source: branches/2994-AutoDiffForIntervals/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis.Symbolic-3.4/AutoDiffIntervalInterpreterTest.cs @ 17288

using System;
using System.Collections.Generic;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
using Microsoft.VisualStudio.TestTools.UnitTesting;

namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Tests {
  [TestClass]
  public class AutoDiffIntervalInterpreterTest {
    private IRegressionProblemData problemData;
    private IDictionary<string, Interval> variableRanges;

    [TestInitialize]
    public void InitTest() {
      double[,] arr = new double[4, 3];

      arr[0, 0] = 3;
      arr[0, 1] = 6;
      arr[0, 2] = 2;
      arr[1, 0] = 5;
      arr[1, 1] = 2;
      arr[1, 2] = 1;
      arr[2, 0] = 8;
      arr[2, 1] = 5;
      arr[2, 2] = 0;
      arr[3, 0] = 3;
      arr[3, 1] = 4;
      arr[3, 2] = 2;

      // intervals for dataset
      // x1: 3 .. 8
      // x2: 2 .. 6

      var ds = new Dataset(new string[] { "x1", "x2", "y" }, arr);
      problemData = (IRegressionProblemData)new RegressionProblemData(ds, new string[] { "x1", "x2" }, "y");


      variableRanges = new Dictionary<string, Interval>();
      variableRanges.Add("x1", new Interval(1, 10));
      variableRanges.Add("x2", new Interval(4, 6));
    }

    private void EvaluateTest(string expression, Interval expectedResult, IDictionary<string, Interval> variableRanges = null, double lowerDelta = 1e-6, double upperDelta = 1e-6) {
      var parser = new InfixExpressionParser();
      var tree = parser.Parse(expression);
      var interpreter = new IntervalEvaluator();
      Interval result;
      if (variableRanges == null) variableRanges = problemData.VariableRanges.GetIntervals();
      result = interpreter.Evaluate(tree, variableRanges, new ISymbolicExpressionTreeNode[0], out double[] _, out double[] __);

      Assert.AreEqual(expectedResult.LowerBound, result.LowerBound, lowerDelta);
      Assert.AreEqual(expectedResult.UpperBound, result.UpperBound, upperDelta);
    }


    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterAdd() {
      EvaluateTest("x1 + x2", new Interval(5, 14));
      EvaluateTest("x1 + x2", new Interval(5, 16), variableRanges);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterLogAdd() {
      EvaluateTest("log(x1 + x2)", new Interval(Math.Log(5), Math.Log(14)));
      EvaluateTest("log(x1 + x2)", new Interval(Math.Log(5), Math.Log(16)), variableRanges);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterLogAddMul() {
      EvaluateTest("log(3*x1 + x2)", new Interval(Math.Log(11), Math.Log(30)));
      EvaluateTest("log(3*x1 + x2)", new Interval(Math.Log(7), Math.Log(36)), variableRanges);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterSin() {
      EvaluateTest("sin(x1+x2)", new Interval(-1, 1));
      EvaluateTest("sin(x1+x2)", new Interval(-1, 1), variableRanges);
      EvaluateTest("sin(1+2)", new Interval(Math.Sin(3), Math.Sin(3)));

      var localVarRanges = new Dictionary<string, Interval>();
      localVarRanges.Add("x1", new Interval(-1, 1));
      localVarRanges.Add("x2", new Interval(-(Math.PI / 2), 0));
      localVarRanges.Add("x3", new Interval(0, Math.PI / 2));
      localVarRanges.Add("x4", new Interval(-Math.PI, Math.PI));
      localVarRanges.Add("x5", new Interval(Math.PI / 4, Math.PI * 3.0 / 4));

      EvaluateTest("sin(x1)", new Interval(Math.Sin(-1), Math.Sin(1)), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("sin(x2)", new Interval(-1, 0), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("sin(x3)", new Interval(0, 1), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("sin(x4)", new Interval(-1, 1), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("sin(x5)", new Interval(Math.Sin(Math.PI / 4), 1), localVarRanges, 1E-8, 1E-8);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterCos() {
      EvaluateTest("cos(x1+x2)", new Interval(-1, 1));
      EvaluateTest("cos(x1+x2)", new Interval(-1, 1), variableRanges);
      EvaluateTest("cos(1+2)", new Interval(Math.Cos(3), Math.Cos(3)));

      var localVarRanges = new Dictionary<string, Interval>();
      localVarRanges.Add("x1", new Interval(-1, 1));
      localVarRanges.Add("x2", new Interval(-(Math.PI / 2), 0));
      localVarRanges.Add("x3", new Interval(0, Math.PI / 2));
      localVarRanges.Add("x4", new Interval(-Math.PI, Math.PI));
      localVarRanges.Add("x5", new Interval(Math.PI / 4, Math.PI * 3.0 / 4));

