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Commons Math example source code file (HarmonicCoefficientsGuesser.java)

This example Commons Math source code file (HarmonicCoefficientsGuesser.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

harmoniccoefficientsguesser, harmoniccoefficientsguesser, optimizationexception, optimizationexception, weightedobservedpoint, weightedobservedpoint

The Commons Math HarmonicCoefficientsGuesser.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/LICENSE-2.0
 *
 * 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.optimization.fitting;

import org.apache.commons.math.optimization.OptimizationException;

/** This class guesses harmonic coefficients from a sample.

 * <p>The algorithm used to guess the coefficients is as follows:

* <p>We know f (t) at some sampling points ti and want to find a, * ? and ? such that f (t) = a cos (? t + ?). * </p> * * <p>From the analytical expression, we can compute two primitives : * <pre> * If2 (t) = ? f<sup>2 = a2 × [t + S (t)] / 2 * If'2 (t) = ? f'<sup>2 = a2 ?2 × [t - S (t)] / 2 * where S (t) = sin (2 (? t + ?)) / (2 ?) * </pre> * </p> * * <p>We can remove S between these expressions : * <pre> * If'2 (t) = a<sup>2 ?2 t - ?2 If2 (t) * </pre> * </p> * * <p>The preceding expression shows that If'2 (t) is a linear * combination of both t and If2 (t): If'2 (t) = A × t + B × If2 (t) * </p> * * <p>From the primitive, we can deduce the same form for definite * integrals between t<sub>1 and ti for each ti : * <pre> * If2 (t<sub>i) - If2 (t1) = A × (ti - t1) + B × (If2 (ti) - If2 (t1)) * </pre> * </p> * * <p>We can find the coefficients A and B that best fit the sample * to this linear expression by computing the definite integrals for * each sample points. * </p> * * <p>For a bilinear expression z (xi, yi) = A × xi + B × yi, the * coefficients A and B that minimize a least square criterion * ? (z<sub>i - z (xi, yi))2 are given by these expressions:

* <pre> * * ?y<sub>iyi ?xizi - ?xiyi ?yizi * A = ------------------------ * ?x<sub>ixi ?yiyi - ?xiyi ?xiyi * * ?x<sub>ixi ?yizi - ?xiyi ?xizi * B = ------------------------ * ?x<sub>ixi ?yiyi - ?xiyi ?xiyi * </pre> * </p> * * * <p>In fact, we can assume both a and ? are positive and * compute them directly, knowing that A = a<sup>2 ?2 and that * B = - ?<sup>2. The complete algorithm is therefore:

