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Various small fixes in imfreq Gfs.

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- documentation of matsubara_freq_mesh
- fixing doc of fit_tail
- fixing right conventions for matsubara_freq_mesh
This commit is contained in:
tayral 2014-02-19 11:59:47 +00:00
parent 2b315fcdea
commit 8c1f7945e4
7 changed files with 127 additions and 34 deletions
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4
doc/reference/c++/gf/gf_imfreq.rst
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@ -2,7 +2,7 @@
.. _gf_imfreq: .. _gf_imfreq:
Matsubara frequencies Green function on Matsubara frequencies
========================================================== ==========================================================
This is a specialisation of :ref:`gf<gf_and_view>` for imaginary Matsubara frequencies. This is a specialisation of :ref:`gf<gf_and_view>` for imaginary Matsubara frequencies.
@ -31,7 +31,7 @@ The domain is :doxy:`matsubara_freq_domain<triqs::gfs::matsubara_domain>`.
The Matsubara frequencies are :math:`\omega_n=\frac{(2n+1)\pi}{\beta}` for fermions and :math:`\omega_n=\frac{2n\pi}{\beta}` for bosons. The Matsubara frequencies are :math:`\omega_n=\frac{(2n+1)\pi}{\beta}` for fermions and :math:`\omega_n=\frac{2n\pi}{\beta}` for bosons.
The mesh is :doxy:`matsubara_freq_mesh<triqs::gfs::matsubara_freq_mesh>`. The mesh is :doc:`matsubara_freq_mesh<matsubara_freq_mesh>`.
Singularity Singularity

89
doc/reference/c++/gf/matsubara_freq_mesh.rst Normal file
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@ -0,0 +1,89 @@
Mesh of Matsubara frequencies
==============================
Synopsis
------------
The class `matsubara_freq_mesh` is the implementation of a mesh of fermionic (:math:`\frac{(2n+1)\pi}{\beta}`) or bosonic (:math:`\frac{2n\pi}{\beta}`) Matsubara frequencies.
The mesh can span either only positive frequencies or both positive and negative frequencies (which is necessary for complex functions :math:`G(\tau)`).
Public member functions
------------------------
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| type | name | description |
+==================+=============================================================================================+==========================================================================================+
| | matsubara_freq_mesh() | constructor |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| | matsubara_freq_mesh(domain_t dom, int n_pts=1025, bool positive_only=true) | constructor |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| | matsubara_freq_mesh(double beta, statistic_enum S, int n_pts=1025, bool positive_only=true) | constructor |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| domain_t const & | domain() const | corresponding :doxy:`domain<triqs::gfs::matsubara_domain>` |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| int | first_index() const | first Matsubara index |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| int | last_index() const | last Matsubara index |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| long | size() const | Size (linear) of the mesh |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| domain_pt_t | index_to_point(index_t ind) const | From an index of a point in the mesh, returns the corresponding point in the domain. |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| long | index_to_linear(index_t ind) const | Flatten the index in the positive linear index for memory storage (almost trivial here). |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| bool | positive_only() const | Is the mesh only for positive omega_n (G(tau) real)) |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| mesh_point_t | operator[](index_t i) const | Accessing a point of the mesh from its index. |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| const_iterator | begin() const | |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| const_iterator | end() const | |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| const_iterator | cbegin() const | |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| const_iterator | cend() const | |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| bool | operator== (matsubara_freq_mesh const &M) const | |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
| bool | operator!= (matsubara_freq_mesh const &M) const | |
+------------------+---------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------+
Public member types
------------------------
+--------------+-------------------------+
| type | description |
+==============+=========================+
| mesh_point_t | type of the mesh point |
+--------------+-------------------------+
Example
----------
.. compileblock::
#include <triqs/gfs/meshes/matsubara_freq.hpp>
using namespace triqs::gfs;
int main(){
double beta=1;
int n_pts=4;
matsubara_freq_mesh m(beta,Fermion, n_pts);
std::cout << "Mesh m with only positive Matsubara frequencies : " << std::endl;
for(auto & w:m) std::cout << w << std::endl;
std::cout << "m.first_index() = " << m.first_index() << std::endl;
std::cout << "m.last_index() = " << m.last_index() << std::endl;
std::cout << "m.size() = " << m.size() << std::endl;
matsubara_freq_mesh m2(beta,Fermion, n_pts, false);
std::cout << "Mesh m2 with positive and negative Matsubara frequencies : " << std::endl;
for(auto & w:m2) std::cout << w << std::endl;
std::cout << "m2.first_index() = " << m2.first_index() << std::endl;
std::cout << "m2.last_index() = " << m2.last_index() << std::endl;
std::cout << "m2.size() = " << m2.size() << std::endl;
return 0;
}

