Integral of a one-dimensional function. More...
#include <ql/math/integrals/trapezoidintegral.hpp>
Inherits Integrator.
Public Member Functions | |
TrapezoidIntegral (Real accuracy, Size maxIterations) | |
Protected Member Functions | |
Real | integrate (const ext::function< Real(Real)> &f, Real a, Real b) const |
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.