mirror of
https://github.com/triqs/dft_tools
synced 2024-11-14 18:13:49 +01:00
d25bd40560
- fabs for complex ? It is not defined. - replaced by std::abs. - How could the code compile before ?
483 lines
12 KiB
C++
483 lines
12 KiB
C++
/*******************************************************************************
|
|
*
|
|
* This file is part of the ATM library.
|
|
*
|
|
* Copyright (C) 2010 by O. E. Peil
|
|
*
|
|
* 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/>.
|
|
*
|
|
*******************************************************************************/
|
|
#include <triqs/arrays.hpp>
|
|
#include <iostream>
|
|
#include <complex>
|
|
|
|
#include "argsort.hpp"
|
|
#include "dos_tetra3d.hpp"
|
|
|
|
//#define __TETRA_DEBUG
|
|
#define __TETRA_ARRAY_VIEW
|
|
|
|
using triqs::arrays::array;
|
|
using triqs::arrays::array_view;
|
|
|
|
/***************************************************
|
|
|
|
Analytical tetrahedron method as described in
|
|
Lambin et al., PRB 29, 6, 3430 (1984).
|
|
|
|
***************************************************/
|
|
|
|
/// Main function
|
|
//#ifdef __TETRA_ARRAY_VIEW
|
|
//void tet_dos3d(double en, array_view<double, 1>& eigk,
|
|
// array_view<long, 2>& itt, int ntet,
|
|
// array<double, 2>& cti);
|
|
//#else
|
|
//void tet_dos3d(double en, array<double, 1>& eigk,
|
|
// array<long, 2>& itt, int ntet,
|
|
// array<double, 2>& cti);
|
|
//#endif
|
|
|
|
|
|
/// Internal functions
|
|
int dos_corner_weights(double en, double *eigs, int *inds, double *ci);
|
|
int dos_tet_weights(double en, double *eigs, int *inds, double *ct);
|
|
int dos_reorder(double en, double *e, int *inds);
|
|
|
|
static double F(double en, double e1, double e2, double e3, double e4);
|
|
static double K2(double en, double e1, double e2, double e3);
|
|
static double K1(double en, double e1, double e2);
|
|
|
|
static void fun_dos_case1(double en, double *eigs, double *ci);
|
|
static void fun_dos_case2(double en, double *eigs, double *ci);
|
|
static void fun_dos_case3(double en, double *eigs, double *ci);
|
|
|
|
static const int NUM_TET_CORNERS = 4;
|
|
static const std::complex<double> I(0.0, 1.0);
|
|
static const double small = 2.5e-2, tol = 1e-8;
|
|
|
|
/*
|
|
Returns corner contributions to the DOS of a band
|
|
*/
|
|
#ifdef __TETRA_ARRAY_VIEW
|
|
array_view<double, 2> dos_tetra_weights_3d(array_view<double, 1> eigk, double en, array_view<long, 2> itt)
|
|
#else
|
|
