mmc
Class Integral

java.lang.Object
  mmc.MathModel
      mmc.Integral

public class Integral
extends MathModel

This class provides routines for function integration using Romberg method. Include the function to be integrated in a class that implements the interface FunctionOfx (defined below). Methods contained here are based on the Numerical Recipes (W. H. Press et al.) with the following modifications:

• Algorithm of route choice in the interpolate method is different: it keeps the partial approximations centered on the target x by keeping two of the grid points closest to x in the middle as long as possible.
• Power of Substitution (POS) is any real number. If it is zero, no substitution is made. Otherwise the substitution is 1/x^POS if POS>0 or 1/(-x)^(-POS), if POS<0. If one of the limits of integration is zero or has opposite sign than that of POS, it is replaced with infinity. If both limits of integration are zero or have opposite sign than that of POS, integral is considered to have equal to each other (and to infinity) limits, and the returned value is zero.

It is possible to evaluate x(rand) such that the integral from xmin to x(rand) is a fraction rand of the original full integral from xmin to xmax. Set the ratio 0<rand<1 as the last argument of one of the open integration methods (integrateOpened or integrateWithSubstitution), and get x(rand) by the subsequent call to getUpperLimit. If rand<0, then -rand is assumed to be the absolute value of the portion of the original integral such that the integral from xmin to x(rand) is equal to this portion. Its sign is determined as the sign of the whole integral (or, rather, the N-1st approximation to its value). If rand is given, it is generally assumed that the function does not change sign on the integration interval. Otherwise, the resulting x(rand) is less predictable. In any case, an approximation to x(rand) is found during evaluation of the original integral, and then refined by the combination of the Newton-Raphson method and bisection.

 interface FunctionOfx{
     double function(double x);
 }
 

Field Summary

Fields inherited from class mmc.MathModel

computerPrecision

Constructor Summary

Integral()
initializes class with default settings

Integral(int romberg, int maxSteps, double precision)
initializes class - this is the main constructor

Method Summary

double	getUpperLimit() refines and returns the value of the upper limit x(rand)
double	integrateClosed(double min, double max, FunctionOfx function2use) finds integral for closed intervals
double	integrateOpened(double min, double max, FunctionOfx function2use) finds integral for opened intervals
double	integrateOpened(double min, double max, FunctionOfx function2use, double randomRatio) finds integral for opened intervals and computes the value of the x(rand)
double	integrateWithLog(double min, double max, FunctionOfx function2use) finds integral for opened intervals using log substitution
double	integrateWithLog(double min, double max, FunctionOfx function2use, double randomRatio) finds integral for opened intervals and computes the value of the x(rand)
double	integrateWithLogSubstitution(double min, double max, FunctionOfx function2use, double powerOfSubstitution) finds integral for opened intervals using substitution x -> 1/log(x)^(powerOfSubstitution)
double	integrateWithSubstitution(double min, double max, FunctionOfx function2use, double powerOfSubstitution) finds integral for opened intervals using substitution x -> 1/x^(powerOfSubstitution)
double	integrateWithSubstitution(double min, double max, FunctionOfx function2use, double powerOfSubstitution, double randomRatio) finds integral for opened intervals using substitution x -> 1/x^(powerOfSubstitution) and computes the value of the x(rand)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Integral

public Integral()

initializes class with default settings

Integral

public Integral(int romberg,
                int maxSteps,
                double precision)

initializes class - this is the main constructor

Method Detail

integrateClosed

public double integrateClosed(double min,
                              double max,
                              FunctionOfx function2use)

finds integral for closed intervals

integrateOpened

public double integrateOpened(double min,
                              double max,
                              FunctionOfx function2use)

finds integral for opened intervals

integrateOpened

public double integrateOpened(double min,
                              double max,
                              FunctionOfx function2use,
                              double randomRatio)

finds integral for opened intervals and computes the value of the x(rand)

integrateWithSubstitution

public double integrateWithSubstitution(double min,
                                        double max,
                                        FunctionOfx function2use,
                                        double powerOfSubstitution)

finds integral for opened intervals using substitution x -> 1/x^(powerOfSubstitution)

integrateWithSubstitution

public double integrateWithSubstitution(double min,
                                        double max,
                                        FunctionOfx function2use,
                                        double powerOfSubstitution,
                                        double randomRatio)

finds integral for opened intervals using substitution x -> 1/x^(powerOfSubstitution) and computes the value of the x(rand)

getUpperLimit

public double getUpperLimit()

refines and returns the value of the upper limit x(rand)

integrateWithLog

public double integrateWithLog(double min,
                               double max,
                               FunctionOfx function2use)

finds integral for opened intervals using log substitution

integrateWithLog

public double integrateWithLog(double min,
                               double max,
                               FunctionOfx function2use,
                               double randomRatio)

finds integral for opened intervals and computes the value of the x(rand)

integrateWithLogSubstitution

public double integrateWithLogSubstitution(double min,
                                           double max,
                                           FunctionOfx function2use,
                                           double powerOfSubstitution)

finds integral for opened intervals using substitution x -> 1/log(x)^(powerOfSubstitution)