Java tutorial
/* * 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 java.util.Arrays; import java.util.Comparator; import org.apache.commons.math3.analysis.function.Gaussian; import org.apache.commons.math3.exception.NullArgumentException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.OutOfRangeException; import org.apache.commons.math3.exception.ZeroException; import org.apache.commons.math3.exception.NotStrictlyPositiveException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer; import org.apache.commons.math3.util.FastMath; /** * Fits points to a {@link * org.apache.commons.math3.analysis.function.Gaussian.Parametric Gaussian} function. * <p> * Usage example: * <pre> * GaussianFitter fitter = new GaussianFitter( * new LevenbergMarquardtOptimizer()); * fitter.addObservedPoint(4.0254623, 531026.0); * fitter.addObservedPoint(4.03128248, 984167.0); * fitter.addObservedPoint(4.03839603, 1887233.0); * fitter.addObservedPoint(4.04421621, 2687152.0); * fitter.addObservedPoint(4.05132976, 3461228.0); * fitter.addObservedPoint(4.05326982, 3580526.0); * fitter.addObservedPoint(4.05779662, 3439750.0); * fitter.addObservedPoint(4.0636168, 2877648.0); * fitter.addObservedPoint(4.06943698, 2175960.0); * fitter.addObservedPoint(4.07525716, 1447024.0); * fitter.addObservedPoint(4.08237071, 717104.0); * fitter.addObservedPoint(4.08366408, 620014.0); * double[] parameters = fitter.fit(); * </pre> * * @since 2.2 * @version $Id: GaussianFitter.java 1416643 2012-12-03 19:37:14Z tn $ */ public class GaussianFitter extends CurveFitter<Gaussian.Parametric> { /** * Constructs an instance using the specified optimizer. * * @param optimizer Optimizer to use for the fitting. */ public GaussianFitter(MultivariateVectorOptimizer optimizer) { super(optimizer); } /** * Fits a Gaussian function to the observed points. * * @param initialGuess First guess values in the following order: * <ul> * <li>Norm</li> * <li>Mean</li> * <li>Sigma</li> * </ul> * @return the parameters of the Gaussian function that best fits the * observed points (in the same order as above). * @since 3.0 */ public double[] fit(double[] initialGuess) { final Gaussian.Parametric f = new Gaussian.Parametric() { @Override public double value(double x, double... p) { double v = Double.POSITIVE_INFINITY; try { v = super.value(x, p); } catch (NotStrictlyPositiveException e) { // NOPMD // Do nothing. } return v; } @Override public double[] gradient(double x, double... p) { double[] v = { Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY }; try { v = super.gradient(x, p); } catch (NotStrictlyPositiveException e) { // NOPMD // Do nothing. } return v; } }; return fit(f, initialGuess); } /** * Fits a Gaussian function to the observed points. * * @return the parameters of the Gaussian function that best fits the * observed points (in the same order as above). */ public double[] fit() { final double[] guess = (new ParameterGuesser(getObservations())).guess(); return fit(guess); } /** * Guesses the parameters {@code norm}, {@code mean}, and {@code sigma} * of a {@link org.apache.commons.math3.analysis.function.Gaussian.Parametric} * based on the specified observed points. */ public static class ParameterGuesser { /** Normalization factor. */ private final double norm; /** Mean. */ private final double mean; /** Standard deviation. */ private final double sigma; /** * Constructs instance with the specified observed points. * * @param observations Observed points from which to guess the * parameters of the Gaussian. * @throws NullArgumentException if {@code observations} is * {@code null}. * @throws NumberIsTooSmallException if there are less than 3 * observations. */ public ParameterGuesser(WeightedObservedPoint[] observations) { if (observations == null) { throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY); } if (observations.length < 3) { throw new NumberIsTooSmallException(observations.length, 3, true); } final WeightedObservedPoint[] sorted = sortObservations(observations); final double[] params = basicGuess(sorted); norm = params[0]; mean = params[1]; sigma = params[2]; } /** * Gets an estimation of the parameters. * * @return the guessed parameters, in the following order: * <ul> * <li>Normalization factor</li> * <li>Mean</li> * <li>Standard deviation</li> * </ul> */ public double[] guess() { return new double[] { norm, mean, sigma }; } /** * Sort the observations. * * @param unsorted Input observations. * @return the input observations, sorted. */ private WeightedObservedPoint[] sortObservations(WeightedObservedPoint[] unsorted) { final WeightedObservedPoint[] observations = unsorted.clone(); final Comparator<WeightedObservedPoint> cmp = new Comparator<WeightedObservedPoint>() { public int compare(WeightedObservedPoint p1, WeightedObservedPoint p2) { if (p1 == null && p2 == null) { return 0; } if (p1 == null) { return -1; } if (p2 == null) { return 1; } if (p1.getX() < p2.getX()) { return -1; } if (p1.getX() > p2.getX()) { return 1; } if (p1.getY() < p2.getY()) { return -1; } if (p1.getY() > p2.getY()) { return 1; } if (p1.getWeight() < p2.getWeight()) { return -1; } if (p1.getWeight() > p2.getWeight()) { return 1; } return 0; } }; Arrays.sort(observations, cmp); return observations; } /** * Guesses the parameters based on the specified observed points. * * @param points Observed points, sorted. * @return the guessed parameters (normalization factor, mean and * sigma). */ private double[] basicGuess(WeightedObservedPoint[] points) { final int maxYIdx = findMaxY(points); final double n = points[maxYIdx].getY(); final double m = points[maxYIdx].getX(); double fwhmApprox; try { final double halfY = n + ((m - n) / 2); final double fwhmX1 = interpolateXAtY(points, maxYIdx, -1, halfY); final double fwhmX2 = interpolateXAtY(points, maxYIdx, 1, halfY); fwhmApprox = fwhmX2 - fwhmX1; } catch (OutOfRangeException e) { // TODO: Exceptions should not be used for flow control. fwhmApprox = points[points.length - 1].getX() - points[0].getX(); } final double s = fwhmApprox / (2 * FastMath.sqrt(2 * FastMath.log(2))); return new double[] { n, m, s }; } /** * Finds index of point in specified points with the largest Y. * * @param points Points to search. * @return the index in specified points array. */ private int findMaxY(WeightedObservedPoint[] points) { int maxYIdx = 0; for (int i = 1; i < points.length; i++) { if (points[i].getY() > points[maxYIdx].getY()) { maxYIdx = i; } } return maxYIdx; } /** * Interpolates using the specified points to determine X at the * specified Y. * * @param points Points to use for interpolation. * @param startIdx Index within points from which to start the search for * interpolation bounds points. * @param idxStep Index step for searching interpolation bounds points. * @param y Y value for which X should be determined. * @return the value of X for the specified Y. * @throws ZeroException if {@code idxStep} is 0. * @throws OutOfRangeException if specified {@code y} is not within the * range of the specified {@code points}. */ private double interpolateXAtY(WeightedObservedPoint[] points, int startIdx, int idxStep, double y) throws OutOfRangeException { if (idxStep == 0) { throw new ZeroException(); } final WeightedObservedPoint[] twoPoints = getInterpolationPointsForY(points, startIdx, idxStep, y); final WeightedObservedPoint p1 = twoPoints[0]; final WeightedObservedPoint p2 = twoPoints[1]; if (p1.getY() == y) { return p1.getX(); } if (p2.getY() == y) { return p2.getX(); } return p1.getX() + (((y - p1.getY()) * (p2.getX() - p1.getX())) / (p2.getY() - p1.getY())); } /** * Gets the two bounding interpolation points from the specified points * suitable for determining X at the specified Y. * * @param points Points to use for interpolation. * @param startIdx Index within points from which to start search for * interpolation bounds points. * @param idxStep Index step for search for interpolation bounds points. * @param y Y value for which X should be determined. * @return the array containing two points suitable for determining X at * the specified Y. * @throws ZeroException if {@code idxStep} is 0. * @throws OutOfRangeException if specified {@code y} is not within the * range of the specified {@code points}. */ private WeightedObservedPoint[] getInterpolationPointsForY(WeightedObservedPoint[] points, int startIdx, int idxStep, double y) throws OutOfRangeException { if (idxStep == 0) { throw new ZeroException(); } for (int i = startIdx; idxStep < 0 ? i + idxStep >= 0 : i + idxStep < points.length; i += idxStep) { final WeightedObservedPoint p1 = points[i]; final WeightedObservedPoint p2 = points[i + idxStep]; if (isBetween(y, p1.getY(), p2.getY())) { if (idxStep < 0) { return new WeightedObservedPoint[] { p2, p1 }; } else { return new WeightedObservedPoint[] { p1, p2 }; } } } // Boundaries are replaced by dummy values because the raised // exception is caught and the message never displayed. // TODO: Exceptions should not be used for flow control. throw new OutOfRangeException(y, Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY); } /** * Determines whether a value is between two other values. * * @param value Value to test whether it is between {@code boundary1} * and {@code boundary2}. * @param boundary1 One end of the range. * @param boundary2 Other end of the range. * @return {@code true} if {@code value} is between {@code boundary1} and * {@code boundary2} (inclusive), {@code false} otherwise. */ private boolean isBetween(double value, double boundary1, double boundary2) { return (value >= boundary1 && value <= boundary2) || (value >= boundary2 && value <= boundary1); } } }