using System; using System.Collections.Generic; using Microsoft.VisualStudio.TestTools.UnitTesting; namespace HeuristicLab.Problems.DataAnalysis.Tests { [TestClass] public class IntervalTest { private readonly Interval a = new Interval(-1, 1); private readonly Interval b = new Interval(-2, 2); private readonly Interval c = new Interval(0, 3); private readonly Interval d = new Interval(1, 3); private readonly Interval e = new Interval(4, 6); [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void AddIntervalTest() { //add [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2] // [-1,1] + [-2,2] = [-3,3] Assert.AreEqual(Interval.Add(a, b), new Interval(-3, 3)); //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6] Assert.AreEqual(Interval.Add(Interval.Add(a, b), c), new Interval(-3, 6)); //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6] Assert.AreEqual(Interval.Add(Interval.Add(a, c), b), new Interval(-3, 6)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void SubtractIntervalTest() { //subtract [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1] //[-1, 1] - [-2, 2] = [-3, 3] Assert.AreEqual(Interval.Subtract(a, b), new Interval(-3, 3)); //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3] Assert.AreEqual(Interval.Subtract(Interval.Subtract(a, b), c), new Interval(-6, 3)); //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3] Assert.AreEqual(Interval.Subtract(Interval.Subtract(a, c), b), new Interval(-6, 3)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void MultiplyIntervalTest() { //multiply [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)] //[-1, 1] * [-2, 2] = [-2, 2] Assert.AreEqual(Interval.Multiply(a, b), new Interval(-2, 2)); //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6] Assert.AreEqual(Interval.Multiply(Interval.Multiply(a, b), c), new Interval(-6, 6)); //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6] Assert.AreEqual(Interval.Multiply(Interval.Multiply(a, c), b), new Interval(-6, 6)); // [-2, 0] * [-2, 0] = [0, 4] Assert.AreEqual(new Interval(0, 4), Interval.Multiply(new Interval(-2, 0), new Interval(-2, 0))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void DivideIntervalTest() { //divide [x1, x2] / [y1, y2] = [x1, x2] * (1/[y1, y2]), where 1 / [y1,y2] = [1 / y2,1 / y1] if 0 not in [y_1, y_2]. //[4, 6] / [1, 3] = [4/3, 6] Assert.AreEqual(Interval.Divide(e, d), new Interval(4.0 / 3.0, 6)); //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6] Assert.AreEqual(Interval.Divide(Interval.Divide(e, d), d), new Interval(4.0 / 9.0, 6)); //[4, 6] / [0, 3] = [4/3, +Inf] Assert.AreEqual(Interval.Divide(e, c), new Interval(4.0 / 3.0, double.PositiveInfinity)); //[-1, 1] / [0, 3] = [+Inf, -Inf] Assert.AreEqual(Interval.Divide(a, c), new Interval(double.NegativeInfinity, double.PositiveInfinity)); //Devision by 0 ==> IsInfiniteOrUndefined == true Assert.IsTrue(Interval.Divide(e, c).IsInfiniteOrUndefined); //Devision by 0 ==> IsInfiniteOrUndefined == true Assert.IsTrue(Interval.Divide(a, c).IsInfiniteOrUndefined); Assert.AreEqual(Interval.Divide(d, b), new Interval(double.NegativeInfinity, double.PositiveInfinity)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void SineIntervalTest() { //sine depends on interval //sin([0, 2*pi]) = [-1, 1] Assert.AreEqual(Interval.Sine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1)); //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)] Assert.AreEqual(Interval.Sine(new