src/gmxlib/nrjac.c

   1 /*
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   9  *                        VERSION 3.2.0
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  12  * Copyright (c) 2001-2004, The GROMACS development team,
  13  * check out http://www.gromacs.org for more information.
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  15  * This program is free software; you can redistribute it and/or
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  35 /* This file is completely threadsafe - keep it that way! */
  36 #ifdef HAVE_CONFIG_H
  37 #include <config.h>
  38 #endif
  39
  40 #include <stdio.h>
  41 #include <stdlib.h>
  42 #include <math.h>
  43 #include "gstat.h"
  44 #include "smalloc.h"
  45 #include "gmx_fatal.h"
  46 #include "nrjac.h"
  47
  48
  49 #define ROTATE(a,i,j,k,l) g=a[i][j];h=a[k][l];a[i][j]=g-s*(h+g*tau);\
  50   a[k][l]=h+s*(g-h*tau);
  51
  52 void jacobi(double **a,int n,double d[],double **v,int *nrot)
  53 {
  54   int j,i;
  55   int iq,ip;
  56   double tresh,theta,tau,t,sm,s,h,g,c,*b,*z;
  57
  58   snew(b,n);
  59   snew(z,n);
  60   for (ip=0; ip<n; ip++) {
  61     for (iq=0; iq<n; iq++) v[ip][iq]=0.0;
  62     v[ip][ip]=1.0;
  63  }
  64   for (ip=0; ip<n;ip++) {
  65     b[ip]=d[ip]=a[ip][ip];
  66     z[ip]=0.0;
  67   }
  68   *nrot=0;
  69   for (i=1; i<=50; i++) {
  70     sm=0.0;
  71     for (ip=0; ip<n-1; ip++) {
  72       for (iq=ip+1; iq<n; iq++)
  73         sm += fabs(a[ip][iq]);
  74     }
  75     if (sm == 0.0) {
  76       sfree(z);
  77       sfree(b);
  78       return;
  79     }
  80     if (i < 4)
  81       tresh=0.2*sm/(n*n);
  82     else
  83       tresh=0.0;
  84     for (ip=0; ip<n-1; ip++) {
  85       for (iq=ip+1; iq<n; iq++) {
  86         g=100.0*fabs(a[ip][iq]);
  87         if (i > 4 && fabs(d[ip])+g == fabs(d[ip])
  88             && fabs(d[iq])+g == fabs(d[iq]))
  89           a[ip][iq]=0.0;
  90         else if (fabs(a[ip][iq]) > tresh) {
  91           h=d[iq]-d[ip];
  92           if (fabs(h)+g == fabs(h))
  93             t=(a[ip][iq])/h;
  94           else {
  95             theta=0.5*h/(a[ip][iq]);
  96             t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
  97             if (theta < 0.0) t = -t;
  98           }
  99           c=1.0/sqrt(1+t*t);
 100           s=t*c;
 101           tau=s/(1.0+c);
 102           h=t*a[ip][iq];
 103           z[ip] -= h;
 104           z[iq] += h;
 105           d[ip] -= h;
 106           d[iq] += h;
 107           a[ip][iq]=0.0;
 108           for (j=0; j<ip; j++) {
 109             ROTATE(a,j,ip,j,iq)
 110           }
 111           for (j=ip+1; j<iq; j++) {
 112             ROTATE(a,ip,j,j,iq)
 113             }
 114           for (j=iq+1; j<n; j++) {
 115             ROTATE(a,ip,j,iq,j)
 116             }
 117           for (j=0; j<n; j++) {
 118             ROTATE(v,j,ip,j,iq)
 119             }
 120           ++(*nrot);
 121         }
 122       }
 123     }
 124     for (ip=0; ip<n; ip++) {
 125       b[ip] +=  z[ip];
 126       d[ip]  =  b[ip];
 127       z[ip]  =  0.0;
 128     }
 129   }
 130   gmx_fatal(FARGS,"Error: Too many iterations in routine JACOBI\n");
 131 }
 132
 133 int m_inv_gen(real **m,int n,real **minv)
 134 {
 135   double **md,**v,*eig,tol,s;
 136   int    nzero,i,j,k,nrot;
 137
 138   snew(md,n);
 139   for(i=0; i<n; i++)
 140     snew(md[i],n);
 141   snew(v,n);
 142   for(i=0; i<n; i++)
 143     snew(v[i],n);
 144   snew(eig,n);
 145   for(i=0; i<n; i++)
 146     for(j=0; j<n; j++)
 147       md[i][j] = m[i][j];
 148
 149   tol = 0;
 150   for(i=0; i<n; i++)
 151     tol += fabs(md[i][i]);
 152   tol = 1e-6*tol/n;
 153
 154   jacobi(md,n,eig,v,&nrot);
 155
 156   nzero = 0;
 157   for(i=0; i<n; i++)
 158     if (fabs(eig[i]) < tol) {
 159       eig[i] = 0;
 160       nzero++;
 161     } else
 162       eig[i] = 1.0/eig[i];
 163
 164   for(i=0; i<n; i++)
 165     for(j=0; j<n; j++) {
 166       s = 0;
 167       for(k=0; k<n; k++)
 168         s += eig[k]*v[i][k]*v[j][k];
 169       minv[i][j] = s;
 170     }
 171
 172   sfree(eig);
 173   for(i=0; i<n; i++)
 174     sfree(v[i]);
 175   sfree(v);
 176   for(i=0; i<n; i++)
 177     sfree(md[i]);
 178   sfree(md);
 179
 180   return nzero;
 181 }