/*
computes the svd of a complex matrix. Missing in gsl.
*/
int
svd(gsl_matrix_complex *A, gsl_matrix_complex *V, gsl_vector *S)
{
int n = A->size1;
gsl_eigen_hermv_workspace *gsl_work = gsl_eigen_hermv_alloc(n);
gsl_matrix_complex *Asq = gsl_matrix_complex_alloc(n, n);
gsl_complex zero = gsl_complex_rect(0., 0.);
gsl_complex one = gsl_complex_rect(1., 0.);
gsl_vector *e = gsl_vector_alloc(n);
gsl_matrix_complex *U = gsl_matrix_complex_alloc(n, n);
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, one, A, A, zero, Asq);
gsl_eigen_hermv(Asq, e, U, gsl_work);
gsl_eigen_hermv_sort(e, U, GSL_EIGEN_SORT_VAL_DESC);
gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one, A, A, zero, Asq);
gsl_eigen_hermv(Asq, e, V, gsl_work);
gsl_eigen_hermv_sort(e, V, GSL_EIGEN_SORT_VAL_DESC);
gsl_blas_zgemm(CblasNoTrans, CblasNoTrans, one, A, V, zero, Asq);
gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one, U, Asq, zero, A);
for(int i=0; i<n; i++){
gsl_complex x = gsl_matrix_complex_get(A, i, i);
double phase = gsl_complex_arg(gsl_complex_mul_real(x, 1./sqrt(e->data[i])));
gsl_vector_complex_view U_col = gsl_matrix_complex_column(U, i);
gsl_vector_complex_scale(&U_col.vector, gsl_complex_polar(1., phase));
gsl_vector_set(S, i, sqrt(gsl_vector_get(e, i)));
}
gsl_matrix_complex_memcpy(A, U);
gsl_vector_free(e);
gsl_matrix_complex_free(U);
gsl_matrix_complex_free(Asq);
gsl_eigen_hermv_free(gsl_work);
return 0;
}
/// Multiply by a number
/// @param d :: The number
ComplexVector &ComplexVector::operator*=(const ComplexType d) {
gsl_vector_complex_scale(gsl(), gsl_complex{{d.real(), d.imag()}});
return *this;
}
int
lls_complex_stdform(gsl_matrix_complex *A, gsl_vector_complex *b,
const gsl_vector *wts, const gsl_vector *L,
lls_complex_workspace *w)
{
const size_t n = A->size1;
const size_t p = A->size2;
if (p != w->p)
{
fprintf(stderr, "lls_complex_stdform: A has wrong size2\n");
return GSL_EBADLEN;
}
else if (n != b->size)
{
fprintf(stderr, "lls_complex_stdform: b has wrong size\n");
return GSL_EBADLEN;
}
else if (wts != NULL && n != wts->size)
{
fprintf(stderr, "lls_complex_stdform: wts has wrong size\n");
return GSL_EBADLEN;
}
else if (L != NULL && p != L->size)
{
fprintf(stderr, "lls_complex_stdform: L has wrong size\n");
return GSL_EBADLEN;
}
else
{
int s = 0;
size_t i;
if (wts != NULL)
{
for (i = 0; i < n; ++i)
{
gsl_vector_complex_view rv = gsl_matrix_complex_row(A, i);
gsl_complex bi = gsl_vector_complex_get(b, i);
double wi = gsl_vector_get(wts, i);
double sqrtwi = sqrt(wi);
gsl_complex val;
GSL_SET_COMPLEX(&val, sqrtwi, 0.0);
/* A <- sqrt(W) A */
gsl_vector_complex_scale(&rv.vector, val);
/* b <- sqrt(W) b */
val = gsl_complex_mul_real(bi, sqrtwi);
gsl_vector_complex_set(b, i, val);
}
}
if (L != NULL)
{
/* A <- sqrt(W) A L^{-1} */
for (i = 0; i < p; ++i)
{
gsl_vector_complex_view cv = gsl_matrix_complex_column(A, i);
double Li = gsl_vector_get(L, i);
gsl_complex val;
if (Li == 0.0)
{
GSL_ERROR("L matrix is singular", GSL_ESING);
}
GSL_SET_COMPLEX(&val, 1.0 / Li, 0.0);
gsl_vector_complex_scale(&cv.vector, val);
}
}
return s;
}
} /* lls_complex_stdform() */
