integrate.h File Reference

Utility functions for numerical integration of 1D functions. More...

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Typedefs
typedef enum integrationSchemes	integrationScheme
	Numerical integration methods.

Enumerations
enum	integrationSchemes {   RIEMANN_LEFT, RIEMANN_RIGHT, RIEMANN_CENTER, TRAPEZOIDAL,   SIMPSONS, SIMPSONS38, BOOLES }
	Numerical integration methods. More...

Functions
template<typename T , typename U >
void	cumulativeIntegral (T *x, T *y, U *cdf, int length, integrationScheme scheme)
	Performs a cumulative numerical integral over arrays of x and y values using the specificed integration method. More...
template<typename T >
double	computeRiemannLeft (T *x, T *y, int length)
	Performs a numerical integral using the left-centered Riemann numerical integration method. More...
template<typename T >
double	computeRiemannRight (T *x, T *y, int length)
	Performs a numerical integral using the right-centered Riemann numerical integration method. More...
template<typename T >
double	computeRiemannCenter (T *x, T *y, int length)
	Performs a numerical integral using the midpoint-centered Riemann numerical integration method. More...
template<typename T >
double	computeTrapezoidal (T *x, T *y, int length)
	Performs a numerical integral using the trapezoidal numerical integration method. More...
template<typename T >
double	computeSimpsons (T *x, T *y, int length)
	Performs a numerical integral using the Simpson's numerical integration method. More...
template<typename T >
double	computeSimpsons38 (T *x, T *y, int length)
	Performs a numerical integral using the Simpson's 3/8ths numerical integration method. More...
template<typename T >
double	computeBooles (T *x, T *y, int length)
	Performs a numerical integral using the Boole's numerical integration method. More...
template<typename T >
double	integrate (T *x, T *y, int length, integrationScheme scheme)
	Performs a 1D numerical integral over arrays of x and y values using the specified integration scheme. More...

Detailed Description

Utility functions for numerical integration of 1D functions.

This module provides a set of templated integration methods for both normal numerical integration and cumulative numerical integration. It implements the Riemann integration method with left-aligned, right-aligned and midpoint methods, the trapezoidal integration, and higher-order Simpsons, Simpson's 3/8ths and Boole's methods.

Author

William Boyd (wboyd.nosp@m.@mit.nosp@m..edu)

Date

February 9, 2012

Enumeration Type Documentation

enum integrationSchemes

Numerical integration methods.

Enumerator
RIEMANN_LEFT	Left-aligned Riemann integration method
RIEMANN_RIGHT	Right-aligned Riemann integration method
RIEMANN_CENTER	Midpoint Riemann integration method
TRAPEZOIDAL	Trapezoidal integration method
SIMPSONS	Simpson's integration method
SIMPSONS38	Simpson's 3/8ths integration method
BOOLES	Boole's integration method

Function Documentation

template<typename T >

double computeBooles	(	T *	x,
		T *	y,
		int	length
	)

Performs a numerical integral using the Boole's numerical integration method.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays

Returns

the integral value

template<typename T >

double computeRiemannCenter	(	T *	x,
		T *	y,
		int	length
	)

Performs a numerical integral using the midpoint-centered Riemann numerical integration method.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays

Returns

the integral value

template<typename T >

double computeRiemannLeft	(	T *	x,
		T *	y,
		int	length
	)

Performs a numerical integral using the left-centered Riemann numerical integration method.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays

Returns

the integral value

template<typename T >

double computeRiemannRight	(	T *	x,
		T *	y,
		int	length
	)

Performs a numerical integral using the right-centered Riemann numerical integration method.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays

Returns

the integral value

template<typename T >

double computeSimpsons	(	T *	x,
		T *	y,
		int	length
	)

Performs a numerical integral using the Simpson's numerical integration method.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays

Returns

the integral value

template<typename T >

double computeSimpsons38	(	T *	x,
		T *	y,
		int	length
	)

Performs a numerical integral using the Simpson's 3/8ths numerical integration method.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays

Returns

the integral value

template<typename T >

double computeTrapezoidal	(	T *	x,
		T *	y,
		int	length
	)

Performs a numerical integral using the trapezoidal numerical integration method.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays

Returns

the integral value

template<typename T , typename U >

void cumulativeIntegral	(	T *	x,
		T *	y,
		U *	cdf,
		int	length,
		integrationScheme	scheme
	)

Performs a cumulative numerical integral over arrays of x and y values using the specificed integration method.

Parameters

x	the the x values
y	the y values
cdf	the array of cdf values at each value of x and y
length	the length of the x and y arrays
scheme	the integration scheme

template<typename T >

double integrate	(	T *	x,
		T *	y,
		int	length,
		integrationScheme	scheme
	)

Performs a 1D numerical integral over arrays of x and y values using the specified integration scheme.

Parameters

x	the the x values
y	the y values
length	the length of the x and y arrays
scheme	integration scheme

Returns

the integral value