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标题: 请问FindRoot外面套一个For循环的问题 [打印本页]
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
  1. lamda = 1.55 10^-6;: I4 R% s3 \6 x2 j% A' R4 B
  2. k0 = 2*Pi/lamda;
    4 G) B2 `" l- U' \" I4 _
  3. n1 = 1.4677;(*纤芯折射率*)/ X( ~' O! G% ~4 q9 g; h
  4. n2 = 1.4628;(*包层折射率*)$ k; P$ y. b  q) `3 @1 M* k
  5. n3 = 0.469 + 9.32*I;(*银折射率*)/ ]( l6 ~* j, |7 \- K* a
  6. a1 = 4.1 10^-6;(*纤芯半径*)' e4 I: k; e4 A2 m' A
  7. a2 = 62.5 10^-6;(*包层半径*)
    4 `5 P8 t" Y5 u, r4 S" r+ j  Z4 u
  8. d = 40 10^-9;(*金属厚度*)
    # z. J$ h) z% a+ ~( g
  9. a3 = a2 + d;' d2 g4 c2 c2 o8 o( q
  10. mu = Pi*4 10^-7;(*真空磁导率*)& E* P  m  z& k/ ~1 L; h- U
  11. epsi0 = 8.85 10^-12;(*介电常数*)
    : n, k+ f6 k% w

  12. $ R7 b7 m6 C0 k5 h  u, a
  13. n4 = 1.330;$ C, v! p' _! r) B5 ?

  14. 2 t. Y  D1 Z6 V6 K& x8 k, M: Y
  15. neffcl = neffclre + neffclim*I;. T0 O% e- T" X, w, p. ~

  16. * m( I+ ~7 g; k0 D
  17. betacl = k0*neffcl;) f4 b# k2 k  S4 g
  18. omega = 2*Pi*299792458/lamda;: a# a/ h; _+ s+ p

  19. ' Y6 R+ j4 @3 J! A
  20. epsi1 = n1^2*epsi0;
    3 H" n& A: N: c4 T7 M
  21. epsi2 = n2^2*epsi0;7 ^" b% T: D2 W8 n5 E3 ~1 V
  22. epsi3 = n3^2*epsi0;
    5 d$ P" J4 A2 \% Z# c4 A; M9 i, o
  23. epsi4 = n4^2*epsi0;; x% T4 v- e4 t
  24.   }! m+ Y' c+ o
  25. u1 = k0*Sqrt[neffcl^2 - n1^2];' i+ S& J4 H8 z0 g" y& |+ b+ Y
  26. u2 = k0*Sqrt[neffcl^2 - n2^2];' D- ~6 @, ?& [, k9 p- b
  27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    7 G" b+ W' {  [
  28. w4 = k0*Sqrt[neffcl^2 - n4^2];
    9 w- l+ H9 Q/ R5 b, N4 {, Y
  29. . j8 [  B1 {$ P( ]! f. A2 N
  30. Iua111 = BesselI[1, u1*a1];
    & L, f& o' [. w
  31. Iua121 = BesselI[1, u2*a1];) u; L4 s, _6 O9 l/ ~
  32. Iua122 = BesselI[1, u2*a2];) C0 I' p* m) u6 |
  33. Iua132 = BesselI[1, u3*a2];1 N0 v3 K) u( ^: d' ~
  34. Iua133 = BesselI[1, u3*a3];
    : M, F3 G; Q2 u5 v4 K1 \( g
  35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;0 c" L( i9 Y  O6 f6 `4 G
  36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
    . T" F5 M; z' P5 w9 c) G
  37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;& E. o  b2 A9 s3 Z1 z
  38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
    & u: |0 g& X' ^5 B" ~3 Y+ Z
  39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
    ' j# ?2 s2 ~3 J1 u1 a5 Q3 {; w
  40. 0 z, T2 a! o5 k9 S% a6 B* @
  41. Kua121 = BesselK [1, u2*a1];  _9 S7 t# [% q6 @: b) W
  42. Kua122 = BesselK [1, u2*a2];
    5 n% S$ c7 S8 H
  43. Kua132 = BesselK [1, u3*a2];; ]3 Q& V9 h, J& P+ L* u* P
  44. Kua133 = BesselK [1, u3*a3];2 t1 M3 d+ G& O- B. d! Q
  45. Kwa143 = BesselK [1, w4*a3];. _+ W- J9 J: N0 I9 G% J! J' }
  46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
    - V/ ^& @( U: M- @; ~6 c# P& a0 V
  47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;
      a+ }) r4 h) r: A
  48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
    ; w8 n+ N" N! b9 }4 F9 B
  49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    7 j. o4 M" g3 {1 I
  50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
    ) Z/ _" J/ |9 I# c

