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

#include <pade_approximant.hh>

Inheritance diagram for PadeApproximant:

Collaboration diagram for PadeApproximant:

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...

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 Attributes
static Input::Type::Record	input_type

Static Public Attributes inherited from LinearODESolverBase
static Input::Type::AbstractRecord	input_type = AbstractRecord("LinearODESolver", "Solver of a linear system of ODEs.")

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...

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 23 of file pade_approximant.hh.

Constructor & Destructor Documentation

PadeApproximant::PadeApproximant ( Input::Record in_rec )

Constructor from input record.

Definition at line 22 of file pade_approximant.cc.

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

Constructor.

Definition at line 29 of file pade_approximant.cc.

PadeApproximant::~PadeApproximant ( void )

Destructor.

Definition at line 34 of file pade_approximant.cc.

PadeApproximant::PadeApproximant ( )

inlineprotected

Hide default constructor.

Definition at line 44 of file pade_approximant.hh.

Member Function Documentation

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

protected

Approximate the matrix function.

Definition at line 51 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 78 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 107 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 38 of file pade_approximant.cc.

Member Data Documentation

int PadeApproximant::denominator_degree_

protected

Degree of the polynomial in the denominator.

Definition at line 70 of file pade_approximant.hh.

Record PadeApproximant::input_type

static

Initial value:

= Record("PadeApproximant", "Record with an information about pade approximant parameters.")
    .derive_from(LinearODESolverBase::input_type)
    .declare_key("nominator_degree", Integer(1), Default("2"),
                "Polynomial degree of the nominator of Pade approximant.")
    .declare_key("denominator_degree", Integer(1), Default("2"),
                "Polynomial degree of the nominator of Pade approximant")

Input record for class PadeApproximant.

Definition at line 29 of file pade_approximant.hh.

int PadeApproximant::nominator_degree_

protected

Degree of the polynomial in the nominator.

Definition at line 69 of file pade_approximant.hh.

arma::mat PadeApproximant::solution_matrix_

protected

Solution matrix $e^{At}$ .

Definition at line 72 of file pade_approximant.hh.

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

/home/builder/jenkins/F123-linux-release/flow123d/src/reaction/pade_approximant.hh
/home/builder/jenkins/F123-linux-release/flow123d/src/reaction/pade_approximant.cc

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation