'*********************************************************************************
'**************************Cholesky factorization*********************************
'*********************************************************************************

Function Cholesky(Mat As Range)
Dim A, L() As Double, s As Double
A = Mat
n = Mat.Rows.Count
M = Mat.Columns.Count
If n <> M Then
    Cholesky = "?"
    Exit Function
End If

ReDim L(1 To n, 1 To n)
For j = 1 To n
    s = 0
    For k = 1 To j - 1
        s = s + L(j, k) ^ 2
    Next k
    L(j, j) = A(j, j) - s
    If L(j, j) <= 0 Then Exit For
    L(j, j) = Sqr(L(j, j))
    
    For i = j + 1 To n
        s = 0
        For k = 1 To j - 1
            s = s + L(i, k) * L(j, k)
        Next k
        L(i, j) = (A(i, j) - s) / L(j, j)
    Next i
Next j
Cholesky = L
End Function