mkl_sparse

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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mkl_sparse_sypr

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

Syntax

stat = mkl_sparse_sypr (operation, A, B, descrB, C, request)

Include Files

mkl_spblas.f90

Description

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

C:=A*B*opA(A)

C:=opA(A)*B*A

depending on the matrix modifier operation.

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. opA 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 matrix. If the data is unsorted, call the mkl_sparse_order routine before either mkl_sparse_sypr or mkl_sparse_?_syprd.

Input Parameters

operation

C_INT.

Specifies operation on the input sparse matrices.

SPARSE_OPERATION_NON_TRANSPOSE

Non-transpose case.

C:=A*B*(A^T) for real precision

C:=A*B*(A^H) for complex precision.

SPARSE_OPERATION_TRANSPOSE

Transpose case. This is not supported for complex matrices.

C:=(A^T)*B*A

SPARSE_OPERATION_CONJUGATE_TRANSPOSE

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

C:=(A^H)*B*A

SPARSE_MATRIX_T.

Handle which contains the sparse matrix A.

SPARSE_MATRIX_T.

Handle which contains the sparse matrix B.

descrB

MATRIX_DESCR.

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 cannot be equal to one.

NOTE:

This routine also supports C=AA^T,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

INTEGER.

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

SPARSE_MATRIX_T.

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

stat

INTEGER

Value indicating whether the operation was successful, or the reason why it failed.

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.

Parent topic: Inspector-Executor Sparse BLAS Execution Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_sparse_sypr