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Initial commit. 

git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@141141 13f79535-47bb-0310-9956-ffa450edef68
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Phil Steitz 2004-04-02 20:58:11 +00:00
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src/java/org/apache/commons/math/analysis/PolynomialSplineFunction.java Normal file
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/*
*
* Copyright (c) 2004 The Apache Software Foundation. All rights reserved.
*
* 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.MathException;
/**
* 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 and the first two
* derivatives of "adjacent" polynomials are constrained to agree 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 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: 1.1 $ $Date: 2004/04/02 20:58:11 $
*/
public class PolynomialSplineFunction implements UnivariateRealFunction, Serializable {
/** 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[]) {
super();
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.");
}
// TODO: check that knots is 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.
*
* @param v the point for which the function value should be computed
* @return the value
* @throws MathException if the function couldn't be computed due to
* missing additional data or other environmental problems.
* @see UnivariateRealFunction#value(double)
*/
public double value(double v) throws MathException {
if (v < knots[0] || v >= knots[n]) {
throw new IllegalArgumentException("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;
}
}