* <pre> * * for each t<sub>i from t1 to tn-1, compute: * f (t<sub>i) * f' (t<sub>i) = (f (ti+1) - f(ti-1)) / (ti+1 - ti-1) * x<sub>i = ti - t1 * y<sub>i = ? f2 from t1 to ti * z<sub>i = ? f'2 from t1 to ti * update the sums ?x<sub>ixi, ?yiyi, ?xiyi, ?xizi and ?yizi * end for * * |-------------------------- * \ | ?y<sub>iyi ?xizi - ?xiyi ?yizi * a = \ | ------------------------ * \| ?x<sub>iyi ?xizi - ?xixi ?yizi * * * |-------------------------- * \ | ?x<sub>iyi ?xizi - ?xixi ?yizi * ? = \ | ------------------------ * \| ?x<sub>ixi ?yiyi - ?xiyi ?xiyi * * </pre> * </p> * <p>Once we know ?, we can compute: * <pre> * fc = ? f (t) cos (? t) - f' (t) sin (? t) * fs = ? f (t) sin (? t) + f' (t) cos (? t) * </pre> * </p> * <p>It appears that fc = a ? cos (?) and * <code>fs = -a ? sin (?), so we can use these * expressions to compute ?. The best estimate over the sample is * given by averaging these expressions. * </p> * <p>Since integrals and means are involved in the preceding * estimations, these operations run in O(n) time, where n is the * number of measurements.</p> * @version $Revision: 786479 $ $Date: 2009-06-19 08:36:16 -0400 (Fri, 19 Jun 2009) $ * @since 2.0 */ public class HarmonicCoefficientsGuesser { /** Sampled observations. */ private final WeightedObservedPoint[] observations; /** Guessed amplitude. */ private double a; /** Guessed pulsation ?. */ private double omega; /** Guessed phase ?. */ private double phi; /** Simple constructor. * @param observations sampled observations */ public HarmonicCoefficientsGuesser(WeightedObservedPoint[] observations) { this.observations = observations.clone(); a = Double.NaN; omega = Double.NaN; } /** Estimate a first guess of the coefficients. * @exception OptimizationException if the sample is too short or if * the first guess cannot be computed (when the elements under the * square roots are negative). * */ public void guess() throws OptimizationException { sortObservations(); guessAOmega(); guessPhi(); } /** Sort the observations with respect to the abscissa. */ private void sortObservations() { // Since the samples are almost always already sorted, this // method is implemented as an insertion sort that reorders the // elements in place. Insertion sort is very efficient in this case. WeightedObservedPoint curr = observations[0]; for (int j = 1; j < observations.length; ++j) { WeightedObservedPoint prec = curr; curr = observations[j]; if (curr.getX() < prec.getX()) { // the current element should be inserted closer to the beginning int i = j - 1; WeightedObservedPoint mI = observations[i]; while ((i >= 0) && (curr.getX() < mI.getX())) { observations[i + 1] = mI; if (i-- != 0) { mI = observations[i]; } else { mI = null; } } observations[i + 1] = curr; curr = observations[j]; } } } /** Estimate a first guess of the a and ? coefficients. * @exception OptimizationException if the sample is too short or if * the first guess cannot be computed (when the elements under the * square roots are negative). */ private void guessAOmega() throws OptimizationException { // initialize the sums for the linear model between the two integrals double sx2 = 0.0; double sy2 = 0.0; double sxy = 0.0; double sxz = 0.0; double syz = 0.0; double currentX = observations[0].getX(); double currentY = observations[0].getY(); double f2Integral = 0; double fPrime2Integral = 0; final double startX = currentX; for (int i = 1; i < observations.length; ++i) { // one step forward final double previousX = currentX; final double previousY = currentY; currentX = observations[i].getX(); currentY = observations[i].getY(); // update the integrals of f<sup>2 and f'2 // considering a linear model for f (and therefore constant f') final double dx = currentX - previousX; final double dy = currentY - previousY; final double f2StepIntegral = dx * (previousY * previousY + previousY * currentY + currentY * currentY) / 3; final double fPrime2StepIntegral = dy * dy / dx; final double x = currentX - startX; f2Integral += f2StepIntegral; fPrime2Integral += fPrime2StepIntegral; sx2 += x * x; sy2 += f2Integral * f2Integral; sxy += x * f2Integral; sxz += x * fPrime2Integral; syz += f2Integral * fPrime2Integral; } // compute the amplitude and pulsation coefficients double c1 = sy2 * sxz - sxy * syz; double c2 = sxy * sxz - sx2 * syz; double c3 = sx2 * sy2 - sxy * sxy; if ((c1 / c2 < 0.0) || (c2 / c3 < 0.0)) { throw new OptimizationException("unable to first guess the harmonic coefficients"); } a = Math.sqrt(c1 / c2); omega = Math.sqrt(c2 / c3); } /** Estimate a first guess of the ? coefficient. */ private void guessPhi() { // initialize the means double fcMean = 0.0; double fsMean = 0.0; double currentX = observations[0].getX(); double currentY = observations[0].getY(); for (int i = 1; i < observations.length; ++i) { // one step forward final double previousX = currentX; final double previousY = currentY; currentX = observations[i].getX(); currentY = observations[i].getY(); final double currentYPrime = (currentY - previousY) / (currentX - previousX); double omegaX = omega * currentX; double cosine = Math.cos(omegaX); double sine = Math.sin(omegaX); fcMean += omega * currentY * cosine - currentYPrime * sine; fsMean += omega * currentY * sine + currentYPrime * cosine; } phi = Math.atan2(-fsMean, fcMean); } /** Get the guessed amplitude a. * @return guessed amplitude a; */ public double getGuessedAmplitude() { return a; } /** Get the guessed pulsation ?. * @return guessed pulsation ? */ public double getGuessedPulsation() { return omega; } /** Get the guessed phase ?. * @return guessed phase ? */ public double getGuessedPhase() { return phi; } }

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