4
doc/reference/c++/gf/set_tail_from_fit.rst
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@ -22,9 +22,9 @@ where
+------------+----------------+----------------------------------------------------------------------+---------+ +------------+----------------+----------------------------------------------------------------------+---------+
| int | n_moments | number of moments in the final tail (including known ones) | no | | int | n_moments | number of moments in the final tail (including known ones) | no |
+------------+----------------+----------------------------------------------------------------------+---------+ +------------+----------------+----------------------------------------------------------------------+---------+
| size_t | n_min | linear index on mesh to start the fit | no | | size_t | n_min | Matsubara index on mesh to start the fit | no |
+------------+----------------+----------------------------------------------------------------------+---------+ +------------+----------------+----------------------------------------------------------------------+---------+
| size_t | n_max | final linear index for fit (included) | no | | size_t | n_max | final Matsubara index for fit (included) | no |
+------------+----------------+----------------------------------------------------------------------+---------+ +------------+----------------+----------------------------------------------------------------------+---------+
| bool | replace_by_fit | if true, replace the gf data in the fitting range by the tail values | true | | bool | replace_by_fit | if true, replace the gf data in the fitting range by the tail values | true |
+------------+----------------+----------------------------------------------------------------------+---------+ +------------+----------------+----------------------------------------------------------------------+---------+

6
test/triqs/gfs/test_fit_tail.output
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@ -66,7 +66,7 @@
... Order 2 = ... Order 2 =
[[(1,0)]] [[(1,0)]]
... Order 3 = ... Order 3 =
[[(0.999247,0)]] [[(0.999288,0)]]
... Order 4 = ... Order 4 =
[[(0.998655,0)]] [[(0.998655,0)]]
@ -80,7 +80,7 @@
... Order 2 = ... Order 2 =
[[(1,0)]] [[(1,0)]]
... Order 3 = ... Order 3 =
[[(0.999186,0)]] [[(0.999209,0)]]
... Order 4 = ... Order 4 =
[[(0.998631,0)]] [[(0.998631,0)]]
@ -94,7 +94,7 @@
... Order 2 = ... Order 2 =
[[(1,0)]] [[(1,0)]]
... Order 3 = ... Order 3 =
[[(0.999214,0)]] [[(0.999251,0)]]
... Order 4 = ... Order 4 =
[[(0.998655,0)]] [[(0.998655,0)]]

