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

namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Tests {
  [TestClass]
  public class IntervalEvaluatorTest {
    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 IntervalEvaluatorAdd() {
      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 IntervalEvaluatorLogAdd() {
      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 IntervalEvaluatorLogAddMul() {
      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 IntervalEvaluatorSin() {
      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 IntervalEvaluatorCos() {
      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 IntervalEvaluatorTan() {
      // 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 IntervalEvaluatorTanh() {
      // 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 IntervalEvaluatorExp() {
      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 IntervalEvaluatorExpRoot() {
      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 IntervalEvaluatorSqr() {
      EvaluateTest("sqr(x1)", new Interval(Math.Pow(3, 2), Math.Pow(8, 2)));
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void IntervalEvaluatorSqrAndDiv() {
      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);
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis.Symbolic")]
    [TestProperty("Time", "short")]
    public void IntervalEvaluatorSqrt() {
      EvaluateTest("sqrt(x1)", new Interval(0, 1), new Dictionary<string, Interval>() { {"x1", new Interval(0, 1) }});
    }


    [TestMethod]
    [TestCategory("Problems.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void IntervalEvaluatorExamples() {
      var parser = new InfixExpressionParser();
      var evaluator = new IntervalEvaluator();
      var intervals = new Dictionary<string, Interval>() {
        {"x", new Interval(1, 2) },
        {"unit", new Interval(0, 1) },
      };

      var t = parser.Parse("SQR(EXP(CUBE((2.10981074965936*'x'))))");
      AssertInterval(143638040.396283, 1.81198989971641E+65, evaluator.Evaluate(t, intervals));


      t = parser.Parse("sqrt(unit)");
      AssertInterval(0, 1, evaluator.Evaluate(t, intervals));

    }

    private void AssertInterval(double expectedLow, double expectedHigh, Interval r) {
      Assert.AreEqual(expectedLow, r.LowerBound, Math.Abs(expectedLow * 1e-5));
      Assert.AreEqual(expectedHigh, r.UpperBound, Math.Abs(expectedHigh * 1e-5));
    }


    [TestMethod]
    [TestCategory("Problems.DataAnalysis")]
    [TestProperty("Time", "long")]
    public void IntervalEvaluatorConsistencyForRandomExpressions() {
      var grammar = new TypeCoherentExpressionGrammar();
      grammar.ConfigureAsDefaultRegressionGrammar();
      // activate supported symbols
      grammar.Symbols.First(s => s is Square).Enabled = true;
      grammar.Symbols.First(s => s is SquareRoot).Enabled = true;
      grammar.Symbols.First(s => s is Cube).Enabled = true;
      grammar.Symbols.First(s => s is CubeRoot).Enabled = true;
      grammar.Symbols.First(s => s is Sine).Enabled = true;
      grammar.Symbols.First(s => s is Cosine).Enabled = true;
      grammar.Symbols.First(s => s is Exponential).Enabled = true;
      grammar.Symbols.First(s => s is Logarithm).Enabled = true;
      grammar.Symbols.First(s => s is Absolute).Enabled = false; // XXX not yet supported by old interval calculator
      grammar.Symbols.First(s => s is AnalyticQuotient).Enabled = false; // not yet supported by old interval calculator

      var varSy = (Variable)grammar.Symbols.First(s => s is Variable);
      varSy.AllVariableNames = new string[] { "x", "y" };
      varSy.VariableNames = varSy.AllVariableNames;
      varSy.WeightMu = 1.0;
      varSy.WeightSigma = 1.0;
      var rand = new FastRandom(1234);
      var eval1 = new IntervalEvaluator();
      var eval2 = new IntervalInterpreter();

      IDictionary<string, Interval> posIntervals = new Dictionary<string, Interval>() {
        { "x", new Interval(1, 2) },
        { "y", new Interval(0, 1) }
      };
      IDictionary<string, Interval> negIntervals = new Dictionary<string, Interval>() {
        { "x", new Interval(-2, -1) },
        { "y", new Interval(-1, 0) }
      };
      IDictionary<string, Interval> fullIntervals = new Dictionary<string, Interval>() {
        { "x", new Interval(-2, 2) },
        { "y", new Interval(-1, 1) }
      };
      IDictionary<string, Interval> specialIntervals = new Dictionary<string, Interval>() {
        { "x", new Interval(1, double.PositiveInfinity) },
        { "y", new Interval(double.NegativeInfinity, double.PositiveInfinity) }
      };

      var formatter = new InfixExpressionFormatter();
      var sb = new StringBuilder();
      foreach (var interval in new[] { posIntervals, negIntervals, fullIntervals, specialIntervals }) {
        int N = 10000;
        int i = 0;
        while (i < N) {
          var t = ProbabilisticTreeCreator.Create(rand, grammar, maxTreeLength: 5, maxTreeDepth: 5);
          var r1 = eval1.Evaluate(t, interval);
          var r2 = eval2.GetSymbolicExpressionTreeInterval(t, interval);
          // Console.WriteLine(formatter.Format(t));