array<double, 2> dos_tetra_weights_3d(array<double, 1> eigk, double en, array<long, 2> itt)
|
|
#endif
|
|
{
|
|
int ntet; /// Number of tetrahedra
|
|
// Auxiliary variables and loop indices
|
|
|
|
if (first_dim(itt) != NUM_TET_CORNERS + 1)
|
|
{
|
|
TRIQS_RUNTIME_ERROR << " The first dimension of 'itt' must be equal to 5";
|
|
}
|
|
|
|
ntet = second_dim(itt);
|
|
|
|
array<double, 2> cti(NUM_TET_CORNERS, ntet); // Corner weights to be returned
|
|
|
|
// tet_dos3d(e, eigk, itt, ntet, cti);
|
|
|
|
//
|
|
// Main algorithm (transferred from 'tet_dos3d()')
|
|
//
|
|
double eigs[4], ci[4];
|
|
|
|
int i, it, ik, inds[4], flag;
|
|
#ifdef __TETRA_DEBUG
|
|
double ct, ci_sum;
|
|
#endif
|
|
|
|
// Loop over tetrahedra (triangles)
|
|
for (it = 0; it < ntet; it++)
|
|
{
|
|
for (i = 1; i < 5; i++)
|
|
{
|
|
ik = itt(i, it);
|
|
eigs[i - 1] = eigk(ik);
|
|
}
|
|
|
|
// Corner weights for a single tetrahedron
|
|
dos_corner_weights(en, eigs, inds, ci);
|
|
|
|
#ifdef __TETRA_DEBUG
|
|
for(i = 0, ci_sum = 0.0; i < 4; i++)
|
|
ci_sum += ci[i];
|
|
|
|
flag = dos_tet_weights(en, eigs, inds, &ct);
|
|
if(std::abs(ct - ci_sum) > tol)
|
|
{
|
|
std::cout << " *** Error in weights: it = " << it <<" flag = " << flag << ", en = " << en;
|
|
for(i = 0; i < 4; i++)
|
|
std::cout << ", e[" << i << "] = " << eigs[i];
|
|
std::cout << ", c_diff = " << std::abs(ct - ci_sum) << std::endl;
|
|
|
|
TRIQS_RUNTIME_ERROR << " Failed consistency check";
|
|
}
|
|
#endif
|
|
|
|
for(i = 0; i < 4; i++)
|
|
{
|
|
cti(inds[i], it) = ci[i];
|
|
}
|
|
|
|
} // it = 1, ntet
|
|
|
|
return array_view<double,2>(cti);
|
|
}
|
|
|
|
//#ifdef __TETRA_ARRAY_VIEW
|
|
//void tet_dos3d(double en, array_view<double, 1>& eigk,
|
|
// array_view<long, 2>& itt, int ntet,
|
|
// array<double, 2>& cti)
|
|
//#else
|
|
//void tet_dos3d(double en, array<double, 1>& eigk,
|
|
// array<long, 2>& itt, int ntet,
|
|
// array<double, 2>& cti)
|
|
//#endif
|
|
//{
|
|
// double eigs[4], ci[4];
|
|
//
|
|
// int i, it, ik, inds[4], flag;
|
|
//#ifdef __TETRA_DEBUG
|
|
// double ct, ci_sum;
|
|
//#endif
|
|
//
|
|
//// Loop over tetrahedra (triangles)
|
|
// for (it = 0; it < ntet; it++)
|
|
// {
|
|
// for (i = 1; i < 5; i++)
|
|
// {
|
|
// ik = itt(i, it);
|
|
// eigs[i - 1] = eigk(ik);
|
|
// }
|
|
//
|
|
//// Corner weights for a single tetrahedron
|
|
// dos_corner_weights(en, eigs, inds, ci);
|
|
//
|
|
//#ifdef __TETRA_DEBUG
|
|
// for(i = 0, ci_sum = 0.0; i < 4; i++)
|
|
// ci_sum += ci[i];
|
|
//
|
|
