/// <summary>
/// 計算Tsquare
/// </summary>
/// <param name="item">a observation</param>
/// <param name="mean">mean vector</param>
/// <param name="invS">inverse of covariance matrix</param>
/// <returns></returns>
public static double CalculateTSquare(LinearAlgebra.Matrix <double> item, LinearAlgebra.Matrix <double> mean, LinearAlgebra.Matrix <double> invS)
{
if (item.ColumnCount != mean.ColumnCount || item.ColumnCount != invS.ColumnCount || mean.ColumnCount != invS.ColumnCount)
{
throw new ArgumentException("矩陣的維度無法計算");
}
LinearAlgebra.Matrix <double> diff = item - mean;
var t2 = diff.Multiply(invS).Multiply(diff.Transpose());
return(t2.At(0, 0));
}
public LinearAlgebra.Matrix <double> ComputeStiffnessMatrix()
{
LinearAlgebra.Matrix <double> K = LinearAlgebra.Matrix <double> .Build.Dense(2, 2);
double x1 = Nodes[0].Point.X;
double y1 = Nodes[0].Point.Y;
double z1 = Nodes[0].Point.Z;
double x2 = Nodes[1].Point.X;
double y2 = Nodes[1].Point.Y;
double z2 = Nodes[1].Point.Z;
ElemLength = Math.Sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1) + (z2 - z1) * (z2 - z1));
K[0, 0] = Area * StiffnessModulus / ElemLength;
K[0, 1] = -Area * StiffnessModulus / ElemLength;
K[1, 0] = -Area * StiffnessModulus / ElemLength;
K[1, 1] = Area * StiffnessModulus / ElemLength;
// Tranform to global element stiffness matrix using transformation matrix G
double nxx = (x2 - x1) / ElemLength;
double nyx = (y2 - y1) / ElemLength;
double nzx = (z2 - z1) / ElemLength;
G[0, 0] = nxx;
G[0, 1] = nyx;
G[0, 2] = nzx;
G[1, 3] = nxx;
G[1, 4] = nyx;
G[1, 5] = nzx;
LinearAlgebra.Matrix <double> GT = G.Transpose();
LinearAlgebra.Matrix <double> KGlobal = (GT.Multiply(K)).Multiply(G);
return(KGlobal);
}