505 lines
12 KiB
C
505 lines
12 KiB
C
/* @(#) Allocate, and return a pointer to, a DOUBLEMASK representing the LU
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* @(#) decomposition of the matrix in DOUBLEMASK *mat. Give it the filename
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* @(#) member *name. Returns NULL on error. Scale and offset are ignored.
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* @(#)
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* @(#) DOUBLEMASK *im_lu_decomp( const DOUBLEMASK *mat, const char *name );
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* @(#)
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* @(#) Solve the system of linear equations Ax=b, where matrix A has already
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* @(#) been decomposed into LU form in DOUBLEMASK *lu. Input vector b is in
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* @(#) vec and is overwritten with vector x.
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* @(#)
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* @(#) int im_lu_solve( const DOUBLEMASK *lu, double *vec );
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* @(#)
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* @(#) Allocate, and return a pointer to, a DOUBLEMASK representing the
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* @(#) inverse of the matrix represented in mat. Give it the filename
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* @(#) member *name. Returns NULL on error. Scale and offset are ignored.
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* @(#)
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* @(#) DOUBLEMASK *im_matinv( const DOUBLEMASK *mat, const char *name );
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* @(#)
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* @(#) Invert the matrix represented by the DOUBLEMASK *mat, and store
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* @(#) it in the place of *mat. Returns -1 on error. Scale and offset
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* @(#) are ignored.
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* @(#)
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* @(#) int im_matinv_inplace( DOUBLEMASK *mat );
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*
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* Author: Tom Vajzovic
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* Copyright: 2006, Tom Vajzovic
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* Written on: 2006-09-08
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*
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* undated:
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* - page 43-45 of numerical recipes in C 1998
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*
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* 2006-09-08 tcv:
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* - complete rewrite; algorithm unchanged
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*/
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/*
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This file is part of VIPS.
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VIPS is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*/
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/*
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These files are distributed with VIPS - http://www.vips.ecs.soton.ac.uk
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*/
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/** HEADERS **/
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#ifdef HAVE_CONFIG_H
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#include <config.h>
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#endif /*HAVE_CONFIG_H*/
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#include <vips/intl.h>
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#include <float.h>
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#include <math.h>
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#include <string.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <vips/vips.h>
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#ifdef WITH_DMALLOC
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#include <dmalloc.h>
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#endif /*WITH_DMALLOC*/
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/** CONSTANTS **/
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#define TOO_SMALL ( 2.0 * DBL_MIN )
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/* DBL_MIN is smallest *normalized* double precision float */
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/** MACROS **/
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#define MATRIX( mask, i, j ) ( (mask)-> coeff[ (j) + (i) * (mask)-> xsize ] )
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/* use DOUBLEMASK or INTMASK as matrix type */
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/** LOCAL FUNCTION DECLARATIONS **/
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static int
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mat_inv_lu(
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DOUBLEMASK *inv,
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const DOUBLEMASK *lu
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);
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static int
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mat_inv_direct(
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DOUBLEMASK *inv,
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const DOUBLEMASK *mat,
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const char *function_name
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);
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/** EXPORTED FUNCTION DEFINITIONS **/
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DOUBLEMASK *
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im_lu_decomp(
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const DOUBLEMASK *mat,
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const char *name
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){
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#define FUNCTION_NAME "im_lu_decomp"
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/* This function takes any square NxN DOUBLEMASK treats it as a matrix.
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* It allocates a DOUBLEMASK which is (N+1)xN.
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*
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* It calculates the PLU decomposition, storing the upper and diagonal parts
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* of U, together with the lower parts of L, as an NxN matrix in the first
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* N rows of the new matrix. The diagonal parts of L are all set to unity
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* and are not stored.
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*
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* The final row of the new DOUBLEMASK has only integer entries, which
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* represent the row-wise permutations made by the permuatation matrix P.
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*
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* The scale and offset members of the input DOUBLEMASK are ignored.
