A cubic spline class. More...

#include <cubicspline.h>

Inheritance diagram for votca::tools::CubicSpline:

Collaboration diagram for votca::tools::CubicSpline:

Public Member Functions
	CubicSpline ()=default

	~CubicSpline () override=default

void	Interpolate (const Eigen::VectorXd &x, const Eigen::VectorXd &y) override
	Calculate interpolating spline for given (x,y) values. Points on resulting spline can be obtained via Calculate().

void	Fit (const Eigen::VectorXd &x, const Eigen::VectorXd &y) override
	Fit spline through noisy (x,y) values. Points on resulting fitted spline can be obtained via Calculate().

double	Calculate (double r) override
	Calculate spline function value for a given x value on the spline created by Interpolate() or Fit()

double	CalculateDerivative (double r) override
	Calculate y value for a given x value on the derivative of the spline created by function Interpolate or Fit.

void	setSplineData (const Eigen::VectorXd &f, const Eigen::VectorXd &f2)

template<typename matrix_type >
void	AddToFitMatrix (matrix_type &M, double x, Index offset1, Index offset2=0, double scale=1)
	Add a point (one entry) to fitting matrix.

template<typename matrix_type >
void	AddToFitMatrix (matrix_type &M, double x, Index offset1, Index offset2, double scale1, double scale2)
	Add a point (one entry) to fitting matrix.

template<typename matrix_type , typename vector_type >
void	AddToFitMatrix (matrix_type &M, vector_type &x, Index offset1, Index offset2=0)
	Add a vector of points to fitting matrix.

template<typename matrix_type >
void	AddBCSumZeroToFitMatrix (matrix_type &M, Index offset1, Index offset2=0)
	Add boundary condition of sum_i f_i =0 to fitting matrix.

template<typename matrix_type >
void	AddBCToFitMatrix (matrix_type &M, Index offset1, Index offset2=0)
	Add boundary conditions to fitting matrix.

virtual double	Calculate (double x)=0
	Calculate spline function value for a given x value on the spline created by Interpolate() or Fit()

Eigen::VectorXd	Calculate (const Eigen::VectorXd &x)
	Calculate spline function values for given x values on the spline created by Interpolate() or Fit()

virtual double	CalculateDerivative (double x)=0
	Calculate y value for a given x value on the derivative of the spline created by function Interpolate or Fit.

Eigen::VectorXd	CalculateDerivative (const Eigen::VectorXd &x)
	Calculate y values for given x values on the derivative of the spline created by function Interpolate or Fit.

Public Member Functions inherited from votca::tools::Spline
	Spline ()=default

virtual	~Spline ()=default

virtual void	Interpolate (const Eigen::VectorXd &x, const Eigen::VectorXd &y)=0
	Calculate interpolating spline for given (x,y) values. Points on resulting spline can be obtained via Calculate().

virtual void	Fit (const Eigen::VectorXd &x, const Eigen::VectorXd &y)=0
	Fit spline through noisy (x,y) values. Points on resulting fitted spline can be obtained via Calculate().

virtual double	Calculate (double x)=0
	Calculate spline function value for a given x value on the spline created by Interpolate() or Fit()

virtual double	CalculateDerivative (double x)=0
	Calculate y value for a given x value on the derivative of the spline created by function Interpolate or Fit.

void	setBC (eBoundary bc)
	Set the boundary type of the spline.

void	setBCInt (Index bc)
	Set the boundary type of the spline.

double	getGridPoint (int i)
	Get the grid point of certain index.

Eigen::VectorXd	Calculate (const Eigen::VectorXd &x)
	Calculate spline function values for given x values on the spline created by Interpolate() or Fit()

Eigen::VectorXd	CalculateDerivative (const Eigen::VectorXd &x)
	Calculate y values for given x values on the derivative of the spline created by function Interpolate or Fit.

void	Print (std::ostream &out, double interval)
	Print spline values (using Calculate()) on output "out" on the entire grid in steps of "interval".

