Calculation engine for Lanczos algorithm. More...

#include <lambda_lanczos.hpp>

Public Member Functions
	LambdaLanczos (std::function< void(const std::vector< T > &, std::vector< T > &)> mv_mul, size_t matrix_size, bool find_maximum, size_t num_eigs)
	Constructs Lanczos calculation engine. More...

template<typename Iterable >
size_t	run_iteration (std::vector< real_t< T > > &eigvalues, std::vector< std::vector< T > > &eigvecs, size_t nroot, Iterable orthogonalizeTo) const
	Not documented (In most cases, `run()` is preferred). More...

void	run (std::vector< real_t< T > > &eigenvalues, std::vector< std::vector< T > > &eigenvectors)
	Executes Lanczos algorithm and stores the result into reference variables passed as arguments. More...

std::tuple< std::vector< real_t< T > >, std::vector< std::vector< T > > >	run ()
	Executes Lanczos algorithm and return result as a tuple. More...

void	run (real_t< T > &eigenvalue, std::vector< T > &eigenvector)
	Executes Lanczos algorithm that calculate one eigenpair regardless of `num_eigs`. More...

const std::vector< size_t > &	getIterationCounts () const
	Returns the latest iteration counts. More...

Public Attributes
std::function< void(const std::vector< T > &in, std::vector< T > &out)>	mv_mul
	Matrix-vector multiplication routine. More...

std::function< void(std::vector< T > &vec)>	init_vector = VectorRandomInitializer<T>::init
	Function to initialize the initial Lanczos vector. More...

size_t	matrix_size
	Dimension of the matrix to be diagonalized. More...

size_t	max_iteration
	Iteration limit of Lanczos algorithm, set to `matrix_size` automatically. More...

real_t< T >	eps = std::numeric_limits<real_t<T>>::epsilon() * 1e3
	Convergence threshold of Lanczos iteration. More...

bool	find_maximum
	true to calculate maximum eigenvalue, false to calculate minimum one. More...

size_t	num_eigs = 1
	Number of eigenpairs to be calculated. More...

real_t< T >	eigenvalue_offset = 0.0
	Shifts the eigenvalues of the given matrix A. More...

size_t	num_eigs_per_iteration = 5
	(Not necessary to change) More...

size_t	initial_vector_size = 200
	(Not necessary to change) More...

Private Types
template<typename n_type >
using	real_t = util::real_t< n_type >
	See util::real_t for details. More...

Private Attributes
std::vector< size_t >	iter_counts
	Iteration counts of the latest run. More...

Detailed Description

template<typename T>
class lambda_lanczos::LambdaLanczos< T >

Calculation engine for Lanczos algorithm.

Member Typedef Documentation

◆ real_t

template<typename T >

template<typename n_type >

using lambda_lanczos::LambdaLanczos< T >::real_t = util::real_t<n_type>

private

See util::real_t for details.

Constructor & Destructor Documentation

◆ LambdaLanczos()

template<typename T >

lambda_lanczos::LambdaLanczos< T >::LambdaLanczos	(	std::function< void(const std::vector< T > &, std::vector< T > &)>	mv_mul,
		size_t	matrix_size,
		bool	find_maximum,
		size_t	num_eigs
	)

inline

Constructs Lanczos calculation engine.

Parameters

mv_mul	Matrix-vector multiplication routine. See mv_mul for details.
matrix_size	The size of your matrix, i.e. if your matrix is n by n, `matrix_size` should be n.
find_maximum	specifies which of the minimum or maximum eigenvalue to be calculated.
num_eigs	specifies how many eigenpairs to be calculate, e.g., if `find_maximum = true` and `num_eig = 3`, LambdaLanczos calculates 3 maximum eigenpairs.

Member Function Documentation

◆ getIterationCounts()

template<typename T >

const std::vector< size_t > & lambda_lanczos::LambdaLanczos< T >::getIterationCounts ( ) const

inline

Returns the latest iteration counts.

◆ run() [1/3]

template<typename T >

std::tuple< std::vector< real_t< T > >, std::vector< std::vector< T > > > lambda_lanczos::LambdaLanczos< T >::run ( )

inline

Executes Lanczos algorithm and return result as a tuple.

This function provides C++17 multiple-value-return interface.

Returns: Eigenvalues. eigenvalues[k] stores the k-th eigenvalue.; Eigenvectors. eigenvectors[k][:] stores the k-th eigenvector.

◆ run() [2/3]

template<typename T >

void lambda_lanczos::LambdaLanczos< T >::run	(	real_t< T > &	eigenvalue,
		std::vector< T > &	eigenvector
	)

inline

Executes Lanczos algorithm that calculate one eigenpair regardless of num_eigs.

Parameters

[out]	eigenvalue	Eigenvalue.
[out]	eigenvector	Eigenvector.