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*
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* See:
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* PRESS, W. et al, 1992. Numerical Recipies in C; The Art of Scientific
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* Computing, 2nd ed. Cambridge: Cambridge University Press, pp. 43-50.
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*/
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int i, j, k;
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double *row_scale;
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DOUBLEMASK *lu;
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if( mat-> xsize != mat-> ysize ){
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im_error( FUNCTION_NAME, "non-square matrix" );
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return NULL;
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}
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#define N ( mat -> xsize )
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lu= im_create_dmask( name, N, N + 1 );
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row_scale= IM_ARRAY( NULL, N, double );
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if( ! row_scale || ! lu ){
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im_free_dmask( lu );
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im_free( row_scale );
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return NULL;
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}
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/* copy all coefficients and then perform decomposition in-place */
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memcpy( lu-> coeff, mat-> coeff, N * N * sizeof( double ) );
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#define LU( i, j ) MATRIX( lu, (i), (j) )
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#define perm ( lu-> coeff + N * N )
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for( i= 0; i < N; ++i ){
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row_scale[ i ]= 0.0;
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for( j= 0; j < N; ++j ){
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double abs_val= fabs( LU( i, j ) );
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/* find largest in each ROW */
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if( abs_val > row_scale[ i ] )
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row_scale[ i ]= abs_val;
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}
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if( ! row_scale[ i ] ){
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im_error( FUNCTION_NAME, "singular matrix" );
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im_free_dmask( lu );
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im_free( row_scale );
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return NULL;
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}
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/* fill array with scaling factors for each ROW */
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row_scale[ i ]= 1.0 / row_scale[ i ];
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}
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for( j= 0; j < N; ++j ){ /* loop over COLs */
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double max= -1.0;
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int i_of_max;
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/* not needed, but stops a compiler warning */
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i_of_max= 0;
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/* loop over ROWS in upper-half, except diagonal */
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for( i= 0; i < j; ++i )
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for( k= 0; k < i; ++k )
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LU( i, j )-= LU( i, k ) * LU( k, j );
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/* loop over ROWS in diagonal and lower-half */
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for( i= j; i < N; ++i ){
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double abs_val;
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for( k= 0; k < j; ++k )
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LU( i, j )-= LU( i, k ) * LU( k, j );
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/* find largest element in each COLUMN scaled so that */
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/* largest in each ROW is 1.0 */
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abs_val= row_scale[ i ] * fabs( LU( i, j ) );
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if( abs_val > max ){
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max= abs_val;
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i_of_max= i;
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}
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}
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if( fabs( LU( i_of_max, j ) ) < TOO_SMALL ){
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/* divisor is near zero */
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im_error( FUNCTION_NAME, "singular or near-singular matrix" );
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im_free_dmask( lu );
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im_free( row_scale );
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return NULL;
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}
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if( i_of_max != j ){
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/* swap ROWS */
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for( k= 0; k < N; ++k ){
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double temp= LU( j, k );
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LU( j, k )= LU( i_of_max, k );
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LU( i_of_max, k )= temp;
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}
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row_scale[ i_of_max ]= row_scale[ j ];
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/* no need to copy this scale back up - we won't use it */
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}
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/* record permutation */
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perm[ j ]= i_of_max;
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/* divide by best (largest scaled) pivot found */
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for( i= j + 1; i < N; ++i )
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LU( i, j )/= LU( j, j );
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}
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im_free( row_scale );
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return lu;
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#undef N
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#undef LU
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#undef perm
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#undef FUNCTION_NAME
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}
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int
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im_lu_solve(
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const DOUBLEMASK *lu,
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double *vec
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){
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#define FUNCTION_NAME "im_lu_solve"
