From 65ed3a8dc2e2df429d877c8814575ba8c0a72e17 Mon Sep 17 00:00:00 2001
From: Hartmut Hafermann <soliton77@gmail.com>
Date: Mon, 3 Feb 2014 21:51:40 +0100
Subject: [PATCH] gf: new tail fitting

---
 test/triqs/gfs/test_fit_tail.cpp |  77 +++++++++++++++
 triqs/gfs/local/fit_tail.hpp     | 164 +++++++++++++++++++++++++++++++
 2 files changed, 241 insertions(+)
 create mode 100644 test/triqs/gfs/test_fit_tail.cpp
 create mode 100644 triqs/gfs/local/fit_tail.hpp

diff --git a/test/triqs/gfs/test_fit_tail.cpp b/test/triqs/gfs/test_fit_tail.cpp
new file mode 100644
index 00000000..d7bf9a80
--- /dev/null
+++ b/test/triqs/gfs/test_fit_tail.cpp
@@ -0,0 +1,77 @@
+#//define TRIQS_ARRAYS_ENFORCE_BOUNDCHECK
+
+#include <triqs/gfs.hpp>
+#include <triqs/gfs/local/fit_tail.hpp>
+
+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() {
+
+ double precision=10e-9;
+
+ triqs::clef::placeholder<0> iom_;
+ double beta =10;
+ int N=100;
+
+ auto gw = gf<imfreq>{{beta, Fermion, N}, {1, 1}};
+
+ triqs::arrays::array<double,1> c(3);
+ triqs::clef::placeholder<1> i_;
+
+ c(i_) << (2*i_+1);
+
+ int size=0; //means we don't know any moments
+ 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
+
+ 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;
+
+ //erase tail
+ for(auto &i : gw.singularity().data()) i = 0.0;
+
+ size_t wn_min=50; //frequency to start the fit
+ size_t wn_max=90; //final fitting frequency (included)
+ int n_moments=3;  //number of moments in the final tail (including known ones)
+
+ //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;
+
+ 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;
+
+ //now with a known moment
+ size=1; //means that we know one moment
+ order_min=1; //means that the first moment in the final tail will be the first moment
+ 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
+
+
+ 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";
+ }
+
+
+}
+
+
diff --git a/triqs/gfs/local/fit_tail.hpp b/triqs/gfs/local/fit_tail.hpp
new file mode 100644
index 00000000..fc98151d
--- /dev/null
+++ b/triqs/gfs/local/fit_tail.hpp
@@ -0,0 +1,164 @@
+/*******************************************************************************
+ *
+ * TRIQS: a Toolbox for Research in Interacting Quantum Systems
+ *
+ * Copyright (C) 2012 by H. Hafermann, O. Parcollet
+ *
+ * TRIQS is free software: you can redistribute it and/or modify it under the
+ * terms of the GNU General Public License as published by the Free Software
+ * Foundation, either version 3 of the License, or (at your option) any later
+ * version.
+ *
+ * TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
+ * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+ * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+ * details.
+ *
+ * You should have received a copy of the GNU General Public License along with
+ * TRIQS. If not, see <http://www.gnu.org/licenses/>.
+ *
+ ******************************************************************************/
+#ifndef TRIQS_GF_LOCAL_FIT_TAIL_H
+#define TRIQS_GF_LOCAL_FIT_TAIL_H
+#include <triqs/gfs/imfreq.hpp>
+#include <triqs/gfs/block.hpp>
+#include <triqs/gfs/local/tail.hpp>
+#include <triqs/arrays/blas_lapack/gelss.hpp>
+#include <triqs/python_tools/cython_proxy.hpp>
+
+namespace triqs {
+namespace gfs {
+ namespace local {
+
+  using triqs::gfs::imfreq;
+  using triqs::gfs::block_index;
+  using triqs::gfs::block_index;
+
+  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
+
+  // 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): wn_min, wn_max
+
+  // output: returns the tail obtained by fitting
+
+  tail fit_tail_impl(gf<imfreq> &gf, const tail_view known_moments, int n_moments, int wn_min, int wn_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);
+
+   // 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;
+
+   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 = wn_max - wn_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;
+
+   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 = wn_min + k;
+      auto iw = std::complex<double>(0.0, (2 * n + 1) * M_PI / beta);
+
+      B(k, 0) = imag(gf.data()(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 = wn_min + k;
+      auto iw = std::complex<double>(0.0, (2 * n + 1) * M_PI / beta);
+
+      B(k, 0) = real(gf.data()(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);
+     }
+    }
+   }
+
+   return res; // return tail
+  }
+
+
+  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) {
+   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, wn_min, wn_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(wn_min,wn_max+1)) {
+     if ((i >= wn_min) && (i <= wn_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 wn_min,
+                         size_t wn_max, bool replace_by_fit = false) {
+   // for(auto &gf : block_gf) set_tail_from_fit(gf, known_moments, n_moments, wn_min, wn_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, wn_min, wn_max, replace_by_fit);
+  }
+ }
+}
+} // namespace
+#endif