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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 N" Q; j: m( w: C, \$ N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。+ p) d+ d0 [3 w( e$ }( U6 g
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- Q2 |% z0 y: L5 {2 t( n定义待求解函数：
4 F7 X$ R9 C; u. ^# ~" X, ^Public Function QesFun(ByVal Var_AC As Double) As Double
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QesFun = Var_AC - Atn(Var_AC / 80) * 80 - 13 [) K1 Z3 |( L/ N6 n9 z
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End Function
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$ s- A! ~1 \ x: S1. 二分法
6 t" ^0 M; W6 D, V2 w1.1 由 Arctan(AC/80)=(AC-1)/809 z+ z$ }! H' F- g5 M
知 -PI()/2<(AC-1)/80< PI()/2: ]* E" E q8 h% X, \
即 1 -80*PI()/2<AC<1+ 80*PI()/2
9 I) V ?! |- D! G& ?4 L9 h' R++++++++++++++++++++++++++++++++++++++
2 J5 f. j) G6 [3 n1 h0 V1.2定义求解函数：
% L7 N6 y* O& F0 iPublic Function SolFunDic(ByVal MaxLim As Double, ByVal MinLim As Double) As Double
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Dim Res#, VarAdj#2 y& u$ l+ u' y& A# Z' q
: n4 }) r- [7 V1 KVarAdj = 10 ^ -6
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4 S, v+ f) p7 _If QesFun(MinLim + VarAdj) < QesFun(MaxLim - VarAdj) Then
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! N0 F- s& _) q, R% c/ n' S9 u Do While (1), @; [) [7 ?: E% u8 l4 x
* L0 M6 x1 E. G6 O4 k! ` Res = (MaxLim + MinLim) / 2
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If Abs(QesFun(Res)) <= 10 ^ -12 Then
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SolFunDic = Res: Exit Do2 d5 a: a! F, x
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ElseIf (QesFun(Res) < 0) Then" `- p; }3 R) J! u
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MinLim = Res3 J# ^9 {9 K3 R5 V' U2 q1 H4 _
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Else
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MaxLim = Res' K( C* O- G* s v7 J% E9 ?% z
, d; M q- l& t) r+ n# m6 Q End If- K8 Z- N, C' m. i' V
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Loop
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+ z5 ?7 G/ D, j, z K Do While (1)7 K# [2 X% X8 J
! o5 ?% D! _7 l# p Res = (MaxLim + MinLim) / 23 z, n9 {2 W9 S5 W
( I+ e2 J3 I8 y+ b* C If Abs(QesFun(Res)) <= 10 ^ -12 Then
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! |# c" e8 x3 e8 K$ l SolFunDic = Res: Exit Do( Y2 Z& v4 h5 N0 M3 @
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ElseIf (QesFun(Res) > 0) Then n2 M$ p# G. I7 @% v( k* k
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MinLim = Res3 P& C/ o" A; _, _2 M5 L {
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$ }$ m0 M7 X+ Q MaxLim = Res
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End If" {. ^9 b5 i, v3 {1 {6 R4 ]6 D
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Loop
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End If
: X) _/ Z8 }+ U5 X- zEnd Function2 f# i( u3 p1 Y5 ~# _1 ^0 P
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2. 牛顿法) f% a8 j. z6 V: t7 M8 P
2.1 由 f(AC)＝arctan(AC/80)*80+1-AC
% Y; J5 ~8 M+ t; x4 e% K! o" t 求导 f(AC)’=1/(1+(AC/80)^2)-1
3 r0 K+ Z* V: G' y 即 AC_1=AC_0- f(AC)/ f(AC)’* `) P! x! X4 l, Q; a2 U
--------------------------------------------------------------4 R' l h& }* {* l3 {5 P5 o( l
2.2定义迭代函数： C* q; o( ~9 |" F/ |$ N
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
/ I% T, T" [9 L2 U z* @---------------------------------------------------------------
4 @4 |$ H5 A$ A0 Q2 c1 v- y2.3定义求解函数0 `( w4 X% W( i" A
Public Function SolFunNew(ByVal IniAC As Double) As Double h& |# }* q6 H9 ?9 e7 G
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Dim Res#
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6 \; y q8 ]( FDo While (1)
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& Y: u. h, G! p' ]3 u+ ]/ ]! N5 a Res = QesFunNew(IniAC); Z$ o1 Y3 j3 J1 m0 i/ D7 [* [4 }
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If Abs(QesFun(Res)) <= 10 ^ -12 Then
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SolFunNew = Res: Exit Do" e b1 S) k. N" D
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Else/ w- U* ^7 ^; l+ q) W. ~8 }# B
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IniAC = Res, T/ s1 e+ ~& m W/ |
T1 B/ I" v. z9 | d# s3 g End If
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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。/ p8 w' _5 Q5 r5 }) ?
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