Class implementing cubic splines. More...

#include <Spline.hpp>

Classes
struct	ComparatorX_
	Helper class needed to sort the input sampling points. More...

Public Types
enum	SplineType { Full , Natural , Periodic , Monotonic }
	The type of the spline to be created. More...

Public Member Functions
	Spline ()
	Default constructor for a spline.

	Spline (Scalar x0, Scalar x1, Scalar y0, Scalar y1, Scalar m0, Scalar m1)
	Convenience constructor for a full spline with just two sampling points.

template<class ScalarArrayX , class ScalarArrayY >
	Spline (size_t nSamples, const ScalarArrayX &x, const ScalarArrayY &y, SplineType splineType=Natural, bool sortInputs=true)
	Convenience constructor for a natural or a periodic spline.

template<class PointArray >
	Spline (size_t nSamples, const PointArray &points, SplineType splineType=Natural, bool sortInputs=true)
	Convenience constructor for a natural or a periodic spline.

template<class ScalarContainer >
	Spline (const ScalarContainer &x, const ScalarContainer &y, SplineType splineType=Natural, bool sortInputs=true)
	Convenience constructor for a natural or a periodic spline.

template<class PointContainer >
	Spline (const PointContainer &points, SplineType splineType=Natural, bool sortInputs=true)
	Convenience constructor for a natural or a periodic spline.

template<class ScalarArray >
	Spline (size_t nSamples, const ScalarArray &x, const ScalarArray &y, Scalar m0, Scalar m1, bool sortInputs=true)
	Convenience constructor for a full spline.

template<class PointArray >
	Spline (size_t nSamples, const PointArray &points, Scalar m0, Scalar m1, bool sortInputs=true)
	Convenience constructor for a full spline.

template<class ScalarContainerX , class ScalarContainerY >
	Spline (const ScalarContainerX &x, const ScalarContainerY &y, Scalar m0, Scalar m1, bool sortInputs=true)
	Convenience constructor for a full spline.

template<class PointContainer >
	Spline (const PointContainer &points, Scalar m0, Scalar m1, bool sortInputs=true)
	Convenience constructor for a full spline.

void	set (Scalar x0, Scalar x1, Scalar y0, Scalar y1, Scalar m0, Scalar m1)
	Set the sampling points and the boundary slopes of the spline with two sampling points.

template<class ScalarArrayX , class ScalarArrayY >
void	setXYArrays (size_t nSamples, const ScalarArrayX &x, const ScalarArrayY &y, Scalar m0, Scalar m1, bool sortInputs=true)
	Set the sampling points and the boundary slopes of a full spline using C-style arrays.

template<class ScalarContainerX , class ScalarContainerY >
void	setXYContainers (const ScalarContainerX &x, const ScalarContainerY &y, Scalar m0, Scalar m1, bool sortInputs=true)
	Set the sampling points and the boundary slopes of a full spline using STL-compatible containers.

template<class PointArray >
void	setArrayOfPoints (size_t nSamples, const PointArray &points, Scalar m0, Scalar m1, bool sortInputs=true)
	Set the sampling points and the boundary slopes of a full spline using a C-style array.

template<class XYContainer >
void	setContainerOfPoints (const XYContainer &points, Scalar m0, Scalar m1, bool sortInputs=true)
	Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of array-like objects.

template<class XYContainer >
void	setContainerOfTuples (const XYContainer &points, Scalar m0, Scalar m1, bool sortInputs=true)
	Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of tuple-like objects.

template<class ScalarArrayX , class ScalarArrayY >
void	setXYArrays (size_t nSamples, const ScalarArrayX &x, const ScalarArrayY &y, SplineType splineType=Natural, bool sortInputs=true)
	Set the sampling points natural spline using C-style arrays.

template<class ScalarContainerX , class ScalarContainerY >
void	setXYContainers (const ScalarContainerX &x, const ScalarContainerY &y, SplineType splineType=Natural, bool sortInputs=true)
	Set the sampling points of a natural spline using STL-compatible containers.

template<class PointArray >
void	setArrayOfPoints (size_t nSamples, const PointArray &points, SplineType splineType=Natural, bool sortInputs=true)
	Set the sampling points of a natural spline using a C-style array.

template<class XYContainer >
void	setContainerOfPoints (const XYContainer &points, SplineType splineType=Natural, bool sortInputs=true)
	Set the sampling points of a natural spline using a STL-compatible container of array-like objects.

template<class XYContainer >
void	setContainerOfTuples (const XYContainer &points, SplineType splineType=Natural, bool sortInputs=true)
	Set the sampling points of a natural spline using a STL-compatible container of tuple-like objects.

template<class Evaluation >
bool	applies (const Evaluation &x) const
	Return true iff the given x is in range [x1, xn].

size_t	numSamples () const
	Return the number of (x, y) values.

