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https://github.com/triqs/dft_tools
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911f127789
In order to wrap the ATM routines by Python using TRIQS wrapping tools it is necessary to modify the interface to 'dos_tetra3d'. The major changes involved replacing direct NumPy arrays with TRIQS arrays which can be converted to Python arrays using library tools. Also, some small changes were necessary to port the functions from C99 complex numbers to C++ style. CMakeList is added to automatize building of the ATM library.
483 lines
12 KiB
C++
483 lines
12 KiB
C++
/*******************************************************************************
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*
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* This file is part of the ATM library.
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*
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* Copyright (C) 2010 by O. E. Peil
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*
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* TRIQS is free software: you can redistribute it and/or modify it under the
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* terms of the GNU General Public License as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option) any later
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* version.
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*
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* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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* details.
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*
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* You should have received a copy of the GNU General Public License along with
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* TRIQS. If not, see <http://www.gnu.org/licenses/>.
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*
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*******************************************************************************/
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#include <triqs/arrays.hpp>
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#include <iostream>
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#include <complex>
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#include "argsort.hpp"
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#include "dos_tetra3d.hpp"
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//#define __TETRA_DEBUG
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#define __TETRA_ARRAY_VIEW
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using triqs::arrays::array;
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using triqs::arrays::array_view;
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/***************************************************
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Analytical tetrahedron method as described in
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Lambin et al., PRB 29, 6, 3430 (1984).
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***************************************************/
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/// Main function
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//#ifdef __TETRA_ARRAY_VIEW
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//void tet_dos3d(double en, array_view<double, 1>& eigk,
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// array_view<long, 2>& itt, int ntet,
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// array<double, 2>& cti);
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//#else
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//void tet_dos3d(double en, array<double, 1>& eigk,
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// array<long, 2>& itt, int ntet,
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// array<double, 2>& cti);
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//#endif
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/// Internal functions
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int dos_corner_weights(double en, double *eigs, int *inds, double *ci);
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int dos_tet_weights(double en, double *eigs, int *inds, double *ct);
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int dos_reorder(double en, double *e, int *inds);
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static double F(double en, double e1, double e2, double e3, double e4);
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static double K2(double en, double e1, double e2, double e3);
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static double K1(double en, double e1, double e2);
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static void fun_dos_case1(double en, double *eigs, double *ci);
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static void fun_dos_case2(double en, double *eigs, double *ci);
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static void fun_dos_case3(double en, double *eigs, double *ci);
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static const int NUM_TET_CORNERS = 4;
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static const std::complex<double> I(0.0, 1.0);
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static const double small = 2.5e-2, tol = 1e-8;
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/*
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Returns corner contributions to the DOS of a band
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*/
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#ifdef __TETRA_ARRAY_VIEW
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array_view<double, 2> dos_tetra_weights_3d(array_view<double, 1> eigk, double en, array_view<long, 2> itt)
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#else
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array<double, 2> dos_tetra_weights_3d(array<double, 1> eigk, double en, array<long, 2> itt)
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#endif
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{
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int ntet; /// Number of tetrahedra
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// Auxiliary variables and loop indices
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if (first_dim(itt) != NUM_TET_CORNERS + 1)
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{
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TRIQS_RUNTIME_ERROR << " The first dimension of 'itt' must be equal to 5";
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}
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ntet = second_dim(itt);
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array<double, 2> cti(NUM_TET_CORNERS, ntet); // Corner weights to be returned
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// tet_dos3d(e, eigk, itt, ntet, cti);
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//
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// Main algorithm (transferred from 'tet_dos3d()')
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//
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double eigs[4], ci[4];
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int i, it, ik, inds[4], flag;
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#ifdef __TETRA_DEBUG
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double ct, ci_sum;
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#endif
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// Loop over tetrahedra (triangles)
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for (it = 0; it < ntet; it++)
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{
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for (i = 1; i < 5; i++)
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{
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ik = itt(i, it);
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eigs[i - 1] = eigk(ik);
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}
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// Corner weights for a single tetrahedron
