The common code for all 3rd order polynomial splines. More...

#include <dumux/common/splinecommon_.hh>

Inheritance diagram for Dumux::SplineCommon_< ScalarT, ImplementationT >:

Description

template<class ScalarT, class ImplementationT>
class Dumux::SplineCommon_< ScalarT, ImplementationT >

The common code for all 3rd order polynomial splines.

Public Member Functions
bool	applies (Scalar x) const
	Return true if the given x is in range [x1, xn]. More...

Scalar	xMin () const
	Return the x value of the leftmost sampling point. More...

Scalar	xMax () const
	Return the x value of the rightmost sampling point. More...

void	printCSV (Scalar xi0, Scalar xi1, int k) const
	Prints k tuples of the format (x, y, dx/dy, isMonotonic) to stdout. More...

Scalar	eval (Scalar x, bool extrapolate=false) const
	Evaluate the spline at a given position. More...

Scalar	evalDerivative (Scalar x, bool extrapolate=false) const
	Evaluate the spline's derivative at a given position. More...

Scalar	intersect (Scalar a, Scalar b, Scalar c, Scalar d) const
	Find the intersections of the spline with a cubic polynomial in the whole intervall, throws Dune::MathError exception if there is more or less than one solution. More...

Scalar	intersectInterval (Scalar x0, Scalar x1, Scalar a, Scalar b, Scalar c, Scalar d) const
	Find the intersections of the spline with a cubic polynomial in a sub-intervall of the spline, throws Dune::MathError exception if there is more or less than one solution. More...

int	monotonic (Scalar x0, Scalar x1) const
	Returns 1 if the spline is monotonically increasing, -1 if the spline is mononously decreasing and 0 if the spline is not monotonous in the interval (x0, x1). More...

int	monotonic () const
	Same as monotonic(x0, x1), but with the entire range of the spline as interval. More...

Protected Member Functions
	SplineCommon_ ()=default

template<class DestVector , class SourceVector >
void	assignSamplingPoints_ (DestVector &destX, DestVector &destY, const SourceVector &srcX, const SourceVector &srcY, int numSamples)
	Set the sampling point vectors. More...

template<class DestVector , class ListIterator >
void	assignFromArrayList_ (DestVector &destX, DestVector &destY, const ListIterator &srcBegin, const ListIterator &srcEnd, int numSamples)

template<class DestVector , class ListIterator >
void	assignFromTupleList_ (DestVector &destX, DestVector &destY, ListIterator srcBegin, ListIterator srcEnd, int numSamples)
	Set the sampling points. More...

template<class Vector , class Matrix >
void	makePeriodicSystem_ (Matrix &M, Vector &d)
	Make the linear system of equations Mx = d which results in the moments of the periodic spline. More...

template<class Vector , class Matrix >
void	makeFullSystem_ (Matrix &M, Vector &d, Scalar m0, Scalar m1)
	Make the linear system of equations Mx = d which results in the moments of the full spline. More...

template<class Vector , class Matrix >
void	makeNaturalSystem_ (Matrix &M, Vector &d)
	Make the linear system of equations Mx = d which results in the moments of the natural spline. Stoer 2005: Numerische Mathematik 1, p. 111 [64]. More...

Scalar	eval_ (Scalar x, int i) const

Scalar	evalDerivative_ (Scalar x, int i) const

int	monotonic_ (int i, Scalar x0, Scalar x1) const

int	intersectSegment_ (Scalar *sol, int segIdx, Scalar a, Scalar b, Scalar c, Scalar d, Scalar x0=-1e100, Scalar x1=1e100) const
	Find all the intersections of a segment of the spline with a cubic polynomial within a specified interval. More...

int	segmentIdx_ (Scalar x) const

Scalar	h_ (int i) const
	Returns x[i] - x[i - 1]. More...

Scalar	x_ (int i) const
	Returns the y coordinate of the i-th sampling point. More...

Scalar	y_ (int i) const
	Returns the y coordinate of the i-th sampling point. More...

Scalar	moment_ (int i) const
	Returns the moment (i.e. second derivative) of the spline at the i-th sampling point. More...

Scalar	a_ (int i) const

Scalar	b_ (int i) const

Scalar	c_ (int i) const

Scalar	d_ (int i) const

int	numSamples_ () const
	Returns the number of sampling points. More...

