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 |正序浏览

|招呼Ta 关注Ta |邮箱已经成功绑定

lamda = 1.55 10^-6;
9 y3 n/ l& `6 O& s, i
k0 = 2*Pi/lamda;1 o\" O4 [! F( d
n1 = 1.4677;(*纤芯折射率*)
+ ^1 B2 z- F) X, ~6 j
n2 = 1.4628;(*包层折射率*)
/ e% b; w0 Z0 ]9 @
n3 = 0.469 + 9.32*I;(*银折射率*)
( U& R' d1 u/ v. T; c
a1 = 4.1 10^-6;(*纤芯半径*); v7 ~4 p% S+ z\" t% M7 w
a2 = 62.5 10^-6;(*包层半径*); M5 i0 a2 `\" p5 o# S3 q
d = 40 10^-9;(*金属厚度*)\" o2 m7 x5 g( r) _, r
a3 = a2 + d;
1 B* W3 N& J' a. L+ |( [
mu = Pi*4 10^-7;(*真空磁导率*)( R8 E2 t6 T+ c2 i: {8 a
epsi0 = 8.85 10^-12;(*介电常数*)9 C ~* X( A! ~$ v+ m* S
+ i7 H3 P. K G
n4 = 1.330;' }) ^; K2 i1 a+ N1 l
; U' ?4 b* m\" S& f' ]9 S
neffcl = neffclre + neffclim*I;
: f8 K5 Q4 ?1 ~' ~1 n/ h% j
* i# \- F; h1 F- o) v9 C4 u
betacl = k0*neffcl;) o1 d. K- l2 I0 v$ Q
omega = 2*Pi*299792458/lamda;* q/ l# U+ O! X4 k' B, q
+ s- _4 x6 m! ?& ]\" G
epsi1 = n1^2*epsi0;& R1 N\" L& Y( ?- L6 D1 P5 L
epsi2 = n2^2*epsi0;5 g! ^( Y1 `+ }+ }; D
epsi3 = n3^2*epsi0;
. E$ F- R\" H5 z$ A0 J
epsi4 = n4^2*epsi0;0 ^( R/ `, b5 l$ t' I$ Q( z* k
! g2 ?0 O. Q, o) K- Q9 m1 u8 m5 U
u1 = k0*Sqrt[neffcl^2 - n1^2];
. S# S% }9 {\" s$ @: J
u2 = k0*Sqrt[neffcl^2 - n2^2];& `5 p) a4 D4 X4 R7 Q% b+ T3 M
u3 = k0*Sqrt[neffcl^2 - n3^2];
. ?2 f. K! y0 Z, v
w4 = k0*Sqrt[neffcl^2 - n4^2];1 U7 w8 a* m1 `: C; }9 D2 G! L+ }' X
\" h3 c5 B$ x' G8 J
Iua111 = BesselI[1, u1*a1];* B! i8 l& e8 P\" I
Iua121 = BesselI[1, u2*a1];
. q- X) R& Y5 Y2 }8 k
Iua122 = BesselI[1, u2*a2];
6 f+ y& H/ x& |
Iua132 = BesselI[1, u3*a2];9 r* f; D. q! ?9 u
Iua133 = BesselI[1, u3*a3];# I( w# L+ q2 N, N' ^0 n- K- ^
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;* ^- t r* u5 {3 ~
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
2 |5 V8 ]; D* d0 F+ E& v0 e
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
4 T( N' p) m% n! |% E2 v
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;9 J' W( Z1 J8 } d5 {. ?\" ^& l1 @/ I, f
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
& y5 x3 V8 X/ U9 v
: R) x\" u* l/ E# I) V+ @
Kua121 = BesselK [1, u2*a1];& g5 l8 _% g% }7 f3 I
Kua122 = BesselK [1, u2*a2];\" A( x\" n4 Z* E0 b
Kua132 = BesselK [1, u3*a2];0 D5 G% V! u\" S6 o' a: [
Kua133 = BesselK [1, u3*a3];
0 v5 h. n$ H6 E( X/ q5 s9 \
Kwa143 = BesselK [1, w4*a3];
+ Z3 h$ V- `) T! \
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;9 m0 q/ F, {) W# h* k
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;# d\" K5 W8 t o\" C G
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
8 Y7 B( a+ B$ k3 F+ r) X
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;) D1 g6 `, w* I* u; I
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
7 ^7 f; W2 t8 V1 f% H0 x' q
6 d! ^% Q0 Z/ a8 \. u$ S1 }& h
H1 = (betacl*Kwa143*( z% o) ?9 U+ l8 @ j3 ?$ N# G
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*; l! ?. y% t( o/ G
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
0 C+ p3 ]* f6 G3 \
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
1 Z6 x$ o, B+ E/ r0 J* S4 N& E
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*, e; {' z\" X, ~; o. t6 s g
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*7 T W! ~, U- P
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
6 n# a& \8 B& G1 V7 o
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143* }1 ]$ K. d) B( |
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);$ K* s' D7 ? \1 w8 ^
: J; [' L; D3 }7 r' ^7 [: o. ^5 Q
H2 = (betacl*Kwa143*
1 B1 y: T* N4 G+ o* Z
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*% k* [6 ^4 D6 H( j( ^% n2 }. [
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
- Z1 q, {4 h; ~0 R: p! _0 @, u
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
n3 y2 O; E0 p
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*' v. @, e [* M& c; G$ \8 b
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*) Z7 Y9 M6 a+ D2 u
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
. U& i9 v- I9 R) D' Q
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*, B! ]. M& M4 n U# u
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);' G+ [% U- T4 Z7 M' @+ e- g
+ ]. ^3 s. C6 v2 c: Z\" \
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
: k6 m4 W0 u1 G5 v
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*9 J\" o2 ?& `' Z7 k; T) ?
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*# Y4 H$ E; E; B6 _. }( g6 ^4 t
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*2 e4 v\" }0 G! }1 H8 f
Kua122 -
+ d# O9 M; V5 y0 K\" {! ?9 v
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
5 U2 ^ m9 x a7 N
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 3 u( R* B\" L0 j, M4 E- ~3 H m3 ?
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - * w7 i+ n) t( l+ z+ T$ H' S$ t
