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AC-arctan(AC/80)*80=1是數(shù)學(xué)問題。! O) @8 u+ N' R% V9 C5 ^ u/ H
子子大俠既然讀過VB,，那么讀VBA代碼就應(yīng)該沒什么困難,，核心是數(shù)值計(jì)算。
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/ W) M9 ^0 P5 ~7 L定義待求解函數(shù)：$ c9 Y9 b# I/ P) l+ f4 p
Public Function QesFun(ByVal Var_AC As Double) As Double
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+ N, D8 i' N: x ?, \ QesFun = Var_AC - Atn(Var_AC / 80) * 80 - 14 [* b$ f: C' {, h( n7 H A4 e
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End Function
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7 M: B! c8 b7 E. A: x6 L. y6 _: Z1. 二分法
% O/ T3 m! `9 e5 x) c5 q1.1 由 Arctan(AC/80)=(AC-1)/80
; ]) E0 K* [- K- j# D U8 ` 知 -PI()/2<(AC-1)/80< PI()/2
+ M' ]2 \- p( i) i! t. c$ N9 ^+ E 即 1 -80*PI()/2<AC<1+ 80*PI()/2" N& b2 K G& m( _* |8 a+ D( ~, f
++++++++++++++++++++++++++++++++++++++5 T2 E3 l+ K/ y* x& Z, |. O
1.2定義求解函數(shù)：% Y) k* t; R- o
Public Function SolFunDic(ByVal MaxLim As Double, ByVal MinLim As Double) As Double4 n! |4 i4 A& }" b1 ^& M0 A- o* a
' W4 O, U1 T! F" }0 |5 NDim Res#, VarAdj#4 i1 e& @/ D# D# C# |
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VarAdj = 10 ^ -6
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If QesFun(MinLim + VarAdj) < QesFun(MaxLim - VarAdj) Then6 P: X9 |# J U/ P
; |* ^! ^9 l& w Do While (1)
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Res = (MaxLim + MinLim) / 2( c6 `6 R# E5 o4 w4 ]* X7 B
# u! ?; l; Y0 O8 R If Abs(QesFun(Res)) <= 10 ^ -12 Then
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+ `# ]" t+ `9 [" D" q0 z SolFunDic = Res: Exit Do! n" G7 ^' t# {& h+ E# ~! B6 d
3 U# o$ p" o8 V/ d) p$ f j6 m8 ?% n ElseIf (QesFun(Res) < 0) Then0 n/ H2 j% g/ _2 B
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MinLim = Res
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Else
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MaxLim = Res
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End If, `5 C" p! b9 [5 I) x
s$ K# P3 M2 ` Loop, q: S9 x* K+ ~( X- B
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Else( A5 v+ q2 G4 f' b0 Z9 Y; y, c
9 U" q" R. Z6 }8 C, Z Do While (1)
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5 t# D: k! I4 \. q+ b% c8 b: ~ Res = (MaxLim + MinLim) / 2; s- t% E# G( M& a3 H e+ h
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If Abs(QesFun(Res)) <= 10 ^ -12 Then
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SolFunDic = Res: Exit Do) g$ U5 L# x1 M: Q3 X; i
. r8 l6 k, u% ^( a' O' ~0 y+ Z ElseIf (QesFun(Res) > 0) Then4 E& P9 H8 v+ G) @% d2 @ V8 _
& t2 {2 u9 I% k; o MinLim = Res
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6 g8 e0 G2 f% @/ R: N4 s& B- H' `3 ~ Else
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MaxLim = Res2 l$ W# [8 c# T5 x2 i* F
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End If
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Loop
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+ b- B; H" H0 R' v; J; g' DEnd If
! u- A0 E( j- J; B1 r4 `* kEnd Function: B0 R2 n; ~1 m+ E& e9 t
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! F" F' c5 c6 f* N6 j2. 牛頓法
+ r' \8 J& e# R: n3 r2.1 由 f(AC)＝arctan(AC/80)*80+1-AC* l/ J2 g! `* u- S; `0 v
求導(dǎo) f(AC)’=1/(1+(AC/80)^2)-1- p Y! ^0 M- E7 h* g: p
即 AC_1=AC_0- f(AC)/ f(AC)’; G# u; J' b" e+ M* l" e
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2.2定義迭代函數(shù)：
, D, G% X9 B4 UPublic 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
% v2 I7 Z/ L5 I( r4 M+ e9 _% e---------------------------------------------------------------
, G( ]: D* \( T# O. {. L2.3定義求解函數(shù)' b8 V+ f5 ^$ k. {& W% w
Public Function SolFunNew(ByVal IniAC As Double) As Double
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5 V1 I( S) q) x) J+ P- C6 f$ dDim Res#' Y$ L* r( W- D( d
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Do While (1)
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Res = QesFunNew(IniAC)
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If Abs(QesFun(Res)) <= 10 ^ -12 Then$ M7 \% b& s/ M% i2 i
/ }6 t5 [# L( s; V SolFunNew = Res: Exit Do
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Else
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IniAC = Res3 [, }' ^ W6 _ ?
* z. f) ^4 A6 B& | End If& Y- E7 M' _5 Q. v7 j# t
+ y: u$ S M5 E3 @/ w1 X4 o: D+ \Loop. V9 O9 V3 L" N/ j% E0 @
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這樣做可能有點(diǎn)麻煩,，但涉及到循環(huán),，迭代時(shí)，可自由調(diào)用自定義VBA函數(shù)和工作表函數(shù)（矩陣計(jì)算連桿機(jī)構(gòu)）,，還可控制輸出表格,，便于插圖。計(jì)算冷卻塔時(shí),，積分得用辛普遜,；解汽水比，得解非線性方程,。對這些問題,，EXCEL 工作表自身好像很吃力。
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樓主: 子子61961
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發(fā)表于 2016-2-15 12:48:43
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