Constructor & Destructor Documentation

◆ SplineCommon_()

template<class ScalarT , class ImplementationT >

Dumux::SplineCommon_< ScalarT, ImplementationT >::SplineCommon_ ( )

protecteddefault

Member Function Documentation

◆ a_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::a_ ( int i ) const

inlineprotected

◆ applies()

template<class ScalarT , class ImplementationT >

bool Dumux::SplineCommon_< ScalarT, ImplementationT >::applies ( Scalar x ) const

inline

Return true if the given x is in range [x1, xn].

◆ assignFromArrayList_()

template<class ScalarT , class ImplementationT >

template<class DestVector , class ListIterator >

void Dumux::SplineCommon_< ScalarT, ImplementationT >::assignFromArrayList_	(	DestVector &	destX,
		DestVector &	destY,
		const ListIterator &	srcBegin,
		const ListIterator &	srcEnd,
		int	numSamples
	)

inlineprotected

◆ assignFromTupleList_()

template<class ScalarT , class ImplementationT >

template<class DestVector , class ListIterator >

void Dumux::SplineCommon_< ScalarT, ImplementationT >::assignFromTupleList_	(	DestVector &	destX,
		DestVector &	destY,
		ListIterator	srcBegin,
		ListIterator	srcEnd,
		int	numSamples
	)

inlineprotected

Set the sampling points.

Here we assume that the elements of the source vector have an [] operator where v[0] is the x value and v[1] is the y value if the sampling point.

◆ assignSamplingPoints_()

template<class ScalarT , class ImplementationT >

template<class DestVector , class SourceVector >

void Dumux::SplineCommon_< ScalarT, ImplementationT >::assignSamplingPoints_	(	DestVector &	destX,
		DestVector &	destY,
		const SourceVector &	srcX,
		const SourceVector &	srcY,
		int	numSamples
	)

inlineprotected

Set the sampling point vectors.

This takes care that the order of the x-values is ascending, although the input must be ordered already!

◆ b_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::b_ ( int i ) const

inlineprotected

◆ c_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::c_ ( int i ) const

inlineprotected

◆ d_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::d_ ( int i ) const

inlineprotected

◆ eval()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::eval	(	Scalar	x,
		bool	extrapolate = `false`
	)		const

inline

Evaluate the spline at a given position.

Parameters

x	The value on the abscissa where the spline ought to be evaluated
extrapolate	If this parameter is set to true, the spline will be extended beyond its range by straight lines, if false calling extrapolate for $x \not [x_{min}, x_{max}]$ will cause a failed assertation.

◆ eval_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::eval_	(	Scalar	x,
		int	i
	)		const

inlineprotected

◆ evalDerivative()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::evalDerivative	(	Scalar	x,
		bool	extrapolate = `false`
	)		const

inline

Evaluate the spline's derivative at a given position.

Parameters

x	The value on the abscissa where the spline's derivative ought to be evaluated
extrapolate	If this parameter is set to true, the spline will be extended beyond its range by straight lines, if false calling extrapolate for $x \not [x_{min}, x_{max}]$ will cause a failed assertation.

◆ evalDerivative_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::evalDerivative_	(	Scalar	x,
		int	i
	)		const

inlineprotected

◆ h_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::h_ ( int i ) const

inlineprotected

Returns x[i] - x[i - 1].

◆ intersect()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::intersect	(	Scalar	a,
		Scalar	b,
		Scalar	c,
		Scalar	d
	)		const

inline

Find the intersections of the spline with a cubic polynomial in the whole intervall, throws Dune::MathError exception if there is more or less than one solution.

◆ intersectInterval()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::intersectInterval	(	Scalar	x0,
		Scalar	x1,
		Scalar	a,
		Scalar	b,
		Scalar	c,
		Scalar	d
	)		const

inline

Find the intersections of the spline with a cubic polynomial in a sub-intervall of the spline, throws Dune::MathError exception if there is more or less than one solution.

◆ intersectSegment_()

template<class ScalarT , class ImplementationT >

int Dumux::SplineCommon_< ScalarT, ImplementationT >::intersectSegment_	(	Scalar *	sol,
		int	segIdx,
		Scalar	a,
		Scalar	b,
		Scalar	c,
		Scalar	d,
		Scalar	x0 = `-1e100`,
		Scalar	x1 = `1e100`
	)		const

inlineprotected

Find all the intersections of a segment of the spline with a cubic polynomial within a specified interval.

◆ makeFullSystem_()

template<class ScalarT , class ImplementationT >

template<class Vector , class Matrix >

void Dumux::SplineCommon_< ScalarT, ImplementationT >::makeFullSystem_	(	Matrix &	M,
		Vector &	d,
		Scalar	m0,
		Scalar	m1
	)

inlineprotected

Make the linear system of equations Mx = d which results in the moments of the full spline.

