                                    const sparse_matrix_t A,
                                          MKL_Complex8 alpha,
                                    const struct matrix_descr descr,
                                          sparse_layout_t layout,
                                    const MKL_Complex8 *x,
                                          MKL_INT columns,
                                          MKL_INT ldx,
                                          MKL_Complex8 *y,
                                          MKL_INT ldy );

sparse_status_t mkl_sparse_z_trsm (       sparse_operation_t operation,
                                    const sparse_matrix_t A,
                                          MKL_Complex16 alpha,
                                    const struct matrix_descr descr,
                                          sparse_layout_t layout,
                                    const MKL_Complex16 *x,
                                          MKL_INT columns,
                                          MKL_INT ldx,
                                          MKL_Complex16 *y,
                                          MKL_INT ldy );

Include Files

mkl_spblas.h

Description

The mkl_sparse_?_trsm routine solves a system of linear equations with multiple right hand sides for a triangular sparse matrix:

\[Y \leftarrow \alpha \cdot \text{inv}(op(A)) \cdot X\]

where:

\(\alpha\) is a scalar, \(X\) and \(Y\) are dense matrices, \(A\) is a sparse matrix, and \(op()\) is a matrix modifier for matrix \(A\).

The mkl_sparse_?_mm and mkl_sparse_?_trsm routines support these configurations:

	Column-major dense matrix: `layout = SPARSE_LAYOUT_COLUMN_MAJOR`	Row-major dense matrix: `layout = SPARSE_LAYOUT_ROW_MAJOR`
0-based sparse matrix: `SPARSE_INDEX_BASE_ZERO`	CSR BSR: general non-transposed matrix multiplication only	All formats
1-based sparse matrix: `SPARSE_INDEX_BASE_ONE`	All formats	CSR BSR: general non-transposed matrix multiplication only

Column-major dense matrix: layout = SPARSE_LAYOUT_COLUMN_MAJOR

Row-major dense matrix: layout = SPARSE_LAYOUT_ROW_MAJOR

0-based sparse matrix: SPARSE_INDEX_BASE_ZERO

CSR

BSR: general non-transposed matrix multiplication only

All formats

1-based sparse matrix: SPARSE_INDEX_BASE_ONE

All formats

CSR

BSR: general non-transposed matrix multiplication only

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:

`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

Specifies the scalar, \(\alpha\) .

A

Handle which contains the sparse matrix A .

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.

layout

Describes the storage scheme for the dense matrix:

`SPARSE_LAYOUT_COLUMN_MAJOR`	Storage of elements uses column major layout.
`SPARSE_LAYOUT_ROW_MAJOR`	Storage of elements uses row major layout.

x

Array of size at least rows * cols .

	`layout = SPARSE_LAYOUT_COLUMN_MAJOR`	`layout = SPARSE_LAYOUT_ROW_MAJOR`
`rows (X_nrows)`	`ldx`	number of rows in `\(A\)`
`cols (X_ncols)`	`columns`	`ldx`

On entry, the array x must contain the matrix, X .

columns

Number of columns of matrix \(Y\) .

ldx

Specifies the leading dimension of matrix \(X\) .

y

Array of size at least rows * cols , where

	`layout = SPARSE_LAYOUT_COLUMN_MAJOR`	`layout = SPARSE_LAYOUT_ROW_MAJOR`
`rows (Y_nrows)`	`ldy`	number of rows in `\(A\)`
`cols (Y_ncols)`	`columns`	`ldy`

Output Parameters

y

Overwritten by the updated matrix \(Y\) .

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.

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