mkl_sparse_?_lu_smoother

Syntax

sparse_status_t mkl_sparse_s_lu_smoother (const sparse_operation_t op, const sparse_matrix_t A, const struct matrix descr descr, const float *diag, const float *approx_diag_inverse, float *x, const float *b);

sparse_status_t mkl_sparse_d_lu_smoother (const sparse_operation_t op, const sparse_matrix_t A, const struct matrix descr descr, const double *diag, const double *approx_diag_inverse, double *x, const double *b);

sparse_status_t mkl_sparse_c_lu_smoother (const sparse_operation_t op, const sparse_matrix_t A, const struct matrix descr descr, const MKL_COMPLEX8 *diag, const MKL_COMPLEX8 *approx_diag_inverse, MKL_COMPLEX8 *x, const MKL_COMPLEX8 *b);

sparse_status_t mkl_sparse_z_lu_smoother (const sparse_operation_t op, const sparse_matrix_t A, const struct matrix descr descr, const MKL_COMPLEX16 *diag, const MKL_COMPLEX16 *approx_diag_inverse, MKL_COMPLEX16 *x, const MKL_COMPLEX16 *b);

Include Files

• mkl_spblas.h

Description

This routine computes an update for an iterative solution x of the system Ax=b by means of applying one iteration of an approximate preconditioner which is based on the following approximation:

, where E is an approximate inverse of the diagonal (using exact inverse will result in Gauss-Seidel preconditioner), L and U are lower/upper triangular parts of A, D is the diagonal (block diagonal in case of BSR format) of A.

The mkl_sparse_?_lu_smoother routine performs these operations:

r = b - A*x    /* 1. Computes the residual */
(L + D)*E*(U + D)*dx = r    /* 2. Finds the update dx by solving the system */
y = x + dx    /* 3. Performs an update */

This is also equal to the Symmetric Gauss-Seidel operation in the case of a CSR format and 1x1 diagonal blocks:

(L + D)*x^1 = b - U*x  /* Lower solve for intermediate x^1 */
(U + D)*x = b - L*x^1  /* Upper solve */

Input Parameters

operation

Specifies the operation performed on matrix A.

SPARSE_OPERATION_NON_TRANSPOSE, op(A) := A

Note Transpose and conjugate transpose (SPARSE_OPERATION_TRANSPOSE and SPARSE_OPERATION_CONJUGATE_TRANSPOSE) are not supported. Non-transpose, op(A)= A.

A

Handle which contains the sparse matrix A.

descr

Structure specifying sparse matrix properties.

sparse_matrix_type_ttype - 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 the 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_tmode - 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_tdiag - Specifies the 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.

Note

Only SPARSE_MATRIX_TYPE_GENERAL is supported.

diag

Array of size at least m, where m is the number of rows (or nrows * block_size * block_size in case of BSR format) of matrix A.

The array diag must contain the diagonal values of matrix A.

approx_diag_inverse

Array of size at least m, where m is the number of rows (or the number of rows * block_size * block_size in case of BSR format) of matrix A.

The array approx_diag_inverse will be used as E, approximate inverse of the diagonal of the matrix A.

x

Array of size at least k, where k is the number of columns (or columns * block_size in case of BSR format) of matrix A.

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

b

Array of size at least m, where m is the number of rows ( or rows * block_size in case of BSR format ) of matrix A. The array b must contain the values of the right-hand side of the system.

Output Parameters

x

Overwritten by the computed vector y.

Return Values

The function returns a value indicating whether the operation was successful or not, and why.