TBTK::Solver::Diagonalizer Class Reference

Solves a Model using diagonalization. More...

#include <Diagonalizer.h>

Inheritance diagram for TBTK::Solver::Diagonalizer:

Classes
class	SelfConsistencyCallback

Public Member Functions
	Diagonalizer ()
void	setSelfConsistencyCallback (SelfConsistencyCallback &selfConsistencyCallback)
void	setMaxIterations (int maxIterations)
void	run ()
const CArray< double > &	getEigenValues ()
CArray< double > &	getEigenValuesRW ()
const CArray< std::complex< double > > &	getEigenVectors ()
CArray< std::complex< double > > &	getEigenVectorsRW ()
const double	getEigenValue (int state)
const std::complex< double >	getAmplitude (int state, const Index &index)
Public Member Functions inherited from TBTK::Solver::Solver
	Solver ()
virtual	~Solver ()
virtual void	setModel (Model &model)
Model &	getModel ()
const Model &	getModel () const
Public Member Functions inherited from TBTK::Communicator
	Communicator (bool verbose)
void	setVerbose (bool verbose)
bool	getVerbose () const

Additional Inherited Members
Static Public Member Functions inherited from TBTK::Communicator
static void	setGlobalVerbose (bool globalVerbose)
static bool	getGlobalVerbose ()

Detailed Description

Solves a Model using diagonalization.

Solves a Model by Diagonalizing the Hamiltonian. Use PropertyExtractor::Diagonalizer to extract Properties.

Scaling behavior:
Time: \(O(h^3)\)
Space: \(O(h^2)\)

Here \(h\) is the size of the Hilbert space basis.

Example

#include "TBTK/Model.h"
#include "TBTK/PropertyExtractor/Diagonalizer.h"
#include "TBTK/Solver/Diagonalizer.h"
#include "TBTK/Streams.h"
#include "TBTK/TBTK.h"
 
using namespace TBTK;
 
int main(){
    Initialize();
 
    Model model;
    model << HoppingAmplitude(1, {0}, {1});
    model << HoppingAmplitude(1, {1}, {0});
    model.construct();
 
    Solver::Diagonalizer solver;
    solver.setVerbose(true);
    solver.setModel(model);
    solver.run();
 
    Streams::out << "--- Results ----\n";
 
    PropertyExtractor::Diagonalizer propertyExtractor(solver);
    for(int n = 0; n < solver.getModel().getBasisSize(); n++){
        Streams::out
            << propertyExtractor.getEigenValue(n) << "\t["
            << propertyExtractor.getAmplitude(n, {0}) << "\t"
            << propertyExtractor.getAmplitude(n, {1}) << "]\n";
    }
}

Output

Initializing Diagonalizer
    Basis size: 2
Running Diagonalizer
 
.
--- Results ----
-1  [(-0.707107,0)  (0.707107,0)]
1   [(0.707107,0)   (0.707107,0)]

Constructor & Destructor Documentation

Diagonalizer()

TBTK::Solver::Diagonalizer::Diagonalizer

(

)

Constructs a Solver::Diagonalizer.

Member Function Documentation

getAmplitude()

const std::complex< double > TBTK::Solver::Diagonalizer::getAmplitude ( int  state, const Index &  index  )

inline

Get amplitude for given eigenvector \(n\) and physical index \(x\): \(\Psi_{n}(x)\).

Parameters

state	Eigenstate number \(n\).
index	Physical index \(x\).

Returns

The amplitude \(\Psi_{n}(x)\).

getEigenValue()

const double TBTK::Solver::Diagonalizer::getEigenValue ( int  state )

inline

Get eigenvalue for a specific state.

Parameters

state

The state number, ordered in accending order.

Returns

The eigenvalue for the given state.

getEigenValues()

const CArray< double > & TBTK::Solver::Diagonalizer::getEigenValues ( )

inline

Get eigenvalues. Eigenvalues are ordered in accending order.

Returns

A pointer to the internal storage for the eigenvalues.

getEigenValuesRW()

CArray< double > & TBTK::Solver::Diagonalizer::getEigenValuesRW ( )

inline

Get eigenvalues. Eigenvalues are ordered in accending order. Same as getEigenValues(), but with write access. Use with caution.

Returns

A pointer to the internal storage for the eigenvalues.

getEigenVectors()

const CArray< std::complex< double > > & TBTK::Solver::Diagonalizer::getEigenVectors ( )

inline

Get eigenvectors. The eigenvectors are stored successively in memory, with the eigenvector corresponding to the smallest eigenvalue occupying the 'basisSize' first positions, the second occupying the next 'basisSize' elements, and so forth, where 'basisSize' is the basis size of the Model.

Returns

A pointer to the internal storage for the eigenvectors.

getEigenVectorsRW()

CArray< std::complex< double > > & TBTK::Solver::Diagonalizer::getEigenVectorsRW ( )

inline

Get eigenvectors. The eigenvectors are stored successively in memory, with the eigenvector corresponding to the smallest eigenvalue occupying the 'basisSize' first positions, the second occupying the next 'basisSize' elements, and so forth, where 'basisSize' is the basis size of the Model. Same as getEigenVectors(), but with write access. Use with caution.

Returns

A pointer to the internal storage for the eigenvectors.

run()

void TBTK::Solver::Diagonalizer::run

(

)

Run calculations. Diagonalizes ones if no self-consistency callback have been set, or otherwise multiple times until self-consistencey or maximum number of iterations has been reached.

setMaxIterations()

void TBTK::Solver::Diagonalizer::setMaxIterations ( int  maxIterations )

inline

Set the maximum number of iterations for the self-consistency loop. Only used if Diagonalizer::setSelfConsistencyCallback() has been called with a non-nullptr argument. If the self-consistency callback does not return true, maxIterations determines the maximum number of times it is called.

Parameters

maxIterations

Maximum number of iterations to use in a self-consistent callculation.

setSelfConsistencyCallback()

void TBTK::Solver::Diagonalizer::setSelfConsistencyCallback ( SelfConsistencyCallback &  selfConsistencyCallback )

inline

Set SelfConsistencyCallback. If never called, the self-consistency loop will not be run.

Parameters

selfConsistencyCallback

A SelfConsistencyCallback that will be called after the Model has been diagonalized. The callback should calculate relevant quantities, modify the Model if necessary, and return false if further iteration is necessary. If true is returned, self-consistency is considered to be reached and the iteration stops.

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

• /TBTK/Lib/include/TBTK/Solver/Diagonalizer.h