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Java example source code file (AkimaSplineInterpolator.java)

This example Java source code file (AkimaSplineInterpolator.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

akimasplineinterpolator, dimensionmismatchexception, minimum_number_points, nonmonotonicsequenceexception, nullargumentexception, numberistoosmallexception, polynomialfunction, polynomialsplinefunction, univariateinterpolator

The AkimaSplineInterpolator.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.interpolation;

import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
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.util.LocalizedFormats;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.Precision;

/**
 * Computes a cubic spline interpolation for the data set using the Akima
 * algorithm, as originally formulated by Hiroshi Akima in his 1970 paper
 * "A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures."
 * J. ACM 17, 4 (October 1970), 589-602. DOI=10.1145/321607.321609
 * http://doi.acm.org/10.1145/321607.321609
 * <p>
 * This implementation is based on the Akima implementation in the CubicSpline
 * class in the Math.NET Numerics library. The method referenced is
 * CubicSpline.InterpolateAkimaSorted
 * </p>
 * <p>
 * The {@link #interpolate(double[], double[]) interpolate} method returns a
 * {@link PolynomialSplineFunction} consisting of n cubic polynomials, defined
 * over the subintervals determined by the x values, {@code x[0] < x[i] ... < x[n]}.
 * The Akima algorithm requires that {@code n >= 5}.
 * </p>
 */
public class AkimaSplineInterpolator
    implements UnivariateInterpolator {
    /** The minimum number of points that are needed to compute the function. */
    private static final int MINIMUM_NUMBER_POINTS = 5;

    /**
     * Computes an interpolating function for the data set.
     *
     * @param xvals the arguments for the interpolation points
     * @param yvals the values for the interpolation points
     * @return a function which interpolates the data set
     * @throws DimensionMismatchException if {@code xvals} and {@code yvals} have
     *         different sizes.
     * @throws NonMonotonicSequenceException if {@code xvals} is not sorted in
     *         strict increasing order.
     * @throws NumberIsTooSmallException if the size of {@code xvals} is smaller
     *         than 5.
     */
    public PolynomialSplineFunction interpolate(double[] xvals,
                                                double[] yvals)
        throws DimensionMismatchException,
               NumberIsTooSmallException,
               NonMonotonicSequenceException {
        if (xvals == null ||
            yvals == null) {
            throw new NullArgumentException();
        }

        if (xvals.length != yvals.length) {
            throw new DimensionMismatchException(xvals.length, yvals.length);
        }

        if (xvals.length < MINIMUM_NUMBER_POINTS) {
            throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                                xvals.length,
                                                MINIMUM_NUMBER_POINTS, true);
        }

        MathArrays.checkOrder(xvals);

        final int numberOfDiffAndWeightElements = xvals.length - 1;

        final double[] differences = new double[numberOfDiffAndWeightElements];
        final double[] weights = new double[numberOfDiffAndWeightElements];

        for (int i = 0; i < differences.length; i++) {
            differences[i] = (yvals[i + 1] - yvals[i]) / (xvals[i + 1] - xvals[i]);
        }

        for (int i = 1; i < weights.length; i++) {
            weights[i] = FastMath.abs(differences[i] - differences[i - 1]);
        }

        // Prepare Hermite interpolation scheme.
        final double[] firstDerivatives = new double[xvals.length];

        for (int i = 2; i < firstDerivatives.length - 2; i++) {
            final double wP = weights[i + 1];
            final double wM = weights[i - 1];
            if (Precision.equals(wP, 0.0) &&
                Precision.equals(wM, 0.0)) {
                final double xv = xvals[i];
                final double xvP = xvals[i + 1];
                final double xvM = xvals[i - 1];
                firstDerivatives[i] = (((xvP - xv) * differences[i - 1]) + ((xv - xvM) * differences[i])) / (xvP - xvM);
            } else {
                firstDerivatives[i] = ((wP * differences[i - 1]) + (wM * differences[i])) / (wP + wM);
            }
        }