◆ run() [3/3]

template<typename T >

void lambda_lanczos::LambdaLanczos< T >::run	(	std::vector< real_t< T > > &	eigenvalues,
		std::vector< std::vector< T > > &	eigenvectors
	)

inline

Executes Lanczos algorithm and stores the result into reference variables passed as arguments.

Parameters

[out]	eigenvalues	Eigenvalues. `eigenvalues[k]` stores the k-th eigenvalue.
[out]	eigenvectors	Eigenvectors. `eigenvectors[k][:]` stores the k-th eigenvector.

◆ run_iteration()

template<typename T >

template<typename Iterable >

size_t lambda_lanczos::LambdaLanczos< T >::run_iteration	(	std::vector< real_t< T > > &	eigvalues,
		std::vector< std::vector< T > > &	eigvecs,
		size_t	nroot,
		Iterable	orthogonalizeTo
	)		const

inline

Not documented (In most cases, run() is preferred).

Lanczos algorithm and stores the result into reference variables passed as arguments.

Returns: Lanczos-iteration count

Member Data Documentation

◆ eigenvalue_offset

template<typename T >

real_t<T> lambda_lanczos::LambdaLanczos< T >::eigenvalue_offset = 0.0

Shifts the eigenvalues of the given matrix A.

The algorithm will calculate the eigenvalue of matrix (A+eigenvalue_offset*E), here E is the identity matrix. The result eigenvalue from run() will take this shifting into account, so you don't have to "reshift" the result with eigenvalue_offset.

◆ eps

template<typename T >

real_t<T> lambda_lanczos::LambdaLanczos< T >::eps = std::numeric_limits<real_t<T>>::epsilon() * 1e3

Convergence threshold of Lanczos iteration.

eps = 1e-12 means that the eigenvalue will be calculated with 12 digits of precision.

Default value is system-dependent. On usual 64-bit systems:

type (including complex one)	size (system-dep.)	`eps`
float	4 bytes	1e-4
double	8 bytes	1e-12
long double	16 bytes	1e-19

◆ find_maximum

template<typename T >

bool lambda_lanczos::LambdaLanczos< T >::find_maximum

true to calculate maximum eigenvalue, false to calculate minimum one.

◆ init_vector

template<typename T >

std::function<void(std::vector<T>& vec)> lambda_lanczos::LambdaLanczos< T >::init_vector = VectorRandomInitializer<T>::init

Function to initialize the initial Lanczos vector.

After this function called, the output vector will be normalized automatically. Default value is lambda_lanczos::VectorRandomInitializer::init.

◆ initial_vector_size

template<typename T >

size_t lambda_lanczos::LambdaLanczos< T >::initial_vector_size = 200

(Not necessary to change)

This variable specifies the initial reserved size of Lanczos vectors. Controlling this variable might affect reserving efficiency, but that would be very small compared to matrix-vector-multiplication cost.

◆ iter_counts

template<typename T >

std::vector<size_t> lambda_lanczos::LambdaLanczos< T >::iter_counts

private

Iteration counts of the latest run.

◆ matrix_size

template<typename T >

size_t lambda_lanczos::LambdaLanczos< T >::matrix_size

Dimension of the matrix to be diagonalized.

◆ max_iteration

template<typename T >

size_t lambda_lanczos::LambdaLanczos< T >::max_iteration

Iteration limit of Lanczos algorithm, set to matrix_size automatically.

◆ mv_mul

template<typename T >

std::function<void(const std::vector<T>& in, std::vector<T>& out)> lambda_lanczos::LambdaLanczos< T >::mv_mul

Matrix-vector multiplication routine.

This must be a function to calculate A*in and store the result into out, where A is the matrix to be diagonalized. You can assume the output vector out has been initialized with zeros before the mv_mul is called.

◆ num_eigs

template<typename T >

size_t lambda_lanczos::LambdaLanczos< T >::num_eigs = 1

Number of eigenpairs to be calculated.

◆ num_eigs_per_iteration

template<typename T >

size_t lambda_lanczos::LambdaLanczos< T >::num_eigs_per_iteration = 5

(Not necessary to change)

This variable specifies the number of eigenpairs to be calculated per Lanczos iteration. For example, when num_eigs == 20 and num_eigs_per_iteration == 5, run() will executes 4 Lanczos iterations.

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

include/lambda_lanczos/lambda_lanczos.hpp

Public Member Functions

Public Attributes

Private Types

Private Attributes

Detailed Description

Member Typedef Documentation

◆ real_t

Constructor & Destructor Documentation

◆ LambdaLanczos()

Member Function Documentation

◆ getIterationCounts()

◆ run() [1/3]

◆ run() [2/3]

◆ run() [3/3]

◆ run_iteration()

Member Data Documentation

◆ eigenvalue_offset

◆ eps

◆ find_maximum

◆ init_vector

◆ initial_vector_size

◆ iter_counts

◆ matrix_size

◆ max_iteration

◆ mv_mul

◆ num_eigs

◆ num_eigs_per_iteration