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;* l; A3 U# K9 r) e, }) D) `) X
k0 = 2*Pi/lamda;
~8 V# J; R: i& V( [$ a: q8 e% E
n1 = 1.4677;(*纤芯折射率*)
- _) q, K4 `7 Z2 Q G3 @
n2 = 1.4628;(*包层折射率*)
% \\" r; i. @' u) G
n3 = 0.469 + 9.32*I;(*银折射率*)
4 x3 C) n t9 l2 H! `3 ^7 D
a1 = 4.1 10^-6;(*纤芯半径*)
! t1 U4 n0 U' R/ z
a2 = 62.5 10^-6;(*包层半径*)! \3 _: S: ]9 `& P0 X
d = 40 10^-9;(*金属厚度*)
) {& i% P9 j2 E8 b
a3 = a2 + d;
. ?7 V9 G0 o' L* B% h& d
mu = Pi*4 10^-7;(*真空磁导率*)
4 j1 L b S j
epsi0 = 8.85 10^-12;(*介电常数*)
) j2 y2 t3 Q. y$ a7 A
$ x7 E9 n: K; G, u* s! h2 f' G
n4 = 1.330;
! c% T. ?2 c7 t+ W' f
' D: P+ k2 u w' t% Z) }
neffcl = neffclre + neffclim*I;% @\" q* P3 l5 N, P, f' n! n
9 N6 ~' r$ A: j$ N1 c
betacl = k0*neffcl;
% i2 ~/ |4 G; {7 t) A
omega = 2*Pi*299792458/lamda;
\" X, T! O+ c) V- f& O B* h
# C5 |; e0 l$ |2 _
epsi1 = n1^2*epsi0;
0 h% J. ~& O( p# W/ {
epsi2 = n2^2*epsi0;0 k! M; Y# E$ ~; U: [
epsi3 = n3^2*epsi0;
7 n& Q% r* v$ C+ W: i9 l
epsi4 = n4^2*epsi0;
' e1 T, {+ g9 W; W+ ?* f
+ `1 ]* T' H6 R
u1 = k0*Sqrt[neffcl^2 - n1^2];
7 T/ s/ d\" s% x) E( H+ \
u2 = k0*Sqrt[neffcl^2 - n2^2];
+ N+ v8 ^1 c/ p- W! Q+ q
u3 = k0*Sqrt[neffcl^2 - n3^2];0 ?/ f4 L( M\" D/ G) F6 t% j
w4 = k0*Sqrt[neffcl^2 - n4^2];
% q& d3 z; w2 m9 ^* L& h
+ p3 ^2 Q# V$ c4 O& K. l+ x3 i+ u5 ~
Iua111 = BesselI[1, u1*a1];
' Q$ U0 b% @& u: |\" I8 w
Iua121 = BesselI[1, u2*a1];\" q& x' G' ?7 n- n) q9 {. ^
Iua122 = BesselI[1, u2*a2];% j/ T1 q* S8 n& F( ]2 U3 J
Iua132 = BesselI[1, u3*a2];5 C. K0 ? ]4 A) ~0 w& [6 c
Iua133 = BesselI[1, u3*a3];
+ q+ V! [4 p1 M
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;4 g3 j0 p. Z\" b/ p1 t9 D5 z! I; k
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;1 i& E$ \( D\" |0 X$ f
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
& B% C! K$ C& e i
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;4 j: m7 @& s+ y\" |! m ^ x, C4 K
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;9 Z2 N, I3 C2 v
! ]\" V& P+ H9 s; S
Kua121 = BesselK [1, u2*a1];- f1 p/ C$ b% ^- l
Kua122 = BesselK [1, u2*a2];
5 G% S2 D( Y! k
Kua132 = BesselK [1, u3*a2];% L* ~0 ?, J5 m! }) G
Kua133 = BesselK [1, u3*a3];
/ @& A0 [8 P5 u: ^6 r
Kwa143 = BesselK [1, w4*a3];\" F; u- O/ W M- ^ ?* u. W
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;3 d! m7 V$ v\" w# s\" Q
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
! C+ l9 J) Q4 W. p6 L b0 A2 g S
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
: q7 n; U8 K2 W: d) n# P8 I/ l! h
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
. s2 a% l* l/ l- R' c/ I- Q
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
1 c0 C: q7 L2 j/ f7 u2 r
1 r5 m8 d7 n7 B; W; T4 J
H1 = (betacl*Kwa143*7 X' L) g- B, O0 H- s8 K0 m
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
Z\" ?9 [% h; m7 J0 O1 e
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
. W! e( I) N; }
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*\" _. ~% s' m' t; A0 P
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
\" }! x! B* p8 t
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*. i/ t* X: s2 U: l% l: i7 P& u5 h
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*& o, v- j9 e& {
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
( e7 Q* H5 k1 V# B' k. q( V
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);# U& C/ _ Q u! D# ~
\" z- J1 o# c9 D l1 t
H2 = (betacl*Kwa143* ]/ o; G1 z% ?
