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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 Lanczos.h Class for building Krylov subspaces with the Lanczos method
*
* Copyright(c) Emanuel Rubensson 2006
*
* @author Emanuel Rubensson
* @date December 2006
*
*/
#ifndef MAT_LANCZOS
#define MAT_LANCZOS
#include "MatrixTridiagSymmetric.h"
#include "mat_utils.h"
namespace mat { /* Matrix namespace */
namespace arn { /* Arnoldi type methods namespace */
/** Class template for building Krylov subspaces with Lanczos
*
* Build up Krylov subspace for symmetric matrix with
* a Lanczos process.
*
*
* Treal: Type for real numbers
*
* Tmatrix: The matrix class
*
* Tvector: Vector class
*
*/
template<typename Treal, typename Tmatrix, typename Tvector>
class Lanczos {
public:
Lanczos(Tmatrix const & AA, Tvector const & startVec,
int maxIt = 100, int cap = 100)
: A(AA), v(new Tvector[cap]), capacity(cap), j(0), maxIter(maxIt),
alpha(0), beta(0) {
assert(cap > 1);
Treal const ONE = 1.0;
v[0] = startVec;
if(v[0].eucl() < template_blas_sqrt(getRelPrecision<Treal>())) {
v[0].rand();
}
v[0] *= (ONE / v[0].eucl());
r = v[0];
}
void restart(Tvector const & startVec) {
j = 0;
alpha = 0;
beta = 0;
delete[] v;
v = new Tvector[capacity];
Treal const ONE = 1.0;
v[0] = startVec;
v[0] *= (ONE / startVec.eucl());
r = startVec;
Tri.clear();
}
virtual void run() {
do {
step();
update();
if (j > maxIter)
throw AcceptableMaxIter("Lanczos::run() did not converge within maxIter");
}
while (!converged());
}
inline void copyTridiag(MatrixTridiagSymmetric<Treal> & Tricopy) {
Tricopy = Tri;
}
virtual ~Lanczos() {
delete[] v;
}
protected:
Tmatrix const & A;
Tvector* v; /** Vectors spanning Krylov subspace.
* In step j: Vectors 0 : j-2 is on file
* Vectors j-1 : j is in memory
*/
Tvector r; /** Residual vector */
MatrixTridiagSymmetric<Treal> Tri;
int capacity;
int j; /** Current step */
int maxIter;
void increaseCapacity(int const newCapacity);
void step();
void getEigVector(Tvector& eigVec, Treal const * const eVecTri) const;
virtual void update() = 0;
virtual bool converged() const = 0;
private:
Treal alpha;
Treal beta;
}; /* end class definition Lanczos */
template<typename Treal, typename Tmatrix, typename Tvector>
void Lanczos<Treal, Tmatrix, Tvector>::step() {
if (j + 1 >= capacity)
increaseCapacity(capacity * 2);
Treal const ONE = 1.0;
A.matVecProd(r, v[j]); // r = A * v[j]
alpha = transpose(v[j]) * r;
r += (-alpha) * v[j];
if (j) {
r += (-beta) * v[j-1];
v[j-1].writeToFile();
}
beta = r.eucl();
v[j+1] = r;
v[j+1] *= ONE / beta;
Tri.increase(alpha, beta);
++j;
}
/* FIXME: If several eigenvectors are needed it is more optimal to
* compute all of them at once since then the krylov subspace vectors
* only need to be read from memory once.
*/
template<typename Treal, typename Tmatrix, typename Tvector>
void Lanczos<Treal, Tmatrix, Tvector>::
getEigVector(Tvector& eigVec, Treal const * const eVecTri) const {
if (j <= 1) {
eigVec = v[0];
}
else {
v[0].readFromFile();
eigVec = v[0];
v[0].writeToFile();
}
eigVec *= eVecTri[0];
for (int ind = 1; ind <= j - 2; ++ind) {
v[ind].readFromFile();
eigVec += eVecTri[ind] * v[ind];
v[ind].writeToFile();
}
eigVec += eVecTri[j-1] * v[j-1];
}
template<typename Treal, typename Tmatrix, typename Tvector>
void Lanczos<Treal, Tmatrix, Tvector>::
increaseCapacity(int const newCapacity) {
assert(newCapacity > capacity);
assert(j > 0);
capacity = newCapacity;
Tvector* new_v = new Tvector[capacity];
/* FIXME: Fix so that file is copied when operator= is called in Vector
* class
*/
for (int ind = 0; ind <= j - 2; ind++){
v[ind].readFromFile();
new_v[ind] = v[ind];
new_v[ind].writeToFile();
}
for (int ind = j - 1; ind <= j; ind++){
new_v[ind] = v[ind];
}
delete[] v;
v = new_v;
}
} /* end namespace arn */
} /* end namespace mat */
#endif
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