Base class for interpolation. More...

#include <interpolant.hh>

Inheritance diagram for InterpolantBase:

Collaboration diagram for InterpolantBase:

Classes
struct	Check

struct	EvalStatistics
	Structure that keeps statistics of evaluation. More...

Public Member Functions
	InterpolantBase ()
	Default constructor. More...

virtual	~InterpolantBase ()
	Destructor. More...

Interpolation.
double	error ()
	Returns error of the interpolation. More...

double	bound_a () const
	Returns left boundary of the interval. More...

double	bound_b () const
	Returns right boundary of the interval. More...

unsigned int	size () const
	Returns the size of the interpolation table. More...

void	set_interval (double bound_a, double bound_b)
	Sets the interpolation interval boundaries. More...

void	set_size (unsigned int size)
	Sets size of the interpolation table. It is also equal to the number of intervals. More...

void	set_norm (ErrorNorm::Type norm_type=ErrorNorm::max, double p=2)
	Sets the type of norm used for computing estimate of the error of the interpolation. More...

void	set_size_automatic (double user_tol, unsigned int init_size, unsigned int max_size=default_max_size)
	Sets automatic choice of the size of the table. More...

void	set_extrapolation (Extrapolation::Type extrapolation)
	Sets the type of extrapolation. Functor type is default. More...

virtual int	interpolate ()=0
	Creates piecewise polynomial interpolation. More...

Evaluation statistics.
These members are used recording the statistics of the evaluation.
double	bound_a_
	Left interval boundary. More...

double	bound_b_
	Right interval boundary. More...

double	step
	Chosen interpolation step. More...

double	a_div_step
	bound_ divided by step - precomputed value for evaluation More...

unsigned int	size_
	Number of dividing intervals. More...

unsigned int	n_nodes
	Number of nodes in the interval . More...

double	user_tol
	User set tolerance which is used during automatic step choice. More...

unsigned int	max_size
	Maximal size of the interpolation table. More...

bool	automatic_size
	Is true if step/size should be chosen automatically. More...

ErrorNorm::Type	norm_type
	Type of norm used to compute error of the interpolation. More...

double	p
	Exponent used in norms and when computing error. More...

double	error_
	Error of the interpolation. More...

Extrapolation::Type	extrapolation

const static unsigned int	n_derivatives = 10
	Defines how many derivatives we allow to be returned from Taylor's coeficients. More...

const static unsigned int	default_max_size = 10*1000
	Default maximal size of the interpolation table. More...

const static double	simpson_tolerance = 1e-10
	Tolerance in Adaptive Simpson intergration. More...

EvalStatistics	statistics () const
	Returns structure with evaluation statistics. More...

void	reset_stat ()
	Resets all measured statistics. More...

void	check_stats_and_reinterpolate (double percentage=0.3)
	Can be called to check automatically the evaluation statistics and possibly reinterpolate. More...

long	fact (long x)
	Recursive factorial function (used in Taylor row expansion in n-th derivative computation). More...

Internal check system.
This is internal check system which checks the values of parameters before making interpolation.
std::vector< bool >	checks
	Vector of boolean values telling us which parameters are set or not. More...

EvalStatistics	stats
	Structure which keeps evaluation statistics. See InterpolantBase::eval_statistics. More...

void	check_all ()
	Checks that the parameters are set before interpolation. More...

Detailed Description

Base class for interpolation.

This class serves as the common interface for interpolation classes. It provides functions for setting the common parameters of an interpolation such as interval, size of the table and extrapolation.

See also: Interpolant; InterpolantImplicit

Definition at line 78 of file interpolant.hh.

Constructor & Destructor Documentation

◆ InterpolantBase()

InterpolantBase::InterpolantBase ( )

Default constructor.

Definition at line 32 of file interpolant.cc.

◆ ~InterpolantBase()

InterpolantBase::~InterpolantBase ( )

virtual

Destructor.

Definition at line 46 of file interpolant.cc.

Member Function Documentation

◆ bound_a()

double InterpolantBase::bound_a ( ) const

inline

Returns left boundary of the interval.