Interval(-1 * Math.PI / 2, Math.PI / 2)), new Interval(-1, 1)); //sin([0, pi/2]) = [sin(0), sin(pi/2)] Assert.AreEqual(Interval.Sine(new Interval(0, Math.PI / 2)), new Interval(0, 1)); //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)] Assert.AreEqual(Interval.Sine(new Interval(Math.PI, 3 * Math.PI / 2)), new Interval(-1, 0)); Assert.AreEqual(Interval.Sine(new Interval(1, 2)), new Interval(Math.Min(Math.Sin(1), Math.Sin(2)), 1)); Assert.AreEqual(Interval.Sine(new Interval(1, 3)), new Interval(Math.Min(Math.Sin(1), Math.Sin(3)), 1)); Assert.AreEqual(Interval.Sine(new Interval(Math.PI, 5 * Math.PI / 2)), new Interval(-1, 1)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void CosineIntervalTest() { //Cosine uses sine Interval.Sine(Interval.Subtract(a, new Interval(Math.PI / 2, Math.PI / 2))); Assert.AreEqual(Interval.Cosine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1)); Assert.AreEqual(new Interval(-1, 1), Interval.Cosine(new Interval(Math.PI, 4 * Math.PI / 2))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void LogIntervalTest() { //Log([3, 5]) = [log(3), log(5)] Assert.AreEqual(new Interval(Math.Log(3), Math.Log(5)), Interval.Logarithm(new Interval(3, 5))); //Log([0.5, 1]) = [log(0.5), log(1)] Assert.AreEqual(new Interval(Math.Log(0.5), 0), Interval.Logarithm(new Interval(0.5, 1))); //Log([-1, 5]) = [NaN, log(5)] var result = Interval.Logarithm(new Interval(-1, 5)); Assert.AreEqual(new Interval(double.NaN, Math.Log(5)),result); Assert.IsTrue(result.IsInfiniteOrUndefined); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void ExponentialIntervalTest() { //Exp([0, 1]) = [exp(0), exp(1)] Assert.AreEqual(new Interval(1, Math.Exp(1)), Interval.Exponential(new Interval(0, 1))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void SquareIntervalTest() { Assert.AreEqual(new Interval(1, 4), Interval.Square(new Interval(1, 2))); Assert.AreEqual(new Interval(1, 4), Interval.Square(new Interval(-2, -1))); Assert.AreEqual(new Interval(0, 4), Interval.Square(new Interval(-2, 2))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void SquarerootIntervalTest() { Assert.AreEqual(new Interval(-2, 2), Interval.SquareRoot(new Interval(1, 4))); Assert.AreEqual(new Interval(double.NaN, double.NaN), Interval.SquareRoot(new Interval(-4, -1))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void CubeIntervalTest() { Assert.AreEqual(new Interval(1, 8), Interval.Cube(new Interval(1, 2))); Assert.AreEqual(new Interval(-8, -1), Interval.Cube(new Interval(-2, -1))); Assert.AreEqual(new Interval(-8, 8), Interval.Cube(new Interval(-2, 2))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void CubeRootIntervalTest() { Assert.AreEqual(new Interval(1, 2), Interval.CubicRoot(new Interval(1, 8))); Assert.AreEqual(new Interval(-2, -2), Interval.CubicRoot(new Interval(-8, -8))); Assert.AreEqual(new Interval(-2, 2), Interval.CubicRoot(new Interval(-8, 8))); Assert.AreEqual(new Interval(2, 2), Interval.CubicRoot(new Interval(8, 8))); Assert.AreEqual(new Interval(-Math.Pow(6, 1.0 / 3), 2), Interval.CubicRoot(new Interval(-6, 8))); Assert.AreEqual(new Interval(2, 2), Interval.CubicRoot(new Interval(8, 8))); Assert.AreEqual(new Interval(-2, 0), Interval.CubicRoot(new Interval(-8, 0))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void AbsoluteIntervalTest() { Assert.AreEqual(new Interval(2, 5), Interval.Absolute(new