d9r2.frm

矩阵特征值的求解过程之一

VERSION 5.00
Begin VB.Form Form1 
   Caption         =   "Form1"
   ClientHeight    =   5250
   ClientLeft      =   60
   ClientTop       =   345
   ClientWidth     =   4920
   LinkTopic       =   "Form1"
   ScaleHeight     =   5250
   ScaleWidth      =   4920
   StartUpPosition =   3  'Windows Default
   Begin VB.CommandButton Command1 
      Caption         =   "Command1"
      Height          =   375
      Left            =   3000
      TabIndex        =   0
      Top             =   4680
      Width           =   1335
   End
End
Attribute VB_Name = "Form1"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Private Sub Command1_Click()
    'PROGRAM D9R2
     'Driver for routine GOLDEN
     TOL = 0.000001
     EQL = 0.001
     Dim AMIN(20)
     NMIN = 0
     Print
     Print Tab(5); "Minima of the function BESSJ0"
     Print
     Print Tab(3); "Min. #         X          BESSJ0(X)      BESSJ1(X)"
     For I = 1 To 100
         AX = I
         BX = I + 1#
         Call MNBRAK(AX, BX, CX, FA, FB, FC)
         G = GOLDEN(AX, BX, CX, TOL, XMIN)
         If NMIN = 0 Then
             AMIN(1) = XMIN
             NMIN = 1
             Print Tab(5); Format$(NMIN, "##");
             Print Tab(15); Format$(XMIN, "##.####00");
             Print Tab(29); Format$(BESSJ0(XMIN), ".#####0");
             Print Tab(43); Format$(BESSJ1(XMIN), ".#####0")
         Else
             IFLAG = 0
             For j = 1 To NMIN
                 If Abs(XMIN - AMIN(j)) <= EQL * XMIN Then IFLAG = 1
             Next j
             If IFLAG = 0 Then
                 NMIN = NMIN + 1
                 AMIN(NMIN) = XMIN
                 Print Tab(5); Format$(NMIN, "##");
                 Print Tab(15); Format$(XMIN, "##.####00");
                 Print Tab(29); Format$(BESSJ0(XMIN), ".#####0");
                 Print Tab(43); Format$(BESSJ1(XMIN), ".#####0")
             End If
         End If
     Next I
End Sub
Function FUNC(X)
    FUNC = BESSJ0(X)
End Function
Function GOLDEN(AX, BX, CX, TOL, XMIN)
    R = 0.61803399
    C = 0.38196601
    X0 = AX
    X3 = CX
    If Abs(CX - BX) > Abs(BX - AX) Then
        X1 = BX
        X2 = BX + C * (CX - BX)
    Else
        X2 = BX
        X1 = BX - C * (BX - AX)
    End If
    F1 = FUNC(X1)
    F2 = FUNC(X2)
    While Abs(X3 - X0) > TOL * (Abs(X1) + Abs(X2))
        If F2 < F1 Then
            X0 = X1
            X1 = X2
            X2 = R * X1 + C * X3
            F0 = F1
            F1 = F2
            F2 = FUNC(X2)
        Else
            X3 = X2
            X2 = X1
            X1 = R * X2 + C * X0
            F3 = F2
            F2 = F1
            F1 = FUNC(X1)
        End If
    Wend
    If F1 < F2 Then
        GOLDEN = F1
        XMIN = X1
    Else
        GOLDEN = F2
        XMIN = X2
    End If
End Function
Function BESSJ0(X)
    P1# = 1#
    P2# = -0.001098628627
    P3# = 0.00002734510407
    P4# = -0.000002073370639
    P5# = 2.093887211E-07
    Q1# = -0.01562499995
    Q2# = 0.0001430488765
    Q3# = -0.000006911147651
    Q4# = 7.621095161E-07
    Q5# = -9.34945152E-08
    R1# = 57568490574#
    R2# = -13362590354#
    R3# = 651619640.7
    R4# = -11214424.18
    R5# = 77392.33017
    R6# = -184.9052456
    S1# = 57568490411#
    S2# = 1029532985#
    S3# = 9494680.718
    S4# = 59272.64853
    S5# = 267.8532712
    S6# = 1#
    If Abs(X) < 8# Then
       Y# = X * X
       BBB# = Y# * (R4# + Y# * (R5# + Y# * R6#))
