AutoCAD 2016

Function EIGEN_JK(ByRef M As Variant) As Variant
'***************************************************************************
'**  Function computes the eigenvalues and eigenvectors for a real        **
'**  symmetric positive definite matrix using the "JK Method".  The       **
'**  first column of the return matrix contains the eigenvalues and       **
'**  the rest of the p+1 columns contain the eigenvectors.                **
'**  See:                                                                 **
'**  KAISER,H.F. (1972) "THE JK METHOD: A PROCEDURE FOR FINDING THE       **
'**  EIGENVALUES OF A REAL SYMMETRIC MATRIX", The Computer Journal,       **
'**  VOL.15, 271-273.                                                     **
'***************************************************************************
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)   ': numerator eq. 11
                    den = den + (A(i, j) + A(i, k)) * _
                        (A(i, j) - A(i, k))             ': denominator eq. 11
                Next i
                
                'Skip rotation if aij is zero and correct ordering
                If Abs(num) = 0 Then Exit For
                
                'Perform Rotation
                If Abs(num)  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