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source: stable/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/SymbolicDataAnalysisExpressionTreeSimplifierTest.cs @ 17932

Last change on this file since 17932 was 17862, checked in by gkronber, 4 years ago

#2985: merged r17797,r17796,r17820 from trunk to stable
File size: 18.7 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21using System;
22using System.Globalization;
23using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
24using Microsoft.VisualStudio.TestTools.UnitTesting;
25
26namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Tests {
27
28  [TestClass()]
29  public class SymbolicDataAnalysisExpressionTreeSimplifierTest {
30
31    [TestMethod]
32    [TestCategory("Problems.DataAnalysis")]
33    [TestProperty("Time", "short")]
34    public void SimplifierAxiomsTest() {
35      SymbolicExpressionImporter importer = new SymbolicExpressionImporter();
36      SymbolicExpressionTreeStringFormatter formatter = new SymbolicExpressionTreeStringFormatter();
37      #region single argument arithmetics
38
39      AssertEqualAfterSimplification("(+ 1.0)", "1.0");
40      AssertEqualAfterSimplification("(- 1.0)", "-1.0");
41      AssertEqualAfterSimplification("(- (variable 2.0 a))", "(variable -2.0 a)");
42      AssertEqualAfterSimplification("(* 2.0)", "2.0");
43      AssertEqualAfterSimplification("(* (variable 2.0 a))", "(variable 2.0 a)");
44      AssertEqualAfterSimplification("(/ 2.0)", "0.5");
45      AssertEqualAfterSimplification("(/ (variable 2.0 a))", "(/ 1.0 (variable 2.0 a))");
46      #endregion
47
48      #region aggregation of constants into factors
49      AssertEqualAfterSimplification("(* 2.0 (variable 2.0 a))", "(variable 4.0 a)");
50      AssertEqualAfterSimplification("(/ (variable 2.0 a) 2.0)", "(variable 1.0 a)");
51      AssertEqualAfterSimplification("(/ (variable 2.0 a) (* 2.0 2.0))", "(variable 0.5 a)");
52      #endregion
53
54      #region constant and variable folding
55      AssertEqualAfterSimplification("(+ 1.0 2.0)", "3.0");
56      AssertEqualAfterSimplification("(+ (variable 2.0 a) (variable 2.0 a))", "(variable 4.0 a)");
57      AssertEqualAfterSimplification("(- (variable 2.0 a) (variable 1.0 a))", "(variable 1.0 a)");
58      AssertEqualAfterSimplification("(* (variable 2.0 a) (variable 2.0 a))", "(* (* (variable 1.0 a) (variable 1.0 a)) 4.0)");
59      AssertEqualAfterSimplification("(/ (variable 1.0 a) (variable 2.0 a))", "0.5");
60      #endregion
61
62      #region logarithm rules
63
64      // cancellation
65      AssertEqualAfterSimplification("(log (exp (variable 2.0 a)))", "(variable 2.0 a)");
66      // must not transform logs in this way as we do not know wether both variables are positive
67      AssertEqualAfterSimplification("(log (* (variable 1.0 a) (variable 1.0 b)))", "(log (* (variable 1.0 a) (variable 1.0 b)))");
68      // must not transform logs in this way as we do not know wether both variables are positive
69      AssertEqualAfterSimplification("(log (/ (variable 1.0 a) (variable 1.0 b)))", "(log (/ (variable 1.0 a) (variable 1.0 b)))");
70      #endregion
71
72      #region exponentiation rules
73      // cancellation
74      AssertEqualAfterSimplification("(exp (log (variable 2.0 a)))", "(variable 2.0 a)");
75      // exp transformation
76      AssertEqualAfterSimplification("(exp (+ (variable 2.0 a) (variable 3.0 b)))", "(* (exp (variable 2.0 a)) (exp (variable 3.0 b)))");
77      // exp transformation
78      AssertEqualAfterSimplification("(exp (- (variable 2.0 a) (variable 3.0 b)))", "(* (exp (variable 2.0 a)) (exp (variable -3.0 b)))");
79      // exp transformation
80      AssertEqualAfterSimplification("(exp (- (variable 2.0 a) (* (variable 3.0 b) (variable 4.0 c))))", "(* (exp (variable 2.0 a)) (exp (* (variable 1.0 b) (variable 1.0 c) -12.0)))");
