6.1 Overview

The org.apache.commons.math.util package collects a group of array utilities, value transformers, and numerical routines used by implementation classes in commons-math.

6.2 Double array utilities

To maintain statistics based on a "rolling" window of values, a resizable array implementation was developed and is provided for reuse in the util package. The core functionality provided is described in the documentation for the interface, org.apache.commons.math.util.DoubleArray. This interface adds one method, addElementRolling(double) to basic list accessors. The addElementRolling method adds an element (the actual parameter) to the end of the list and removes the first element in the list.

The org.apache.commons.math.util.ResizableDoubleArray class provides a configurable, array-backed implementation of the DoubleArray interface. When addElementRolling is invoked, the underlying array is expanded if necessary, the new element is added to the end of the array and the "usable window" of the array is moved forward, so that the first element is effectively discarded, what was the second becomes the first, and so on. To efficiently manage storage, two maintenance operations need to be periodically performed -- orphaned elements at the beginning of the array need to be reclaimed and space for new elements at the end needs to be created. Both of these operations are handled automatically, with frequency / effect driven by the configuration properties expansionMode, expansionFactor and contractionCriteria. See ResizableDoubleArray for details.

6.3 Continued Fractions

The org.apache.commons.math.util.ContinuedFraction class provides a generic way to create and evaluate continued fractions. The easiest way to create a continued fraction is to subclass ContinuedFraction and override the getA and getB methods which return the continued fraction terms. The precise definition of these terms is explained in Continued Fraction, equation (1) from MathWorld.

As an example, the constant Pi could be computed using the continued fraction defined at http://functions.wolfram.com/Constants/Pi/10/0002/ . The following anonymous class provides the implementation:

ContinuedFraction c = new ContinuedFraction() {
    public double getA(int n, double x) {
        switch(n) {
            case 0: return 3.0;
            default: return 6.0;
        }
    }
    
    public double getB(int n, double x) {
        double y = (2.0 * n) - 1.0;
        return y * y;
    }
}

Then, to evalute Pi, simply call any of the evalute methods (Note, the point of evalution in this example is meaningless since Pi is a constant).

For a more practical use of continued fractions, consider the exponential function with the continued fraction definition of http://functions.wolfram.com/ElementaryFunctions/Exp/10/ . The following anonymous class provides its implementation:

ContinuedFraction c = new ContinuedFraction() {
    public double getA(int n, double x) {
        if (n % 2 == 0) {
            switch(n) {
                case 0: return 1.0;
                default: return 2.0;
            }
        } else {
            return n;
        }
    }
    
    public double getB(int n, double x) {
        if (n % 2 == 0) {
            return -x;
        } else {
            return x;
        }
    }
}

Then, to evalute e^x for any value x, simply call any of the evalute methods.

6.4 binomial coefficients, factorials and other common math functions

A collection of reusable math functions is provided in the MathUtils utility class. MathUtils currently includes methods to compute the following:

• Binomial coeffiecients -- "n choose k" available as an (exact) long value, binomialCoefficient(int, int) for small n, k; as a double, binomialCoefficientDouble(int, int) for larger values; and in a "super-sized" version, binomialCoefficientLog(int, int) that returns the natural logarithm of the value.
• Factorials -- like binomial coefficients, these are available as exact long values, factorial(int); doubles, factorialDouble(int); or logs, factorialLog(int).
• Hyperbolic sine and cosine functions -- cosh(double), sinh(double)
• sign (+1 if argument > 0, 0 if x = 0, and -1 if x < 0) and indicator (+1.0 if argument >= 0 and -1.0 if argument < 0) functions for variables of all primitive numeric types.
• a hash function, hash(double), returning a long-valued hash code for a double value.