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
$ o! m\" B5 \2 @' C/ X1 ^
& S$ }; O( I, Y4 K
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
& ?! ~8 C1 j' d' f% [0 Z$ ~$ ~
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*: g! I0 M; t; i
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*$ x* F$ m W M _4 C3 D+ u
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
$ r( Q' y2 {1 N+ m; I$ ?# I' Q `
Iua122 - \" }' v d( s4 @
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
$ E$ }$ X* O( t5 {- v
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
; P5 X( U. W x+ D/ H. C+ \* ~) Y
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
3 H; `# i$ S$ H' W' p5 k
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
h0 N0 N5 {: _2 ?
$ |0 ]0 G) ^+ Y& D) Y. N+ z# |* \
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*& ?1 c2 f& i# f
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*% B7 x5 I7 R# v
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*% K% U& H- C9 e. I
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
! s\" O& u3 I) c) u+ v
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
, ?* y v- d8 P. D8 p& y
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
6 l2 e7 B7 E3 F! Y7 S8 n
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
- U c' f! y\" L' u$ G\" j9 R: \
w4^2/u3^2*Kwa143*IIua133);
/ ?: z- S2 V5 e3 ?) @
& c2 d! i+ w! e/ I$ J# \
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
, u3 I! j\" t$ ?# Z# k4 Z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
]) H! Q, H0 |& M3 d\" N9 h
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143* N# u& n6 F\" h& ^- I2 o8 h
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
: F8 Q3 K/ }# v. O9 Y' a# Q
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 3 I8 Z) b3 A& `: I0 ~
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
! G1 @+ t5 h2 D& @/ `! j/ S5 h
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - % d\" A$ ~% M* e- S; Q; [
w4^2/u3^2*Kwa143*IIua133);1 s7 T0 J; b9 v6 V0 Q8 r/ f+ b
3 Q f, O% P# j) C( l+ Z
M3 = (betacl*Kwa143*
4 Y# k- q9 y3 ~5 k$ \. ~
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
8 ?$ y0 [* n8 @' L; z+ @; }
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*\" {$ s8 v$ Z/ `% v/ T
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 8 Z+ R+ K! p0 Q. R& H# w
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*' h+ c: O3 P& t+ j' x
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - , r4 r9 ]; P6 O* B0 i
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132** E5 @' E3 H9 A2 j- y
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
# q9 A. c! p. |: O
w4^2/u3^2*Kwa143*IIua133);
& i( e6 |# M5 }; t) @% T& b$ N
- j% d( W% `% H! z9 v
M4 = (betacl*Kwa143*1 Q) W) \6 [\" m* F\" d8 p1 b( w$ `7 Z
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 7 P3 S\" k$ }. d$ F K
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
. y i5 E4 M, i& D* ~
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - , Q$ V' F% n0 Y5 a
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
: l: T0 P3 z* J( v$ M* c8 M# A& s4 T
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
9 m% @: Q' d& v\" y9 n5 A
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*, c! A1 e& K) O
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - X5 I2 }) f5 A9 A\" D9 V' T
w4^2/u3^2*Kwa143*IIua133);
, F; d5 \8 c- j5 ~! g9 j
\" q& o! I- W+ F5 x\" R$ t1 C8 s
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;- p\" N7 ]7 Y8 b- v- J8 O% R% Q
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;- x+ L9 y$ |( e
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
4 m( [+ u) |# ?7 x6 b6 j
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
1 ^5 ~1 z. A+ n7 \% ~0 S: b
3 }3 @$ Q1 ?! F
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;; U2 n, ~; a8 o! K* E0 \8 u
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
$ h1 O* i [ u& A1 X
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;: C' R1 O' O: K- c
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;; ^9 {6 e0 t7 k! o; C
( p( H# _, c5 p7 z! g0 G
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
0 @$ z0 |4 i* R1 [, v# X+ O, B% y
V1*M4);
9 Q- W2 E0 c% K' T! | @
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
4 `% q$ a+ U+ W$ P; P
V2*M2);
# }4 S9 E6 L( g3 \% q
P) X, j+ I$ o& i% h' v7 v
x = xicl1 - xicl2;
7 B8 q/ V% R# B, k& h: v5 O; R, q
x1 = Re[x];
3 z) u& A\" f& n6 }- c
x2 = Im[x];
5 k: n4 Y. }: c
3 R) E; h w3 \5 I
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
0 u4 l5 e6 _! h! o+ P) R
]
\" _* G4 f6 I8 y6 R3 ~
2 O+ R/ V0 X) Q; @

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