Java tutorial
/* * To change this license header, choose License Headers in Project Properties. * To change this template file, choose Tools | Templates * and open the template in the editor. */ package uk.ac.leeds.ccg.andyt.projects.fluvialglacial; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.analysis.UnivariateRealFunction; import org.apache.commons.math.FunctionEvaluationException; import org.apache.commons.math.exception.util.LocalizedFormats; /** * Implements the representation of a real polynomial function in * Newton Form. For reference, see <b>Elementary Numerical Analysis</b>, * ISBN 0070124477, chapter 2. * <p> * The formula of polynomial in Newton form is * p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... + * a[n](x-c[0])(x-c[1])...(x-c[n-1]) * Note that the length of a[] is one more than the length of c[]</p> * * @version $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 fvr. 2011) $ * @since 1.2 */ public class PolynomialFunctionNewtonForm implements UnivariateRealFunction { /** * The coefficients of the polynomial, ordered by degree -- i.e. * coefficients[0] is the constant term and coefficients[n] is the * coefficient of x^n where n is the degree of the polynomial. */ private double coefficients[]; /** * Centers of the Newton polynomial. */ private final double c[]; /** * When all c[i] = 0, a[] becomes normal polynomial coefficients, * i.e. a[i] = coefficients[i]. */ private final double a[]; /** * Whether the polynomial coefficients are available. */ private boolean coefficientsComputed; /** * Construct a Newton polynomial with the given a[] and c[]. The order of * centers are important in that if c[] shuffle, then values of a[] would * completely change, not just a permutation of old a[]. * <p> * The constructor makes copy of the input arrays and assigns them.</p> * * @param a the coefficients in Newton form formula * @param c the centers * @throws IllegalArgumentException if input arrays are not valid */ public PolynomialFunctionNewtonForm(double a[], double c[]) throws IllegalArgumentException { verifyInputArray(a, c); this.a = new double[a.length]; this.c = new double[c.length]; System.arraycopy(a, 0, this.a, 0, a.length); System.arraycopy(c, 0, this.c, 0, c.length); coefficientsComputed = false; } /** * Calculate the function value at the given point. * * @param z the point at which the function value is to be computed * @return the function value * @throws FunctionEvaluationException if a runtime error occurs * @see UnivariateRealFunction#value(double) */ public double value(double z) throws FunctionEvaluationException { return evaluate(a, c, z); } /** * Returns the degree of the polynomial. * * @return the degree of the polynomial */ public int degree() { return c.length; } /** * Returns a copy of coefficients in Newton form formula. * <p> * Changes made to the returned copy will not affect the polynomial.</p> * * @return a fresh copy of coefficients in Newton form formula */ public double[] getNewtonCoefficients() { double[] out = new double[a.length]; System.arraycopy(a, 0, out, 0, a.length); return out; } /** * Returns a copy of the centers array. * <p> * Changes made to the returned copy will not affect the polynomial.</p> * * @return a fresh copy of the centers array */ public double[] getCenters() { double[] out = new double[c.length]; System.arraycopy(c, 0, out, 0, c.length); return out; } /** * Returns a copy of the coefficients array. * <p> * Changes made to the returned copy will not affect the polynomial.</p> * * @return a fresh copy of the coefficients array */ public double[] getCoefficients() { if (!coefficientsComputed) { computeCoefficients(); } double[] out = new double[coefficients.length]; System.arraycopy(coefficients, 0, out, 0, coefficients.length); return out; } /** * Evaluate the Newton polynomial using nested multiplication. It is * also called <a href="http://mathworld.wolfram.com/HornersRule.html"> * Horner's Rule</a> and takes O(N) time. * * @param a the coefficients in Newton form formula * @param c the centers * @param z the point at which the function value is to be computed * @return the function value * @throws FunctionEvaluationException if a runtime error occurs * @throws IllegalArgumentException if inputs are not valid */ public static double evaluate(double a[], double c[], double z) throws FunctionEvaluationException, IllegalArgumentException { verifyInputArray(a, c); int n = c.length; double value = a[n]; for (int i = n - 1; i >= 0; i--) { value = a[i] + (z - c[i]) * value; } return value; } /** * Calculate the normal polynomial coefficients given the Newton form. * It also uses nested multiplication but takes O(N^2) time. */ protected void computeCoefficients() { final int n = degree(); coefficients = new double[n + 1]; for (int i = 0; i <= n; i++) { coefficients[i] = 0.0; } coefficients[0] = a[n]; for (int i = n - 1; i >= 0; i--) { for (int j = n - i; j > 0; j--) { coefficients[j] = coefficients[j - 1] - c[i] * coefficients[j]; } coefficients[0] = a[i] - c[i] * coefficients[0]; } coefficientsComputed = true; } /** * Verifies that the input arrays are valid. * <p> * The centers must be distinct for interpolation purposes, but not * for general use. Thus it is not verified here.</p> * * @param a the coefficients in Newton form formula * @param c the centers * @throws IllegalArgumentException if not valid * @see org.apache.commons.math.analysis.interpolation.DividedDifferenceInterpolator#computeDividedDifference(double[], * double[]) */ protected static void verifyInputArray(double a[], double c[]) throws IllegalArgumentException { if (a.length < 1 || c.length < 1) { throw MathRuntimeException .createIllegalArgumentException(LocalizedFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY); } if (a.length != c.length + 1) { throw MathRuntimeException.createIllegalArgumentException( LocalizedFormats.ARRAY_SIZES_SHOULD_HAVE_DIFFERENCE_1, a.length, c.length); } } }