void variational_H(){
/* Fill matricies */
read_basis();
printf("CALCULATING MATRIX ELEMENTS\n");
gsl_matrix *coefficents = gsl_matrix_alloc (num_eigenvalues, num_eigenvalues);
gsl_vector *energy = gsl_vector_alloc (num_eigenvalues);
for(char i=num_eigenvalues;i>=0;i--){
for(char j=num_eigenvalues;j>=i;j--){
overlap[num_eigenvalues*i + j] = overlap_elem(i,j);
overlap[num_eigenvalues*j + i] = overlap[num_eigenvalues*i + j];
hamiltonian[num_eigenvalues*i + j] = hamiltonian_elem(i,j);
hamiltonian[num_eigenvalues*j + i] = hamiltonian[num_eigenvalues*i + j];
}
}
printf("DIAGONALIZING MATRIX\n");
gsl_matrix_view s = gsl_matrix_view_array (overlap, 4, 4);
gsl_matrix_view h = gsl_matrix_view_array (hamiltonian, 4, 4);
gsl_eigen_gensymmv_workspace * eigen_sys = gsl_eigen_gensymmv_alloc(num_eigenvalues);
gsl_eigen_gensymmv(&h.matrix, &s.matrix, energy, coefficents, eigen_sys);
gsl_eigen_gensymmv_free(eigen_sys);
gsl_eigen_gensymmv_sort(energy, coefficents, GSL_EIGEN_SORT_VAL_DESC);
printf("DONE!\n");
printf("OUTPUT:\n");
for(char i=num_eigenvalues-1;i>=0;i--){
double energy_i = gsl_vector_get (energy, i);
printf("Energy level %d = %g\n", abs(i-num_eigenvalues) , energy_i);
}
printf("Coefficent Matrix for plotting\n");
for(char i=num_eigenvalues-1;i>=0;i--){
for(char j=num_eigenvalues-1;j>=0;j--){
printf("%g\t", gsl_matrix_get(coefficents,i,j));
}
printf("\n");
}
}
void
test_eigen_gensymm(void)
{
size_t N_max = 20;
size_t n, i;
gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
for (n = 1; n <= N_max; ++n)
{
gsl_matrix * A = gsl_matrix_alloc(n, n);
gsl_matrix * B = gsl_matrix_alloc(n, n);
gsl_matrix * ma = gsl_matrix_alloc(n, n);
gsl_matrix * mb = gsl_matrix_alloc(n, n);
gsl_vector * eval = gsl_vector_alloc(n);
gsl_vector * evalv = gsl_vector_alloc(n);
gsl_vector * x = gsl_vector_alloc(n);
gsl_vector * y = gsl_vector_alloc(n);
gsl_matrix * evec = gsl_matrix_alloc(n, n);
gsl_eigen_gensymm_workspace * w = gsl_eigen_gensymm_alloc(n);
gsl_eigen_gensymmv_workspace * wv = gsl_eigen_gensymmv_alloc(n);
for (i = 0; i < 5; ++i)
{
create_random_symm_matrix(A, r, -10, 10);
create_random_posdef_matrix(B, r);
gsl_matrix_memcpy(ma, A);
gsl_matrix_memcpy(mb, B);
gsl_eigen_gensymmv(ma, mb, evalv, evec, wv);
test_eigen_gensymm_results(A, B, evalv, evec, i, "random", "unsorted");
gsl_matrix_memcpy(ma, A);
gsl_matrix_memcpy(mb, B);
gsl_eigen_gensymm(ma, mb, eval, w);
/* eval and evalv have to be sorted? not sure why */
gsl_vector_memcpy(x, eval);
gsl_vector_memcpy(y, evalv);
gsl_sort_vector(x);
gsl_sort_vector(y);
test_eigenvalues_real(y, x, "gensymm, random", "unsorted");
gsl_eigen_gensymmv_sort(evalv, evec, GSL_EIGEN_SORT_VAL_ASC);
test_eigen_gensymm_results(A, B, evalv, evec, i, "random", "val/asc");
gsl_eigen_gensymmv_sort(evalv, evec, GSL_EIGEN_SORT_VAL_DESC);
test_eigen_gensymm_results(A, B, evalv, evec, i, "random", "val/desc");
gsl_eigen_gensymmv_sort(evalv, evec, GSL_EIGEN_SORT_ABS_ASC);
test_eigen_gensymm_results(A, B, evalv, evec, i, "random", "abs/asc");
gsl_eigen_gensymmv_sort(evalv, evec, GSL_EIGEN_SORT_ABS_DESC);
test_eigen_gensymm_results(A, B, evalv, evec, i, "random", "abs/desc");
}
gsl_matrix_free(A);
gsl_matrix_free(B);
gsl_matrix_free(ma);
gsl_matrix_free(mb);
gsl_vector_free(eval);
gsl_vector_free(evalv);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_matrix_free(evec);
gsl_eigen_gensymm_free(w);
gsl_eigen_gensymmv_free(wv);
}
gsl_rng_free(r);
} /* test_eigen_gensymm() */
