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标题:
请问FindRoot外面套一个For循环的问题
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作者:
cxy623157929
时间:
2015-6-2 12:57
标题:
请问FindRoot外面套一个For循环的问题
lamda = 1.55 10^-6;
$ s, C2 X1 L O! D
k0 = 2*Pi/lamda;
: I |5 `0 p& B0 \% b. n
n1 = 1.4677;(*纤芯折射率*)
; ^5 T: x( V% r8 [6 ^6 J9 {
n2 = 1.4628;(*包层折射率*)
6 L; g+ b1 D" j0 K/ v1 }# N
n3 = 0.469 + 9.32*I;(*银折射率*)
, g9 |3 ~5 D6 V& S1 N! b
a1 = 4.1 10^-6;(*纤芯半径*)
[( {6 P7 L/ Y+ u' I, L
a2 = 62.5 10^-6;(*包层半径*)
1 J. s5 L; k; x4 K: O
d = 40 10^-9;(*金属厚度*)
) C6 [9 N6 X! l2 ]
a3 = a2 + d;
, D6 y0 @( V4 R5 P5 D1 t& d: }
mu = Pi*4 10^-7;(*真空磁导率*)
5 @: |$ Z% `% d0 _ z- D
epsi0 = 8.85 10^-12;(*介电常数*)
' [- ], w5 |5 K. n3 o
8 J9 W6 t% Z: B/ C
n4 = 1.330;
4 J( v& ~$ A! z2 f* [4 x
4 M; H" L9 N" P4 E. |, A
neffcl = neffclre + neffclim*I;
; A3 q8 W. F" m
* |; c+ K' V% P# L
betacl = k0*neffcl;
& n$ M1 H' f) l/ l5 {7 m- _' ^
omega = 2*Pi*299792458/lamda;
& `) t* B0 @/ ^4 w( W
2 H: n* p X2 ], M( v6 ^
epsi1 = n1^2*epsi0;
/ C& t. D& K+ A4 R2 i. T
epsi2 = n2^2*epsi0;
+ w3 o9 e7 l4 _ u% b
epsi3 = n3^2*epsi0;
5 x X' M5 E) S D( S
epsi4 = n4^2*epsi0;
7 x7 q. ^2 p, K2 X; ^
* }' _( L( B+ I; i3 n4 e7 i$ c% x9 }/ }
u1 = k0*Sqrt[neffcl^2 - n1^2];
4 ~3 w6 L2 d* L: o. M
u2 = k0*Sqrt[neffcl^2 - n2^2];
6 o* U( A% i$ \2 Q
u3 = k0*Sqrt[neffcl^2 - n3^2];
7 g' s# H& O. S0 E6 r T
w4 = k0*Sqrt[neffcl^2 - n4^2];
' S: E6 S0 t7 F' Q' O) H( o
3 z& D3 W1 _" d$ p7 L9 |; \
Iua111 = BesselI[1, u1*a1];
/ W7 Z4 f) b) M1 @+ u5 d
Iua121 = BesselI[1, u2*a1];
6 n; r& y4 ?. {" G) Q
Iua122 = BesselI[1, u2*a2];
+ S; a j, p4 Q
Iua132 = BesselI[1, u3*a2];
" M" W% _, ~* p0 [5 y
Iua133 = BesselI[1, u3*a3];
. L! Z3 P" ?' C6 l
IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
; l5 b7 W& O. [: W
IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
; w% |8 c0 V& K* {
IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
# u! q+ }- D* H8 @) ?
IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
/ w8 c. i$ _9 @* F$ ^0 x: V9 m
IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
+ U5 K4 c( I5 w0 U5 ? Y/ _" g
3 v- V8 L6 d0 I/ ?7 _0 K( n
Kua121 = BesselK [1, u2*a1];
3 c# ?% v7 F1 \
Kua122 = BesselK [1, u2*a2];
" b: d. {" z l) V( C& J% q) S
Kua132 = BesselK [1, u3*a2];
/ ~* A( P$ [1 k, j5 B: h7 v1 |
Kua133 = BesselK [1, u3*a3];
* t5 Q G$ \+ n: R+ ~! b
Kwa143 = BesselK [1, w4*a3];
0 d" k/ n, R, @6 q+ h8 `
KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
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KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
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KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
7 E- x) N* f& v1 n) C
KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
( d6 x/ z" W% E
KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
; D! a m2 Z# I
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H1 = (betacl*Kwa143*
% F* `% O2 l! a `& E. N4 V- p5 H
Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
& U. \3 N: D; H2 h& i G7 X/ w
Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
' ^3 N$ S4 Z, X4 \5 s8 u+ @
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
+ F0 {/ v5 e4 }4 P, W2 V
Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
. K. a+ s& W U( N
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
, ~6 C5 O0 e, m# h
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
/ P2 e. y: g5 ]1 c9 I$ ^
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
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Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
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H2 = (betacl*Kwa143*
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Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
5 y) E, b/ _& G) r4 t* c4 y
Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
' G2 v* A7 E @0 j/ ~& m
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
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Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
7 [& h3 c3 k0 ~( R9 t
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
- j# o) F" X& G# l* U& e3 b7 C
Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
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Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
2 j$ ?% z( Z7 V: A0 a+ P1 ]' Q
Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
0 Z8 d$ c" u2 A; h+ I
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H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
& G) ^" W/ c2 [7 D
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
# x: R4 o/ \$ Q8 o. o
Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
! {( P+ L- c% w1 G% H% O" G7 m
Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
3 x' s$ t: h. _' e- G1 k" }% @
Kua122 -
$ X( d% N3 l! Z; t' h
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
( h& W+ b' c8 |& x
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
5 \; x/ X% e( G0 B1 F Y5 A
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
y4 c" Q9 r% Q- l
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
% E4 Q# k6 ^8 c& C8 V6 k' `6 z" `
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H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
