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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  package org.apache.commons.math3.optimization.fitting;
19  
20  import java.util.Arrays;
21  import java.util.Comparator;
22  
23  import org.apache.commons.math3.analysis.function.Gaussian;
24  import org.apache.commons.math3.exception.NullArgumentException;
25  import org.apache.commons.math3.exception.NumberIsTooSmallException;
26  import org.apache.commons.math3.exception.OutOfRangeException;
27  import org.apache.commons.math3.exception.ZeroException;
28  import org.apache.commons.math3.exception.NotStrictlyPositiveException;
29  import org.apache.commons.math3.exception.util.LocalizedFormats;
30  import org.apache.commons.math3.optimization.DifferentiableMultivariateVectorOptimizer;
31  import org.apache.commons.math3.util.FastMath;
32  
33  /**
34   * Fits points to a {@link
35   * org.apache.commons.math3.analysis.function.Gaussian.Parametric Gaussian} function.
36   * <p>
37   * Usage example:
38   * <pre>
39   *   GaussianFitter fitter = new GaussianFitter(
40   *     new LevenbergMarquardtOptimizer());
41   *   fitter.addObservedPoint(4.0254623,  531026.0);
42   *   fitter.addObservedPoint(4.03128248, 984167.0);
43   *   fitter.addObservedPoint(4.03839603, 1887233.0);
44   *   fitter.addObservedPoint(4.04421621, 2687152.0);
45   *   fitter.addObservedPoint(4.05132976, 3461228.0);
46   *   fitter.addObservedPoint(4.05326982, 3580526.0);
47   *   fitter.addObservedPoint(4.05779662, 3439750.0);
48   *   fitter.addObservedPoint(4.0636168,  2877648.0);
49   *   fitter.addObservedPoint(4.06943698, 2175960.0);
50   *   fitter.addObservedPoint(4.07525716, 1447024.0);
51   *   fitter.addObservedPoint(4.08237071, 717104.0);
52   *   fitter.addObservedPoint(4.08366408, 620014.0);
53   *   double[] parameters = fitter.fit();
54   * </pre>
55   *
56   * @since 2.2
57   * @version $Id: GaussianFitter.java 1422230 2012-12-15 12:11:13Z erans $
58   * @deprecated As of 3.1 (to be removed in 4.0).
59   */
60  @Deprecated
61  public class GaussianFitter extends CurveFitter<Gaussian.Parametric> {
62      /**
63       * Constructs an instance using the specified optimizer.
64       *
65       * @param optimizer Optimizer to use for the fitting.
66       */
67      public GaussianFitter(DifferentiableMultivariateVectorOptimizer optimizer) {
68          super(optimizer);
69      }
70  
71      /**
72       * Fits a Gaussian function to the observed points.
73       *
74       * @param initialGuess First guess values in the following order:
75       * <ul>
76       *  <li>Norm</li>
77       *  <li>Mean</li>
78       *  <li>Sigma</li>
79       * </ul>
80       * @return the parameters of the Gaussian function that best fits the
81       * observed points (in the same order as above).
82       * @since 3.0
83       */
84      public double[] fit(double[] initialGuess) {
85          final Gaussian.Parametric f = new Gaussian.Parametric() {
86                  @Override
87                  public double value(double x, double ... p) {
88                      double v = Double.POSITIVE_INFINITY;
89                      try {
90                          v = super.value(x, p);
91                      } catch (NotStrictlyPositiveException e) { // NOPMD
92                          // Do nothing.
93                      }
94                      return v;
95                  }
96  
97                  @Override
98                  public double[] gradient(double x, double ... p) {
99                      double[] v = { Double.POSITIVE_INFINITY,
100                                    Double.POSITIVE_INFINITY,
101                                    Double.POSITIVE_INFINITY };
102                     try {
103                         v = super.gradient(x, p);
104                     } catch (NotStrictlyPositiveException e) { // NOPMD
105                         // Do nothing.
106                     }
107                     return v;
108                 }
109             };
110 
111         return fit(f, initialGuess);
112     }
113 
114     /**
115      * Fits a Gaussian function to the observed points.
116      *
117      * @return the parameters of the Gaussian function that best fits the
118      * observed points (in the same order as above).
