using System.Linq;
using System.Numerics;
using Skeleton.Samples;
using Skeleton.Utils.Helpers;

namespace SkeletonTest.tests;

public static class JordanPowerTest
{
    private static readonly Complex ii = new Complex(0, 1);
    [DatapointSource]
    public static readonly Complex[] Basic0TestData = 10.ScaleSamples(-1, 1).UCSamples().ToArray();
    [Theory]
    public static void J22TestBasic0(Complex eigenValue)
    {
	    C22 block = new(
		    eigenValue, 1,
		    0, eigenValue
	    );
	    Assert.IsTrue(AlgebraHelper.JordanBlock2Power(eigenValue, 0).IsEqualApprox(C22.One));
	    Assert.IsTrue(
		    (
			    AlgebraHelper.JordanBlock2Power(eigenValue, 3.4d) *
			    AlgebraHelper.JordanBlock2Power(eigenValue, -3.4d)
		    ).IsEqualApprox(C22.One)
	    );
	    Assert.IsTrue(
		    (
			    AlgebraHelper.JordanBlock2Power(eigenValue, -2 - ii) *
			    AlgebraHelper.JordanBlock2Power(eigenValue, 2 + ii)
		    ).IsEqualApprox(C22.One)
	    );
    }

    [Test]
    public static void J22TestBasic1()
    {
	    C22 u2 = new(
		    1 + 2 * ii, 1,
		    0, 1 + 2 * ii
	    );
	    Complex eigenValue = 1 + 2 * ii;
	    Assert.IsTrue(AlgebraHelper.JordanBlock2Power(eigenValue, 3 - ii).IsEqualApprox(new C22(
		    (-11 - 2 * ii) * Complex.Pow(1 + 2 * ii, -ii), (-5 + 15 * ii) * Complex.Pow(1 + 2 * ii, -ii),
		    0, (-11 - 2 * ii) * Complex.Pow(1 + 2 * ii, -ii)
	    )));
	    Assert.IsTrue(AlgebraHelper.JordanBlock2Power(eigenValue, 2).IsEqualApprox(u2*u2));
    }

    [Test]
    public static void J22TestBasic2()
    {
	    Assert.IsTrue(AlgebraHelper.JordanBlock2Power(0, 2).IsEqualApprox(C22.Zero));
	    Assert.IsTrue(AlgebraHelper.JordanBlock2Power(0, 0).IsEqualApprox(C22.One));
    }

    [Theory]
    public static void J33TestBasic0(Complex eigenValue)
    {
	    C33 uw = new(
		    eigenValue, 1, 0,
		    0, eigenValue, 1,
		    0, 0, eigenValue
	    );
	    Assert.IsTrue(
		    (
			    AlgebraHelper.JordanBlock3Power(eigenValue, 4.2) * AlgebraHelper.JordanBlock3Power(eigenValue, -4.2)
		    ).IsEqualApprox(C33.One)
	    );
	    Assert.IsTrue(AlgebraHelper.JordanBlock3Power(eigenValue, 2).IsEqualApprox(uw * uw));
    }

    [Test]
    public static void J33TestBasic1()
    {
	    C33 ux = new(
		    0, 1, 0,
		    0, 0, 1,
		    0, 0, 0
	    );
	    Assert.IsTrue(AlgebraHelper.JordanBlock3Power(0, 0).IsEqualApprox(C33.One));
	    Assert.IsTrue(AlgebraHelper.JordanBlock3Power(0, 1).IsEqualApprox(ux));
	    Assert.IsTrue(AlgebraHelper.JordanBlock3Power(0, 2).IsEqualApprox(new C33(
		    0, 0, 1,
		    0, 0, 0,
		    0, 0, 0
	    )));
	    Assert.IsTrue(AlgebraHelper.JordanBlock3Power(0, 3).IsEqualApprox(C33.Zero));
    }
    [Theory]
	public static void J44Test(Complex eigenValue)
	{
		C44 uf = new(
			eigenValue, 1, 0, 0,
			0, eigenValue, 1, 0,
			0, 0, eigenValue, 1,
			0, 0, 0, eigenValue
		);
		Assert.IsTrue(AlgebraHelper.JordanBlock4Power(eigenValue, 0).IsEqualApprox(C44.One));
		Assert.IsTrue(AlgebraHelper.JordanBlock4Power(eigenValue, 1).IsEqualApprox(uf));
		Assert.IsTrue(AlgebraHelper.JordanBlock4Power(eigenValue, 2).IsEqualApprox(uf * uf));
		Assert.IsTrue(AlgebraHelper.JordanBlock4Power(eigenValue, 3).IsEqualApprox(uf * uf * uf));
		Assert.IsTrue(AlgebraHelper.JordanBlock4Power(eigenValue, 4).IsEqualApprox(uf * uf * uf * uf));
		Assert.IsTrue(
			(
				uf * AlgebraHelper.JordanBlock4Power(eigenValue, 1.4)
			).IsEqualApprox(
				AlgebraHelper.JordanBlock4Power(eigenValue, 2.4)
			)
		);
		
	}
	
}