Scalar	xAt (size_t sampleIdx) const
	Return the x value of a given sampling point.

Scalar	valueAt (size_t sampleIdx) const
	Return the x value of a given sampling point.

void	printCSV (Scalar xi0, Scalar xi1, size_t k, std::ostream &os) const
	Prints k tuples of the format (x, y, dx/dy, isMonotonic) to stdout.

template<class Evaluation >
Evaluation	eval (const Evaluation &x, bool extrapolate=false) const
	Evaluate the spline at a given position.

template<class Evaluation >
Evaluation	evalDerivative (const Evaluation &x, bool extrapolate=false) const
	Evaluate the spline's derivative at a given position.

template<class Evaluation >
Evaluation	evalSecondDerivative (const Evaluation &x, bool extrapolate=false) const
	Evaluate the spline's second derivative at a given position.

template<class Evaluation >
Evaluation	evalThirdDerivative (const Evaluation &x, bool extrapolate=false) const
	Evaluate the spline's third derivative at a given position.

template<class Evaluation >
Evaluation	intersect (const Evaluation &a, const Evaluation &b, const Evaluation &c, const Evaluation &d) const
	Find the intersections of the spline with a cubic polynomial in the whole interval, throws Opm::MathError exception if there is more or less than one solution.

template<class Evaluation >
Evaluation	intersectInterval (Scalar x0, Scalar x1, const Evaluation &a, const Evaluation &b, const Evaluation &c, const Evaluation &d) const
	Find the intersections of the spline with a cubic polynomial in a sub-interval of the spline, throws Opm::MathError exception if there is more or less than one solution.

int	monotonic (Scalar x0, Scalar x1, bool extrapolate=false) 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).

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

Protected Member Functions
void	sortInput_ ()
	Sort the sample points in ascending order of their x value.

void	reverseSamplingPoints_ ()
	Reverse order of the elements in the arrays which contain the sampling points.

void	setNumSamples_ (size_t nSamples)
	Resizes the internal vectors to store the sample points.

void	makeFullSpline_ (Scalar m0, Scalar m1)
	Create a natural spline from the already set sampling points.

void	makeNaturalSpline_ ()
	Create a natural spline from the already set sampling points.

void	makePeriodicSpline_ ()
	Create a periodic spline from the already set sampling points.

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

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

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

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.

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.

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

template<class Vector >
void	makeMonotonicSpline_ (Vector &slopes)
	Create a monotonic spline from the already set sampling points.

template<class MomentsVector , class SlopeVector >
void	setSlopesFromMoments_ (SlopeVector &slopes, const MomentsVector &moments)
	Convert the moments at the sample points to slopes.

template<class Evaluation >
Evaluation	eval_ (const Evaluation &x, size_t i) const

template<class Evaluation >
Evaluation	evalDerivative_ (const Evaluation &x, size_t i) const

template<class Evaluation >
Evaluation	evalDerivative2_ (const Evaluation &x, size_t i) const

template<class Evaluation >
Evaluation	evalDerivative3_ (const Evaluation &x, size_t i) const

template<class Evaluation >
Evaluation	h00_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h10_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h01_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h11_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h00_prime_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h10_prime_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h01_prime_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h11_prime_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h00_prime2_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h10_prime2_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h01_prime2_ (const Evaluation &t) const

template<class Evaluation >
Evaluation	h11_prime2_ (const Evaluation &t) const

template<class Evaluation >
Scalar	h00_prime3_ (const Evaluation &) const

template<class Evaluation >
Scalar	h10_prime3_ (const Evaluation &) const

template<class Evaluation >
Scalar	h01_prime3_ (const Evaluation &) const

template<class Evaluation >
Scalar	h11_prime3_ (const Evaluation &) const

int	monotonic_ (size_t i, Scalar x0, Scalar x1, int &r) const

template<class Evaluation >
size_t	intersectSegment_ (Evaluation *sol, size_t segIdx, const Evaluation &a, const Evaluation &b, const Evaluation &c, const Evaluation &d, Scalar x0=-1e30, Scalar x1=1e30) const
	Find all the intersections of a segment of the spline with a cubic polynomial within a specified interval.

size_t	segmentIdx_ (Scalar x) const

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

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

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

Scalar	slope_ (size_t i) const
	Returns the slope (i.e.

