TBTK::Solver::BlockDiagonalizer Class Reference

Solves a block diagonal Model using diagonalization. More...

#include <BlockDiagonalizer.h>

Inheritance diagram for TBTK::Solver::BlockDiagonalizer:

Classes
class	SelfConsistencyCallback

Public Member Functions
	BlockDiagonalizer ()
void	setSelfConsistencyCallback (SelfConsistencyCallback &selfConsistencyCallback)
void	setMaxIterations (int maxIterations)
void	run ()
const double	getEigenValue (int state)
const double	getEigenValue (const Index &blockIndex, int state)
const std::complex< double >	getAmplitude (int state, const Index &index)
const std::complex< double >	getAmplitude (const Index &blockIndex, int state, const Index &intraBlockIndex)
unsigned int	getFirstStateInBlock (const Index &index) const
unsigned int	getLastStateInBlock (const Index &index) const
void	setParallelExecution (bool parallelExecution)
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 block diagonal Model using diagonalization.

Solves a Model by Diagonalizing the Hamiltonian. Is similar to Diagonalizer, but is able to take advantage of a Hamiltonian's block diagonal structure. Use PropertyExtractor::BlockDiagonalizer to extract Properties.

The BlockDiagonalizer is able to take advantage of a Model's block diagonal structure if the Subindices that the Model is block diagonal in appear to the left of Subindices that are not block indices. Therefore, if for example kx, ky, and kz are block labels, while sublattice and orbital are not, make sure the Model is specified such that the Index structure is {kx, ky, kz, sublattice, orbital} rather than {sublattice, orbital, kx, ky, kz}.

Scaling behavior:
If the Model has no blocks, the scaling behavior is the same as for the Diagonalizer, but with a larger prefactor. If the Model consists of \(b\) blocks, each of dimension \(h\), the scaling behavior is:
Time: \(O(nh^3)\)
Space: \(O(nh^2)\)

If the Model consists of \(b\) blocks of varying size, the above scaling behavior instead becomes an upper bound, with \(h\) the maximum block dimension.

Example

#include "TBTK/Array.h"
#include "TBTK/Model.h"
#include "TBTK/PropertyExtractor/BlockDiagonalizer.h"
#include "TBTK/Solver/BlockDiagonalizer.h"
#include "TBTK/Streams.h"
#include "TBTK/TBTK.h"
 
#include <complex>
 
using namespace std;
using namespace TBTK;
 
int main(){
    Initialize();
 
    Model model;
    //Block 0.
    model << HoppingAmplitude(1, {0, 0}, {0, 1});
    model << HoppingAmplitude(1, {0, 1}, {0, 0});
    //Block 1.
    model << HoppingAmplitude(2, {1, 0}, {1, 1});
    model << HoppingAmplitude(2, {1, 1}, {1, 0});
    model.construct();
 
    Solver::BlockDiagonalizer solver;
    solver.setVerbose(true);
    solver.setModel(model);
    solver.run();
 
    PropertyExtractor::BlockDiagonalizer propertyExtractor(solver);
 
    Streams::out << "----------------\n";
 
    //Blockwise access.
    Array<double> eigenValues({2, 2});
    Array<complex<double>> eigenVectors({4, 2});
    for(unsigned int block = 0; block < 2; block++){
        for(unsigned int state = 0; state < 2; state++){
            eigenValues[{block, state}]
                = propertyExtractor.getEigenValue(
                    {block},
                    state
                );
            for(unsigned int n = 0; n < 2; n++){
                eigenVectors[{2*block + state, n}]
                    = propertyExtractor.getAmplitude(
                        {block},
                        state,
                        {n}
                    );
            }
        }
    }
    Streams::out << eigenValues << "\n";
    Streams::out << eigenVectors << "\n";
 
    Streams::out << "----------------\n";
 
