1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 package org.apache.commons.math.analysis.interpolation; 18 19 import org.apache.commons.math.MathRuntimeException; 20 import org.apache.commons.math.analysis.polynomials.PolynomialFunction; 21 import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction; 22 23 /** 24 * Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set. 25 * <p> 26 * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction} 27 * consisting of n cubic polynomials, defined over the subintervals determined by the x values, 28 * x[0] < x[i] ... < x[n]. The x values are referred to as "knot points."</p> 29 * <p> 30 * The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest 31 * knot point and strictly less than the largest knot point is computed by finding the subinterval to which 32 * x belongs and computing the value of the corresponding polynomial at <code>x - x[i] </code> where 33 * <code>i</code> is the index of the subinterval. See {@link PolynomialSplineFunction} for more details. 34 * </p> 35 * <p> 36 * The interpolating polynomials satisfy: <ol> 37 * <li>The value of the PolynomialSplineFunction at each of the input x values equals the 38 * corresponding y value.</li> 39 * <li>Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials 40 * "match up" at the knot points, as do their first and second derivatives).</li> 41 * </ol></p> 42 * <p> 43 * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires, 44 * <u>Numerical Analysis</u>, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131. 45 * </p> 46 * 47 * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $ 48 * 49 */ 50 public class SplineInterpolator implements UnivariateRealInterpolator { 51 52 /** 53 * Computes an interpolating function for the data set. 54 * @param x the arguments for the interpolation points 55 * @param y the values for the interpolation points 56 * @return a function which interpolates the data set 57 */ 58 public PolynomialSplineFunction interpolate(double x[], double y[]) { 59 if (x.length != y.length) { 60 throw MathRuntimeException.createIllegalArgumentException( 61 "dimension mismatch {0} != {1}", x.length, y.length); 62 } 63 64 if (x.length < 3) { 65 throw MathRuntimeException.createIllegalArgumentException( 66 "{0} points are required, got only {1}", 3, x.length); 67 } 68 69 // Number of intervals. The number of data points is n + 1. 70 int n = x.length - 1; 71 72 for (int i = 0; i < n; i++) { 73 if (x[i] >= x[i + 1]) { 74 throw MathRuntimeException.createIllegalArgumentException( 75 "points {0} and {1} are not strictly increasing ({2} >= {3})", 76 i, i+1, x[i], x[i+1]); 77 } 78 } 79 80 // Differences between knot points 81 double h[] = new double[n]; 82 for (int i = 0; i < n; i++) { 83 h[i] = x[i + 1] - x[i]; 84 } 85 86 double mu[] = new double[n]; 87 double z[] = new double[n + 1]; 88 mu[0] = 0d; 89 z[0] = 0d; 90 double g = 0; 91 for (int i = 1; i < n; i++) { 92 g = 2d * (x[i+1] - x[i - 1]) - h[i - 1] * mu[i -1]; 93 mu[i] = h[i] / g; 94 z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) / 95 (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g; 96 } 97 98 // cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants) 99 double b[] = new double[n]; 100 double c[] = new double[n + 1]; 101 double d[] = new double[n]; 102 103 z[n] = 0d; 104 c[n] = 0d; 105 106 for (int j = n -1; j >=0; j--) { 107 c[j] = z[j] - mu[j] * c[j + 1]; 108 b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d; 109 d[j] = (c[j + 1] - c[j]) / (3d * h[j]); 110 } 111 112 PolynomialFunction polynomials[] = new PolynomialFunction[n]; 113 double coefficients[] = new double[4]; 114 for (int i = 0; i < n; i++) { 115 coefficients[0] = y[i]; 116 coefficients[1] = b[i]; 117 coefficients[2] = c[i]; 118 coefficients[3] = d[i]; 119 polynomials[i] = new PolynomialFunction(coefficients); 120 } 121 122 return new PolynomialSplineFunction(x, polynomials); 123 } 124 125 }