Interval(-5, -2))); Assert.AreEqual(new Interval(2, 5), Interval.Absolute(new Interval(2, 5))); Assert.AreEqual(new Interval(0, 3), Interval.Absolute(new Interval(-3, 0))); Assert.AreEqual(new Interval(0, 5), Interval.Absolute(new Interval(0, 5))); Assert.AreEqual(new Interval(0, 5), Interval.Absolute(new Interval(-2, 5))); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void AnalyticalQuotientIntervalTest() { //Analytical Quotient ==> a / sqrt(b^2 + 1) var aPos = new Interval(3, 5); var aZero = new Interval(-3, 5); var aNeg = new Interval(-5, -3); var bPos = new Interval(2, 4); var bZero = new Interval(-2, 4); var bNeg = new Interval(-4, -2); //Second interval goes over zero //Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound), Interval.AnalyticalQuotient(aPos, bZero)); //Assert.AreEqual(new Interval(aZero.LowerBound, aZero.UpperBound), Interval.AnalyticalQuotient(aZero, bZero)); //Assert.AreEqual(new Interval(aNeg.LowerBound, aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bZero)); ////Second interval is positive //Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aPos, bPos)); //Assert.AreEqual(new Interval(aZero.LowerBound/Math.Sqrt(5), aZero.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aZero, bPos)); //Assert.AreEqual(new Interval(aNeg.LowerBound/Math.Sqrt(5), aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bPos)); ////Second interval is negative //Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aPos, bNeg)); //Assert.AreEqual(new Interval(aZero.LowerBound/Math.Sqrt(5), aZero.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aZero, bNeg)); //Assert.AreEqual(new Interval(aNeg.LowerBound/Math.Sqrt(5), aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bNeg)); Assert.AreEqual(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.AnalyticalQuotient(aPos, bZero)); Assert.AreEqual(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.AnalyticalQuotient(aPos, bPos)); Assert.AreEqual(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.AnalyticalQuotient(aZero, bNeg)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void IsNegativeIntervalTest() { Assert.IsTrue(new Interval(-2, -1).IsNegative); Assert.IsFalse(new Interval(-2, 0).IsNegative); Assert.IsFalse(new Interval(-2, 2).IsNegative); Assert.IsFalse(new Interval(2, 4).IsNegative); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void IsPositiveIntervalTest() { Assert.IsTrue(new Interval(3, 5).IsPositive); Assert.IsFalse(new Interval(0, 5).IsPositive); Assert.IsFalse(new Interval(-1, 5).IsPositive); Assert.IsFalse(new Interval(-5, -2).IsPositive); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void IsAlmostIntervalTest() { var negativeLowerBound = -2E-13; var negativeUpperBound = -1E-13; var positiveLowerBound = 3E-13; var positiveUpperBound = 5E-13; var negativeInterval = new Interval(negativeLowerBound, negativeUpperBound); var positiveInterval = new Interval(positiveLowerBound, positiveUpperBound); var zeroInterval = new Interval(negativeUpperBound, positiveLowerBound); //Check for right-shift of negative interval Assert.AreEqual(negativeUpperBound, negativeInterval.LowerBound); Assert.AreEqual(negativeUpperBound, negativeInterval.UpperBound); //Check for left-shift of positive interval Assert.AreEqual(positiveLowerBound, positiveInterval.LowerBound); Assert.AreEqual(positiveLowerBound, positiveInterval.UpperBound); //Check for setting interval to zero