?? d11r2.frm
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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 D11R2
'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
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