Trace correcting purification. More...

#include <TC2.h>

Classes
class	Fun
	Help class for bisection root finding calls. More...
Public Member Functions
	TC2 (Tmatrix &F, Tmatrix &DM, const int size, const int noc, const Treal trunc=0, const int maxmm=100)
	Constructor Initializes everything.
Treal	fermi_level (Treal tol=1e-15) const
	Returns the Fermi level.
Treal	homo (Treal tol=1e-15) const
	Returns upper bound of the HOMO eigenvalue.
Treal	lumo (Treal tol=1e-15) const
	Returns lower bound of the LUMO eigenvalue.
int	n_multiplies () const
	Returns the number of used matrix matrix multiplications.
void	print_data (int const start, int const stop) const
virtual	~TC2 ()
	Destructor.
Protected Member Functions
void	purify ()
	Runs purification.
Protected Attributes
Tmatrix &	X
	Fock / Kohn-Sham matrix at initialization.
Tmatrix &	D
	Density matrix after purification.
const int	n
	System size.
const int	nocc
	Number of occupied orbitals.
const Treal	frob_trunc
	Threshold for the truncation.
const int	maxmul
	Number of tolerated matrix multiplications.
Treal	lmin
	Lower bound for eigenvalue spectrum.
Treal	lmax
	Upper bound for eigenvalue spectrum.
int	nmul
	Number of used matrix multiplications.
int	nmul_firstpart
	Number of used matrix multiplications in the first part of the purification.
Treal *	idemerror
	Upper bound of euclidean norm \|\|D-D^2\|\|_2 before each step.
Treal *	tracediff
	The difference between the trace of the matrix and the number of occupied orbitals before each step.
int *	polys
	Choices of polynomials 0 for x^2 and 1 for 2x-x^2 Length: nmul.

Detailed Description

Trace correcting purification.

This template instantiates the trace correcting purification algorithm developed by Niklasson [Phys. Rev. B 66, 155115 (2002)] with modifications by Rubensson and Rudberg [unpublished]. The template can be used with any matrix class Tmatrix that has the following member functions:

gersgorin(Treal&, Treal&) const
add_identity(Treal)
operator*=(Treal)
operator=(Tmatrix const &)
trace() const
frob_thresh(Treal)

The matrix class should also support the following syntax:

A = alpha * B * B
A = alpha * B * B + beta * A

where A and B are of type Tmatrix and alpha and beta are of type Treal.

Constructor & Destructor Documentation

mat::TC2::TC2	(	Tmatrix &	F,
		Tmatrix &	DM,
		const int	size,
		const int	noc,
		const Treal	trunc = `0`,
		const int	maxmm = `100`
	)

Constructor Initializes everything.

Constructor.

< Run purification

Parameters:

F	Fock/Kohn-Sham matrix (input/workspace)
DM	Density matrix (output)
size	System size (Number of basis functions)
noc	Number of occupied orbitals.
trunc	Threshold for truncation in Frobenius norm.
maxmm	Maximum aloud number of mm-multiplications.

References frob_trunc, nocc, maxmul, X, lmin, lmax, D, idemerror, tracediff, polys, and purify().

virtual mat::TC2::~TC2 ( ) [inline, virtual]

Destructor.

References idemerror, tracediff, and polys.

Member Function Documentation

Treal mat::TC2::fermi_level ( Treal tol = 1e-15 ) const

Returns the Fermi level.

Run after call to purify().

Parameters:

tol	Fault-tolerance for result.

References mat::bisection().

Treal mat::TC2::homo ( Treal tol = 1e-15 ) const

Returns upper bound of the HOMO eigenvalue.

Run after call to purify().

Parameters:

tol	Fault-tolerance for result.

References template_blas_sqrt(), and mat::bisection().

Treal mat::TC2::lumo ( Treal tol = 1e-15 ) const

Returns lower bound of the LUMO eigenvalue.

Run after call to purify().

Parameters:

tol	Fault-tolerance for result.

References template_blas_sqrt(), and mat::bisection().

int mat::TC2::n_multiplies ( ) const [inline]

Returns the number of used matrix matrix multiplications.

References nmul.

void mat::TC2::print_data	(	int const	start,
		int const	stop
	)		const

void mat::TC2::purify ( ) [protected]

Runs purification.

Run by constructor.

References template_blas_sqrt().

Referenced by TC2().

Member Data Documentation

Tmatrix& mat::TC2::D [protected]

Density matrix after purification.

Referenced by TC2().

const Treal mat::TC2::frob_trunc [protected]

Threshold for the truncation.

Referenced by TC2().

Treal* mat::TC2::idemerror [protected]

Upper bound of euclidean norm ||D-D^2||_2 before each step.

This means: idemerror[i] = norm(D[i]-D[i]^2) where D[0] is the initial matrix and D[i] is the matrix after i steps in the purification. This value is calculated after the step since D[i]^2 or 2D[i] - D[i]^2 is needed. Length: nmul

Referenced by ~TC2(), and TC2().

Treal mat::TC2::lmax [protected]

Upper bound for eigenvalue spectrum.

Referenced by TC2().

Treal mat::TC2::lmin [protected]

Lower bound for eigenvalue spectrum.

Referenced by TC2().

const int mat::TC2::maxmul [protected]

Number of tolerated matrix multiplications.

Referenced by TC2().

const int mat::TC2::n [protected]

System size.

int mat::TC2::nmul [protected]

Number of used matrix multiplications.

Referenced by n_multiplies().

int mat::TC2::nmul_firstpart [protected]

Number of used matrix multiplications in the first part of the purification.

const int mat::TC2::nocc [protected]

Number of occupied orbitals.

Referenced by TC2().

int* mat::TC2::polys [protected]

Choices of polynomials 0 for x^2 and 1 for 2x-x^2 Length: nmul.

Referenced by ~TC2(), and TC2().

Treal* mat::TC2::tracediff [protected]

The difference between the trace of the matrix and the number of occupied orbitals before each step.

Length: nmul + 1

Referenced by ~TC2(), and TC2().

Tmatrix& mat::TC2::X [protected]

Fock / Kohn-Sham matrix at initialization.

Then used as workspace by purify(). Empty after call to purify().

Referenced by TC2().

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

source/matrix/TC2.h

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation