M2

2024-06-21 21:48:07 +08:00
commit 42ba33d229
129 changed files with 10711 additions and 0 deletions
--- a/src/Algebra/Matrices/MatrixProperty/MatrixProperty.cs
+++ b/src/Algebra/Matrices/MatrixProperty/MatrixProperty.cs
@@ -0,0 +1,102 @@
+using Skeleton.Algebra.ScalarFieldStructure;
+using Skeleton.Algebra.Vectors;
+
+namespace Skeleton.Algebra.Matrices.MatrixProperty;
+
+/// <summary>
+/// test properties of matrix
+/// </summary>
+/// <typeparam name="TScalar"></typeparam>
+/// <typeparam name="TVector"></typeparam>
+/// <typeparam name="TMatrix"></typeparam>
+public class MatrixProperty<TScalar, TVector, TMatrix>
+    where TVector : Vector<TScalar, TVector>, new()
+    where TMatrix : Matrix<TScalar, TVector, TMatrix>, new()
+    where TScalar : notnull
+{
+    private TMatrix Mat { get; }
+    private static readonly FieldStructure<TScalar> Structure = FieldStructure<TScalar>.Dispatch();
+    internal MatrixProperty(TMatrix m) => Mat = m;
+
+    /// <summary>
+    /// M[i, j] = 0 if i!= j
+    /// </summary>
+    public bool IsDiagonal => Mat.OffDiagonals
+        .All(x => Structure.IsEqualApprox(x, StaticAccess<TScalar>.AdditionUnit));
+
+    /// <summary>
+    /// exist of inv(M)
+    /// </summary>
+    /// <returns></returns>
+    public bool IsInvertible => !Structure.IsEqualApprox(Mat.Det(), StaticAccess<TScalar>.AdditionUnit);
+
+    /// <summary>
+    /// M M* = M* M
+    /// </summary>
+    public bool IsNormal => (Mat * Mat.Hermitian()).IsEqualApprox(Mat.Hermitian() * Mat);
+
+    /// <summary>
+    /// M = M*
+    /// </summary>
+    public bool IsHermitian => Mat.IsEqualApprox(Mat.Hermitian());
+
+    /// <summary>
+    /// M[i, j] = 0 for all j &lt; i
+    /// </summary>
+    public bool IsUpperTriangle
+    {
+        get
+        {
+            for (int i = 2; i <= Mat.Dim; i++)
+            for (int j = 1; j < i; j++)
+                if (!Structure.IsEqualApprox(Mat[i, j], StaticAccess<TScalar>.AdditionUnit))
+                    return false;
+            return true;
+        }
+    }
+
+    /// <summary>
+    /// M[i, j] = 0 for all j &gt; i
+    /// </summary>
+    public bool IsLowerTriangle
+    {
+        get
+        {
+            for (int i = 1; i <= Mat.Dim; i++)
+            for (int j = i + 1; j <= Mat.Dim; j++)
+                if (!Structure.IsEqualApprox(Mat[i, j], StaticAccess<TScalar>.AdditionUnit))
+                    return false;
+            return true;
+        }
+    }
+
+    /// <summary>
+    /// U*U = UU* = I
+    /// </summary>
+    public bool IsUnitary => (Mat * Mat.Hermitian()).IsEqualApprox(Mat.VarOne);
+
+    /// <summary>
+    /// U + U* = 0
+    /// </summary>
+    public bool IsSkewHermitian => (Mat + Mat.Hermitian()).IsEqualApprox(Mat.VarZero);
+
+    /// <summary>
+    /// tr(M) = 0
+    /// </summary>
+    public bool IsTraceless => Structure.IsEqualApprox(Mat.Trace(), StaticAccess<TScalar>.AdditionUnit);
+
+    /// <summary>
+    /// M M^T = I
+    /// </summary>
+    public bool IsOrthogonal => (Mat * Mat.Transpose()).IsEqualApprox(Mat.VarOne);
+
+    /// <summary>
+    /// M = M^T
+    /// </summary>
+    public bool IsSymmetric => Mat.IsEqualApprox(Mat.Transpose());
+
+    /// <summary>
+    /// M = -M^T
+    /// </summary>
+    public bool IsSkewSymmetric => Mat.IsEqualApprox(-Mat.Transpose());
+}