Scalar	a_ (size_t i) const

Scalar	b_ (size_t i) const

Scalar	c_ (size_t i) const

Scalar	d_ (size_t i) const

Protected Attributes
Vector	xPos_

Vector	yPos_

Vector	slopeVec_

Detailed Description

template<class Scalar>
class Opm::Spline< Scalar >

Class implementing cubic splines.

This class supports full, natural, periodic and monotonic cubic splines.

Full a splines are splines which, given sampling points $x_1, \dots, x_n$ , fulfill the following conditions

$\begin{align*} s(x_i) & = y_i \quad \forall i \in \{1, \dots, n \} \\ s'(x_1) & = m_1 \\ s'(x_n) & = m_n \end{align*}$

for any given boundary slopes and .

Natural splines which are defined by

$\begin{align*} s(x_i) & = y_i \quad \forall i \in \{1, \dots, n \} \\ s''(x_1) & = 0 \\ s''(x_n) & = 0 *\end{align*}$

For periodic splines of splines the slopes at the boundaries are identical:

$\begin{align*} s(x_i) & = y_i \quad \forall i \in \{1, \dots, n \} \\ s'(x_1) & = s'(x_n) \\ s''(x_1) & = s''(x_n) \;. *\end{align*}$

Finally, there are monotonic splines which guarantee that the curve is confined by its sampling points, i.e.,

$y_i \leq s(x) \leq y_{i+1} \quad \text{for} x_i \leq x \leq x_{i+1} \;.$

For more information on monotonic splines, see http://en.wikipedia.org/wiki/Monotone_cubic_interpolation

Full, natural and periodic splines are continuous in their first and second derivatives, i.e.,

$s \in \mathcal{C}^2$

holds for such splines. Monotonic splines are only continuous up to their first derivative, i.e., for these only

$s \in \mathcal{C}^1$

is true.

Member Enumeration Documentation

◆ SplineType

template<class Scalar >

enum Opm::Spline::SplineType

The type of the spline to be created.

To specfiy the acutal curve, use one of the set() methods.

Constructor & Destructor Documentation

◆ Spline() [1/10]

template<class Scalar >

Opm::Spline< Scalar >::Spline ( )

inline

Default constructor for a spline.

To specfiy the acutal curve, use one of the set() methods.

◆ Spline() [2/10]

template<class Scalar >

Opm::Spline< Scalar >::Spline	(	Scalar	x0,
		Scalar	x1,
		Scalar	y0,
		Scalar	y1,
		Scalar	m0,
		Scalar	m1
	)

inline

Convenience constructor for a full spline with just two sampling points.

Parameters

x0	The value of the first sampling point
x1	The value of the second sampling point
y0	The value of the first sampling point
y1	The value of the second sampling point
m0	The slope of the spline at
m1	The slope of the spline at

◆ Spline() [3/10]

template<class Scalar >

template<class ScalarArrayX , class ScalarArrayY >

Opm::Spline< Scalar >::Spline	(	size_t	nSamples,
		const ScalarArrayX &	x,
		const ScalarArrayY &	y,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Convenience constructor for a natural or a periodic spline.

Parameters

nSamples	The number of sampling points (must be > 2)
x	An array containing the values of the spline's sampling points
y	An array containing the values of the spline's sampling points
splineType	Type of spline
sortInputs	True to sort inputs

◆ Spline() [4/10]

template<class Scalar >

template<class PointArray >

Opm::Spline< Scalar >::Spline	(	size_t	nSamples,
		const PointArray &	points,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Convenience constructor for a natural or a periodic spline.

