Integral of a one-dimensional function. More...

Inheritance diagram for SegmentIntegral:

Collaboration diagram for SegmentIntegral:

Public Member Functions
	SegmentIntegral (Size intervals)

Public Member Functions inherited from Integrator
	Integrator (Real absoluteAccuracy, Size maxEvaluations)

virtual	~Integrator ()=default

Real	operator() (const ext::function< Real(Real)> &f, Real a, Real b) const

void	setAbsoluteAccuracy (Real)

void	setMaxEvaluations (Size)

Real	absoluteAccuracy () const

Size	maxEvaluations () const

Real	absoluteError () const

Size	numberOfEvaluations () const

virtual bool	integrationSuccess () const

Protected Member Functions
Real	integrate (const ext::function< Real(Real)> &f, Real a, Real b) const override

Protected Member Functions inherited from Integrator
void	setAbsoluteError (Real error) const

void	setNumberOfEvaluations (Size evaluations) const

void	increaseNumberOfEvaluations (Size increase) const

Detailed Description

Integral of a one-dimensional function.

Given a number \( N \) of intervals, the integral of a function \( f \) between \( a \) and \( b \) is calculated by means of the trapezoid formula

\[ \int_{a}^{b} f \mathrm{d}x = \frac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + \dots + f(x_{N-1}) + \frac{1}{2} f(x_{N}) \]

where \( x_0 = a \), \( x_N = b \), and \( x_i = a+i \Delta x \) with \( \Delta x = (b-a)/N \).

Tests:: the correctness of the result is tested by checking it against known good values.

Definition at line 50 of file segmentintegral.hpp.

Constructor & Destructor Documentation

SegmentIntegral ( Size intervals )

explicit

Definition at line 24 of file segmentintegral.cpp.

overrideprotectedvirtual

Implements Integrator.

Definition at line 64 of file segmentintegral.hpp.

Here is the call graph for this function:

Size intervals_

private

Definition at line 57 of file segmentintegral.hpp.