  51. " l' _5 x! Q' W* V1 K$ ?
  52. H1 = (betacl*Kwa143*  I0 l! S% p9 O# B( n
  53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*! O# ?% s  R% v& Q9 n$ C4 J0 K
  54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*  n, a. e7 w7 l
  55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*1 H# x/ Q2 n2 Y
  56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*2 O* e  d- @  o. o+ J% ~( s2 N/ e
  57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*  J2 w# C4 g1 |: n. R
  58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    8 w7 A' }; O+ ~
  59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    ; |( E. h% o& W( v( T. w  ^3 y& z2 ]
  60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);4 A5 [! M. J. I3 K. s

  61. 8 H; v& M2 B) h6 V8 b
  62. H2 = (betacl*Kwa143*
    % O0 }8 \! _7 b" P4 D/ O
  63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*0 x/ a, a0 x) I: J4 U
  64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
    2 o0 e, J2 R6 ~; T3 a6 d) v- d
  65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    ! E# U& q0 T' I# F! G
  66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*: i. W6 W; ^' N0 {; \
  67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*4 O$ E9 T. @* }. p1 i
  68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    + r1 q  D& D" J9 P) C0 _: `
  69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    9 A2 x8 t" r) w$ D- I2 \# o
  70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    % h. f7 d; I- e$ y2 z
  71.   k: t% {# U" `! u& d( f5 Q
  72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    * E5 a, Y- u. l
  73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*# j5 k  W5 B. d
  74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*4 W. A0 v1 ~0 I! h
  75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*8 i, X6 V8 w9 K) }1 u6 H! l0 m
  76.        Kua122 -
    # I7 Y; h5 b! T( u4 p3 W
  77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -   ~, C4 F% Z, X
  78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    ' b4 x! R3 N/ I
  79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    ' D( O3 I( O4 {9 s' ]0 n# V
  80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    4 A! o7 l( R, B1 t& d
  81. # x" D! t+ I- p- g- N/ o; R
  82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*, [0 i% B, q" Z+ x. k
  83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*( @- m# x$ c+ T8 i( _
  84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    ' E+ Q# L; t, D6 f
  85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*! d' M: K! a& W. B  e( M
  86.        Iua122 -
    # D9 T' E/ l1 v
  87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    % D' [. Y9 V2 D2 g- l
  88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    7 f8 {' g* U  _. [( ~  o
  89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    # {2 k$ z. ]6 b; `
  90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);& C3 c1 N- ?9 e! p3 E

  91. ( A* e0 T# ~6 ~$ P* W
  92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    3 W# @4 J+ B+ E$ }
  93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    . B, f9 ]6 ?# ~
  94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*( R& H* _( c# r
  95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    0 U( D4 u$ i8 e- \" N* E1 r
  96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - % V% n0 P! x) R: y' T
  97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - " q4 {; i4 P. k
  98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    3 U. a( X% o" e' t) B
  99.       w4^2/u3^2*Kwa143*IIua133);- T4 |# s2 l0 j
  100. % e. D, j" ?1 @7 n
  101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*/ ~, S7 {% Y, d, [- i7 Z
  102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    & i$ K* ]: W$ w, e
  103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
    . R5 f+ B0 D* Y2 @
  104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
    9 M+ @0 k3 v! q$ i& N* a
  105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - + a% G/ [2 l. U6 l; v$ y- c" e7 q
  106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - * ]1 D; Y8 s9 n
  107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - & Z- f& C' G' v, f) p3 V
  108.       w4^2/u3^2*Kwa143*IIua133);
    . a: z! n; C9 F* M. c8 w4 V) D

