power_series< Term > Class Template Reference

#include <powerseries.h>

Inheritance diagram for power_series< Term >:

List of all members.

Public Member Functions
	power_series (Term &t, unsigned int first=0, unsigned int iterations=100, double relative_error=1.0e-13)
	~power_series ()
double	evaluate (double x)

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Detailed Description

template<class Term>
class power_series< Term >

This class provides the means to evaluate infinite power series. To create a power series, authors create an instance of power_series and provide a term functor.

For example, this is the power series for the exponential function defined by (2):

double factorial(unsigned int n) {
    double p = 1.0;
    for(int i = n; i > 0; --i) {
        p *= i;
    }
    return p;
}

double exponential_term(unsigned int n) {
    return 1.0 / factorial(n);
}

num::power_series<num::power_series_term> exponential(exponential_term);
double x = exponential.evaluate(2.0); // std::exp(2.0)
       x = exponential.evaluate(4.0); // std::exp(4.0)

References:

1. Eric W. Weisstein. "Power Series." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PowerSeries.html
2. Exponential Function: Series Representation. http://functions.wolfram.com/01.03.06.0002.01

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Constructor & Destructor Documentation

template<class Term>

power_series< Term >::power_series	(	Term &	t,
		unsigned int	first = 0,
		unsigned int	iterations = 100,
		double	relative_error = 1.0e-13
	)			[inline]

Create a series with the given term functor.

Parameters:

	t	the term functor.
	first	the index of the first series term.
	iterations	the maximum number of iterations.
	relative_error	the maximum allowable relative error.

template<class Term>

power_series< Term >::~power_series

(

)

[inline]

Destructor.

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Member Function Documentation

template<class Term>

double power_series< Term >::evaluate

(

double

x

)

[inline]

Evaluate this series at the given value.

Parameters:

x

the point of evalutation.

Returns:

the value of this series evaluated at x.

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

• src/main/cpp/numerics4cpp/series/powerseries.h

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