class for piecewise-polynomials and cubic spline interpolation More...

#include <piecewise_polynom_function.h>

Inheritance diagram for MBSim::PiecewisePolynomFunction< Ret(Arg)>:

Classes
class	FirstDerivative

class	SecondDerivative

class	ZerothDerivative

Public Types
enum	InterpolationMethod { cSplinePeriodic , cSplineNatural , piecewiseLinear , useBreaksAndCoefs }

enum	ExtrapolationMethod { error , continuePolynom , linear }

Public Types inherited from MBSim::Element
enum	InitStage { resolveStringRef =0 , preInit , plotting , unknownStage , LASTINITSTAGE }
	The stages of the initialization. More...

Public Member Functions
int	getArgSize () const

std::pair< int, int >	getRetSize () const

void	init (Element::InitStage stage, const InitConfigSet &config=InitConfigSet())
	plots time series header More...

void	calculateSpline ()

void	reset ()

Ret	operator() (const Arg &x)

fmatvec::Der< Ret, Arg >::type	parDer (const Arg &x)

fmatvec::Der< Ret, Arg >::type	parDerDirDer (const Arg &argDir, const Arg &arg)

fmatvec::VecV	getBreaks ()

void	setInterpolationMethod (InterpolationMethod method_)
	set interpolation More...

void	setExtrapolationMethod (ExtrapolationMethod method_)

void	setx (const fmatvec::VecV &x_)

void	sety (const fmatvec::MatV &y_)

void	setxy (const fmatvec::MatV &xy)

void	setCoefficientsArray (const std::vector< fmatvec::MatV > &allCoefs)
	set polynomial coefficients More...

void	addCoefficients (const fmatvec::MatV &coef)

void	setBreaks (const fmatvec::VecV &breaks_u)
	set interval boundaries More...

virtual void	initializeUsingXML (xercesc::DOMElement *element)
	initialize function with XML code More...

Public Member Functions inherited from MBSim::Function< Ret(Arg)>
	Function ()

void	initializeUsingXML (xercesc::DOMElement *element) override

Public Member Functions inherited from MBSim::FunctionBase
	FunctionBase ()

virtual Element *	getDependency () const

Public Member Functions inherited from MBSim::Element
	Element (const std::string &name)
	constructor

	~Element () override=default
	destructor

void	throwError (const std::string &msg) const

virtual void	setDynamicSystemSolver (DynamicSystemSolver *sys)
	sets the used dynamics system solver to the element More...

virtual void	plot ()
	plots time dependent data More...

virtual void	plotAtSpecialEvent ()
	plots time dependent data at special events More...

const std::string &	getName () const

void	setName (const std::string &str)

void	setPath (const std::string &str)

DynamicSystemSolver *	getDynamicSystemSolver ()

virtual void	init (InitStage stage, const InitConfigSet &config=InitConfigSet())
	plots time series header More...

virtual void	createPlotGroup ()
	creates the plotGroup for H5-output More...

H5::GroupBase *	getPlotGroup ()

virtual H5::GroupBase *	getFramesPlotGroup ()

virtual H5::GroupBase *	getContoursPlotGroup ()

virtual H5::GroupBase *	getGroupsPlotGroup ()

virtual H5::GroupBase *	getObjectsPlotGroup ()

virtual H5::GroupBase *	getLinksPlotGroup ()

virtual H5::GroupBase *	getConstraintsPlotGroup ()

virtual H5::GroupBase *	getObserversPlotGroup ()

bool	getPlotFeature (const PlotFeatureEnum &pf)

virtual void	setPlotFeature (const PlotFeatureEnum &pf, bool value)
	Set a plot feature. More...

void	setPlotFeatureForChildren (const PlotFeatureEnum &pf, bool value)
	Set a plot feature for the children of this object. More...

void	setPlotFeatureRecursive (const PlotFeatureEnum &pf, bool value)
	Set a plot feature for this object and the children of this object. More...

template<class T >
void	setPlotAttribute (const std::string &name, const T &value)
	Set a plot attribute: static data attached as key/value pairs to the plot datasets/groups.

void	setPlotAttribute (const std::string &name)

virtual void	initializeUsingXML (xercesc::DOMElement *element)

template<class T >
T *	getByPath (const std::string &path, bool initialCaller=true) const
	Get the object of type T represented by the path path. Do not set any argurment other than path!

std::string	getPath (const Element *relTo=nullptr, std::string sep="/") const
	Return the path of this object. If relativeTo is not NULL return a relative path to relativeTo. Do not set any argurment other than relTo and sep!

