inline
typename T1::pod_type
op_norm::mat_norm_2(const SpProxy<T1>& P, const typename arma_real_only<typename T1::elem_type>::result* junk)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
// norm = sqrt( largest eigenvalue of (A^H)*A ), where ^H is the conjugate transpose
// http://math.stackexchange.com/questions/4368/computing-the-largest-eigenvalue-of-a-very-large-sparse-matrix
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
const unwrap_spmat<typename SpProxy<T1>::stored_type> tmp(P.Q);
const SpMat<eT>& A = tmp.M;
const SpMat<eT> B = trans(A);
const SpMat<eT> C = (A.n_rows <= A.n_cols) ? (A*B) : (B*A);
Col<T> eigval;
eigs_sym(eigval, C, 1);
return (eigval.n_elem > 0) ? std::sqrt(eigval[0]) : T(0);
}
void fmat_pca_from_covariance(int d,const float *cov, float *singvals, float * pcamat)
{
float *evals=singvals;
if(!singvals) evals=fvec_new(d);
if(eigs_sym(d,cov,evals,pcamat)!=0) {
free(pcamat);
pcamat=NULL;
goto error;
}
eigs_reorder(d,evals,pcamat,1); /* 1 = descending */
error:
if(!singvals) free(evals);
}
int main()
{
int i, j, k, d = 10,d2=5;
float * a = fvec_new (d * d);
float * b = fvec_new (d * d);
float * b0 = fvec_new (d * d);
#define B0(i,j) b0[(i)+(j)*d]
#define A(i,j) a[(i)+(j)*d]
#define B(i,j) b[(i)+(j)*d]
float * lambda = fvec_new (d);
float * v = fvec_new (d * d);
float *v_part=fvec_new (d * d2);
for (i = 0 ; i < d ; i++)
for (j = 0 ; j <= i ; j++) {
A(i,j) = A(j,i) = drand48();
B0(i,j)=drand48();
B0(j,i)=drand48();
/* B(i,j) = B(j,i) = drand48(); */
}
/* make a positive definite b (with b=b0*b0') */
for (i = 0 ; i < d ; i++)
for (j = 0 ; j < d ; j++) {
double accu=0;
for(k=0;k<d;k++)
accu+=B0(i,k)*B0(j,k);
B(i,j)=accu;
}
printf ("a = ");
fmat_print(a,d,d);
printf ("\nb = ");
fmat_print(b,d,d);
printf ("Solution of the eigenproblem Av=lambda v\n");
printf ("\n");
int ret=eigs_sym (d, a, lambda, v);
assert(ret==0);
printf ("\n");
printf("Eigenvectors:\n");
fmat_print(v,d,d);
fprintf(stdout, "lambda = ");
fvec_print (lambda, d);
printf ("\n");
printf("Partial eigenvalues/vectors:\n");
printf ("\n");
ret=eigs_sym_part (d, a, d2, lambda, v_part);
assert(ret>0);
if(ret<d2)
printf("!!! only %d / %d eigenvalues converged\n",ret,d2);
printf ("\n");
printf("Eigenvectors:\n");
fmat_print(v_part,d,d2);
fprintf(stdout, "lambda = ");
fvec_print (lambda, d2);
printf ("\n");
printf ("Solution of the generalized eigenproblem Av=lambda B v\n");
printf ("\n");
ret=geigs_sym (d, a, b, lambda, v);
assert(ret==0);
printf ("\n");
fmat_print(v,d,d);
fprintf(stdout, "lambda = ");
fvec_print (lambda, d);
printf ("\n");
free (a);
free (lambda);
free (v);
return 0;
}
