MathNet.NumericsExample.cs

using Vector = MathNet.Numerics.LinearAlgebra.Vector<float>;
using Matrix = MathNet.Numerics.LinearAlgebra.Matrix<float>;
using UnityEngine;

public class ConfigureNumerics : MonoBehaviour {

    public Vector3 v1;
    public Vector3 v2;
    public Vector3 v3;

    void Start() {

        // 行列の定義
        Matrix A = Matrix.Build.DenseOfArray(new float[,] { { v1.x, v1.y, v1.z }, { v2.x, v2.y, v2.z }, { v3.x, v3.y, v3.z } });
        Vector v = Vector.Build.DenseOfArray(new float[] { v1.x, v1.y, v1.z });

        // 各行列の要素の四則演算
        Debug.Log("A + A = " + (A + A));
        Debug.Log("A - A = " + (A - A));
        Debug.Log("A * A = " + Matrix.op_DotMultiply(A, A));
        Debug.Log("A / A = " + Matrix.op_DotDivide(A, A));

        // 行列演算
        Debug.Log("A * A = " + (A * A));                    // 積
        Debug.Log("invA = " + A.Inverse());                 // 逆行列
        Debug.Log("A * invA = " + (A * A.Inverse()));       // 行列とその逆行列の積 (= 単位行列)
        Debug.Log("det(A) = " + A.Determinant());           // 行列式

        Matrix B = Matrix.Build.DenseIdentity(3);
        A.CopyTo(B);
        B += B;
        Debug.Log("A += A = " + B);

        // ベクトル演算
        Debug.Log("A * v = " + (A * v));    // 
        Debug.Log("v * A = " + (v * A));    // 
        Debug.Log("v * v = " + (v * v));    // 内積


        // 行列の特殊な演算
        // 特異値分解
        var svd = A.Svd(true);
        Debug.Log("U = " + svd.U);
        Debug.Log("s = " + svd.S);
        Debug.Log("VT = " + svd.VT);
        Debug.Log("U * s * VT = " + (svd.U * Matrix.Build.DenseOfDiagonalArray(new float[] { svd.S[0], svd.S[1], svd.S[2] }) * svd.VT));

        // 行列の固有値分解
        var eig = A.Evd();
        Debug.Log("P = " + eig.EigenVectors);
        Debug.Log("e = " + eig.EigenValues);
        Debug.Log("PAP_inv" + (eig.EigenVectors.Inverse() * Matrix.Build.DiagonalOfDiagonalArray(new float[] { (float)eig.EigenValues[0].Real, (float)eig.EigenValues[1].Real, (float)eig.EigenValues[2].Real } ) * eig.EigenVectors));

        var lu = A.LU();
        Debug.Log("L = " + lu.L);
        Debug.Log("U = " + lu.U);

        
    }

    void VectorToVector3() {

    }
	
	void Update () {
		
	}
}