请问FindRoot外面套一个For循环的问题

[复制链接]

字体大小: 正常放大

cxy623157929

4 主题	10 听众	29 积分

升级 25.26%

TA的每日心情

	郁闷 2015-6-6 15:06

签到天数: 5 天

[LV.2]偶尔看看I

电梯直达

1^#

发表于 2015-6-2 12:57 |只看该作者 |倒序浏览

|招呼Ta 关注Ta |邮箱已经成功绑定

lamda = 1.55 10^-6;
+ o$ V2 Y\" k9 F; r# m# L* B: H a( y
k0 = 2*Pi/lamda;! @' h, z4 P0 }8 Q* l
n1 = 1.4677;(*纤芯折射率*)6 E7 B, L3 C0 T4 x( a2 N
n2 = 1.4628;(*包层折射率*)5 q0 M5 F7 }! D7 o5 L- C! A7 m
n3 = 0.469 + 9.32*I;(*银折射率*)9 L1 m M$ U, `# h: P
a1 = 4.1 10^-6;(*纤芯半径*)( k) }, `5 h2 x1 J5 | H* E
a2 = 62.5 10^-6;(*包层半径*)
0 e c# V' j\" r
d = 40 10^-9;(*金属厚度*)* p* W: W8 E) ?) J
a3 = a2 + d;0 W\" v3 m\" }$ q
mu = Pi*4 10^-7;(*真空磁导率*)6 Q( L1 X* P, h1 d2 ?
epsi0 = 8.85 10^-12;(*介电常数*)6 ~ [; p! o8 Z8 ?' {' ~0 o
1 D% V5 W/ ^2 ?# [+ X/ p
n4 = 1.330;- O0 p8 m& u# T1 p' P. @
3 B6 x% `8 @3 m9 S
neffcl = neffclre + neffclim*I;2 g0 u4 o/ ?* Z$ Z; ]
, Z2 j6 f# e0 @ E, k, _- f
betacl = k0*neffcl;- ?( l* B% K! L9 M$ l( g
omega = 2*Pi*299792458/lamda; L( f8 z8 x* K. R$ s+ Q. m
, x/ |/ y4 {0 `3 O
epsi1 = n1^2*epsi0;
: _6 f8 V O$ n) L; b
epsi2 = n2^2*epsi0;
# K. w0 d( E\" u
epsi3 = n3^2*epsi0;
1 Q7 R7 s( H$ P\" ^* Q
epsi4 = n4^2*epsi0;
; P5 l3 |) l9 z: M& { x
* h$ y2 D7 W! p0 L z' ` A
u1 = k0*Sqrt[neffcl^2 - n1^2];! k3 ]% Q8 h( U) X
u2 = k0*Sqrt[neffcl^2 - n2^2];
u3 = k0*Sqrt[neffcl^2 - n3^2];
& t* ~* K9 `& w( v; [- e
w4 = k0*Sqrt[neffcl^2 - n4^2];
8 ^' t\" C0 x7 G- Z
8 B' A. M/ _. M7 A
Iua111 = BesselI[1, u1*a1];( y5 O: w; f0 a9 S. e/ c7 K7 f
Iua121 = BesselI[1, u2*a1];\" H, \2 m4 H2 b\" w% ^+ D0 e
Iua122 = BesselI[1, u2*a2];2 F5 u! e$ n# H$ g7 ^: c
Iua132 = BesselI[1, u3*a2];# V! z s# Q2 L2 u8 I% E) h2 `: X/ s
Iua133 = BesselI[1, u3*a3];# p/ y9 d' P, N- V
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
8 f7 {. Z# I! X; T
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
- [' G0 R! [# L6 [$ V
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
C- }: Q. r/ q7 I' T5 d7 m( e
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;! K0 L/ E\" f% ~6 q3 ?1 g\" u
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
/ |$ M4 l* D: p' [' k6 N' a N
8 R K& Q# h2 o\" D
Kua121 = BesselK [1, u2*a1];
. A) g% E6 G/ @/ i/ b$ D
Kua122 = BesselK [1, u2*a2];4 m: y3 P0 M( ]0 ?
Kua132 = BesselK [1, u3*a2];
- i1 l, [' p\" t
Kua133 = BesselK [1, u3*a3];
* W/ I: u$ D* M\" z6 [2 E
Kwa143 = BesselK [1, w4*a3];2 U) \/ N: U+ ]% a: u
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;6 B9 D: I$ s A( g
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
* c- V& P\" P: ]2 @( a4 F. f
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
7 i' s2 u. x! z# q u( T
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
! h4 `- L% L1 N' t0 [$ O! c
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
6 p' X' n- [5 \; Z! W
. d. k o+ W) Y. p5 K
H1 = (betacl*Kwa143*( I% n+ b3 ?8 w9 f0 x2 r1 W6 }
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*+ d& n8 G6 p. C8 y5 u$ s: b
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*: v3 w% o7 O\" x: |! G6 {
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
' B+ S8 s* p4 j, N; o+ |# ^
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
5 C! b: M- c3 i
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
& ?# g/ v1 q) V/ q( N- r
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
5 `# O8 A/ _ {3 t( X
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
$ M: f, T8 `# T! ]
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);6 ~8 k/ t8 i! t% _
% \* D) |1 A) u. y4 h8 m5 }# r
H2 = (betacl*Kwa143*3 m8 `) T* c, a# T
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
4 D; V; v; M# S* ^; r2 P: | B5 D
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*1 i% j7 d( b+ ~- [5 k6 D% t6 k
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*% T: B) j# Q3 i1 X5 s
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
6 m; e6 A! O4 {% B! h\" v; H/ t
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
# c! f/ e0 J2 Z5 s4 X
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*/ X% U- D: i. F; e3 x( {+ @
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*- y# ~9 u; g, }: _' a
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);( O+ {- K3 D3 ]4 N$ k
0 u/ p% O6 {\" a r3 D0 }
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
' z) U+ u- t& N/ I
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
4 N+ ?) X1 F$ ]# d! w: [
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
% f- s. P2 k5 L/ C u% v! v, m0 V5 Z
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*( m2 y, _% O# n, H/ v\" N% x
Kua122 - ( H% q& Y5 `: C: K
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - , c- r6 i' N\" d9 q
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 7 d2 l8 q2 g, A3 s4 p( \
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
4 T6 J- W, K* D% Q
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);/ t& ?\" `0 B$ s1 h
