#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2013 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion

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

namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Tests {

  [TestClass()]
  public class SymbolicDataAnalysisExpressionTreeSimplifierTest {
    [TestMethod]
    public void SimplifierAxiomsTest() {
      SymbolicExpressionImporter importer = new SymbolicExpressionImporter();
      SymbolicDataAnalysisExpressionTreeSimplifier simplifier = new SymbolicDataAnalysisExpressionTreeSimplifier();
      SymbolicExpressionTreeStringFormatter formatter = new SymbolicExpressionTreeStringFormatter();
      #region single argument arithmetics
      {
        var actualTree = simplifier.Simplify(importer.Import("(+ 1.0)"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(+ (variable 2.0 a))"));
        var expectedTree = importer.Import("(variable 2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(- 1.0)"));
        var expectedTree = importer.Import("-1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(- (variable 2.0 a))"));
        var expectedTree = importer.Import("(variable -2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(* 2.0)"));
        var expectedTree = importer.Import("2.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(* (variable 2.0 a))"));
        var expectedTree = importer.Import("(variable 2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(/ 2.0)"));
        var expectedTree = importer.Import("0.5");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(/ (variable 2.0 a))"));
        var expectedTree = importer.Import("(/ 1.0 (variable 2.0 a))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region aggregation of constants into factors
      {
        var actualTree = simplifier.Simplify(importer.Import("(* 2.0 (variable 2.0 a))"));
        var expectedTree = importer.Import("(variable 4.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(/ (variable 2.0 a) 2.0)"));
        var expectedTree = importer.Import("(variable 1.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(/ (variable 2.0 a) (* 2.0 2.0))"));
        var expectedTree = importer.Import("(variable 0.5 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region constant and variable folding
      {
        var actualTree = simplifier.Simplify(importer.Import("(+ 1.0 2.0)"));
        var expectedTree = importer.Import("3.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(+ (variable 2.0 a) (variable 2.0 a))"));
        var expectedTree = importer.Import("(variable 4.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(- (variable 2.0 a) (variable 1.0 a))"));
        var expectedTree = importer.Import("(variable 1.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(* (variable 2.0 a) (variable 2.0 a))"));
        var expectedTree = importer.Import("(* (* (variable 1.0 a) (variable 1.0 a)) 4.0)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        var actualTree = simplifier.Simplify(importer.Import("(/ (variable 1.0 a) (variable 2.0 a))"));
        var expectedTree = importer.Import("0.5");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region logarithm rules
      {
        // cancellation
        var actualTree = simplifier.Simplify(importer.Import("(log (exp (variable 2.0 a)))"));
        var expectedTree = importer.Import("(variable 2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // must not transform logs in this way as we do not know wether both variables are positive
        var actualTree = simplifier.Simplify(importer.Import("(log (* (variable 1.0 a) (variable 1.0 b)))"));
        var expectedTree = importer.Import("(log (* (variable 1.0 a) (variable 1.0 b)))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // must not transform logs in this way as we do not know wether both variables are positive
        var actualTree = simplifier.Simplify(importer.Import("(log (/ (variable 1.0 a) (variable 1.0 b)))"));
        var expectedTree = importer.Import("(log (/ (variable 1.0 a) (variable 1.0 b)))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region exponentiation rules
      {
        // cancellation
        var actualTree = simplifier.Simplify(importer.Import("(exp (log (variable 2.0 a)))"));
        var expectedTree = importer.Import("(variable 2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // exp transformation
        var actualTree = simplifier.Simplify(importer.Import("(exp (+ (variable 2.0 a) (variable 3.0 b)))"));
        var expectedTree = importer.Import("(* (exp (variable 2.0 a)) (exp (variable 3.0 b)))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // exp transformation
        var actualTree = simplifier.Simplify(importer.Import("(exp (- (variable 2.0 a) (variable 3.0 b)))"));
        var expectedTree = importer.Import("(* (exp (variable 2.0 a)) (exp (variable -3.0 b)))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // exp transformation
        var actualTree = simplifier.Simplify(importer.Import("(exp (- (variable 2.0 a) (* (variable 3.0 b) (variable 4.0 c))))"));
        var expectedTree = importer.Import("(* (exp (variable 2.0 a)) (exp (* (variable 1.0 b) (variable 1.0 c) -12.0)))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // exp transformation
        var actualTree = simplifier.Simplify(importer.Import("(exp (- (variable 2.0 a) (* (variable 3.0 b) (cos (variable 4.0 c)))))"));
        var expectedTree = importer.Import("(* (exp (variable 2.0 a)) (exp (* (variable 1.0 b) (cos (variable 4.0 c)) -3.0)))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region power rules
      {
        // cancellation
        var actualTree = simplifier.Simplify(importer.Import("(pow (variable 2.0 a) 0.0)"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // fixed point
        var actualTree = simplifier.Simplify(importer.Import("(pow (variable 2.0 a) 1.0)"));
        var expectedTree = importer.Import("(variable 2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // inversion fixed point
