/*
* 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.exception.util.LocalizedFormats;
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.NullArgumentException;
/**
* Guesses the parameters ({@code a}, {@code b}, {@code c}, and {@code d})
* of a {@link ParametricGaussianFunction} based on the specified observed
* points.
*
* @since 2.2
* @version $Revision: 983921 $ $Date: 2010-08-10 12:46:06 +0200 (mar. 10 août 2010) $
*/
public class GaussianParametersGuesser {
/** 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 GaussianParametersGuesser(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 guessed parameters array <code>{a, b, c, d}</code>
*/
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 guessed parameters array <code>{a, b, c, d}</code>
*/
private double[] basicGuess(WeightedObservedPoint[] points) {
Arrays.sort(points, createWeightedObservedPointComparator());
double[] params = new double[4];
int minYIdx = findMinY(points);
params[0] = points[minYIdx].getY();
int maxYIdx = findMaxY(points);
params[1] = points[maxYIdx].getY();
params[2] = 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[3] = fwhmApprox / (2.0 * Math.sqrt(2.0 * Math.log(2.0)));
return params;
}
/**
* Finds index of point in specified points with the smallest Y.
*
* @param points points to search
*
* @return index in specified points array
*/
private int findMinY(WeightedObservedPoint[] points) {
int minYIdx = 0;
for (int i = 1; i < points.length; i++) {
if (points[i].getY() < points[minYIdx].getY()) {
minYIdx = i;
}
}
return minYIdx;
}
/**
* Finds index of point in specified points with the largest Y.
*
* @param points points to search
*
* @return 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 value of X at the specified Y
*
* @throws IllegalArgumentException if idxStep is 0
* @throws OutOfRangeException if specified <code>y</code> is not within the
* range of the specified <code>points</code>
*/
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 array containing two points suitable for determining X at the
* specified Y
*
* @throws IllegalArgumentException if idxStep is 0
* @throws OutOfRangeException if specified <code>y</code> is not within the
* range of the specified <code>points</code>
*/
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</code>
* and <code>boundary2</code>
* @param boundary1 one end of the range
* @param boundary2 other end of the range
*
* @return true if <code>value</code> is between <code>boundary1</code> and
* <code>boundary2</code> (inclusive); 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</code> for comparing
* <code>WeightedObservedPoint</code> instances.
*
* @return new <code>Comparator</code> 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;
}
};
}
}