
Commons Math example source code file (SplineInterpolator.java)
The Commons Math SplineInterpolator.java source code/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You 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/LICENSE2.0 * * 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.interpolation; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.analysis.polynomials.PolynomialFunction; import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction; /** * Computes a natural (also known as "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." where * <code>i is the index of the subinterval. See {@link PolynomialSplineFunction} for more details. * </p> * <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, 4th Ed., 1989, PWSKent, ISBN 053491585X, pp 126131. * </p> * * @version $Revision: 811685 $ $Date: 20090905 13:36:48 0400 (Sat, 05 Sep 2009) $ * */ 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 PolynomialSplineFunction interpolate(double x[], double y[]) { if (x.length != y.length) { throw MathRuntimeException.createIllegalArgumentException( "dimension mismatch {0} != {1}", x.length, y.length); } if (x.length < 3) { throw MathRuntimeException.createIllegalArgumentException( "{0} points are required, got only {1}", 3, x.length); } // 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 MathRuntimeException.createIllegalArgumentException( "points {0} and {1} are not strictly increasing ({2} >= {3})", i, i+1, x[i], x[i+1]); } } // 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); } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math SplineInterpolator.java source code file: 
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