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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    *      https://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  /*
19   * This is not the original file distributed by the Apache Software Foundation
20   * It has been modified by the Hipparchus project
21   */
22  
23  package org.hipparchus.optim.nonlinear.scalar.noderiv;
24  
25  import java.util.Arrays;
26  import java.util.Comparator;
27  
28  import org.hipparchus.analysis.MultivariateFunction;
29  import org.hipparchus.exception.LocalizedCoreFormats;
30  import org.hipparchus.exception.MathIllegalArgumentException;
31  import org.hipparchus.exception.NullArgumentException;
32  import org.hipparchus.optim.LocalizedOptimFormats;
33  import org.hipparchus.optim.OptimizationData;
34  import org.hipparchus.optim.PointValuePair;
35  import org.hipparchus.util.MathUtils;
36  
37  /**
38   * This class implements the simplex concept.
39   * It is intended to be used in conjunction with {@link SimplexOptimizer}.
40   * <br>
41   * The initial configuration of the simplex is set by the constructors
42   * {@link #AbstractSimplex(double[])} or {@link #AbstractSimplex(double[][])}.
43   * The other {@link #AbstractSimplex(int) constructor} will set all steps
44   * to 1, thus building a default configuration from a unit hypercube.
45   * <br>
46   * Users <em>must</em> call the {@link #build(double[]) build} method in order
47   * to create the data structure that will be acted on by the other methods of
48   * this class.
49   *
50   * @see SimplexOptimizer
51   */
52  public abstract class AbstractSimplex implements OptimizationData {
53      /** Simplex. */
54      private PointValuePair[] simplex;
55      /** Start simplex configuration. */
56      private double[][] startConfiguration;
57      /** Simplex dimension (must be equal to {@code simplex.length - 1}). */
58      private final int dimension;
59  
60      /**
61       * Build a unit hypercube simplex.
62       *
63       * @param n Dimension of the simplex.
64       */
65      protected AbstractSimplex(int n) {
66          this(n, 1d);
67      }
68  
69      /**
70       * Build a hypercube simplex with the given side length.
71       *
72       * @param n Dimension of the simplex.
73       * @param sideLength Length of the sides of the hypercube.
74       */
75      protected AbstractSimplex(int n,
76                                double sideLength) {
77          this(createHypercubeSteps(n, sideLength));
78      }
79  
80      /**
81       * The start configuration for simplex is built from a box parallel to
82       * the canonical axes of the space. The simplex is the subset of vertices
83       * of a box parallel to the canonical axes. It is built as the path followed
84       * while traveling from one vertex of the box to the diagonally opposite
85       * vertex moving only along the box edges. The first vertex of the box will
86       * be located at the start point of the optimization.
87       * As an example, in dimension 3 a simplex has 4 vertices. Setting the
88       * steps to (1, 10, 2) and the start point to (1, 1, 1) would imply the
89       * start simplex would be: { (1, 1, 1), (2, 1, 1), (2, 11, 1), (2, 11, 3) }.
90       * The first vertex would be set to the start point at (1, 1, 1) and the
91       * last vertex would be set to the diagonally opposite vertex at (2, 11, 3).
92       *
93       * @param steps Steps along the canonical axes representing box edges. They
94       * may be negative but not zero.
95       * @throws NullArgumentException if {@code steps} is {@code null}.
96       * @throws MathIllegalArgumentException if one of the steps is zero.
97       */
98      protected AbstractSimplex(final double[] steps) {
99          if (steps == null) {
100             throw new NullArgumentException();
101         }
102         if (steps.length == 0) {
103             throw new MathIllegalArgumentException(LocalizedCoreFormats.ZERO_NOT_ALLOWED);
104         }
105         dimension = steps.length;
106 
107         // Only the relative position of the n final vertices with respect
108         // to the first one are stored.