81      // exp transformation
82      AssertEqualAfterSimplification("(exp (- (variable 2.0 a) (* (variable 3.0 b) (cos (variable 4.0 c)))))", "(* (exp (variable 2.0 a)) (exp (* (variable 1.0 b) (cos (variable 4.0 c)) -3.0)))");
83      #endregion
84
85      #region power rules
86
87      // cancellation
88      AssertEqualAfterSimplification("(pow (variable 2.0 a) 0.0)", "1.0");
89      // fixed point
90      AssertEqualAfterSimplification("(pow (variable 2.0 a) 1.0)", "(variable 2.0 a)");
91      // inversion fixed point
92      AssertEqualAfterSimplification("(pow (variable 2.0 a) -1.0)", "(/ 1.0 (variable 2.0 a))");
93      // inversion
94      AssertEqualAfterSimplification("(pow (variable 2.0 a) -2.0)", "(/ 1.0 (pow (variable 2.0 a) 2.0))");
95      // constant folding
96      AssertEqualAfterSimplification("(pow 3.0 2.0)", "9.0");
97      #endregion
98
99      #region root rules
100      // cancellation
101      AssertEqualAfterSimplification("(root (variable 2.0 a) 0.0)", "NaN");
102      // fixed point
103      AssertEqualAfterSimplification("(root (variable 2.0 a) 1.0)", "(variable 2.0 a)");
104      // inversion fixed point
105      AssertEqualAfterSimplification("(root (variable 2.0 a) -1.0)", "(/ 1.0 (variable 2.0 a))");
106      // inversion
107      AssertEqualAfterSimplification("(root (variable 2.0 a) -2.0)", "(/ 1.0 (root (variable 2.0 a) 2.0))");
108      // constant folding
109      AssertEqualAfterSimplification("(root 9.0 2.0)", "3.0");
110      #endregion
111
112      #region boolean operations
113      // always true and
114      AssertEqualAfterSimplification("(and 1.0 2.0)", "1.0");
115      // always false and
116      AssertEqualAfterSimplification("(and 1.0 -2.0)", "-1.0");
117      // always true or
118      AssertEqualAfterSimplification("(or -1.0 2.0)", "1.0");
119      // always false or
120      AssertEqualAfterSimplification("(or -1.0 -2.0)", "-1.0");
121      // constant not
122      AssertEqualAfterSimplification("(not -2.0)", "1.0");
123      // constant not
124      AssertEqualAfterSimplification("(not 2.0)", "-1.0");
125      // constant not
126      AssertEqualAfterSimplification("(not 0.0)", "1.0");
127      // nested nots
128      AssertEqualAfterSimplification("(not (not 1.0))", "1.0");
129      // not of non-Boolean argument
130      AssertEqualAfterSimplification("(not (variable 1.0 a))", "(not (> (variable 1.0 a) 0.0))");
131      // not Boolean argument
132      AssertEqualAfterSimplification("(not (and (> (variable 1.0 a) 0.0) (> (variable 1.0 a) 0.0)))", "(not (and (> (variable 1.0 a) 0.0) (> (variable 1.0 a) 0.0)))");
133      #endregion
134
135      #region conditionals
136      // always false
137      AssertEqualAfterSimplification("(if -1.0 (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)");
138      // always true
139      AssertEqualAfterSimplification("(if 1.0 (variable 2.0 a) (variable 3.0 a))", "(variable 2.0 a)");
140      // always false (0.0)
141      AssertEqualAfterSimplification("(if 0.0 (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)");
142      // complex constant condition (always false)
143      AssertEqualAfterSimplification("(if (* 1.0 -2.0) (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)");
144      // complex constant condition (always false)
145      AssertEqualAfterSimplification("(if (/ (variable 1.0 a) (variable -2.0 a)) (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)");
146      // insertion of relational operator
147      AssertEqualAfterSimplification("(if (variable 1.0 a) (variable 2.0 a) (variable 3.0 a))", "(if (> (variable 1.0 a) 0.0) (variable 2.0 a) (variable 3.0 a))");
148      #endregion
149
