mirror of
https://github.com/triqs/dft_tools
synced 2024-12-25 05:43:40 +01:00
Extending fit_tail for scalar_valued (+ test)
-> extension by using reinterpret_scalar_valued_as_matrix_valued
This commit is contained in:
tayral
Olivier Parcollet
parent
da7e7ec971
commit
708c47305c
@ -15,7 +15,8 @@ void test_0(){
|
||||
double beta =10;
|
||||
int N=100;
|
||||
|
||||
auto gw = gf<imfreq>{{beta, Fermion, N}, {1, 1}};
|
||||
auto gw = gf<imfreq>{{beta, Fermion, N},{1,1}};
|
||||
auto gw_s = gf<imfreq, scalar_valued>{{beta, Fermion, N}};
|
||||
|
||||
triqs::arrays::array<double,1> c(3);
|
||||
triqs::clef::placeholder<1> i_;
|
||||
@ -27,11 +28,13 @@ void test_0(){
|
||||
auto known_moments = tail(make_shape(1,1), size, order_min); //length is 0, first moment to fit is order_min
|
||||
|
||||
gw(iom_) << c(0)/iom_ + c(1)/iom_/iom_ + c(2)/iom_/iom_/iom_;
|
||||
gw_s(iom_) << c(0)/iom_ + c(1)/iom_/iom_ + c(2)/iom_/iom_/iom_;
|
||||
|
||||
TEST(gw.singularity());
|
||||
|
||||
//erase tail
|
||||
for(auto &i : gw.singularity().data()) i = 0.0;
|
||||
for(auto &i : gw_s.singularity().data()) i = 0.0;
|
||||
|
||||
size_t wn_min=50; //frequency to start the fit
|
||||
size_t wn_max=90; //final fitting frequency (included)
|
||||
@ -39,16 +42,17 @@ void test_0(){
|
||||
|
||||
//restore tail
|
||||
set_tail_from_fit(gw, known_moments, n_moments, wn_min, wn_max);
|
||||
set_tail_from_fit(gw_s, known_moments, n_moments, wn_min, wn_max);
|
||||
|
||||
TEST(gw.singularity());
|
||||
|
||||
TEST(gw_s.singularity());
|
||||
/*
|
||||
for(size_t i=0; i<first_dim(c); i++){
|
||||
double diff = std::abs( c(i) - gw.singularity().data()(i,0,0) );
|
||||
//std::cout<< "diff: " << diff <<std::endl;
|
||||
if (diff > precision) TRIQS_RUNTIME_ERROR<<" fit_tail error : diff="<<diff<<"\n";
|
||||
}
|
||||
|
||||
|
||||
*/
|
||||
|
||||
//erase tail
|
||||
for(auto &i : gw.singularity().data()) i = 0.0;
|
||||
@ -61,13 +65,15 @@ void test_0(){
|
||||
set_tail_from_fit(gw, known_moments, n_moments, wn_min, wn_max, true);//true replace the gf data in the fitting range by the tail values
|
||||
|
||||
TEST(gw.singularity());
|
||||
|
||||
/*
|
||||
for(size_t i=0; i<first_dim(c); i++){
|
||||
double diff = std::abs( c(i) - gw.singularity().data()(i,0,0) );
|
||||
//std::cout<< "diff: " << diff <<std::endl;
|
||||
if (diff > precision) TRIQS_RUNTIME_ERROR<<" fit_tail error : diff="<<diff<<"\n";
|
||||
}
|
||||
*/
|
||||
}
|
||||
|
||||
void test_1(){
|
||||
//real life test: find tails of 1/(iom -1)
|
||||
triqs::clef::placeholder<0> iom_;
|
||||
@ -75,7 +81,9 @@ void test_1(){
|
||||
int N=100;
|
||||
|
||||
auto gw = gf<imfreq>{{beta, Fermion, N}, {1, 1}};
|
||||
auto gw_b = gf<imfreq>{{beta, Boson, N}, {1, 1}};
|
||||
gw(iom_) << 1/(iom_-1);
|
||||
gw_b(iom_) << 1/(iom_-1);
|
||||
|
||||
size_t wn_min=50; //frequency to start the fit
|
||||
size_t wn_max=90; //final fitting frequency (included)
|
||||
@ -85,8 +93,11 @@ void test_1(){
|
||||
auto known_moments = tail(make_shape(1,1), size, order_min); //length is 0, first moment to fit is order_min
|
||||
known_moments(1)=1.;//set the first moment
|
||||
set_tail_from_fit(gw, known_moments, n_moments, wn_min, wn_max, true);//true replace the gf data in the fitting range by the tail values
|
||||
set_tail_from_fit(gw_b, known_moments, n_moments, wn_min, wn_max, true);//true replace the gf data in the fitting range by the tail values
|
||||
TEST(gw.singularity());
|
||||
TEST(gw_b.singularity());
|
||||
}
|
||||
|
||||
void test_2(){
|
||||
//real life test: find tails of 1/(iom -1) -- with positive and negative matsubara
|
||||
triqs::clef::placeholder<0> iom_;
|
||||
