Changeset 16543

Timestamp:

01/21/19 18:07:37 (6 years ago)

Author:

gkronber

Message:

#2948: added support for deriving cube, cuberoot, abs, analytic-quotient

Location:

trunk

Files:

• HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Converters/DerivativeCalculator.cs (modified) (4 diffs)
• HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/DeriveTest.cs (modified) (1 diff)

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

@@ -48 +48 @@
     private static readonly Cosine cosSy = new Cosine();
     private static readonly Square sqrSy = new Square();
+    private static readonly Absolute absSy = new Absolute();
+    private static readonly SquareRoot sqrtSy = new SquareRoot();
 
     public static ISymbolicExpressionTreeNode Derive(ISymbolicExpressionTreeNode branch, string variableName) {
@@ -138 +140 @@
         return Product(Div(CreateConstant(1.0), Product(CreateConstant(2.0), f)), Derive(u, variableName));
       }
+      if (branch.Symbol is CubeRoot) {
+        var f = (ISymbolicExpressionTreeNode)branch.Clone();
+        var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
+        return Product(Div(CreateConstant(1.0), Product(CreateConstant(3.0), Square(f))), Derive(u, variableName));
+      }
+      if (branch.Symbol is Cube) {
+        var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
+        return Product(Product(CreateConstant(3.0), Square(f)), Derive(f, variableName));
+      }
+      if (branch.Symbol is Absolute) {
+        var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
+        var absf = Abs((ISymbolicExpressionTreeNode)f.Clone());
+        return Product(Div(f, absf), Derive(f, variableName));
+      }
+      if (branch.Symbol is AnalyticQuotient) {
+        // aq(a(x), b(x)) = a(x) / sqrt(b(x)²+1)
+        var a = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
+        var b = (ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone();
+
+        var definition = Div(a, SquareRoot(Sum(Square(b), CreateConstant(1.0))));
+        return Derive(definition, variableName);
+      }
       if (branch.Symbol is Sine) {
         var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
@@ -195 +219 @@
       return cos;
     }
+    private static ISymbolicExpressionTreeNode Abs(ISymbolicExpressionTreeNode f) {
+      var abs = absSy.CreateTreeNode();
+      abs.AddSubtree(f);
+      return abs;
+    }
     private static ISymbolicExpressionTreeNode Square(ISymbolicExpressionTreeNode f) {
       var sqr = sqrSy.CreateTreeNode();
       sqr.AddSubtree(f);
       return sqr;
+    }
+    private static ISymbolicExpressionTreeNode SquareRoot(ISymbolicExpressionTreeNode f) {
+      var sqrt = sqrtSy.CreateTreeNode();
+      sqrt.AddSubtree(f);
+      return sqrt;
     }
 
@@ -221 +255 @@
           !(n.Symbol is Square) &&
           !(n.Symbol is SquareRoot) &&
+          !(n.Symbol is Cube) &&
+          !(n.Symbol is CubeRoot) &&
+          !(n.Symbol is Absolute) &&
+          !(n.Symbol is AnalyticQuotient) &&
           !(n.Symbol is Sine) &&
           !(n.Symbol is Cosine) &&

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

@@ -59 +59 @@
       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
+
+      Assert.AreEqual("((9*'x') / ABS((3*'x')))", Derive("abs(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