       AAA# = R1# + Y# * (R2# + Y# * (R3# + BBB#))
       CCC# = Y# * (S3# + Y# * (S4# + Y# * (S5# + Y# * S6#)))
       BESSJ0 = AAA / (S1# + Y# * (S2# + CCC#))
    Else
       AX# = Abs(X)
       Z# = 8# / AX#
       Y# = Z# * Z#
       XX = AX# - 0.785398164
       CCC# = Y# * (P3# + Y# * (P4# + Y# * P5#))
       AAA# = P1# + Y# * (P2# + CCC#)
       DDD# = Y# * (Q3# + Y# * (Q4# + Y# * Q5#))
       EEE# = Z# * Sin(XX) * (Q1# + Y# * (Q2# + DDD#))
       BESSJ0 = Sqr(0.636619772 / AX#) * (Cos(XX) * AAA# - EEE#)
    End If
End Function
   Function BESSJ1(X)
      R1 = 72362614232#
      R2 = -7895059235#
      R3 = 242396853.1
      R4 = -2972611.439
      R5 = 15704.4826
      R6 = -30.16036606
      S1 = 144725228442#
      S2 = 2300535178#
      S3 = 18583304.74
      S4 = 99447.43394
      S5 = 376.9991397
      S6 = 1#
      P1 = 1#
      P2 = 0.00183105
      P3 = -0.00003516396496
      P4 = 0.000002457520174
      P5 = -0.000000240337019
      Q1 = 0.04687499995
      Q2 = -0.0002002690873
      Q3 = 0.000008449199096
      Q4 = -0.00000088228987
      Q5 = 0.000000105787412
      If Abs(X) < 8# Then
          Y# = X ^ 2
          AAA# = R1 + Y * (R2 + Y * (R3 + Y * (R4 + Y * (R5 + Y * R6))))
          BBB# = S1 + Y * (S2 + Y * (S3 + Y * (S4 + Y * (S5 + Y * S6))))
          BESSJ1 = X * AAA# / BBB#
      Else
          AX = Abs(X)
          Z = 8# / AX
          Y# = Z ^ 2
          XX = AX - 2.356194491
          AAA# = P1 + Y * (P2 + Y * (P3 + Y * (P4 + Y * P5)))
          BBB# = Q1 + Y * (Q2 + Y * (Q3 + Y * (Q4 + Y * Q5)))
          CCC# = Sqr(0.636619772 / AX)
          BESSJ1 = CCC# * (Cos(XX) * AAA# - Z * Sin(XX) * BBB# * Sgn(X))
      End If
   End Function
Sub MNBRAK(AX, BX, CX, FA, FB, FC)
    GOLD = 1.618034
    GLIMIT = 100#
    TINY = 1E-20
    FA = FUNC(AX)
    FB = FUNC(BX)
    If FB > FA Then
        DUM = AX
        AX = BX
        BX = DUM
        DUM = FB
        FB = FA
        FA = DUM
    End If
    CX = BX + GOLD * (BX - AX)
    FC = FUNC(CX)
    Do
        If FB < FC Then Exit Do
        DONE% = -1
        R = (BX - AX) * (FB - FC)
        Q = (BX - CX) * (FB - FA)
        DUM = Q - R
        If Abs(DUM) < TINY Then DUM = TINY
        U = BX - ((BX - CX) * Q - (BX - AX) * R) / (2 * DUM)
        ULIM = BX + GLIMIT * (CX - BX)
        If (BX - U) * (U - CX) > 0# Then
            FU = FUNC(U)
            If FU < FC Then
                AX = BX
                FA = FB
                BX = U
                FB = FU
                Exit Sub
            ElseIf FU > FB Then
                CX = U
                FC = FU
                Exit Sub
            End If
            U = CX + GOLD * (CX - BX)
            FU = FUNC(U)
        ElseIf (CX - U) * (U - ULIM) > 0# Then
            FU = FUNC(U)
            If FU < FC Then
                BX = CX
                CX = U
                U = CX + GOLD * (CX - BX)
                FB = FC
                FC = FU
                FU = FUNC(U)
            End If
        ElseIf (U - ULIM) * (ULIM - CX) >= 0# Then
            U = ULIM
            FU = FUNC(U)
        Else
            U = CX + GOLD * (CX - BX)
            FU = FUNC(U)
        End If
        If DONE% Then
            AX = BX
            BX = CX
            CX = U
            FA = FB
            FB = FC
            FC = FU
        Else
            DONE% = 0
        End If
    Loop While Not DONE%
End Sub