Definition at line 37 of file interpolant_impl.hh.

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◆ bound_b()

double InterpolantBase::bound_b ( ) const

inline

Returns right boundary of the interval.

Definition at line 42 of file interpolant_impl.hh.

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◆ check_all()

void InterpolantBase::check_all ( )

protected

Checks that the parameters are set before interpolation.

Definition at line 136 of file interpolant.cc.

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◆ check_stats_and_reinterpolate()

void InterpolantBase::check_stats_and_reinterpolate ( double percentage = 0.3 )

Can be called to check automatically the evaluation statistics and possibly reinterpolate.

The function computes ratio of evaluations outside the interpolation interval - on each side of the interval. Then it compares the results with given percentage and accordingly changes (only streches) the interval and reinterpolate.

Parameters

percentage is the percentage of evaluations outside the interval (on one side)

Definition at line 113 of file interpolant.cc.

◆ error()

double InterpolantBase::error ( )

inline

Returns error of the interpolation.

It is equal to the chosen norm of the difference divided by the lenght of interval. Returns -1.0 if the interpolation has not been computed yet.

Definition at line 27 of file interpolant_impl.hh.

◆ fact()

long InterpolantBase::fact ( long x )

protected

Recursive factorial function (used in Taylor row expansion in n-th derivative computation).

Definition at line 145 of file interpolant.cc.

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◆ interpolate()

virtual int InterpolantBase::interpolate ( )

pure virtual

Creates piecewise polynomial interpolation.

Returns

0 if interpolation has been created
1 if the tolerance has not been satisfied (in case of automatic choice of size)

Implemented in InterpolantImplicit, and Interpolant.

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◆ reset_stat()

void InterpolantBase::reset_stat ( )

Resets all measured statistics.

Definition at line 100 of file interpolant.cc.

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◆ set_extrapolation()

void InterpolantBase::set_extrapolation ( Extrapolation::Type extrapolation )

Sets the type of extrapolation. Functor type is default.

Parameters

extrapolation is the type of extrapolation (defined by enumeration ExtrapolationType)

Definition at line 95 of file interpolant.cc.

◆ set_interval()

void InterpolantBase::set_interval	(	double	bound_a,
		double	bound_b
	)

Sets the interpolation interval boundaries.

Parameters

bound_a	is the left boundary of the interval
bound_b	is the right boundary of the interval

Definition at line 50 of file interpolant.cc.

◆ set_norm()

void InterpolantBase::set_norm	(	ErrorNorm::Type	norm_type = `ErrorNorm::max`,
		double	p = `2`
	)

Sets the type of norm used for computing estimate of the error of the interpolation.

Parameters

norm_type	is the type of norm in which the error of interpolation is computed
p	is the exponent used in norms and

Definition at line 76 of file interpolant.cc.

◆ set_size()

void InterpolantBase::set_size ( unsigned int size )

Sets size of the interpolation table. It is also equal to the number of intervals.

Parameters

size	is the new size of the interpolation table

Definition at line 67 of file interpolant.cc.

◆ set_size_automatic()

void InterpolantBase::set_size_automatic	(	double	user_tol,
		unsigned int	init_size,
		unsigned int	max_size = `default_max_size`
	)

Sets automatic choice of the size of the table.

When interpolate is called than the size is increased (by smaller interval dividing) until the given tolerance or the maximum size of the interpolation table is reached.

Parameters

user_tol	is the tolerance which should the interpolation meet
init_size	is the initial choice of table size
max_size	is maximal size of the table that user allows

Definition at line 83 of file interpolant.cc.

◆ size()

unsigned int InterpolantBase::size ( ) const

inline

Returns the size of the interpolation table.

Definition at line 47 of file interpolant_impl.hh.

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◆ statistics()

InterpolantBase::EvalStatistics InterpolantBase::statistics ( ) const

inline

Returns structure with evaluation statistics.

Definition at line 32 of file interpolant_impl.hh.

Member Data Documentation

◆ a_div_step

double InterpolantBase::a_div_step

protected

bound_ divided by step - precomputed value for evaluation

Definition at line 170 of file interpolant.hh.

