TrapezoidIntegral Class Reference

#include <ql/Math/trapezoidintegral.hpp>

Inheritance diagram for TrapezoidIntegral:

Inheritance graph
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List of all members.

Detailed Description

Integral of a one-dimensional function.

Given a target accuracy $ \epsilon $ , 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 $ . The number $ N $ of intervals is repeatedly increased until the target accuracy is reached.

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


Public Types

enum  Method { Default, MidPoint }

Public Member Functions

 TrapezoidIntegral (Real accuracy, Method method=Default, Size maxIterations=Null< Size >())
template<class F>
Real operator() (const F &f, Real a, Real b) const
Real accuracy () const
Realaccuracy ()
Method method () const
Method & method ()
Size maxIterations () const
SizemaxIterations ()

Protected Member Functions

template<class F>
Real defaultIteration (const F &f, Real a, Real b, Real I, Size N) const
template<class F>
Real midPointIteration (const F &f, Real a, Real b, Real I, Size N) const

Protected Attributes

Real accuracy_
Method method_
Size maxIterations_


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