1dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/* 2dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Licensed to the Apache Software Foundation (ASF) under one or more 3dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * contributor license agreements. See the NOTICE file distributed with 4dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * this work for additional information regarding copyright ownership. 5dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The ASF licenses this file to You under the Apache License, Version 2.0 6dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (the "License"); you may not use this file except in compliance with 7dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the License. You may obtain a copy of the License at 8dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 9dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * http://www.apache.org/licenses/LICENSE-2.0 10dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 11dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Unless required by applicable law or agreed to in writing, software 12dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * distributed under the License is distributed on an "AS IS" BASIS, 13dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See the License for the specific language governing permissions and 15dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * limitations under the License. 16dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 17dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpackage org.apache.commons.math.analysis.interpolation; 18dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 19dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.exception.DimensionMismatchException; 20dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.exception.util.LocalizedFormats; 21dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.exception.NumberIsTooSmallException; 22dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.analysis.polynomials.PolynomialFunction; 23dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction; 24dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.util.MathUtils; 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 26dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/** 27dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set. 28dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 29dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction} 30dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * consisting of n cubic polynomials, defined over the subintervals determined by the x values, 31dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * x[0] < x[i] ... < x[n]. The x values are referred to as "knot points."</p> 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * knot point and strictly less than the largest knot point is computed by finding the subinterval to which 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * x belongs and computing the value of the corresponding polynomial at <code>x - x[i] </code> where 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <code>i</code> is the index of the subinterval. See {@link PolynomialSplineFunction} for more details. 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * </p> 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The interpolating polynomials satisfy: <ol> 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <li>The value of the PolynomialSplineFunction at each of the input x values equals the 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * corresponding y value.</li> 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <li>Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * "match up" at the knot points, as do their first and second derivatives).</li> 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * </ol></p> 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires, 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <u>Numerical Analysis</u>, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131. 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * </p> 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 983921 $ $Date: 2010-08-10 12:46:06 +0200 (mar. 10 août 2010) $ 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class SplineInterpolator implements UnivariateRealInterpolator { 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Computes an interpolating function for the data set. 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param x the arguments for the interpolation points 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param y the values for the interpolation points 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @return a function which interpolates the data set 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @throws DimensionMismatchException if {@code x} and {@code y} 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * have different sizes. 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @throws org.apache.commons.math.exception.NonMonotonousSequenceException 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * if {@code x} is not sorted in strict increasing order. 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @throws NumberIsTooSmallException if the size of {@code x} is smaller 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * than 3. 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public PolynomialSplineFunction interpolate(double x[], double y[]) { 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (x.length != y.length) { 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new DimensionMismatchException(x.length, y.length); 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (x.length < 3) { 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS, 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond x.length, 3, true); 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Number of intervals. The number of data points is n + 1. 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond int n = x.length - 1; 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond MathUtils.checkOrder(x); 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Differences between knot points 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double h[] = new double[n]; 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < n; i++) { 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond h[i] = x[i + 1] - x[i]; 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double mu[] = new double[n]; 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double z[] = new double[n + 1]; 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond mu[0] = 0d; 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond z[0] = 0d; 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double g = 0; 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 1; i < n; i++) { 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond g = 2d * (x[i+1] - x[i - 1]) - h[i - 1] * mu[i -1]; 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond mu[i] = h[i] / g; 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) / 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g; 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants) 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double b[] = new double[n]; 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double c[] = new double[n + 1]; 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double d[] = new double[n]; 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond z[n] = 0d; 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond c[n] = 0d; 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = n -1; j >=0; j--) { 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond c[j] = z[j] - mu[j] * c[j + 1]; 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d; 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond d[j] = (c[j + 1] - c[j]) / (3d * h[j]); 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 113dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 114dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond PolynomialFunction polynomials[] = new PolynomialFunction[n]; 115dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double coefficients[] = new double[4]; 116dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < n; i++) { 117dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond coefficients[0] = y[i]; 118dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond coefficients[1] = b[i]; 119dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond coefficients[2] = c[i]; 120dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond coefficients[3] = d[i]; 121dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond polynomials[i] = new PolynomialFunction(coefficients); 122dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 123dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 124dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return new PolynomialSplineFunction(x, polynomials); 125dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 126dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 127dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 128