// flag = dos_tet_weights(en, eigs, inds, &ct);
|
|
// if(std::abs(ct - ci_sum) > tol)
|
|
// {
|
|
// std::cout << " *** Error in weights: it = " << it <<" flag = " << flag << ", en = " << en;
|
|
// for(i = 0; i < 4; i++)
|
|
// std::cout << ", e[" << i << "] = " << eigs[i];
|
|
// std::cout << ", c_diff = " << std::abs(ct - ci_sum) << std::endl;
|
|
// return;
|
|
// }
|
|
//#endif
|
|
//
|
|
// for(i = 0; i < 4; i++)
|
|
// {
|
|
// cti(inds[i], it) = ci[i];
|
|
// }
|
|
//
|
|
// } // it = 1, ntet
|
|
//}
|
|
|
|
/// Corner contributions to DOS
|
|
int dos_corner_weights(double en, double *eigs, int *inds,
|
|
double *ci)
|
|
{
|
|
int flag, i;
|
|
// Sort eigenvalues and obtain indices of the sorted array
|
|
// eigs: sorted eigenvalues
|
|
// inds: index map
|
|
flag = dos_reorder(en, eigs, inds);
|
|
|
|
switch(flag)
|
|
{
|
|
// E1 <= E <= E2
|
|
case 1:
|
|
fun_dos_case1(en, eigs, ci);
|
|
break;
|
|
|
|
// E2 <= E <= E3
|
|
case 2:
|
|
fun_dos_case2(en, eigs, ci);
|
|
break;
|
|
|
|
// E3 <= E <= E4
|
|
case 3:
|
|
fun_dos_case3(en, eigs, ci);
|
|
break;
|
|
|
|
// E < E1 || E4 < E
|
|
case 4:
|
|
case 5:
|
|
for(i = 0; i < 4; i++) ci[i] = 0.0;
|
|
break;
|
|
|
|
// E1 == E4 == E
|
|
case 6:
|
|
for(i = 0; i < 4; i++) ci[i] = 0.25;
|
|
break;
|
|
}
|
|
|
|
return flag;
|
|
}
|
|
|
|
/// Total (tetrahedron) contribution to DOS.
|
|
/// Here, it is calculated directly using an analytical formula.
|
|
/// This is mainly needed for debugging.
|
|
int dos_tet_weights(double en, double *eigs, int *inds,
|
|
double *ct)
|
|
{
|
|
double e1, e2, e3, e4;
|
|
std::complex<double> s;
|
|
int flag;
|
|
flag = dos_reorder(en, eigs, inds);
|
|
|
|
e1 = eigs[0];
|
|
e2 = eigs[1];
|
|
e3 = eigs[2];
|
|
e4 = eigs[3];
|
|
|
|
switch(flag)
|
|
{
|
|
// E1 <= E <= E2
|
|
case 1:
|
|
if(std::abs(e2 - e1) > tol && std::abs(e3 - e1) > tol && std::abs(e4 - e1) > tol)
|
|
*ct = 3.0 * (en - e1) * (en - e1) / ((e2 - e1) * (e3 - e1) * (e4 - e1));
|
|
else
|
|
{
|
|
s = fmin(std::abs(e1 - e2), std::abs(e3 - e1));
|
|
s = fmin(std::abs(s), std::abs(e4 - e1));
|
|
s /= 100.0;
|
|
s = fmax(std::abs(s), 1.0e-20) * I;
|
|
|
|
*ct = 3.0 * std::real((en - e1 + s) * (en - e1 + s) / ((e2 - e1 + s) * (e3 - e1 + s) * (e4 - e1 + s)));
|
|
}
|
|
|
|
break;
|
|
|
|
// E2 <= E <= E3
|
|
case 2:
|
|
if(std::abs(e4 - e2) > tol && std::abs(e3 - e2) > tol && std::abs(e4 - e1) > tol && std::abs(e3 - e1) > tol)
|
|
*ct = 3.0 * (
|
|
