/*
* 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 java.util.Arrays;
import java.util.Comparator;
import org.apache.commons.math.analysis.function.Gaussian;
import org.apache.commons.math.analysis.ParametricUnivariateRealFunction;
import org.apache.commons.math.exception.NullArgumentException;
import org.apache.commons.math.exception.NumberIsTooSmallException;
import org.apache.commons.math.exception.OutOfRangeException;
import org.apache.commons.math.exception.ZeroException;
import org.apache.commons.math.exception.NotStrictlyPositiveException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
import org.apache.commons.math.optimization.fitting.CurveFitter;
import org.apache.commons.math.optimization.fitting.WeightedObservedPoint;
/**
* Fits points to a {@link
* org.apache.commons.math.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 1131229 2011-06-03 20:49:25Z luc $
*/
public class GaussianFitter extends CurveFitter {
/**
* Constructs an instance using the specified optimizer.
*
* @param optimizer Optimizer to use for the fitting.
*/
public GaussianFitter(DifferentiableMultivariateVectorialOptimizer 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).
*/
public double[] fit(double[] initialGuess) {
final ParametricUnivariateRealFunction f = new ParametricUnivariateRealFunction() {
private final ParametricUnivariateRealFunction g = new Gaussian.Parametric();
public double value(double x, double ... p) {
double v = Double.POSITIVE_INFINITY;
try {
v = g.value(x, p);
} catch (NotStrictlyPositiveException e) {
// Do nothing.
}
return v;
}
public double[] gradient(double x, double ... p) {
double[] v = { Double.POSITIVE_INFINITY,
Double.POSITIVE_INFINITY,
Double.POSITIVE_INFINITY };
try {
v = g.gradient(x, p);
} catch (NotStrictlyPositiveException e) {
// 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.math.analysis.function.Gaussian.Parametric}
* based on the specified observed points.
*/
public static class ParameterGuesser {
/** Observed points. */
private final WeightedObservedPoint[] observations;
/** Resulting guessed parameters. */
private double[] parameters;
/**
* Constructs instance with the specified observed points.
*
* @param observations observed points upon which should base guess
*/
public ParameterGuesser(WeightedObservedPoint[] observations) {
if (observations == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
if (observations.length < 3) {
throw new NumberIsTooSmallException(observations.length, 3, true);
}
this.observations = observations.clone();
}
/**
* Guesses the parameters based on the observed points.
*
* @return the guessed parameters: norm, mean and sigma.
*/
public double[] guess() {
if (parameters == null) {
parameters = basicGuess(observations);
}
return parameters.clone();
}
/**
* Guesses the parameters based on the specified observed points.
*
* @param points Observed points upon which should base guess.
* @return the guessed parameters: norm, mean and sigma.
*/
private double[] basicGuess(WeightedObservedPoint[] points) {
Arrays.sort(points, createWeightedObservedPointComparator());
double[] params = new double[3];
int maxYIdx = findMaxY(points);
params[0] = points[maxYIdx].getY();
params[1] = points[maxYIdx].getX();
double fwhmApprox;
try {
double halfY = params[0] + ((params[1] - params[0]) / 2.0);
double fwhmX1 = interpolateXAtY(points, maxYIdx, -1, halfY);
double fwhmX2 = interpolateXAtY(points, maxYIdx, +1, halfY);
fwhmApprox = fwhmX2 - fwhmX1;
} catch (OutOfRangeException e) {
fwhmApprox = points[points.length - 1].getX() - points[0].getX();
}
params[2] = fwhmApprox / (2.0 * Math.sqrt(2.0 * Math.log(2.0)));
return params;
}
/**
* 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 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 value of 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 double interpolateXAtY(WeightedObservedPoint[] points,
int startIdx, int idxStep, double y)
throws OutOfRangeException {
if (idxStep == 0) {
throw new ZeroException();
}
WeightedObservedPoint[] twoPoints = getInterpolationPointsForY(points, startIdx, idxStep, y);
WeightedObservedPoint pointA = twoPoints[0];
WeightedObservedPoint pointB = twoPoints[1];
if (pointA.getY() == y) {
return pointA.getX();
}
if (pointB.getY() == y) {
return pointB.getX();
}
return pointA.getX() +
(((y - pointA.getY()) * (pointB.getX() - pointA.getX())) /
(pointB.getY() - pointA.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) {
if (isBetween(y, points[i].getY(), points[i + idxStep].getY())) {
return (idxStep < 0) ?
new WeightedObservedPoint[] { points[i + idxStep], points[i] } :
new WeightedObservedPoint[] { points[i], points[i + idxStep] };
}
}
double minY = Double.POSITIVE_INFINITY;
double maxY = Double.NEGATIVE_INFINITY;
for (final WeightedObservedPoint point : points) {
minY = Math.min(minY, point.getY());
maxY = Math.max(maxY, point.getY());
}
throw new OutOfRangeException(y, minY, maxY);
}
/**
* Determines whether a value is between two other values.
*
* @param value Value to determine whether 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);
}
/**
* Factory method creating {@code Comparator} for comparing
* {@code WeightedObservedPoint} instances.
*
* @return the new {@code Comparator} instance.
*/
private Comparator<WeightedObservedPoint> createWeightedObservedPointComparator() {
return 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;
}
};
}
}
}