using System; using System.Collections.Generic; using HeuristicLab.Problems.DataAnalysis.Symbolic; using Microsoft.VisualStudio.TestTools.UnitTesting; namespace HeuristicLab.Problems.DataAnalysis.Tests { [TestClass] public class AutoDiffIntervalTest { private readonly AlgebraicInterval a = new AlgebraicInterval(-1, 1); private readonly AlgebraicInterval b = new AlgebraicInterval(-2, 2); private readonly AlgebraicInterval c = new AlgebraicInterval(0, 3); private readonly AlgebraicInterval d = new AlgebraicInterval(1, 3); private readonly AlgebraicInterval e = new AlgebraicInterval(4, 6); private readonly IntervalEvaluator eval = new IntervalEvaluator(); [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalAddOperation() { //add [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2] // [-1,1] + [-2,2] = [-3,3] AssertAreEqualInterval(Add(a, b), new AlgebraicInterval(-3, 3)); //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6] AssertAreEqualInterval(Add(Add(a, b), c), new AlgebraicInterval(-3, 6)); //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6] AssertAreEqualInterval(Add(Add(a, c), b), new AlgebraicInterval(-3, 6)); } private void AssertAreEqualInterval(AlgebraicInterval a, AlgebraicInterval b) { if (double.IsNaN(a.LowerBound.Value)) { Assert.IsTrue(double.IsNaN(b.LowerBound.Value)); } else { Assert.AreEqual(a.LowerBound.Value.Value, b.LowerBound.Value.Value, Math.Abs(a.LowerBound.Value.Value)*1e-4); // relative error < 0.1% } if (double.IsNaN(a.UpperBound.Value)) { Assert.IsTrue(double.IsNaN(b.UpperBound.Value)); } else { Assert.AreEqual(a.UpperBound.Value.Value, b.UpperBound.Value.Value, Math.Abs(a.UpperBound.Value.Value) * 1e-4); } } private static AlgebraicInterval Add(AlgebraicInterval a, AlgebraicInterval b) { return a.Clone().Add(b); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalSubOperation() { //subtract [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1] //[-1, 1] - [-2, 2] = [-3, 3] AssertAreEqualInterval(Subtract(a, b), new AlgebraicInterval(-3, 3)); //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3] AssertAreEqualInterval(Subtract(Subtract(a, b), c), new AlgebraicInterval(-6, 3)); //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3] AssertAreEqualInterval(Subtract(Subtract(a, c), b), new AlgebraicInterval(-6, 3)); } private AlgebraicInterval Subtract(AlgebraicInterval a, AlgebraicInterval b) { return a.Clone().Sub(b); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalMutlipyOperation() { //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] AssertAreEqualInterval(Multiply(a, b), new AlgebraicInterval(-2, 2)); //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6] AssertAreEqualInterval(Multiply(Multiply(a, b), c), new AlgebraicInterval(-6, 6)); //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6] AssertAreEqualInterval(Multiply(Multiply(a, c), b), new AlgebraicInterval(-6, 6)); // [-2, 0] * [-2, 0] = [0, 4] AssertAreEqualInterval(new AlgebraicInterval(0, 4), Multiply(new AlgebraicInterval(-2, 0), new AlgebraicInterval(-2, 0))); } private AlgebraicInterval Multiply(AlgebraicInterval a, AlgebraicInterval b) { return a.Clone().Mul(b); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalDivideOperation() { //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] AssertAreEqualInterval(Divide(e, d), new AlgebraicInterval(4.0 / 3.0, 6)); //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6] AssertAreEqualInterval(Divide(Divide(e, d), d), new AlgebraicInterval(4.0 / 9.0, 6)); //[4, 6] / [0, 3] = [4/3, +Inf] AssertAreEqualInterval(Divide(e, c), new AlgebraicInterval(4.0 / 3.0, double.PositiveInfinity)); //[-1, 1] / [0, 3] = [+Inf, -Inf] AssertAreEqualInterval(Divide(a, c), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity)); //Division by 0 ==> IsInfiniteOrUndefined == true AssertAreEqualInterval(Divide(d, b), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity)); // [0, 1] / [0, 1] AssertAreEqualInterval(new AlgebraicInterval(0, 1).Div(new AlgebraicInterval(0, 1)), new AlgebraicInterval(1, double.PositiveInfinity)); // returns [NaN, PositiveInfinity] } private AlgebraicInterval Divide(AlgebraicInterval e, AlgebraicInterval d) { return e.Clone().Div(d); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalSineOperator() { //sine depends on interval //sin([0, 2*pi]) = [-1, 