Index	getInterval (double r)
	Determine the index of the interval containing value r.

Index	GenerateGrid (double min, double max, double h)
	Generate the grid for fitting from "min" to "max" in steps of "h".

Eigen::VectorXd &	getX ()
	Get the grid array x.

const Eigen::VectorXd &	getX () const

Private Member Functions
double	A (double r)

double	B (double r)

double	C (double r)

double	D (double r)

double	Aprime (double r)

double	Bprime (double r)

double	Cprime (double r)

double	Dprime (double r)

double	A_prime_l (Index i)

double	A_prime_r (Index i)

double	B_prime_l (Index i)

double	B_prime_r (Index i)

double	C_prime_l (Index i)

double	C_prime_r (Index i)

double	D_prime_l (Index i)

double	D_prime_r (Index i)

Private Attributes
Eigen::VectorXd	f_

Eigen::VectorXd	f2_

Additional Inherited Members
Public Types inherited from votca::tools::Spline
enum	eBoundary { splineNormal = 0 , splinePeriodic = 1 , splineDerivativeZero = 2 }
	enum for type of boundary condition More...

Protected Attributes inherited from votca::tools::Spline
eBoundary	boundaries_ = eBoundary::splineNormal
	Get the spline data f_.

Eigen::VectorXd	r_

Detailed Description

A cubic spline class.

This class does cubic piecewise spline interpolation and spline fitting. As representation of a single spline, the general form

\[ S_i(x) = A(x,h_i) f_i + B(x,h_i) f_{i+1} + C(x,h_i) f''_i + d(x,h_i) f''_{i+1} \]

with

\[ x_i \le x < x_{i+1}\,,\\ h_i = x_{i+1} - x_{i} \]

The \(f_i\,,\,,f'' i_\) are the function values and second derivates at point \(x_i\).

The parameters \(f''_i\) are no free parameters, they are determined by the smoothing condition that the first derivatives are continuous. So the only free paramers are the grid points x_i as well as the functon values f_i at these points. A spline can be generated in several ways:

Interpolation spline
Fitting spline (fit to noisy data)
calculate the parameters elsewere and fill the spline class

Definition at line 54 of file cubicspline.h.

Constructor & Destructor Documentation

◆ CubicSpline()

votca::tools::CubicSpline::CubicSpline ( )

default

◆ ~CubicSpline()

votca::tools::CubicSpline::~CubicSpline ( )

overridedefault

Member Function Documentation

◆ A()

double votca::tools::CubicSpline::A ( double r )

private

Definition at line 141 of file cubicspline.cc.

◆ A_prime_l()

double votca::tools::CubicSpline::A_prime_l ( Index i )

private

Definition at line 190 of file cubicspline.cc.

◆ A_prime_r()

double votca::tools::CubicSpline::A_prime_r ( Index i )

private

Definition at line 202 of file cubicspline.cc.

◆ AddBCSumZeroToFitMatrix()

template<typename matrix_type >

void votca::tools::CubicSpline::AddBCSumZeroToFitMatrix	(	matrix_type &	M,
		Index	offset1,
		Index	offset2 = `0`
	)

inline

Add boundary condition of sum_i f_i =0 to fitting matrix.

Parameters

M	pointer to matrix
offset1	relative to getInterval(x)
offset2	relative to getInterval(x)

Definition at line 212 of file cubicspline.h.

◆ AddBCToFitMatrix()

template<typename matrix_type >

void votca::tools::CubicSpline::AddBCToFitMatrix	(	matrix_type &	M,
		Index	offset1,
		Index	offset2 = `0`
	)

inline

Add boundary conditions to fitting matrix.

Parameters

M	pointer to matrix
offset1	relative to getInterval(x)
offset2	relative to getInterval(x)

Definition at line 221 of file cubicspline.h.

◆ AddToFitMatrix() [1/3]

template<typename matrix_type >

void votca::tools::CubicSpline::AddToFitMatrix	(	matrix_type &	M,
		double	x,
		Index	offset1,
		Index	offset2,
		double	scale1,
		double	scale2
	)

inline

Add a point (one entry) to fitting matrix.