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dos_corner_weights(en, eigs, inds, ci);
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#ifdef __TETRA_DEBUG
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for(i = 0, ci_sum = 0.0; i < 4; i++)
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ci_sum += ci[i];
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flag = dos_tet_weights(en, eigs, inds, &ct);
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if(fabs(ct - ci_sum) > tol)
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{
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std::cout << " *** Error in weights: it = " << it <<" flag = " << flag << ", en = " << en;
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for(i = 0; i < 4; i++)
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std::cout << ", e[" << i << "] = " << eigs[i];
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std::cout << ", c_diff = " << fabs(ct - ci_sum) << std::endl;
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TRIQS_RUNTIME_ERROR << " Failed consistency check";
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}
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#endif
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for(i = 0; i < 4; i++)
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{
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cti(inds[i], it) = ci[i];
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}
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} // it = 1, ntet
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return array_view<double,2>(cti);
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}
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//#ifdef __TETRA_ARRAY_VIEW
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//void tet_dos3d(double en, array_view<double, 1>& eigk,
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// array_view<long, 2>& itt, int ntet,
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// array<double, 2>& cti)
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//#else
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//void tet_dos3d(double en, array<double, 1>& eigk,
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// array<long, 2>& itt, int ntet,
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// array<double, 2>& cti)
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//#endif
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//{
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// double eigs[4], ci[4];
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//
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// int i, it, ik, inds[4], flag;
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//#ifdef __TETRA_DEBUG
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// double ct, ci_sum;
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//#endif
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//
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//// Loop over tetrahedra (triangles)
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// for (it = 0; it < ntet; it++)
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// {
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// for (i = 1; i < 5; i++)
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// {
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// ik = itt(i, it);
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// eigs[i - 1] = eigk(ik);
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// }
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//
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//// Corner weights for a single tetrahedron
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// dos_corner_weights(en, eigs, inds, ci);
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//
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//#ifdef __TETRA_DEBUG
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// for(i = 0, ci_sum = 0.0; i < 4; i++)
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// ci_sum += ci[i];
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//
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// flag = dos_tet_weights(en, eigs, inds, &ct);
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// if(fabs(ct - ci_sum) > tol)
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// {
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// std::cout << " *** Error in weights: it = " << it <<" flag = " << flag << ", en = " << en;
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// for(i = 0; i < 4; i++)
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// std::cout << ", e[" << i << "] = " << eigs[i];
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// std::cout << ", c_diff = " << fabs(ct - ci_sum) << std::endl;
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// return;
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// }
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//#endif
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//
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// for(i = 0; i < 4; i++)
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// {
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// cti(inds[i], it) = ci[i];
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// }
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//
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// } // it = 1, ntet
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//}
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/// Corner contributions to DOS
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int dos_corner_weights(double en, double *eigs, int *inds,
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double *ci)
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{
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int flag, i;
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// Sort eigenvalues and obtain indices of the sorted array
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// eigs: sorted eigenvalues
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// inds: index map
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flag = dos_reorder(en, eigs, inds);
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switch(flag)
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{
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// E1 <= E <= E2
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case 1:
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fun_dos_case1(en, eigs, ci);
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break;
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// E2 <= E <= E3
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case 2:
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fun_dos_case2(en, eigs, ci);
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break;
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// E3 <= E <= E4
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case 3:
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fun_dos_case3(en, eigs, ci);
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break;
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// E < E1 || E4 < E
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case 4:
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case 5:
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for(i = 0; i < 4; i++) ci[i] = 0.0;
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break;
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// E1 == E4 == E
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case 6:
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for(i = 0; i < 4; i++) ci[i] = 0.25;
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break;
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}
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return flag;
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}
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/// Total (tetrahedron) contribution to DOS.
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/// Here, it is calculated directly using an analytical formula.
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/// This is mainly needed for debugging.
