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Commons Math example source code file (PolynomialSplineFunction.java)

This example Commons Math source code file (PolynomialSplineFunction.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

argumentoutsidedomainexception, argumentoutsidedomainexception, differentiableunivariaterealfunction, differentiableunivariaterealfunction, polynomialfunction, polynomialfunction, polynomialsplinefunction, polynomialsplinefunction, univariaterealfunction, util

The Commons Math PolynomialSplineFunction.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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.polynomials;

import java.util.Arrays;

import org.apache.commons.math.ArgumentOutsideDomainException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;

/**
 * Represents a polynomial spline function.
 * <p>
 * A <strong>polynomial spline function consists of a set of
 * <i>interpolating polynomials and an ascending array of domain
 * <i>knot points, 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 itself, but are assumed to hold among
 * the polynomials and knot points passed to the constructor.</p>
 * <p>
 * N.B.:  The polynomials in the <code>polynomials property must be
 * centered on the knot points to compute the spline function values.
 * See below.</p>
 * <p>
 * The domain of the polynomial spline function is
 * <code>[smallest knot, largest knot].  Attempts to evaluate the
 * function at values outside of this range generate IllegalArgumentExceptions.
 * </p>
 * <p>
 * The value of the polynomial spline function for an argument <code>x
 * is computed as follows:
 * <ol>
 * <li>The knot array is searched to find the segment to which x
 * belongs.  If <code>x is less than the smallest knot point or greater
 * than the largest one, an <code>IllegalArgumentException
 * is thrown.</li>
 * <li> Let j be the index of the largest knot point that is less
 * than or equal to <code>x.  The value returned is 
* <code>polynomials[j](x - knot[j])

* * @version $Revision: 922708 $ $Date: 2010-03-13 20:15:47 -0500 (Sat, 13 Mar 2010) $ */ public class PolynomialSplineFunction implements DifferentiableUnivariateRealFunction { /** Spline segment interval delimiters (knots). Size is n+1 for n segments. */ private final 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]) where i is the * knot segment to which x belongs. */ private final PolynomialFunction polynomials[]; /** * Number of spline segments = number of polynomials * = number of partition points - 1 */ private final int n; /** * 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.</p> * * @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 , or the knots array * is not strictly increasing. * */ public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[]) { if (knots.length < 2) { throw MathRuntimeException.createIllegalArgumentException( "spline partition must have at least {0} points, got {1}", 2, knots.length); } if (knots.length - 1 != polynomials.length) { throw MathRuntimeException.createIllegalArgumentException( "number of polynomial interpolants must match the number of segments ({0} != {1} - 1)", polynomials.length, knots.length); } if (!isStrictlyIncreasing(knots)) { throw MathRuntimeException.createIllegalArgumentException( "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> * <p> * See {@link PolynomialSplineFunction} for details on the algorithm for * computing the value of the function.</p> * * @param v the point for which the function value should be computed * @return the value * @throws ArgumentOutsideDomainException if v is outside of the domain of * of the spline function (less than the smallest knot point or greater * than the largest knot point) */ public double value(double v) throws ArgumentOutsideDomainException { if (v < knots[0] || v > knots[n]) { throw new ArgumentOutsideDomainException(v, knots[0], knots[n]); } int i = Arrays.binarySearch(knots, v); if (i < 0) { i = -i - 2; } //This will handle the case where v is the last knot value //There are only n-1 polynomials, so if v is the last knot //then we will use the last polynomial to calculate the value. if ( i >= polynomials.length ) { i--; } 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.</p> * * @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.</p> * * @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 if the elements in x are ordered * in a stricly increasing manner. <code>false, 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; } }

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