Assert.AreEqual(0, zeroInterval.LowerBound); Assert.AreEqual(0, zeroInterval.UpperBound); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void ContaintsTest() { var negativeInterval = new Interval(-10, -5); var positiveInterval = new Interval(5, 10); var overZeroInterval = new Interval(-5, 5); //Tests for negative intervals Assert.AreEqual(true, negativeInterval.Contains(new Interval(-9, -7))); Assert.AreEqual(false, negativeInterval.Contains(new Interval(-11, -3))); Assert.AreEqual(false, negativeInterval.Contains(positiveInterval)); Assert.AreEqual(false, negativeInterval.Contains(overZeroInterval)); Assert.AreEqual(true, negativeInterval.Contains(-8)); Assert.AreEqual(false, negativeInterval.Contains(-12)); Assert.AreEqual(false, negativeInterval.Contains(0)); //Testes for positive intervals Assert.AreEqual(true, positiveInterval.Contains(new Interval(6, 10))); Assert.AreEqual(false, positiveInterval.Contains(new Interval(6, 12))); Assert.AreEqual(false, positiveInterval.Contains(negativeInterval)); Assert.AreEqual(false, positiveInterval.Contains(overZeroInterval)); Assert.AreEqual(true, positiveInterval.Contains(7)); Assert.AreEqual(false, positiveInterval.Contains(11)); Assert.AreEqual(false, positiveInterval.Contains(0)); //Tests for over zero intervals Assert.AreEqual(true, overZeroInterval.Contains(new Interval(-3, 3))); Assert.AreEqual(true, overZeroInterval.Contains(new Interval(-4, -1))); Assert.AreEqual(true, overZeroInterval.Contains(new Interval(1, 5))); Assert.AreEqual(false, overZeroInterval.Contains(new Interval(-6, 0))); Assert.AreEqual(false, overZeroInterval.Contains(new Interval(0, 6))); Assert.AreEqual(false, overZeroInterval.Contains(new Interval(-7, 7))); Assert.AreEqual(true, overZeroInterval.Contains(-3)); Assert.AreEqual(true, overZeroInterval.Contains(0)); Assert.AreEqual(true, overZeroInterval.Contains(3)); Assert.AreEqual(false, overZeroInterval.Contains(12)); Assert.AreEqual(false, overZeroInterval.Contains(-7)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void GetIntervalTest() { var values = new List() { -2.5, -9, 2, 7, 0 ,12, 12.4, 12.4, 9.29, 1002, -29.9}; var valuesNan = new List() { double.NaN, 2, 4, 19, -2, -12.2}; var valuesInf = new List() {double.NegativeInfinity, double.PositiveInfinity, 12, 2, -2, -12.2}; var valuesInterval = new Interval(-29.9, 1002); var valuesNanInterval = new Interval(double.NaN, double.NaN); var valuesInfInterval = new Interval(double.NegativeInfinity, double.PositiveInfinity); Assert.AreEqual(valuesInterval, Interval.GetInterval(values)); Assert.AreEqual(valuesNanInterval, Interval.GetInterval(valuesNan)); Assert.AreEqual(valuesInfInterval, Interval.GetInterval(valuesInf)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void EqualsTest() { var interval1 = new Interval(0, 12); var interval2 = new Interval(-12, 8); var interval3 = new Interval(double.NegativeInfinity, 0); Assert.AreEqual(true, interval1.Equals(new Interval(0, 12))); Assert.AreEqual(false, interval1.Equals(interval2)); Assert.AreEqual(true, interval3 == new Interval(double.NegativeInfinity, 0)); Assert.AreEqual(true, interval1 != interval2); Assert.AreEqual(false, interval2 == interval3); Assert.AreEqual(false, interval1 != new Interval(0, 12)); } //[TestMethod] //[TestCategory("Problems.DataAnalysis")] //[TestProperty("Time", "short")] //public void RootTest() { // var posInterval = new Interval(3, 5); // var negInterval = new