source: branches/2994-AutoDiffForIntervals/Tests/AutoDiffTest.cs

using System;
using System.Collections.Generic;
using HeuristicLab.Problems.DataAnalysis;
using HeuristicLab.Problems.DataAnalysis.Symbolic;
using Microsoft.VisualStudio.TestTools.UnitTesting;
using System.Linq;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;

namespace Tests {
  [TestClass]
  public class AutoDiffTestClass {
    [TestMethod]
    public void AutoDiffTest() {
      {
        // eval
        var parser = new InfixExpressionParser();
        var t = parser.Parse("2.0*x+y");

        // interval eval
        var evaluator = new IntervalEvaluator();
        var intervals = new Dictionary<string, Interval>();
        intervals.Add("x", new Interval(-1.0, 1.0));
        intervals.Add("y", new Interval(2.0, 10.0));
        var resultInterval = evaluator.Evaluate(t, intervals);
        Assert.AreEqual(0, resultInterval.LowerBound);
        Assert.AreEqual(12, resultInterval.UpperBound);
      }

      {
        // vector eval
        var parser = new InfixExpressionParser();
        var t = parser.Parse("2.0*x+y");

        var evaluator = new VectorEvaluator();
        var vars = new string[] { "x", "y", "f(x)" };
        var values = new double[,] {
          { 1,  1, 0 },
          { 2,  1, 0 },
          { 3, -1, 0 },
          { 4, -1, 0 },
          { 5, -1, 0 },
        };

        var ds = new Dataset(vars, values);
        var problemData = new RegressionProblemData(ds, vars, "f(x)");
        var train = evaluator.Evaluate(t, ds, problemData.TrainingIndices.ToArray());
        Assert.AreEqual(2, train.Length);
        Assert.AreEqual(3, train[0]);
        Assert.AreEqual(5, train[1]);

        var test = evaluator.Evaluate(t, ds, problemData.TestIndices.ToArray());
        Assert.AreEqual(3, test.Length);
        Assert.AreEqual(5, test[0]);
        Assert.AreEqual(7, test[1]);
        Assert.AreEqual(9, test[2]);
      }

      {
        // vector eval and auto-diff
        var parser = new InfixExpressionParser();
        var t = parser.Parse("2.0*x+y");
        var p0 = t.IterateNodesPostfix().First(n => n is ConstantTreeNode);
        var p1 = t.IterateNodesPostfix().First(n => (n is VariableTreeNode var) && var.VariableName == "y");
        var paramNodes = new ISymbolicExpressionTreeNode[] { p0, p1 };

        var evaluator = new VectorAutoDiffEvaluator();
        var vars = new string[] { "x", "y", "f(x)" };
        var values = new double[,] {
          { 1,  1, 0 },
          { 2,  1, 0 },
          { 3, -1, 0 },
          { 4, -1, 0 },
          { 5, -1, 0 },
        };

        var ds = new Dataset(vars, values);
        var problemData = new RegressionProblemData(ds, vars, "f(x)");
        var train = new double[problemData.TrainingIndices.Count()];
        var trainJac = new double[train.Length, 2];
        evaluator.Evaluate(t, ds, problemData.TrainingIndices.ToArray(), paramNodes, train, trainJac);
        Assert.AreEqual(2, train.Length);
        Assert.AreEqual(3, train[0]);
        Assert.AreEqual(5, train[1]);
        // check jac
        Assert.AreEqual(1, trainJac[0, 0]);
        Assert.AreEqual(1, trainJac[0, 1]);
        Assert.AreEqual(2, trainJac[1, 0]);
        Assert.AreEqual(1, trainJac[1, 1]);

        var test = new double[problemData.TestIndices.Count()];
        var testJac = new double[test.Length, 2];
        evaluator.Evaluate(t, ds, problemData.TestIndices.ToArray(), paramNodes, test, testJac);
        Assert.AreEqual(3, test.Length);
        Assert.AreEqual(5, test[0]);
        Assert.AreEqual(7, test[1]);
        Assert.AreEqual(9, test[2]);

