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AC-arctan(AC/80)*80=1是數(shù)學(xué)問題。
/ H2 _$ Z5 K% ]: G* w& c0 ?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)值計算。; N# E. t: W4 J/ j) b
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: I8 T, Z. H. S3 @( v定義待求解函數(shù)：
( j7 |4 N$ n5 ?% H+ k0 f6 ~8 T/ WPublic Function QesFun(ByVal Var_AC As Double) As Double% U9 g% b0 N* z" _% S0 w
4 I4 ~9 _& V; b3 g( ?3 r2 r QesFun = Var_AC - Atn(Var_AC / 80) * 80 - 1
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# z8 L3 G J7 t$ a- T2 {End Function- G- \3 n& U% |
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6 f4 t) f& i" {1. 二分法
7 o' Q' d0 _6 U* M, H: i1.1 由 Arctan(AC/80)=(AC-1)/80
3 \, _2 |( f' d6 @7 ~2 g 知 -PI()/2<(AC-1)/80< PI()/26 V: j8 s) r* k; k3 `
即 1 -80*PI()/2<AC<1+ 80*PI()/2+ _+ \- ?2 b$ M9 L
++++++++++++++++++++++++++++++++++++++5 H& v6 A2 a$ `) F( u9 g
1.2定義求解函數(shù)：/ a2 T7 T0 {! c3 J \1 g
Public Function SolFunDic(ByVal MaxLim As Double, ByVal MinLim As Double) As Double
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( X# p4 e' G: ]) c- d( t+ V) tDim Res#, VarAdj#
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7 S- a3 W4 t2 w, ]4 p( v) Z9 T4 S GVarAdj = 10 ^ -6
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0 I; E X6 P* q6 H! |% AIf QesFun(MinLim + VarAdj) < QesFun(MaxLim - VarAdj) Then8 N: H {2 J6 G( ^2 ?- w3 q9 f
7 s" u& f% a% R; ?- I7 t- ^1 G2 ^ Do While (1)
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Res = (MaxLim + MinLim) / 2
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2 _2 x {) X; M: K. h6 u If Abs(QesFun(Res)) <= 10 ^ -12 Then
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. k1 P8 H1 t* j) n# Y! P% X SolFunDic = Res: Exit Do) `, v8 `8 K8 n9 i4 ?, m1 Q5 h
7 o) H9 o. S5 h9 o0 e' w! G ElseIf (QesFun(Res) < 0) Then
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- X6 V. |% d) C6 l. F) _2 O+ l, O" ? MinLim = Res
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Else
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. ?/ m4 w p: d% l MaxLim = Res
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. r( t, j2 k- I- w8 b7 r$ I% I End If; M$ r3 ~- x* z; y$ A
" w' p; \: X* A' X/ K Loop: S7 F: J$ B6 I
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Else" Z; {. }6 ?+ u" E
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Do While (1)( q7 x, R3 Z# h7 e) N. w1 ^* S9 @7 M
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Res = (MaxLim + MinLim) / 2- u5 ]% |" O* b6 b
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If Abs(QesFun(Res)) <= 10 ^ -12 Then) h8 M# w7 |: a( {" c) t! ]
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SolFunDic = Res: Exit Do
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ElseIf (QesFun(Res) > 0) Then
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MinLim = Res
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0 z$ V5 C3 K$ O# \9 z( A- y Else
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$ N' T8 I; g7 n0 L z. D+ q7 f8 c MaxLim = Res
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End If
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Loop
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1 t8 U! i" j2 h/ U0 |8 @% oEnd If) Y/ r( W# S$ D3 Q2 I' ]
End Function
) o! r: L7 [" D! |3 v8 o) s& L4 w% n--------------------------------------------------------------7 U Y$ A! O m4 e" b; g
2. 牛頓法
5 b% N0 ~" k' i8 K. @3 G0 H2.1 由 f(AC)＝arctan(AC/80)*80+1-AC
% }9 a7 g/ p+ e- m 求導(dǎo) f(AC)’=1/(1+(AC/80)^2)-1
6 u. R$ ~ d2 T1 k; @8 w$ \ 即 AC_1=AC_0- f(AC)/ f(AC)’
/ ~- F, [8 I3 b--------------------------------------------------------------- \2 W, Y- k7 q7 S6 y- d
2.2定義迭代函數(shù)：
) T7 U1 ]7 H5 n. L7 e& U" b5 a1 XPublic 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)% J+ M" i$ i0 A# X+ g$ E
! E" p3 D; {) VEnd Function: F0 c* D3 O, f8 ]; O
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) X& M0 O0 O& P* q/ a8 x2.3定義求解函數(shù)
/ U2 S0 X5 }; K; w- l6 bPublic Function SolFunNew(ByVal IniAC As Double) As Double
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7 R1 m8 b- M3 ]6 i! ~! ^Dim Res#
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) n4 ?5 \9 T# gDo While (1)0 g0 L: |+ ?1 h. l
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Res = QesFunNew(IniAC); l0 U) ]: [7 x' @) b6 C3 k
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If Abs(QesFun(Res)) <= 10 ^ -12 Then" l% L" q$ U P! G1 F' V
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SolFunNew = Res: Exit Do
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Else5 N0 p5 u2 U/ u# k* s( |, ?
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IniAC = Res2 S4 ~4 D8 o- {6 }4 D
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Loop
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$ N0 {: R2 C0 I9 V3 k這樣做可能有點麻煩，但涉及到循環(huán)，迭代時，可自由調(diào)用自定義VBA函數(shù)和工作表函數(shù)（矩陣計算連桿機構(gòu)），還可控制輸出表格，便于插圖。計算冷卻塔時，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
發(fā)表于 2016-2-15 12:48:43