◆ automatic_size

bool InterpolantBase::automatic_size

protected

Is true if step/size should be chosen automatically.

Definition at line 177 of file interpolant.hh.

◆ bound_a_

double InterpolantBase::bound_a_

protected

Left interval boundary.

Definition at line 167 of file interpolant.hh.

◆ bound_b_

double InterpolantBase::bound_b_

protected

Right interval boundary.

Definition at line 168 of file interpolant.hh.

◆ checks

std::vector<bool> InterpolantBase::checks

protected

Vector of boolean values telling us which parameters are set or not.

Definition at line 206 of file interpolant.hh.

◆ default_max_size

const unsigned int InterpolantBase::default_max_size = 10*1000

staticprotected

Default maximal size of the interpolation table.

Definition at line 190 of file interpolant.hh.

◆ error_

double InterpolantBase::error_

protected

Error of the interpolation.

Definition at line 181 of file interpolant.hh.

◆ extrapolation

Extrapolation::Type InterpolantBase::extrapolation

protected

Extrapolation type - 'what' is evaluated outside the interpolation interval. Default value after interpolant construction is InterpolantBase::functor.

Definition at line 186 of file interpolant.hh.

◆ max_size

unsigned int InterpolantBase::max_size

protected

Maximal size of the interpolation table.

Definition at line 176 of file interpolant.hh.

◆ n_derivatives

const unsigned int InterpolantBase::n_derivatives = 10

staticprotected

Defines how many derivatives we allow to be returned from Taylor's coeficients.

Definition at line 189 of file interpolant.hh.

◆ n_nodes

unsigned int InterpolantBase::n_nodes

protected

Number of nodes in the interval $(a,b)$ .

Definition at line 173 of file interpolant.hh.

◆ norm_type

ErrorNorm::Type InterpolantBase::norm_type

protected

Type of norm used to compute error of the interpolation.

Definition at line 178 of file interpolant.hh.

◆ p

double InterpolantBase::p

protected

Exponent used in norms $ L_p $ and $ W_p^1 $ when computing error.

Definition at line 179 of file interpolant.hh.

◆ simpson_tolerance

const double InterpolantBase::simpson_tolerance = 1e-10

staticprotected

Tolerance in Adaptive Simpson intergration.

See also: AdaptiveSimpson

Definition at line 191 of file interpolant.hh.

◆ size_

unsigned int InterpolantBase::size_

protected

Number of dividing intervals.

Definition at line 172 of file interpolant.hh.

◆ stats

EvalStatistics InterpolantBase::stats

protected

Structure which keeps evaluation statistics. See InterpolantBase::eval_statistics.

Definition at line 214 of file interpolant.hh.

◆ step

double InterpolantBase::step

protected

Chosen interpolation step.

Definition at line 169 of file interpolant.hh.

◆ user_tol

double InterpolantBase::user_tol

protected

User set tolerance which is used during automatic step choice.

Definition at line 175 of file interpolant.hh.

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

/opt/flow123d/flow123d/src/tools/interpolant.hh
/opt/flow123d/flow123d/src/tools/interpolant.cc
/opt/flow123d/flow123d/src/tools/interpolant_impl.hh

Classes

Public Member Functions

Evaluation statistics.

Internal check system.

Detailed Description

Constructor & Destructor Documentation

◆ InterpolantBase()

◆ ~InterpolantBase()

Member Function Documentation

◆ bound_a()

◆ bound_b()

◆ check_all()

◆ check_stats_and_reinterpolate()

◆ error()

◆ fact()

◆ interpolate()

◆ reset_stat()

◆ set_extrapolation()

◆ set_interval()

◆ set_norm()

◆ set_size()

◆ set_size_automatic()

◆ size()

◆ statistics()

Member Data Documentation

◆ a_div_step

◆ automatic_size

◆ bound_a_

◆ bound_b_

◆ checks

◆ default_max_size

◆ error_

◆ extrapolation

◆ max_size

◆ n_derivatives

◆ n_nodes

◆ norm_type

◆ p

◆ simpson_tolerance

◆ size_

◆ stats

◆ step

◆ user_tol