Namespace MathEx

    Public Class Broyden

        Shared Sub broydn(ByVal N As Integer, ByVal X As Double(), ByVal F As Double(), ByRef P As Double(),
                          ByRef XB As Double(), ByRef FB As Double(), ByRef H As Double(,), ByRef IFLAG As Integer)
            '
            '**********************************************************************
            '
            '       N = NUMBER OF EQUATIONS
            '       X(N) = CURRENT VALUE OF X, INITAL GUESS X0 ON FIRST CALL
            '              THE VALUE OF X IS NOT UPDATED AND MUST BE UPDATED IN
            '              CALLING PROGRAM
            '       F(N) = VALUE OF F(X) MUST BE PROVIDED ON ALL CALLS
            '       P(N) = STEP PREDICTED BY BROYDN (USED TO UPDATE X)
            '              THE NEW VALUE OF X IS X+P
            '       XB(N) = RETENTION FOR X VECTOR
            '       FB(N) = RETENTION FOR F VECTOR
            '       H(N,N) = BROYDEN H MATRIX IT MUST BE INITIALIZED TO A CLOSE
            '                J(X0)**-1 OR IDENTITY MATRIX
            '       IFLAG = CALCULATION CONTROL FLAG
            '               0 INITIAL CALL, NO H UPDATE
            '               1 UPDATE CALL, NO H DAMPING
            '
            Dim I As Short
            Dim J As Short
            Dim PTP As Double
            Dim PTH As Double
            Dim THETA As Double
            Dim PTHY As Double
            Dim PTHF As Double
            Dim HY As Double
            Dim DENOM As Double
            '
            '      INITIAL CALL
            '
            If (IFLAG <> 0) Then
                PTP = 0.0#
                '
                For I = 0 To N 'do 30 I=1,N
                    P(I) = X(I) - XB(I)
                    PTP = PTP + P(I) * P(I)
                    HY = 0.0#
                    For J = 0 To N '  DO 20 J=1,N
                        HY = HY + H(I, J) * (F(J) - FB(J))
20:                 Next J
                    XB(I) = HY - P(I)
30:             Next I
                PTHY = 0.0#
                PTHF = 0.0#
                '
                For I = 0 To N ' DO 40 I=1,N
                    PTH = 0.0#
                    For J = 0 To N '  DO 35 J=1,N
                        PTH = PTH + P(J) * H(J, I)
35:                 Next J
                    PTHY = PTHY + PTH * (F(I) - FB(I))
                    PTHF = PTHF + PTH * F(I)
                    FB(I) = PTH
40:             Next I
                THETA = 1.0#
                '
                DENOM = (1.0# - THETA) * PTP + THETA * PTHY
                '
                For I = 0 To N ' DO 50 I=1,N
                    For J = 0 To N ' DO 50 J=1,N
                        H(I, J) = H(I, J) - THETA * XB(I) * FB(J) / DENOM
                    Next J
50:             Next I
                '
            End If
            For I = 0 To N '  DO 70 I=1,N
                XB(I) = X(I)
                FB(I) = F(I)
                P(I) = 0.0#
                '
                For J = 0 To N '  DO 70 J=1,N
                    P(I) = P(I) - H(I, J) * F(J)
                Next J
70:         Next I
            ''
        End Sub

    End Class

End Namespace