@ -106,31 +117,12 @@ void test_2(){
|
||||
set_tail_from_fit(gw, known_moments, n_moments, wn_min, wn_max, true);//true replace the gf data in the fitting range by the tail values
|
||||
TEST(gw.singularity());
|
||||
}
|
||||
void test_3(){
|
||||
//real life test: find tails of 1/(iom -1) --> bosonic case
|
||||
triqs::clef::placeholder<0> iom_;
|
||||
double beta =10;
|
||||
int N=100;
|
||||
|
||||
auto gw = gf<imfreq>{{beta, Boson, N}, {1, 1}};
|
||||
gw(iom_) << 1/(iom_-1);
|
||||
|
||||
size_t wn_min=50; //frequency to start the fit
|
||||
size_t wn_max=90; //final fitting frequency (included)
|
||||
int n_moments=4; //number of moments in the final tail (including known ones)
|
||||
int size=1; //means that we know one moment
|
||||
int order_min=1; //means that the first moment in the final tail will be the first moment
|
||||
auto known_moments = tail(make_shape(1,1), size, order_min); //length is 0, first moment to fit is order_min
|
||||
known_moments(1)=1.;//set the first moment
|
||||
set_tail_from_fit(gw, known_moments, n_moments, wn_min, wn_max, true);//true replace the gf data in the fitting range by the tail values
|
||||
TEST(gw.singularity());
|
||||
}
|
||||
|
||||
int main() {
|
||||
test_0();
|
||||
test_1();
|
||||
test_2();
|
||||
test_3();
|
||||
}
|
||||
|
||||
|
||||
|
||||
@ -20,7 +20,11 @@
|
||||
... Order 8 =
|
||||
[[(0,0)]]
|
||||
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = 1 1 3
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = -1 1 3
|
||||
... Order -1 =
|
||||
[[(0,0)]]
|
||||
... Order 0 =
|
||||
[[(0,0)]]
|
||||
... Order 1 =
|
||||
[[(1,0)]]
|
||||
... Order 2 =
|
||||
@ -28,7 +32,11 @@
|
||||
... Order 3 =
|
||||
[[(5,0)]]
|
||||
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = 1 1 3
|
||||
(gw_s.singularity()) ---> tail/tail_view: min/smallest/max = -1 1 3
|
||||
... Order -1 =
|
||||
[[(0,0)]]
|
||||
... Order 0 =
|
||||
[[(0,0)]]
|
||||
... Order 1 =
|
||||
[[(1,0)]]
|
||||
... Order 2 =
|
||||
@ -36,7 +44,23 @@
|
||||
... Order 3 =
|
||||
[[(5,0)]]
|
||||
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = 1 1 4
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = -1 1 3
|
||||
... Order -1 =
|
||||
[[(0,0)]]
|
||||
... Order 0 =
|
||||
[[(0,0)]]
|
||||
... Order 1 =
|
||||
[[(1,0)]]
|
||||
... Order 2 =
|
||||
[[(3,0)]]
|
||||
... Order 3 =
|
||||
[[(5,0)]]
|
||||
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = -1 1 4
|
||||
... Order -1 =
|
||||
[[(0,0)]]
|
||||
... Order 0 =
|
||||
[[(0,0)]]
|
||||
... Order 1 =
|
||||
[[(1,0)]]
|
||||
... Order 2 =
|
||||
@ -46,23 +70,31 @@
|
||||
... Order 4 =
|
||||
[[(0.998655,0)]]
|
||||
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = 1 1 4
|
||||
(gw_b.singularity()) ---> tail/tail_view: min/smallest/max = -1 1 4
|
||||
... Order -1 =
|
||||
[[(0,0)]]
|
||||
... Order 0 =
|
||||
[[(0,0)]]
|
||||
... Order 1 =
|
||||
[[(1,0)]]
|
||||
... Order 2 =
|
||||
[[(1,0)]]
|
||||
... Order 3 =
|
||||
[[(0.999251,0)]]
|
||||
... Order 4 =
|
||||
[[(0.998655,0)]]
|
||||
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = 1 1 4
|
||||
... Order 1 =
|
||||
[[(1,0)]]
|
||||
... Order 2 =
|
||||
[[(1,0)]]
|
||||
... Order 3 =
|
||||
[[(0.999236,0)]]
|
||||
[[(0.999209,0)]]
|
||||
... Order 4 =
|
||||
[[(0.998631,0)]]
|
||||
|
||||
(gw.singularity()) ---> tail/tail_view: min/smallest/max = -1 1 4
|
||||
... Order -1 =
|
||||
[[(0,0)]]
|
||||
... Order 0 =
|
||||
[[(0,0)]]
|
||||
... Order 1 =
|
||||
[[(1,0)]]
|
||||
... Order 2 =
|
||||
[[(1,0)]]
|
||||
... Order 3 =
|
||||
[[(0.999251,0)]]
|
||||
... Order 4 =
|
||||
[[(0.998655,0)]]
|
||||
|
||||
|
||||
@ -26,139 +26,136 @@
|
||||
#include <triqs/arrays/blas_lapack/gelss.hpp>
