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_sypr

Computes the symmetric product of three sparse matrices and stores the result in a newly allocated sparse matrix.

Syntax

sparse_status_t mkl_sparse_sypr ( const sparse_operation_t operation,
                                  const sparse_matrix_t A,
                                  const sparse_matrix_t B,
                                  const struct matrix_descr descrB,
                                        sparse_matrix_t *C,
                                  const sparse_request_t request );

Include Files

mkl_spblas.h

Description

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

\[C \leftarrow A \cdot B \cdot op(A)\]

\[C \leftarrow op(A)\cdot B\cdot A\]

depending on the matrix modifier, \(op()\) and whether it is REAL or COMPLEX precision.

Here, \(A\), \(B\), and \(C\) are sparse matrices, where \(A\) has a general structure while \(B\) and \(C\) are symmetric (for real data types) or Hermitian (for complex data types) matrices. \(op(A)\) is the transpose (real data types) or conjugate transpose (complex data types) operator.

NOTE:

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

Input Parameters

op

Specifies operation on the input sparse matrices.

`op`	Description
`SPARSE_OPERATION_NON_TRANSPOSE`	Non-transpose case. `\(C \leftarrow A \cdot B \cdot A^T\)` for real precision `\(C \leftarrow A \cdot B \cdot A^H\)` for complex precision.
`SPARSE_OPERATION_TRANSPOSE`	Transpose case. This is not supported for complex matrices. `\(C \leftarrow A^T \cdot B \cdot A\)`
`SPARSE_OPERATION_CONJUGATE_TRANSPOSE`	Conjugate transpose case. This is not supported for real matrices. `\(C \leftarrow A^H \cdot B \cdot A\)`

op

Description

SPARSE_OPERATION_NON_TRANSPOSE

Non-transpose case.

\(C \leftarrow A \cdot B \cdot A^T\) for real precision

\(C \leftarrow A \cdot B \cdot A^H\) for complex precision.

SPARSE_OPERATION_TRANSPOSE

Transpose case. This is not supported for complex matrices.

\(C \leftarrow A^T \cdot B \cdot A\)

SPARSE_OPERATION_CONJUGATE_TRANSPOSE

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

\(C \leftarrow A^H \cdot B \cdot A\)

A

Handle which contains the sparse matrix \(A\) .

B

Handle which contains the sparse matrix \(B\) .

descrB

Structure specifying properties of the sparse matrix.

sparse_matrix_type_t type specifies the type of a sparse matrix

`SPARSE_MATRIX_TYPE_SYMMETRIC`	The matrix is symmetric (only the specified triangle is processed).
`SPARSE_MATRIX_TYPE_HERMITIAN`	The matrix is Hermitian (only the specified triangle is processed).

sparse_fill_mode_t mode specifies the triangular matrix part.

`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 the type of diagonal.

SPARSE_DIAG_NON_UNIT

Diagonal elements are what they are.

NOTE:

This routine also supports \(C = A \cdot A^T\) or \(C = A \cdot A^H\) with these parameters:

descrB.type = SPARSE_MATRIX_TYPE_DIAGONAL
descrB.diag = SPARSE_DIAG_UNIT

In this case, you do not need to allocate structure \(B\). Use the routine as a 2-stage version of mkl_sparse_syrk.

request

Use this routine to specify if the computations should be performed in a single step or using the two-stage algorithm. See Two-stage Algorithm for Inspector-executor Sparse BLAS Routines for more information.

`SPARSE_STAGE_NNZ_COUNT`	Only rowIndex (BSR/CSR format) or colIndex (CSC format) array of the matrix is computed internally. The computation can be extracted to measure the memory required for full operation.
`SPARSE_STAGE_FINALIZE_MULT_NO_VAL`	Finalize computations of the matrix structure (values will not be computed). Use only after the call with `SPARSE_STAGE_NNZ_COUNT` parameter.
`SPARSE_STAGE_FINALIZE_MULT`	Finalize computation. Can be used after the call with the `SPARSE_STAGE_NNZ_COUNT` or `SPARSE_STAGE_FINALIZE_MULT_NO_VAL`. Can also be used when the matrix structure remains unchanged and only values of the resulting matrix `C` need to be recomputed.
`SPARSE_STAGE_FULL_MULT_NO_VAL`	Perform computations of the matrix structure.
`SPARSE_STAGE_FULL_MULT`	Perform the entire computation in a single step.

Output Parameters

C

Handle which contains the resulting sparse matrix. Only the upper-triangular part of the matrix is computed.

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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Developer Reference for Intel® oneAPI Math Kernel Library for C

mkl_sparse_sypr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values