CubicSpline Class Reference

Natural cubic spline interpolator. More...

#include <CubicSpline.h>

Inheritance diagram for CubicSpline:

Collaboration diagram for CubicSpline:

Public Member Functions
	CubicSpline ()=default
	Default constructor.
	CubicSpline (const std::vector< double > &x, const std::vector< double > &y)
	Construct and initialize from tabulated data.
void	init (const std::vector< double > &x, const std::vector< double > &y) override
	Initialize from tabulated data (natural spline).
double	eval (double x, Accelerator &accel) const override
	Evaluate the spline at x using an accelerator.
double	evalIntegral (double xa, double xb, Accelerator &accel) const override
	Evaluate the integral of the spline at x.

Protected Member Functions
size_t	findInterval (double x, size_t &intervalCache) const
	Return the interval index for the given x-coordinate, using the supplied cached value if possible.

Protected Attributes
std::vector< double >	x_ {}
std::vector< double >	y_ {}

Private Member Functions
void	computeCoefficients ()
	Compute natural spline coefficients.
void	computeIntegrals ()
	Compute the integrals of the intervals.
double	integral (size_t i, double dx) const
	Calculate the integral from x_[i] to x_[i]+dx.
double	extrapolateLeft (double x) const
	Linear extrapolation to the left of the data range.
double	extrapolateRight (double x) const
	Linear extrapolation to the right of the data range.

Private Attributes
std::vector< double >	b_
std::vector< double >	c_
std::vector< double >	d_
std::vector< double >	integrals_

Detailed Description

Natural cubic spline interpolator.

See also

https://www.gnu.org/software/gsl/doc/html/interp.html

https://www.gnu.org/software/gsl/

Definition at line 28 of file CubicSpline.h.

Constructor & Destructor Documentation

CubicSpline() [1/2]

CubicSpline::CubicSpline ( )

default

Default constructor.

CubicSpline() [2/2]

CubicSpline::CubicSpline	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

Construct and initialize from tabulated data.

Parameters

x	Input: strictly increasing x-coordinates.
y	Input: y-values corresponding to x.

Definition at line 20 of file CubicSpline.cpp.

References init().

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Member Function Documentation

computeCoefficients()

void CubicSpline::computeCoefficients ( )

private

Compute natural spline coefficients.

Definition at line 88 of file CubicSpline.cpp.

References b_, c_, d_, AbstractSpline::x_, and AbstractSpline::y_.

Referenced by init().

computeIntegrals()

void CubicSpline::computeIntegrals ( )

private

Compute the integrals of the intervals.

Definition at line 124 of file CubicSpline.cpp.

References integral(), integrals_, and AbstractSpline::x_.

Referenced by init().

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eval()

double CubicSpline::eval ( double  x, Accelerator &  accel  ) const

overridevirtual

Evaluate the spline at x using an accelerator.

Parameters

x	Input: x-coordinate.
accel	Input/Output: cached interval index.

Returns

Output: interpolated value.

Implements AbstractSpline.

Definition at line 33 of file CubicSpline.cpp.

References b_, c_, d_, extrapolateLeft(), extrapolateRight(), AbstractSpline::findInterval(), AbstractSpline::Accelerator::last_index_, AbstractSpline::x_, and AbstractSpline::y_.

Referenced by TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

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evalIntegral()

double CubicSpline::evalIntegral ( double  xa, double  xb, Accelerator &  accel  ) const

overridevirtual

Evaluate the integral of the spline at x.

Parameters

xa	Input: x-coordinate lower bound.
xb	Input: x-coordinate upper bound.
accel	Input/output: accelerator for interval caching.

Returns

Output: interpolated integral value (with linear extrapolation).

Implements AbstractSpline.

Definition at line 50 of file CubicSpline.cpp.

References extrapolateLeft(), extrapolateRight(), AbstractSpline::findInterval(), integral(), integrals_, AbstractSpline::Accelerator::last_index_, AbstractSpline::Accelerator::last_upper_index_, AbstractSpline::x_, and AbstractSpline::y_.

