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_?_syrkd

Computes the product of sparse matrix with its transpose (or conjugate transpose) and stores the result as a dense matrix.

Syntax

stat = mkl_sparse_s_syrkd ( operation, A, alpha, beta, C, layout, ldc )

stat = mkl_sparse_d_syrkd ( operation, A, alpha, beta, C, layout, ldc )

stat = mkl_sparse_c_syrkd ( operation, A, alpha, beta, C, layout, ldc )

stat = mkl_sparse_z_syrkd ( operation, A, alpha, beta, C, layout, ldc )

Include Files

mkl_spblas.f90

Description

The mkl_sparse_?_syrkd routine performs a sparse matrix-matrix operation which results in a dense matrix C that is either symmetric (real case) or Hermitian (complex case):

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

where \(op()\) is the transpose for real matrices and conjugate transpose for complex matrices OR

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

depending on the matrix modifier \(op()\) which can be the transpose for real matrices or conjugate transpose for complex matrices. Here, \(A\) is a sparse matrix and \(C\) is a dense matrix.

NOTE:

This routine is not supported for sparse matrices in COO or CSC formats. It supports only CSR and BSR formats. Additionally, this routine supports only the sorted CSR and sorted BSR formats for the input matrix. If data is unsorted, call the mkl_sparse_order routine before either mkl_sparse_syrk or mkl_sparse_?_syrkd .

Input Parameters

operation

C_INT .

Specifies operation op() on input matrix:

`operation`	Description
`SPARSE_OPERATION_NON_TRANSPOSE`	`\(C \leftarrow \beta\cdot C + \alpha\cdot A\cdot A^{T}\)` for real matrices and `\(C \leftarrow \beta\cdot C + \alpha\cdot A\cdot A^{H}\)` for complex matrices.
`SPARSE_OPERATION_TRANSPOSE`	`\(C \leftarrow \beta\cdot C + \alpha\cdot A^{T}\cdot A\)` for real matrix `\(A\)`.
`SPARSE_OPERATION_CONJUGATE_TRANSPOSE`	`\(C \leftarrow \beta\cdot C + \alpha\cdot A^{H}\cdot A\)` for complex matrix `\(A\)`.

A

SPARSE_MATRIX_T.

Handle which contains the sparse matrix \(A\) . The matrix must be in sorted CSR or sorted BSR format. See mkl_sparse_order for more details on sorting the data.

alpha

`C_FLOAT`	for `mkl_sparse_s_syrkd`
`C_DOUBLE`	for `mkl_sparse_d_syrkd`
`C_FLOAT_COMPLEX`	for `mkl_sparse_c_syrkd`
`C_DOUBLE_COMPLEX`	for `mkl_sparse_z_syrkd`

Specifies the scalar, \(\alpha\).

beta

`C_FLOAT`	for `mkl_sparse_s_syrkd`
`C_DOUBLE`	for `mkl_sparse_d_syrkd`
`C_FLOAT_COMPLEX`	for `mkl_sparse_c_syrkd`
`C_DOUBLE_COMPLEX`	for `mkl_sparse_z_syrkd`

Specifies the scalar, \(\beta\).

layout

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 \(C\).

NOTE:

Only the upper triangular part of matrix C is processed. Therefore, you must set real values of \(\alpha\) and \(\beta\) for complex matrices in order to obtain a Hermitian matrix.

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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