bool Matrix_Transpose(gsl_matrix_complex *A, gsl_matrix_complex *B){
gsl_matrix_complex_transpose_memcpy(A,B);
return true;
}
int
lls_complex_lcurve(gsl_vector *reg_param, gsl_vector *rho, gsl_vector *eta,
lls_complex_workspace *w)
{
const size_t N = rho->size; /* number of points on L-curve */
if (N != reg_param->size)
{
GSL_ERROR("size of reg_param and rho do not match", GSL_EBADLEN);
}
else if (N != eta->size)
{
GSL_ERROR("size of eta and rho do not match", GSL_EBADLEN);
}
else
{
int s;
const gsl_complex negtwo = gsl_complex_rect(-2.0, 0.0);
/* smallest regularization parameter */
const double smin_ratio = 16.0 * GSL_DBL_EPSILON;
double s1, sp, ratio, tmp;
size_t i;
/* compute eigenvalues of A^H A */
gsl_matrix_complex_transpose_memcpy(w->work_A, w->AHA);
s = gsl_eigen_herm(w->work_A, w->eval, w->eigen_p);
if (s)
return s;
/* find largest and smallest eigenvalues */
gsl_vector_minmax(w->eval, &sp, &s1);
/* singular values are square roots of eigenvalues */
s1 = sqrt(s1);
if (sp > GSL_DBL_EPSILON)
sp = sqrt(fabs(sp));
tmp = GSL_MAX(sp, s1*smin_ratio);
gsl_vector_set(reg_param, N - 1, tmp);
/* ratio so that reg_param(1) = s(1) */
ratio = pow(s1 / tmp, 1.0 / (N - 1.0));
/* calculate the regularization parameters */
for (i = N - 1; i > 0 && i--; )
{
double rp1 = gsl_vector_get(reg_param, i + 1);
gsl_vector_set(reg_param, i, ratio * rp1);
}
for (i = 0; i < N; ++i)
{
double r2;
double lambda = gsl_vector_get(reg_param, i);
gsl_complex val;
lls_complex_solve(lambda, w->c, w);
/* store ||c|| */
gsl_vector_set(eta, i, gsl_blas_dznrm2(w->c));
/* compute: A^H A c - 2 A^H b */
gsl_vector_complex_memcpy(w->work_b, w->AHb);
gsl_blas_zhemv(CblasUpper, GSL_COMPLEX_ONE, w->AHA, w->c, negtwo, w->work_b);
/* compute: c^T A^T A c - 2 c^T A^T b */
gsl_blas_zdotc(w->c, w->work_b, &val);
r2 = GSL_REAL(val) + w->bHb;
gsl_vector_set(rho, i, sqrt(r2));
}
return GSL_SUCCESS;
}
} /* lls_complex_lcurve() */