150      #region factor variables
151      AssertEqualAfterSimplification("(factor a 1.0)", "(factor a 1.0)");
152      // factor folding
153      AssertEqualAfterSimplification("(+ (factor a 1.0 1.0) (factor a 2.0 3.0))", "(factor a 3.0 4.0)");
154      AssertEqualAfterSimplification("(- (factor a 1.0 1.0) (factor a 2.0 3.0))", "(factor a -1.0 -2.0)");
155      AssertEqualAfterSimplification("(* (factor a 2.0 2.0) (factor a 2.0 3.0))", "(factor a 4.0 6.0)");
156      AssertEqualAfterSimplification("(/ (factor a 2.0 5.0))", "(factor a 0.5 0.2)");
157      AssertEqualAfterSimplification("(/ (factor a 4.0 6.0) (factor a 2.0 3.0))", "(factor a 2.0 2.0)");
158      AssertEqualAfterSimplification("(+ 3.0 (factor a 4.0 6.0))", "(factor a 7.0 9.0)");
159      AssertEqualAfterSimplification("(+ (factor a 4.0 6.0) 3.0)", "(factor a 7.0 9.0)");
160      AssertEqualAfterSimplification("(- 3.0 (factor a 4.0 6.0))", "(factor a -1.0 -3.0)");
161      AssertEqualAfterSimplification("(- (factor a 4.0 6.0) 3.0)", "(factor a 1.0 3.0)");
162      AssertEqualAfterSimplification("(* 2.0 (factor a 4.0 6.0))", "(factor a 8.0 12.0)");
163      AssertEqualAfterSimplification("(* (factor a 4.0 6.0) 2.0)", "(factor a 8.0 12.0)");
164      AssertEqualAfterSimplification("(* (factor a 4.0 6.0) (variable 2.0 a))", "(* (factor a 8.0 12.0) (variable 1.0 a))"); // not possible (a is used as factor and double variable) interpreter will fail
165      AssertEqualAfterSimplification(
166        "(log (factor a 10.0 100.0))",
167        string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1})", Math.Log(10.0), Math.Log(100.0)));
168      AssertEqualAfterSimplification(
169        "(exp (factor a 2.0 3.0))",
170        string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1})", Math.Exp(2.0), Math.Exp(3.0)));
171      AssertEqualAfterSimplification("(sqrt (factor a 9.0 16.0))", "(factor a 3.0 4.0))");
172      AssertEqualAfterSimplification("(sqr (factor a 2.0 3.0))", "(factor a 4.0 9.0))");
173      AssertEqualAfterSimplification("(root (factor a 8.0 27.0) 3)", "(factor a 2.0 3.0))");
174      AssertEqualAfterSimplification("(pow (factor a 2.0 3.0) 3)", "(factor a 8.0 27.0))");
175
176      AssertEqualAfterSimplification("(sin (factor a 1.0 2.0) )",
177        string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1}))", Math.Sin(1.0), Math.Sin(2.0)));
178      AssertEqualAfterSimplification("(cos (factor a 1.0 2.0) )",
179        string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1}))", Math.Cos(1.0), Math.Cos(2.0)));
180      AssertEqualAfterSimplification("(tan (factor a 1.0 2.0) )",
181        string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1}))", Math.Tan(1.0), Math.Tan(2.0)));
182
183
184      AssertEqualAfterSimplification("(binfactor a val 1.0)", "(binfactor a val 1.0)");
185      // binfactor folding
186      AssertEqualAfterSimplification("(+ (binfactor a val 1.0) (binfactor a val 2.0))", "(binfactor a val 3.0)");
187      AssertEqualAfterSimplification("(+ (binfactor a val0 1.0) (binfactor a val1 2.0))", "(+ (binfactor a val0 1.0) (binfactor a val1 2.0))"); // cannot be simplified (different vals)
188      AssertEqualAfterSimplification("(+ (binfactor a val 1.0) (binfactor b val 2.0))", "(+ (binfactor a val 1.0) (binfactor b val 2.0))"); // cannot be simplified (different vars)
189      AssertEqualAfterSimplification("(- (binfactor a val 1.0) (binfactor a val 2.0))", "(binfactor a val -1.0)");
190      AssertEqualAfterSimplification("(* (binfactor a val 2.0) (binfactor a val 3.0))", "(binfactor a val 6.0)");
191      AssertEqualAfterSimplification("(/ (binfactor a val 6.0) (binfactor a val 3.0))", "(/ (binfactor a val 6.0) (binfactor a val 3.0))"); // not allowed! 0/0 for other values than 'val'