5 w1 o) @9 t2 _% {
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
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Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
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Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
* w8 i( B: A9 z; Y- l
Iua122 -
1 Q6 a% ^" I, j+ A
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
v, X7 G: o' H, B% B, y
w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
5 W' v2 b9 q0 q/ d! O6 j) B5 x
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
2 L' s3 c# L$ M! S
w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
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M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
/ C, w7 Z# ?2 t5 D$ w. C1 S2 R' Z/ u
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
2 E1 o' ` f" ~7 b1 x7 r2 a( c2 ?" k
Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
R3 g/ z. {% }7 n- D
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
T) \6 \0 S! w; ~
u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
4 S# E# N" J1 E! w4 e6 }
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
- s3 ?& \ T; T6 O) H1 i0 Q1 w/ s2 \" w
u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
4 V2 p' W9 R$ z, m3 a- n9 [. s9 L
w4^2/u3^2*Kwa143*IIua133);
4 g6 F# C6 u7 \7 l4 r$ {0 X
* z% B1 A, i5 |) \
M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
! I2 ]1 Z5 B6 \( a' N* ?6 G
Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
9 ^7 D, F: _# m
Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
- }- N- K" T, k
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
4 {" @8 a4 r, D& H8 N- l
u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
3 Z# B5 S6 ?2 _6 P; Y
w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
" x3 }% _1 D' [$ d
u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
/ v% v& I7 v) h; c
w4^2/u3^2*Kwa143*IIua133);
0 Z( n6 g1 \. m U/ L% {
( [6 w: v R0 a- i) X) m1 E
M3 = (betacl*Kwa143*
5 Z/ x9 V3 {* d4 g. x
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
" l9 T' x* a" f/ Y/ F
u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
- j( y" N# m( ^/ }& u Q/ K$ x
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
. W' v4 k( _' z( ?. J! s4 O
u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
! [& z1 O4 B7 v7 J
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
% ?+ A" I1 ?8 `! J& [( |' Q7 o4 P
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
# N6 S y( |" _5 k' F; _9 I% `# t2 M
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
( b; O/ U3 Z- D7 g4 C; Z9 S
w4^2/u3^2*Kwa143*IIua133);
4 l) ]* y0 r# Z/ v* j+ i) L9 p
+ _. k# t4 Q) `- ^8 Q1 S
M4 = (betacl*Kwa143*
6 f1 y( K* k9 G! W" r
Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
( F/ D2 C( {# s u9 E1 R6 a
u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
$ r& Z* b& H, I+ T% x% b' g& _
Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
7 f1 f8 A6 N, g4 O' B( b3 Q
u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
7 I1 H h- y# q6 Y
Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
* W% p9 c! G$ Y7 U0 {% i
w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
0 X; {" _ O/ O4 e0 p
Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
( i( E/ H1 y6 }! i
w4^2/u3^2*Kwa143*IIua133);
+ @7 N+ P/ |1 p
" u1 k, S7 S2 k6 W. [: S% \
R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
2 b1 Z6 U- Q, z3 A- w
T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
5 y# n5 y: ~+ z
U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
* b; f; j9 D7 M1 O
V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
6 V/ e. i, B4 ^' u& Y4 `
/ m" C( W9 h/ N& O
R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
. B+ @$ `: M0 c! n! j0 H
T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
3 z! Y! T6 P& P1 m4 N
U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
* _( T. O: x( j
V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
6 x3 @; r; V; ?" V5 P ^
& w8 H/ k/ W3 l) P
xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
, Y) l5 d; f M- E
V1*M4);
6 E4 U, d& z0 @4 m2 `
xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
2 T0 n: ^8 T0 N. W; {9 x# g
V2*M2);
2 p; V6 R* j {' D, z( G- R
1 [% O0 g, J3 i) `
x = xicl1 - xicl2;
# X6 u+ u9 u4 u$ J9 j
x1 = Re[x];
5 e( J% I' f, l: {; o4 U8 _
x2 = Im[x];
* N; j* `5 b% |4 Z5 n& \. X
2 {7 B( ]! K( G% ^0 G2 w6 u1 y& ^
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
7 N; L3 L/ q5 b& j
]
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+ L( U8 `$ ?& M6 m6 n2 {. k2 F
复制代码
代码如上,结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
8 p' {2 u! `$ j5 ~) u9 I
但我把
FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
- z$ x0 _" F! ~) i# @* w4 H
换成
+ \0 M0 N. t4 _
For[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
6 R5 G2 |3 i- p# X, ]5 q+ \5 ?6 `) W
FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];
% E# X, R, `$ P/ Q3 X
]
% C! n G. ~% P0 m8 @" [/ w# c$ \
就会出现
) }3 V- O8 s$ |8 B6 X; a4 y
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.
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请问是怎么回事?
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