mkl_sparse_?_lu

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_?_lu_smoother

Computes an action of a preconditioner which corresponds to the approximate matrix decomposition for the system (see description below).

Syntax

status = mkl_sparse_s_lu_smoother (op, A, indx, descr, diag, approx_diag_inverse, x, b)

status = mkl_sparse_d_lu_smoother (op, A, indx, descr, diag, approx_diag_inverse, x, b)

status = mkl_sparse_c_lu_smoother (op, A, indx, descr, diag, approx_diag_inverse, x, b)

status = mkl_sparse_z_lu_smoother (op, A, indx, descr, diag, approx_diag_inverse, x, b)

Include Files

mkl_spblas.f90

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 */

NOTE:

This routine is supported only for non-transpose operation, real data types, and CSR/BSR sparse formats. In a BSR format, both diagonal values and approximate diagonal inverse arrays should be passed explicitly. For CSR format, diagonal values should be passed explicitly.

Input Parameters

operation

C_INT .

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

SPARSE_MATRIX_T.

Handle which contains the sparse matrix A.

descr

MATRIX_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

C_FLOAT for mkl_sparse_s_lu_smoother

C_DOUBLE for mkl_sparse_d_lu_smoother

C_FLOAT_COMPLEX for mkl_sparse_c_lu_smoother

C_DOUBLE_COMPLEX for mkl_sparse_z_lu_smoother

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

C_FLOAT for mkl_sparse_s_lu_smoother

C_DOUBLE for mkl_sparse_d_lu_smoother

C_FLOAT_COMPLEX for mkl_sparse_c_lu_smoother

C_DOUBLE_COMPLEX for mkl_sparse_z_lu_smoother

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

C_FLOAT for mkl_sparse_s_lu_smoother

C_DOUBLE for mkl_sparse_d_lu_smoother

C_FLOAT_COMPLEX for mkl_sparse_c_lu_smoother

C_DOUBLE_COMPLEX for mkl_sparse_z_lu_smoother

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

C_FLOAT for mkl_sparse_s_lu_smoother

C_DOUBLE for mkl_sparse_d_lu_smoother

C_FLOAT_COMPLEX for mkl_sparse_c_lu_smoother

C_DOUBLE_COMPLEX for mkl_sparse_z_lu_smoother

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

C_FLOAT for mkl_sparse_s_lu_smoother

C_DOUBLE for mkl_sparse_d_lu_smoother

C_FLOAT_COMPLEX for mkl_sparse_c_lu_smoother

C_DOUBLE_COMPLEX for mkl_sparse_z_lu_smoother

Overwritten by the computed vector y.

status

INTEGER

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.

Parent topic: Inspector-Executor Sparse BLAS Execution Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_sparse_?_lu_smoother