18
triqs/gfs/imfreq.hpp
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@ -59,7 +59,7 @@ namespace gfs {
evaluator_fnt_on_mesh() = default; evaluator_fnt_on_mesh() = default;
template <typename MeshType> evaluator_fnt_on_mesh(MeshType const &m, long p) { n = p; w=1; } template <typename MeshType> evaluator_fnt_on_mesh(MeshType const &m, long p) { n = p; w=1; }
template <typename MeshType> evaluator_fnt_on_mesh(MeshType const &m, matsubara_freq const &p) { template <typename MeshType> evaluator_fnt_on_mesh(MeshType const &m, matsubara_freq const &p) {
if ((p.n >= m.index_start()) && (p.n < m.size()+m.index_start())) {w=1; n =p.n;} if ((p.n >= m.first_index()) && (p.n < m.size()+m.first_index())) {w=1; n =p.n;}
else {w=0; n=0;} else {w=0; n=0;}
} }
template <typename F> auto operator()(F const &f) const DECL_AND_RETURN(w*f(n)); template <typename F> auto operator()(F const &f) const DECL_AND_RETURN(w*f(n));
@ -76,24 +76,24 @@ namespace gfs {
// dispatch for 2x2 cases : matrix/scalar and tail/no_tail ( true means no_tail) // dispatch for 2x2 cases : matrix/scalar and tail/no_tail ( true means no_tail)
template <typename G> template <typename G>
std::complex<double> _call_impl(G const *g, matsubara_freq const &f, scalar_valued, std::false_type) const { std::complex<double> _call_impl(G const *g, matsubara_freq const &f, scalar_valued, std::false_type) const {
if (g->mesh().index_start()==0){//only positive Matsubara frequencies if (g->mesh().positive_only()){//only positive Matsubara frequencies
if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n]; if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n];
if ((f.n < 0) && (-f.n < g->mesh().size())) return conj((*g)[-f.n]); if ((f.n < 0) && (-f.n < g->mesh().size())) return conj((*g)[-f.n]);
} }
else{ else{
if ((f.n >= g->mesh().index_start()) && (f.n < g->mesh().size()+g->mesh().index_start())) return (*g)[f.n]; if ((f.n >= g->mesh().first_index()) && (f.n < g->mesh().size()+g->mesh().first_index())) return (*g)[f.n];
} }
return g->singularity().evaluate(f)(0, 0); return g->singularity().evaluate(f)(0, 0);
} }
template <typename G> template <typename G>
std::complex<double> _call_impl(G const *g, matsubara_freq const &f, scalar_valued, std::true_type) const { std::complex<double> _call_impl(G const *g, matsubara_freq const &f, scalar_valued, std::true_type) const {
if (g->mesh().index_start()==0){//only positive Matsubara frequencies if (g->mesh().positive_only()){//only positive Matsubara frequencies
if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n]; if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n];
if ((f.n < 0) && (-f.n < g->mesh().size())) return conj((*g)[-f.n]); if ((f.n < 0) && (-f.n < g->mesh().size())) return conj((*g)[-f.n]);
} }
else{ else{
if ((f.n >= g->mesh().index_start()) && (f.n < g->mesh().size()+g->mesh().index_start())) return (*g)[f.n]; if ((f.n >= g->mesh().first_index()) && (f.n < g->mesh().size()+g->mesh().first_index())) return (*g)[f.n];
} }
return 0; return 0;
} }
@ -101,13 +101,13 @@ namespace gfs {
template <typename G> template <typename G>
arrays::matrix_const_view<std::complex<double>> _call_impl(G const *g, matsubara_freq const &f, matrix_valued, arrays::matrix_const_view<std::complex<double>> _call_impl(G const *g, matsubara_freq const &f, matrix_valued,
std::false_type) const { std::false_type) const {
if (g->mesh().index_start()==0){//only positive Matsubara frequencies if (g->mesh().positive_only()){//only positive Matsubara frequencies
if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n](); if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n]();
if ((f.n < 0) && (-f.n < g->mesh().size())) if ((f.n < 0) && (-f.n < g->mesh().size()))
return arrays::matrix<std::complex<double>>{conj((*g)[-f.n]())}; return arrays::matrix<std::complex<double>>{conj((*g)[-f.n]())};
} }
else{ else{
if ((f.n >= g->mesh().index_start()) && (f.n < g->mesh().size()+g->mesh().index_start())) return (*g)[f.n]; if ((f.n >= g->mesh().first_index()) && (f.n < g->mesh().size()+g->mesh().first_index())) return (*g)[f.n];
} }
return g->singularity().evaluate(f); return g->singularity().evaluate(f);
} }
@ -115,13 +115,13 @@ namespace gfs {
template <typename G> template <typename G>
arrays::matrix_const_view<std::complex<double>> _call_impl(G const *g, matsubara_freq const &f, matrix_valued, arrays::matrix_const_view<std::complex<double>> _call_impl(G const *g, matsubara_freq const &f, matrix_valued,
std::true_type) const { std::true_type) const {
if (g->mesh().index_start()==0){//only positive Matsubara frequencies if (g->mesh().positive_only()){//only positive Matsubara frequencies
if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n](); if ((f.n >= 0) && (f.n < g->mesh().size())) return (*g)[f.n]();
if ((f.n < 0) && (-f.n < g->mesh().size())) if ((f.n < 0) && (-f.n < g->mesh().size()))
return arrays::matrix<std::complex<double>>{conj((*g)[-f.n]())}; return arrays::matrix<std::complex<double>>{conj((*g)[-f.n]())};
} }
else{ else{
if ((f.n >= g->mesh().index_start()) && (f.n < g->mesh().size()+g->mesh().index_start())) return (*g)[f.n]; if ((f.n >= g->mesh().first_index()) && (f.n < g->mesh().size()+g->mesh().first_index())) return (*g)[f.n];
} }
auto r = arrays::matrix<std::complex<double>>{get_target_shape(*g)}; auto r = arrays::matrix<std::complex<double>>{get_target_shape(*g)};
r() = 0; r() = 0;