Parameters

M	pointer to matrix [in] [out]
x	value [in]
offset1	relative to getInterval(x) [in]
offset2	relative to getInterval(x) [in]
scale1	parameters for terms "A,B,C,D" [in]
scale2	parameters for terms "AA,BB,CC,DD" [in] When creating a matrix to fit data with a spline, this function creates one entry in that fitting matrix.

Definition at line 187 of file cubicspline.h.

◆ AddToFitMatrix() [2/3]

template<typename matrix_type >

void votca::tools::CubicSpline::AddToFitMatrix	(	matrix_type &	M,
		double	x,
		Index	offset1,
		Index	offset2 = `0`,
		double	scale = `1`
	)

inline

Add a point (one entry) to fitting matrix.

Parameters

M	pointer to matrix
x	value
offset1	relative to getInterval(x)
offset2	relative to getInterval(x)
scale	parameters for terms "A,B,C,D" When creating a matrix to fit data with a spline, this function creates one entry in that fitting matrix.

Definition at line 176 of file cubicspline.h.

◆ AddToFitMatrix() [3/3]

template<typename matrix_type , typename vector_type >

void votca::tools::CubicSpline::AddToFitMatrix	(	matrix_type &	M,
		vector_type &	x,
		Index	offset1,
		Index	offset2 = `0`
	)

inline

Add a vector of points to fitting matrix.

Parameters

M	pointer to matrix
x	vector of x values
offset1	relative to getInterval(x)
offset2	relative to getInterval(x) Same as previous function, but vector-valued and with scale=1.0

Definition at line 200 of file cubicspline.h.

◆ Aprime()

double votca::tools::CubicSpline::Aprime ( double r )

private

Definition at line 146 of file cubicspline.cc.

◆ B()

double votca::tools::CubicSpline::B ( double r )

private

Definition at line 150 of file cubicspline.cc.

◆ B_prime_l()

double votca::tools::CubicSpline::B_prime_l ( Index i )

private

Definition at line 192 of file cubicspline.cc.

◆ B_prime_r()

double votca::tools::CubicSpline::B_prime_r ( Index i )

private

Definition at line 206 of file cubicspline.cc.

◆ Bprime()

double votca::tools::CubicSpline::Bprime ( double r )

private

Definition at line 155 of file cubicspline.cc.

◆ C()

double votca::tools::CubicSpline::C ( double r )

private

Definition at line 159 of file cubicspline.cc.

◆ C_prime_l()

double votca::tools::CubicSpline::C_prime_l ( Index i )

private

Definition at line 194 of file cubicspline.cc.

◆ C_prime_r()

double votca::tools::CubicSpline::C_prime_r ( Index i )

private

Definition at line 208 of file cubicspline.cc.

◆ Calculate() [1/3]

Eigen::VectorXd votca::tools::Spline::Calculate ( const Eigen::VectorXd & x )

Calculate spline function values for given x values on the spline created by Interpolate() or Fit()

Parameters

x	vector of data values

Returns: vector of y value

Definition at line 116 of file spline.cc.

◆ Calculate() [2/3]

double votca::tools::CubicSpline::Calculate ( double x )

overridevirtual

Calculate spline function value for a given x value on the spline created by Interpolate() or Fit()

Parameters

x	data value

Returns: y value

Implements votca::tools::Spline.

Definition at line 129 of file cubicspline.cc.

◆ Calculate() [3/3]

virtual double votca::tools::Spline::Calculate ( double x )

virtual

Calculate spline function value for a given x value on the spline created by Interpolate() or Fit()

Parameters

x	data value

Returns: y value

Implements votca::tools::Spline.

◆ CalculateDerivative() [1/3]

Eigen::VectorXd votca::tools::Spline::CalculateDerivative ( const Eigen::VectorXd & x )

Calculate y values for given x values on the derivative of the spline created by function Interpolate or Fit.