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int i, j;
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if( lu-> xsize + 1 != lu-> ysize ){
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im_error( FUNCTION_NAME, "not an LU decomposed matrix" );
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return -1;
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}
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#define N ( lu -> xsize )
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#define LU( i, j ) MATRIX( lu, (i), (j) )
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#define perm ( lu-> coeff + N * N )
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for( i= 0; i < N; ++i ){
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int i_perm= perm[ i ];
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if( i_perm != i ){
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double temp= vec[ i ];
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vec[ i ]= vec[ i_perm ];
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vec[ i_perm ]= temp;
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}
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for( j= 0; j < i; ++j )
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vec[ i ]-= LU( i, j ) * vec [ j ];
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}
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for( i= N - 1; i >= 0; --i ){
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for( j= i + 1; j < N; ++j )
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vec[ i ]-= LU( i, j ) * vec [ j ];
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vec[ i ]/= LU( i, i );
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}
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return 0;
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#undef LU
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#undef perm
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#undef N
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#undef FUNCTION_NAME
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}
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DOUBLEMASK *
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im_matinv(
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const DOUBLEMASK *mat,
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const char *name
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){
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#define FUNCTION_NAME "im_matinv"
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DOUBLEMASK *inv;
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if( mat-> xsize != mat-> ysize ){
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im_error( FUNCTION_NAME, "non-square matrix" );
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return NULL;
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}
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#define N ( mat -> xsize )
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inv= im_create_dmask( name, N, N );
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if( ! inv )
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return NULL;
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if( N < 4 ){
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if( mat_inv_direct( inv, (const DOUBLEMASK *) mat, FUNCTION_NAME ) ){
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im_free_dmask( inv );
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return NULL;
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}
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return inv;
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}
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else {
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DOUBLEMASK *lu= im_lu_decomp( mat, "temp" );
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if( ! lu || mat_inv_lu( inv, (const DOUBLEMASK*) lu ) ){
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im_free_dmask( lu );
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im_free_dmask( inv );
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return NULL;
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}
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im_free_dmask( lu );
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return inv;
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}
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#undef N
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#undef FUNCTION_NAME
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}
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int
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im_matinv_inplace(
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DOUBLEMASK *mat
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){
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#define FUNCTION_NAME "im_matinv_inplace"
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int to_return= 0;
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if( mat-> xsize != mat-> ysize ){
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im_error( FUNCTION_NAME, "non-square matrix" );
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return -1;
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}
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#define N ( mat -> xsize )
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if( N < 4 ){
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DOUBLEMASK *dup= im_dup_dmask( mat, "temp" );
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if( ! dup )
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return -1;
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to_return= mat_inv_direct( mat, (const DOUBLEMASK*) dup, FUNCTION_NAME );
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im_free_dmask( dup );
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return to_return;
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}
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{
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DOUBLEMASK *lu;
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lu= im_lu_decomp( mat, "temp" );
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if( ! lu || mat_inv_lu( mat, (const DOUBLEMASK*) lu ) )
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to_return= -1;
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im_free_dmask( lu );
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return to_return;
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}
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#undef N
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#undef FUNCTION_NAME
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}
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/* Invert a square size x size matrix stored in matrix[][]
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* result is returned in the same matrix
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*/
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int
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im_invmat(
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double **matrix,
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int size
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){
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DOUBLEMASK *mat= im_create_dmask( "temp", size, size );
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int i;
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int to_return= 0;
