GSL complex matrix - eigenvalues/eigenvectors - c++

Question

I've written a program which is computing the eigenvalues and eigenvectors of a hermitian matrix.
Does anyone know how this is done in GSL properly? Here is what I already have.
//hermitian matrix
0 1 0 -i
1 0 -i 0
0 i 0 1
i 0 1 0
#include <iostream>
#include <stdio.h>
#include <cmath>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>
#include <gsl/gsl_eigen.h>
using namespace std;
const int N = 4;
int main(){
gsl_eigen_hermv_workspace *workN = gsl_eigen_hermv_alloc(N);
gsl_matrix_complex *A = gsl_matrix_complex_alloc(N, N);
gsl_complex i = gsl_complex_rect(0.0,1.0);
gsl_complex ii = gsl_complex_rect(0.0,-1.0);
gsl_vector *eval = gsl_vector_alloc(N);
gsl_matrix_complex *evec = gsl_matrix_complex_alloc(N, N);
double mTab[] = {
0, 1, 0, 5,
1, 0, 5, 0,
0, 5, 0, 1,
5, 0, 1, 0
};
gsl_matrix_complex_view tmpM = gsl_matrix_complex_view_array(mTab, N, N);
gsl_matrix_complex_memcpy(A, &tmpM.matrix);
gsl_matrix_complex_set(A, 0, 3, ii);
gsl_matrix_complex_set(A, 1, 2, ii);
gsl_matrix_complex_set(A, 2, 1, i);
gsl_matrix_complex_set(A, 3, 0, i);
gsl_eigen_hermv(A, eval, evec, workN);
for(int i=0; i < N; i++){
for(int j=0; j < N; j++){
gsl_complex z = gsl_matrix_complex_get(A, i, j);
cout << GSL_REAL(z) << "+ i" << GSL_IMAG(z) << " ";
}
cout << "\n";
}
cout << "\n";
for(int i=0; i < N; i++){
cout << gsl_vector_get(eval, i) << " ";
}
return 0;
}
This is how I output the eigenvectors
for(int i=0; i < N; i++){
for(int j=0; j < N; j++){
gsl_complex z = gsl_matrix_complex_get(A, i, j);
cout << GSL_REAL(z) << "+ i" << GSL_IMAG(z) << " ";
}
cout << "\n";
}
Finally, here's the way I declared the matrix in question.
double mTab[] = {
0, 1, 0, 5,
1, 0, 5, 0,
0, 5, 0, 1,
5, 0, 1, 0
};
Later, I added the complex numbers.
I managed to print the eigenvectors but I don't know how to do that for the eigenvalues. Any help with that is appreciated?.

Answer 1

You have an error in using the double mTab for gsl_matrix_complex_view_array. This assumes an array of complex numbers represented as real parts followed by imaginary parts in one large array of double values. You can change your definition to:
double mTab[] = {
0, 0, 1, 0, 0, 0, 5, 0,
1, 0, 0, 0, 5, 0, 0, 0,
0, 0, 5, 0, 0, 0, 1, 0,
5, 0, 0, 0, 1, 0, 0, 0,
};
(Which also means you don't need to use a "dummy" variable of 5 just to rewrite it by ±i later.) Then the code for printing eigenvalues works well.
Also you have a typo in the eigenvector printing loop: it should be
gsl_complex z = gsl_matrix_complex_get(evec, i, j);
not
gsl_complex z = gsl_matrix_complex_get(A, i, j);