public static decimal[] LinearLeastSquares(decimal[,] A, decimal[] b, String method = "SVD")
{
decimal[] res = new decimal[A.GetLength(1)];
if (method == "Gauss")
{
decimal[,] B = MathDecimal.Prod(MathDecimal.Transpose(A), A);
decimal[] y = MathDecimal.Prod(MathDecimal.Transpose(A), b);
res = LinearAlgebra.Gauss(B, y);
}
else if (method == "LUDecomposition")
{
List <decimal[, ]> LU = LinearAlgebra.LUDecomposition(A);// L, U, PI1, Pi2;
//Solve system Ly=b1, where b1=PI1*b
//L^T*L*y=L^T*b1
// M=L^T * L , N=L^T*PI1*b
decimal[,] M = MathDecimal.Prod(MathDecimal.Transpose(LU[0]), LU[0]);
decimal[] N = MathDecimal.Prod(MathDecimal.Transpose(LU[0]), MathDecimal.Prod(LU[2], b));
decimal[] y = LinearAlgebra.Gauss(M, N);
//Solve system y=U*x1=U*PI2^T*x
res = MathDecimal.Prod(LU[3], LinearAlgebra.BackwardSubstitutionUpp(LU[1], y));
}
else if (method == "SVD")
{
double[,] ADouble = new double[A.GetLength(0), A.GetLength(1)];
for (int i = 0; i < A.GetLength(0); i++)
{
for (int j = 0; j < A.GetLength(1); j++)
{
ADouble[i, j] = (double)A[i, j];
}
}
Matrix <double> JMatrix = DenseMatrix.OfArray(ADouble);
MathNet.Numerics.LinearAlgebra.Factorization.Svd <double> Jsvd = JMatrix.Svd();
double[,] LDouble = Jsvd.W.ToArray();
double[,] UDouble = Jsvd.U.ToArray();
double[,] VtDouble = Jsvd.VT.ToArray();
decimal[,] L = new decimal[A.GetLength(0), A.GetLength(1)];
decimal[,] U = new decimal[A.GetLength(0), A.GetLength(0)];
decimal[,] Vt = new decimal[A.GetLength(1), A.GetLength(1)];
for (int i = 0; i < A.GetLength(0); i++)
{
for (int j = 0; j < A.GetLength(1); j++)
{
L[i, j] = (decimal)LDouble[i, j];
}
}
for (int i = 0; i < A.GetLength(0); i++)
{
for (int j = 0; j < A.GetLength(0); j++)
{
U[i, j] = (decimal)UDouble[i, j];
}
}
for (int i = 0; i < A.GetLength(1); i++)
{
for (int j = 0; j < A.GetLength(1); j++)
{
Vt[i, j] = (decimal)VtDouble[i, j];
}
}
for (int i = 0; i < L.GetLength(1); i++)
{
if (L[i, i] < 0.0000000000001M && L[i, i] > -0.0000000000001M)
{
L[i, i] = 0;
}
else
{
L[i, i] = 1 / L[i, i];
}
}
res = MathDecimal.Prod(MathDecimal.Transpose(Vt), MathDecimal.Prod(MathDecimal.Transpose(L), MathDecimal.Prod(MathDecimal.Transpose(U), b)));
}
return(res);
}