% J; e7 W9 ~& N$ q( |
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*+ m0 _# r% I( ^( S
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*; W, M- e9 e8 L\" y
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*8 p+ U `. ~% M0 z/ O# [
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
% g4 {- r9 b- x/ f
Iua122 -
, {1 [) Z# r+ S. I( t4 O# r4 [
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
* }* a6 h9 S9 z- h# R2 l/ y
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
* D( V6 M( J) [- w
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 1 ~5 F- J6 _9 t
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);3 _, v, `1 `& P$ ?3 U* g
# j6 v& c7 x, n: a) t; L& k( q
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
9 u. `* b2 \+ }
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
! |% {1 v( Z1 Z. _
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
\" K4 [: O- s; `; l4 k3 h4 f
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -3 E g, @; N& e! x
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ; i$ H- _2 B7 M\" t3 a
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - . y7 u\" l; t9 J! j$ g# P0 t
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - # `* o3 c\" M5 R2 L, T' z4 i
w4^2/u3^2*Kwa143*IIua133);- E. @& G2 s% s0 {9 ^
6 O6 F% _. i\" ?. L- n
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*: k4 S* O\" w$ z4 h9 K$ c7 W
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*, ]1 P7 X4 G! r$ b- n/ s! i& ?
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*3 I\" v4 Y0 z- W7 g! a3 |. \& X1 A3 o
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -) x. u- l6 Q# \/ M4 `, Y, H( U
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
4 H5 y0 Z% U1 k W( r N
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 6 {* f* p! ]. s4 z4 Y
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 6 t- }( R5 C* x3 V; K/ B% A; [ X0 A( H
w4^2/u3^2*Kwa143*IIua133);
8 s4 z6 L+ m( w
- w5 s& ?1 ]6 o- l% N
M3 = (betacl*Kwa143*3 M% R1 s1 }+ n- X\" Z
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - & a) [1 q: V, D: v
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*9 G0 |' R( f0 k) p. {
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 3 N4 s* \: D: Z) |1 Y1 K' [9 B2 n
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
: H2 o2 `- X2 {8 _4 {3 w d
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
, a; B; H+ R; [
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
2 G4 Y0 d4 R3 H* V8 R
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - - `0 ?4 H$ N, i7 u3 ^
w4^2/u3^2*Kwa143*IIua133);
% r* Z6 s' o4 f/ [. T, A. d) U2 l8 c
m, M2 N& B/ W
M4 = (betacl*Kwa143*$ s& h7 j9 j1 @9 X- b\" C. ]
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
q* i# ~! z+ U& Q% v5 p
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
3 E* }$ M, h3 i7 A4 `8 D
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
6 f8 O1 ]) P. @\" [% b
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
/ T) V+ g) Q\" P/ e
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - & M* F: b# f9 U. v0 T% e
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*' P5 R/ M1 I Z& H6 ?
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - / {- |) u* {1 j9 s
w4^2/u3^2*Kwa143*IIua133);
% y6 z' r3 i3 @+ G! L' M
& p: [$ {: ~% w/ @+ E) X5 y! w
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;4 ?. [4 U9 ?# L7 B. {1 i/ {
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
; D' ~4 G+ r2 z, S8 E
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
9 t( M: n* W8 J/ A8 u
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;/ z7 s\" C& R8 T$ ?
/ k2 `8 F) K z8 a3 [
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;6 |6 k0 b! E G8 h c9 E' P
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
l: ~/ P) S& I' q
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
9 I5 q- t5 b* p2 ~1 X& j
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
1 S |2 ^1 C& C8 w$ h/ C( c
6 Q- \+ C9 N0 a9 N
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
8 o# d+ A# N0 M2 W. A/ f; i# `1 c
V1*M4);
8 k+ m0 X' ]' H+ ], q% d/ s, q
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
, g, t' u; j1 [' G' R P) p
V2*M2);+ k, S: C( C! G& e, `8 O' a5 d
+ U- @! Z: d' C- Y& n: j5 e
x = xicl1 - xicl2;2 e; i) V7 E) [; R5 v, H\" \
x1 = Re[x];/ I! v, `* s- u7 S8 ~, ^0 M/ f
x2 = Im[x];
8 b0 p) k0 K' H( k, T
! P- d' W& q% u3 f/ O. l+ S0 v
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
: M1 W! G8 u6 s* k/ K
]% q: z4 T4 ^, [: M# m3 o- ?+ f9 x' t
9 }: } V4 `\" Y

复制代码

代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
换成
For[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
]
就会出现
FindRoot::lstol: 线搜索把步长降低到由 AccuracyGoal 和 PrecisionGoal 指定的容差范围内，但是无法找到 merit 函数的充足的降低. 您可能需要多于 MachinePrecision 位工作精度以满足这些容差.

请问是怎么回事?

zan