| /* |
| * 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; |
| import org.apache.commons.math.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 $Revision: 1037327 $ $Date: 2010-11-20 21:57:37 +0100 (sam. 20 nov. 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])</code> 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 </code>, or the knots array |
| * is not strictly increasing. |
| * |
| */ |
| public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[]) { |
| if (knots.length < 2) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NOT_ENOUGH_POINTS_IN_SPLINE_PARTITION, |
| 2, knots.length); |
| } |
| if (knots.length - 1 != polynomials.length) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.POLYNOMIAL_INTERPOLANTS_MISMATCH_SEGMENTS, |
| polynomials.length, knots.length); |
| } |
| if (!isStrictlyIncreasing(knots)) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NOT_STRICTLY_INCREASING_KNOT_VALUES); |
| } |
| |
| 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.</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</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; |
| } |
| } |