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;
: P/ d. t! e% l9 b; V+ e1 L
k0 = 2*Pi/lamda;; M- H7 g; v; A w
n1 = 1.4677;(*纤芯折射率*)
- G) s- \! I& P
n2 = 1.4628;(*包层折射率*)
/ B8 y; u, `/ L$ ~5 Q
n3 = 0.469 + 9.32*I;(*银折射率*)\" R6 \* H$ R5 M1 z; _) R( W
a1 = 4.1 10^-6;(*纤芯半径*); W# U/ O5 m6 F) H% s: `
a2 = 62.5 10^-6;(*包层半径*)% H; f3 {' B/ X5 D+ x9 a. g6 L
d = 40 10^-9;(*金属厚度*)
3 n. D5 G7 M2 S7 `! W d5 @+ I
a3 = a2 + d;
4 J& \! Z, d5 O X: C
mu = Pi*4 10^-7;(*真空磁导率*)
6 I( U5 b' u! C- J
epsi0 = 8.85 10^-12;(*介电常数*)\" f\" x2 L/ {3 F4 R9 S. \
! r5 I+ U' z) W- V- L0 k; l/ s
n4 = 1.330;, X& Q+ N, B* G
- q& D5 c; e5 h6 z+ f
neffcl = neffclre + neffclim*I;\" H6 I9 K4 p/ z' i3 g- X# O+ ^ v7 j
. O' C6 k; b* I9 I
betacl = k0*neffcl;7 U4 g# l, E7 }1 r- n; w5 a
omega = 2*Pi*299792458/lamda;! ?+ m/ J; |! W\" `/ g( X& v; F
$ M9 q% ]. Y2 g0 r9 F5 C& W# R
epsi1 = n1^2*epsi0;
7 T9 B E% l, z! R; U# Y) M
epsi2 = n2^2*epsi0;
! d- @' ?& Z/ q9 q5 I9 R, i
epsi3 = n3^2*epsi0;( r5 l7 X4 l8 b8 |/ @
epsi4 = n4^2*epsi0;1 x' e: p1 w6 e+ c! n. E
- ?9 p8 s: D m1 p# A7 Q6 g; I
u1 = k0*Sqrt[neffcl^2 - n1^2];9 j' i+ K& G3 F% R
u2 = k0*Sqrt[neffcl^2 - n2^2];
& O5 Q. W# n( g2 H
u3 = k0*Sqrt[neffcl^2 - n3^2];\" m3 u7 G% S. A4 o2 I7 a
w4 = k0*Sqrt[neffcl^2 - n4^2];$ L9 h1 z P$ h1 }6 Q
n! f$ D8 w7 H7 i! J% w
Iua111 = BesselI[1, u1*a1];: }+ ~8 S, J' t- D' q
Iua121 = BesselI[1, u2*a1];
8 s9 W; i: \( h' z6 m! [! ~. m
Iua122 = BesselI[1, u2*a2];
. c m0 C v3 d/ |% c
Iua132 = BesselI[1, u3*a2];
. B$ U\" O2 C. X4 y& x0 g
Iua133 = BesselI[1, u3*a3];
$ G+ \+ m8 b! D) M
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
: Y) P) A, ~$ a7 x9 ?$ `
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
) N5 x7 ]$ Q$ ^5 M5 A
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;' G& M: e) e# C- x* h' j$ z- W
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
\" R% P( X1 |( v& y* [
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
. ?: S3 |2 F3 D- D$ ]\" Z
! F3 f6 N1 S5 X
Kua121 = BesselK [1, u2*a1];+ d) K w' V! Y* j0 h2 G/ E
Kua122 = BesselK [1, u2*a2];. ^! {, z/ a* `3 {
Kua132 = BesselK [1, u3*a2];; B4 [: @9 ^5 n1 d
Kua133 = BesselK [1, u3*a3];6 }) ^( D! V. a+ Y
Kwa143 = BesselK [1, w4*a3];1 q/ Q% N, C; s) _3 u\" O# z( `3 b
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
9 i6 f, \1 ^( Z# y: p
KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;; e/ U* V2 M9 M4 [
KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
/ r$ G5 }3 ^4 H/ k
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;/ H% b- B; {8 {6 ^. z
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;4 a W6 Y, i0 E. N3 y$ [8 k' @
, L: m) x8 B( @4 p1 s3 _& ^- J
H1 = (betacl*Kwa143*9 B5 l! K1 k, V% ^1 p; r3 p
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*) `* V% Y) c( t* q7 u; g7 r
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*7 ]2 E4 ~( D& e$ L: {
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
. L1 S( B& Y( n6 x6 Z' g8 e
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*/ b; C$ O# j$ R7 |- r; e7 l
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*1 M- Q+ u\" m! g8 [3 a
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*' P. w c5 ~0 H* n- F* V
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*9 V& ~& e7 \% m h
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);; a2 F# o0 f. V$ j! C0 r
# R5 W ^: `4 x) F' P
H2 = (betacl*Kwa143*& N- }: z B\" l& D
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*) G% d0 O2 I) w- b\" ^
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*+ s\" x4 b2 m: i
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
3 h: X/ | v0 O6 i7 ~; _
Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*2 y0 f0 e$ N# M+ {2 g# B
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*/ `# w/ u3 v( h0 v
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
/ K9 D& N& Z# N6 R
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*, }# h5 U. S* z5 k
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
) `4 T( E& U8 a* D/ U# \3 \: f5 a8 I
' V' d- H( K' d6 Y- l9 }# c3 }* I
H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
; P( {6 L; G) g+ }6 u( D
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
7 m) z0 _9 h8 E
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
\" d% d3 q& L G2 X2 E
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*; f9 h' Z& B) T7 {/ e3 L; x' L3 E
Kua122 -
9 S- b8 ?* N9 }2 Y/ B9 C% K; x
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
- A, B4 |8 [2 e2 n+ ~* \! O
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - % p$ U3 e' @/ y% ]* J W& t; ?