        firstDerivatives[0] = differentiateThreePoint(xvals, yvals, 0, 0, 1, 2);
        firstDerivatives[1] = differentiateThreePoint(xvals, yvals, 1, 0, 1, 2);
        firstDerivatives[xvals.length - 2] = differentiateThreePoint(xvals, yvals, xvals.length - 2,
                                                                     xvals.length - 3, xvals.length - 2,
                                                                     xvals.length - 1);
        firstDerivatives[xvals.length - 1] = differentiateThreePoint(xvals, yvals, xvals.length - 1,
                                                                     xvals.length - 3, xvals.length - 2,
                                                                     xvals.length - 1);

        return interpolateHermiteSorted(xvals, yvals, firstDerivatives);
    }

    /**
     * Three point differentiation helper, modeled off of the same method in the
     * Math.NET CubicSpline class. This is used by both the Apache Math and the
     * Math.NET Akima Cubic Spline algorithms
     *
     * @param xvals x values to calculate the numerical derivative with
     * @param yvals y values to calculate the numerical derivative with
     * @param indexOfDifferentiation index of the elemnt we are calculating the derivative around
     * @param indexOfFirstSample index of the first element to sample for the three point method
     * @param indexOfSecondsample index of the second element to sample for the three point method
     * @param indexOfThirdSample index of the third element to sample for the three point method
     * @return the derivative
     */
    private double differentiateThreePoint(double[] xvals, double[] yvals,
                                           int indexOfDifferentiation,
                                           int indexOfFirstSample,
                                           int indexOfSecondsample,
                                           int indexOfThirdSample) {
        final double x0 = yvals[indexOfFirstSample];
        final double x1 = yvals[indexOfSecondsample];
        final double x2 = yvals[indexOfThirdSample];

        final double t = xvals[indexOfDifferentiation] - xvals[indexOfFirstSample];
        final double t1 = xvals[indexOfSecondsample] - xvals[indexOfFirstSample];
        final double t2 = xvals[indexOfThirdSample] - xvals[indexOfFirstSample];

        final double a = (x2 - x0 - (t2 / t1 * (x1 - x0))) / (t2 * t2 - t1 * t2);
        final double b = (x1 - x0 - a * t1 * t1) / t1;

        return (2 * a * t) + b;
    }

    /**
     * Creates a Hermite cubic spline interpolation from the set of (x,y) value
     * pairs and their derivatives. This is modeled off of the
     * InterpolateHermiteSorted method in the Math.NET CubicSpline class.
     *
     * @param xvals x values for interpolation
     * @param yvals y values for interpolation
     * @param firstDerivatives first derivative values of the function
     * @return polynomial that fits the function
     */
    private PolynomialSplineFunction interpolateHermiteSorted(double[] xvals,
                                                              double[] yvals,
                                                              double[] firstDerivatives) {
        if (xvals.length != yvals.length) {
            throw new DimensionMismatchException(xvals.length, yvals.length);
        }

        if (xvals.length != firstDerivatives.length) {
            throw new DimensionMismatchException(xvals.length,
                                                 firstDerivatives.length);
        }

        final int minimumLength = 2;
        if (xvals.length < minimumLength) {
            throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                                xvals.length, minimumLength,
                                                true);
        }

        final int size = xvals.length - 1;
        final PolynomialFunction[] polynomials = new PolynomialFunction[size];
        final double[] coefficients = new double[4];

        for (int i = 0; i < polynomials.length; i++) {
            final double w = xvals[i + 1] - xvals[i];
            final double w2 = w * w;

            final double yv = yvals[i];
            final double yvP = yvals[i + 1];

            final double fd = firstDerivatives[i];
            final double fdP = firstDerivatives[i + 1];

            coefficients[0] = yv;
            coefficients[1] = firstDerivatives[i];
            coefficients[2] = (3 * (yvP - yv) / w - 2 * fd - fdP) / w;
            coefficients[3] = (2 * (yv - yvP) / w + fd + fdP) / w2;
            polynomials[i] = new PolynomialFunction(coefficients);
        }

        return new PolynomialSplineFunction(xvals, polynomials);

    }
}

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