        // check jac
        Assert.AreEqual(3, testJac[0, 0]);
        Assert.AreEqual(-1, testJac[0, 1]);
        Assert.AreEqual(4, testJac[1, 0]);
        Assert.AreEqual(-1, testJac[1, 1]);
        Assert.AreEqual(5, testJac[2, 0]);
        Assert.AreEqual(-1, testJac[2, 1]);

      }

      {
        // Interval tests
        var intervals = new Dictionary<string, Interval>();
        intervals.Add("x", new Interval(-2.0, 3.0));
        intervals.Add("p", new Interval(1.0, 2.0));
        intervals.Add("n", new Interval(-2.0, -1.0));

        AssertInterval("10*x", intervals, -20, 30);
        AssertInterval("sqr(p)", intervals, 1, 4);
        AssertInterval("sqr(n)", intervals, 1, 4);
        AssertInterval("sqr(x)", intervals, 0, 9);

        AssertInterval("cube(p)", intervals, 1, 8);
        AssertInterval("cube(n)", intervals, -8, -1);
        AssertInterval("cube(x)", intervals, -8, 27);
      }

      {
        // interval eval and auto-diff
        var parser = new InfixExpressionParser();
        var t = parser.Parse("2.0*x+y");
        var p0 = t.IterateNodesPostfix().First(n => n is ConstantTreeNode);
        var p1 = t.IterateNodesPostfix().First(n => (n is VariableTreeNode var) && var.VariableName == "y");
        var paramNodes = new ISymbolicExpressionTreeNode[] { p0, p1 };

        var evaluator = new IntervalEvaluator();
        var intervals = new Dictionary<string, Interval>();
        intervals.Add("x", new Interval(-1.0, 1.0));
        intervals.Add("y", new Interval(2.0, 10.0));
        var resultInterval = evaluator.Evaluate(t, intervals, paramNodes, out double[] lowerGradient, out double[] upperGradient);
        Assert.AreEqual(0, resultInterval.LowerBound);
        Assert.AreEqual(12, resultInterval.UpperBound);

        Assert.AreEqual(-1, lowerGradient[0]);
        Assert.AreEqual(2, lowerGradient[1]);
        Assert.AreEqual(1, upperGradient[0]);
        Assert.AreEqual(10, upperGradient[1]);
      }

      {
        // as discussed with Fabrício
        var intervals = new Dictionary<string, Interval>();
        intervals.Add("x1", new Interval(60.0, 65.0));
        intervals.Add("x2", new Interval(30.0, 40.0));
        intervals.Add("x3", new Interval(5.0, 10.0));
        intervals.Add("x4", new Interval(0.5, 0.8));
        intervals.Add("x5", new Interval(0.2, 0.5));

        var parser = new InfixExpressionParser();

        var t1 = parser.Parse("x5/x4");
        var t2 = parser.Parse("log(x5/x4)");
        var t3 = parser.Parse("x3 * log(x5/x4)");
        var t4 = parser.Parse("x1*x2*x5");
        var t5 = parser.Parse("x4/x5");
        var t6 = parser.Parse("sqr(x4/x5)");
        var t7 = parser.Parse("(1 - sqr(x4/x5)) ");
        var t8 = parser.Parse("x1*x2*x5 *(1 - sqr(x4/x5))");
        var t9 = parser.Parse("x1*x2*x5 *(1 - sqr(x4/x5)) + x3 * log(x5/x4)");

        var evaluator = new IntervalEvaluator();
        var result = evaluator.Evaluate(t1, intervals);
        Assert.AreEqual(0.25, result.LowerBound);
        Assert.AreEqual(1, result.UpperBound);

        result = evaluator.Evaluate(t2, intervals);
        Assert.AreEqual(-1.386294361, result.LowerBound, 1e-6);
        Assert.AreEqual(0, result.UpperBound);

        result = evaluator.Evaluate(t3, intervals);
        Assert.AreEqual(-13.86294361, result.LowerBound, 1e-6);
        Assert.AreEqual(0, result.UpperBound);

