111 lines
3.7 KiB
C#
111 lines
3.7 KiB
C#
using System.Collections.Generic;
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using System.Numerics;
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namespace Skeleton.Test.tests;
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/// <summary>
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/// test for vector spaces
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/// </summary>
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public static class VectorSpaceTest
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{
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private static readonly Complex ii = new Complex(0, 1);
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[Test]
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public static void Dim2Test()
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{
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R2Space r2a = new R2Space(new List<R2>() { new R2(3, 2) });
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Assert.IsTrue(r2a.Rank == 1);
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Assert.IsTrue(r2a.ContainsVector(new R2(9, 6)));
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Assert.IsTrue(!r2a.ContainsVector(new R2(1,0)));
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R2Space r2ac = r2a.OrthogonalComplementSpace;
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Assert.IsTrue(r2ac.ContainsVector(new R2(2, -3)));
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C2Space c2a = new C2Space(new List<C2>() { new C2(1 - ii, 1 + ii) });
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Assert.IsTrue(c2a.Rank == 1);
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Assert.IsTrue(c2a.ContainsVector(new C2(2 - 2 * ii, 2 + 2 * ii)));
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Assert.IsTrue(!c2a.ContainsVector(new C2(1 + ii, 0)));
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C2Space c2ac = c2a.OrthogonalComplementSpace;
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Assert.IsTrue(c2ac.ContainsVector(new C2(ii, 1)));
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}
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[Test]
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public static void Dim3Test()
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{
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R3Space r3a = new R3Space(new List<R3>() { new R3(1, 1, 1), new R3(1, 1, 0) });
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Assert.IsTrue(r3a.Rank == 2);
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Assert.IsTrue(r3a.ContainsVector(new R3(2,2,1)));
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Assert.IsTrue(r3a.ContainsVector(new R3(3,3,3)));
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Assert.IsTrue(r3a.OrthogonalComplementSpace.ContainsVector(new R3(-2, 2, 0)));
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C3Space c3a = new C3Space(new List<C3>() { new C3(1 + ii, 1 - ii, ii), new C3(1, 0, 1) });
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Assert.IsTrue(c3a.Rank == 2);
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Assert.IsTrue(c3a.OrthogonalComplementSpace.Rank == 1);
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Assert.IsTrue(c3a.ContainsVector(new C3(2 + ii, 1 - ii, 1 + ii)));
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Assert.IsTrue(c3a.OrthogonalComplementSpace.ContainsVector(new C3(-2, 1-ii, 2)));
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}
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[Test]
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public static void Dim4Test()
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{
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R4Space r4a = new R4Space(new List<R4>() { new R4(1, 1, 0, 0), new R4(0, 1, 0, 1) });
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Assert.IsTrue(r4a.Rank==2);
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Assert.IsTrue(r4a.OrthogonalComplementSpace.Rank==2);
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Assert.IsTrue(r4a.ContainsVector(new R4(1, 0, 0, -1)));
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Assert.IsTrue(r4a.OrthogonalComplementSpace.ContainsVector(new R4(0, 0, 1, 0)));
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Assert.IsTrue(r4a.OrthogonalComplementSpace.ContainsVector(new R4(1,-1,0,1)));
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C44 a = new C44(
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, ii,
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0, 0, 0, 1
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);
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C44 b = new C44(
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ii, 1, -1, -ii,
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1, -1, 0, 0,
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ii, 0, 0, 0,
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0, 0, 0, 0
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);
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C4Space c4a = new C4Space(new List<C4>()
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{
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new C4(ii, 1, -1, -ii),
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new C4(1, -1, 0, 0),
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new C4(ii, 0, 0, 0)
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});
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Assert.IsTrue(c4a.Rank == 3);
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Assert.IsTrue(c4a.OrthogonalComplementSpace.Rank == 1);
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Assert.IsTrue(c4a.ContainsVector(new C4(1+ii,-1,0,0)));
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Assert.IsTrue(c4a.ContainsVector(new C4(1+ii,0,-1, -ii)));
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Assert.IsTrue(c4a.ContainsVector(new C4(1+2*ii,0,-1, -ii)));
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Assert.IsTrue(c4a.OrthogonalComplementSpace.ContainsVector(new C4(0, 0, ii, 1)));
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}
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[Test]
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public static void ContainsVectorTest()
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{
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C3Space c3s = new (new C3[] { new(1, 4, 2), new(2, 4, 1) });
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Assert.IsFalse(c3s.ContainsVector(new (0.62469505d, -0.46852129, 0.62469505)));
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}
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[Test]
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public static void UnionTest()
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{
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C3Space c3s1 = new (new C3[] { new(1, 4, 2) });
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C3Space c3s2 = new(new C3[] { new(2, 4, 1) });
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C3Space union = c3s1.UnionWith(c3s2);
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Assert.That(union.Rank, Is.EqualTo(2));
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Assert.IsTrue(union.ContainsVector(new(1, 4, 2)));
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Assert.IsTrue(union.ContainsVector(new(2, 4, 1)));
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Assert.IsTrue(union.ContainsVector(new (3, 8, 3)));
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Assert.IsFalse(union.ContainsVector(new(0.62469505d, -0.46852129, 0.62469505)));
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}
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[Test]
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public static void OrthogonalComplementTest()
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{
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C3Space space = new(new C3[] { new(1, -3d/4d, 1) });
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C3Space otcSpace = space.OrthogonalComplementSpace;
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Assert.IsTrue(otcSpace.ContainsVector(new(1, 4, 2)));
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Assert.IsTrue(otcSpace.ContainsVector(new(2, 4, 1)));
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Assert.That(otcSpace.Rank, Is.EqualTo(2));
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Assert.IsFalse(otcSpace.ContainsVector(new(0.62469505d, -0.46852129, 0.62469505)));
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}
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}
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