/*
* 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;
}
}