m3

2024-06-21 21:59:13 +08:00
commit 614bc59897
28 changed files with 2049 additions and 0 deletions
--- a/tests/JordanPowerTest.cs
+++ b/tests/JordanPowerTest.cs
@@ -0,0 +1,114 @@
+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)
+			)
+		);
+		
+	}
+	
+}