Changeset 17203 for branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Interpreter/Interpreter.cs

Timestamp:

08/13/19 09:28:45 (5 years ago)

Author:

gkronber

Message:

#2994: re-wrote implementation of interval arithmetic for Sin()

File:

• branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Interpreter/Interpreter.cs (modified) (1 diff)

branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Interpreter/Interpreter.cs

@@ -940 +940 @@
 
     public AlgebraicInterval AssignSin(AlgebraicInterval a) {
-      if (Math.Abs(a.UpperBound.Value.Value - a.LowerBound.Value.Value) >= Math.PI * 2) {
-        low = new MultivariateDual<AlgebraicDouble>(-1.0);
+      var lower = a.LowerBound.Value.Value;
+      var size = a.UpperBound.Value.Value - lower;
+      if (size < 0) throw new InvalidProgramException(); // ASSERT interval >= 0;
+
+      if (size >= Math.PI * 2) {
+        low = new MultivariateDual<AlgebraicDouble>(-1.0); // zero gradient
         high = new MultivariateDual<AlgebraicDouble>(1.0);
       }
 
-      //divide the interval by PI/2 so that the optima lie at x element of N (0,1,2,3,4,...)
-      double Pihalf = Math.PI / 2;
-      var scaled = a.Clone().Scale(1.0 / Pihalf);
-      //move to positive scale
-      if (scaled.LowerBound.Value.Value < 0) {
-        int periodsToMove = Math.Abs((int)scaled.LowerBound.Value.Value / 4) + 1;
-        scaled.Add(new AlgebraicInterval(periodsToMove * 4, periodsToMove * 4));
-      }
-
-      double scaledLowerBound = scaled.LowerBound.Value.Value % 4.0;
-      double scaledUpperBound = scaled.UpperBound.Value.Value % 4.0;
-      if (scaledUpperBound < scaledLowerBound) scaledUpperBound += 4.0;
-      List<double> sinValues = new List<double>();
-      sinValues.Add(Math.Sin(scaledLowerBound * Pihalf));
-      sinValues.Add(Math.Sin(scaledUpperBound * Pihalf));
-
-      int startValue = (int)Math.Ceiling(scaledLowerBound);
-      while (startValue < scaledUpperBound) {
-        sinValues.Add(Math.Sin(startValue * Pihalf));
-        startValue += 1;
-      }
-
-      low = new MultivariateDual<AlgebraicDouble>(sinValues.Min()); // TODO, XXX FIX CALCULATION TO SUPPORT GRADIENTS!
-      high = new MultivariateDual<AlgebraicDouble>(sinValues.Max());
+      // assume low and high are in the same quadrant
+      low = Algebraic.Min(a.LowerBound.Clone().Sin(), a.UpperBound.Clone().Sin());
+      high = Algebraic.Max(a.LowerBound.Clone().Sin(), a.UpperBound.Clone().Sin());
+
+      // override min and max if necessary
+
+      // shift interval 'a' into the range [-2pi .. 2pi] without changing the size of the interval to simplify the checks
+      lower = lower % (2 * Math.PI); // lower in [-2pi .. 2pi]      
+
+      // handle min = -1 and max = 1 cases explicitly
+      var pi_2 = Math.PI / 2.0;
+      var maxima = new double[] { -3 * pi_2, pi_2 };
+      var minima = new double[] { -pi_2, 3 * pi_2 };
+
+      // override min and max if necessary
+      if (maxima.Any(m => lower < m && lower + size > m)) {
+        // max = 1
+        high = new MultivariateDual<AlgebraicDouble>(1.0); // zero gradient
+      }
+
+      if (minima.Any(m => lower < m && lower + size > m)) {
+        // min = -1;
+        low = new MultivariateDual<AlgebraicDouble>(-1.0); // zero gradient
+      }
       return this;
     }