| 1 | /*
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| 2 | *+
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| 3 | * Name:
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| 4 | * palDmat
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| 5 |
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| 6 | * Purpose:
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| 7 | * Matrix inversion & solution of simultaneous equations
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| 8 |
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| 9 | * Language:
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| 10 | * Starlink ANSI C
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| 11 |
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| 12 | * Type of Module:
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| 13 | * Library routine
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| 14 |
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| 15 | * Invocation:
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| 16 | * void palDmat( int n, double *a, double *y, double *d, int *jf,
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| 17 | * int *iw );
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| 18 |
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| 19 | * Arguments:
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| 20 | * n = int (Given)
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| 21 | * Number of simultaneous equations and number of unknowns.
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| 22 | * a = double[] (Given & Returned)
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| 23 | * A non-singular NxN matrix (implemented as a contiguous block
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| 24 | * of memory). After calling this routine "a" contains the
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| 25 | * inverse of the matrix.
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| 26 | * y = double[] (Given & Returned)
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| 27 | * On input the vector of N knowns. On exit this vector contains the
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| 28 | * N solutions.
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| 29 | * d = double * (Returned)
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| 30 | * The determinant.
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| 31 | * jf = int * (Returned)
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| 32 | * The singularity flag. If the matrix is non-singular, jf=0
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| 33 | * is returned. If the matrix is singular, jf=-1 & d=0.0 are
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| 34 | * returned. In the latter case, the contents of array "a" on
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| 35 | * return are undefined.
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| 36 | * iw = int[] (Given)
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| 37 | * Integer workspace of size N.
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| 38 |
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| 39 | * Description:
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| 40 | * Matrix inversion & solution of simultaneous equations
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| 41 | * For the set of n simultaneous equations in n unknowns:
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| 42 | * A.Y = X
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| 43 | * this routine calculates the inverse of A, the determinant
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| 44 | * of matrix A and the vector of N unknowns.
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| 45 |
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| 46 | * Authors:
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| 47 | * PTW: Pat Wallace (STFC)
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| 48 | * TIMJ: Tim Jenness (JAC, Hawaii)
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| 49 | * {enter_new_authors_here}
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| 50 |
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| 51 | * History:
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| 52 | * 2012-02-11 (TIMJ):
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| 53 | * Combination of a port of the Fortran and a comparison
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| 54 | * with the obfuscated GPL C routine.
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| 55 | * Adapted with permission from the Fortran SLALIB library.
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| 56 | * {enter_further_changes_here}
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| 57 |
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| 58 | * Notes:
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| 59 | * - Implemented using Gaussian elimination with partial pivoting.
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| 60 | * - Optimized for speed rather than accuracy with errors 1 to 4
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| 61 | * times those of routines optimized for accuracy.
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| 62 |
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| 63 | * Copyright:
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| 64 | * Copyright (C) 2001 Rutherford Appleton Laboratory.
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| 65 | * Copyright (C) 2012 Science and Technology Facilities Council.
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| 66 | * All Rights Reserved.
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| 67 |
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| 68 | * Licence:
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| 69 | * This program is free software: you can redistribute it and/or
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| 70 | * modify it under the terms of the GNU Lesser General Public
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| 71 | * License as published by the Free Software Foundation, either
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| 72 | * version 3 of the License, or (at your option) any later
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| 73 | * version.
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| 74 | *
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| 75 | * This program is distributed in the hope that it will be useful,
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| 76 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 77 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 78 | * GNU Lesser General Public License for more details.
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| 79 | *
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| 80 | * You should have received a copy of the GNU Lesser General
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| 81 | * License along with this program. If not, see
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| 82 | * <http://www.gnu.org/licenses/>.
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| 83 |
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| 84 | * Bugs:
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| 85 | * {note_any_bugs_here}
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| 86 | *-
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| 87 | */
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| 88 |
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| 89 | #include "pal.h"
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| 90 |
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| 91 | void palDmat ( int n, double *a, double *y, double *d, int *jf, int *iw ) {
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| 92 |
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| 93 | const double SFA = 1e-20;
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| 94 |
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| 95 | int k;
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| 96 | double*aoff;
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| 97 |
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| 98 | *jf=0;
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| 99 | *d=1.0;
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| 100 | for(k=0,aoff=a; k<n; k++, aoff+=n){
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| 101 | int imx;
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| 102 | double * aoff2 = aoff;
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| 103 | double amx=fabs(aoff[k]);
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| 104 | imx=k;
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| 105 | if(k!=n){
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| 106 | int i;
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| 107 | double *apos2;
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| 108 | for(i=k+1,apos2=aoff+n;i<n;i++,apos2+=n){
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| 109 | double t=fabs(apos2[k]);
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| 110 | if(t>amx){
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| 111 | amx=t;
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| 112 | imx=i;
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| 113 | aoff2=apos2;
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| 114 | }
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| 115 | }
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| 116 | }
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| 117 | if(amx<SFA){
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| 118 | *jf=-1;
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| 119 | } else {
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| 120 | if(imx!=k){
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| 121 | double t;
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| 122 | int j;
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| 123 | for(j=0;j<n;j++){
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| 124 | t=aoff[j];
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| 125 | aoff[j]=aoff2[j];
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| 126 | aoff2[j]=t;
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| 127 | }
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| 128 | t=y[k];
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| 129 | y[k]=y[imx];
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| 130 | y[imx]=t;*d=-*d;
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| 131 | }
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| 132 | iw[k]=imx;
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| 133 | *d*=aoff[k];
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| 134 | if(fabs(*d)<SFA){
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| 135 | *jf=-1;
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| 136 | } else {
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| 137 | double yk;
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| 138 | double * apos2;
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| 139 | int i, j;
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| 140 | aoff[k]=1.0/aoff[k];
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| 141 | for(j=0;j<n;j++){
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| 142 | if(j!=k){
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| 143 | aoff[j]*=aoff[k];
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| 144 | }
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| 145 | }
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| 146 | yk=y[k]*aoff[k];
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| 147 | y[k]=yk;
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| 148 | for(i=0,apos2=a;i<n;i++,apos2+=n){
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| 149 | if(i!=k){
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| 150 | for(j=0;j<n;j++){
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| 151 | if(j!=k){
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| 152 | apos2[j]-=apos2[k]*aoff[j];
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| 153 | }
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| 154 | }
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| 155 | y[i]-=apos2[k]*yk;
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| 156 | }
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| 157 | }
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| 158 | for(i=0,apos2=a;i<n;i++,apos2+=n){
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| 159 | if(i!=k){
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| 160 | apos2[k]*=-aoff[k];
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| 161 | }
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| 162 | }
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| 163 | }
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| 164 | }
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| 165 | }
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| 166 | if(*jf!=0){
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| 167 | *d=0.0;
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| 168 | } else {
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| 169 | for(k=n;k-->0;){
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| 170 | int ki=iw[k];
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| 171 | if(k!=ki){
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| 172 | int i;
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| 173 | double *apos = a;
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| 174 | for(i=0;i<n;i++,apos+=n){
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| 175 | double t=apos[k];
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| 176 | apos[k]=apos[ki];
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| 177 | apos[ki]=t;
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| 178 | }
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| 179 | }
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| 180 | }
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| 181 | }
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| 182 | }
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