VBA Function for Eigen decomposition returns only positive eigenvalues

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8.2

VBA Function for Eigen decomposition returns only positive eigenvalues

Asked by burk12 in Math & Science, VB Objects

Hi

I have below VBA code to determine the eigenvalues/vectors of a symmetric matrix. It seems that for some reason, the code only returns positive eigenvalues (although the absolute #s are correct)

Eg for the following symmetric matrix
1 2
2 1
The code returns the Eigenvalues {3;1}, whereas the 'true' eigenvalues are {-1;3}
The Eigenvectors though seem correct
(0.707; 0.707) for +3
(-0.707; 0.707) for 1

Any idea how I may change the below code such that it gives me the correct sign?

Thanks a lot!

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             Public Function EIGEN_JK(ByRef M() As Variant) As Variant
 
Dim A() As Variant, Ematrix() As Double
Dim i As Long, j As Long, k As Long, iter As Long, p As Long
Dim den As Double, hold As Double, Sin_ As Double, num As Double
Dim Sin2 As Double, Cos2 As Double, Cos_ As Double, Test As Double
Dim Tan2 As Double, Cot2 As Double, tmp As Double
Const eps As Double = 1E-16
    
    On Error GoTo EndProc
    
    A = M
    p = UBound(A, 1)
    ReDim Ematrix(1 To p, 1 To p + 1)
    
    For iter = 1 To 15
        
        'Orthogonalize pairs of columns in upper off diag
        For j = 1 To p - 1
            For k = j + 1 To p
                
                den = 0#
                num = 0#
                'Perform single plane rotation
                For i = 1 To p
                    num = num + 2 * A(i, j) * A(i, k)
                    den = den + (A(i, j) + A(i, k)) * _
                        (A(i, j) - A(i, k))
                Next i
                
                'Skip rotation if aij is zero and correct ordering
                If Abs(num) < eps And den >= 0 Then Exit For
                
                'Perform Rotation
                If Abs(num) <= Abs(den) Then
                    Tan2 = Abs(num) / Abs(den)
                    Cos2 = 1 / Sqr(1 + Tan2 * Tan2)
                    Sin2 = Tan2 * Cos2
                Else
                    Cot2 = Abs(den) / Abs(num)
                    Sin2 = 1 / Sqr(1 + Cot2 * Cot2)
                    Cos2 = Cot2 * Sin2
                End If
                
                Cos_ = Sqr((1 + Cos2) / 2)
                Sin_ = Sin2 / (2 * Cos_)
                
                If den < 0 Then
                    tmp = Cos_
                    Cos_ = Sin_
                    Sin_ = tmp
                End If
                
                Sin_ = Sgn(num) * Sin_
                
                'Rotate
                For i = 1 To p
                    tmp = A(i, j)
                    A(i, j) = tmp * Cos_ + A(i, k) * Sin_
                    A(i, k) = -tmp * Sin_ + A(i, k) * Cos_
                Next i
                
            Next k
        Next j
        
        'Test for convergence
        Test = Application.SumSq(A)
        If Abs(Test - hold) < eps And iter > 5 Then Exit For
        hold = Test
    Next iter
    
    If iter = 16 Then MsgBox "JK Iteration has not converged."
    
    'Compute eigenvalues/eigenvectors
    For j = 1 To p
        'Compute eigenvalues
        For k = 1 To p
            Ematrix(j, 1) = Ematrix(j, 1) + A(k, j) ^ 2
        Next k
        Ematrix(j, 1) = Sqr(Ematrix(j, 1))
        
        'Normalize eigenvectors
        For i = 1 To p
            If Ematrix(j, 1) <= 0 Then
                Ematrix(i, j + 1) = 0
            Else
                Ematrix(i, j + 1) = A(i, j) / Ematrix(j, 1)
            End If
        Next i
    Next j
        
    EIGEN_JK = Ematrix
    
    Exit Function
    
EndProc:
    MsgBox prompt:="Error in function EIGEN_JK!" & vbCr & vbCr & _
        "Error: " & Err.Description & ".", Buttons:=48, _
        Title:="Run time error!"
End Function

           
         

20091111-EE-VQP-92 - Hierarchy / EE_QW_3_20080625

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VBA Function for Eigen decomposition returns only positive eigenvalues

Asked by burk12 in Math & Science, VB Objects

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