119      */
120     public double[] fit() {
121         final double[] guess = (new ParameterGuesser(getObservations())).guess();
122         return fit(guess);
123     }
124 
125     /**
126      * Guesses the parameters {@code norm}, {@code mean}, and {@code sigma}
127      * of a {@link org.apache.commons.math3.analysis.function.Gaussian.Parametric}
128      * based on the specified observed points.
129      */
130     public static class ParameterGuesser {
131         /** Normalization factor. */
132         private final double norm;
133         /** Mean. */
134         private final double mean;
135         /** Standard deviation. */
136         private final double sigma;
137 
138         /**
139          * Constructs instance with the specified observed points.
140          *
141          * @param observations Observed points from which to guess the
142          * parameters of the Gaussian.
143          * @throws NullArgumentException if {@code observations} is
144          * {@code null}.
145          * @throws NumberIsTooSmallException if there are less than 3
146          * observations.
147          */
148         public ParameterGuesser(WeightedObservedPoint[] observations) {
149             if (observations == null) {
150                 throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
151             }
152             if (observations.length < 3) {
153                 throw new NumberIsTooSmallException(observations.length, 3, true);
154             }
155 
156             final WeightedObservedPoint[] sorted = sortObservations(observations);
157             final double[] params = basicGuess(sorted);
158 
159             norm = params[0];
160             mean = params[1];
161             sigma = params[2];
162         }
163 
164         /**
165          * Gets an estimation of the parameters.
166          *
167          * @return the guessed parameters, in the following order:
168          * <ul>
169          *  <li>Normalization factor</li>
170          *  <li>Mean</li>
171          *  <li>Standard deviation</li>
172          * </ul>
173          */
174         public double[] guess() {
175             return new double[] { norm, mean, sigma };
176         }
177 
178         /**
179          * Sort the observations.
180          *
181          * @param unsorted Input observations.
182          * @return the input observations, sorted.
183          */
184         private WeightedObservedPoint[] sortObservations(WeightedObservedPoint[] unsorted) {
185             final WeightedObservedPoint[] observations = unsorted.clone();
186             final Comparator<WeightedObservedPoint> cmp
187                 = new Comparator<WeightedObservedPoint>() {
188                 public int compare(WeightedObservedPoint p1,
189                                    WeightedObservedPoint p2) {
190                     if (p1 == null && p2 == null) {
191                         return 0;
192                     }
193                     if (p1 == null) {
194                         return -1;
195                     }
196                     if (p2 == null) {
197                         return 1;
198                     }
199                     if (p1.getX() < p2.getX()) {
200                         return -1;
201                     }
202                     if (p1.getX() > p2.getX()) {
203                         return 1;
204                     }
205                     if (p1.getY() < p2.getY()) {
206                         return -1;
207                     }
208                     if (p1.getY() > p2.getY()) {
209                         return 1;
210                     }
211                     if (p1.getWeight() < p2.getWeight()) {
212                         return -1;
213                     }
214                     if (p1.getWeight() > p2.getWeight()) {
215                         return 1;
216                     }
217                     return 0;
218                 }
219             };
220 
221             Arrays.sort(observations, cmp);
222             return observations;
223         }
224 
225         /**
226          * Guesses the parameters based on the specified observed points.
227          *
228          * @param points Observed points, sorted.
229          * @return the guessed parameters (normalization factor, mean and
230          * sigma).
231          */
232         private double[] basicGuess(WeightedObservedPoint[] points) {
233             final int maxYIdx = findMaxY(points);
234             final double n = points[maxYIdx].getY();
235             final double m = points[maxYIdx].getX();
236 
237             double fwhmApprox;
238             try {
239                 final double halfY = n + ((m - n) / 2);
240                 final double fwhmX1 = interpolateXAtY(points, maxYIdx, -1, halfY);
241                 final double fwhmX2 = interpolateXAtY(points, maxYIdx, 1, halfY);
242                 fwhmApprox = fwhmX2 - fwhmX1;
243             } catch (OutOfRangeException e) {
244                 // TODO: Exceptions should not be used for flow control.
245                 fwhmApprox = points[points.length - 1].getX() - points[0].getX();
246             }
247             final double s = fwhmApprox / (2 * FastMath.sqrt(2 * FastMath.log(2)));
248 
249             return new double[] { n, m, s };
250         }
251 
252         /**
253          * Finds index of point in specified points with the largest Y.