Interval(-6, -2); // var posIntervalConst = new Interval(5, 5); // var negIntervalConst = new Interval(-3, -3); // var zeroIntervalConst = new Interval(0, 0); // var zeroPosInterval = new Interval(0, 2); // var zeroNegInterval = new Interval(-2, 0); // var posRoot = new Interval(4, 4); // var negRoot = new Interval(-4, -4); // var zeroRoot = new Interval(0, 0); // var oneRoot = new Interval(1, 1); // Assert.AreEqual(Interval.Root(posInterval, posRoot), new Interval(Math.Pow(3, (1.0/4)), Math.Pow(5, (1.0/4)))); // Assert.AreEqual(Interval.Root(posInterval, negRoot), new Interval(Math.Pow(5, -(1.0/4)), Math.Pow(3, -(1.0/4)))); // Assert.AreEqual(Interval.Root(posInterval, zeroRoot), new Interval(double.NaN, double.NaN)); // Assert.AreEqual(Interval.Root(posInterval, oneRoot), new Interval(3, 5)); // Assert.AreEqual(Interval.Root(negInterval, posRoot), new Interval(Math.Pow(-6, (1.0 / 4)), Math.Pow(-2, (1.0 / 4)))); // Assert.AreEqual(Interval.Root(negInterval, negRoot), new Interval(Math.Pow(-2, -(1.0 / 4)), Math.Pow(-6, -(1.0 / 4)))); // Assert.AreEqual(Interval.Root(negInterval, zeroRoot), new Interval(double.NaN, double.NaN)); // Assert.AreEqual(Interval.Root(negInterval, oneRoot), new Interval(-6, -2)); // Assert.AreEqual(Interval.Root(posIntervalConst, posRoot), new Interval(Math.Pow(5, (1.0 / 4)), Math.Pow(5, (1.0 / 4)))); // Assert.AreEqual(Interval.Root(posIntervalConst, negRoot), new Interval(Math.Pow(5, -(1.0 / 4)), Math.Pow(5, -(1.0 / 4)))); // Assert.AreEqual(Interval.Root(posIntervalConst, zeroRoot), new Interval(double.NaN, double.NaN)); // Assert.AreEqual(Interval.Root(posIntervalConst, oneRoot), new Interval(5, 5)); // Assert.AreEqual(Interval.Root(negIntervalConst, posRoot), new Interval(Math.Pow(-3, (1.0 / 4)), Math.Pow(-3, (1.0 / 4)))); // Assert.AreEqual(Interval.Root(negIntervalConst, negRoot), new Interval(Math.Pow(-3, -(1.0 / 4)), Math.Pow(-3, -(1.0 / 4)))); // Assert.AreEqual(Interval.Root(negIntervalConst, zeroRoot), new Interval(double.NaN, double.NaN)); // Assert.AreEqual(Interval.Root(negIntervalConst, oneRoot), new Interval(-3, -3)); // Assert.AreEqual(Interval.Root(zeroIntervalConst, posRoot), new Interval(0, 0)); // //Compley Infinity https://www.wolframalpha.com/input/?i=root%28-4%2C+0%29 // Assert.AreEqual(Interval.Root(zeroIntervalConst, negRoot), new Interval(double.PositiveInfinity, double.PositiveInfinity)); // Assert.AreEqual(Interval.Root(zeroIntervalConst, zeroRoot), new Interval(0, 0)); // Assert.AreEqual(Interval.Root(zeroIntervalConst, oneRoot), new Interval(0, 0)); // Assert.AreEqual(Interval.Root(zeroPosInterval, posRoot), new Interval(0, Math.Pow(2, (1.0 / 4)))); // //Check for complex infinity // Assert.AreEqual(Interval.Root(zeroPosInterval, negRoot), new Interval(Math.Pow(2, -(1.0 / 4)), double.PositiveInfinity)); // Assert.AreEqual(Interval.Root(zeroPosInterval, zeroRoot), new Interval(0, 0)); // Assert.AreEqual(Interval.Root(zeroPosInterval, oneRoot), new Interval(0, 2)); // Assert.AreEqual(Interval.Root(zeroNegInterval, posRoot), new Interval(Math.Pow(-2, (1.0 / 4)),0)); // //Check for complex infinity // Assert.AreEqual(Interval.Root(zeroNegInterval, negRoot), new Interval(Math.Pow(-2, -(1.0 / 4)), double.PositiveInfinity)); // Assert.AreEqual(Interval.Root(zeroNegInterval, zeroRoot), new Interval(double.NaN, double.NaN)); // Assert.AreEqual(Interval.Root(zeroNegInterval, oneRoot), new Interval(-2, 0)); //} } }