This class implements the Pade approximation of exponential function. More...

#include <pade_approximant.hh>

Inheritance diagram for PadeApproximant:

Collaboration diagram for PadeApproximant:

Public Types
typedef LinearODESolverBase	FactoryBaseType

Public Member Functions
	PadeApproximant (Input::Record in_rec)
	Constructor from input record. More...

	PadeApproximant (unsigned int nominator_degree, unsigned int denominator_degree)
	Constructor. More...

	~PadeApproximant (void)
	Destructor. More...

void	update_solution (arma::vec &init_vector, arma::vec &output_vec) override
	Updates solution of the ODEs system. More...

bool	evaluate_time_constraint (double &time_constraint) override
	Estimate upper bound for time step. Return true if constraint was set. More...

Public Member Functions inherited from LinearODESolver< PadeApproximant >
	LinearODESolver ()

virtual	~LinearODESolver ()

virtual void	update_solution (arma::mat &init_vecs, arma::mat &output_vecs, const std::vector< unsigned int > &mask=std::vector< unsigned int >(0)) override
	Updates solution of the system with different initial vectors. More...

Public Member Functions inherited from LinearODESolverBase
	LinearODESolverBase ()

virtual	~LinearODESolverBase ()

void	set_system_matrix (const arma::mat &matrix)
	Sets the matrix of ODE system. More...

void	set_step (double step)
	Sets the step of the numerical method. More...

Static Public Member Functions
static const Input::Type::Record &	get_input_type ()

Static Public Member Functions inherited from LinearODESolverBase
static Input::Type::Abstract &	get_input_type ()

Protected Member Functions
	PadeApproximant ()
	Hide default constructor. More...

void	approximate_matrix (arma::mat &matrix)

void	compute_exp_coefs (unsigned int nominator_degree, unsigned int denominator_degree, std::vector< double > &nominator_coefs, std::vector< double > &denominator_coefs)
	Evaluates nominator and denominator coeficients of PadeApproximant for exponencial function. More...

void	evaluate_matrix_polynomial (arma::mat &polynomial_matrix, const arma::mat &input_matrix, const std::vector< double > &coefs)
	Evaluates the matrix polynomial by Horner scheme. More...

Protected Attributes
int	nominator_degree_
	Degree of the polynomial in the nominator. More...

int	denominator_degree_
	Degree of the polynomial in the denominator. More...

arma::mat	solution_matrix_
	Solution matrix $e^{At}$ . More...

Protected Attributes inherited from LinearODESolverBase
arma::mat	system_matrix_
	the square matrix of ODE system More...

arma::vec	rhs_
	the column vector of RHS values (not used currently) More...

double	step_
	the step of the numerical method More...

bool	step_changed_
	flag is true if the step has been changed More...

bool	system_matrix_changed_
	Indicates that the system_matrix_ was recently updated. More...

Static Private Attributes
static const int	registrar
	Registrar of class to factory. More...

Detailed Description

This class implements the Pade approximation of exponential function.

The exponential function is considered in the form $e^{At}$ where $ A $ is a constant matrix. It is then approximated by a fraction of polynomials

$e^{At} = \frac{P(t)}{Q(t)},$

where the degrees of polynomials in nominator and denominator, $ P(t) $ and $ Q(t) $ , are set from the input record.

Definition at line 34 of file pade_approximant.hh.

Member Typedef Documentation

typedef LinearODESolverBase PadeApproximant::FactoryBaseType

Definition at line 37 of file pade_approximant.hh.

Constructor & Destructor Documentation

PadeApproximant::PadeApproximant ( Input::Record in_rec )

Constructor from input record.

Definition at line 55 of file pade_approximant.cc.

PadeApproximant::PadeApproximant	(	unsigned int	nominator_degree,
		unsigned int	denominator_degree
	)

Constructor.

Definition at line 64 of file pade_approximant.cc.

PadeApproximant::~PadeApproximant ( void )

Destructor.

Definition at line 69 of file pade_approximant.cc.

PadeApproximant::PadeApproximant ( )

inlineprotected

Hide default constructor.

Definition at line 59 of file pade_approximant.hh.

Member Function Documentation

void PadeApproximant::approximate_matrix ( arma::mat & matrix )

protected

Approximate the matrix function.

Definition at line 86 of file pade_approximant.cc.

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void PadeApproximant::compute_exp_coefs	(	unsigned int	nominator_degree,
		unsigned int	denominator_degree,
		std::vector< double > &	nominator_coefs,
		std::vector< double > &	denominator_coefs
	)

protected

Evaluates nominator and denominator coeficients of PadeApproximant for exponencial function.

Parameters

nominator_degree	is the degree of polynomial in the nominator
denominator_degree	is the degree of polynomial in the denominator
nominator_coefs	is the vector of coeficients of the polynomial in the nominator
denominator_coefs	is the vector of coeficients of the polynomial in the denominator

Definition at line 113 of file pade_approximant.cc.

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void PadeApproximant::evaluate_matrix_polynomial	(	arma::mat &	polynomial_matrix,
		const arma::mat &	input_matrix,
		const std::vector< double > &	coefs
	)

protected

Evaluates the matrix polynomial by Horner scheme.

Parameters

polynomial_matrix	is the output matrix
input_matrix	is the input matrix (with elements -kt)
coefs	is the vector of coeficients of the polynomial

Horner scheme for evaluating polynomial a0 + [a1 + [a2 + [a3 +...]*R(t)]*R(t)]*R(t)

Definition at line 142 of file pade_approximant.cc.

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bool PadeApproximant::evaluate_time_constraint ( double & time_constraint )

inlineoverridevirtual

Estimate upper bound for time step. Return true if constraint was set.

Implements LinearODESolverBase.

Definition at line 55 of file pade_approximant.hh.

const Record & PadeApproximant::get_input_type ( )

static

Input record for class PadeApproximant.

Definition at line 34 of file pade_approximant.cc.

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void PadeApproximant::update_solution	(	arma::vec &	init_vec,
		arma::vec &	output_vec
	)

overridevirtual

Updates solution of the ODEs system.

Parameters

init_vec	is the column initial vector
output_vec	is the column output vector containing the result

Implements LinearODESolverBase.

Definition at line 73 of file pade_approximant.cc.

Member Data Documentation

int PadeApproximant::denominator_degree_

protected

Degree of the polynomial in the denominator.

Definition at line 85 of file pade_approximant.hh.

int PadeApproximant::nominator_degree_

protected

Degree of the polynomial in the nominator.

Definition at line 84 of file pade_approximant.hh.

const int PadeApproximant::registrar

staticprivate

Initial value:

=
        Input::register_class< PadeApproximant, Input::Record >("PadeApproximant") +
        PadeApproximant::get_input_type().size()

Registrar of class to factory.

Definition at line 91 of file pade_approximant.hh.

arma::mat PadeApproximant::solution_matrix_

protected

Solution matrix $e^{At}$ .

Definition at line 87 of file pade_approximant.hh.

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

/opt/flow123d/flow123d/src/reaction/pade_approximant.hh
/opt/flow123d/flow123d/src/reaction/pade_approximant.cc

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation