CheMPS2::Davidson Class Reference

#include <Davidson.h>

Public Member Functions
	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')
	Constructor. More...
virtual	~Davidson ()
	Destructor.
char	FetchInstruction (double **pointers)
	The iterator to converge the ground state vector. More...
int	GetNumMultiplications () const
	Get the number of matrix vector multiplications which have been performed. More...

Detailed Description

Davidson class.

Author

Sebastian Wouters sebas.nosp@m.tian.nosp@m.woute.nosp@m.rs@g.nosp@m.mail..nosp@m.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
[1] E.R. Davidson, J. Comput. Phys. 17 (1), 87-94 (1975). http://dx.doi.org/10.1016/0021-9991(75)90065-0
[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).)

Definition at line 34 of file Davidson.h.

Constructor & Destructor Documentation

CheMPS2::Davidson::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'
	)

Constructor.

Parameters

veclength	Linear dimension of the symmetric matrix, or the length of the vectors
MAX_NUM_VEC	The maximum number of vectors in which the symmetric matrix is approximately diagonalized
NUM_VEC_KEEP	The number of vectors to keep during deflation
RTOL	The tolerance for the two-norm of the residual ( for convergence )
DIAG_CUTOFF	Cutoff value for the diagonal preconditioner
debug_print	Whether or not to debug print
problem_type	'E' for eigenvalue or 'L' for linear problem.

Definition at line 31 of file Davidson.cpp.

Member Function Documentation

char CheMPS2::Davidson::FetchInstruction

(

double **

pointers

)

The iterator to converge the ground state vector.

Parameters

pointers

Array of double* of length 2 when problem_type=='E' or length 3 when problem_type=='L'.

Returns

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.

Definition at line 105 of file Davidson.cpp.

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int CheMPS2::Davidson::GetNumMultiplications

(

)

const

Get the number of matrix vector multiplications which have been performed.

Returns

The number of matrix vector multiplications which have been performed

Definition at line 103 of file Davidson.cpp.

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The documentation for this class was generated from the following files:

• Davidson.h
• Davidson.cpp