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int dos_tet_weights(double en, double *eigs, int *inds,
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double *ct)
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{
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double e1, e2, e3, e4;
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std::complex<double> s;
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int flag;
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flag = dos_reorder(en, eigs, inds);
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e1 = eigs[0];
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e2 = eigs[1];
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e3 = eigs[2];
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e4 = eigs[3];
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switch(flag)
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{
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// E1 <= E <= E2
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case 1:
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if(fabs(e2 - e1) > tol && fabs(e3 - e1) > tol && fabs(e4 - e1) > tol)
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*ct = 3.0 * (en - e1) * (en - e1) / ((e2 - e1) * (e3 - e1) * (e4 - e1));
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else
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{
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s = fmin(fabs(e1 - e2), fabs(e3 - e1));
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s = fmin(fabs(s), fabs(e4 - e1));
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s /= 100.0;
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s = fmax(std::abs(s), 1.0e-20) * I;
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*ct = 3.0 * std::real((en - e1 + s) * (en - e1 + s) / ((e2 - e1 + s) * (e3 - e1 + s) * (e4 - e1 + s)));
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}
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break;
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// E2 <= E <= E3
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case 2:
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if(fabs(e4 - e2) > tol && fabs(e3 - e2) > tol && fabs(e4 - e1) > tol && fabs(e3 - e1) > tol)
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*ct = 3.0 * (
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(e3 - en) * (en - e2) / ((e4 - e2) * (e3 - e2) * (e3 - e1)) +
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(e4 - en) * (en - e1) / ((e4 - e1) * (e4 - e2) * (e3 - e1)));
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else
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{
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s = fmin(fabs(e3 - e2), fabs(e3 - e1));
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s = fmin(fabs(s), fabs(e4 - e1));
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s = fmin(fabs(s), fabs(e4 - e2));
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s /= 100.0;
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s = fmax(std::abs(s), 1.0e-20) * I;
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*ct = 3.0 * std::real((
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(e3 - en + s) * (en - e2 + s) / ((e4 - e2 + s) * (e3 - e2 + s) * (e3 - e1 + s)) +
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(e4 - en + s) * (en - e1 + s) / ((e4 - e1 + s) * (e4 - e2 + s) * (e3 - e1 + s))));
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}
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break;
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// E3 <= E <= E4
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case 3:
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if(fabs(e4 - e2) > tol && fabs(e4 - e3) > tol && fabs(e4 - e1) > tol)
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*ct = 3.0 * (e4 - en) * (e4 - en) / ((e4 - e1) * (e4 - e2) * (e4 - e3));
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else
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{
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s = fmin(fabs(e4 - e2), fabs(e4 - e1));
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s = fmin(fabs(s), fabs(e4 - e3));
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s /= 100.0;
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s = fmax(std::abs(s), 1.0e-20) * I;
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*ct = 3.0 * std::real((e4 - en + s) * (e4 - en + s) / ((e4 - e1 + s) * (e4 - e2 + s) * (e4 - e3 + s)));
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}
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break;
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// E < E1 || E4 < E
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case 4:
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case 5:
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*ct = 0.0;
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break;
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// E1 == E4 == E
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case 6:
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*ct = 1.0;
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break;
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}
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return flag;
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}
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/// Sorts eigenvalues and also determines eigenvalue degeneracies.
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/// Returns a case number corresponding to a combination of degeneracies.
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int dos_reorder(double en, double *e, int *inds)
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{
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double *ptrs[4], e_tmp[4];
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int i;
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for(i = 0; i < 4; i++)
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e_tmp[i] = e[i];
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argsort(e_tmp, inds, ptrs, 4);
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for(i = 0; i < 4; i++)
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e[i] = e_tmp[inds[i]];
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if((e[0] <= en && en <= e[3]) && fabs(e[3] - e[0]) < tol) return 6;
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if(e[0] <= en && en <= e[1]) return 1;
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if(e[1] <= en && en <= e[2]) return 2;
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if(e[2] <= en && en <= e[3]) return 3;
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if(en < e[0]) return 4;
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if(e[3] < en) return 5;
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return -1;
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}
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static void fun_dos_case1(double en, double *eigs, double *ci)
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{
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double e1, e2, e3, e4;
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e1 = eigs[0];