        result = evaluator.Evaluate(t4, intervals);
        Assert.AreEqual(360, result.LowerBound);
        Assert.AreEqual(1300, result.UpperBound);

        result = evaluator.Evaluate(t5, intervals);
        Assert.AreEqual(1, result.LowerBound, 1e-6);
        Assert.AreEqual(4, result.UpperBound);

        result = evaluator.Evaluate(t6, intervals);
        Assert.AreEqual(1, result.LowerBound);
        Assert.AreEqual(16, result.UpperBound);

        result = evaluator.Evaluate(t7, intervals);
        Assert.AreEqual(-15, result.LowerBound);
        Assert.AreEqual(0, result.UpperBound);

        result = evaluator.Evaluate(t8, intervals);
        Assert.AreEqual(-19500, result.LowerBound);
        Assert.AreEqual(0, result.UpperBound);

        result = evaluator.Evaluate(t9, intervals);
        Assert.AreEqual(-19513.86294, result.LowerBound, 1e-3);
        Assert.AreEqual(0, result.UpperBound);


      }

      {

        // derivatives and intervals for flow psi problem
        var intervals = new Dictionary<string, Interval>();
        intervals.Add("x1", new Interval(60.0, 65.0));
        intervals.Add("x2", new Interval(30.0, 40.0));
        intervals.Add("x3", new Interval(5.0, 10.0));
        intervals.Add("x4", new Interval(0.5, 0.8));
        intervals.Add("x5", new Interval(0.2, 0.5));

        var parser = new InfixExpressionParser();
        var formatter = new InfixExpressionFormatter();

        var expr = parser.Parse("x1*x2*x5*(1 - sqr(x4/x5)) + x3 * log(x5/x4)");

        var dfdx1 = DerivativeCalculator.Derive(expr, "x1");
        Assert.AreEqual("('x2' * 'x5' * ((SQR(('x4' / 'x5')) * (-1)) + 1))", formatter.Format(dfdx1));
        // x2 x5 (1 - sqr(x4/x5))

        var dfdx2 = DerivativeCalculator.Derive(expr, "x2");
        Assert.AreEqual("('x1' * 'x5' * ((SQR(('x4' / 'x5')) * (-1)) + 1))", formatter.Format(dfdx2));
        // x1 x5 (1 - sqr(x4/x5))

        var dfdx3 = DerivativeCalculator.Derive(expr, "x3");
        Assert.AreEqual("LOG(('x5' / 'x4'))", formatter.Format(dfdx3));
        // log(x5/x4)

        var dfdx4 = DerivativeCalculator.Derive(expr, "x4");
        Assert.AreEqual("((('x1' * 'x2' * 'x5' * 'x4' * 2) / ('x5' * (-1*'x5'))) + (('x4' * 'x5' * 'x3') / ('x5' * SQR('x4') * (-1))))", formatter.Format(dfdx4));
        // -2*x1*x2*x5*x4/x5*1/x5 + x3*1/(x5/x4)*x5/sqr(x4)

        var dfdx5 = DerivativeCalculator.Derive(expr, "x5");
        Assert.AreEqual("((('x4' * 'x3') / ('x5' * 'x4')) + ('x1' * 'x2' * ((SQR(('x4' / 'x5')) * (-1)) + 1)) + (('x1' * 'x2' * 'x5' * ('x4' * 'x4') * 2) / ('x5' * SQR('x5') * 1)))", formatter.Format(dfdx5));
      }


    }

    private void AssertInterval(string expression, Dictionary<string, Interval> intervals, double expectedLow, double expectedHigh) {
      var parser = new InfixExpressionParser();
      var t = parser.Parse(expression);
      var evaluator = new IntervalEvaluator();
      var result = evaluator.Evaluate(t, intervals);
      Assert.AreEqual(expectedLow, result.LowerBound);
      Assert.AreEqual(expectedHigh, result.UpperBound);
    }
  }
}