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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;
    $ s, C2 X1 L  O! D
  2. k0 = 2*Pi/lamda;: I  |5 `0 p& B0 \% b. n
  3. n1 = 1.4677;(*纤芯折射率*)
    ; ^5 T: x( V% r8 [6 ^6 J9 {
  4. n2 = 1.4628;(*包层折射率*)
    6 L; g+ b1 D" j0 K/ v1 }# N
  5. n3 = 0.469 + 9.32*I;(*银折射率*), g9 |3 ~5 D6 V& S1 N! b
  6. a1 = 4.1 10^-6;(*纤芯半径*)  [( {6 P7 L/ Y+ u' I, L
  7. a2 = 62.5 10^-6;(*包层半径*)
    1 J. s5 L; k; x4 K: O
  8. d = 40 10^-9;(*金属厚度*)
    ) C6 [9 N6 X! l2 ]
  9. a3 = a2 + d;, D6 y0 @( V4 R5 P5 D1 t& d: }
  10. mu = Pi*4 10^-7;(*真空磁导率*)
    5 @: |$ Z% `% d0 _  z- D
  11. epsi0 = 8.85 10^-12;(*介电常数*)' [- ], w5 |5 K. n3 o
  12. 8 J9 W6 t% Z: B/ C
  13. n4 = 1.330;4 J( v& ~$ A! z2 f* [4 x

  14. 4 M; H" L9 N" P4 E. |, A
  15. neffcl = neffclre + neffclim*I;
    ; A3 q8 W. F" m
  16. * |; c+ K' V% P# L
  17. betacl = k0*neffcl;
    & n$ M1 H' f) l/ l5 {7 m- _' ^
  18. omega = 2*Pi*299792458/lamda;& `) t* B0 @/ ^4 w( W
  19. 2 H: n* p  X2 ], M( v6 ^
  20. epsi1 = n1^2*epsi0;
    / C& t. D& K+ A4 R2 i. T
  21. epsi2 = n2^2*epsi0;+ w3 o9 e7 l4 _  u% b
  22. epsi3 = n3^2*epsi0;5 x  X' M5 E) S  D( S
  23. epsi4 = n4^2*epsi0;7 x7 q. ^2 p, K2 X; ^
  24. * }' _( L( B+ I; i3 n4 e7 i$ c% x9 }/ }
  25. u1 = k0*Sqrt[neffcl^2 - n1^2];4 ~3 w6 L2 d* L: o. M
  26. u2 = k0*Sqrt[neffcl^2 - n2^2];6 o* U( A% i$ \2 Q
  27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    7 g' s# H& O. S0 E6 r  T
  28. w4 = k0*Sqrt[neffcl^2 - n4^2];' S: E6 S0 t7 F' Q' O) H( o

  29. 3 z& D3 W1 _" d$ p7 L9 |; \
  30. Iua111 = BesselI[1, u1*a1];
    / W7 Z4 f) b) M1 @+ u5 d
  31. Iua121 = BesselI[1, u2*a1];
    6 n; r& y4 ?. {" G) Q
  32. Iua122 = BesselI[1, u2*a2];
    + S; a  j, p4 Q
  33. Iua132 = BesselI[1, u3*a2];
    " M" W% _, ~* p0 [5 y
  34. Iua133 = BesselI[1, u3*a3];
    . L! Z3 P" ?' C6 l
  35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
    ; l5 b7 W& O. [: W
  36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
    ; w% |8 c0 V& K* {
  37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;# u! q+ }- D* H8 @) ?
  38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;/ w8 c. i$ _9 @* F$ ^0 x: V9 m
  39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
    + U5 K4 c( I5 w0 U5 ?  Y/ _" g

  40. 3 v- V8 L6 d0 I/ ?7 _0 K( n
  41. Kua121 = BesselK [1, u2*a1];
    3 c# ?% v7 F1 \
  42. Kua122 = BesselK [1, u2*a2];
    " b: d. {" z  l) V( C& J% q) S
  43. Kua132 = BesselK [1, u3*a2];
    / ~* A( P$ [1 k, j5 B: h7 v1 |
  44. Kua133 = BesselK [1, u3*a3];* t5 Q  G$ \+ n: R+ ~! b
  45. Kwa143 = BesselK [1, w4*a3];0 d" k/ n, R, @6 q+ h8 `
  46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;, O+ [) m7 ^6 N6 ~3 m7 H
  47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;) c  N5 s8 ^4 n# e% W$ e
  48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
    7 E- x) N* f& v1 n) C
  49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;( d6 x/ z" W% E
  50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;; D! a  m2 Z# I

  51. ' N0 K( O5 F/ g: H
  52. H1 = (betacl*Kwa143*
    % F* `% O2 l! a  `& E. N4 V- p5 H
  53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*& U. \3 N: D; H2 h& i  G7 X/ w
  54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*' ^3 N$ S4 Z, X4 \5 s8 u+ @
  55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*+ F0 {/ v5 e4 }4 P, W2 V
  56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*. K. a+ s& W  U( N
  57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    , ~6 C5 O0 e, m# h
  58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*/ P2 e. y: g5 ]1 c9 I$ ^
  59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*, U( p- r- A7 j( T& G( g
  60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    7 ^7 G  I4 i5 J' o% J

