Changeset 17102

Timestamp:

07/08/19 00:03:06 (5 years ago)

Author:

mkommend

Message:

#2948: Merged 16358, 16494, 16543, 16737 into stable.

Location:

stable

Files:

• . (modified) (1 prop)
• HeuristicLab.Problems.DataAnalysis.Symbolic (modified) (1 prop)
• HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Converters/DerivativeCalculator.cs (modified) (5 diffs)
• HeuristicLab.Tests (modified) (1 prop)
• HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/DeriveTest.cs (modified) (2 diffs)

stable/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) {
@@ -81 +83 @@
         if (branch.SubtreeCount >= 2) {
           var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
-          var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone();
           var fprime = Derive(f, variableName);
-          var gprime = Derive(g, variableName);
-          var fgPrime = Sum(Product(f, gprime), Product(fprime, g));
-          for (int i = 2; i < branch.SubtreeCount; i++) {
+          for (int i = 1; i < branch.SubtreeCount; i++) {
+            var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(i).Clone();
             var fg = Product((ISymbolicExpressionTreeNode)f.Clone(), (ISymbolicExpressionTreeNode)g.Clone());
-            var h = (ISymbolicExpressionTreeNode)branch.GetSubtree(i).Clone();
-            var hPrime = Derive(h, variableName);
-            fgPrime = Sum(Product(fgPrime, h), Product(fg, hPrime));
+            var gPrime = Derive(g, variableName);
+            var fgPrime = Sum(Product(fprime, g), Product(gPrime, f));
+            // prepare for next iteration
+            f = fg;
+            fprime = fgPrime;
           }
-          return fgPrime;
+          return fprime;
         } else
           // multiplication with only one argument has no effect -> derive the argument
@@ -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) &&

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

@@ -60 +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
 
+      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
+
+
+      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")); 
+
       {
         // special case: Inv(x) using only one argument to the division symbol
@@ -113 +123 @@
         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
+        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' * '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 
+        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' * 'z' * 20)))",
+        Assert.AreEqual("(('x' * 'y' * (-60)) / (SQR('y') * SQR('z') * 400))",
           formatter.Format(DerivativeCalculator.Derive(t, "z")));
       }