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Added basic doc + additional test for tail fitting

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- added test for a 'real-life' GF + corresponding output
- added basic usage documentation for tail fitting from c++. Full implementation details yet to be written
This commit is contained in:
tayral 2014-02-04 11:24:28 +00:00 committed by Olivier Parcollet
parent 2a71d2e54a
commit b129b3d17b
4 changed files with 182 additions and 13 deletions
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67
doc/reference/c++/gf/set_tail_from_fit.rst Normal file
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@ -0,0 +1,67 @@
Fitting the tail of a Matsubara Green's function
#################################################
API
~~~~~
The tail of a given ``gf<imfreq>/gf<block_index, gf<imfreq>> gw`` can be fitted using the two following functions:
``void set_tail_from_fit(gf<imfreq> &gf, tail_view known_moments, int n_moments, size_t wn_min, size_t wn_max, bool replace_by_fit = false);``
``void set_tail_from_fit(gf<block_index, gf<imfreq>> &block_gf, tail_view known_moments, int n_moments, size_t wn_min, size_t wn_max, bool replace_by_fit = false);``
where
+-------------+----------------+----------------------------------------------------------------------+----------+
| type | name | description | default |
+=============+================+======================================================================+==========+
| gf<imfreq> | gf | Green's function to be fit | no |
+-------------+----------------+----------------------------------------------------------------------+----------+
| tail_view | known_moments | known part of the tail | no |
+-------------+----------------+----------------------------------------------------------------------+----------+
| int | n_moments | number of moments in the final tail (including known ones) | no |
+-------------+----------------+----------------------------------------------------------------------+----------+
| size_t | wn_min | frequency to start the fit | no |
+-------------+----------------+----------------------------------------------------------------------+----------+
| size_t | wn_max | final fitting frequency (included) | no |
+-------------+----------------+----------------------------------------------------------------------+----------+
| bool | replace_by_fit | if true, replace the gf data in the fitting range by the tail values | true |
+-------------+----------------+----------------------------------------------------------------------+----------+
Example
~~~~~~~~
.. compileblock::
#include <triqs/gfs.hpp>
#include <triqs/gfs/local/fit_tail.hpp>
using namespace triqs::gfs;
int main(){
triqs::clef::placeholder<0> iom_;
double beta =10;
int N=100;
auto gw = gf<imfreq>{{beta, Fermion, N}, {1, 1}};
gw(iom_) << 1/(iom_-1);
size_t wn_min=50, wn_max=90;
int n_moments=4;
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 = local::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);
std::cout << gw.singularity() << std::endl;
}
Implementation
~~~~~~~~~~~~~~~
The fitting problem is written as a linear system of equations, which is solved by SVD.

35
doc/reference/c++/gf/tail.rst
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@ -38,6 +38,41 @@ In TRIQS, the tail is implemented as an object ``tail``. Here is a simple exampl
std::cout << t << std::endl;
}
Fitting the tail of a Green's function
---------------------------------------
Given an imaginary-frequency Green's function, one can compute the moments of its high-frequency tail with the function ``set_tail_from_fit``:
.. compileblock::
#include <triqs/gfs.hpp>
#include <triqs/gfs/local/fit_tail.hpp>
using namespace triqs::gfs;
int main(){
triqs::clef::placeholder<0> iom_;
double beta =10;
int N=100;
auto gw = gf<imfreq>{{beta, Fermion, 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 = local::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
std::cout << gw.singularity() << std::endl;
}
The full documentation of ``set_tail_from_fit`` is :doc:`here<set_tail_from_fit>`.
API
****
Here are the main methods of the ``tail`` class:

45
test/triqs/gfs/test_fit_tail.cpp
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@ -7,8 +7,7 @@ using triqs::arrays::make_shape;
using namespace triqs::gfs;
using triqs::gfs::local::tail;
#define TEST(X) std::cout << BOOST_PP_STRINGIZE((X)) << " ---> "<< (X) <<std::endl<<std::endl;
int main() {
void test_0(){
double precision=10e-9;
@ -29,9 +28,7 @@ int main() {
gw(iom_) << c(0)/iom_ + c(1)/iom_/iom_ + c(2)/iom_/iom_/iom_;
//show tail
// std::cout<< "before fitting:" <<std::endl;
// for(auto &i : gw.singularity().data()) std::cout << i << std::endl;
TEST(gw.singularity());
//erase tail
for(auto &i : gw.singularity().data()) i = 0.0;
@ -43,13 +40,12 @@ int main() {
//restore tail
set_tail_from_fit(gw, known_moments, n_moments, wn_min, wn_max);
// std::cout<< "after fitting:" <<std::endl;
// for(auto &i : gw.singularity().data()) std::cout << i << std::endl;
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";
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";
}
@ -64,14 +60,37 @@ int main() {
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());
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";
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_;
double beta =10;
int N=100;
auto gw = gf<imfreq>{{beta, Fermion, 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();
}

48
test/triqs/gfs/test_fit_tail.output Normal file
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(gw.singularity()) ---> tail/tail_view: min/smallest/max = -1 1 8
... Order -1 =
[[(0,0)]]
... Order 0 =
[[(0,0)]]
... Order 1 =
[[(1,0)]]
... Order 2 =
[[(3,0)]]
... Order 3 =
[[(5,0)]]
... Order 4 =
[[(0,0)]]
... Order 5 =
[[(0,0)]]
... Order 6 =
[[(0,0)]]
... Order 7 =
[[(0,0)]]
... Order 8 =
[[(0,0)]]
(gw.singularity()) ---> tail/tail_view: min/smallest/max = 1 1 3
... Order 1 =
[[(1,0)]]
... Order 2 =
[[(3,0)]]
... Order 3 =
[[(5,0)]]
(gw.singularity()) ---> tail/tail_view: min/smallest/max = 1 1 3
... 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 =
[[(1,0)]]
... Order 2 =
[[(1,0)]]
... Order 3 =
[[(0.999251,0)]]
... Order 4 =
[[(0.998655,0)]]