src/gmxlib/nrjac.c

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