001 /* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017 package org.apache.commons.math.analysis.interpolation; 018 019 import org.apache.commons.math.MathRuntimeException; 020 import org.apache.commons.math.analysis.polynomials.PolynomialFunction; 021 import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction; 022 023 /** 024 * Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set. 025 * <p> 026 * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction} 027 * consisting of n cubic polynomials, defined over the subintervals determined by the x values, 028 * x[0] < x[i] ... < x[n]. The x values are referred to as "knot points."</p> 029 * <p> 030 * The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest 031 * knot point and strictly less than the largest knot point is computed by finding the subinterval to which 032 * x belongs and computing the value of the corresponding polynomial at <code>x - x[i] </code> where 033 * <code>i</code> is the index of the subinterval. See {@link PolynomialSplineFunction} for more details. 034 * </p> 035 * <p> 036 * The interpolating polynomials satisfy: <ol> 037 * <li>The value of the PolynomialSplineFunction at each of the input x values equals the 038 * corresponding y value.</li> 039 * <li>Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials 040 * "match up" at the knot points, as do their first and second derivatives).</li> 041 * </ol></p> 042 * <p> 043 * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires, 044 * <u>Numerical Analysis</u>, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131. 045 * </p> 046 * 047 * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $ 048 * 049 */ 050 public class SplineInterpolator implements UnivariateRealInterpolator { 051 052 /** 053 * Computes an interpolating function for the data set. 054 * @param x the arguments for the interpolation points 055 * @param y the values for the interpolation points 056 * @return a function which interpolates the data set 057 */ 058 public PolynomialSplineFunction interpolate(double x[], double y[]) { 059 if (x.length != y.length) { 060 throw MathRuntimeException.createIllegalArgumentException( 061 "dimension mismatch {0} != {1}", x.length, y.length); 062 } 063 064 if (x.length < 3) { 065 throw MathRuntimeException.createIllegalArgumentException( 066 "{0} points are required, got only {1}", 3, x.length); 067 } 068 069 // Number of intervals. The number of data points is n + 1. 070 int n = x.length - 1; 071 072 for (int i = 0; i < n; i++) { 073 if (x[i] >= x[i + 1]) { 074 throw MathRuntimeException.createIllegalArgumentException( 075 "points {0} and {1} are not strictly increasing ({2} >= {3})", 076 i, i+1, x[i], x[i+1]); 077 } 078 } 079 080 // Differences between knot points 081 double h[] = new double[n]; 082 for (int i = 0; i < n; i++) { 083 h[i] = x[i + 1] - x[i]; 084 } 085 086 double mu[] = new double[n]; 087 double z[] = new double[n + 1]; 088 mu[0] = 0d; 089 z[0] = 0d; 090 double g = 0; 091 for (int i = 1; i < n; i++) { 092 g = 2d * (x[i+1] - x[i - 1]) - h[i - 1] * mu[i -1]; 093 mu[i] = h[i] / g; 094 z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) / 095 (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g; 096 } 097 098 // cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants) 099 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 }