continued_fraction< A, B > Class Template Reference

#include <continuedfraction.h>

Inheritance diagram for continued_fraction< A, B >:

List of all members.

Public Member Functions
	continued_fraction (A &coefA, B &coefB, unsigned int iterations=100, double relative_error=1.0e-15)
	~continued_fraction ()
double	evaluate (double x)

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Detailed Description

template<class A, class B>
class continued_fraction< A, B >

This class provides the means to evaluate continued fractions (1). To create a continued fraction, authors create an instance of continued_fraction and provide a and b coefficient functors.

For example, this is the continued fraction for the exponential function defined by (2):

double exponential_a(unsigned int n, double x) {
    if (n == 0) {
        return 1.0;
    } else if (n % 2 == 0) { // even
        return 2.0;
    } else { // odd
        return n;
    }
}

double exponential_b(unsigned int n, double x) {
    if (n % 2 == 0) { // even
        return x;
    } else { // odd
        return -x;
    }
}

num::continued_fraction<num::continued_fraction_coefficient, num::continued_fraction_coefficient>
    exponential(exponential_a, exponential_b);

double x = exponential.evaluate(2.0); // std::exp(2.0)
       x = exponential.evaluate(4.0); // std::exp(4.0)

References:

1. Eric W. Weisstein. "Continued Fraction." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ContinuedFraction.html
2. Exponential Function: Continued Fraction Representation. http://functions.wolfram.com/01.03.10.0001.01

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Constructor & Destructor Documentation

template<class A, class B>

continued_fraction< A, B >::continued_fraction	(	A &	coefA,
		B &	coefB,
		unsigned int	iterations = 100,
		double	relative_error = 1.0e-15
	)			[inline]

Create a continued fraction with the given coefficient functors.

Parameters:

	coefA	the a coefficient functor.
	coefB	the b coefficient functor.
	iterations	the maximum number of iterations.
	relative_error	the maximum allowable relative error.

template<class A, class B>

continued_fraction< A, B >::~continued_fraction

(

)

[inline]

Destructor.

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Member Function Documentation

template<class A, class B>

double continued_fraction< A, B >::evaluate

(

double

x

)

[inline]

Evaluate this continued fraction at the given value.

Parameters:

x

the point of evalutation.

Returns:

the value of this continued fraction evaluated at x.

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

• src/main/cpp/numerics4cpp/continuedfraction/continuedfraction.h

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