Java tutorial
/* * 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.math3.analysis.polynomials; import java.util.Arrays; import org.apache.commons.math3.util.MathArrays; import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction; import org.apache.commons.math3.analysis.UnivariateFunction; import org.apache.commons.math3.analysis.differentiation.DerivativeStructure; import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction; import org.apache.commons.math3.exception.OutOfRangeException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.NullArgumentException; import org.apache.commons.math3.exception.util.LocalizedFormats; /** * 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> * <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> * <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> * <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 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></p> * * @version $Id: PolynomialSplineFunction.java 1383441 2012-09-11 14:56:39Z luc $ */ public class PolynomialSplineFunction implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction { /** * 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. It is equal to the number of polynomials and * to the number of partition points - 1. */ private final int n; /** * Construct a polynomial spline function with the given segment delimiters * and interpolating polynomials. * 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 NullArgumentException if either of the input arrays is {@code null}. * @throws NumberIsTooSmallException if knots has length less than 2. * @throws DimensionMismatchException if {@code polynomials.length != knots.length - 1}. * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException if * the {@code knots} array is not strictly increasing. * */ public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[]) { if (knots == null || polynomials == null) { throw new NullArgumentException(); } if (knots.length < 2) { throw new NumberIsTooSmallException(LocalizedFormats.NOT_ENOUGH_POINTS_IN_SPLINE_PARTITION, 2, knots.length, false); } if (knots.length - 1 != polynomials.length) { throw new DimensionMismatchException(polynomials.length, knots.length); } MathArrays.checkOrder(knots); 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. * See {@link PolynomialSplineFunction} for details on the algorithm for * computing the value of the function. * * @param v Point for which the function value should be computed. * @return the value. * @throws OutOfRangeException if {@code v} is outside of the domain of the * spline function (smaller than the smallest knot point or larger than the * largest knot point). */ public double value(double v) { if (v < knots[0] || v > knots[n]) { throw new OutOfRangeException(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]); } /** * Get the derivative of the polynomial spline function. * * @return the derivative function. */ public UnivariateFunction derivative() { return polynomialSplineDerivative(); } /** * Get the derivative of the polynomial spline function. * * @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); } /** {@inheritDoc} * @since 3.1 */ public DerivativeStructure value(final DerivativeStructure t) { final double t0 = t.getValue(); if (t0 < knots[0] || t0 > knots[n]) { throw new OutOfRangeException(t0, knots[0], knots[n]); } int i = Arrays.binarySearch(knots, t0); if (i < 0) { i = -i - 2; } // This will handle the case where t is the last knot value // There are only n-1 polynomials, so if t is the last knot // then we will use the last polynomial to calculate the value. if (i >= polynomials.length) { i--; } return polynomials[i].value(t.subtract(knots[i])); } /** * Get the number of spline segments. * It is also the number of polynomials and the number of knot points - 1. * * @return the number of spline segments. */ public int getN() { return n; } /** * Get a copy of the interpolating polynomials array. * It 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; } /** * Get an array copy of the knot points. * It 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; } }