source: trunk/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/DeriveTest.cs @ 16294

Last change on this file since 16294 was 16294, checked in by gkronber, 11 months ago

#2948: worked on review comments.

File size: 6.6 KB
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1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2018 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
21
22
23using System;
24using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
25using Microsoft.VisualStudio.TestTools.UnitTesting;
26namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Tests {
27
28
29  [TestClass]
30  public class DerivativeTest {
31    [TestMethod]
32    [TestCategory("Problems.DataAnalysis.Symbolic")]
33    [TestProperty("Time", "short")]
34    public void DeriveExpressions() {
35      var formatter = new InfixExpressionFormatter();
36      var parser = new InfixExpressionParser();
37      Assert.AreEqual("0", Derive("3", "x"));
38      Assert.AreEqual("1", Derive("x", "x"));
39      Assert.AreEqual("10", Derive("10*x", "x"));
40      Assert.AreEqual("10", Derive("x*10", "x"));
41      Assert.AreEqual("(2*'x')", Derive("x*x", "x"));
42      Assert.AreEqual("((('x' * 'x') * 2) + ('x' * 'x'))", Derive("x*x*x", "x")); // simplifier does not merge (x*x)*2 + x*x  to 3*x*x
43      Assert.AreEqual("0", Derive("10*x", "y"));
44      Assert.AreEqual("20", Derive("10*x+20*y", "y"));
45      Assert.AreEqual("6", Derive("2*3*x", "x"));
46      Assert.AreEqual("(10*'y')", Derive("10*x*y+20*y", "x"));
47      Assert.AreEqual("(1 / (SQR('x') * (-1)))", Derive("1/x", "x"));
48      Assert.AreEqual("('y' / (SQR('x') * (-1)))", Derive("y/x", "x"));
49      Assert.AreEqual("((((-2*'x') + (-1)) * ('a' + 'b')) / SQR(('x' + ('x' * 'x'))))",
50        Derive("(a+b)/(x+x*x)", "x"));
51      Assert.AreEqual("((((-2*'x') + (-1)) * ('a' + 'b')) / SQR(('x' + SQR('x'))))", Derive("(a+b)/(x+SQR(x))", "x"));
52      Assert.AreEqual("EXP('x')", Derive("exp(x)", "x"));
53      Assert.AreEqual("(EXP((3*'x')) * 3)", Derive("exp(3*x)", "x"));
54      Assert.AreEqual("(1 / 'x')", Derive("log(x)", "x"));
55      Assert.AreEqual("(1 / 'x')", Derive("log(3*x)", "x"));   // 3 * 1/(3*x)
56      Assert.AreEqual("(1 / ('x' + (0.333333333333333*'y')))", Derive("log(3*x+y)", "x"));  // simplifier does not try to keep fractions
57      Assert.AreEqual("(1 / (SQRT(((3*'x') + 'y')) * 0.666666666666667))", Derive("sqrt(3*x+y)", "x"));   // 3 / (2 * sqrt(3*x+y)) = 1 / ((2/3) * sqrt(3*x+y))
58      Assert.AreEqual("(COS((3*'x')) * 3)", Derive("sin(3*x)", "x"));
59      Assert.AreEqual("(SIN((3*'x')) * (-3))", Derive("cos(3*x)", "x"));
60      Assert.AreEqual("(1 / (SQR(COS((3*'x'))) * 0.333333333333333))", Derive("tan(3*x)", "x")); // diff(tan(f(x)), x) = 1.0 / cos²(f(x)), simplifier puts constant factor into the denominator
61
62      {
63        // special case: Inv(x) using only one argument to the division symbol
64        // f(x) = 1/x
65        var root = new ProgramRootSymbol().CreateTreeNode();
66        var start = new StartSymbol().CreateTreeNode();
67        var div = new Division().CreateTreeNode();
68        var varNode = (VariableTreeNode)(new Variable().CreateTreeNode());
69        varNode.Weight = 1.0;
70        varNode.VariableName = "x";
71        div.AddSubtree(varNode);
72        start.AddSubtree(div);
73        root.AddSubtree(start);
74        var t = new SymbolicExpressionTree(root);
75        Assert.AreEqual("(1 / (SQR('x') * (-1)))",
76          formatter.Format(DerivativeCalculator.Derive(t, "x")));
77      }
78
79      {
80        // special case: multiplication with only one argument
81        var root = new ProgramRootSymbol().CreateTreeNode();
82        var start = new StartSymbol().CreateTreeNode();
83        var mul = new Multiplication().CreateTreeNode();
84        var varNode = (VariableTreeNode)(new Variable().CreateTreeNode());
85        varNode.Weight = 3.0;
86        varNode.VariableName = "x";
87        mul.AddSubtree(varNode);
88        start.AddSubtree(mul);
89        root.AddSubtree(start);
90        var t = new SymbolicExpressionTree(root);
91        Assert.AreEqual("3",
92          formatter.Format(DerivativeCalculator.Derive(t, "x")));
93      }
94
95      {
96        // division with multiple arguments
97        // div(x, y, z) is interpreted as (x / y) / z
98        var root = new ProgramRootSymbol().CreateTreeNode();
99        var start = new StartSymbol().CreateTreeNode();
100        var div = new Division().CreateTreeNode();
101        var varNode1 = (VariableTreeNode)(new Variable().CreateTreeNode());
102        varNode1.Weight = 3.0;
103        varNode1.VariableName = "x";
104        var varNode2 = (VariableTreeNode)(new Variable().CreateTreeNode());
105        varNode2.Weight = 4.0;
106        varNode2.VariableName = "y";
107        var varNode3 = (VariableTreeNode)(new Variable().CreateTreeNode());
108        varNode3.Weight = 5.0;
109        varNode3.VariableName = "z";
110        div.AddSubtree(varNode1); div.AddSubtree(varNode2); div.AddSubtree(varNode3);
111        start.AddSubtree(div);
112        root.AddSubtree(start);
113        var t = new SymbolicExpressionTree(root);
114
115        Assert.AreEqual("(('y' * 'z' * 60) / SQR(('y' * 'z' * 20)))", // actually 3 / (4y  5z) but simplifier is not smart enough to cancel numerator and denominator
116                                                                      // 60 y z / y² z² 20² == 6 / y z 40 == 3 / y z 20
117          formatter.Format(DerivativeCalculator.Derive(t, "x")));
118        Assert.AreEqual("(('x' * 'z' * (-60)) / SQR(('y' * 'z' * 20)))", // actually 3x * -(4 5 z) / (4y 5z)² = -3x / (20 y² z)
119                                                                         // -3 4 5 x z / 4² y² 5² z² = -60 x z / 20² z² y² ==    -60 x z / y² z² 20²
120          formatter.Format(DerivativeCalculator.Derive(t, "y")));
121        Assert.AreEqual("(('x' * 'y' * (-60)) / SQR(('y' * 'z' * 20)))",
122          formatter.Format(DerivativeCalculator.Derive(t, "z")));
123      }
124    }
125
126    private string Derive(string expr, string variable) {
127      var parser = new InfixExpressionParser();
128      var formatter = new InfixExpressionFormatter();
129
130      var t = parser.Parse(expr);
131      var tPrime = DerivativeCalculator.Derive(t, variable);
132
133      return formatter.Format(tPrime);
134    }
135  }
136}
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