    //Global access.
    eigenValues = Array<double>({4});
    eigenVectors = Array<complex<double>>({4, 4});
    for(
        unsigned int state = 0;
        (int)state < solver.getModel().getBasisSize();
        state++
    ){
        eigenValues[{state}] = propertyExtractor.getEigenValue(state);
        for(unsigned int block = 0; block < 2; block++){
            for(unsigned int n = 0; n < 2; n++){
                eigenVectors[{state, 2*block + n}]
                    = propertyExtractor.getAmplitude(
                        state,
                        {block, n}
                    );
            }
        }
    }
    Streams::out << eigenValues << "\n";
    Streams::out << eigenVectors << "\n";
}

Output

Initializing BlockDiagonalizer
    Basis size: 4
    Hamiltonian size: 1536B
    Eigenvectors size: 128B
    Number of blocks: 2
Running Diagonalizer
 
.
----------------
[[-1, 1]
[-2, 2]]
[[(-0.707107,0), (0.707107,0)]
[(0.707107,0), (0.707107,0)]
[(-0.707107,0), (0.707107,0)]
[(0.707107,0), (0.707107,0)]]
----------------
[-1, 1, -2, 2]
[[(-0.707107,0), (0.707107,0), (0,0), (0,0)]
[(0.707107,0), (0.707107,0), (0,0), (0,0)]
[(0,0), (0,0), (-0.707107,0), (0.707107,0)]
[(0,0), (0,0), (0.707107,0), (0.707107,0)]]

Constructor & Destructor Documentation

BlockDiagonalizer()

TBTK::Solver::BlockDiagonalizer::BlockDiagonalizer

(

)

Constructs a Solver::Diagonalizer.

Member Function Documentation

getAmplitude() [1/2]

const std::complex< double > TBTK::Solver::BlockDiagonalizer::getAmplitude ( const Index &  blockIndex, int  state, const Index &  intraBlockIndex  )

inline

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

Parameters

blockIndex	Block index \(b\)
state	Eigenstate number \(n\) relative to the given block.
index	Physical index \(x\).

Returns

The amplitude \(\Psi_{nb}(\mathbf{x})\).

getAmplitude() [2/2]

const std::complex< double > TBTK::Solver::BlockDiagonalizer::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 \(\Psi_{n}(\mathbf{x})\).

getEigenValue() [1/2]

const double TBTK::Solver::BlockDiagonalizer::getEigenValue ( const Index &  blockIndex, int  state  )

inline

Get eigenvalue for specific block. Note that in contrast to getEigenValue(int state), 'state' here is relative to the first state of the block.

Parameters

blockIndex	Block index to get the eigenvalue for.
state	State index relative to the block in accending order.

Returns

The eigenvalue for the given state in the given block.

getEigenValue() [2/2]

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

inline

Get eigenvalue. The eigenvalues are ordered first by block, and then in accending order. This means that eigenvalues for blocks with smaller Indices comes before eigenvalues for blocks with larger Indices , while inside each block the eigenvalues are in accending order.

Parameters

state

The state number.

Returns

The eigenvalue for the given state.

getFirstStateInBlock()

unsigned int TBTK::Solver::BlockDiagonalizer::getFirstStateInBlock ( const Index &  index ) const

inline

Get first state in the block corresponding to the given Index.

Parameters

index

A physical Index.

Returns

The global state index for the first state that belongs to the block for which the given Index is part of the basis.

getLastStateInBlock()

unsigned int TBTK::Solver::BlockDiagonalizer::getLastStateInBlock ( const Index &  index ) const

inline

Get last state in the block corresponding to the given Index.

Parameters

index

A physical Index.

Returns

The global state index for the last state that belongs to the block for which the given Index is part of the basis.

run()

void TBTK::Solver::BlockDiagonalizer::run

(

)

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

setMaxIterations()

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

inline

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

Parameters

maxIterations

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

setParallelExecution()

void TBTK::Solver::BlockDiagonalizer::setParallelExecution ( bool  parallelExecution )

inline

Set whether parallel execution is enabled or not. Parallel execution is only possible if OpenMP is available.

@pragma parallelExecution True to enable parallel execution.

setSelfConsistencyCallback()

void TBTK::Solver::BlockDiagonalizer::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/BlockDiagonalizer.h