tail fit_tail_impl(gf_view<imfreq> gf, const tail_view known_moments, int n_moments, int n_min, int n_max) {
// precondition : check that n_max is not too large
n_max = std::min(n_max, int(gf.mesh().size()-1));
tail res(get_target_shape(gf));
if (known_moments.size())
for (int i = known_moments.order_min(); i <= known_moments.order_max(); i++) res(i) = known_moments(i);
// if known_moments.size()==0, the lowest order to be obtained from the fit is determined by order_min in known_moments
// if known_moments.size()==0, the lowest order is the one following order_max in known_moments
int n_unknown_moments = n_moments - known_moments.size();
if (n_unknown_moments < 1) return known_moments;
// get the number of even unknown moments: it is n_unknown_moments/2+1 if the first
// moment is even and n_moments is odd; n_unknown_moments/2 otherwise
int omin = known_moments.size() == 0 ? known_moments.order_min() : known_moments.order_max() + 1; // smallest unknown moment
int omin_even = omin % 2 == 0 ? omin : omin + 1;
int omin_odd = omin % 2 != 0 ? omin : omin + 1;
int size_even = n_unknown_moments / 2;
if (n_unknown_moments % 2 != 0 && omin % 2 == 0) size_even += 1;
int size_odd = n_unknown_moments - size_even;
int size1 = n_max - n_min + 1;
// size2 is the number of moments
arrays::matrix<double> A(size1, std::max(size_even, size_odd), FORTRAN_LAYOUT);
arrays::matrix<double> B(size1, 1, FORTRAN_LAYOUT);
arrays::vector<double> S(std::max(size_even, size_odd));
const double rcond = 0.0;
int rank;
for (int i = 0; i < get_target_shape(gf)[0]; i++) {
for (int j = 0; j < get_target_shape(gf)[1]; j++) {
// fit the odd moments
S.resize(size_odd);
A.resize(size1,size_odd); //when resizing, gelss segfaults
for (int k = 0; k < size1; k++) {
auto n = n_min + k;
auto iw = std::complex<double>(gf.mesh().index_to_point(n));
B(k, 0) = imag(gf.data()(gf.mesh().index_to_linear(n), i, j));
// subtract known tail if present
if (known_moments.size() > 0)
B(k, 0) -= imag(evaluate(slice_target(known_moments, arrays::range(i, i + 1), arrays::range(j, j + 1)), iw)(0, 0));
for (int l = 0; l < size_odd; l++) {
int order = omin_odd + 2 * l;
A(k, l) = imag(pow(iw, -1.0 * order)); // set design matrix for odd moments
}
}
arrays::lapack::gelss(A, B, S, rcond, rank);
for (int m = 0; m < size_odd; m++) {
res(omin_odd + 2 * m)(i, j) = B(m, 0);
}
// fit the even moments
S.resize(size_even);
A.resize(size1,size_even); //when resizing, gelss segfaults
for (int k = 0; k < size1; k++) {
auto n = n_min + k;
auto iw = std::complex<double>(gf.mesh().index_to_point(n));
B(k, 0) = real(gf.data()(gf.mesh().index_to_linear(n), i, j));
// subtract known tail if present
if (known_moments.size() > 0)
B(k, 0) -= real(evaluate(slice_target(known_moments, arrays::range(i, i + 1), arrays::range(j, j + 1)), iw)(0, 0));
for (int l = 0; l < size_even; l++) {
int order = omin_even + 2 * l;
A(k, l) = real(pow(iw, -1.0 * order)); // set design matrix for odd moments
}
}
arrays::lapack::gelss(A, B, S, rcond, rank);
for (int m = 0; m < size_even; m++) {
res(omin_even + 2 * m)(i, j) = B(m, 0);
}
}
}
res.mask()()=n_moments;
return res; // return tail
}
inline tail_const_view slice_target(tail const &t, range R1, range R2) { return slice_target(tail_const_view{t}, R1, R2);}