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);. L5 \* @; L5 ~% k; f& p4 @
5 @, \& u7 W) U p1 m/ F- E& b
H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
- _5 X5 k$ Q# B/ ~
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*9 }9 D q4 R0 _9 t/ m* K0 \ z
Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
% v6 R% ]\" n1 T7 Y\" O- ]& P8 f
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*) M+ {8 C# m+ r, J
Iua122 - 7 Y# o9 N3 N( l* i$ E- w0 ?
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - $ c3 J2 n# A, w\" T1 m( A2 n; q
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
% Q& L0 f6 ^/ y; c
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - ( u1 [6 i. X0 L; ~6 _' U
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
, W8 U( q' h4 u0 P& Y, P q
, P% H4 w1 B5 Y: R0 _
M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
- G3 F( O% q/ Q
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
\" H! `2 b6 \+ i7 H0 W; |, Q6 ^: {
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*1 o2 W4 c% n6 e, Z. I4 E
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
( T5 I$ b% j' ]1 q& g# t
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
y! t/ d Z; c* s* H5 _# M
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
$ S% r4 r D8 y& {+ I
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - % ]$ C) _# _2 Z
w4^2/u3^2*Kwa143*IIua133);1 c4 @ j1 ^! }+ s
# X! w% u: Q4 j
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
) i: A0 L: p# K6 ^# s: o- Z
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
4 h( Z$ |; ]6 p7 Y
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*) e& R8 c4 r5 Q9 a. X: H* {! h9 [
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
& L, w/ o: I: I
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
3 F3 D0 f; z: W. ~
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
9 d8 N( E6 E6 @& f7 v
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 0 w7 R: I\" y& D' ~
w4^2/u3^2*Kwa143*IIua133);
+ |: p/ m: j0 j# U, I5 h
; r5 o: f1 R: m+ s
M3 = (betacl*Kwa143*
8 a3 ^* F* n3 m& `' g9 T/ g/ R# I, D
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
) O) L3 [! u: A' t6 p# O6 [
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
3 V* ~, V3 v1 G\" m' k
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
6 ]) ^' k4 E6 m1 ^4 @
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*. e( Y, A2 x$ k7 c8 m0 a! [( m
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 1 d& W# o2 X0 W
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
; y# a1 }8 R/ k- e
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
' ` Q' j5 F% m
w4^2/u3^2*Kwa143*IIua133);+ B! E* u9 b' K; X
6 c3 t B0 b, V8 r
M4 = (betacl*Kwa143*
2 s; n5 j0 Z# k& Z6 c
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - . R# z0 c! D4 i6 Y# f/ |; E5 N: G
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*\" O+ G3 i% @. s: ~7 q& F
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 0 p2 ^& {' y\" p9 M8 i( j5 Z2 u3 D
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
. u; d+ B6 f7 S$ `
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
( i/ X2 H& q1 \7 T\" J; _4 H/ ]& h
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
3 n7 a' _8 [) p( @5 F
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
' G: X: c2 k: V5 ^ p
w4^2/u3^2*Kwa143*IIua133);) B: _1 A( t3 h: n- W
% C1 o$ F5 p6 R. Q7 j+ F
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
+ U' J( E+ k8 ]* {7 e6 Q* H
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
. Z9 J9 _# r T% B
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
; L8 O( C6 R c: c4 N. x/ @( {
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1; X# t8 g% m6 g t0 ]+ @
1 ?3 V' V* G# M8 H& E# ]2 E: m
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
. ~4 a y2 }; Y: Y) v @) d- H1 W
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
' h; e8 Z+ O R2 N
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
: K7 x- W7 \. B
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
3 U) x( @+ ]0 h& y0 B+ C* B5 B
# T) w* @6 r# t4 T+ D. `- P, m
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + + `5 ^% E5 ^& E# R# [; m8 K# D\" F( C7 K
V1*M4);6 Q- Q; P2 |6 X+ O9 u f; ^1 C1 c
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + % n+ [5 Q4 }. a% P0 k% I- M
V2*M2);5 e6 u3 h/ U1 d
! \. O! ]. u) n% |: S9 _
x = xicl1 - xicl2;9 W* X; g* t7 `, R6 U6 I: E
x1 = Re[x];- G }+ Z9 f\" E4 A A
x2 = Im[x];( p$ |1 E- X( [- Y. g% E, q
/ S3 K; Q8 y d9 u/ l; R
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];+ i0 Z1 T8 D. h/ I+ h- G+ |
]6 q( h/ V. y! \2 H5 m C
d' \( m. Y- U

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