Java tutorial
/******************************************************************************* * Copyright 2014 Geoscience Australia (www.ga.gov.au) * @author - Johnathan Kool (Geoscience Australia) * * Licensed under the BSD-3 License * * http://opensource.org/licenses/BSD-3-Clause * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * 1. Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright notice, * this list of conditions and the following disclaimer in the documentation * and/or other materials provided with the distribution. * * 3. Neither the name of the copyright holder nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. ******************************************************************************/ package au.gov.ga.conn4d.utils; /* * 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. */ import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.NonMonotonicSequenceException; import org.apache.commons.math3.analysis.polynomials.PolynomialFunction; import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction; import org.apache.commons.math3.util.MathArrays; /** * Computes a natural (also known as "free", "unclamped") cubic spline * interpolation for the data set. * * MODIFIED from the original on 19/05/2014 by Johnathan Kool to accept * float arrays * <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, x[0] < x[i] ... < x[n]. The * x values are referred to as "knot points." * </p> * <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] </code> where * <code>i</code> 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> * <p> * The cubic spline interpolation algorithm implemented is as described in R.L. * Burden, J.D. Faires, <u>Numerical Analysis</u>, 4th Ed., 1989, PWS-Kent, ISBN * 0-53491-585-X, pp 126-131. * </p> * * @version $Id: SplineInterpolator.java 1379905 2012-09-01 23:56:50Z erans $ */ 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); } public PolynomialSplineFunction interpolate(double x[], float 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); } }