lambda_lanczos::Exponentiator< T > Class Template Reference

Calculation engine for Lanczos exponentiation. More...

#include <exponentiator.hpp>

Public Member Functions
	Exponentiator (std::function< void(const std::vector< T > &, std::vector< T > &)> mv_mul, size_t matrix_size)
	Constructs Lanczos exponetiation engine. More...
size_t	run (const T &a, const std::vector< T > &input, std::vector< T > &output) const
	Apply matrix exponentiation exp(a*A) to input and store the result into output. More...
size_t	taylor_run (const T &a, const std::vector< T > &input, std::vector< T > &output)

Public Attributes
std::function< void(const std::vector< T > &in, std::vector< T > &out)>	mv_mul
	Matrix-vector multiplication routine. More...
size_t	matrix_size
	Dimension of the matrix to be exponentiated. 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() * 1e2
	Convergence threshold of Lanczos iteration. More...
bool	full_orthogonalize = false
	Flag to execute explicit Lanczos-vector orthogonalization. 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...

Detailed Description

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

Calculation engine for Lanczos exponentiation.

Member Typedef Documentation

real_t

template<typename T >

template<typename n_type >

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

private

See util::real_t for details.

Constructor & Destructor Documentation

Exponentiator()

template<typename T >

lambda_lanczos::Exponentiator< T >::Exponentiator ( std::function< void(const std::vector< T > &, std::vector< T > &)>  mv_mul, size_t  matrix_size  )

inline

Constructs Lanczos exponetiation 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.

Member Function Documentation

run()

template<typename T >

size_t lambda_lanczos::Exponentiator< T >::run ( const T &  a, const std::vector< T > &  input, std::vector< T > &  output  ) const

inline

Apply matrix exponentiation exp(a*A) to input and store the result into output.

Returns

Lanczos-iteration count

taylor_run()

template<typename T >

size_t lambda_lanczos::Exponentiator< T >::taylor_run ( const T &  a, const std::vector< T > &  input, std::vector< T > &  output  )

inline

Member Data Documentation

eps

template<typename T >

real_t<T> lambda_lanczos::Exponentiator< T >::eps = std::numeric_limits<real_t<T>>::epsilon() * 1e2

Convergence threshold of Lanczos iteration.

eps = 1e-14 means that the eigenvalue will be calculated with 14 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-6
double	8 bytes	1e-14
long double	16 bytes	1e-21

full_orthogonalize

template<typename T >

bool lambda_lanczos::Exponentiator< T >::full_orthogonalize = false

Flag to execute explicit Lanczos-vector orthogonalization.

initial_vector_size

template<typename T >

size_t lambda_lanczos::Exponentiator< 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.

matrix_size

template<typename T >

size_t lambda_lanczos::Exponentiator< T >::matrix_size

Dimension of the matrix to be exponentiated.

max_iteration

template<typename T >

size_t lambda_lanczos::Exponentiator< 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::Exponentiator< 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 exponentiated. You can assume the output vector out has been initialized with zeros before the mv_mul is called.

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

• include/lambda_lanczos/exponentiator.hpp