uk.ac.starlink.dpac.math

Class Integral

java.lang.Object

uk.ac.starlink.dpac.math.Integral

public class Integral
extends Object

Performs indefinite numerical integration using an adaptive Simpson's rule. An instance of this class represents the definite integral over a given interval, but it provides methods that permit adaptive integration and the extraction of (a numerical form) of the antiderivative function.

Since:

15 Mar 2018

Author:

Mark Taylor

Constructor Summary

Constructors

Constructor and Description
Integral(Function f, double lo, double hi) Constructs an integral with given bounds.
Integral(Function f, double lo, double hi, double flo, double fhi) Constructs an integral with given bounds and supplied function evaluations.
Integral(Function f, Integral[] subs) Constructs an integral with a number of sub-integrals covering the interval of interest.

Method Summary

Modifier and Type	Method and Description
int	count() Returns the number of nodes whose recursive data provides the output of this integral function.
void	fill(double tol) Recursively populates the child nodes of this integral so as to achieve a given tolerance in calculation accuracy.
static NumericFunction	integrate(Function f, double[] points, double tol) Adaptively integrates a given function with the calculation broken up into sub-intervals at supplied points.
int	store(double[] x, double[] y, int index) Flattens the recursive information contained by this integral into a pair of arrays represting (x,y) samples giving the antiderivative function.

Methods inherited from class java.lang.Object

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

Constructor Detail

Integral

public Integral(Function f,
                double lo,
                double hi,
                double flo,
                double fhi)

Constructs an integral with given bounds and supplied function evaluations.

Parameters:

f - function to integrate

lo - lower bound of integration interval

hi - upper bound of integration interval

flo - function evaluattion at lo

fhi - function evaluattion at hi

Integral

public Integral(Function f,
                double lo,
                double hi)

Constructs an integral with given bounds.

Parameters:

f - function to integrate

lo - lower bound of integration interval

hi - upper bound of integration interval

Integral

public Integral(Function f,
                Integral[] subs)

Constructs an integral with a number of sub-integrals covering the interval of interest.

Parameters:

f - function to integrate

subs - contiguous sub-intervals; it is the responsibility of the caller to populate these with their own recursive sub-intervals as required

Method Detail

fill

public void fill(double tol)

Recursively populates the child nodes of this integral so as to achieve a given tolerance in calculation accuracy.

Parameters:

tol - tolerance

count

public int count()

Returns the number of nodes whose recursive data provides the output of this integral function.

store

public int store(double[] x,
                 double[] y,
                 int index)

Flattens the recursive information contained by this integral into a pair of arrays represting (x,y) samples giving the antiderivative function.

Parameters:

x - array to populate with X values

y - array to populate with Y (integrated) values

index - index of the x and y arrays from which the results should be inserted

Returns:

number of samples inserted

integrate

public static NumericFunction integrate(Function f,
                                        double[] points,
                                        double tol)

Adaptively integrates a given function with the calculation broken up into sub-intervals at supplied points. The result will be aggregated from sub-integrals with boundaries at each of the X points supplied, and further broken up within each such sub-region as the adaptive algorithm requires to reach the supplied tolerance.

Parameters:

f - function to integrate

points - ordered list of samples on X axis at which evaluations will be forced

tol - tolerance parameter controlling recursion

Returns:

numeric function giving integral of f over the range given by the first and last elements of points