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Java example source code file (HarmonicFitter.java)

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

Learn more about this Java project at its project page.

Java - Java tags/keywords

deprecated, harmonicfitter, multivariatevectoroptimizer, parameterguesser, weightedobservedpoint, zeroexception

The HarmonicFitter.java Java example 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.math3.fitting;

import org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer;
import org.apache.commons.math3.analysis.function.HarmonicOscillator;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.FastMath;

/**
 * Class that implements a curve fitting specialized for sinusoids.
 *
 * Harmonic fitting is a very simple case of curve fitting. The
 * estimated coefficients are the amplitude a, the pulsation ω and
 * the phase φ: <code>f (t) = a cos (ω t + φ). They are
 * searched by a least square estimator initialized with a rough guess
 * based on integrals.
 *
 * @since 2.0
 * @deprecated As of 3.3. Please use {@link HarmonicCurveFitter} and
 * {@link WeightedObservedPoints} instead.
 */
@Deprecated
public class HarmonicFitter extends CurveFitter<HarmonicOscillator.Parametric> {
    /**
     * Simple constructor.
     * @param optimizer Optimizer to use for the fitting.
     */
    public HarmonicFitter(final MultivariateVectorOptimizer optimizer) {
        super(optimizer);
    }

    /**
     * Fit an harmonic function to the observed points.
     *
     * @param initialGuess First guess values in the following order:
     * <ul>
     *  <li>Amplitude
     *  <li>Angular frequency
     *  <li>Phase
     * </ul>
     * @return the parameters of the harmonic function that best fits the
     * observed points (in the same order as above).
     */
    public double[] fit(double[] initialGuess) {
        return fit(new HarmonicOscillator.Parametric(), initialGuess);
    }

    /**
     * Fit an harmonic function to the observed points.
     * An initial guess will be automatically computed.
     *
     * @return the parameters of the harmonic function that best fits the
     * observed points (see the other {@link #fit(double[]) fit} method.
     * @throws NumberIsTooSmallException if the sample is too short for the
     * the first guess to be computed.
     * @throws ZeroException if the first guess cannot be computed because
     * the abscissa range is zero.
     */
    public double[] fit() {
        return fit((new ParameterGuesser(getObservations())).guess());
    }

    /**
     * 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, * ω and φ such that f (t) = a cos (ω t + φ). * </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 ω2 × [t - S (t)] / 2 * where S (t) = sin (2 (ω t + φ)) / (2 ω) * </pre> * </p> * * <p>We can remove S between these expressions : * <pre> * If'2 (t) = a<sup>2 ω2 t - ω2 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 ω are positive and * compute them directly, knowing that A = a<sup>2 ω2 and that * B = - ω<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 * ω = \ | ------------------------ * \| ∑x<sub>ixi ∑yiyi - ∑xiyi ∑xiyi * * </pre> * </p> * * <p>Once we know ω, we can compute: * <pre> * fc = ω f (t) cos (ω t) - f' (t) sin (ω t) * fs = ω f (t) sin (ω t) + f' (t) cos (ω t) * </pre> * </p> * * <p>It appears that fc = a ω cos (φ) and * <code>fs = -a ω sin (φ), so we can use these * expressions to compute φ. 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> */ public static class ParameterGuesser { /** Amplitude. */ private final double a; /** Angular frequency. */ private final double omega; /** Phase. */ private final double phi; /** * Simple constructor. * * @param observations Sampled observations. * @throws NumberIsTooSmallException if the sample is too short. * @throws ZeroException if the abscissa range is zero. * @throws MathIllegalStateException when the guessing procedure cannot * produce sensible results. */ public ParameterGuesser(WeightedObservedPoint[] observations) { if (observations.length < 4) { throw new NumberIsTooSmallException(LocalizedFormats.INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE, observations.length, 4, true); } final WeightedObservedPoint[] sorted = sortObservations(observations); final double aOmega[] = guessAOmega(sorted); a = aOmega[0]; omega = aOmega[1]; phi = guessPhi(sorted); } /** * Gets an estimation of the parameters. * * @return the guessed parameters, in the following order: * <ul> * <li>Amplitude * <li>Angular frequency * <li>Phase * </ul> */ public double[] guess() { return new double[] { a, omega, phi }; } /** * Sort the observations with respect to the abscissa. * * @param unsorted Input observations. * @return the input observations, sorted. */ private WeightedObservedPoint[] sortObservations(WeightedObservedPoint[] unsorted) { final WeightedObservedPoint[] observations = unsorted.clone(); // 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]; } } observations[i + 1] = curr; curr = observations[j]; } } return observations; } /** * Estimate a first guess of the amplitude and angular frequency. * This method assumes that the {@link #sortObservations(WeightedObservedPoint[])} method * has been called previously. * * @param observations Observations, sorted w.r.t. abscissa. * @throws ZeroException if the abscissa range is zero. * @throws MathIllegalStateException when the guessing procedure cannot * produce sensible results. * @return the guessed amplitude (at index 0) and circular frequency * (at index 1). */ private double[] guessAOmega(WeightedObservedPoint[] observations) { final double[] aOmega = new double[2]; // initialize the sums for the linear model between the two integrals double sx2 = 0; double sy2 = 0; double sxy = 0; double sxz = 0; double syz = 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) || (c2 / c3 < 0)) { final int last = observations.length - 1; // Range of the observations, assuming that the // observations are sorted. final double xRange = observations[last].getX() - observations[0].getX(); if (xRange == 0) { throw new ZeroException(); } aOmega[1] = 2 * Math.PI / xRange; double yMin = Double.POSITIVE_INFINITY; double yMax = Double.NEGATIVE_INFINITY; for (int i = 1; i < observations.length; ++i) { final double y = observations[i].getY(); if (y < yMin) { yMin = y; } if (y > yMax) { yMax = y; } } aOmega[0] = 0.5 * (yMax - yMin); } else { if (c2 == 0) { // In some ill-conditioned cases (cf. MATH-844), the guesser // procedure cannot produce sensible results. throw new MathIllegalStateException(LocalizedFormats.ZERO_DENOMINATOR); } aOmega[0] = FastMath.sqrt(c1 / c2); aOmega[1] = FastMath.sqrt(c2 / c3); } return aOmega; } /** * Estimate a first guess of the phase. * * @param observations Observations, sorted w.r.t. abscissa. * @return the guessed phase. */ private double guessPhi(WeightedObservedPoint[] observations) { // initialize the means double fcMean = 0; double fsMean = 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 = FastMath.cos(omegaX); double sine = FastMath.sin(omegaX); fcMean += omega * currentY * cosine - currentYPrime * sine; fsMean += omega * currentY * sine + currentYPrime * cosine; } return FastMath.atan2(-fsMean, fcMean); } } }

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