192      AssertEqualAfterSimplification("(/ (binfactor a val 4.0))", "(/ 1.0 (binfactor a val 4.0))"); // not allowed!
193
194      AssertEqualAfterSimplification("(+ 3.0 (binfactor a val 4.0 ))", "(+ (binfactor a val 4.0 ) 3.0))"); // not allowed
195      AssertEqualAfterSimplification("(- 3.0 (binfactor a val 4.0 ))", "(+ (binfactor a val -4.0 ) 3.0)");
196      AssertEqualAfterSimplification("(+ (binfactor a val 4.0 ) 3.0)", "(+ (binfactor a val 4.0 ) 3.0)");  // not allowed
197      AssertEqualAfterSimplification("(- (binfactor a val 4.0 ) 3.0)", "(+ (binfactor a val 4.0 ) -3.0)");
198      AssertEqualAfterSimplification("(* 2.0 (binfactor a val 4.0))", "(binfactor a val 8.0 )");
199      AssertEqualAfterSimplification("(* (binfactor a val 4.0) 2.0)", "(binfactor a val 8.0 )");
200      AssertEqualAfterSimplification("(* (binfactor a val 4.0) (variable 2.0 a))", "(* (binfactor a val 1.0) (variable 1.0 a) 8.0)");   // not possible (a is used as factor and double variable) interpreter will fail
201      AssertEqualAfterSimplification("(log (binfactor a val 10.0))", "(log (binfactor a val 10.0))"); // not allowed (log(0))
202
203      // exp( binfactor w val=a) = if(val=a) exp(w) else exp(0) = binfactor( (exp(w) - 1) val a) + 1
204      AssertEqualAfterSimplification("(exp (binfactor a val 3.0))",
205        string.Format(CultureInfo.InvariantCulture, "(+ (binfactor a val {0}) 1.0)", Math.Exp(3.0) - 1)
206        );
207      AssertEqualAfterSimplification("(sqrt (binfactor a val 16.0))", "(binfactor a val 4.0))"); // sqrt(0) = 0
208      AssertEqualAfterSimplification("(sqr (binfactor a val 3.0))", "(binfactor a val 9.0))"); // 0*0 = 0
209      AssertEqualAfterSimplification("(root (binfactor a val 27.0) 3)", "(binfactor a val 3.0))");
210      AssertEqualAfterSimplification("(pow (binfactor a val 3.0) 3)", "(binfactor a val 27.0))");
211
212      AssertEqualAfterSimplification("(sin (binfactor a val 2.0) )",
213        string.Format(CultureInfo.InvariantCulture, "(binfactor a val {0}))", Math.Sin(2.0))); // sin(0) = 0
214      AssertEqualAfterSimplification("(cos (binfactor a val 2.0) )",
215        string.Format(CultureInfo.InvariantCulture, "(+ (binfactor a val {0}) 1.0)", Math.Cos(2.0) - 1)); // cos(0) = 1
216      AssertEqualAfterSimplification("(tan (binfactor a val 2.0) )",
217        string.Format(CultureInfo.InvariantCulture, "(binfactor a val {0}))", Math.Tan(2.0))); // tan(0) = 0
218
219      // combination of factor and binfactor
220      AssertEqualAfterSimplification("(+ (binfactor a x0 2.0) (factor a 2.0 3.0))", "(factor a 4.0 3.0)");
221      AssertEqualAfterSimplification("(+ (factor a 2.0 3.0) (binfactor a x0 2.0))", "(factor a 4.0 3.0)");
222      AssertEqualAfterSimplification("(* (binfactor a x1 2.0) (factor a 2.0 3.0))", "(binfactor a x1 6.0)"); // all other values have weight zero in binfactor
223      AssertEqualAfterSimplification("(* (factor a 2.0 3.0) (binfactor a x1 2.0))", "(binfactor a x1 6.0)"); // all other values have weight zero in binfactor
224      AssertEqualAfterSimplification("(/ (binfactor a x0 2.0) (factor a 2.0 3.0))", "(binfactor a x0 1.0)");
225      AssertEqualAfterSimplification("(/ (factor a 2.0 3.0) (binfactor a x0 2.0))",
226        string.Format(CultureInfo.InvariantCulture, "(factor a 1.0 {0})", 3.0 / 0.0));
227      AssertEqualAfterSimplification("(- (binfactor a x0 2.0) (factor a 2.0 3.0))", "(factor a 0.0 -3.0)");
228      AssertEqualAfterSimplification("(- (factor a 2.0 3.0) (binfactor a x0 2.0))", "(factor a 0.0 3.0)");
229      #endregion
230
231      #region abs
232      AssertEqualAfterSimplification("(abs 2.0)", "2.0");
233      AssertEqualAfterSimplification("(abs -2.0)", "2.0"); // constant folding
234      AssertEqualAfterSimplification("(abs (exp (variable 2.0 x)))", "(exp (variable 2.0 x)))"); // exp is always positive
235      AssertEqualAfterSimplification("(abs (exp (variable 2.0 x)))", "(exp (variable 2.0 x)))"); // exp is always positive
