Interp Class Template Reference

Class template generates interpolation data of known functions using Chebyshev polynomials. More...

#include <Cheb.h>

Inherits Cheb< xType, yType >.

Inheritance diagram for Interp:

[legend]List of all members.

Public Member Functions
	Interp (const Cheb< xType, yType > &ch)
	Interp (const Interp< xType, yType > &ch)
	Interp (const yType *arCn, xType x1, xType x2, int nCount)
	Interp (yType(&rFn)(xType), xType x1, xType x2, int nCount)
	Interp (yType(&rFn)(xType), xType x1, xType x2, xType dEps)
	~Interp (void)

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Detailed Description

template<typename xType, typename yType>
class calc::Interp< xType, yType >

Class template generates interpolation data of known functions using Chebyshev polynomials.

To develop an interpolation polynomial, a continuous single-valued function, over a specific domain and range, is passed to this object's constructor. In initialization, the user-supplied function is evaluated to determine interpolation coefficients of Chebyshev polynomials. These polynomials coefficients are stored, and approximate the user-supplied function. When this object is evaluated after instantiation, an approximation of a user-supplied function is made with no access to the user-supplied function.

The declaration typename <xType> specifies the form of independent variables used in interpolation calculations. The declaration typename <yType> specifies the form of solution variables used in interpolation calculations. In general, the <yType> variables should be the equal or superset of the <xType> variables.

Author

efgeorge

Date

2006/07/18 01:45:34

Revision

1.2

Examples:

example_Cheb.txt.

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Constructor & Destructor Documentation

Interp	(	yType(&)(xType)	rFn,
		xType	x1,
		xType	x2,
		xType	dEps
	)

Constructor initializes a Chebyshev polynomial interpolation object from the specified function rFn within the specified interval x1 to x2 and at the specified tolerance dEps.

Parameters:

	rFn	a reference to an evaluation function to be interpolated
	x1	interpolation lower bound (x units)
	x2	interpolation upper bound (x units)
	dEps	required absolute error of interpolation (y units)

Remarks:

• The interpolation bounds x1 and x2 cannot be equal.
• The specified function rFn(x) returns a value from which interpolation parameters are calculated given an independent variable value between x1 and x2.
• The function rFn(x) accepts a single independent value (x units).
• The function rFn(x) returns a single value at the specified point (y units).
• rFn(x) declaration: yType fn(xType x);
• The error parameter dEps must have a value greater than zero.
• The parameter dEps is in absolute units of the function return value (y units).

Interp	(	yType(&)(xType)	rFn,
		xType	x1,
		xType	x2,
		int	nCount
	)

Constructor initializes a Chebyshev polynomial interpolation object from the specified function rFn within the specified interval x1 to x2 with the specified coefficient count nCount.

Parameters:

	rFn	a reference to an evaluation function to be interpolated
	x1	interpolation lower bound (x units)
	x2	interpolation upper bound (x units)
	nCount	coefficient count of interpolation polynomial

Remarks:

• The interpolation bounds x1 and x2 cannot be equal.
• The specified function rFn(x) returns a value from which interpolation parameters are calculated given an independent variable value between x1 and x2.
• The function rFn(x) accepts a single independent value (x units).
• The function rFn(x) returns a single value at the specified point (y units).
• rFn(x) declaration: yType fn(xType x);
• The coefficient count nCount must have a value greater than or equal to Cheb::POINT_MIN.

Interp	(	const yType *	arCn,
		xType	x1,
		xType	x2,
		int	nCount
	)

Constructor initializes a Chebyshev polynomial interpolation object from the specified coefficient array arCn within the specified interval x1 to x2.

Parameters:

	arCn	a pointer to nCount Chebyshev polynomial coefficients (y units)
	x1	interpolation lower bound (x units)
	x2	interpolation upper bound (x units)
	nCount	coefficient count of the interpolation polynomial

Remarks:

• The interpolation bounds x1 and x2 cannot be equal.
• The coefficient count nCount must have a value greater than or equal to Cheb::POINT_MIN.

Interp

(

const Interp< xType, yType > &

ch

)

Copy constructor initializes a function interpolation object from the specified existing interpolation object.

Parameters:

ch

a reference to a function interpolation object

Remarks:

An information copy is made of the interpolation object.

Interp

(

const Cheb< xType, yType > &

ch

)

Copy constructor initializes a function interpolation object from the specified existing interpolation object.

Parameters:

ch

a reference to a function interpolation object

Remarks:

An information copy is made of the interpolation object.

~Interp

(

void

)

Destructor frees allocated memory.

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

• Cheb.h
• Interp.cpp

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