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AC-arctan(AC/80)*80=1是数学问题。+ t! s/ \+ t5 g- ~7 u% o* a
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。6 R$ _+ X* v( n: J2 }
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( X6 P6 d: Y0 Q Y7 P% c! P定义待求解函数：
' ~" u3 @' W1 M0 xPublic Function QesFun(ByVal Var_AC As Double) As Double
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/ X) U* a" ]& `3 D; oQesFun = Var_AC - Atn(Var_AC / 80) * 80 - 1
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End Function
) D7 K+ Z) `: m4 r6 f--------------------------------------------------------------------------------------------------
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1.1 由 Arctan(AC/80)=(AC-1)/806 N7 W9 v, {, t! {2 g$ P
知 -PI()/2<(AC-1)/80< PI()/21 M! \8 w- a. V2 f t6 w2 c2 I0 v
即 1 -80*PI()/2! D* \1 ~/ b) K# v r- W* c7 p++++++++++++++++++++++++++++++++++++++G3 \5 x! U2 P
1.2定义求解函数：
1 C% p4 ~. }0 d1 p# y( x3 J' hPublic Function SolFunDic(ByVal MaxLim As Double, ByVal MinLim As Double) As Double0 z. B3 ^" Y& N/ W& U# L
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Dim Res#, VarAdj#% M8 S9 Y9 O; r- S; z6 f- d% [
}, L* J: v kVarAdj = 10 ^ -6$ N& h$ `7 _3 z
+ O7 {3 e' }. K
If QesFun(MinLim + VarAdj) < QesFun(MaxLim - VarAdj) Then
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Do While (1)$ L; O# `' }4 P, c( [
$ K7 w$ r2 Z4 V" [Res = (MaxLim + MinLim) / 28 d+ J) Q G! L ]- v
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If Abs(QesFun(Res)) <= 10 ^ -12 Then
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5 L" J$ q' `$ J; \& ?6 u$ L- O6 O" HSolFunDic = Res: Exit Do" V/ b# j+ \$ m# C+ O& J8 _" E
! X& o) G% q" QElseIf (QesFun(Res) < 0) Then
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MinLim = Res
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& _* h% G; d$ a# n( l6 L- ^! AElse
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MaxLim = Res
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End If5 R0 X8 s' _- ~* Z
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Else+ z$ y9 X+ J H$ H+ R& j
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Do While (1). p3 G) t+ J! c3 K9 J8 D. U% I8 j
9 S+ }# M. T7 z+ H0 D4 [# i2 mRes = (MaxLim + MinLim) / 28 O: b$ Q5 N6 Q$ a; g
) U9 m& C3 s: y l# XIf Abs(QesFun(Res)) <= 10 ^ -12 Then
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. O. q7 p8 M1 ?5 C; {6 \SolFunDic = Res: Exit Do+ i/ f6 x5 U. K- `( k$ ]6 n
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ElseIf (QesFun(Res) > 0) Then& X, A- B1 g* m/ H; \: ]$ s
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MinLim = Res
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Else& s" ^3 H+ r7 Q) u- K
1 h5 R. L# H3 a0 [MaxLim = Res
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" w% @2 u6 Y% D7 _' o" n2 B% HEnd If
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; R: e7 q4 H8 DLoop4 [5 V+ C8 t- M% ^: w/ L5 A
+ K3 K+ C4 f+ T" s- H( lEnd If4 Y! @( X& t) v! Q; X& T$ O
End Function) `0 t$ r4 t, i* ?+ r5 S* N3 T
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2. 牛顿法9 \5 |; L: J& B5 p6 O
2.1 由 f(AC)＝arctan(AC/80)*80+1-AC/ s( a$ n D! P- ~; y
求导 f(AC)’=1/(1+(AC/80)^2)-1) D: \& P0 H+ g5 h/ X4 f' L) B" s3 v' Y
即 AC_1=AC_0- f(AC)/ f(AC)’: D4 @' \2 g# P
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2 I2 O3 P X4 X* n2 ]2.2定义迭代函数：) e) R9 z. Z; _- b, s( P; Q4 G
Public Function QesFunNew(ByVal Var_AC As Double) As Double
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QesFunNew = Var_AC - (Atn(Var_AC / 80) * 80 + 1 - Var_AC) / (1 / (1 + (Var_AC / 80) ^ 2) - 1)
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End Function/ T3 ~0 H! P* {' B7 D8 o
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7 o" X' Z S+ c2 t4 ?2.3定义求解函数& ]$ @$ g- @+ |7 j% D
Public Function SolFunNew(ByVal IniAC As Double) As Double
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Dim Res#' M* v9 S: Z* ^# e9 Q4 Z, E& ^
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Do While (1)* r2 M* e* f( U3 q0 V4 @
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Res = QesFunNew(IniAC)3 W$ g$ c+ T' M5 C: P8 U1 _# Y& I
0 _# p0 ?3 l! x. S# R& TIf Abs(QesFun(Res)) <= 10 ^ -12 Then
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+ b, O& J2 y" y1 U5 d% ySolFunNew = Res: Exit Do
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Else
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! l+ b# y5 E, i6 f0 {0 I, k% WIniAC = Res
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End If* M0 E7 I4 \0 l& {
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/ t7 ]$ q! @. ^ w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。
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子子61961
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发表于 2016-2-15 12:48:43
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