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for( i= 0; i < size; ++i )
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memcpy( mat-> coeff + i * size, matrix[ i ], size * sizeof( double ) );
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to_return= im_matinv_inplace( mat );
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if( ! to_return )
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for( i= 0; i < size; ++i )
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memcpy( matrix[ i ], mat-> coeff + i * size, size * sizeof( double ) );
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im_free_dmask( mat );
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return to_return;
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}
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/** LOCAL FUNCTION DEFINITIONS **/
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static int
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mat_inv_lu(
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DOUBLEMASK *inv,
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const DOUBLEMASK *lu
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){
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#define N ( lu-> xsize )
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#define INV( i, j ) MATRIX( inv, (i), (j) )
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int i, j;
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double *vec= IM_ARRAY( NULL, N, double );
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if( ! vec )
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return -1;
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for( j= 0; j < N; ++j ){
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for( i= 0; i < N; ++i )
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vec[ i ]= 0.0;
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vec[ j ]= 1.0;
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im_lu_solve( lu, vec );
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for( i= 0; i < N; ++i )
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INV( i, j )= vec[ i ];
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}
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im_free( vec );
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inv-> scale= 1.0;
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inv-> offset= 0.0;
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return 0;
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#undef N
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#undef INV
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}
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static int
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mat_inv_direct(
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DOUBLEMASK *inv,
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const DOUBLEMASK *mat,
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const char *function_name
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){
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#define N ( mat -> xsize )
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#define MAT( i, j ) MATRIX( mat, (i), (j) )
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#define INV( i, j ) MATRIX( inv, (i), (j) )
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inv-> scale= 1.0;
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inv-> offset= 0.0;
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switch( N ){
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case 1: {
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if( fabs( MAT( 0, 0 ) ) < TOO_SMALL ){
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im_error( function_name, "singular or near-singular matrix" );
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return -1;
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}
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INV( 0, 0 )= 1.0 / MAT( 0, 0 );
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return 0;
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}
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case 2: {
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double det= MAT( 0, 0 ) * MAT( 1, 1 ) - MAT( 0, 1 ) * MAT( 1, 0 );
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if( fabs( det ) < TOO_SMALL ){
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im_error( function_name, "singular or near-singular matrix" );
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return -1;
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}
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INV( 0, 0 )= MAT( 1, 1 ) / det;
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INV( 0, 1 )= -MAT( 0, 1 ) / det;
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INV( 1, 0 )= -MAT( 1, 0 ) / det;
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INV( 1, 1 )= MAT( 0, 0 ) / det;
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return 0;
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}
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case 3: {
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double det= MAT( 0, 0 ) * ( MAT( 1, 1 ) * MAT( 2, 2 ) - MAT( 1, 2 ) * MAT( 2, 1 ) )
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- MAT( 0, 1 ) * ( MAT( 1, 0 ) * MAT( 2, 2 ) - MAT( 1, 2 ) * MAT( 2, 0 ) )
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+ MAT( 0, 2 ) * ( MAT( 1, 0 ) * MAT( 2, 1 ) - MAT( 1, 1 ) * MAT( 2, 0 ) );
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if( fabs( det ) < TOO_SMALL ){
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im_error( function_name, "singular or near-singular matrix" );
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return -1;
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}
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INV( 0, 0 )= ( MAT( 1, 1 ) * MAT( 2, 2 ) - MAT( 1, 2 ) * MAT( 2, 1 ) ) / det;
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INV( 0, 1 )= ( MAT( 0, 2 ) * MAT( 2, 1 ) - MAT( 0, 1 ) * MAT( 2, 2 ) ) / det;
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INV( 0, 2 )= ( MAT( 0, 1 ) * MAT( 1, 2 ) - MAT( 0, 2 ) * MAT( 1, 1 ) ) / det;
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INV( 1, 0 )= ( MAT( 1, 2 ) * MAT( 2, 0 ) - MAT( 1, 0 ) * MAT( 2, 2 ) ) / det;
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INV( 1, 1 )= ( MAT( 0, 0 ) * MAT( 2, 2 ) - MAT( 0, 2 ) * MAT( 2, 0 ) ) / det;
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INV( 1, 2 )= ( MAT( 0, 2 ) * MAT( 1, 0 ) - MAT( 0, 0 ) * MAT( 1, 2 ) ) / det;
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INV( 2, 0 )= ( MAT( 1, 0 ) * MAT( 2, 1 ) - MAT( 1, 1 ) * MAT( 2, 0 ) ) / det;
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INV( 2, 1 )= ( MAT( 0, 1 ) * MAT( 2, 0 ) - MAT( 0, 0 ) * MAT( 2, 1 ) ) / det;
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INV( 2, 2 )= ( MAT( 0, 0 ) * MAT( 1, 1 ) - MAT( 0, 1 ) * MAT( 1, 0 ) ) / det;
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return 0;
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}
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default:
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return -1;
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}
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#undef N
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#undef MAT
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#undef INV
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}
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