Romberg Class Reference

#include <integration.h>

Inheritance diagram for Romberg:

Collaboration diagram for Romberg:

Public Member Functions
virtual double	operator() ()
double	operator() (double min, double max, double precision=1.0e-7)
	Romberg (doubleFunction &f, double &Var, double min, double max, double precision=1.0e-7)
double	midpnt (int n)
Public Member Functions inherited from doubleFunction
virtual	~doubleFunction ()

Detailed Description

More accurate integration.

More accurate integration than Trapeze with smaller truncation error (interpolation is made with polynomials)

Example of use:

1) Define function to NumericalIntegration as class:

// Actual function to be NumericalIntegration
class Func1: public doubleFunction
{
// This should be in testinteg
public:
    double x;
    double cte1, cte2;
    // Overloads pure virtual
    virtual double operator()()
    {
        return sqrt(1 + cte1 * cte1 * sin(cte2 * x) * sin(cte2 * x));
    }
};

2) In the main code

#include <data/integration.h>

Func1 cosine;   // cosine surface
cosine.cte1 = fabs(cteA * cteA * cteB * cteB * vx * vx);
cosine.cte2 = fabs(cteB * vx);

Romberg Rom(cosine, cosine.x, inte_low, inte_high);
integralt = Rom();

Definition at line 189 of file integration.h.

Constructor & Destructor Documentation

Romberg()

Romberg::Romberg ( doubleFunction &  f, double &  Var, double  min, double  max, double  precision = 1.0e-7  )

inline

Constructor.

Parameter: f Pointer to function to be integrated Parameter: var Integration variable Parameter: min Integration lower limit Parameter: max Integration upper limit Parameter: precision Maximum error allowed Parameter: max_iter Maximum number of iterations

Definition at line 226 of file integration.h.

                                       : func(f), x(Var)
    {
        s = 0.0;
        a = min;
        b = max;
        EPS = precision;
    }

Member Function Documentation

midpnt()

double Romberg::midpnt

(

int

n

)

Workhorse that doublely does the integral

Definition at line 151 of file integration.cpp.

{   //adapted from midpoint
    double tnm;
    double sum;
    double del;
    double ddel;
    int it;
    int j;
    if (n == 1)
    {
        x = 0.5 * (a + b);     //changed; set x
        return (s = (b - a) * func());  //changed; evaluate func
    }
    else
    {
        for (it = 1, j = 1;j < n - 1;j++)
            it *= 3;
        tnm = it;
        del = (b - a) / (3.0 * tnm);
        ddel = del + del;
        x = a + 0.5 * del;
        sum = 0.0;
        for (j = 1;j <= it;j++)
        {
            sum += func();   //changed; evaluate func
            x += ddel;    //changed; set x
            sum += func();   //changed; evaluate func
            x += del;    //changed; set x
        }
        s = (s + (b - a) * sum / tnm) / 3.0;
        return s;
    }
}

operator()() [1/2]

double Romberg::operator() ( )

virtual

Implements doubleFunction.

Definition at line 125 of file integration.cpp.

{  //adapted from qromb
    int j;
    double ss;
    double dss;
    std::array<double, JMAXP+2> h;
    std::array<double, JMAXP+2> s_internal;
    h[1] = 1.0;
    for (j = 1;j <= JMAXP;j++)
    {
        s_internal[j] = midpnt(j); //changed; midpnt is integrating
        if (j >= K)
        {     //function
            polint(&h[j-K], &s_internal[j-K], K, 0.0, ss, dss);
            if (fabs(dss) <= EPS*fabs(ss))
                return ss;
        }
        s_internal[j+1] = s_internal[j];
        h[j+1] = h[j] / 9.0;
    }
    REPORT_ERROR(ERR_NUMERICAL,"Too many steps in routine Romberg");
}

operator()() [2/2]

double Romberg::operator() ( double  min, double  max, double  precision = 1.0e-7  )

inline

With parameters.

Parameter: min Integration lower limit Parameter: max Integration upper limit Parameter: precision Maximum error allowed Parameter: max_iter Maximum number of iterations

Definition at line 209 of file integration.h.

    {
        a = min;
        b = max;
        EPS = precision;
        return (*this)();
    }

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The documentation for this class was generated from the following files:

• xmipp/libraries/data/integration.h
• xmipp/libraries/data/integration.cpp