        var actualTree = simplifier.Simplify(importer.Import("(pow (variable 2.0 a) -1.0)"));
        var expectedTree = importer.Import("(/ 1.0 (variable 2.0 a))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // inversion 
        var actualTree = simplifier.Simplify(importer.Import("(pow (variable 2.0 a) -2.0)"));
        var expectedTree = importer.Import("(/ 1.0 (pow (variable 2.0 a) 2.0))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // constant folding
        var actualTree = simplifier.Simplify(importer.Import("(pow 3.0 2.0)"));
        var expectedTree = importer.Import("9.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region root rules
      {
        // cancellation
        var actualTree = simplifier.Simplify(importer.Import("(root (variable 2.0 a) 0.0)"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // fixed point
        var actualTree = simplifier.Simplify(importer.Import("(root (variable 2.0 a) 1.0)"));
        var expectedTree = importer.Import("(variable 2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // inversion fixed point
        var actualTree = simplifier.Simplify(importer.Import("(root (variable 2.0 a) -1.0)"));
        var expectedTree = importer.Import("(/ 1.0 (variable 2.0 a))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // inversion
        var actualTree = simplifier.Simplify(importer.Import("(root (variable 2.0 a) -2.0)"));
        var expectedTree = importer.Import("(/ 1.0 (root (variable 2.0 a) 2.0))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // constant folding
        var actualTree = simplifier.Simplify(importer.Import("(root 9.0 2.0)"));
        var expectedTree = importer.Import("3.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region boolean operations
      {
        // always true and
        var actualTree = simplifier.Simplify(importer.Import("(and 1.0 2.0)"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // always false and
        var actualTree = simplifier.Simplify(importer.Import("(and 1.0 -2.0)"));
        var expectedTree = importer.Import("-1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // always true or
        var actualTree = simplifier.Simplify(importer.Import("(or -1.0 2.0)"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // always false or
        var actualTree = simplifier.Simplify(importer.Import("(or -1.0 -2.0)"));
        var expectedTree = importer.Import("-1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // constant not 
        var actualTree = simplifier.Simplify(importer.Import("(not -2.0)"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // constant not 
        var actualTree = simplifier.Simplify(importer.Import("(not 2.0)"));
        var expectedTree = importer.Import("-1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // constant not 
        var actualTree = simplifier.Simplify(importer.Import("(not 0.0)"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // nested nots
        var actualTree = simplifier.Simplify(importer.Import("(not (not 1.0))"));
        var expectedTree = importer.Import("1.0");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // not of non-Boolean argument
        var actualTree = simplifier.Simplify(importer.Import("(not (variable 1.0 a))"));
        var expectedTree = importer.Import("(not (> (variable 1.0 a) 0.0))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // not Boolean argument
        var actualTree = simplifier.Simplify(importer.Import("(not (and (> (variable 1.0 a) 0.0) (> (variable 1.0 a) 0.0)))"));
        var expectedTree = importer.Import("(not (and (> (variable 1.0 a) 0.0) (> (variable 1.0 a) 0.0)))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
      #region conditionals
      {
        // always false
        var actualTree = simplifier.Simplify(importer.Import("(if -1.0 (variable 2.0 a) (variable 3.0 a))"));
        var expectedTree = importer.Import("(variable 3.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // always true
        var actualTree = simplifier.Simplify(importer.Import("(if 1.0 (variable 2.0 a) (variable 3.0 a))"));
        var expectedTree = importer.Import("(variable 2.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // always false (0.0)
        var actualTree = simplifier.Simplify(importer.Import("(if 0.0 (variable 2.0 a) (variable 3.0 a))"));
        var expectedTree = importer.Import("(variable 3.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // complex constant condition (always false)
        var actualTree = simplifier.Simplify(importer.Import("(if (* 1.0 -2.0) (variable 2.0 a) (variable 3.0 a))"));
        var expectedTree = importer.Import("(variable 3.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // complex constant condition (always false)
        var actualTree = simplifier.Simplify(importer.Import("(if (/ (variable 1.0 a) (variable -2.0 a)) (variable 2.0 a) (variable 3.0 a))"));
        var expectedTree = importer.Import("(variable 3.0 a)");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      {
        // insertion of relational operator
        var actualTree = simplifier.Simplify(importer.Import("(if (variable 1.0 a) (variable 2.0 a) (variable 3.0 a))"));
        var expectedTree = importer.Import("(if (> (variable 1.0 a) 0.0) (variable 2.0 a) (variable 3.0 a))");
        Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree));
      }
      #endregion
    }

    private void AssertEqualEnumerations(IEnumerable<double> expected, IEnumerable<double> actual) {
      var expectedEnumerator = expected.GetEnumerator();
      var actualEnumerator = actual.GetEnumerator();
      while (expectedEnumerator.MoveNext() & actualEnumerator.MoveNext()) {
        Assert.AreEqual(expectedEnumerator.Current, actualEnumerator.Current, Math.Abs(1E-6 * expectedEnumerator.Current));
      }
      if (expectedEnumerator.MoveNext() | actualEnumerator.MoveNext())
        Assert.Fail("Number of elements in enumerations do not match");
    }
  }
}