Intel® Math Kernel Library 2018 Developer Reference - C

mkl_sparse_?_symgs

Computes a symmetric Gauss-Zeidel preconditioner.

Syntax

sparse_status_t mkl_sparse_s_symgs (const sparse_operation_t operation, const sparse_matrix_t A, struct matrix_descr descr, const float alpha, float *b, float *x);

sparse_status_t mkl_sparse_d_symgs (const sparse_operation_t operation, const sparse_matrix_t A, struct matrix_descr descr, const double alpha, double *b, double *x);

sparse_status_t mkl_sparse_c_symgs (const sparse_operation_t operation, const sparse_matrix_t A, struct matrix_descr descr, const MKL_Complex8 alpha, MKL_Complex8 *b, MKL_Complex8 *x);

sparse_status_t mkl_sparse_z_symgs (const sparse_operation_t operation, const sparse_matrix_t A, struct matrix_descr descr, const MKL_Complex16 alpha, MKL_Complex16 *b, MKL_Complex16 *x);

Include Files

Description

The mkl_sparse_?_symgs routine performs this operation:

x0 := x*alpha;
(L + D)*x1 = b - U*x0;
(U + D)*x = b - L*x1;

where A = L + D + U.

Note

Only symmetric matrices are supported, so desc.type must be SPARSE_MATRIX_TYPE_SYMMETRIC.

Input Parameters

operation

Specifies the operation performed on matrix A.

SPARSE_OPERATION_NON_TRANSPOSE, op(A) := A.

Note

Transpose (SPARSE_OPERATION_TRANSPOSE) and conjugate transpose (SPARSE_OPERATION_CONJUGATE_TRANSPOSE) are not supported.

A

Handle containing sparse matrix in internal data structure.

alpha

Specifies the scalar alpha.

descr

Structure 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 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.
x

Array of size at least m, where m is the number of rows of matrix A.

On entry, the array x must contain the vector x.

b

Array of size at least m, where m is the number of rows of matrix A.

On entry, the array b must contain the vector b.

Output Parameters

x

Overwritten by the computed vector x.

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.