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_?_syprd

Computes the symmetric triple product of a sparse matrix and a dense matrix and stores the result as a dense matrix.

Syntax

stat = mkl_sparse_s_syprd ( op, A, B, denselayoutB, ldb, alpha, beta, C, denselayoutC, ldc )

stat = mkl_sparse_d_syprd ( op, A, B, denselayoutB, ldb, alpha, beta, C, denselayoutC, ldc )

stat = mkl_sparse_c_syprd ( op, A, B, denselayoutB, ldb, alpha, beta, C, denselayoutC, ldc )

stat = mkl_sparse_z_syprd ( op, A, B, denselayoutB, ldb, alpha, beta, C, denselayoutC, ldc )

Include Files

mkl_spblas.f90

Description

The mkl_sparse_?_syprd routine performs a multiplication of three sparse matrices that results in a symmetric or Hermitian matrix \(C\).

\[C \leftarrow \alpha \cdot A \cdot B \cdot op(A) + \beta \cdot C\]

\[C \leftarrow \alpha \cdot op(A) \cdot B \cdot A + \beta \cdot C\]

depending on the matrix modifier operation . Here \(A\) is a sparse matrix, \(B\) and \(C\) are dense and symmetric (or Hermitian) matrices.

\(op()\) is the transpose (real precision) or conjugate transpose (complex precision) operator.

NOTE:

This routine is not supported for sparse matrices in COO or CSC formats. It supports only CSR and BSR formats. In addition, this routine supports only the sorted CSR and sorted BSR formats for the input matrix \(A\). If the data is unsorted, call the mkl_sparse_order routine before either mkl_sparse_sypr or mkl_sparse_?_syprd.

Input Parameters

op

C_INT .

Specifies operation on the input sparse matrix.

SPARSE_OPERATION_NON_TRANSPOSE

Non-transpose case.

\(C := \alpha\cdot A\cdot B\cdot A^{T} + \beta\cdot C\) for real precision.
\(C := \alpha\cdot A\cdot B\cdot A^{H} + \beta\cdot C\) for complex precision.

SPARSE_OPERATION_TRANSPOSE

Transpose case. This is not supported for complex matrices.

\(C := \alpha\cdot A^{T}\cdot B\cdot A + \beta\cdot C\).

SPARSE_OPERATION_CONJUGATE_TRANSPOSE

Conjugate transpose case. This is not supported for real matrices.

\(C := \alpha\cdot A^{H}\cdot B\cdot A + \beta\cdot C\).

A

SPARSE_MATRIX_T .

Handle which contains the sparse matrix, A .

B

SPARSE_MATRIX_T .

Input dense matrix. Only the upper triangular part of the matrix is used for computation.

denselayoutB

C_INT .

Structure that describes the storage scheme for the dense matrix.

`SPARSE_LAYOUT_COLUMN_MAJOR`	Store elements in a column-major layout.
`SPARSE_LAYOUT_ROW_MAJOR`	Store elements in a row-major layout.

ldb

SPARSE_MATRIX_T .

Leading dimension of dense matrix \(B\).

alpha

Scalar parameter, \(\alpha\).

`C_FLOAT`	for `mkl_sparse_s_syprd`
`C_DOUBLE`	for `mkl_sparse_d_syprd`
`C_FLOAT_COMPLEX`	for `mkl_sparse_c_syprd`
`C_DOUBLE_COMPLEX`	for `mkl_sparse_z_syprd`

beta

Scalar parameter, \(\beta\).

`C_FLOAT`	for `mkl_sparse_s_syprd`
`C_DOUBLE`	for `mkl_sparse_d_syprd`
`C_FLOAT_COMPLEX`	for `mkl_sparse_c_syprd`
`C_DOUBLE_COMPLEX`	for `mkl_sparse_z_syprd`

NOTE:

Since the upper triangular part of matrix \(C\) is the only portion that is processed, set real values of \(\alpha\) and \(\beta\) in the complex case to obtain the Hermitian matrix.

denselayoutC

C_INT .

Structure that describes the storage scheme for the dense matrix \(C\).

`SPARSE_LAYOUT_COLUMN_MAJOR`	Store elements in a column-major layout.
`SPARSE_LAYOUT_ROW_MAJOR`	Store elements in a row-major layout.

ldc

C_INT.

Leading dimension of matrix \(C\).

Output Parameters

C

SPARSE_MATRIX_T .

Handle which contains the resulting dense matrix \(C\). Only the upper-triangular part of the matrix is computed.

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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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_sparse_?_syprd

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values