109         startConfiguration = new double[dimension][dimension];
110         for (int i = 0; i < dimension; i++) {
111             final double[] vertexI = startConfiguration[i];
112             for (int j = 0; j < i + 1; j++) {
113                 if (steps[j] == 0) {
114                     throw new MathIllegalArgumentException(LocalizedOptimFormats.EQUAL_VERTICES_IN_SIMPLEX);
115                 }
116                 System.arraycopy(steps, 0, vertexI, 0, j + 1);
117             }
118         }
119     }
120 
121     /**
122      * The real initial simplex will be set up by moving the reference
123      * simplex such that its first point is located at the start point of the
124      * optimization.
125      *
126      * @param referenceSimplex Reference simplex.
127      * @throws MathIllegalArgumentException if the reference simplex does not
128      * contain at least one point.
129      * @throws MathIllegalArgumentException if there is a dimension mismatch
130      * in the reference simplex.
131      * @throws IllegalArgumentException if one of its vertices is duplicated.
132      */
133     protected AbstractSimplex(final double[][] referenceSimplex) {
134         if (referenceSimplex.length <= 0) {
135             throw new MathIllegalArgumentException(LocalizedOptimFormats.SIMPLEX_NEED_ONE_POINT,
136                                                    referenceSimplex.length);
137         }
138         dimension = referenceSimplex.length - 1;
139 
140         // Only the relative position of the n final vertices with respect
141         // to the first one are stored.
142         startConfiguration = new double[dimension][dimension];
143         final double[] ref0 = referenceSimplex[0];
144 
145         // Loop over vertices.
146         for (int i = 0; i < referenceSimplex.length; i++) {
147             final double[] refI = referenceSimplex[i];
148 
149             // Safety checks.
150             if (refI.length != dimension) {
151                 throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
152                                                        refI.length, dimension);
153             }
154             for (int j = 0; j < i; j++) {
155                 final double[] refJ = referenceSimplex[j];
156                 boolean allEquals = true;
157                 for (int k = 0; k < dimension; k++) {
158                     if (refI[k] != refJ[k]) {
159                         allEquals = false;
160                         break;
161                     }
162                 }
163                 if (allEquals) {
164                     throw new MathIllegalArgumentException(LocalizedOptimFormats.EQUAL_VERTICES_IN_SIMPLEX,
165                                                            i, j);
166                 }
167             }
168 
169             // Store vertex i position relative to vertex 0 position.
170             if (i > 0) {
171                 final double[] confI = startConfiguration[i - 1];
172                 for (int k = 0; k < dimension; k++) {
173                     confI[k] = refI[k] - ref0[k];
174                 }
175             }
176         }
177     }
178 
179     /**
180      * Get simplex dimension.
181      *
182      * @return the dimension of the simplex.
183      */
184     public int getDimension() {
185         return dimension;
186     }
187 
188     /**
189      * Get simplex size.
190      * After calling the {@link #build(double[]) build} method, this method will
191      * will be equivalent to {@code getDimension() + 1}.
192      *
193      * @return the size of the simplex.
194      */
195     public int getSize() {
196         return simplex.length;
197     }
198 
199     /**
200      * Compute the next simplex of the algorithm.
201      *
202      * @param evaluationFunction Evaluation function.
203      * @param comparator Comparator to use to sort simplex vertices from best
204      * to worst.
205      * @throws org.hipparchus.exception.MathIllegalStateException
206      * if the algorithm fails to converge.
207      */
208     public abstract void iterate(MultivariateFunction evaluationFunction,
209                                  Comparator<PointValuePair> comparator);
210 
211     /**
212      * Build an initial simplex.
213      *
214      * @param startPoint First point of the simplex.
215      * @throws MathIllegalArgumentException if the start point does not match
216      * simplex dimension.
217      */
218     public void build(final double[] startPoint) {
219         if (dimension != startPoint.length) {
220             throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
221                                                    dimension, startPoint.length);
222         }
223 
224         // Set first vertex.
225         simplex = new PointValuePair[dimension + 1];
226         simplex[0] = new PointValuePair(startPoint, Double.NaN);
227 
228         // Set remaining vertices.
