/*                               20.MAY.2003                          tred2.cc
                                                 from "Numerical Recipes in C"
 
   This function performs a Householder reduction of a real, symmetric
   matrix **a to tridiagonal form. On output, a is replaced by
   the orthogonal matrix effecting the transformation. The diagonal
   elements are stored in d[], and the subdiagonal elements are stored
   in e[].
 
*/
 
#include <math.h>
#include "corso.h"
 
void tred2(double **a,double *d,double *e,int n)
{
  int i,j,k,l;
  double f,g,h,hh,scale;
 
  for (i=n-1;i>0;i--)
    { l=i-1;h=scale=0.0;
      if (l>0)
        { for (k=0;k<=l;k++) scale+=fabs(a[i][k]);
	  if (scale==0.0) {e[i]=a[i][l];continue;}// .....skip transformation
          // .............................. use scaled a's for transformation
	  for (k=0;k<=l;k++) { a[i][k]/=scale;h+=a[i][k]*a[i][k];}
	  f=a[i][l];
	  g=sqrt(h);
	  if (f>0.0) g=-g;
	  e[i]=scale*g;
	  h-=f*g;
	  a[i][l]=f-g;
	  f=0.0;
	  for (j=0;j<=l;j++)
	    { a[j][i]=a[i][j]/h;g=0.0;
	      for (k=0;k<=j;k++) g+=a[j][k]*a[i][k];
	      for (k=j+1;k<=l;k++) g+=a[k][j]*a[i][k];
	      e[j]=g/h;
	      f += e[j]*a[i][j];
	    }
	  hh=f/(h+h);
	  for (j=0;j<=l;j++)
	    { f=a[i][j];e[j]=g=e[j]-hh*f;
	      for (k=0;k<=j;k++) a[j][k]-=(f*e[k]+g*a[i][k]);
	    }
        }
      else e[i]=a[i][l];
      d[i]=h;
    }
  // ............................................................ eigenvectors
  d[0]=0.0;e[0]=0.0;
  for (i=0;i<n;i++)
    { l=i-1;
      if (d[i])
        { for (j=0;j<=l;j++)
            { g=0.0;
              for (k=0;k<=l;k++) g+=a[i][k]*a[k][j];
              for (k=0;k<=l;k++) a[k][j]-=g*a[k][i];
            }
        }
      d[i]=a[i][i];
      a[i][i]=1.0;
      for (j=0;j<=l;j++) a[j][i]=a[i][j]=0.0;
    }
  for (i=0;i<n-1;i++) e[i]=e[i+1];
  e[n-1]=0;
  // .......................................... complete transformation matrix
  for (i=0;i<n;i++) for (j=i+1;j<n;j++) a[i][j]=a[j][i];
}