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Ignore:
Timestamp:
07/04/19 15:15:58 (4 years ago)
Author:
mkommend
Message:

#2948: Merged 16206, 16207, 16213, 16216, 16294 to stable.

File:
1 copied

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  • stable/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/DeriveTest.cs

    r16207 r17066  
    3535      var formatter = new InfixExpressionFormatter();
    3636      var parser = new InfixExpressionParser();
    37       Console.WriteLine(Derive("3", "x"));
    38       Console.WriteLine(Derive("x", "x"));
    39       Console.WriteLine(Derive("10*x", "x"));
    40       Console.WriteLine(Derive("x*10", "x"));
    41       Console.WriteLine(Derive("x*x", "x"));
    42       Console.WriteLine(Derive("x*x*x", "x"));
    43       Console.WriteLine(Derive("10*x", "y"));
    44       Console.WriteLine(Derive("10*x+20*y", "y"));
    45       Console.WriteLine(Derive("2*3*x", "x"));
    46       Console.WriteLine(Derive("10*x*y+20*y", "x"));
    47       Console.WriteLine(Derive("1/x", "x"));
    48       Console.WriteLine(Derive("y/x", "x"));
    49       Console.WriteLine(Derive("(a+b)/(x+x*x)", "x"));
    50       Console.WriteLine(Derive("(a+b)/(x+SQR(x))", "x"));
    51       Console.WriteLine(Derive("exp(x)", "x"));
    52       Console.WriteLine(Derive("exp(3*x)", "x"));
    53       Console.WriteLine(Derive("log(x)", "x"));
    54       Console.WriteLine(Derive("log(3*x)", "x"));
    55       Console.WriteLine(Derive("log(3*x+y)", "x"));
    56       Console.WriteLine(Derive("sqrt(3*x+y)", "x"));
    57       Console.WriteLine(Derive("sin(3*x)", "x"));
    58       Console.WriteLine(Derive("cos(3*x)", "x"));
     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
    5961
    60       // special case: Inv(x) using only one argument to the division symbol
    61       var root = new ProgramRootSymbol().CreateTreeNode();
    62       var start = new StartSymbol().CreateTreeNode();
    63       var div = new Division().CreateTreeNode();
    64       var varNode = (VariableTreeNode)(new Variable().CreateTreeNode());
    65       varNode.Weight = 1.0;
    66       varNode.VariableName = "x";
    67       div.AddSubtree(varNode);
    68       start.AddSubtree(div);
    69       root.AddSubtree(start);
    70       var t = new SymbolicExpressionTree(root);
    71       Console.WriteLine(formatter.Format(DerivativeCalculator.Derive(t, "x")));
     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      }
    72124    }
    73125
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