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*. y% t3 K8 C; b: E8 C
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*' |\" G+ f\" j& c- G6 m6 X- c8 N
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
( U1 u9 K5 |0 u: n* K
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*' Q. K3 @% T0 u6 r P
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
2 M( l+ s/ V: f$ o! K) t
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*2 X8 n) j8 T0 k
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143* W( L0 s, _. j; W7 b; v9 C$ ^ A
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);5 P# R, k8 i8 h6 m/ |5 t: g
; a9 d* c% W. v1 J
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*: @/ W' w, r; o( Z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
3 R, a1 P3 m' I! ?2 a* b( U% ]$ o
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
: ` w7 W: ^- i! h: d\" k
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
8 k, r! U: P9 W
Kua122 - . K. _\" B6 m1 n( @) y) v# b# S
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
5 s# v U! w; ~ A
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ( r& s; }$ j; G: \$ C
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 2 N9 b% N+ @ Y, |0 _, k1 S; h
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);# J# f+ d1 q& ~
, s9 L) z5 s/ p1 u7 H6 m
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*( e9 ^/ X- G8 }; }
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
5 U) q: w8 i1 d+ x7 [
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*, ` p, x9 L+ B3 K* n; c
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*) W; }% U# w: l! K; J- O! {
Iua122 -
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
2 I; Z- a& v, F2 n: w9 q
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
+ ?( Y, h$ O% p S
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ! }1 N, G. G' w! T\" B3 p
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);& k* R4 d @& c6 S1 |
2 N. K) S8 r1 y\" x; _. |9 E
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
/ d4 Q: k5 t: o
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*+ ?+ g! z5 R$ ], M' T
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
! K: \9 c) F3 b5 J
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
( G' t& c1 A) |\" `! U+ Q$ \4 |; [
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 9 o: x0 c; i- T& C
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - o3 Z5 }# D) N' v$ |
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
, W9 a) V! ]7 }& H1 T/ K. l3 l
w4^2/u3^2*Kwa143*IIua133);) \4 [$ d6 V6 j' K n$ m
: _% t2 |/ i6 C S7 K. ~
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*1 j1 T% T. F; o+ U, ^: M9 Y3 \/ Z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
: N) c( L+ O8 Y$ ^' o) ~+ x9 u' U* s+ e
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
& O& H7 n; i. ~4 l* \
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -0 m$ I; k7 m. g6 u9 R; L. ~
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 9 z( M: i- v R/ [+ i
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 5 k D! o& T L1 i7 m
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ! b6 }- W2 \, R5 ]+ f0 i8 q( A
w4^2/u3^2*Kwa143*IIua133);. `+ Y9 H4 _& U+ Q6 U& ~6 _
6 @& ]0 o3 {1 q8 U& a
M3 = (betacl*Kwa143*+ Q, ?: _ D7 m7 w( a4 M d
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - : u+ a* {/ g- u1 r2 `
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*8 ?) C& ^& @2 ]; k! o& ?% i% z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 3 D; Z. O4 c% n( T7 Z
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*7 M& ?0 m\" w\" X
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
2 Z+ w5 j\" o# U t, t2 B
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
$ }5 U! O+ u% k$ U$ l
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 5 O' W6 D% U1 i% R
w4^2/u3^2*Kwa143*IIua133);
: G8 K9 R1 `2 O2 ~# U4 J
2 U4 G6 m- y: P/ X
M4 = (betacl*Kwa143*
, i+ n) ^! V4 ~5 L
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - , @\" a2 D! N( i8 i3 Z5 C( o9 H
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
& R% G. r6 ?8 j! v: Z
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
5 L; O1 j- _! N9 Y$ C
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
( e( M7 b7 Z\" v% ^% h
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - m' v* N7 o: U! y+ r
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*. V* U! |! I: S! ]9 a( M
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - ! k7 A8 M6 ^4 i9 c+ k\" y5 X
w4^2/u3^2*Kwa143*IIua133);; o9 T3 S8 w ?
9 J/ s. N6 \0 d6 h\" V2 B8 A
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
* R( d. |# }7 M+ r; Q; S
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
- f7 ]% s0 V* T8 N
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
! e1 {% C/ r: I* ]) e- N
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
6 T3 O. A3 n9 T$ K% C6 n
( ]7 S$ b [, ` x8 D
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
( l8 X5 j' d' z# p4 F- t7 C
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
; i. u* e0 R: \) I( }/ }0 j$ W
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;5 A/ W2 I* \9 M) o1 Y
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
8 y4 W( n3 w6 P- s, n9 {
8 o1 P/ ?! x1 e/ [
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
$ O$ ]. G) s n( s9 P
V1*M4);
9 X5 c+ t6 H6 ~
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 1 e2 e; @: s7 J! e4 Q. h! i
V2*M2);
. P\" r- l3 \* O: _9 {\" ^8 h
+ z, M8 n/ k$ l0 S( r) |. z
x = xicl1 - xicl2;
\" ~% e# ~( t3 p# k b# O
x1 = Re[x];* T- F8 _( Z2 m3 `5 I2 y
x2 = Im[x];
7 ^; m5 [; K7 F( k; B' l! b
3 h% s! m, p; G1 Z# C$ x& Y
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];9 k3 q& V* `\" V
]
8 l. p& C; L! l
2 Z8 l4 B3 g, ^

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