Referenced by TEST_F().

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extrapolateLeft()

double CubicSpline::extrapolateLeft ( double  x ) const

private

Linear extrapolation to the left of the data range.

Parameters

x	Input: x-coordinate.

Returns

Output: extrapolated value.

Definition at line 136 of file CubicSpline.cpp.

References b_, AbstractSpline::x_, and AbstractSpline::y_.

Referenced by eval(), and evalIntegral().

extrapolateRight()

double CubicSpline::extrapolateRight ( double  x ) const

private

Linear extrapolation to the right of the data range.

Parameters

x	Input: x-coordinate.

Returns

Output: extrapolated value.

Definition at line 141 of file CubicSpline.cpp.

References b_, AbstractSpline::x_, and AbstractSpline::y_.

Referenced by eval(), and evalIntegral().

findInterval()

size_t AbstractSpline::findInterval ( double  x, size_t &  intervalCache  ) const

protectedinherited

Return the interval index for the given x-coordinate, using the supplied cached value if possible.

Parameters

x	Input: x-coordinate.
intervalCache	Input/output: The cached interval index.

Returns

Output: The index of the interval containing x.

Definition at line 39 of file AbstractSpline.cpp.

References AbstractSpline::x_.

Referenced by eval(), LinearSpline::eval(), evalIntegral(), and LinearSpline::evalIntegral().

init()

void CubicSpline::init ( const std::vector< double > &  x, const std::vector< double > &  y  )

overridevirtual

Initialize from tabulated data (natural spline).

Parameters

x	Input: strictly increasing x-coordinates.
y	Input: y-values corresponding to x.

Reimplemented from AbstractSpline.

Definition at line 24 of file CubicSpline.cpp.

References computeCoefficients(), computeIntegrals(), and AbstractSpline::init().

Referenced by CubicSpline(), and TEST_F().

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integral()

double CubicSpline::integral ( size_t  i, double  dx  ) const

private

Calculate the integral from x_[i] to x_[i]+dx.

Parameters

i	Input: the interval index
dx	Input: the distance in the interval over which to calculate

Returns

Output: The integral.

Definition at line 131 of file CubicSpline.cpp.

References b_, c_, d_, and AbstractSpline::y_.

Referenced by computeIntegrals(), and evalIntegral().

Member Data Documentation

b_

std::vector<double> CubicSpline::b_

private

Definition at line 79 of file CubicSpline.h.

Referenced by computeCoefficients(), eval(), extrapolateLeft(), extrapolateRight(), and integral().

c_

std::vector<double> CubicSpline::c_

private

Definition at line 80 of file CubicSpline.h.

Referenced by computeCoefficients(), eval(), and integral().

d_

std::vector<double> CubicSpline::d_

private

Definition at line 81 of file CubicSpline.h.

Referenced by computeCoefficients(), eval(), and integral().

integrals_

std::vector<double> CubicSpline::integrals_

private

Definition at line 82 of file CubicSpline.h.

Referenced by computeIntegrals(), and evalIntegral().

x_

std::vector<double> AbstractSpline::x_ {}

protectedinherited

Definition at line 73 of file AbstractSpline.h.

Referenced by computeCoefficients(), LinearSpline::computeCoefficients(), computeIntegrals(), LinearSpline::computeIntegrals(), eval(), LinearSpline::eval(), evalIntegral(), LinearSpline::evalIntegral(), extrapolateLeft(), extrapolateRight(), AbstractSpline::findInterval(), AbstractSpline::init(), and LinearSpline::integral().

y_

std::vector<double> AbstractSpline::y_ {}

protectedinherited

Definition at line 74 of file AbstractSpline.h.

Referenced by computeCoefficients(), LinearSpline::computeCoefficients(), eval(), evalIntegral(), LinearSpline::evalIntegral(), extrapolateLeft(), extrapolateRight(), AbstractSpline::init(), and integral().

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

• CubicSpline.h
• CubicSpline.cpp