◆ makeNaturalSystem_()

template<class ScalarT , class ImplementationT >

template<class Vector , class Matrix >

void Dumux::SplineCommon_< ScalarT, ImplementationT >::makeNaturalSystem_	(	Matrix &	M,
		Vector &	d
	)

inlineprotected

Make the linear system of equations Mx = d which results in the moments of the natural spline. Stoer 2005: Numerische Mathematik 1, p. 111 [64].

◆ makePeriodicSystem_()

template<class ScalarT , class ImplementationT >

template<class Vector , class Matrix >

void Dumux::SplineCommon_< ScalarT, ImplementationT >::makePeriodicSystem_	(	Matrix &	M,
		Vector &	d
	)

inlineprotected

Make the linear system of equations Mx = d which results in the moments of the periodic spline.

When solving Mx = d, it should be noted that x[0] is trash and needs to be set to x[n-1]

◆ moment_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::moment_ ( int i ) const

inlineprotected

Returns the moment (i.e. second derivative) of the spline at the i-th sampling point.

◆ monotonic() [1/2]

template<class ScalarT , class ImplementationT >

int Dumux::SplineCommon_< ScalarT, ImplementationT >::monotonic ( ) const

inline

Same as monotonic(x0, x1), but with the entire range of the spline as interval.

◆ monotonic() [2/2]

template<class ScalarT , class ImplementationT >

int Dumux::SplineCommon_< ScalarT, ImplementationT >::monotonic	(	Scalar	x0,
		Scalar	x1
	)		const

inline

Returns 1 if the spline is monotonically increasing, -1 if the spline is mononously decreasing and 0 if the spline is not monotonous in the interval (x0, x1).

In the corner case where the whole spline is flat, it returns 2.

◆ monotonic_()

template<class ScalarT , class ImplementationT >

int Dumux::SplineCommon_< ScalarT, ImplementationT >::monotonic_	(	int	i,
		Scalar	x0,
		Scalar	x1
	)		const

inlineprotected

◆ numSamples_()

template<class ScalarT , class ImplementationT >

int Dumux::SplineCommon_< ScalarT, ImplementationT >::numSamples_ ( ) const

inlineprotected

Returns the number of sampling points.

◆ printCSV()

template<class ScalarT , class ImplementationT >

void Dumux::SplineCommon_< ScalarT, ImplementationT >::printCSV	(	Scalar	xi0,
		Scalar	xi1,
		int	k
	)		const

inline

Prints k tuples of the format (x, y, dx/dy, isMonotonic) to stdout.

If the spline does not apply for parts of [x0, x1] it is extrapolated using a straight line. The result can be inspected using the following commands:

--------— snip --------— ./yourProgramm > spline.csv gnuplot

gnuplot> plot "spline.csv" using 1:2 w l ti "Curve", \ "spline.csv" using 1:3 w l ti "Derivative", \ "spline.csv" using 1:4 w p ti "Monotonic" --------— snap --------—

◆ segmentIdx_()

template<class ScalarT , class ImplementationT >

int Dumux::SplineCommon_< ScalarT, ImplementationT >::segmentIdx_ ( Scalar x ) const

inlineprotected

◆ x_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::x_ ( int i ) const

inlineprotected

Returns the y coordinate of the i-th sampling point.

◆ xMax()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::xMax ( ) const

inline

Return the x value of the rightmost sampling point.

◆ xMin()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::xMin ( ) const

inline

Return the x value of the leftmost sampling point.

◆ y_()

template<class ScalarT , class ImplementationT >

Scalar Dumux::SplineCommon_< ScalarT, ImplementationT >::y_ ( int i ) const

inlineprotected

Returns the y coordinate of the i-th sampling point.

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

splinecommon_.hh

Description

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

◆ SplineCommon_()

Member Function Documentation

◆ a_()

◆ applies()

◆ assignFromArrayList_()

◆ assignFromTupleList_()

◆ assignSamplingPoints_()

◆ b_()

◆ c_()

◆ d_()

◆ eval()

◆ eval_()

◆ evalDerivative()

◆ evalDerivative_()

◆ h_()

◆ intersect()

◆ intersectInterval()

◆ intersectSegment_()

◆ makeFullSystem_()

◆ makeNaturalSystem_()

◆ makePeriodicSystem_()

◆ moment_()

◆ monotonic() [1/2]

◆ monotonic() [2/2]

◆ monotonic_()

◆ numSamples_()

◆ printCSV()

◆ segmentIdx_()

◆ x_()

◆ xMax()

◆ xMin()

◆ y_()