source: branches/3140_NumberSymbol/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/DeriveTest.cs @ 18126

#region License Information
/* HeuristicLab
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#endregion


using System;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
using Microsoft.VisualStudio.TestTools.UnitTesting;
namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Tests {


  [TestClass]
  public class DerivativeTest {
    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void DeriveExpressions() {
      var formatter = new InfixExpressionFormatter();
      var parser = new InfixExpressionParser();
      Assert.AreEqual("0", Derive("<num=3>", "x"));
      Assert.AreEqual("1", Derive("x", "x"));
      Assert.AreEqual("10", Derive("<num=10>*x", "x"));
      Assert.AreEqual("10", Derive("x*<num=10>", "x"));
      Assert.AreEqual("(2*'x')", Derive("x*x", "x"));
      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
      Assert.AreEqual("0", Derive("<num=10>*x", "y"));
      Assert.AreEqual("20", Derive("<num=10>*x+<num=20>*y", "y"));
      Assert.AreEqual("6", Derive("<num=2>*<num=3>*x", "x"));
      Assert.AreEqual("(10*'y')", Derive("<num=10>*x*y+<num=20>*y", "x"));
      Assert.AreEqual("(1 / (SQR('x') * (-1)))", Derive("1/x", "x"));
      Assert.AreEqual("('y' / (SQR('x') * (-1)))", Derive("y/x", "x"));
      Assert.AreEqual("((((-2*'x') + (-1)) * ('a' + 'b')) / SQR(('x' + ('x' * 'x'))))",
        Derive("(a+b)/(x+x*x)", "x"));
      Assert.AreEqual("((((-2*'x') + (-1)) * ('a' + 'b')) / SQR(('x' + SQR('x'))))", Derive("(a+b)/(x+SQR(x))", "x"));
      Assert.AreEqual("EXP('x')", Derive("exp(x)", "x"));
      Assert.AreEqual("(EXP((3*'x')) * 3)", Derive("exp(<num=3>*x)", "x"));
      Assert.AreEqual("(1 / 'x')", Derive("log(x)", "x"));
      Assert.AreEqual("(1 / 'x')", Derive("log(<num=3>*x)", "x"));   // 3 * 1/(3*x)
      Assert.AreEqual("(1 / ('x' + (0.333333333333333*'y')))", Derive("log(<num=3>*x+y)", "x"));  // simplifier does not try to keep fractions
      Assert.AreEqual("(1 / (SQRT(((3*'x') + 'y')) * 0.666666666666667))", Derive("sqrt(<num=3>*x+y)", "x"));   // 3 / (2 * sqrt(3*x+y)) = 1 / ((2/3) * sqrt(3*x+y)) 
      Assert.AreEqual("(COS((3*'x')) * 3)", Derive("sin(<num=3>*x)", "x"));
      Assert.AreEqual("(SIN((3*'x')) * (-3))", Derive("cos(<num=3>*x)", "x"));
      Assert.AreEqual("(1 / (SQR(COS((3*'x'))) * 0.333333333333333))", Derive("tan(<num=3>*x)", "x")); // diff(tan(f(x)), x) = 1.0 / cos²(f(x)), simplifier puts constant factor into the denominator

      Assert.AreEqual("((9*'x') / ABS((3*'x')))", Derive("abs(<num=3>*x)", "x"));
      Assert.AreEqual("(SQR('x') * 3)", Derive("cube(x)", "x"));
      Assert.AreEqual("(1 / (SQR(CUBEROOT('x')) * 3))", Derive("cuberoot(x)", "x"));

      Assert.AreEqual("0", Derive("(a+b)/(x+SQR(x))", "y")); // df(a,b,x) / dy = 0


      Assert.AreEqual("('a' * 'b' * 'c')", Derive("a*b*c*d", "d"));
      Assert.AreEqual("('a' / ('b' * 'c' * SQR('d') * (-1)))", Derive("a/b/c/d", "d"));

      Assert.AreEqual("('x' * ((SQR(TANH(SQR('x'))) * (-1)) + 1) * 2)", Derive("tanh(sqr(x))", "x")); // (2*'x'*(1 - SQR(TANH(SQR('x'))))

      {
        // special case: Inv(x) using only one argument to the division symbol
        // f(x) = 1/x
        var root = new ProgramRootSymbol().CreateTreeNode();
        var start = new StartSymbol().CreateTreeNode();
        var div = new Division().CreateTreeNode();
        var varNode = (VariableTreeNode)(new Variable().CreateTreeNode());
        varNode.Weight = 1.0;
        varNode.VariableName = "x";
        div.AddSubtree(varNode);
        start.AddSubtree(div);
        root.AddSubtree(start);
        var t = new SymbolicExpressionTree(root);
        Assert.AreEqual("(1 / (SQR('x') * (-1)))",
          formatter.Format(DerivativeCalculator.Derive(t, "x")));
      }

      {
        // special case: multiplication with only one argument
        var root = new ProgramRootSymbol().CreateTreeNode();
        var start = new StartSymbol().CreateTreeNode();
        var mul = new Multiplication().CreateTreeNode();
        var varNode = (VariableTreeNode)(new Variable().CreateTreeNode());
        varNode.Weight = 3.0;
        varNode.VariableName = "x";
        mul.AddSubtree(varNode);
        start.AddSubtree(mul);
        root.AddSubtree(start);
        var t = new SymbolicExpressionTree(root);
        Assert.AreEqual("3",
          formatter.Format(DerivativeCalculator.Derive(t, "x")));
      }

      {
        // division with multiple arguments
        // div(x, y, z) is interpreted as (x / y) / z
        var root = new ProgramRootSymbol().CreateTreeNode();
        var start = new StartSymbol().CreateTreeNode();
        var div = new Division().CreateTreeNode();
        var varNode1 = (VariableTreeNode)(new Variable().CreateTreeNode());
        varNode1.Weight = 3.0;
        varNode1.VariableName = "x";
        var varNode2 = (VariableTreeNode)(new Variable().CreateTreeNode());
        varNode2.Weight = 4.0;
        varNode2.VariableName = "y";
        var varNode3 = (VariableTreeNode)(new Variable().CreateTreeNode());
        varNode3.Weight = 5.0;
        varNode3.VariableName = "z";
        div.AddSubtree(varNode1); div.AddSubtree(varNode2); div.AddSubtree(varNode3);
        start.AddSubtree(div);
        root.AddSubtree(start);
        var t = new SymbolicExpressionTree(root);

        Assert.AreEqual("(('y' * 'z' * 60) / (SQR('y') * SQR('z') * 400))", // actually 3 / (4y  5z) but simplifier is not smart enough to cancel numerator and denominator
                                                                            // 60 y z / y² z² 20² == 6 / y z 40 == 3 / y z 20
          formatter.Format(DerivativeCalculator.Derive(t, "x")));
        Assert.AreEqual("(('x' * 'z' * (-60)) / (SQR('y') * SQR('z') * 400))", // actually 3x * -(4 5 z) / (4y 5z)² = -3x / (20 y² z)
                                                                               // -3 4 5 x z / 4² y² 5² z² = -60 x z / 20² z² y² ==    -60 x z / y² z² 20² 
          formatter.Format(DerivativeCalculator.Derive(t, "y")));
        Assert.AreEqual("(('x' * 'y' * (-60)) / (SQR('y') * SQR('z') * 400))",
          formatter.Format(DerivativeCalculator.Derive(t, "z")));
      }
    }

    private string Derive(string expr, string variable) {
      var parser = new InfixExpressionParser();
      var formatter = new InfixExpressionFormatter();

      var t = parser.Parse(expr);
      var tPrime = DerivativeCalculator.Derive(t, variable);

      return formatter.Format(tPrime);
    }
  }
}