16
triqs/gfs/local/fit_tail.hpp
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@ -78,8 +78,8 @@ namespace triqs { namespace gfs { namespace local {
const double rcond = 0.0; const double rcond = 0.0;
int rank; int rank;
for (size_t i = 0; i < get_target_shape(gf)[0]; i++) { for (int i = 0; i < get_target_shape(gf)[0]; i++) {
for (size_t j = 0; j < get_target_shape(gf)[1]; j++) { for (int j = 0; j < get_target_shape(gf)[1]; j++) {
// fit the odd moments // fit the odd moments
// S.resize(size_odd); // S.resize(size_odd);
@ -132,12 +132,12 @@ namespace triqs { namespace gfs { namespace local {
return res; // return tail 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, void set_tail_from_fit(gf_view<imfreq> gf, tail_view known_moments, int n_moments, int n_min, int n_max,
bool replace_by_fit = false) { 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"; 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); 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 if (replace_by_fit) { // replace data in the fitting range by the values from the fitted tail
size_t i = 0; int i = 0;
for (auto iw : gf.mesh()) { // (arrays::range(n_min,n_max+1)) { 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); if ((i >= n_min) && (i <= n_max)) gf[iw] = gf.singularity().evaluate(iw);
i++; i++;
@ -145,13 +145,13 @@ namespace triqs { namespace gfs { namespace local {
} }
} }
void set_tail_from_fit(gf_view<block_index, gf<imfreq>> block_gf, tail_view known_moments, int n_moments, size_t n_min, void set_tail_from_fit(gf_view<block_index, gf<imfreq>> block_gf, tail_view known_moments, int n_moments, int n_min,
size_t n_max, bool replace_by_fit = false) { int 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(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++) for (int 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); 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) { void set_tail_from_fit(gf_view<imfreq, scalar_valued> gf, tail_view known_moments, int n_moments, int n_min, int 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 ); set_tail_from_fit(reinterpret_scalar_valued_gf_as_matrix_valued(gf), known_moments, n_moments, n_min, n_max, replace_by_fit );
} }

22
triqs/gfs/meshes/matsubara_freq.hpp
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@ -58,7 +58,12 @@ namespace gfs {
* For fermions : -Nmax - 1 * For fermions : -Nmax - 1
* For Bosons : -Nmax * For Bosons : -Nmax
**/ **/
int index_start() const { return -(_positive_only ? 0 : n_max() + (_dom.statistic == Fermion)); }
/// last Matsubara index
int last_index() const { return (_positive_only ? _n_pts : (_n_pts - (_dom.statistic == Boson ? 1 : 2))/2);}
/// first Matsubara index
int first_index() const { return -(_positive_only ? 0 : last_index() + (_dom.statistic == Fermion)); }
/// Size (linear) of the mesh /// Size (linear) of the mesh
long size() const { return _n_pts;} long size() const { return _n_pts;}
@ -67,7 +72,7 @@ namespace gfs {
domain_pt_t index_to_point(index_t ind) const { return 1_j * M_PI * (2 * ind + (_dom.statistic == Fermion)) / _dom.beta; } domain_pt_t index_to_point(index_t ind) const { return 1_j * M_PI * (2 * ind + (_dom.statistic == Fermion)) / _dom.beta; }
/// Flatten the index in the positive linear index for memory storage (almost trivial here). /// Flatten the index in the positive linear index for memory storage (almost trivial here).
long index_to_linear(index_t ind) const { return ind - index_start(); } long index_to_linear(index_t ind) const { return ind - first_index(); }
/// Is the mesh only for positive omega_n (G(tau) real)) /// Is the mesh only for positive omega_n (G(tau) real))
bool positive_only() const { return _positive_only;} bool positive_only() const { return _positive_only;}
@ -81,17 +86,17 @@ namespace gfs {
mesh_point_t() = default; mesh_point_t() = default;
mesh_point_t(matsubara_freq_mesh const &mesh, index_t const &index_) mesh_point_t(matsubara_freq_mesh const &mesh, index_t const &index_)
: matsubara_freq(index_, mesh.domain().beta, mesh.domain().statistic), : matsubara_freq(index_, mesh.domain().beta, mesh.domain().statistic),
index_start(mesh.index_start()), first_index(mesh.first_index()),
index_stop(mesh.index_start() + mesh.size() - 1) {} index_stop(mesh.first_index() + mesh.size() - 1) {}
mesh_point_t(matsubara_freq_mesh const &mesh) : mesh_point_t(mesh, mesh.index_start()) {} mesh_point_t(matsubara_freq_mesh const &mesh) : mesh_point_t(mesh, mesh.first_index()) {}
void advance() { ++n; } void advance() { ++n; }
long linear_index() const { return n - index_start; } long linear_index() const { return n - first_index; }
long index() const { return n; } long index() const { return n; }
bool at_end() const { return (n == index_stop); } bool at_end() const { return (n == index_stop); }
void reset() { n = index_start; } void reset() { n = first_index; }
private: private:
index_t index_start, index_stop; index_t first_index, index_stop;
}; };
/// Accessing a point of the mesh from its index /// Accessing a point of the mesh from its index
@ -155,7 +160,6 @@ namespace gfs {
private: private:
domain_t _dom; domain_t _dom;
int _n_pts; int _n_pts;
long n_max() const { return (_positive_only ? _n_pts : (_n_pts - (_dom.statistic == Boson ? 1 : 2))/2);}
bool _positive_only; bool _positive_only;
}; };