Changeset 16294

Timestamp:

11/12/18 20:45:01 (5 years ago)

Author:

gkronber

Message:

#2948: worked on review comments.

Location:

trunk

Files:

• HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Converters/DerivativeCalculator.cs (modified) (9 diffs)
• HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/DeriveTest.cs (modified) (2 diffs)

trunk/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Converters/DerivativeCalculator.cs

@@ -21 +21 @@
 
 using System;
+using System.Collections.Generic;
 using System.Linq;
 using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
@@ -27 +28 @@
   public static class DerivativeCalculator {
     public static ISymbolicExpressionTree Derive(ISymbolicExpressionTree tree, string variableName) {
+      if (tree.Root.SubtreeCount != 1)
+        throw new NotImplementedException("Derive is not implemented for symbolic expressions with automatically defined functions (ADF)");
+      if (tree.Root.GetSubtree(0).SubtreeCount != 1)
+        throw new NotImplementedException("Derive is not implemented for multi-variate symbolic expressions");
       var mainBranch = tree.Root.GetSubtree(0).GetSubtree(0);
       var root = new ProgramRootSymbol().CreateTreeNode();
       root.AddSubtree(new StartSymbol().CreateTreeNode());
       var dTree = TreeSimplifier.GetSimplifiedTree(Derive(mainBranch, variableName));
-      // var dTree = Derive(mainBranch, variableName);
+      //var dTree = Derive(mainBranch, variableName);
       root.GetSubtree(0).AddSubtree(dTree);
       return new SymbolicExpressionTree(root);
     }
 
-    private static Constant constantSy = new Constant();
-    private static Addition addSy = new Addition();
-    private static Subtraction subSy = new Subtraction();
-    private static Multiplication mulSy = new Multiplication();
-    private static Division divSy = new Division();
+    private static readonly Constant constantSy = new Constant();
+    private static readonly Addition addSy = new Addition();
+    private static readonly Subtraction subSy = new Subtraction();
+    private static readonly Multiplication mulSy = new Multiplication();
+    private static readonly Division divSy = new Division();
+    private static readonly Cosine cosSy = new Cosine();
+    private static readonly Square sqrSy = new Square();
 
     public static ISymbolicExpressionTreeNode Derive(ISymbolicExpressionTreeNode branch, string variableName) {
@@ -85 +92 @@
           }
           return fgPrime;
-        } else throw new ArgumentException();
+        } else
+          // multiplication with only one argument has no effect -> derive the argument
+          return Derive(branch.GetSubtree(0), variableName);
       }
       if (branch.Symbol is Division) {
@@ -95 +104 @@
           sqrNode.AddSubtree(g);
           return Div(gPrime, sqrNode);
-        } else if (branch.SubtreeCount == 2) {
+        } else {
+          // for two subtrees:
+          // (f/g)' = (f'g - fg')/g²
+
+          // if there are more than 2 subtrees
+          // div(x,y,z) is interpretered as (x/y)/z
+          // which is the same as x / (y*z)
+
+          // --> make a product of all but the first subtree and differentiate as for the 2-argument case above
           var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
-          var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone();
+          var g = Product(branch.Subtrees.Skip(1).Select(n => (ISymbolicExpressionTreeNode)n.Clone()));
           var fprime = Derive(f, variableName);
           var gprime = Derive(g, variableName);
-          var sqrNode = new Square().CreateTreeNode();
-          sqrNode.AddSubtree((ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone());
-          return Div(Subtract(Product(fprime, g), Product(f, gprime)), sqrNode);
-        } else throw new NotSupportedException();
+          var gSqr = Square(g);
+          return Div(Subtract(Product(fprime, g), Product(f, gprime)), gSqr);
+        }
       }
       if (branch.Symbol is Logarithm) {
@@ -113 +129 @@
         return Product(f, Derive(branch.GetSubtree(0), variableName));
       }
-      if(branch.Symbol is Square) {
+      if (branch.Symbol is Square) {
         var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
         return Product(Product(CreateConstant(2.0), f), Derive(f, variableName));
-      }     
-      if(branch.Symbol is SquareRoot) {
+      }
+      if (branch.Symbol is SquareRoot) {
         var f = (ISymbolicExpressionTreeNode)branch.Clone();
         var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
@@ -133 +149 @@
         sin.AddSubtree(u);
         return Product(CreateConstant(-1.0), Product(sin, Derive(u, variableName)));
+      }
+      if (branch.Symbol is Tangent) {
+        // tan(x)' = 1 / cos²(x)
+        var fxp = Derive(branch.GetSubtree(0), variableName);
+        var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
+        return Div(fxp, Square(Cosine(u)));
       }
       throw new NotSupportedException(string.Format("Symbol {0} is not supported.", branch.Symbol));
@@ -144 +166 @@
       return product;
     }
+    private static ISymbolicExpressionTreeNode Product(IEnumerable<ISymbolicExpressionTreeNode> fs) {
+      var product = mulSy.CreateTreeNode();
+      foreach (var f in fs) product.AddSubtree(f);
+      return product;
+    }
     private static ISymbolicExpressionTreeNode Div(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
       var div = divSy.CreateTreeNode();
@@ -163 +190 @@
       return sum;
     }
-                          
+    private static ISymbolicExpressionTreeNode Cosine(ISymbolicExpressionTreeNode f) {
+      var cos = cosSy.CreateTreeNode();
+      cos.AddSubtree(f);
+      return cos;
+    }
+    private static ISymbolicExpressionTreeNode Square(ISymbolicExpressionTreeNode f) {
+      var sqr = sqrSy.CreateTreeNode();
+      sqr.AddSubtree(f);
+      return sqr;
+    }
+
     private static ISymbolicExpressionTreeNode CreateConstant(double v) {
       var constNode = (ConstantTreeNode)constantSy.CreateTreeNode();
@@ -186 +223 @@
           !(n.Symbol is Sine) &&
           !(n.Symbol is Cosine) &&
+          !(n.Symbol is Tangent) &&
           !(n.Symbol is StartSymbol)
         select n).Any();

trunk/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/DeriveTest.cs

@@ -45 +45 @@
       Assert.AreEqual("6", Derive("2*3*x", "x"));
       Assert.AreEqual("(10*'y')", Derive("10*x*y+20*y", "x"));
-      Assert.AreEqual("(1 / (SQR('x') * (-1)))",  Derive("1/x", "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'))))",
@@ -58 +58 @@
       Assert.AreEqual("(COS((3*'x')) * 3)", Derive("sin(3*x)", "x"));
       Assert.AreEqual("(SIN((3*'x')) * (-3))", Derive("cos(3*x)", "x"));
+      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
 
+      {
+        // 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: 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' * 'z' * 20)))", // 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' * 'z' * 20)))", // 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' * 'z' * 20)))",
+          formatter.Format(DerivativeCalculator.Derive(t, "z")));
+      }
     }