(e3 - en) * (en - e2) / ((e4 - e2) * (e3 - e2) * (e3 - e1)) +
|
|
(e4 - en) * (en - e1) / ((e4 - e1) * (e4 - e2) * (e3 - e1)));
|
|
else
|
|
{
|
|
s = fmin(std::abs(e3 - e2), std::abs(e3 - e1));
|
|
s = fmin(std::abs(s), std::abs(e4 - e1));
|
|
s = fmin(std::abs(s), std::abs(e4 - e2));
|
|
s /= 100.0;
|
|
s = fmax(std::abs(s), 1.0e-20) * I;
|
|
|
|
*ct = 3.0 * std::real((
|
|
(e3 - en + s) * (en - e2 + s) / ((e4 - e2 + s) * (e3 - e2 + s) * (e3 - e1 + s)) +
|
|
(e4 - en + s) * (en - e1 + s) / ((e4 - e1 + s) * (e4 - e2 + s) * (e3 - e1 + s))));
|
|
}
|
|
break;
|
|
|
|
// E3 <= E <= E4
|
|
case 3:
|
|
if(std::abs(e4 - e2) > tol && std::abs(e4 - e3) > tol && std::abs(e4 - e1) > tol)
|
|
*ct = 3.0 * (e4 - en) * (e4 - en) / ((e4 - e1) * (e4 - e2) * (e4 - e3));
|
|
else
|
|
{
|
|
s = fmin(std::abs(e4 - e2), std::abs(e4 - e1));
|
|
s = fmin(std::abs(s), std::abs(e4 - e3));
|
|
s /= 100.0;
|
|
s = fmax(std::abs(s), 1.0e-20) * I;
|
|
|
|
*ct = 3.0 * std::real((e4 - en + s) * (e4 - en + s) / ((e4 - e1 + s) * (e4 - e2 + s) * (e4 - e3 + s)));
|
|
}
|
|
|
|
break;
|
|
|
|
// E < E1 || E4 < E
|
|
case 4:
|
|
case 5:
|
|
*ct = 0.0;
|
|
break;
|
|
|
|
// E1 == E4 == E
|
|
case 6:
|
|
*ct = 1.0;
|
|
break;
|
|
}
|
|
|
|
return flag;
|
|
}
|
|
|
|
/// Sorts eigenvalues and also determines eigenvalue degeneracies.
|
|
/// Returns a case number corresponding to a combination of degeneracies.
|
|
int dos_reorder(double en, double *e, int *inds)
|
|
{
|
|
double *ptrs[4], e_tmp[4];
|
|
int i;
|
|
|
|
for(i = 0; i < 4; i++)
|
|
e_tmp[i] = e[i];
|
|
|
|
argsort(e_tmp, inds, ptrs, 4);
|
|
|
|
for(i = 0; i < 4; i++)
|
|
e[i] = e_tmp[inds[i]];
|
|
|
|
if((e[0] <= en && en <= e[3]) && std::abs(e[3] - e[0]) < tol) return 6;
|
|
if(e[0] <= en && en <= e[1]) return 1;
|
|
if(e[1] <= en && en <= e[2]) return 2;
|
|
if(e[2] <= en && en <= e[3]) return 3;
|
|
if(en < e[0]) return 4;
|
|
if(e[3] < en) return 5;
|
|
return -1;
|
|
}
|
|
|
|
static void fun_dos_case1(double en, double *eigs, double *ci)
|
|
{
|
|
double e1, e2, e3, e4;
|
|
|
|
e1 = eigs[0];
|
|
e2 = eigs[1];
|
|
e3 = eigs[2];
|
|
e4 = eigs[3];
|
|
|
|
ci[0] = K2(en, e1, e2, e4) * F(en, e2, e1, e1, e3) +
|
|
K2(en, e1, e2, e3) * F(en, e3, e1, e1, e4) +
|
|
K2(en, e1, e3, e4) * F(en, e4, e1, e1, e2);
|
|
|
|
ci[1] = -K1(en, e1, e2) * F(en, e1, e1, e3, e4);
|
|
|
|
ci[2] = -K1(en, e1, e3) * F(en, e1, e1, e2, e4);
|
|
|
|
ci[3] = -K1(en, e1, e4) * F(en, e1, e1, e2, e3);
|
|
}
|
|
|
|
static void fun_dos_case2(double en, double *eigs, double *ci)
