100 lines
3.0 KiB
C#
100 lines
3.0 KiB
C#
using System;
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using System.Linq;
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using System.Numerics;
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using Skeleton.Algebra.Extensions;
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using Skeleton.DataStructure.Packs.MatrixDecompositions;
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using Skeleton.Samples;
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using Skeleton.Utils.Helpers;
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namespace Skeleton.Test;
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[TestFixture]
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public class EigenDecompositionTest : BaseTest
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{
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private static readonly Complex I = Complex.ImaginaryOne;
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[DatapointSource]
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public static readonly C22[] DataPoints = 30
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.WithSeed(Seed)
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.ScaleSamples(-1, 1)
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.C22InvertibleSamples()
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.ToArray();
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[Theory]
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public static void DecompositionIdentityTest(C22 data)
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{
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JDPair<C22> decomp = data.EigenDecomposition();
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C22 J = decomp.J;
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C22 D = decomp.D;
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Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(data));
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}
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[Theory]
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public static void UnitaryDecompositionTest(C22 data)
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{
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U2 unitaryData = new U2(data);
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Console.WriteLine(data.Representation);
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Console.WriteLine(unitaryData.Representation);
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Console.WriteLine(unitaryData.Hermitian().Representation);
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Console.WriteLine((unitaryData * unitaryData.Hermitian()).Representation);
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Assert.IsTrue((unitaryData * unitaryData.Hermitian()).IsEqualApprox(U2.One));
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Assert.IsTrue(unitaryData.Det().Magnitude.IsEqualApprox(1));
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JDPair<C22> decomp = unitaryData.EigenDecomposition();
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C22 J = decomp.J;
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C22 D = decomp.D;
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Assert.IsTrue(D.Property.IsDiagonal);
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Assert.IsTrue((J * J.Hermitian()).IsEqualApprox(C22.One));
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Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(unitaryData));
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}
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[Test]
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public static void DecompositionTest()
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{
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C22 a = new C22(I, 1, 1, I);
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JDPair<C22> t = a.EigenDecomposition();
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C22 J = t.J;
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C22 D = t.D;
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Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(a));
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}
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[Test]
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public static void UnitaryDecompositionCase0()
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{
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U2 m = new U2(
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-0.08908708063747477 + 0.44543540318737385 * I, 0.3008484477213831 + 0.8385350351383227 * I,
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-0.5345224838248488 + 0.7126966450997985 * I, 0.04608742177859454 - 0.45191277466233243 * I
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);
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JDPair<C22> t = m.EigenDecomposition();
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C22 J = t.J;
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C22 D = t.D;
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Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(m));
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Assert.IsTrue((J * J.Hermitian()).IsEqualApprox(C22.One));
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//C22 JH = J.Hermitian();
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D.SwapRow(1, 2);
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J.SwapColumn(1, 2);
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Console.WriteLine((J.Hermitian()*m*J).Representation);
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Console.WriteLine(" -- ");
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Console.WriteLine(D.Representation);
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//Assert.IsTrue((JH.Hermitian() * D * JH).IsEqualApprox(m));
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}
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[Test]
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public static void UnitaryDecompositionCase1()
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{
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U2 m = new U2(
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0.8666666666666667 - 0.8666666666666667 * I, -0.4 + 0.46666666666666656 * I,
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-0.8666666666666667 - 0.6 * I, 0.6666666666666667
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);
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Console.WriteLine(m.PythonRepresentation);
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Assert.IsTrue((m * m.Hermitian()).IsEqualApprox(C22.One));
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}
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}
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