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/*===========================================================================
Copyright (C) 2001 European Southern Observatory (ESO)
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2 of
the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public
License along with this program; if not, write to the Free
Software Foundation, Inc., 675 Massachusetss Ave, Cambridge,
MA 02139, USA.
Corresponding concerning ESO-MIDAS should be addressed as follows:
Internet e-mail: midas@eso.org
Postal address: European Southern Observatory
Data Management Division
Karl-Schwarzschild-Strasse 2
D 85748 Garching bei Muenchen
GERMANY
===========================================================================*/
/* Program : scatter.c */
/* Author : G. Mulas - ITAL_FLAMES Consortium */
/* Date : */
/* */
/* Purpose : Missing */
/* */
/* */
/* Input: see interface */
/* */
/* Output: */
/* */
/* DRS Functions called: */
/* none */
/* */
/* Pseudocode: */
/* Missing */
/* */
/* Version : */
/* Last modification date: 2002/08/05 */
/* Who When Why Where */
/* AMo 02-08-05 Add header header */
/*-------------------------------------------------------------------------*/
#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include <uves_msg.h>
#include <string.h> //memset
#include <flames_gauss_jordan.h> //DRS_VERBOSITY
#include <flames_newmatrix.h> //DRS_VERBOSITY
#include <flames_def_drs_par.h> //DRS_VERBOSITY
static int nold = -1;
static int *indxc, *indxr, *ipiv;
static double
d_abs_f(double x)
{
if (x<0) return(-x);
return(x);
}
#define SWAP(a,b) {float temp=(a);(a)=(b);(b)=(temp);}
/* Wikipedia pseudocode
*
* Gaussian elimination writes a given m × n matrix A uniquely as a product of
* an invertible m × m matrix S and a row-echelon matrix T. Here, S is the
* product of the matrices corresponding to the row operations performed.
* The formal algorithm to compute T from A follows. We write A[i,j] for the
* entry in row i, column j in matrix A with 1 being the first index. The
* transformation is performed in place, meaning that the original matrix A is
* lost and successively replaced by T.
*
* for k = 1 ... min(m,n):
* Find the k-th pivot:
* i_max := argmax (i = k ... m, abs(A[i, k]))
* if A[i_max, k] = 0
* error "Matrix is singular!"
* swap rows(k, i_max)
* Do for all rows below pivot:
* for i = k + 1 ... m:
* Do for all remaining elements in current row:
* for j = k + 1 ... n:
* A[i, j] := A[i, j] - A[k, j] * (A[i, k] / A[k, k])
* Fill lower triangular matrix with zeros:
* A[i, k] := 0
*/
static int *indxc, *indxr, *ipiv;
int
flames_gauss_jordan(double **mA, int n, double **mB, int m)
{
int min_m_n= ( m < n ) ? m: n;
int k=0;
register int i=0;
register int j=0;
register int pivot;
double eps=1.e-30, epsn=-1.e-30;
int nr_mA=n;
//int nc_mA=n;
//int nr_mB=n;
//int nc_mB=n;
int ll=0;
int irow=0;
int icol=0;
int l=0;
double abs_ajk=0;
/* initialisation part */
/* we use an integer vector to know if pivot (divisor) was already found or
* not we use another integer vector to store the location of found rows or
* columns of the found pivots (divisors)
*/
if (n > nold)
{
/* initialise arrays */
if (nold > -1) /* not the very first time */
{
free_ivector(ipiv,1,nold);
free_ivector(indxr,1,nold);
free_ivector(indxc,1,nold);
}
indxc=ivector(1,n);
indxr=ivector(1,n);
ipiv=ivector(1,n);
nold = n;
}
for (j=1;j<=n;j++) ipiv[j]=0;
/* solving linear equation system Ax=B */
/* Note that our indexes all start from 1 and ends to the last element */
for( i = 1; i <= n; i++ ){
/* main loop over the columns to be reduced:
*
* we first need to find the so called input matrix pivot, which is the
* input matrix element used as reference to start to normalise to all
* the other elements. As wikipedia indicates the best choice is to get
* as pivot the coefficient with maximum absolute value. Thus the
* algorithm starts with a maximum search.
* See also implementation by Stoer, Numerische Mathematik, 1. Teil.
*/
register double max=0.0;
for ( j = 1; j <= n; j++ ) {
/* outer loop of the search of the j-th pivot (divisor) element: */
if ( ipiv[j] != 1 ) {
/* search for maximum of matrix Ajk coefficients */
for (k=1;k<=n;k++) {
pivot = ipiv[k];
if ( pivot == 0 ) {
//int jj = j * nr_mA;
abs_ajk = d_abs_f( mA[j][k] );
if ( abs_ajk >= max ) {
/* found a maximum candidate
* update its value and position in the matrix
*/
max = abs_ajk;
irow=j;
icol=k;
}
} else if ( pivot > 1 ) {
uves_msg_error("GAUSSJ: Singular Matrix-1");
free_ivector(ipiv,1,nold);
free_ivector(indxr,1,nold);
free_ivector(indxc,1,nold);
nold = -1;
return(-1);
}
}
}
}
/* We now have the pivot, so we swap rows, for all rows below pivot,
* if needed, to put the pivot element on the diagonal. The columns are
* not physically interchanged, they are only re-labeled
*/
++(ipiv[icol]);
if (irow != icol) {
for (l = 1; l <= n; l++) {
SWAP(mA[irow][l], mA[icol][l])
}
for (l = 1; l <= m; l++) {
SWAP(mB[irow][l], mB[icol][l])
}
}
indxr[i] = irow;
indxc[i] = icol;
register double factor = mA[icol][icol];
/* As on real data factor may be small but not exactly zero we replace
* the check versus 0.0 with a check versus a small number eps=1.e-30
*/
if ( ( factor < eps ) && ( factor > epsn ) ) {
//if ( mA[icol][icol] == 0.0 ) {
/* We cannot divide by 0: matrix singular 2 */
uves_msg_error("GAUSSJ: Singular Matrix-2");
free_ivector(ipiv,1,nold);
free_ivector(indxr,1,nold);
free_ivector(indxc,1,nold);
nold = -1;
return(-2);
}
/* Now we can divide the pivot row by the pivot element */
register double inv_pivot = 1.0 / factor;
/* the diagonal element should be by definition 1: to prevent numerical
* errors we set it as such
*/
mA[icol][icol] = 1.0;
for (l = 1; l <= n; l++) {
mA[icol][l] *= inv_pivot;
}
for (l = 1; l <= m; l++) {
mB[icol][l] *= inv_pivot;
}
for (ll = 1; ll <= n; ll++) {
/* reduce the rows... except for the pivot one */
if (ll != icol) {
factor = mA[ll][icol];
/* the reference column has to be 0.0 by definition */
mA[ll][icol] = 0.0;
for (l = 1; l <= n; l++) {
mA[ll][l] -= mA[icol][l] * factor;
}
for (l = 1; l <= m; l++) {
mB[ll][l] -= mB[icol][l] * factor;
}
}
}
}
//free_ivector(ipiv,1,nold);
/* re-permute columns */
for (l = n; l >= 1; l--) {
if (indxr[l] != indxc[l]) {
for (k = 1; k <= n; k++) {
SWAP( mA[k][indxr[l]], mA[k][indxc[l]]);
}
}
}
//free_ivector(indxr,1,nold);
//free_ivector(indxc,1,nold);
return 0;
}
#undef SWAP
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