using System;
using System.Linq;
using System.Numerics;
using Skeleton.Algebra.Extensions;
using Skeleton.DataStructure.Packs.MatrixDecompositions;
using Skeleton.Samples;

namespace SkeletonTest.tests;

public class EigenDecompositionTest
{
    private static readonly Complex I = Complex.ImaginaryOne;
    [DatapointSource] 
    public static readonly C22[] DataPoints = 
        30.ScaleSamples(-1, 1).C22InvertibleSamples().ToArray();

    [Theory]
    public static void DecompositionIdentityTest(C22 data)
    {
        JDPair<C22> decomp = data.EigenDecomposition();
        C22 J = decomp.J;
        C22 D = decomp.D;
        Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(data));
    }

    [Theory]
    public static void UnitaryDecompositionTest(C22 data)
    {
        U2 unitaryData = new U2(data);
        Console.WriteLine(data.Representation);
        Assert.IsTrue((unitaryData * unitaryData.Hermitian()).IsEqualApprox(U2.One));
        Assert.IsTrue(unitaryData.Det().Magnitude.IsEqualApprox(1));
        JDPair<C22> decomp = unitaryData.EigenDecomposition();

        C22 J = decomp.J;
        C22 D = decomp.D;
        Assert.IsTrue(D.Property.IsDiagonal);
        Assert.IsTrue((J * J.Hermitian()).IsEqualApprox(C22.One));
        Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(unitaryData));
    }

    [Test]
    public static void DecompositionTest()
    {
        C22 a = new C22(I, 1, 1, I);
        JDPair<C22> t = a.EigenDecomposition();
        C22 J = t.J;
        C22 D = t.D;
        Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(a));
    }

    [Test]
    public static void UnitaryDecompositionCase0()
    {
        U2 m = new U2(
            -0.08908708063747477 + 0.44543540318737385 * I, 0.3008484477213831 + 0.8385350351383227 * I,
            -0.5345224838248488 + 0.7126966450997985 * I, 0.04608742177859454 - 0.45191277466233243 * I
        );
        JDPair<C22> t = m.EigenDecomposition();
        C22 J = t.J;
        C22 D = t.D;
        
        Assert.IsTrue((J * D * J.Inv()).IsEqualApprox(m));
        Assert.IsTrue((J * J.Hermitian()).IsEqualApprox(C22.One));


        //C22 JH = J.Hermitian();
        D.SwapRow(1, 2);
        J.SwapColumn(1, 2);
        Console.WriteLine((J.Hermitian()*m*J).Representation);
        Console.WriteLine("  --  ");
        Console.WriteLine(D.Representation);
        //Assert.IsTrue((JH.Hermitian() * D * JH).IsEqualApprox(m));
        
        
    }

    [Test]
    public static void UnitaryDecompositionCase1()
    {
        U2 m = new U2(
            0.8666666666666667 - 0.8666666666666667 * I, -0.4 + 0.46666666666666656 * I,
            -0.8666666666666667 - 0.6 * I, 0.6666666666666667
        );
        Assert.IsTrue((m * m.Hermitian()).IsEqualApprox(C22.One));
    }
}