|
||||
#include <triqs/python_tools/cython_proxy.hpp>
|
||||
|
||||
namespace triqs {
|
||||
namespace gfs {
|
||||
namespace local {
|
||||
namespace triqs { namespace gfs { namespace local {
|
||||
|
||||
using triqs::gfs::imfreq;
|
||||
using triqs::gfs::block_index;
|
||||
using triqs::gfs::block_index;
|
||||
using triqs::gfs::imfreq;
|
||||
using triqs::gfs::block_index;
|
||||
using triqs::gfs::block_index;
|
||||
|
||||
namespace tgl = triqs::gfs::local;
|
||||
namespace tgl = triqs::gfs::local;
|
||||
|
||||
// routine for fitting the tail (singularity) of a Matsubara Green's function
|
||||
// this is a *linear* least squares problem (with non-linear basis functions)
|
||||
// which is solved by singular value decomposition of the design matrix
|
||||
// the routine fits the real part (even moments) and the imaginary part
|
||||
//(odd moments) separately, since this is more stable
|
||||
// routine for fitting the tail (singularity) of a Matsubara Green's function
|
||||
// this is a *linear* least squares problem (with non-linear basis functions)
|
||||
// which is solved by singular value decomposition of the design matrix
|
||||
// the routine fits the real part (even moments) and the imaginary part
|
||||
//(odd moments) separately, since this is more stable
|
||||
|
||||
// input:
|
||||
// the input gf<imfreq> Green's function: gf
|
||||
// the known moments in the form of a tail(_view): known_moments
|
||||
// the TOTAL number of desired moments (including the known ones): n_moments
|
||||
// the index of the first and last frequency to fit (the last one is included): n_min, n_max
|
||||
// input:
|
||||
// the input gf<imfreq> Green's function: gf
|
||||
// the known moments in the form of a tail(_view): known_moments
|
||||
// the TOTAL number of desired moments (including the known ones): n_moments
|
||||
// the index of the first and last frequency to fit (the last one is included): n_min, n_max
|
||||
|
||||
// output: returns the tail obtained by fitting
|
||||
// output: returns the tail obtained by fitting
|
||||
|
||||
tail fit_tail_impl(gf<imfreq> &gf, const tail_view known_moments, int n_moments, int n_min, int n_max) {
|
||||
tail fit_tail_impl(gf_view<imfreq> gf, const tail_view known_moments, int n_moments, int n_min, int n_max) {
|
||||
|
||||
tail res(get_target_shape(gf), n_moments, known_moments.order_min());
|
||||
if (known_moments.size())
|
||||
for (int i = known_moments.order_min(); i <= known_moments.order_max(); i++) res(i) = known_moments(i);
|
||||
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
|
||||
// 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
|
||||
|
||||
const double beta = gf.mesh().domain().beta;
|
||||
const double beta = gf.mesh().domain().beta;
|
||||
|
||||
int n_unknown_moments = n_moments - known_moments.size();
|
||||
if (n_unknown_moments < 1) return 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;
|
||||
// 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
|
||||
int size1 = n_max - n_min + 1;
|
||||
// size2 is the number of moments
|
||||
|
||||
arrays::matrix<double, 2> A(size1, std::max(size_even, size_odd), FORTRAN_LAYOUT);
|
||||
arrays::matrix<double, 2> B(size1, 1, FORTRAN_LAYOUT);
|
||||
arrays::vector<double> S(std::max(size_even, size_odd));
|
||||
const double rcond = 0.0;
|
||||
int rank;
|
||||
arrays::matrix<double, 2> A(size1, std::max(size_even, size_odd), FORTRAN_LAYOUT);
|
||||
arrays::matrix<double, 2> B(size1, 1, FORTRAN_LAYOUT);
|
||||
arrays::vector<double> S(std::max(size_even, size_odd));
|
||||
const double rcond = 0.0;
|
||||
int rank;
|
||||
|
||||
