-// This function is taken from Numerical Recipes in C++ by Press et al., 2nd edition, pg. 479
-
-void PCOACommand::tred2(vector<vector<double> >& a, vector<double>& d, vector<double>& e){
- try {
- double scale, hh, h, g, f;
-
- int n = a.size();
-
- d.resize(n);
- e.resize(n);
-
- for(int i=n-1;i>0;i--){
- int l=i-1;
- h = scale = 0.0000;
- if(l>0){
- for(int k=0;k<l+1;k++){
- scale += fabs(a[i][k]);
- }
- if(scale == 0.0){
- e[i] = a[i][l];
- }
- else{
- for(int 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(int j=0;j<l+1;j++){
- a[j][i] = a[i][j] / h;
- g = 0.0;
- for(int k=0;k<j+1;k++){
- g += a[j][k] * a[i][k];
- }
- for(int 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(int j=0;j<l+1;j++){
- f = a[i][j];
- e[j] = g = e[j] - hh * f;
- for(int 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] = 0.0000;
- e[0] = 0.0000;
-
- for(int i=0;i<n;i++){
- int l = i;
- if(d[i] != 0.0){
- for(int j=0;j<l;j++){
- g = 0.0000;
- for(int k=0;k<l;k++){
- g += a[i][k] * a[k][j];
- }
- for(int k=0;k<l;k++){
- a[k][j] -= g * a[k][i];
- }
- }
- }
- d[i] = a[i][i];
- a[i][i] = 1.0000;
- for(int j=0;j<l;j++){
- a[j][i] = a[i][j] = 0.0;
- }
- }
- }
- catch(exception& e) {
- m->errorOut(e, "PCOACommand", "tred2");
- exit(1);
- }
-
-}
-
-/*********************************************************************************************************************************/
-
-// This function is taken from Numerical Recipes in C++ by Press et al., 2nd edition, pg. 479
-
-void PCOACommand::qtli(vector<double>& d, vector<double>& e, vector<vector<double> >& z) {
- try {
- int m, i, iter;
- double s, r, p, g, f, dd, c, b;
-
- int n = d.size();
- for(int i=1;i<=n;i++){
- e[i-1] = e[i];
- }
- e[n-1] = 0.0000;
-
- for(int l=0;l<n;l++){
- iter = 0;
- do {
- for(m=l;m<n-1;m++){
- dd = fabs(d[m]) + fabs(d[m+1]);
- if(fabs(e[m])+dd == dd) break;
- }
- if(m != l){
- if(iter++ == 30) cerr << "Too many iterations in tqli\n";
- g = (d[l+1]-d[l]) / (2.0 * e[l]);
- r = pythag(g, 1.0);
- g = d[m] - d[l] + e[l] / (g + SIGN(r,g));
- s = c = 1.0;
- p = 0.0000;
- for(i=m-1;i>=l;i--){
- f = s * e[i];
- b = c * e[i];
- e[i+1] = (r=pythag(f,g));
- if(r==0.0){
- d[i+1] -= p;
- e[m] = 0.0000;
- break;
- }
- s = f / r;
- c = g / r;
- g = d[i+1] - p;
- r = (d[i] - g) * s + 2.0 * c * b;
- d[i+1] = g + ( p = s * r);
- g = c * r - b;
- for(int k=0;k<n;k++){
- f = z[k][i+1];
- z[k][i+1] = s * z[k][i] + c * f;
- z[k][i] = c * z[k][i] - s * f;
- }
- }
- if(r == 0.00 && i >= l) continue;
- d[l] -= p;
- e[l] = g;
- e[m] = 0.0;
- }
- } while (m != l);
- }
-
- int k;
- for(int i=0;i<n;i++){
- p=d[k=i];
- for(int j=i;j<n;j++){
- if(d[j] >= p){
- p=d[k=j];
- }
- }
- if(k!=i){
- d[k]=d[i];
- d[i]=p;
- for(int j=0;j<n;j++){
- p=z[j][i];
- z[j][i] = z[j][k];
- z[j][k] = p;
- }
- }
- }
- }
- catch(exception& e) {
- m->errorOut(e, "PCOACommand", "qtli");
- exit(1);
- }
-}
-
-/*********************************************************************************************************************************/
-