SSpline< T > Class Template Reference

Public Types

• enum { isVectorizable = 0 }
• typedef T value_type

Public Member Functions

• SSpline (const MArray< T, 1 > &x, const MArray< T, 1 > &y, const MArray< T, 1 > &sigma, const T mu)
• SSpline (const MArray< T, 1 > &x, const MArray< T, 1 > &y, const T mu)
• virtual ~SSpline ()
• T eval (const T x) const
• T operator() (const T x) const
• T eval (const T x, T *dfdx1, T *dfdx2) const

Protected Member Functions

• void calculateCoefficients (const MArray< T, 1 > &x, const MArray< T, 1 > &y, const MArray< T, 1 > &sigma, const T mu)
• void quincunx (MArray< T, 1 > &u, MArray< T, 1 > &v, MArray< T, 1 > &w, MArray< T, 1 > &q)
• int find_index (const MArray< T, 1 > &X, const T x) const

Protected Attributes

• MArray< T, 1 > X
• MArray< T, 1 > A
• MArray< T, 1 > B
• MArray< T, 1 > C
• MArray< T, 1 > D

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Detailed Description

template<typename T>
class SSpline< T >

Approximating cubic spline

Compute an approximating cubic spline to the points {x,y}. The boundary conditions are fixed to zero second derivative. The x values must be strictly monotonically increasing. The degree of smoothing is controlled by the parameter mu, with 0 <= mu <= 1. mu = 0 implies no smoothing (the spline is interpolating), mu = 1 implies maximal smoothing (the spline approaches a linear fit to the data).

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Member Typedef Documentation

template<typename T >

typedef T SSpline< T >::value_type

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Member Enumeration Documentation

template<typename T >

anonymous enum

Enumerator:

isVectorizable

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Constructor & Destructor Documentation

template<typename T >

SSpline< T >::SSpline	(	const MArray< T, 1 > &	x,
		const MArray< T, 1 > &	y,
		const MArray< T, 1 > &	sigma,
		const T	mu
	)			[inline]

Construct an approximating spline to the data {x,y+-sigma} with smoothing parameter mu.

Sigma are the uncertainties in the y data. 0 <= Mu <= 1 is the smoothing paremeter, mu=0 no smoothing, mu=1 maximal smoothing.

References SSpline< T >::calculateCoefficients().

template<typename T >

SSpline< T >::SSpline	(	const MArray< T, 1 > &	x,
		const MArray< T, 1 > &	y,
		const T	mu
	)			[inline]

Construct an approximating spline to the data {x,y} with smoothing parameter mu.

All data are assumed to have the same weights. 0 <= Mu <= 1 is the smoothing paremeter, mu=0 no smoothing, mu=1 maximal smoothing.

References SSpline< T >::calculateCoefficients().

template<typename T >

virtual SSpline< T >::~SSpline

(

)

[inline, virtual]

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Member Function Documentation

template<typename T >

T SSpline< T >::eval

(

const T

x

)

const [inline]

evaluate the spline at position x

References SSpline< T >::A, SSpline< T >::B, SSpline< T >::C, SSpline< T >::D, SSpline< T >::find_index(), and SSpline< T >::X.

Referenced by SSpline< T >::operator()().

template<typename T >

T SSpline< T >::operator()

(

const T

x

)

const [inline]

evaluate the spline at position x

References SSpline< T >::eval().

template<typename T >

T SSpline< T >::eval	(	const T	x,
		T *	dfdx1,
		T *	dfdx2
	)			const [inline]

evaluate the spline at position x, and return the first and second derivatives in dfdx1 and dfdx2, respectively. either may be NULL in which case the derivative is not evaluated.

References SSpline< T >::A, SSpline< T >::B, SSpline< T >::C, SSpline< T >::D, SSpline< T >::find_index(), and SSpline< T >::X.

template<typename T >

void SSpline< T >::calculateCoefficients	(	const MArray< T, 1 > &	x,
		const MArray< T, 1 > &	y,
		const MArray< T, 1 > &	sigma,
		const T	mu
	)			[inline, protected]

References SSpline< T >::A, SSpline< T >::B, SSpline< T >::C, SSpline< T >::D, SSpline< T >::quincunx(), v, and SSpline< T >::X.

Referenced by SSpline< T >::SSpline().

template<typename T >

void SSpline< T >::quincunx	(	MArray< T, 1 > &	u,
		MArray< T, 1 > &	v,
		MArray< T, 1 > &	w,
		MArray< T, 1 > &	q
	)			[inline, protected]

References v.

Referenced by SSpline< T >::calculateCoefficients().

template<typename T >

int SSpline< T >::find_index	(	const MArray< T, 1 > &	X,
		const T	x
	)			const [inline, protected]

Given an MArray X, and given a value x, returns a value j such that x is between X(j) and X(j+1). X must be monotonically increasing. j=minIndex(X) or j=maxIndex(X)-1 is returned if x is out of range.

This routine uses bisection and scales as O(log2 N)

References SSpline< T >::X.

Referenced by SSpline< T >::eval().

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Field Documentation

template<typename T >

MArray<T,1> SSpline< T >::X [protected]

Referenced by SSpline< T >::calculateCoefficients(), SSpline< T >::eval(), and SSpline< T >::find_index().

template<typename T >

MArray<T,1> SSpline< T >::A [protected]

Referenced by SSpline< T >::calculateCoefficients(), and SSpline< T >::eval().

template<typename T >

MArray<T,1> SSpline< T >::B [protected]

Referenced by SSpline< T >::calculateCoefficients(), and SSpline< T >::eval().

template<typename T >

MArray<T,1> SSpline< T >::C [protected]

Referenced by SSpline< T >::calculateCoefficients(), and SSpline< T >::eval().

template<typename T >

MArray<T,1> SSpline< T >::D [protected]

Referenced by SSpline< T >::calculateCoefficients(), and SSpline< T >::eval().