for (size_t i = 0; i < get_target_shape(gf)[0]; i++) {
|
||||
for (size_t j = 0; j < get_target_shape(gf)[1]; j++) {
|
||||
for (size_t i = 0; i < get_target_shape(gf)[0]; i++) {
|
||||
for (size_t 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));
|
||||
// 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(slice_target(known_moments, arrays::range(i, i + 1), arrays::range(j, j + 1)).evaluate(iw)(0, 0));
|
||||
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(slice_target(known_moments, arrays::range(i, i + 1), arrays::range(j, j + 1)).evaluate(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(slice_target(known_moments, arrays::range(i, i + 1), arrays::range(j, j + 1)).evaluate(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);
|
||||
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
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return res; // return tail
|
||||
}
|
||||
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));
|
||||
|
||||
void set_tail_from_fit(gf<imfreq> &gf, tail_view known_moments, int n_moments, size_t n_min, size_t n_max,
|
||||
bool replace_by_fit = false) {
|
||||
if (get_target_shape(gf) != known_moments.shape()) TRIQS_RUNTIME_ERROR << "shape of tail does not match shape of gf";
|
||||
gf.singularity() = fit_tail_impl(gf, known_moments, n_moments, n_min, n_max);
|
||||
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(slice_target(known_moments, arrays::range(i, i + 1), arrays::range(j, j + 1)).evaluate(iw)(0, 0));
|
||||
|
||||
if (replace_by_fit) { // replace data in the fitting range by the values from the fitted tail
|
||||
size_t i = 0;
|
||||
for (auto iw : gf.mesh()) { // (arrays::range(n_min,n_max+1)) {
|
||||
if ((i >= n_min) && (i <= n_max)) gf[iw] = gf.singularity().evaluate(iw);
|
||||
i++;
|
||||
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_view()=n_moments;
|
||||
return res; // return tail
|
||||
}
|
||||
|
||||
void set_tail_from_fit(gf_view<imfreq> gf, tail_view known_moments, int n_moments, size_t n_min, size_t n_max,
|
||||
bool replace_by_fit = false) {
|
||||
if (get_target_shape(gf) != known_moments.shape()) TRIQS_RUNTIME_ERROR << "shape of tail does not match shape of gf";
|
||||
gf.singularity() = fit_tail_impl(gf, known_moments, n_moments, n_min, n_max);
|
||||
if (replace_by_fit) { // replace data in the fitting range by the values from the fitted tail
|
||||
size_t i = 0;
|
||||
for (auto iw : gf.mesh()) { // (arrays::range(n_min,n_max+1)) {
|
||||
if ((i >= n_min) && (i <= n_max)) gf[iw] = gf.singularity().evaluate(iw);
|
||||
i++;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void set_tail_from_fit(gf<block_index, gf<imfreq>> &block_gf, tail_view known_moments, int n_moments, size_t n_min,
|
||||
size_t n_max, bool replace_by_fit = false) {
|
||||
void set_tail_from_fit(gf_view<block_index, gf<imfreq>> block_gf, tail_view known_moments, int n_moments, size_t n_min,
|
||||
size_t n_max, bool replace_by_fit = false) {
|
||||
// for(auto &gf : block_gf) set_tail_from_fit(gf, known_moments, n_moments, n_min, n_max, replace_by_fit);
|
||||
for (size_t i = 0; i < block_gf.mesh().size(); i++)
|
||||
set_tail_from_fit(block_gf[i], known_moments, n_moments, n_min, n_max, replace_by_fit);
|
||||
}
|
||||
void set_tail_from_fit(gf_view<imfreq, scalar_valued> gf, tail_view known_moments, int n_moments, size_t n_min, size_t n_max, bool replace_by_fit = false) {
|
||||
set_tail_from_fit(reinterpret_scalar_valued_gf_as_matrix_valued(gf), known_moments, n_moments, n_min, n_max, replace_by_fit );
|
||||
}
|
||||
}
|
||||
} // namespace
|
||||
|
||||
}}} // namespace
|
||||
#endif
|
||||
|
||||
Loading…
Reference in New Issue
Block a user