mirror of https://github.com/triqs/dft_tools
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<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(std::abs(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 = " << std::abs(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(std::abs(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 = " << std::abs(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(std::abs(e2 - e1) > tol && std::abs(e3 - e1) > tol && std::abs(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(std::abs(e1 - e2), std::abs(e3 - e1));
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s = fmin(std::abs(s), std::abs(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(std::abs(e4 - e2) > tol && std::abs(e3 - e2) > tol && std::abs(e4 - e1) > tol && std::abs(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(std::abs(e3 - e2), std::abs(e3 - e1));
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s = fmin(std::abs(s), std::abs(e4 - e1));
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s = fmin(std::abs(s), std::abs(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(std::abs(e4 - e2) > tol && std::abs(e4 - e3) > tol && std::abs(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(std::abs(e4 - e2), std::abs(e4 - e1));
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s = fmin(std::abs(s), std::abs(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]) && std::abs(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(std::abs(e1 - e3) > tol && std::abs(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(std::abs(e3 - e1), std::abs(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(std::abs(e1 - e3) > tol && std::abs(e1 - e2) > tol)
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return (en - e1) / ((e2 - e1) * (e3 - e1));
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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(std::abs(e3 - e1), std::abs(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(std::abs(e1 - e2) > tol)
|
|
return (e1 - en) / ((e2 - e1) * (e2 - e1));
|
|
else
|
|
{
|
|
// Regularization to avoid division by zero
|
|
s = std::abs(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)));
|
|
}
|
|
}
|
|
|
|
|