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发表于 2016-2-15 19:51:33
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AC-arctan(AC/80)*80=1是数学问题。
3 k+ t3 v2 V; C8 }% _( C$ @子子大侠既然读过VB，那么读VBA代码就应该没什么困难，核心是数值计算。
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定义待求解函数：6 J1 Z7 ^! U; U. d% t" q
Public Function QesFun(ByVal Var_AC As Double) As Double
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QesFun = Var_AC - Atn(Var_AC / 80) * 80 - 18 _+ f: e& o5 J8 T; B% z
- n; i9 X- p6 \+ }% A# v- D, x \End Function
, B9 r' a0 i9 [0 g+ I" Q, o3 m% { d9 ^% Y--------------------------------------------------------------------------------------------------' e8 x/ P3 _+ W( ~( _- _
1. 二分法7 g/ q+ @4 N7 P0 m; ~
1.1 由 Arctan(AC/80)=(AC-1)/80
/ c3 T7 N8 c1 Y/ z, F! @ 知 -PI()/2<(AC-1)/80< PI()/2
- l- H4 u' q. C( ~0 s 即 1 -80*PI()/2<AC<1+ 80*PI()/2
4 q' o. _/ o5 P3 @" P++++++++++++++++++++++++++++++++++++++
, i- t% _( @; \ i1.2定义求解函数： m0 `, g6 i4 G4 G; N5 w: ~
Public Function SolFunDic(ByVal MaxLim As Double, ByVal MinLim As Double) As Double: ^& S, l& V" ]% q* x7 P- W
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Dim Res#, VarAdj#
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VarAdj = 10 ^ -6- f& |% a# y6 K8 n' C
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If QesFun(MinLim + VarAdj) < QesFun(MaxLim - VarAdj) Then
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7 L. Y( S& u2 X. [; S0 Q* Z4 ^. O7 m x Do While (1)) Q8 v. k: y$ a0 J3 R* I
3 Z. d7 u5 h" M( d- y+ N$ _* b Res = (MaxLim + MinLim) / 26 F: S6 d _' |8 S U7 L
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If Abs(QesFun(Res)) <= 10 ^ -12 Then/ i2 j" {! T, X0 _0 s3 o& z
6 {0 d: X' j5 p' o SolFunDic = Res: Exit Do
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ElseIf (QesFun(Res) < 0) Then
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( T5 D s! A" a4 l' r. D/ X# T MinLim = Res
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5 T8 k+ X% F! ]9 _ Else
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9 Z$ I. e+ U0 Z( f! T MaxLim = Res
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) Z! L- K8 k1 I End If: L8 _7 [. c6 C u
9 e) f! y' V7 n/ i# l( z4 R Loop. A$ a# V+ F3 [3 n& V. ~, Q
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Do While (1)
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Res = (MaxLim + MinLim) / 2
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) G! P' d F$ ^; ?! Z$ a# g/ W; F If Abs(QesFun(Res)) <= 10 ^ -12 Then9 x" w8 g J; M
# G2 t. ]6 | { SolFunDic = Res: Exit Do; f$ `( ~3 w1 C) b+ l% V) j
5 p/ C5 ]; I8 |, X1 o ElseIf (QesFun(Res) > 0) Then
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MinLim = Res
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Else
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MaxLim = Res' a4 `% H! ?7 a3 Q
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End If# D" T: E( b: p1 t f
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Loop, [4 V' J/ w; A, Q3 N
; O$ O. f5 }4 H0 m# B% C9 oEnd If$ w% \& A& v t/ p7 y; B/ j9 K8 h
End Function# J& a O: l7 U% Q7 l- A6 h
--------------------------------------------------------------7 d ~, C, C5 _9 X$ D& }1 S
2. 牛顿法
' l( F: X' p3 o( a2.1 由 f(AC)＝arctan(AC/80)*80+1-AC4 C2 a) p3 v2 S) K
求导 f(AC)’=1/(1+(AC/80)^2)-1' O( i# z: P, l7 Z! {- U/ g$ s; e
即 AC_1=AC_0- f(AC)/ f(AC)’3 D% r4 \# s0 l4 D8 Y1 L$ ^3 j3 K
--------------------------------------------------------------8 y5 L, C+ D- p8 s0 D8 d0 l A
2.2定义迭代函数：
; Z& g2 |" m2 v# WPublic Function QesFunNew(ByVal Var_AC As Double) As Double8 l( y7 [% h# J F% f: q) [
) c/ q G4 O9 _ QesFunNew = Var_AC - (Atn(Var_AC / 80) * 80 + 1 - Var_AC) / (1 / (1 + (Var_AC / 80) ^ 2) - 1)
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End Function9 I' ?2 w1 g6 F& z9 c+ t
---------------------------------------------------------------
2 @+ F6 N x0 Q' e/ ?6 M1 S. Y2.3定义求解函数
% X2 L- b- {$ p7 h7 ~+ {8 M7 jPublic Function SolFunNew(ByVal IniAC As Double) As Double: \" T- D, H9 l. G+ k+ b
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Dim Res#( {7 f) q; T0 C
' R/ p* @7 R2 dDo While (1)
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; z) M5 A1 A' o( P4 w8 `" T, Z; Z Res = QesFunNew(IniAC)
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If Abs(QesFun(Res)) <= 10 ^ -12 Then
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SolFunNew = Res: Exit Do0 {9 D. l2 ~7 Z+ N, ~* ?( I
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Else
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* L* O8 t0 V3 q IniAC = Res
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End If) M& _3 `+ a: m8 M
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Loop, q. I4 o+ |+ O' b1 u6 ~ a8 E/ a
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这样做可能有点麻烦，但涉及到循环，迭代时，可自由调用自定义VBA函数和工作表函数（矩阵计算连杆机构），还可控制输出表格，便于插图。计算冷却塔时，积分得用辛普逊；解汽水比，得解非线性方程。对这些问题，EXCEL 工作表自身好像很吃力。 x# S0 X8 B) Z! K4 e
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楼主: 子子61961
