Numerical integration

Collaboration diagram for Numerical integration:

Classes
class	doubleFunction
class	Trapeze
class	Romberg

Functions
double	integrateNewtonCotes (double(*f)(double), double a, double b, int N)

Detailed Description

This code performs numeric integrations as described in the Numerical Recipes Book, in particular it implements the "trapezoidal" (Trapeze) and the Romberg integration. Both are designed for smoothly variant functions.

This module can also perform multidimensional integration.

Function Documentation

integrateNewtonCotes()

double integrateNewtonCotes	(	double(*)(double)	f,
		double	a,
		double	b,
		int	N
	)

Integrate a function using Newton-Cotes formula

Estimate the integral of a function between a and b using N points.

Definition at line 32 of file integration.cpp.

{
    if (N < 2 || N > 9)
        REPORT_ERROR(ERR_VALUE_INCORRECT, "integrateNewtonCotes: N must be greater than 1");
    double h = (b - a) / (N - 1);
    Matrix1D<double> fx(N);
    for (int i = 0; i < N; i++)
        fx(i) = (*f)(a + i * h);
    switch (N)
    {
    case 2:
        return h / 2*(fx(0) + fx(1));
    case 3:
        return h / 3*(fx(0) + 4*fx(1) + fx(2));
    case 4:
        return h*3.0 / 8.0*((fx(0) + fx(3)) + 3*(fx(1) + fx(2)));
    case 5:
        return h*2.0 / 45.0*(7*(fx(0) + fx(4)) + 32*(fx(1) + fx(3)) + 12*fx(2));
    case 6:
        return h*5.0 / 288.0*(19*(fx(0) + fx(5)) + 75*(fx(1) + fx(4)) + 50*(fx(2) + fx(3)));
    case 7:
        return h / 140.0*(41*(fx(0) + fx(6)) + 216*(fx(1) + fx(5)) + 27*(fx(2) + fx(4)) +
                          272*fx(3));
    case 8:
        return h*7.0 / 17280.0*(751*(fx(0) + fx(7)) + 3577*(fx(1) + fx(6)) + 1323*(fx(2) + fx(5)) +
                                2989*(fx(3) + fx(4)));
    case 9:
        return 4.0 / 14175.0*h*(989*(fx(0) + fx(8)) + 5888*(fx(1) + fx(7)) +
                                -928*(fx(2) + fx(6)) + 10496*(fx(3) + fx(5)) - 4540*fx(4));
    }
    REPORT_ERROR(ERR_ARG_INCORRECT,"Number of points is too high");
}