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Java example source code file (PolynomialSplineFunction.java)

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

Learn more about this Java project at its project page.

Java - Java tags/keywords

derivativestructure, differentiableunivariatefunction, dimensionmismatchexception, nonmonotonicsequenceexception, nullargumentexception, numberistoosmallexception, outofrangeexception, polynomialfunction, polynomialsplinefunction, univariatedifferentiablefunction, util

The PolynomialSplineFunction.java Java example 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.math3.analysis.polynomials;

import java.util.Arrays;

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.DimensionMismatchException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.MathArrays;

/**
 * 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])}</li>
 *
 */
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 NonMonotonicSequenceException if the {@code knots} array is not strictly increasing.
     *
     */
    public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[])
        throws NullArgumentException, NumberIsTooSmallException,
               DimensionMismatchException, NonMonotonicSequenceException{
        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;
    }

    /**
     * Indicates whether a point is within the interpolation range.
     *
     * @param x Point.
     * @return {@code true} if {@code x} is a valid point.
     */
    public boolean isValidPoint(double x) {
        if (x < knots[0] ||
            x > knots[n]) {
            return false;
        } else {
            return true;
        }
    }
}

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