          // all NaN is ok (but don't count NaN expressions)
          if (double.IsNaN(r1.LowerBound) && double.IsNaN(r2.LowerBound) && double.IsNaN(r1.UpperBound) && double.IsNaN(r2.UpperBound)) continue;
          if (r1.LowerBound == r2.LowerBound && r1.UpperBound == r2.UpperBound) {
            /* exactly the same value (incl. Inf / -Inf) => ok */
          } else if ((Math.Abs(r1.LowerBound - r2.LowerBound) <= Math.Max(1e-10, Math.Abs(r1.LowerBound * 1e-4))) &&
                     (Math.Abs(r1.UpperBound - r2.UpperBound) <= Math.Max(1e-10, Math.Abs(r1.UpperBound * 1e-4)))) { 
            /* approximately the same value => OK */
          } else {
            sb.AppendLine($"{r1} <> {r2} for {formatter.Format(t)} x={interval["x"]} y={interval["y"]}");
          }
          i++;
        }
      }
      if (sb.Length > 0) {
        Console.WriteLine(sb.ToString());
        Assert.Fail("There were different interval calculation results");
      }
    }

    [TestMethod]
    [TestCategory("Problems.DataAnalysis")]
    [TestProperty("Time", "short")]
    public void IntervalEvaluatorConsistencyForExamples() {
      var parser = new InfixExpressionParser();
      var eval1 = new IntervalEvaluator();
      var eval2 = new IntervalInterpreter();
      IDictionary<string, Interval> interval = new Dictionary<string, Interval>() {
        { "x", new Interval(1, 2) },
        { "y", new Interval(0, 1) },
        { "z", new Interval(double.NegativeInfinity, double.PositiveInfinity) },
      };

      var exprs = new string[] {
        "CUBE((0.642971622547268*'x')) * (-16.5400720573962)",
        "sqr(y / y)", // one interpreter produces [NaN, inf], the other [NaN, 0]
        "cuberoot(-x)", // the old interpreter calculates cuberoot incorrectly
        "sqr(log(-x))", // Interval: [NaN, NaN] <> Interval (old): [NaN, 0]
        "log(1.8*'y' - 1.4*'y')", // Interval: [NaN, 0,587786664902119] <> Interval (old): [0,587786664902119, NaN]
        "log(z)", // Interval: [NaN, ∞] <> Interval (old): [∞, NaN]
        "sqr(sqrt(-1))" // Interval: [NaN, NaN] <> Interval (old): [NaN, 0]
      };

      var formatter = new InfixExpressionFormatter();
      var sb = new StringBuilder();
      foreach (var expr in exprs) {
        var t = parser.Parse(expr);

        var r1 = eval1.Evaluate(t, interval);
        var r2 = eval2.GetSymbolicExpressionTreeInterval(t, interval);
        // Console.WriteLine(formatter.Format(t));

        // all NaN is ok
        if (double.IsNaN(r1.LowerBound) && double.IsNaN(r2.LowerBound) && double.IsNaN(r1.UpperBound) && double.IsNaN(r2.UpperBound)) continue;
        if (r1.LowerBound == r2.LowerBound && r1.UpperBound == r2.UpperBound) continue;  // Inf, -Inf and exactly the same value are ok

        if ((Math.Abs(r1.LowerBound - r2.LowerBound) <= Math.Abs(r1.LowerBound * 1e-4)) &&
            (Math.Abs(r1.UpperBound - r2.UpperBound) <= Math.Abs(r1.UpperBound * 1e-4))) { /* OK */ } else {
          sb.AppendLine($"{r1} <> {r2} for {formatter.Format(t)} x={interval["x"]} y={interval["y"]}");
        }
      }
      if (sb.Length > 0) {
        Console.WriteLine(sb.ToString());
        Assert.Fail("There were different interval calculation results");
      }
    }
  }
}