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Java > Open Source Codes > org > apache > commons > math > analysis > SplineInterpolator


1 /*
2  * Copyright 2003-2004 The Apache Software Foundation.
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  * http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 package org.apache.commons.math.analysis;
17
18 /**
19  * Computes a natural (a.k.a. "free", "unclamped") cubic spline interpolation for the data set.
20  * <p>
21  * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction}
22  * consisting of n cubic polynomials, defined over the subintervals determined by the x values,
23  * x[0] < x[i] ... < x[n]. The x values are referred to as "knot points."
24  * <p>
25  * The value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest
26  * knot point and strictly less than the largest knot point is computed by finding the subinterval to which
27  * x belongs and computing the value of the corresponding polynomial at <code>x - x[i] </code> where
28  * <code>i</code> is the index of the subinterval. See {@link PolynomialSplineFunction} for more details.
29  * <p>
30  * The interpolating polynomials satisfy: <ol>
31  * <li>The value of the PolynomialSplineFunction at each of the input x values equals the
32  * corresponding y value.</li>
33  * <li>Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials
34  * "match up" at the knot points, as do their first and second derivatives).</li>
35  * </ol>
36  * <p>
37  * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires,
38  * <u>Numerical Analysis</u>, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131.
39  *
40  * @version $Revision$ $Date: 2005-02-26 05:11:52 -0800 (Sat, 26 Feb 2005) $
41  *
42  */
43 public class SplineInterpolator implements UnivariateRealInterpolator {
44     
45     /**
46      * Computes an interpolating function for the data set.
47      * @param x the arguments for the interpolation points
48      * @param y the values for the interpolation points
49      * @return a function which interpolates the data set
50      */
51     public UnivariateRealFunction interpolate(double x[], double y[]) {
52         if (x.length != y.length) {
53             throw new IllegalArgumentException JavaDoc("Dataset arrays must have same length.");
54         }
55         
56         if (x.length < 3) {
57             throw new IllegalArgumentException JavaDoc
58                 ("At least 3 datapoints are required to compute a spline interpolant");
59         }
60         
61         // Number of intervals. The number of data points is n + 1.
62 int n = x.length - 1;
63         
64         for (int i = 0; i < n; i++) {
65             if (x[i] >= x[i + 1]) {
66                 throw new IllegalArgumentException JavaDoc("Dataset x values must be strictly increasing.");
67             }
68         }
69         
70         // Differences between knot points
71 double h[] = new double[n];
72         for (int i = 0; i < n; i++) {
73             h[i] = x[i + 1] - x[i];
74         }
75         
76         double mu[] = new double[n];
77         double z[] = new double[n + 1];
78         mu[0] = 0d;
79         z[0] = 0d;
80         double g = 0;
81         for (int i = 1; i < n; i++) {
82             g = 2d * (x[i+1] - x[i - 1]) - h[i - 1] * mu[i -1];
83             mu[i] = h[i] / g;
84             z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /
85                     (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;
86         }
87        
88         // cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants)
89 double b[] = new double[n];
90         double c[] = new double[n + 1];
91         double d[] = new double[n];
92         
93         z[n] = 0d;
94         c[n] = 0d;
95         
96         for (int j = n -1; j >=0; j--) {
97             c[j] = z[j] - mu[j] * c[j + 1];
98             b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
99             d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
100         }
101         
102         PolynomialFunction polynomials[] = new PolynomialFunction[n];
103         double coefficients[] = new double[4];
104         for (int i = 0; i < n; i++) {
105             coefficients[0] = y[i];
106             coefficients[1] = b[i];
107             coefficients[2] = c[i];
108             coefficients[3] = d[i];
109             polynomials[i] = new PolynomialFunction(coefficients);
110         }
111         
112         return new PolynomialSplineFunction(x, polynomials);
113     }
114
115 }
116
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