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/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program 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.
*
* This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/** @file simple_lanczos.h
@brief Simple implementation of the Lanczos method.
@author: Elias Rudberg <em>responsible</em>
*/
#ifndef SIMPLE_LANCZOS_HEADER
#define SIMPLE_LANCZOS_HEADER
#include "realtype.h"
#include <vector>
#include <cstdio>
namespace simple_lanczos {
ergo_real simple_lanczos_get_vector_norm(int n, const ergo_real* v);
void simple_lanczos_normalize_vector(int n, ergo_real* v);
void simple_lanczos_get_eigs(int n, ergo_real* M,
ergo_real & currEig_lo, ergo_real* bestVector_lo,
ergo_real & currEig_hi, ergo_real* bestVector_hi,
ergo_real* eigValListResult);
template<typename Tmatvecmul>
void do_lanczos_method(int n,
const ergo_real* guessVector,
ergo_real & resultEig_lo,
ergo_real* resultVec_lo,
ergo_real & resultEig_hi,
ergo_real* resultVec_hi,
const Tmatvecmul & matvecmul,
int maxIterations_in,
ergo_real shift,
ergo_real extraEnergy) {
if(n == 1) {
// Special case for n=1, in this case we need only one "matrix-vector" (really scalar) multiplication to get all info we need.
ergo_real tmpVec1[1];
tmpVec1[0] = 1;
ergo_real tmpVec2[1];
tmpVec2[0] = 0;
matvecmul.do_mat_vec_mul(n, tmpVec1, tmpVec2);
ergo_real eigenValue = tmpVec2[0];
resultEig_lo = eigenValue;
resultEig_hi = eigenValue;
resultVec_lo[0] = 1;
resultVec_hi[0] = 1;
}
typedef ergo_real* ergo_real_ptr;
int maxIterations = maxIterations_in;
if(maxIterations > n)
maxIterations = n;
ergo_real** q = new ergo_real_ptr[n+1];
q[0] = new ergo_real[n];
for(int i = 0; i < n; i++)
q[0][i] = 0;
q[1] = new ergo_real[n];
for(int i = 0; i < n; i++)
q[1][i] = guessVector[i];
simple_lanczos_normalize_vector(n, q[1]);
std::vector<ergo_real> z(n);
std::vector<ergo_real> alpha(n+1);
std::vector<ergo_real> beta(n+1);
beta[0] = 0;
std::vector<ergo_real> bestVector_lo(maxIterations+1);
std::vector<ergo_real> bestVector_hi(maxIterations+1);
ergo_real currEig_lo = 0;
ergo_real currEig_hi = 0;
ergo_real curr_E_lo = 0;
ergo_real curr_E_hi = 0;
for(int j = 1; j <= maxIterations; j++) {
// Do matrix-vector multiplication
matvecmul.do_mat_vec_mul(n, q[j], &z[0]);
// OK, matrix-vector multiplication done
alpha[j] = 0;
for(int i = 0; i < n; i++)
alpha[j] += q[j][i] * z[i];
for(int i = 0; i < n; i++)
z[i] = z[i] - alpha[j] * q[j][i] - beta[j-1] * q[j-1][i];
beta[j] = simple_lanczos_get_vector_norm(n, &z[0]);
ergo_real* T = new ergo_real[j*j];
for(int i = 0; i < j*j; i++)
T[i] = 0;
for(int i = 0; i < j; i++)
T[i*j+i] = alpha[i+1];
for(int i = 0; i < j-1; i++) {
T[i*j+(i+1)] = beta[i+1];
T[(i+1)*j+i] = beta[i+1];
}
simple_lanczos_get_eigs(j, T, currEig_lo, &bestVector_lo[0], currEig_hi, &bestVector_hi[0], NULL);
// Set resultVec_lo
for(int k = 0; k < n; k++) {
ergo_real sum = 0;
for(int i = 1; i <= j; i++)
sum += bestVector_lo[i-1] * q[i][k];
resultVec_lo[k] = sum;
}
// Set resultVec_hi
for(int k = 0; k < n; k++) {
ergo_real sum = 0;
for(int i = 1; i <= j; i++)
sum += bestVector_hi[i-1] * q[i][k];
resultVec_hi[k] = sum;
}
curr_E_lo = currEig_lo + extraEnergy + shift;
curr_E_hi = currEig_hi + extraEnergy + shift;
if(beta[j] < 1e-11 && j > 1)
break;
if(j == maxIterations)
break;
q[j+1] = new ergo_real[n];
for(int i = 0; i < n; i++)
q[j+1][i] = z[i] / beta[j];
} // end for j
resultEig_lo = curr_E_lo;
resultEig_hi = curr_E_hi;
simple_lanczos_normalize_vector(n, resultVec_lo);
simple_lanczos_normalize_vector(n, resultVec_hi);
}
} // end namespace simple_lanczos
#endif
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