//A = U*S*Vt
//A*At = U*S^2*Ut
//At*A = V*S^2*Vt
//A*At = (At*A)t
//This method is not right
public static void FactorSVD_LDLt(MMatrix A)
{
MMatrix AA = new MMatrix();
MMatrix Eigenvectors = new MMatrix();
Vector Eigenvalues = new Vector();
int index = A.row;
if (A.row > A.col)
index = A.col;
AA = A * A.Transpose();
AA.FactorLDLt();
Eigenvectors = new MMatrix(AA.LDL_L);
Eigenvalues = new Vector(AA.row);
for (int i = 0; i < index; ++i)
Eigenvalues[i] = AA.LDL_D[i, i];
SortEigen(ref Eigenvalues, ref Eigenvectors);
A.SVD_U = Eigenvectors.MArray;
if (A.SVD_S == null)
A.SVD_S = new double[A.row, A.col];
for (int i = 0; i < index; ++i)
A.SVD_S[i, i] = Math.Sqrt(Eigenvalues[i]);
AA = AA.Transpose();
AA.FactorLDLt();
Eigenvectors = new MMatrix(AA.LDL_L);
Eigenvalues = new Vector(AA.row);
for (int i = 0; i < index; ++i)
Eigenvalues[i] = AA.LDL_D[i, i];
SortEigen(ref Eigenvalues, ref Eigenvectors);
A.SVD_Vt = Eigenvectors.Transpose().MArray;
}
