Intg Class Template Reference

Abstract class template supports calculations of definite integrals for user-supplied functions. More...

#include <Intg.h>

Inherits Base.

Inherited by Romb, Simp, and Trap.

Inheritance diagram for Intg:

[legend]List of all members.

Public Types
enum	CTYPE { TRAPEZOID = 0, SIMPSON, ROMBERG, CTYPE_CNT }
	CTYPE_CNT
	LOOP_CURRENT = 0
	LOOP_MAXIMUM
	ROMBERG
	SIMPSON
	TRAPEZOID = 0
enum	VTYPE { LOOP_CURRENT = 0, LOOP_MAXIMUM, VTYPE_CNT }
	VTYPE_CNT
Public Member Functions
yType	eval (xType x1, xType x2) throw (IntgErr)
yType	evalIntegrand (xType x) const
int	getCount (enum Intg< xType, yType >::VTYPE vType) const
xType	getError (void) const
enum Intg< xType, yType >::CTYPE	getMethod (void) const
virtual bool	setCount (int nMaximum)
bool	setEpsilon (xType dEps)
Static Public Attributes
static const int	DEF_LOOP_MAX = 20
Protected Member Functions
	Intg (const Intg &ig)
	Intg (yType(&rFn)(xType), xType dEps)
virtual yType	intgMethod (void)=0 throw (IntgErr)
yType	refine (int ninc)
	~Intg (void)
Protected Attributes
enum Intg< xType, yType >::CTYPE	cTyp
xType	eps
int	nCount [VTYPE_CNT]

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Detailed Description

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

Abstract class template supports calculations of definite integrals for user-supplied functions.

Object instantiation of this class should be made only through classes which inherit this class.

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

See the cited References to obtain more information on the mathematical theory applied here.

Author

efgeorge

Date

2006/07/19 13:21:43

Revision

1.3

Examples:

example_Intg.txt.

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Member Enumeration Documentation

enum CTYPE

Enumeration indicates the class index of the integration method used.

Enumerator:

TRAPEZOID	index of a calc::Trap object using the trapezoid rule
SIMPSON	index of a calc::Simp object using Simpson's rule
ROMBERG	index of a calc::Romb object using Romberg's method
CTYPE_CNT	class type index count

enum VTYPE

Enumeration indicates the variable index of the object property.

Enumerator:

LOOP_CURRENT	index of the current loop count used in the previous integration evaluation
LOOP_MAXIMUM	index of the loop count limit used for the integration evaluations
VTYPE_CNT	variable type index count

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Constructor & Destructor Documentation

Intg	(	yType(&)(xType)	rFn,
		xType	dEps
	)			[protected]

Constructor initializes a function integration object.

Parameters:

	rFn	a reference to an integrand evaluation function
	dEps	required error of the calculated integral (|y| units)

Remarks:

• The specified integration tolerance dEps must be greater than zero.
• The specified function rFn(x) calculates an integrand value given an independent variable value.
• The function rFn(x) accepts a single independent value (x units).
• The function rFn(x) returns a single valued integrand value (y units) at the specified point x.
• Function declaration: yType fn(xType x);

Intg

(

const Intg< xType, yType > &

ig

)

[protected]

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

Parameters:

ig

a reference to a function integration object

~Intg

(

void

)

[protected]

Destructor is a place holder, no dynamic memory is allocated.

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Member Function Documentation

yType eval	(	xType	x1,
		xType	x2
	)			throw (IntgErr)

Function integrates the specified integrand function with the current integration method using decreasing step size until the specified error limit is achieved.

Parameters:

	x1	integral lower bound (x units)
	x2	integral upper bound (x units)

Returns:

the calculated value of the definite integral (x*y units)

Exceptions:

IntgErr

type of object thrown object initialization error (IntgErr::getIndex() = IntgErr::INIT) maximum number of loops exceeded, see Intg::getLoopMax() (IntgErr::getIndex() = IntgErr::LOOP)

yType evalIntegrand

(

xType

x

)

const

Function evaluates the user specified integrand function at the specified value x.

Parameters:

x

value at which to evaluate the integrand function (x units)

Returns:

calculated integrand function value (y units)

int getCount

(

enum Intg< xType, yType >::VTYPE

vType

)

const

Function returns loop information pertaining to algorithm iterations.

Parameters:

vType

variable index indentifying the type of data

Returns:

the loop count property of the object

Remarks:

• Valid loop values should be above 0.
• If the object is not initialized, -1 is returned.
• If the object does not have the variable identified by vType, -1 is returned.

xType getError

(

void

)

const

Function returns the current error criterion used in integration evaluation.

Returns:

error tolerance of the integration value (|y| units)

enum Intg< xType, yType >::CTYPE getMethod

(

void

)

const

Function returns an enumeration index indicating the calculation method used in the integration evaluation.

Returns:

an index of the enumeration Intg::CTYPE identifying the integration method of the integration object

Remarks:

The integration method index (Intg::CTYPE) can be one of the following values:

• TRAPEZOID (trapezoid rule - linear approximation)
• SIMPSON (Simpson's rule - quadratic approximation)
• ROMBERG (Romberg's method - extrapolated error approximation)

virtual yType intgMethod

(

void

)

throw (IntgErr) [protected, pure virtual]

Virtual function integrates the specified user function with a specific method.

Returns:

the calculated integration value using the class integration method (x*y units)

Exceptions:

IntgErr

type of object thrown maximum number of loops exceeded, see Intg::getLoopMax() (IntgErr::getIndex() = IntgErr::LOOP)

yType refine

(

int

ninc

)

[protected]

Function improves integration by adding 2^(ninc-1) integration evaluation steps using the trapezoid rule.

Parameters:

ninc

integration refinement index

Returns:

integral value with improved accuracy (x*y units)

bool setCount

(

int

nMaximum

)

[virtual]

Virtual function sets the current maximum loop count used in the integration evaluation.

Parameters:

nMaximum

the maximum loop count value

Returns:

status flag

• false (successful execution)
• true (execution error, parameter not set)

Remarks:

The loop count value nMaximum must be greater than zero.

Reimplemented in Romb.

bool setEpsilon

(

xType

dEps

)

Function sets the current error criterion used in integration evaluation.

Parameters:

dEps

error tolerance of the integration value (|y| units)

Returns:

status flag

• false (successful execution)
• true (execution error, parameter not set)

Remarks:

The tolerance value of dEps must be greater than zero.

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Member Data Documentation

enum Intg< xType, yType >::CTYPE cTyp [protected]

class type index

const int DEF_LOOP_MAX = 20 [static]

default maximum iteration loop count

xType eps [protected]

required error of integral (|y| units)

int nCount[VTYPE_CNT] [protected]

variable values of integration

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

• Intg.h
• Intg.cpp

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