Java tutorial
/* * 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.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. * <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); } }