virtual Element *	getChildByContainerAndName (const std::string &container, const std::string &name) const
	Get the Element named name in the container named container. More...

virtual std::shared_ptr< OpenMBV::Group >	getOpenMBVGrp ()

virtual std::shared_ptr< OpenMBV::Group >	getFramesOpenMBVGrp ()

virtual std::shared_ptr< OpenMBV::Group >	getContoursOpenMBVGrp ()

virtual std::shared_ptr< OpenMBV::Group >	getGroupsOpenMBVGrp ()

virtual std::shared_ptr< OpenMBV::Group >	getObjectsOpenMBVGrp ()

virtual std::shared_ptr< OpenMBV::Group >	getLinksOpenMBVGrp ()

virtual std::shared_ptr< OpenMBV::Group >	getConstraintsOpenMBVGrp ()

virtual std::shared_ptr< OpenMBV::Group >	getObserversOpenMBVGrp ()

virtual Element *	getParent ()

virtual const Element *	getParent () const

virtual void	setParent (Element *parent_)

std::vector< Element * >	getDependencies () const
	checks dependency on other elements. More...

void	addDependency (Element *ele)

int	computeLevel ()
	computes the length of the pathes in the graph that represents the dependencies between all elements. More...

virtual void	updatePositions (Frame *frame)

virtual void	updateVelocities (Frame *frame)

virtual void	updateAccelerations (Frame *frame)

virtual void	updateJacobians (Frame *frame, int j=0)

virtual void	updateGyroscopicAccelerations (Frame *frame)

virtual void	resetUpToDate ()

const double &	getTime () const

double	getStepSize () const

const MBXMLUtils::DOMEvalException &	getDOMEvalError () const

Protected Types
using	B = fmatvec::Function< Ret(Arg)>

Protected Member Functions
void	calculateSplinePeriodic ()
	calculation of periodic spline by interpolation More...

void	calculateSplineNatural ()
	calculation of natural spline by interpolation More...

void	calculatePLinear ()

Protected Member Functions inherited from MBSim::Element
void	updatePlotFeatures ()

void	addToPlot (const std::string &name)

void	addToPlot (const std::string &name, int size)

void	addToPlot (const std::string &name, const std::vector< std::string > &iname)

template<class AT >
void	plot (const AT &x)

template<class Type , class AT >
void	plot (const fmatvec::Vector< Type, AT > &x)

Protected Attributes
std::vector< fmatvec::MatV >	coefs
	vector of polynomial coefficents

fmatvec::VecV	breaks
	vector of breaks (interval boundaries)

int	nPoly
	number of defined piecewise polynomials

int	order
	order of polynomial (3 for cubic polynomials)

int	index
	for internal use in ppeval functions

fmatvec::VecV	x

fmatvec::MatV	y

InterpolationMethod	interpolationMethod
	interpolation interpolationMethod

ExtrapolationMethod	extrapolationMethod

Protected Attributes inherited from MBSim::Element
Element *	parent { nullptr }

std::string	name
	name of element

std::string	path
	The path of this object. Is set during the init stage reorganizeHierarchy. Before this the path is calculated dynamically using getPath() after this stage getPath just returns this value.

MBXMLUtils::DOMEvalException	domEvalError
	Special XML helper variable.

DynamicSystemSolver *	ds { nullptr }
	dynamic system

H5::VectorSerie< double > *	plotVectorSerie { nullptr }
	time series

std::vector< double >	plotVector
	one entry of time series

std::vector< std::string >	plotColumns
	columns of time series

H5::GroupBase *	plotGroup { nullptr }
	associated plot group

std::vector< Element * >	dependency
	vector containing all dependencies.

PlotFeatureMap	plotFeature
	plot feature

PlotFeatureMap	plotFeatureForChildren

std::map< std::string, std::variant< std::monostate, int, double, std::string, std::vector< int >, std::vector< double >, std::vector< std::vector< double > > > >	plotAttribute

Private Attributes
ZerothDerivative	f

FirstDerivative	fd

SecondDerivative	fdd

Detailed Description

template<typename Ret, typename Arg>
class MBSim::PiecewisePolynomFunction< Ret(Arg)>

class for piecewise-polynomials and cubic spline interpolation

Author: Robert Huber

Date: 2006-08-31 initial commit; 2006-09-05 verified with matlab /octave (Robert Huber); 2008-05-21 C++ beauty treatment, PLinear (Thorsten Schindler); 2009-08-11 kernel_dev (Thorsten Schindler)