254          *
255          * @param points Points to search.
256          * @return the index in specified points array.
257          */
258         private int findMaxY(WeightedObservedPoint[] points) {
259             int maxYIdx = 0;
260             for (int i = 1; i < points.length; i++) {
261                 if (points[i].getY() > points[maxYIdx].getY()) {
262                     maxYIdx = i;
263                 }
264             }
265             return maxYIdx;
266         }
267 
268         /**
269          * Interpolates using the specified points to determine X at the
270          * specified Y.
271          *
272          * @param points Points to use for interpolation.
273          * @param startIdx Index within points from which to start the search for
274          * interpolation bounds points.
275          * @param idxStep Index step for searching interpolation bounds points.
276          * @param y Y value for which X should be determined.
277          * @return the value of X for the specified Y.
278          * @throws ZeroException if {@code idxStep} is 0.
279          * @throws OutOfRangeException if specified {@code y} is not within the
280          * range of the specified {@code points}.
281          */
282         private double interpolateXAtY(WeightedObservedPoint[] points,
283                                        int startIdx,
284                                        int idxStep,
285                                        double y)
286             throws OutOfRangeException {
287             if (idxStep == 0) {
288                 throw new ZeroException();
289             }
290             final WeightedObservedPoint[] twoPoints
291                 = getInterpolationPointsForY(points, startIdx, idxStep, y);
292             final WeightedObservedPoint p1 = twoPoints[0];
293             final WeightedObservedPoint p2 = twoPoints[1];
294             if (p1.getY() == y) {
295                 return p1.getX();
296             }
297             if (p2.getY() == y) {
298                 return p2.getX();
299             }
300             return p1.getX() + (((y - p1.getY()) * (p2.getX() - p1.getX())) /
301                                 (p2.getY() - p1.getY()));
302         }
303 
304         /**
305          * Gets the two bounding interpolation points from the specified points
306          * suitable for determining X at the specified Y.
307          *
308          * @param points Points to use for interpolation.
309          * @param startIdx Index within points from which to start search for
310          * interpolation bounds points.
311          * @param idxStep Index step for search for interpolation bounds points.
312          * @param y Y value for which X should be determined.
313          * @return the array containing two points suitable for determining X at
314          * the specified Y.
315          * @throws ZeroException if {@code idxStep} is 0.
316          * @throws OutOfRangeException if specified {@code y} is not within the
317          * range of the specified {@code points}.
318          */
319         private WeightedObservedPoint[] getInterpolationPointsForY(WeightedObservedPoint[] points,
320                                                                    int startIdx,
321                                                                    int idxStep,
322                                                                    double y)
323             throws OutOfRangeException {
324             if (idxStep == 0) {
325                 throw new ZeroException();
326             }
327             for (int i = startIdx;
328                  idxStep < 0 ? i + idxStep >= 0 : i + idxStep < points.length;
329                  i += idxStep) {
330                 final WeightedObservedPoint p1 = points[i];
331                 final WeightedObservedPoint p2 = points[i + idxStep];
332                 if (isBetween(y, p1.getY(), p2.getY())) {
333                     if (idxStep < 0) {
334                         return new WeightedObservedPoint[] { p2, p1 };
335                     } else {
336                         return new WeightedObservedPoint[] { p1, p2 };
337                     }
338                 }
339             }
340 
341             // Boundaries are replaced by dummy values because the raised
342             // exception is caught and the message never displayed.
343             // TODO: Exceptions should not be used for flow control.
344             throw new OutOfRangeException(y,
345                                           Double.NEGATIVE_INFINITY,
346                                           Double.POSITIVE_INFINITY);
347         }
348 
349         /**
350          * Determines whether a value is between two other values.
351          *
352          * @param value Value to test whether it is between {@code boundary1}
353          * and {@code boundary2}.
354          * @param boundary1 One end of the range.
355          * @param boundary2 Other end of the range.
356          * @return {@code true} if {@code value} is between {@code boundary1} and
357          * {@code boundary2} (inclusive), {@code false} otherwise.
358          */
359         private boolean isBetween(double value,
360                                   double boundary1,
361                                   double boundary2) {
362             return (value >= boundary1 && value <= boundary2) ||
363                 (value >= boundary2 && value <= boundary1);
364         }
365     }
366 }