  109. 0 G2 S5 b/ H/ G# Y5 B
  110. M3 = (betacl*Kwa143*
    5 X7 z' F: S6 Q( F6 X
  111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
    6 W- ~7 F: X0 g. o* d, c$ A
  112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
      Y/ y, s+ L2 c, P. J4 T" K8 U! d
  113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
    , [9 P; Q+ _. W
  114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
    8 o$ Q& V, z. {! a" b. Z
  115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - ! F5 O! A9 B9 X" g4 `+ c0 S
  116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
    4 S2 w# @  b* n" O6 D7 D
  117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    & ]  C" K1 n" r
  118.       w4^2/u3^2*Kwa143*IIua133);; b: \1 c7 e( k
  119. 6 ^1 Y- h+ q# P8 @: m
  120. M4 = (betacl*Kwa143*  ?& [6 W7 M% v' g# b
  121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
    # @" h! d: ^0 e
  122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
    7 R# {/ s' L5 \' b3 c, m; g' A
  123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
    7 r5 }- o  d% j8 k+ N) ^
  124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*- U! B, n, f, B
  125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
    ! F6 X( a' O6 s
  126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*. Y5 J4 K% `2 ]% D+ q& }0 N. w5 y
  127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    1 ~) ?- {( Q) r5 p+ e" s
  128.       w4^2/u3^2*Kwa143*IIua133);# B" m1 r' T# q; e

  129. $ ^+ l! @' d; N
  130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
    & J% I; p* j+ f; X) c
  131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;7 H; m0 R4 s: r8 d- w: @4 t
  132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
    5 Y: b5 Y6 X# x& P) Z$ M0 I
  133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
    ) Q! K! J1 d* H9 x6 B

  134. ' i: q, _& i' l: t
  135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;  x  [2 t' ]( S7 u+ d5 J, b
  136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
    ; x/ q$ P$ v; ]( u* d7 o
  137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;2 L+ b  g4 k7 R' x" s- g6 t$ q9 L6 j
  138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
    " R& f3 o3 b. o# F" h
  139. - k7 h6 E2 X* W& y9 ~2 V
  140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + 8 j2 S6 W. y7 B* F- _
  141.      V1*M4);! }4 U5 h  u' c- M% j& j% Q
  142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + / o* {0 ?8 L/ u8 n& ]8 K: F
  143.      V2*M2);
    3 g) [( V: F$ s: k% L3 x: D& R

  144. 7 S. ?8 l- p! ]
  145. x = xicl1 - xicl2;
    2 A+ a2 e0 A+ R7 z1 S" u) Z8 g
  146. x1 = Re[x];
    0 i/ N1 I1 j% R
  147. x2 = Im[x];/ d+ a6 M3 K1 U  h4 g
  148. ) R3 G0 [; v, g
  149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];$ k* E; t% p( N; k  t/ R
  150. ]
    - z6 ]; G, }. Z1 K9 V$ b

  151. ! Y5 |7 I; Y# V6 h4 H9 i. M
复制代码
代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}5 V) _' k, w0 W3 `' f
但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];) C5 d; A1 _- `4 W3 P6 d/ S
换成
6 v# O: K) I5 |* A8 pFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
  h8 N4 P3 {! M; j6 W) d! T FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];% w: D. _5 w: v, a" Q& N$ i
], ^% t$ _) s: U+ G2 `, g% r
就会出现% @& k/ N7 K7 n9 j- I  J
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.2 |. K, G) E& a4 q% Y4 {0 ?; r
! t# J  |& U! E
请问是怎么回事?' k9 W& T& E3 `, }3 o, W
' V, e1 g$ {9 x




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