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e2 = eigs[1];
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e3 = eigs[2];
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e4 = eigs[3];
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ci[0] = K2(en, e1, e2, e4) * F(en, e2, e1, e1, e3) +
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K2(en, e1, e2, e3) * F(en, e3, e1, e1, e4) +
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K2(en, e1, e3, e4) * F(en, e4, e1, e1, e2);
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ci[1] = -K1(en, e1, e2) * F(en, e1, e1, e3, e4);
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ci[2] = -K1(en, e1, e3) * F(en, e1, e1, e2, e4);
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ci[3] = -K1(en, e1, e4) * F(en, e1, e1, e2, e3);
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}
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static void fun_dos_case2(double en, double *eigs, double *ci)
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{
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double e1, e2, e3, e4;
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e1 = eigs[0];
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e2 = eigs[1];
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e3 = eigs[2];
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e4 = eigs[3];
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ci[0] = 0.5 * (K1(en, e3, e1) * (
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F(en, e3, e2, e2, e4) +
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F(en, e4, e1, e2, e4) +
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F(en, e3, e1, e2, e4)) +
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K1(en, e4, e1) * (
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F(en, e4, e1, e2, e3) +
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F(en, e4, e2, e2, e3) +
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F(en, e3, e1, e2, e3)));
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ci[1] = 0.5 * (K1(en, e3, e2) * (
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F(en, e3, e2, e1, e4) +
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F(en, e4, e2, e1, e4) +
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F(en, e3, e1, e1, e4)) +
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K1(en, e4, e2) * (
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F(en, e3, e2, e1, e3) +
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F(en, e4, e1, e1, e3) +
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F(en, e4, e2, e1, e3)));
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ci[2] = 0.5 * (-K1(en, e2, e3) * (
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F(en, e3, e2, e1, e4) +
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F(en, e4, e2, e1, e4) +
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F(en, e3, e1, e1, e4)) -
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K1(en, e1, e3) * (
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F(en, e3, e2, e2, e4) +
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F(en, e4, e1, e2, e4) +
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F(en, e3, e1, e2, e4)));
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ci[3] = 0.5 * (-K1(en, e2, e4) * (
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F(en, e3, e2, e1, e3) +
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F(en, e4, e1, e1, e3) +
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F(en, e4, e2, e1, e3)) -
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K1(en, e1, e4) * (
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F(en, e4, e1, e2, e3) +
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F(en, e4, e2, e2, e3) +
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F(en, e3, e1, e2, e3)));
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}
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static void fun_dos_case3(double en, double *eigs, double *ci)
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{
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double e1, e2, e3, e4;
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e1 = eigs[0];
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e2 = eigs[1];
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e3 = eigs[2];
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e4 = eigs[3];
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ci[0] = K1(en, e4, e1) * F(en, e4, e4, e2, e3);
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ci[1] = K1(en, e4, e2) * F(en, e4, e4, e1, e3);
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ci[2] = K1(en, e4, e3) * F(en, e4, e4, e1, e2);
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ci[3] = -K2(en, e4, e3, e1) * F(en, e4, e3, e2, e4) -
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K2(en, e4, e2, e3) * F(en, e4, e2, e1, e4) -
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K2(en, e4, e1, e2) * F(en, e4, e1, e3, e4);
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}
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static double F(double en, double e1, double e2, double e3, double e4)
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{
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std::complex<double> s;
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if(fabs(e1 - e3) > tol && fabs(e4 - e2) > tol)
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return (e1 - en) * (en - e2) / ((e1 - e3) * (e4 - e2));
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else
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{
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// Regularization to avoid division by zero
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s = fmin(fabs(e3 - e1), fabs(e4 - e2));
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s /= 100.0;
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s = fmax(std::abs(s), 1.0e-20) * I;
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return std::real((e1 - en + s) * (en - e2 + s) / ((e1 - e3 + s) * (e4 - e2 + s)));
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}
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}
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static double K2(double en, double e1, double e2, double e3)
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{
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std::complex<double> s;
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if(fabs(e1 - e3) > tol && fabs(e1 - e2) > tol)
|
|
return (en - e1) / ((e2 - e1) * (e3 - e1));
|
|
else
|
|
{
|
|
// Regularization to avoid division by zero
|
|
s = fmin(fabs(e3 - e1), fabs(e1 - e2));
|
|
s /= 100.0;
|
|
s = fmax(std::abs(s), 1.0e-20) * I;
|
|
|
|
return std::real((en - e1 + s) / ((e2 - e1 + s) * (e3 - e1 + s)));
|
|
}
|
|
}
|
|
|
|
static double K1(double en, double e1, double e2)
|
|
{
|
|
std::complex<double> s;
|
|
|
|
if(fabs(e1 - e2) > tol)
|
|
return (e1 - en) / ((e2 - e1) * (e2 - e1));
|
|
else
|
|
{
|
|
// Regularization to avoid division by zero
|
|
s = fabs(e1 - e2);
|
|
s /= 100.0;
|
|
s = fmax(std::abs(s), 1.0e-20) * I;
|
|
|
|
return std::real((e1 - en + s) / ((e2 - e1 + s) * (e2 - e1 + s)));
|
|
}
|
|
}
|
|
|
|
|