Java tutorial
/* * Copyright 2003-2004 The Apache Software Foundation. * * Licensed 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.math.analysis; /** * Computes a natural (a.k.a. "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> * 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> * 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</u>, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131. * * @version $Revision: 1.19 $ $Date: 2004/06/23 16:26:14 $ * */ public class SplineInterpolator implements UnivariateRealInterpolator { /** * 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 */ public UnivariateRealFunction interpolate(double x[], double y[]) { if (x.length != y.length) { throw new IllegalArgumentException("Dataset arrays must have same length."); } if (x.length < 3) { throw new IllegalArgumentException( "At least 3 datapoints are required to compute a spline interpolant"); } // Number of intervals. The number of data points is n + 1. int n = x.length - 1; for (int i = 0; i < n; i++) { if (x[i] >= x[i + 1]) { throw new IllegalArgumentException("Dataset x values must be strictly increasing."); } } // Differences between knot points double h[] = new double[n]; for (int i = 0; i < n; i++) { h[i] = x[i + 1] - x[i]; } double mu[] = new double[n]; 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) double b[] = new double[n]; double c[] = new double[n + 1]; 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]); } PolynomialFunction polynomials[] = new PolynomialFunction[n]; 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); } }