Parameters

nSamples	The number of sampling points (must be > 2)
points	An array of tuples of the spline's sampling points
splineType	Type of spline
sortInputs	True to sort inputs

◆ Spline() [5/10]

template<class Scalar >

template<class ScalarContainer >

Opm::Spline< Scalar >::Spline	(	const ScalarContainer &	x,
		const ScalarContainer &	y,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Convenience constructor for a natural or a periodic spline.

Parameters

x	An array containing the values of the spline's sampling points (must have a size() method)
y	An array containing the values of the spline's sampling points (must have a size() method)
splineType	Type of spline
sortInputs	True to sort inputs

◆ Spline() [6/10]

template<class Scalar >

template<class PointContainer >

Opm::Spline< Scalar >::Spline	(	const PointContainer &	points,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inlineexplicit

Convenience constructor for a natural or a periodic spline.

Parameters

points	An array of tuples of the spline's sampling points (must have a size() method)
splineType	Type of spline
sortInputs	True to sort inputs

◆ Spline() [7/10]

template<class Scalar >

template<class ScalarArray >

Opm::Spline< Scalar >::Spline	(	size_t	nSamples,
		const ScalarArray &	x,
		const ScalarArray &	y,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Convenience constructor for a full spline.

Parameters

nSamples	The number of sampling points (must be >= 2)
x	An array containing the values of the spline's sampling points
y	An array containing the values of the spline's sampling points
m0	The slope of the spline at
m1	The slope of the spline at
sortInputs	Indicates whether the sample points should be sorted (this is not necessary if they are already sorted in ascending or descending order)

◆ Spline() [8/10]

template<class Scalar >

template<class PointArray >

Opm::Spline< Scalar >::Spline	(	size_t	nSamples,
		const PointArray &	points,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Convenience constructor for a full spline.

Parameters

nSamples	The number of sampling points (must be >= 2)
points	An array containing the and values of the spline's sampling points
m0	The slope of the spline at
m1	The slope of the spline at
sortInputs	Indicates whether the sample points should be sorted (this is not necessary if they are already sorted in ascending or descending order)

◆ Spline() [9/10]

template<class Scalar >

template<class ScalarContainerX , class ScalarContainerY >

Opm::Spline< Scalar >::Spline	(	const ScalarContainerX &	x,
		const ScalarContainerY &	y,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Convenience constructor for a full spline.

Parameters

x	An array containing the values of the spline's sampling points (must have a size() method)
y	An array containing the values of the spline's sampling points (must have a size() method)
m0	The slope of the spline at
m1	The slope of the spline at
sortInputs	Indicates whether the sample points should be sorted (this is not necessary if they are already sorted in ascending or descending order)

◆ Spline() [10/10]

template<class Scalar >

template<class PointContainer >

Opm::Spline< Scalar >::Spline	(	const PointContainer &	points,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Convenience constructor for a full spline.

Parameters

points	An array of tuples of the spline's sampling points (must have a size() method)
m0	The slope of the spline at
m1	The slope of the spline at
sortInputs	Indicates whether the sample points should be sorted (this is not necessary if they are already sorted in ascending or descending order)

Member Function Documentation

◆ assignFromTupleList_()

template<class Scalar >

template<class DestVector , class ListIterator >

void Opm::Spline< Scalar >::assignFromTupleList_	(	DestVector &	destX,
		DestVector &	destY,
		ListIterator	srcBegin,
		ListIterator	srcEnd,
		unsigned	nSamples
	)

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 Scalar >

template<class DestVector , class SourceVector >

void Opm::Spline< Scalar >::assignSamplingPoints_	(	DestVector &	destX,
		DestVector &	destY,
		const SourceVector &	srcX,
		const SourceVector &	srcY,
		unsigned	nSamples
	)

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!

◆ eval()

template<class Scalar >

template<class Evaluation >

Evaluation Opm::Spline< Scalar >::eval	(	const Evaluation &	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.

◆ evalDerivative()

template<class Scalar >

template<class Evaluation >

Evaluation Opm::Spline< Scalar >::evalDerivative	(	const Evaluation &	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.

◆ evalSecondDerivative()

template<class Scalar >

template<class Evaluation >

Evaluation Opm::Spline< Scalar >::evalSecondDerivative	(	const Evaluation &	x,
		bool	extrapolate = `false`
	)		const

inline

Evaluate the spline's second 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.

