/usr/include/chemps2/Davidson.h is in libchemps2-dev 1.8.5-1.
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CheMPS2: a spin-adapted implementation of DMRG for ab initio quantum chemistry
Copyright (C) 2013-2018 Sebastian Wouters
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 2 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, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#ifndef DAVIDSON_CHEMPS2_H
#define DAVIDSON_CHEMPS2_H
namespace CheMPS2{
/** Davidson class.
\author Sebastian Wouters <sebastianwouters@gmail.com>
\date January 29, 2015
The Davidson class implements Davidson's algorithm to find the lowest eigenvalue and corresponding eigenvector of a symmetric operator.
Information can be found in \n
[1] E.R. Davidson, J. Comput. Phys. 17 (1), 87-94 (1975). http://dx.doi.org/10.1016/0021-9991(75)90065-0 \n
[2] http://people.inf.ethz.ch/arbenz/ewp/Lnotes/chapter11.pdf (In this class algorithm 11.1 is implemented, with equation (11.3) instead of line (16).)
*/
class Davidson{
public:
//! Constructor
/** \param veclength Linear dimension of the symmetric matrix, or the length of the vectors
\param MAX_NUM_VEC The maximum number of vectors in which the symmetric matrix is approximately diagonalized
\param NUM_VEC_KEEP The number of vectors to keep during deflation
\param RTOL The tolerance for the two-norm of the residual ( for convergence )
\param DIAG_CUTOFF Cutoff value for the diagonal preconditioner
\param debug_print Whether or not to debug print
\param problem_type 'E' for eigenvalue or 'L' for linear problem. */
Davidson( const int veclength, const int MAX_NUM_VEC, const int NUM_VEC_KEEP, const double RTOL, const double DIAG_CUTOFF, const bool debug_print, const char problem_type = 'E' );
//! Destructor
virtual ~Davidson();
//! The iterator to converge the ground state vector
/** \param pointers Array of double* of length 2 when problem_type=='E' or length 3 when problem_type=='L'.
\return Instruction character. 'A' means copy the initial guess to pointers[0] and the diagonal of the symmetric matrix to pointers[1]. If 'A' and problem_type=='E', the right-hand side of the problem should be copied to pointers[2]. 'B' means calculate pointers[1] as the result of multiplying the symmetric matrix with pointers[0]. 'C' means that the converged solution can be copied back from pointers[0], and pointers[1][0] contains the ground-state energy if problem_type=='E' or the residual norm if problem_type=='L'. 'D' means that an error has occurred. */
char FetchInstruction( double ** pointers );
//! Get the number of matrix vector multiplications which have been performed
/** \return The number of matrix vector multiplications which have been performed */
int GetNumMultiplications() const;
private:
int veclength; // The vector length
int nMultiplications; // Current number of requested matrix-vector multiplications
char state; // Current state of the algorithm --> based on this parameter the next instruction is given
bool debug_print;
char problem_type;
// Davidson parameters
int MAX_NUM_VEC;
int NUM_VEC_KEEP;
double DIAG_CUTOFF;
double RTOL;
// To store the vectors and the matrix x vectors
int num_vec;
double ** vecs;
double ** Hvecs;
int num_allocated;
// The effective diagonalization problem
double * mxM;
double * mxM_eigs;
double * mxM_vecs;
int mxM_lwork;
double * mxM_work;
double * mxM_rhs;
// Vector spaces
double * t_vec;
double * u_vec;
double * work_vec;
double * diag;
double * RHS;
// For the deflation
double * Reortho_Lowdin;
double * Reortho_Overlap_eigs;
double * Reortho_Overlap;
double * Reortho_Eigenvecs;
// Control script functions
double FrobeniusNorm( double * current_vector );
void SafetyCheckGuess();
void AddNewVec();
double DiagonalizeSmallMatrixAndCalcResidual(); // Returns the residual norm
void CalculateNewVec();
void Deflation();
void MxMafterDeflation();
void SolveLinearSystemDeflation( const int NUM_SOLUTIONS );
};
}
#endif
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