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Java example source code file (SplineInterpolator.java)

This example Java source code file (SplineInterpolator.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

dimensionmismatchexception, nonmonotonicsequenceexception, numberistoosmallexception, polynomialfunction, polynomialsplinefunction, splineinterpolator, univariateinterpolator

The SplineInterpolator.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.NumberIsTooSmallException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.MathArrays;

/**
 * Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set.
 * <p>
 * The {@link #interpolate(double[], double[])} 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 x values are referred to as "knot points."
 * <p>
 * The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest
 * knot point and strictly less than the largest knot point is computed by finding the subinterval to which
 * x belongs and computing the value of the corresponding polynomial at <code>x - x[i]  where
 * <code>i is the index of the subinterval.  See {@link PolynomialSplineFunction} for more details.
 * </p>
 * <p>
 * The interpolating polynomials satisfy: <ol>
 * <li>The value of the PolynomialSplineFunction at each of the input x values equals the
 *  corresponding y value.</li>
 * <li>Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials
 *  "match up" at the knot points, as do their first and second derivatives).</li>
 * </ol>
 * <p>
 * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires,
 * <u>Numerical Analysis, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131.
 * </p>
 *
 */
public class SplineInterpolator implements UnivariateInterpolator {
    /**
     * Computes an interpolating function for the data set.
     * @param x the arguments for the interpolation points
     * @param y the values for the interpolation points
     * @return a function which interpolates the data set
     * @throws DimensionMismatchException if {@code x} and {@code y}
     * have different sizes.
     * @throws NonMonotonicSequenceException if {@code x} is not sorted in
     * strict increasing order.
     * @throws NumberIsTooSmallException if the size of {@code x} is smaller
     * than 3.
     */
    public PolynomialSplineFunction interpolate(double x[], double y[])
        throws DimensionMismatchException,
               NumberIsTooSmallException,
               NonMonotonicSequenceException {
        if (x.length != y.length) {
            throw new DimensionMismatchException(x.length, y.length);
        }

        if (x.length < 3) {
            throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
                                                x.length, 3, true);
        }

        // Number of intervals.  The number of data points is n + 1.
        final int n = x.length - 1;

        MathArrays.checkOrder(x);

        // Differences between knot points
        final double h[] = new double[n];
        for (int i = 0; i < n; i++) {
            h[i] = x[i + 1] - x[i];
        }

        final double mu[] = new double[n];
        final double z[] = new double[n + 1];
        mu[0] = 0d;
        z[0] = 0d;
        double g = 0;
        for (int i = 1; i < n; i++) {
            g = 2d * (x[i+1]  - x[i - 1]) - h[i - 1] * mu[i -1];
            mu[i] = h[i] / g;
            z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
                    (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
        }

        // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
        final double b[] = new double[n];
        final double c[] = new double[n + 1];
        final double d[] = new double[n];

        z[n] = 0d;
        c[n] = 0d;

        for (int j = n -1; j >=0; j--) {
            c[j] = z[j] - mu[j] * c[j + 1];
            b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
            d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
        }

        final PolynomialFunction polynomials[] = new PolynomialFunction[n];
        final double coefficients[] = new double[4];
        for (int i = 0; i < n; i++) {
            coefficients[0] = y[i];
            coefficients[1] = b[i];
            coefficients[2] = c[i];
            coefficients[3] = d[i];
            polynomials[i] = new PolynomialFunction(coefficients);
        }

        return new PolynomialSplineFunction(x, polynomials);
    }
}

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