◆ evalThirdDerivative()

template<class Scalar >

template<class Evaluation >

Evaluation Opm::Spline< Scalar >::evalThirdDerivative	(	const Evaluation &	x,
		bool	extrapolate = `false`
	)		const

inline

Evaluate the spline's third 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.

◆ makeFullSpline_()

template<class Scalar >

void Opm::Spline< Scalar >::makeFullSpline_	(	Scalar	m0,
		Scalar	m1
	)

inlineprotected

Create a natural spline from the already set sampling points.

This creates a temporary matrix and right hand side vector.

◆ makeMonotonicSpline_()

template<class Scalar >

template<class Vector >

void Opm::Spline< Scalar >::makeMonotonicSpline_ ( Vector & slopes )

inlineprotected

Create a monotonic spline from the already set sampling points.

This code is inspired by opm-core's "MonotCubicInterpolator" class and also uses the approach by Fritsch and Carlson, see

http://en.wikipedia.org/wiki/Monotone_cubic_interpolation

◆ makeNaturalSpline_()

template<class Scalar >

void Opm::Spline< Scalar >::makeNaturalSpline_ ( )

inlineprotected

Create a natural spline from the already set sampling points.

This creates a temporary matrix and right hand side vector.

◆ makePeriodicSpline_()

template<class Scalar >

void Opm::Spline< Scalar >::makePeriodicSpline_ ( )

inlineprotected

Create a periodic spline from the already set sampling points.

This creates a temporary matrix and right hand side vector.

◆ monotonic()

template<class Scalar >

int Opm::Spline< Scalar >::monotonic	(	Scalar	x0,
		Scalar	x1,
		bool	extrapolate = `false`
	)		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 that the spline is constant within the given interval, this method returns 3.

◆ printCSV()

template<class Scalar >

template void Opm::Spline< Scalar >::printCSV	(	Scalar	xi0,
		Scalar	xi1,
		size_t	k,
		std::ostream &	os
	)		const

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 --------—

◆ set()

template<class Scalar >

void Opm::Spline< Scalar >::set	(	Scalar	x0,
		Scalar	x1,
		Scalar	y0,
		Scalar	y1,
		Scalar	m0,
		Scalar	m1
	)

inline

Set the sampling points and the boundary slopes of the spline with two sampling points.

Parameters

x0	The value of the first sampling point
x1	The value of the second sampling point
y0	The value of the first sampling point
y1	The value of the second sampling point
m0	The slope of the spline at
m1	The slope of the spline at

◆ setArrayOfPoints() [1/2]

template<class Scalar >

template<class PointArray >

void Opm::Spline< Scalar >::setArrayOfPoints	(	size_t	nSamples,
		const PointArray &	points,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Set the sampling points and the boundary slopes of a full spline using a C-style array.

This method uses a single array of sampling points, which are seen as an array-like object which provides access to the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) The array containing the sampling points must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setArrayOfPoints() [2/2]

template<class Scalar >

template<class PointArray >

void Opm::Spline< Scalar >::setArrayOfPoints	(	size_t	nSamples,
		const PointArray &	points,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Set the sampling points of a natural spline using a C-style array.

This method uses a single array of sampling points, which are seen as an array-like object which provides access to the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) The array containing the sampling points must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setContainerOfPoints() [1/2]

template<class Scalar >

template<class XYContainer >

void Opm::Spline< Scalar >::setContainerOfPoints	(	const XYContainer &	points,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of array-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be array-like objects storing the X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setContainerOfPoints() [2/2]

template<class Scalar >

template<class XYContainer >

void Opm::Spline< Scalar >::setContainerOfPoints	(	const XYContainer &	points,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Set the sampling points of a natural spline using a STL-compatible container of array-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be array-like objects storing the X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setContainerOfTuples() [1/2]

template<class Scalar >

template<class XYContainer >

void Opm::Spline< Scalar >::setContainerOfTuples	(	const XYContainer &	points,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of tuple-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be tuple-like objects storing the X and Y coordinates. "tuple-like" means that the objects provide access to the x values via std::get<0>(obj) and to the y value via std::get<1>(obj) (e.g. std::tuple or std::pair). "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setContainerOfTuples() [2/2]

