static float
f14_maxcorr (float ** const p,
unsigned int const ng) {
/*----------------------------------------------------------------------------
The Maximal Correlation Coefficient
-----------------------------------------------------------------------------*/
unsigned int i;
float *px, *py;
float ** q;
float * x;
float * iy;
float tmp;
px = vector(0, ng);
py = vector(0, ng);
q = matrix(1, ng + 1, 1, ng + 1);
x = vector(1, ng);
iy = vector(1, ng);
/*
* px[i] is the (i-1)th entry in the marginal probability matrix obtained
* by summing the rows of p[i][j]
*/
for (i = 0; i < ng; ++i) {
unsigned int j;
for (j = 0; j < ng; ++j) {
px[i] += p[i][j];
py[j] += p[i][j];
}
}
/* Compute the Q matrix */
for (i = 0; i < ng; ++i) {
unsigned int j;
for (j = 0; j < ng; ++j) {
unsigned int k;
q[i + 1][j + 1] = 0;
for (k = 0; k < ng; ++k)
q[i + 1][j + 1] += p[i][k] * p[j][k] / px[i] / py[k];
}
}
/* Balance the matrix */
mkbalanced(q, ng);
/* Reduction to Hessenberg Form */
reduction(q, ng);
/* Finding eigenvalue for nonsymetric matrix using QR algorithm */
hessenberg(q, ng, x, iy);
if (sortit)
simplesrt(ng, x);
/* Return the sqrt of the second largest eigenvalue of q */
for (i = 2, tmp = x[1]; i <= ng; ++i)
tmp = (tmp > x[i]) ? tmp : x[i];
return sqrt(x[ng - 1]);
}
int main(){
int m,n,i,j;
scanf("%d %d",&n,&m);
mat A(n,m), hessenberg_form(n,m);
printf(" Reading an %d x %d matrix...\n",n,m);
for(i=0;i<A.size1();i++) for(j=0;j<A.size2();j++) scanf("%lf", &A(i,j));
printf(" A= \n");matprintf(A);
hessenberg_form = hessenberg(A,n,m);
printf(" Matrix reduced to Hessenberg form:\n");matprintf(hessenberg_form);
exit(0);
}
void v::eig(vectorn& eigenValues, const matrixn& mat)
{
//#define SYMMETRIC_TRIDIAGONAL
#ifdef SYMMETRIC_TRIDIAGONAL
ASSERT(mat.isValid());
matrixn symData(mat);
ASSERT(symData.isValid());
vectorn e;
eigenValues.setSize(mat.rows());
e.setSize(mat.rows());
NR::tred2(symData, eigenValues, e);
ASSERT(symData.isValid());
NR::tqli(eigenValues, e,symData);
int dim=eigenValues.size();
#else
matrixn hessenberg (mat);
// balance matrix
//NR::balanc(hessenberg);
// reduce to hessenberg form *****"
NR::elmhes(hessenberg);
Vec_CPLX_DP wri(hessenberg.rows());
NR::hqr(hessenberg,wri);
eigenValues.setSize(wri.size());
for (int i=0;i<wri.size();i++)
eigenValues[i]=wri[i].real();
#endif
/*
matrixn& EVectors=*this;
EVectors.setSize(dim,dim);
// Now each row contains EigenVector
for (int i = 0; i < dim; i++) {
for (int j = 0; j < dim; j++) {
EVectors[i][j] = symData[j][i];
}
}*/
}
/* Returns the Maximal Correlation Coefficient */
double f14_maxcorr (double **P, int Ng) {
int i, j, k;
double *px, *py, **Q;
double *x, *iy, tmp;
double f;
px = allocate_vector (0, Ng);
py = allocate_vector (0, Ng);
Q = allocate_matrix (1, Ng + 1, 1, Ng + 1);
x = allocate_vector (1, Ng);
iy = allocate_vector (1, Ng);
/*
* px[i] is the (i-1)th entry in the marginal probability matrix obtained
* by summing the rows of p[i][j]
*/
for (i = 0; i < Ng; ++i) {
for (j = 0; j < Ng; ++j) {
px[i] += P[i][j];
py[j] += P[i][j];
}
}
/* Find the Q matrix */
for (i = 0; i < Ng; ++i) {
for (j = 0; j < Ng; ++j) {
Q[i + 1][j + 1] = 0;
for (k = 0; k < Ng; ++k)
Q[i + 1][j + 1] += P[i][k] * P[j][k] / px[i] / py[k];
}
}
/* Balance the matrix */
mkbalanced (Q, Ng);
/* Reduction to Hessenberg Form */
reduction (Q, Ng);
/* Finding eigenvalue for nonsymetric matrix using QR algorithm */
if (!hessenberg (Q, Ng, x, iy)) {
/* Memmory cleanup */
for (i=1; i<=Ng+1; i++) free(Q[i]+1);
free(Q+1);
free((char *)px);
free((char *)py);
free((x+1));
free((iy+1));
/* computation failed ! */
return 0.0;
}
/* simplesrt(Ng,x); */
/* Returns the sqrt of the second largest eigenvalue of Q */
for (i = 2, tmp = x[1]; i <= Ng; ++i)
tmp = (tmp > x[i]) ? tmp : x[i];
f = sqrt(x[Ng - 1]);
for (i=1; i<=Ng+1; i++) free(Q[i]+1);
free(Q+1);
free((char *)px);
free((char *)py);
free((x+1));
free((iy+1));
return f;
}
