BlaSmallMatLU.c File Reference

LU decomposition and direct solver for small dense matrices. More...

#include <math.h>
#include "fasp.h"

Go to the source code of this file.

Functions
SHORT	fasp_smat_lu_decomp (REAL *A, INT pivot[], const INT n)
	LU decomposition of A using Doolittle's method. More...
SHORT	fasp_smat_lu_solve (const REAL *A, REAL b[], const INT pivot[], REAL x[], const INT n)
	Solving Ax=b using LU decomposition. More...

Detailed Description

LU decomposition and direct solver for small dense matrices.

Note

This file contains Level-1 (Bla) functions.

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Copyright (C) 2009–Present by the FASP team. All rights reserved.

Released under the terms of the GNU Lesser General Public License 3.0 or later.

Definition in file BlaSmallMatLU.c.

Function Documentation

fasp_smat_lu_decomp()

SHORT fasp_smat_lu_decomp	(	REAL *	A,
		INT	pivot[],
		const INT	n
	)

LU decomposition of A using Doolittle's method.

Parameters

A	Pointer to the full matrix
pivot	Pivoting positions
n	Size of matrix A

Returns

FASP_SUCCESS if successed; otherwise, error information.

Note

Use Doolittle's method to decompose the n x n matrix A into a unit lower triangular matrix L and an upper triangular matrix U such that A = LU. The matrices L and U replace the matrix A. The diagonal elements of L are 1 and are not stored.

The Doolittle method with partial pivoting is: Determine the pivot row and interchange the current row with the pivot row, then assuming that row k is the current row, k = 0, ..., n - 1 evaluate in order the following pair of expressions U[k][j] = A[k][j] - (L[k][0]*U[0][j] + ... + L[k][k-1]*U[k-1][j]) for j = k, k+1, ... , n-1 L[i][k] = (A[i][k] - (L[i][0]*U[0][k] + . + L[i][k-1]*U[k-1][k])) / U[k][k] for i = k+1, ... , n-1.

Author

Xuehai Huang

Date

04/02/2009

Definition at line 52 of file BlaSmallMatLU.c.

fasp_smat_lu_solve()

SHORT fasp_smat_lu_solve	(	const REAL *	A,
		REAL	b[],
		const INT	pivot[],
		REAL	x[],
		const INT	n
	)

Solving Ax=b using LU decomposition.

Parameters

A	Pointer to the full matrix
b	Right hand side array (b is used as the working array!!!)
pivot	Pivoting positions
x	Pointer to the solution array
n	Size of matrix A

Returns

FASP_SUCCESS if successed; otherwise, error information.

Note

This routine uses Doolittle's method to solve the linear equation Ax = b. This routine is called after the matrix A has been decomposed into a product of a unit lower triangular matrix L and an upper triangular matrix U with pivoting. The solution proceeds by solving the linear equation Ly = b for y and subsequently solving the linear equation Ux = y for x.

Author

Xuehai Huang

Date

04/02/2009

Definition at line 124 of file BlaSmallMatLU.c.