Todo:: add deletes TODO

Spline / PP-Form info Piecewise polynomial: \( c0 xloc^n + c1 xloc^{n-1} + c2 xloc^{n-2} + \dots + cn \) with [c0 c1 c2 ... cn] ith row vector of coefs-matrix breaks(i) << x << breaks(i+1) defines i and xloc = x-breaks(i)

Ex. cubic spline with breaks= [0; 0.3; 0.5] coefs= [d1 c1 b1 a1;
d2 c2 b2 a2]

\[ S(x) = a1 + b1 xloc + c1 xloc^2 + d1 xloc^3 for x\in[0;0.3] \text{and} x_loc = x \]

\[ S(x) = a2 + b2 xloc + c2 xloc^2 + d2 xloc^3 for x\in[0.3;0.5] \text{and} xloc = x - 0.3 \]

Cubic spline (xi,fi) i=1..N is being interpolated by N-1 piecewise polynomials Si of degree 3 yielding a global \( C^2 \) curve for uniqueness TWO additional boundary conditions are necessary (periodic / natural)

Piecewise linear polynomial (xi,fi) i=1..N is being interpolated by N-1 piecewise polynomials Si of degree 1 yielding a globally weak differentiable curve in the context of this class the second derivative is defined to be zero everywhere (which is mathematically wrong)

Member Function Documentation

◆ calculateSplineNatural()

template<typename Ret , typename Arg >

void MBSim::PiecewisePolynomFunction< Ret(Arg)>::calculateSplineNatural ( )

protected

calculation of natural spline by interpolation

Parameters

interpolated	arguments
interpolated	function values

◆ calculateSplinePeriodic()

template<typename Ret , typename Arg >

void MBSim::PiecewisePolynomFunction< Ret(Arg)>::calculateSplinePeriodic ( )

protected

calculation of periodic spline by interpolation

Parameters

interpolated	arguments
interpolated	function values

◆ getBreaks()

template<typename Ret , typename Arg >

fmatvec::VecV MBSim::PiecewisePolynomFunction< Ret(Arg)>::getBreaks ( )

inline

Returns: interval boundaries

◆ init()

template<typename Ret , typename Arg >

void MBSim::PiecewisePolynomFunction< Ret(Arg)>::init	(	Element::InitStage	stage,
		const InitConfigSet &	config = `InitConfigSet()`
	)

inlinevirtual

plots time series header

Parameters

invocing parent class

Reimplemented from MBSim::Element.

◆ initializeUsingXML()

template<typename Ret , typename Arg >

virtual void MBSim::PiecewisePolynomFunction< Ret(Arg)>::initializeUsingXML ( xercesc::DOMElement * element )

virtual

initialize function with XML code

Parameters

XML element

Reimplemented from MBSim::Element.

◆ setBreaks()

template<typename Ret , typename Arg >

void MBSim::PiecewisePolynomFunction< Ret(Arg)>::setBreaks ( const fmatvec::VecV & breaks_u )

inline

set interval boundaries

Parameters

interval boundaries

◆ setCoefficientsArray()

template<typename Ret , typename Arg >

void MBSim::PiecewisePolynomFunction< Ret(Arg)>::setCoefficientsArray ( const std::vector< fmatvec::MatV > & allCoefs )

set polynomial coefficients

Parameters

polynomial coefficients

◆ setInterpolationMethod()

template<typename Ret , typename Arg >

void MBSim::PiecewisePolynomFunction< Ret(Arg)>::setInterpolationMethod ( InterpolationMethod method_ )

inline

set interpolation

Parameters

InterpolationMethod 'cSplinePeriodic' -> cubic Spline with periodic end conditions (two-times continuously differentiable) S(x1) = S(xN) -> f(0)=f(end) S'(x1) = S'(xN) S''(x1) = S''(xN) 'cSplineNatural' -> cubic Spline with natural end conditions (two-times continuously differentiable) S''(x1) = S''(xN) = 0 'piecewiseLinear' -> piecewise linear function (weak differentiable)

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

/mbsim-env/mbsim/kernel/mbsim/functions/piecewise_polynom_function.h

Classes

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Private Attributes

Detailed Description

Member Function Documentation

◆ calculateSplineNatural()

◆ calculateSplinePeriodic()

◆ getBreaks()

◆ init()

◆ initializeUsingXML()

◆ setBreaks()

◆ setCoefficientsArray()

◆ setInterpolationMethod()