void expm(gsl_matrix_complex * L, gsl_complex t, gsl_matrix * m)
{
int i,j,s;
gsl_vector_complex *eval = gsl_vector_complex_alloc(4);
gsl_matrix_complex *evec = gsl_matrix_complex_alloc(4, 4);
gsl_eigen_nonsymmv_workspace * w = gsl_eigen_nonsymmv_alloc(4);
gsl_matrix_complex *evalmat = gsl_matrix_complex_alloc(4, 4);
gsl_matrix_complex *vd = gsl_matrix_complex_alloc(4, 4);
gsl_complex one = gsl_complex_rect(1, 0);
gsl_complex zero = gsl_complex_rect(0, 0);
gsl_matrix_complex *K = gsl_matrix_complex_alloc(4, 4);
gsl_permutation *p = gsl_permutation_alloc(4);
gsl_vector_complex *x = gsl_vector_complex_alloc(4);
gsl_vector_complex_view bp;
gsl_complex z;
gsl_eigen_nonsymmv(m, eval, evec, w);
gsl_eigen_nonsymmv_sort(eval, evec, GSL_EIGEN_SORT_ABS_DESC);
gsl_eigen_nonsymmv_free(w); // clear workspace
for (i = 0; i < 4; i++)
{
gsl_complex eval_i = gsl_vector_complex_get(eval, i);
gsl_complex expeval = gsl_complex_mul(eval_i,t);
expeval = gsl_complex_exp(expeval);
gsl_matrix_complex_set(evalmat, i, i, expeval);
}
gsl_vector_complex_free(eval); // clear vector for eigenvalues
// v'L'=De'v'
gsl_blas_zgemm(CblasTrans, CblasTrans, one, evalmat, evec, zero, vd);
gsl_matrix_complex_transpose(evec);//transpose v
gsl_matrix_complex_memcpy(K,evec);
for (i = 0; i < 4; i++)
{
bp = gsl_matrix_complex_column(vd, i);
gsl_linalg_complex_LU_decomp(evec, p, &s);
gsl_linalg_complex_LU_solve(evec, p, &bp.vector, x);
for (j = 0; j < 4; j++)
{
z = gsl_vector_complex_get(x, j);
gsl_matrix_complex_set(L,i,j,z); //'through the looking glass' transpose
}
gsl_matrix_complex_memcpy(evec,K);
}
gsl_permutation_free(p);
gsl_vector_complex_free(x);
gsl_matrix_complex_free(vd);
gsl_matrix_complex_free(evec);
gsl_matrix_complex_free(evalmat);
gsl_matrix_complex_free(K);
}
/*!
Returns true if the input matrix is Hermitian.
*/
bool IsHermitian(const gsl_matrix_complex * const M)
{
gsl_matrix_complex *N;
gsl_complex zm, zn;
int i, j;
bool isHerm = true;
N = gsl_matrix_complex_alloc(M->size1, M->size2);
for(i = 0; i < M->size1; ++i)
{
for(j = 0; j < M->size2; ++j)
{
zm = gsl_matrix_complex_get(M, i, j);
GSL_SET_COMPLEX(&zn, GSL_REAL(zm), ((-1)*GSL_IMAG(zm)));
gsl_matrix_complex_set(N, i, j, zn);
}
}
gsl_matrix_complex_transpose(N);
for(i = 0; i < M->size1; ++i)
{
for(j = 0; j < M->size2; ++j)
{
zm = gsl_matrix_complex_get(M, i, j);
zn = gsl_matrix_complex_get(N, i, j);
if( GSL_REAL(zm) != GSL_REAL(zn) ||
GSL_IMAG(zm) != GSL_IMAG(zn) )
{
isHerm = false;
goto _exit;
}
}
}
_exit:
gsl_matrix_complex_free(N);
return isHerm;
}
bool Matrix_Transpose(gsl_matrix_complex *A){
gsl_matrix_complex_transpose(A);
return true;
}