1] AssertAreEqualInterval(Sine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1)); //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)] AssertAreEqualInterval(Sine(new AlgebraicInterval(-1 * Math.PI / 2, Math.PI / 2)), new AlgebraicInterval(-1, 1)); //sin([0, pi/2]) = [sin(0), sin(pi/2)] AssertAreEqualInterval(Sine(new AlgebraicInterval(0, Math.PI / 2)), new AlgebraicInterval(0, 1)); //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)] AssertAreEqualInterval(Sine(new AlgebraicInterval(Math.PI, 3 * Math.PI / 2)), new AlgebraicInterval(-1, 0)); AssertAreEqualInterval(Sine(new AlgebraicInterval(1, 2)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(2)), 1)); AssertAreEqualInterval(Sine(new AlgebraicInterval(1, 3)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(3)), 1)); AssertAreEqualInterval(Sine(new AlgebraicInterval(Math.PI, 5 * Math.PI / 2)), new AlgebraicInterval(-1, 1)); } private AlgebraicInterval Sine(AlgebraicInterval algebraicInterval) { return algebraicInterval.Sin(); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalCosineOperator() { //Cosine uses sine Sine(Subtract(a, new AlgebraicInterval(Math.PI / 2, Math.PI / 2))); AssertAreEqualInterval(Cosine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1)); AssertAreEqualInterval(new AlgebraicInterval(-1, 1), Cosine(new AlgebraicInterval(Math.PI, 4 * Math.PI / 2))); } private AlgebraicInterval Cosine(AlgebraicInterval algebraicInterval) { return algebraicInterval.Cos(); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalLogOperator() { //Log([3, 5]) = [log(3), log(5)] AssertAreEqualInterval(new AlgebraicInterval(Math.Log(3), Math.Log(5)), Logarithm(new AlgebraicInterval(3, 5))); //Log([0.5, 1]) = [log(0.5), log(1)] AssertAreEqualInterval(new AlgebraicInterval(Math.Log(0.5), 0), Logarithm(new AlgebraicInterval(0.5, 1))); //Log([-1, 5]) = [NaN, log(5)] var result = Logarithm(new AlgebraicInterval(-1, 5)); AssertAreEqualInterval(new AlgebraicInterval(double.NaN, Math.Log(5)), result); } private AlgebraicInterval Logarithm(AlgebraicInterval algebraicInterval) { return algebraicInterval.Log(); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalExpOperator() { //Exp([0, 1]) = [exp(0), exp(1)] AssertAreEqualInterval(new AlgebraicInterval(1, Math.Exp(1)), Exponential(new AlgebraicInterval(0, 1))); } private AlgebraicInterval Exponential(AlgebraicInterval algebraicInterval) { return algebraicInterval.Exp(); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalSqrOperator() { AssertAreEqualInterval(new AlgebraicInterval(1, 4), new AlgebraicInterval(1, 2).IntPower(2)); AssertAreEqualInterval(new AlgebraicInterval(1, 4), new AlgebraicInterval(-2, -1).IntPower(2)); AssertAreEqualInterval(new AlgebraicInterval(0, 4), new AlgebraicInterval(-2, 2).IntPower(2)); AssertAreEqualInterval(new AlgebraicInterval(0, 16), new AlgebraicInterval(-2, 2).Mul(new AlgebraicInterval(2, 2)).IntPower(2)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalSqrtOperator() { AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(1, 4).IntRoot(2)); AssertAreEqualInterval(new AlgebraicInterval(double.NaN, double.NaN), new AlgebraicInterval(-4, -1).IntRoot(2)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalCubeOperator() { AssertAreEqualInterval(new AlgebraicInterval(1, 8), new AlgebraicInterval(1, 2).IntPower(3)); AssertAreEqualInterval(new AlgebraicInterval(-8, -1), new AlgebraicInterval(-2, -1).IntPower(3)); AssertAreEqualInterval(new AlgebraicInterval(-8, 8), new AlgebraicInterval(-2, 2).IntPower(3)); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalAbsOperator() { AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(1, 2).Abs()); AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(-2, -1).Abs()); AssertAreEqualInterval(new AlgebraicInterval(0, 2), new AlgebraicInterval(-2, 2).Abs()); AssertAreEqualInterval(new AlgebraicInterval(0, double.PositiveInfinity), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity).Abs()); AssertAreEqualInterval(new AlgebraicInterval(double.NaN, 1), new AlgebraicInterval(-1, double.NaN).Abs()); // XXX unclear how we should handle NaN AssertAreEqualInterval(new AlgebraicInterval(double.NaN, 1), new AlgebraicInterval(double.NaN, -1).Abs()); } [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void TestIntervalCbrtOperator() { AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(1, 8).IntRoot(3)); AssertAreEqualInterval(new AlgebraicInterval(-2, -1), new AlgebraicInterval(-8, -1).IntRoot(3)); } } }