229         for (int i = 0; i < dimension; i++) {
230             final double[] confI = startConfiguration[i];
231             final double[] vertexI = new double[dimension];
232             for (int k = 0; k < dimension; k++) {
233                 vertexI[k] = startPoint[k] + confI[k];
234             }
235             simplex[i + 1] = new PointValuePair(vertexI, Double.NaN);
236         }
237     }
238 
239     /**
240      * Evaluate all the non-evaluated points of the simplex.
241      *
242      * @param evaluationFunction Evaluation function.
243      * @param comparator Comparator to use to sort simplex vertices from best to worst.
244      * @throws org.hipparchus.exception.MathIllegalStateException
245      * if the maximal number of evaluations is exceeded.
246      */
247     public void evaluate(final MultivariateFunction evaluationFunction,
248                          final Comparator<PointValuePair> comparator) {
249         // Evaluate the objective function at all non-evaluated simplex points.
250         for (int i = 0; i < simplex.length; i++) {
251             final PointValuePair vertex = simplex[i];
252             final double[] point = vertex.getPointRef();
253             if (Double.isNaN(vertex.getValue())) {
254                 simplex[i] = new PointValuePair(point, evaluationFunction.value(point), false);
255             }
256         }
257 
258         // Sort the simplex from best to worst.
259         Arrays.sort(simplex, comparator);
260     }
261 
262     /**
263      * Replace the worst point of the simplex by a new point.
264      *
265      * @param pointValuePair Point to insert.
266      * @param comparator Comparator to use for sorting the simplex vertices
267      * from best to worst.
268      */
269     protected void replaceWorstPoint(PointValuePair pointValuePair,
270                                      final Comparator<PointValuePair> comparator) {
271         for (int i = 0; i < dimension; i++) {
272             if (comparator.compare(simplex[i], pointValuePair) > 0) {
273                 PointValuePair tmp = simplex[i];
274                 simplex[i] = pointValuePair;
275                 pointValuePair = tmp;
276             }
277         }
278         simplex[dimension] = pointValuePair;
279     }
280 
281     /**
282      * Get the points of the simplex.
283      *
284      * @return all the simplex points.
285      */
286     public PointValuePair[] getPoints() {
287         final PointValuePair[] copy = new PointValuePair[simplex.length];
288         System.arraycopy(simplex, 0, copy, 0, simplex.length);
289         return copy;
290     }
291 
292     /**
293      * Get the simplex point stored at the requested {@code index}.
294      *
295      * @param index Location.
296      * @return the point at location {@code index}.
297      */
298     public PointValuePair getPoint(int index) {
299         MathUtils.checkRangeInclusive(index, 0, simplex.length - 1);
300         return simplex[index];
301     }
302 
303     /**
304      * Store a new point at location {@code index}.
305      * Note that no deep-copy of {@code point} is performed.
306      *
307      * @param index Location.
308      * @param point New value.
309      */
310     protected void setPoint(int index, PointValuePair point) {
311         MathUtils.checkRangeInclusive(index, 0, simplex.length - 1);
312         simplex[index] = point;
313     }
314 
315     /**
316      * Replace all points.
317      * Note that no deep-copy of {@code points} is performed.
318      *
319      * @param points New Points.
320      */
321     protected void setPoints(PointValuePair[] points) {
322         if (points.length != simplex.length) {
323             throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
324                                                    points.length, simplex.length);
325         }
326         simplex = points.clone();
327     }
328 
329     /**
330      * Create steps for a unit hypercube.
331      *
332      * @param n Dimension of the hypercube.
333      * @param sideLength Length of the sides of the hypercube.
334      * @return the steps.
335      */
336     private static double[] createHypercubeSteps(int n,
337                                                  double sideLength) {
338         final double[] steps = new double[n];
339         for (int i = 0; i < n; i++) {
340             steps[i] = sideLength;
341         }
342         return steps;
343     }
344 }