      EvaluateTest("cos(x1)", new Interval(Math.Cos(-1), 1), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("cos(x2)", new Interval(0, 1), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("cos(x3)", new Interval(0, 1), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("cos(x4)", new Interval(-1, 1), localVarRanges, 1E-8, 1E-8);
      EvaluateTest("cos(x5)", new Interval(Math.Cos(Math.PI * 3.0 / 4), Math.Cos(Math.PI / 4)), localVarRanges, 1E-8, 1E-8);

    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterTan() {
      throw new NotSupportedException();
      // critical values:
      // lim tan(x) = -inf for x => -pi/2
      // lim tan(x) = +inf for x =>  pi/2
      var variableRanges = new Dictionary<string, Interval>();
      variableRanges.Add("x1", new Interval(-1, 1));
      variableRanges.Add("x2", new Interval(-(Math.PI / 2), 0));
      variableRanges.Add("x3", new Interval(0, Math.PI / 2));
      variableRanges.Add("x4", new Interval(-Math.PI, Math.PI));

      EvaluateTest("tan(x1)", new Interval(Math.Tan(-1), Math.Tan(1)), variableRanges, 1E-8, 1E-8);
      EvaluateTest("tan(x2)", new Interval(double.NegativeInfinity, 0), variableRanges, 0, 1E-8);
      EvaluateTest("tan(x3)", new Interval(0, 8.16588936419192E+15), variableRanges, 0, 1E6); // actually upper bound should be infinity.
      EvaluateTest("tan(x4)", new Interval(double.NegativeInfinity, double.PositiveInfinity), variableRanges);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterTanh() {
      // critical values:
      // lim tanh(x) = -1 for x => -inf
      // lim tanh(x) =  1 for x =>  inf
      var variableRanges = new Dictionary<string, Interval>();
      variableRanges.Add("x1", new Interval(-1, 1));
      variableRanges.Add("x2", new Interval(double.NegativeInfinity, 0));
      variableRanges.Add("x3", new Interval(0, double.PositiveInfinity));

      EvaluateTest("tanh(x1)", new Interval(Math.Tanh(-1), Math.Tanh(1)), variableRanges);
      EvaluateTest("tanh(x2)", new Interval(-1, 0), variableRanges);
      EvaluateTest("tanh(x3)", new Interval(0, 1), variableRanges);
    }


    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterExp() {
      EvaluateTest("exp(x1-x2)", new Interval(Math.Exp(-3), Math.Exp(6)));
      EvaluateTest("exp(x1-x2)", new Interval(Math.Exp(-5), Math.Exp(6)), variableRanges);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterExpRoot() {
      EvaluateTest("exp(sqrt(x1*x2))", new Interval(Math.Exp(Math.Sqrt(6)), Math.Exp(Math.Sqrt(48))));
      EvaluateTest("exp(sqrt(x1*x2))", new Interval(Math.Exp(Math.Sqrt(4)), Math.Exp(Math.Sqrt(60))), variableRanges);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void TestIntervalInterpreterSqr() {
      EvaluateTest("sqr(x1)", new Interval(Math.Pow(3, 2), Math.Pow(8, 2)));
    }



    [TestMethod]
    [TestCategory("Problems.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void TestDivisionAndSqr() {
      Dictionary<string, Interval> dataIntervals = new Dictionary<string, Interval>() {
        {"R", new Interval(0.2, 0.5) },
        {"r", new Interval(0.5, 0.8) },
      };

      EvaluateTest("R*R", new Interval(0.2 * 0.2, 0.5 * 0.5), dataIntervals);
      EvaluateTest("sqr(R)", new Interval(0.2 * 0.2, 0.5 * 0.5), dataIntervals);

      EvaluateTest("r*r", new Interval(0.5 * 0.5, 0.8 * 0.8), dataIntervals);
      EvaluateTest("sqr(r)", new Interval(0.5 * 0.5, 0.8 * 0.8), dataIntervals);

      EvaluateTest("R/r", new Interval(0.2 / 0.8, 0.5 / 0.5), dataIntervals);

      EvaluateTest("R/(r*r)", new Interval(0.2 / (0.8 * 0.8), 0.5 / (0.5 * 0.5)), dataIntervals);
      EvaluateTest("R/sqr(r)", new Interval(0.2 / (0.8 * 0.8), 0.5 / (0.5 * 0.5)), dataIntervals);

      EvaluateTest("R*R/sqr(r)", new Interval(0.2 * 0.2 / (0.8 * 0.8), 0.5 * 0.5 / (0.5 * 0.5)), dataIntervals);
      EvaluateTest("sqr(R)/sqr(r)", new Interval(0.2 * 0.2 / (0.8 * 0.8), 0.5 * 0.5 / (0.5 * 0.5)), dataIntervals);
      EvaluateTest("sqr(R/r)", new Interval(0.2 * 0.2 / (0.8 * 0.8), 0.5 * 0.5 / (0.5 * 0.5)), dataIntervals);
    }
  }
}