|
|
{
|
|
double e1, e2, e3, e4;
|
|
|
|
e1 = eigs[0];
|
|
e2 = eigs[1];
|
|
e3 = eigs[2];
|
|
e4 = eigs[3];
|
|
|
|
ci[0] = 0.5 * (K1(en, e3, e1) * (
|
|
F(en, e3, e2, e2, e4) +
|
|
F(en, e4, e1, e2, e4) +
|
|
F(en, e3, e1, e2, e4)) +
|
|
K1(en, e4, e1) * (
|
|
F(en, e4, e1, e2, e3) +
|
|
F(en, e4, e2, e2, e3) +
|
|
F(en, e3, e1, e2, e3)));
|
|
|
|
ci[1] = 0.5 * (K1(en, e3, e2) * (
|
|
F(en, e3, e2, e1, e4) +
|
|
F(en, e4, e2, e1, e4) +
|
|
F(en, e3, e1, e1, e4)) +
|
|
K1(en, e4, e2) * (
|
|
F(en, e3, e2, e1, e3) +
|
|
F(en, e4, e1, e1, e3) +
|
|
F(en, e4, e2, e1, e3)));
|
|
|
|
ci[2] = 0.5 * (-K1(en, e2, e3) * (
|
|
F(en, e3, e2, e1, e4) +
|
|
F(en, e4, e2, e1, e4) +
|
|
F(en, e3, e1, e1, e4)) -
|
|
K1(en, e1, e3) * (
|
|
F(en, e3, e2, e2, e4) +
|
|
F(en, e4, e1, e2, e4) +
|
|
F(en, e3, e1, e2, e4)));
|
|
|
|
ci[3] = 0.5 * (-K1(en, e2, e4) * (
|
|
F(en, e3, e2, e1, e3) +
|
|
F(en, e4, e1, e1, e3) +
|
|
F(en, e4, e2, e1, e3)) -
|
|
K1(en, e1, e4) * (
|
|
F(en, e4, e1, e2, e3) +
|
|
F(en, e4, e2, e2, e3) +
|
|
F(en, e3, e1, e2, e3)));
|
|
}
|
|
|
|
static void fun_dos_case3(double en, double *eigs, double *ci)
|
|
{
|
|
double e1, e2, e3, e4;
|
|
|
|
e1 = eigs[0];
|
|
e2 = eigs[1];
|
|
e3 = eigs[2];
|
|
e4 = eigs[3];
|
|
|
|
ci[0] = K1(en, e4, e1) * F(en, e4, e4, e2, e3);
|
|
|
|
ci[1] = K1(en, e4, e2) * F(en, e4, e4, e1, e3);
|
|
|
|
ci[2] = K1(en, e4, e3) * F(en, e4, e4, e1, e2);
|
|
|
|
ci[3] = -K2(en, e4, e3, e1) * F(en, e4, e3, e2, e4) -
|
|
K2(en, e4, e2, e3) * F(en, e4, e2, e1, e4) -
|
|
K2(en, e4, e1, e2) * F(en, e4, e1, e3, e4);
|
|
|
|
}
|
|
|
|
static double F(double en, double e1, double e2, double e3, double e4)
|
|
{
|
|
std::complex<double> s;
|
|
|
|
if(std::abs(e1 - e3) > tol && std::abs(e4 - e2) > tol)
|
|
return (e1 - en) * (en - e2) / ((e1 - e3) * (e4 - e2));
|
|
else
|
|
{
|
|
// Regularization to avoid division by zero
|
|
s = fmin(std::abs(e3 - e1), std::abs(e4 - e2));
|
|
s /= 100.0;
|
|
s = fmax(std::abs(s), 1.0e-20) * I;
|
|
|
|
return std::real((e1 - en + s) * (en - e2 + s) / ((e1 - e3 + s) * (e4 - e2 + s)));
|
|
}
|
|
}
|
|
|
|
static double K2(double en, double e1, double e2, double e3)
|
|
{
|
|
std::complex<double> s;
|
|
|
|
if(std::abs(e1 - e3) > tol && std::abs(e1 - e2) > tol)
|
|
return (en - e1) / ((e2 - e1) * (e3 - e1));
|
|
else
|
|
{
|
|
// Regularization to avoid division by zero
|
|
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)));
|
|
}
|
|
}
|
|
|
|
|