zbrent.txt

VB常用数值算法集 内含有解线性代数方程组

Function ZBRENT(X1, X2, TOL)
    ITMAX = 100
    EPS = 0.00000003
    A = X1
    B = X2
    FA = FUNC(A)
    FB = FUNC(B)
    If FB * FA > 0# Then
        Print "Root must be bracketed for ZBRENT"
    End If
    FC = FB
    For ITER = 1 To ITMAX
        If FB * FC > 0 Then
            C = A
            FC = FA
            D = B - A
            E = D
        End If
        If Abs(FC) < Abs(FB) Then
            A = B
            B = C
            C = A
            FA = FB
            FB = FC
            FC = FA
        End If
        TOL1 = 2# * EPS * Abs(B) + 0.5 * TOL
        XM = 0.5 * (C - B)
        If Abs(XM) <= TOL1 Or FB = 0 Then
            ZBRENT = B
            Exit Function
        End If
        If Abs(E) >= TOL1 And Abs(FA) > Abs(FB) Then
            S = FB / FA
            If A = C Then
                P = 2# * XM * S
                Q = 1 - S
            Else
                Q = FA / FC
                R = FB / FC
                P = S * (2# * XM * Q * (Q - R) - (B - A) * (R - 1#))
                Q = (Q - 1#) * (R - 1#) * (S - 1#)
            End If
            If P > 0# Then Q = -Q
            P = Abs(P)
            If 3# * XM * Q - Abs(TOL1 * Q) < Abs(E * Q) Then
                AAA = 3# * XM * Q - Abs(TOL1 * Q)
            Else
                AAA = Abs(E * Q)
            End If
            If 2# * P < AAA Then
                E = D
                D = P / Q
            Else
                D = XM
                E = D
            End If
        Else
            D = XM
            E = D
        End If
        A = B
        FA = FB
        If Abs(D) > TOL1 Then
            B = B + D
        Else
            B = B + Abs(TOL1) * Sgn(XM)
        End If
        FB = FUNC(B)
    Next ITER
    Print "ZBRENT exceeding maximum iterations."
    ZBRENT = B
End Function