TrapezoidIntegral Class Reference

#include <ql/Math/trapezoidintegral.hpp>

Inheritance diagram for TrapezoidIntegral:

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.

Public Types

enum Method { Default, MidPoint }

Public Member Functions

TrapezoidIntegral (double accuracy, Method method=Default, Size maxIterations=Null< int >())

template<class F> double operator() (const F &f, double a, double b) const

double accuracy () const

double & accuracy ()

Method method () const

Method & method ()

Size maxIterations () const

Size & maxIterations ()

Protected Member Functions

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

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

Protected Attributes

double accuracy_

Method method_

Size maxIterations_

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TrapezoidIntegral Class Reference

Detailed Description

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes