Changeset 17066 for stable/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic3.4/DeriveTest.cs
 Timestamp:
 07/04/19 15:15:58 (5 years ago)
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stable/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic3.4/DeriveTest.cs
r16207 r17066 35 35 var formatter = new InfixExpressionFormatter(); 36 36 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 59 61 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 } 72 124 } 73 125
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