236      AssertEqualAfterSimplification("(abs (sqr (variable 2.0 a)))", "(sqr (variable 2.0 a))"); // sqr is always positive
237      AssertEqualAfterSimplification("(abs (sqrt (variable 2.0 a)))", "(sqrt (variable 2.0 a))"); // sqrt is always positive (for our cases)
238      AssertEqualAfterSimplification("(abs (cuberoot (variable 2.0 a)))", "(cuberoot (variable 2.0 a))"); // cuberoot is always positive (for our cases)
239
240      AssertEqualAfterSimplification("(* (abs (variable 2.0 x)) 2.0)", "(abs (variable 4.0 x))");  // can multiply positive constants into abs
241      AssertEqualAfterSimplification("(* (abs (variable 2.0 x)) -2.0)", "(* (abs (variable 4.0 x)) -1.0)"); // for negative constants keep the sign
242
243      AssertEqualAfterSimplification("(abs (* (variable 1.0 a) (variable 2.0 b)))", "(* (abs (variable 1.0 a)) (abs (variable 1.0 b)) 2.0))");
244      AssertEqualAfterSimplification("(abs (/ (variable 1.0 a) (variable 2.0 b)))", "(/ (abs (variable 1.0 a)) (abs (variable 2.0 b))))");
245      #endregion
246
247      #region square and sqrt
248      AssertEqualAfterSimplification("(sqr (sqrt (variable 2.0 x)))", "(variable 2.0 x)");
249      AssertEqualAfterSimplification("(sqrt (sqr (variable 2.0 x)))", "(variable 2.0 x)");
250      AssertEqualAfterSimplification("(sqr (abs (variable 2.0 a)))", "(sqr (variable 2.0 a))");
251      AssertEqualAfterSimplification("(sqr (exp (variable 2.0 x)))", "(exp (variable 4.0 x))");
252
253      AssertEqualAfterSimplification("(sqr (* (variable 2.0 a) (variable 3.0 b) (variable 4.0 c)))",
254        "(* (sqr (variable 1.0 a)) (sqr (variable 1.0 b)) (sqr (variable 1.0 c)) 576)"); // 2²*3²*4²
255      #endregion
256
257      #region cube and cuberoot
258      AssertEqualAfterSimplification("(cube (cuberoot (variable 2.0 x)))", "(variable 2.0 x)");
259      AssertEqualAfterSimplification("(cuberoot (cube (variable 2.0 x)))", "(variable 2.0 x)");
260      AssertEqualAfterSimplification("(cube (exp (variable 2.0 x)))", "(exp (variable 6.0 x))");
261
262      AssertEqualAfterSimplification("(sqr (cube (variable 2.0 x)))", "(pow (variable 2.0 x) 6)");
263      AssertEqualAfterSimplification("(cube (sqr (variable 2.0 x)))", "(pow (variable 2.0 x) 6)");
264      #endregion
265
266      #region AQ
267      AssertEqualAfterSimplification("(* (aq (variable 1.0 x) (variable 1.0 y)) 2.0)", "(aq (variable 2.0 x) (variable 1.0 y))");
268      AssertEqualAfterSimplification("(/ (aq (variable 1.0 x) (variable 1.0 y)) 2.0)", "(aq (variable 0.5 x) (variable 1.0 y))");
269
270      #endregion
271
272      #region do not drop subtrees with small weights
273      AssertEqualAfterSimplification("(* 1e-14 (variable 1.0 a))", "(variable 1e-14 a)");
274      AssertEqualAfterSimplification("(+ (variable 1.0 a) 1e-14)",
275                                     "(+ (variable 1.0 a) 1e-14)");
276      // a scenario where a term with small weight can have large effect
277      AssertEqualAfterSimplification("(+ (* (pow (variable 1.0 a) 10) 1e-14) 1.0)",
278                                     "(+ (* (pow (variable 1.0 a) 10) 1e-14) 1.0)");
279      // a test case (from ticket #2985)
280      AssertEqualAfterSimplification("(+ (* (exp (variable 3.5861E+001 a)) 5.5606E-016) 5.9323E-002)",
281                                     "(+ (* (exp (variable 3.5861E+001 a)) 5.5606E-016) 5.9323E-002)");
282      #endregion
283    }
284
285
286    private void AssertEqualAfterSimplification(string original, string expected) {
287      var formatter = new SymbolicExpressionTreeStringFormatter();
288      var importer = new SymbolicExpressionImporter();
289      var actualTree = TreeSimplifier.Simplify(importer.Import(original));
290      var expectedTree = importer.Import(expected);
291      Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
292
293    }
294  }
295}
296
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