Parameters

x	vector of data values

Returns: vector of y value

Definition at line 124 of file spline.cc.

◆ CalculateDerivative() [2/3]

double votca::tools::CubicSpline::CalculateDerivative ( double x )

overridevirtual

Calculate y value for a given x value on the derivative of the spline created by function Interpolate or Fit.

Parameters

x	data value

Returns: y value of derivative

Implements votca::tools::Spline.

Definition at line 135 of file cubicspline.cc.

◆ CalculateDerivative() [3/3]

virtual double votca::tools::Spline::CalculateDerivative ( double x )

virtual

Calculate y value for a given x value on the derivative of the spline created by function Interpolate or Fit.

Parameters

x	data value

Returns: y value of derivative

Implements votca::tools::Spline.

◆ Cprime()

double votca::tools::CubicSpline::Cprime ( double r )

private

Definition at line 168 of file cubicspline.cc.

◆ D()

double votca::tools::CubicSpline::D ( double r )

private

Definition at line 175 of file cubicspline.cc.

◆ D_prime_l()

double votca::tools::CubicSpline::D_prime_l ( Index i )

private

Definition at line 198 of file cubicspline.cc.

◆ D_prime_r()

double votca::tools::CubicSpline::D_prime_r ( Index i )

private

Definition at line 212 of file cubicspline.cc.

◆ Dprime()

double votca::tools::CubicSpline::Dprime ( double r )

private

Definition at line 183 of file cubicspline.cc.

◆ Fit()

void votca::tools::CubicSpline::Fit	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	y
	)

overridevirtual

Fit spline through noisy (x,y) values. Points on resulting fitted spline can be obtained via Calculate().

Parameters

x	values of data to be fitted
y	values of data to be fitted both vectors must be of same size

Implements votca::tools::Spline.

Definition at line 86 of file cubicspline.cc.

◆ Interpolate()

void votca::tools::CubicSpline::Interpolate	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	y
	)

overridevirtual

Calculate interpolating spline for given (x,y) values. Points on resulting spline can be obtained via Calculate().

Parameters

x	values of data to be interpolated
y	values of data to be interpolated both vectors must be of same size

Implements votca::tools::Spline.

Definition at line 31 of file cubicspline.cc.

◆ setSplineData()

void votca::tools::CubicSpline::setSplineData	(	const Eigen::VectorXd &	f,
		const Eigen::VectorXd &	f2
	)

inline

Definition at line 81 of file cubicspline.h.

Member Data Documentation

◆ f2_

Eigen::VectorXd votca::tools::CubicSpline::f2_

private

Definition at line 150 of file cubicspline.h.

◆ f_

Eigen::VectorXd votca::tools::CubicSpline::f_

private

Definition at line 148 of file cubicspline.h.

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

tools/include/votca/tools/cubicspline.h
tools/src/libtools/cubicspline.cc

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ CubicSpline()

◆ ~CubicSpline()

Member Function Documentation

◆ A()

◆ A_prime_l()

◆ A_prime_r()

◆ AddBCSumZeroToFitMatrix()

◆ AddBCToFitMatrix()

◆ AddToFitMatrix() [1/3]

◆ AddToFitMatrix() [2/3]

◆ AddToFitMatrix() [3/3]

◆ Aprime()

◆ B()

◆ B_prime_l()

◆ B_prime_r()

◆ Bprime()

◆ C()

◆ C_prime_l()

◆ C_prime_r()

◆ Calculate() [1/3]

◆ Calculate() [2/3]

◆ Calculate() [3/3]

◆ CalculateDerivative() [1/3]

◆ CalculateDerivative() [2/3]

◆ CalculateDerivative() [3/3]

◆ Cprime()

◆ D()

◆ D_prime_l()

◆ D_prime_r()

◆ Dprime()

◆ Fit()

◆ Interpolate()

◆ setSplineData()

Member Data Documentation

◆ f2_

◆ f_