ABACUS/src/MATRIX/tred2.cc

#include "ABACUS.h"
using namespace std;

void ABACUS::tred2 (SQMat_DP& a, Vect_DP& d, Vect_DP& e)
{
  int l, k, j, i;
  DP scale, hh, h, g, f;

  int n = a.size();
  for (i = n-1; i > 0; i--) {
    l = i - 1;
    h = scale = 0.0;
    if (l > 0) {
      for (k = 0; k < l + 1; k++) scale += fabs(a[i][k]);
      if (scale == 0.0) e[i] = a[i][l];
      else {
	for (k = 0; k < l + 1; k++) {
	  a[i][k] /= scale;
	  h += a[i][k] * a[i][k];
	}
	f = a[i][l];
	g = (f >= 0.0 ? -sqrt(h) : sqrt(h));
	e[i] = scale * g;
	h -= f * g;
	a[i][l] = f - g;
	f = 0.0;
	for (j = 0; j < l + 1; j++) {
	  a[j][i] = a[i][j]/h;
	  g = 0.0;
	  for (k = 0; k < j + 1; k++) g += a[j][k] * a[i][k];
	  for (k = j + 1; k < l + 1; 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 + 1; j++) {
	  f = a[i][j];
	  e[j] = g = e[j] - hh * f;
	  for (k = 0; k < j + 1; k++) a[j][k] -= (f * e[k] + g * a[i][k]);
	}
      }
    } else
      e[i] = a[i][l];
      d[i] = h;
  }
  d[0] = 0.0;
  e[0] = 0.0;

  for (i = 0; i < n; i++) {
    l = i;
    if (d[i] != 0.0) {
      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;
  }
} // void tred2