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/* * Copyright 2003-2004 The Apache Software Foundation. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math.analysis; import java.io.Serializable; import java.util.Arrays; import org.apache.commons.math.FunctionEvaluationException; /** * Represents a polynomial spline function. * <p> * A <strong>polynomial spline function</strong> consists of a set of * <i>interpolating polynomials</i> and an ascending array of domain * <i>knot points</i>, determining the intervals over which the spline function * is defined by the constituent polynomials. The polynomials are assumed to * have been computed to match the values of another function at the knot * points. The value consistency constraints are not currently enforced by * <code>PolynomialSplineFunction</code> itself, but are assumed to hold among * the polynomials and knot points passed to the constructor. * <p> * N.B.: The polynomials in the <code>polynomials</code> property must be * centered on the knot points to compute the spline function values. See below. * <p> * The domain of the polynomial spline function is * <code>[smallest knot, largest knot)</code>. Attempts to evaluate the * function at values outside of this range generate IllegalArgumentExceptions. * <p> * The value of the polynomial spline function for an argument <code>x</code> * is computed as follows: * <ol> * <li>The knot array is searched to find the segment to which <code>x</code> * belongs. If <code>x</code> is less than the smallest knot point or greater * than or equal to the largest one, an <code>IllegalArgumentException</code> * is thrown.</li> * <li> Let <code>j</code> be the index of the largest knot point that is less * than or equal to <code>x</code>. The value returned is <br> * <code>polynomials[j](x - knot[j])</code></li></ol> * * @version $Revision: 1.9 $ $Date: 2004/07/22 02:34:25 $ */ public class PolynomialSplineFunction implements UnivariateRealFunction, Serializable { /** Serializable version identifier */ static final long serialVersionUID = 7011031166416885789L; /** Spline segment interval delimiters (knots). Size is n+1 for n segments. */ private double knots[]; /** * The polynomial functions that make up the spline. The first element * determines the value of the spline over the first subinterval, the * second over the second, etc. Spline function values are determined by * evaluating these functions at <code>(x - knot[i])</code> where i is the * knot segment to which x belongs. */ private PolynomialFunction polynomials[] = null; /** * Number of spline segments = number of polynomials * = number of partition points - 1 */ private int n = 0; /** * Construct a polynomial spline function with the given segment delimiters * and interpolating polynomials. * <p> * The constructor copies both arrays and assigns the copies to the knots * and polynomials properties, respectively. * * @param knots spline segment interval delimiters * @param polynomials polynomial functions that make up the spline * @throws NullPointerException if either of the input arrays is null * @throws IllegalArgumentException if knots has length less than 2, * <code>polynomials.length != knots.length - 1 </code>, or the knots array * is not strictly increasing. * */ public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[]) { if (knots.length < 2) { throw new IllegalArgumentException( "Not enough knot values -- spline partition must have at least 2 points."); } if (knots.length - 1 != polynomials.length) { throw new IllegalArgumentException( "Number of polynomial interpolants must match the number of segments."); } if (!isStrictlyIncreasing(knots)) { throw new IllegalArgumentException("Knot values must be strictly increasing."); } this.n = knots.length - 1; this.knots = new double[n + 1]; System.arraycopy(knots, 0, this.knots, 0, n + 1); this.polynomials = new PolynomialFunction[n]; System.arraycopy(polynomials, 0, this.polynomials, 0, n); } /** * Compute the value for the function. * <p> * Throws FunctionEvaluationException if v is outside of the domain of the * function. The domain is [smallest knot, largest knot). * <p> * See {@link PolynomialSplineFunction} for details on the algorithm for * computing the value of the function. * * @param v the point for which the function value should be computed * @return the value * @throws FunctionEvaluationException if v is outside of the domain of * of the spline function (less than the smallest knot point or greater * than or equal to the largest knot point) */ public double value(double v) throws FunctionEvaluationException { if (v < knots[0] || v >= knots[n]) { throw new FunctionEvaluationException(v, "Argument outside domain"); } int i = Arrays.binarySearch(knots, v); if (i < 0) { i = -i - 2; } return polynomials[i].value(v - knots[i]); } /** * Returns the derivative of the polynomial spline function as a UnivariateRealFunction * @return the derivative function */ public UnivariateRealFunction derivative() { return polynomialSplineDerivative(); } /** * Returns the derivative of the polynomial spline function as a PolynomialSplineFunction * * @return the derivative function */ public PolynomialSplineFunction polynomialSplineDerivative() { PolynomialFunction derivativePolynomials[] = new PolynomialFunction[n]; for (int i = 0; i < n; i++) { derivativePolynomials[i] = polynomials[i].polynomialDerivative(); } return new PolynomialSplineFunction(knots, derivativePolynomials); } /** * Returns the number of spline segments = the number of polynomials * = the number of knot points - 1. * * @return the number of spline segments */ public int getN() { return n; } /** * Returns a copy of the interpolating polynomials array. * <p> * Returns a fresh copy of the array. Changes made to the copy will * not affect the polynomials property. * * @return the interpolating polynomials */ public PolynomialFunction[] getPolynomials() { PolynomialFunction p[] = new PolynomialFunction[n]; System.arraycopy(polynomials, 0, p, 0, n); return p; } /** * Returns an array copy of the knot points. * <p> * Returns a fresh copy of the array. Changes made to the copy * will not affect the knots property. * * @return the knot points */ public double[] getKnots() { double out[] = new double[n + 1]; System.arraycopy(knots, 0, out, 0, n + 1); return out; } /** * Determines if the given array is ordered in a strictly increasing * fashion. * * @param x the array to examine. * @return <code>true</code> if the elements in <code>x</code> are ordered * in a stricly increasing manner. <code>false</code>, otherwise. */ private static boolean isStrictlyIncreasing(double[] x) { for (int i = 1; i < x.length; ++i) { if (x[i - 1] >= x[i]) { return false; } } return true; } }