template<class Scalar >

template<class XYContainer >

void Opm::Spline< Scalar >::setContainerOfTuples	(	const XYContainer &	points,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Set the sampling points of a natural spline using a STL-compatible container of tuple-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be tuple-like objects storing the X and Y coordinates. "tuple-like" means that the objects provide access to the x values via std::get<0>(obj) and to the y value via std::get<1>(obj) (e.g. std::tuple or std::pair). "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setSlopesFromMoments_()

template<class Scalar >

template<class MomentsVector , class SlopeVector >

void Opm::Spline< Scalar >::setSlopesFromMoments_	(	SlopeVector &	slopes,
		const MomentsVector &	moments
	)

inlineprotected

Convert the moments at the sample points to slopes.

This requires to use cubic Hermite interpolation, but it is required because for monotonic splines the second derivative is not continuous.

◆ setXYArrays() [1/2]

template<class Scalar >

template<class ScalarArrayX , class ScalarArrayY >

void Opm::Spline< Scalar >::setXYArrays	(	size_t	nSamples,
		const ScalarArrayX &	x,
		const ScalarArrayY &	y,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Set the sampling points and the boundary slopes of a full spline using C-style arrays.

This method uses separate array-like objects for the values of the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) Each array must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setXYArrays() [2/2]

template<class Scalar >

template<class ScalarArrayX , class ScalarArrayY >

void Opm::Spline< Scalar >::setXYArrays	(	size_t	nSamples,
		const ScalarArrayX &	x,
		const ScalarArrayY &	y,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Set the sampling points natural spline using C-style arrays.

This method uses separate array-like objects for the values of the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) Each array must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setXYContainers() [1/2]

template<class Scalar >

template<class ScalarContainerX , class ScalarContainerY >

void Opm::Spline< Scalar >::setXYContainers	(	const ScalarContainerX &	x,
		const ScalarContainerY &	y,
		Scalar	m0,
		Scalar	m1,
		bool	sortInputs = `true`
	)

inline

Set the sampling points and the boundary slopes of a full spline using STL-compatible containers.

This method uses separate STL-compatible containers for the values of the sampling points' X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setXYContainers() [2/2]

template<class Scalar >

template<class ScalarContainerX , class ScalarContainerY >

void Opm::Spline< Scalar >::setXYContainers	(	const ScalarContainerX &	x,
		const ScalarContainerY &	y,
		SplineType	splineType = `Natural`,
		bool	sortInputs = `true`
	)

inline

Set the sampling points of a natural spline using STL-compatible containers.

This method uses separate STL-compatible containers for the values of the sampling points' X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ slope_()

template<class Scalar >

Scalar Opm::Spline< Scalar >::slope_ ( size_t i ) const

inlineprotected

Returns the slope (i.e.

first derivative) of the spline at the i-th sampling point.

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

opm/material/common/Spline.hpp
opm/material/common/Spline.cpp

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Enumeration Documentation

◆ SplineType

Constructor & Destructor Documentation

◆ Spline() [1/10]

◆ Spline() [2/10]

◆ Spline() [3/10]

◆ Spline() [4/10]

◆ Spline() [5/10]

◆ Spline() [6/10]

◆ Spline() [7/10]

◆ Spline() [8/10]

◆ Spline() [9/10]

◆ Spline() [10/10]

Member Function Documentation

◆ assignFromTupleList_()

◆ assignSamplingPoints_()

◆ eval()

◆ evalDerivative()

◆ evalSecondDerivative()

◆ evalThirdDerivative()

◆ makeFullSpline_()

◆ makeMonotonicSpline_()

◆ makeNaturalSpline_()

◆ makePeriodicSpline_()

◆ monotonic()

◆ printCSV()

◆ set()

◆ setArrayOfPoints() [1/2]

◆ setArrayOfPoints() [2/2]

◆ setContainerOfPoints() [1/2]

◆ setContainerOfPoints() [2/2]

◆ setContainerOfTuples() [1/2]

◆ setContainerOfTuples() [2/2]

◆ setSlopesFromMoments_()

◆ setXYArrays() [1/2]

◆ setXYArrays() [2/2]

◆ setXYContainers() [1/2]

◆ setXYContainers() [2/2]

◆ slope_()