  61. ! k/ G, w2 |2 g7 p+ i
  62. H2 = (betacl*Kwa143*
    - P2 I! f+ N5 u7 P+ A% V- o
  63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
    5 y) E, b/ _& G) r4 t* c4 y
  64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
    ' G2 v* A7 E  @0 j/ ~& m
  65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*. A! j. i, b. Y2 J9 f; P8 _
  66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
    7 [& h3 c3 k0 ~( R9 t
  67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    - j# o) F" X& G# l* U& e3 b7 C
  68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    . q6 }/ s  \2 N% D5 B
  69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    2 j$ ?% z( Z7 V: A0 a+ P1 ]' Q
  70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    0 Z8 d$ c" u2 A; h+ I

  71. + h# C1 W/ x3 O- E5 i, Z
  72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*& G) ^" W/ c2 [7 D
  73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    # x: R4 o/ \$ Q8 o. o
  74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    ! {( P+ L- c% w1 G% H% O" G7 m
  75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*3 x' s$ t: h. _' e- G1 k" }% @
  76.        Kua122 -
    $ X( d% N3 l! Z; t' h
  77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - ( h& W+ b' c8 |& x
  78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - 5 \; x/ X% e( G0 B1 F  Y5 A
  79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
      y4 c" Q9 r% Q- l
  80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    % E4 Q# k6 ^8 c& C8 V6 k' `6 z" `
  81. 9 f1 N# j% s: o; ]! {7 W) d/ X
  82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    5 w1 o) @9 t2 _% {
  83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    ) \) G8 j1 q/ |3 a0 C( X3 J
  84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*& x  g9 I- N: s  W
  85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132** w8 i( B: A9 z; Y- l
  86.        Iua122 -
    1 Q6 a% ^" I, j+ A
  87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -   v, X7 G: o' H, B% B, y
  88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 5 W' v2 b9 q0 q/ d! O6 j) B5 x
  89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - 2 L' s3 c# L$ M! S
  90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);- p. I+ x3 z+ L2 n: o$ E; g% ^4 F

  91. ( T+ ?& l7 l# J) o
  92. 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
  93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    2 E1 o' `  f" ~7 b1 x7 r2 a( c2 ?" k
  94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*  R3 g/ z. {% }7 n- D
  95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -  T) \6 \0 S! w; ~
  96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 4 S# E# N" J1 E! w4 e6 }
  97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - - s3 ?& \  T; T6 O) H1 i0 Q1 w/ s2 \" w
  98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    4 V2 p' W9 R$ z, m3 a- n9 [. s9 L
  99.       w4^2/u3^2*Kwa143*IIua133);4 g6 F# C6 u7 \7 l4 r$ {0 X

  100. * z% B1 A, i5 |) \
  101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*! I2 ]1 Z5 B6 \( a' N* ?6 G
  102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    9 ^7 D, F: _# m
  103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*- }- N- K" T, k
  104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
    4 {" @8 a4 r, D& H8 N- l
  105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    3 Z# B5 S6 ?2 _6 P; Y
  106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - " x3 }% _1 D' [$ d
  107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    / v% v& I7 v) h; c
  108.       w4^2/u3^2*Kwa143*IIua133);
    0 Z( n6 g1 \. m  U/ L% {

  109. ( [6 w: v  R0 a- i) X) m1 E
  110. M3 = (betacl*Kwa143*
    5 Z/ x9 V3 {* d4 g. x
  111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
    " l9 T' x* a" f/ Y/ F
  112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
    - j( y" N# m( ^/ }& u  Q/ K$ x
  113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
    . W' v4 k( _' z( ?. J! s4 O
  114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*! [& z1 O4 B7 v7 J
  115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
    % ?+ A" I1 ?8 `! J& [( |' Q7 o4 P
  116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*# N6 S  y( |" _5 k' F; _9 I% `# t2 M
  117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    ( b; O/ U3 Z- D7 g4 C; Z9 S
  118.       w4^2/u3^2*Kwa143*IIua133);
    4 l) ]* y0 r# Z/ v* j+ i) L9 p

  119. + _. k# t4 Q) `- ^8 Q1 S
  120. M4 = (betacl*Kwa143*6 f1 y( K* k9 G! W" r
  121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
    ( F/ D2 C( {# s  u9 E1 R6 a
  122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*$ r& Z* b& H, I+ T% x% b' g& _
  123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - 7 f1 f8 A6 N, g4 O' B( b3 Q
  124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
    7 I1 H  h- y# q6 Y
  125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
    * W% p9 c! G$ Y7 U0 {% i
  126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*0 X; {" _  O/ O4 e0 p
  127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    ( i( E/ H1 y6 }! i
  128.       w4^2/u3^2*Kwa143*IIua133);+ @7 N+ P/ |1 p
  129. " u1 k, S7 S2 k6 W. [: S% \
  130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
    2 b1 Z6 U- Q, z3 A- w
  131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;5 y# n5 y: ~+ z
  132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
    * b; f; j9 D7 M1 O
  133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;6 V/ e. i, B4 ^' u& Y4 `

  134. / m" C( W9 h/ N& O
  135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;. B+ @$ `: M0 c! n! j0 H
  136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
    3 z! Y! T6 P& P1 m4 N
  137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;* _( T. O: x( j
  138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;6 x3 @; r; V; ?" V5 P  ^
  139. & w8 H/ k/ W3 l) P
  140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
    , Y) l5 d; f  M- E
  141.      V1*M4);
    6 E4 U, d& z0 @4 m2 `
  142. 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
  143.      V2*M2);2 p; V6 R* j  {' D, z( G- R

  144. 1 [% O0 g, J3 i) `
  145. x = xicl1 - xicl2;
    # X6 u+ u9 u4 u$ J9 j
  146. x1 = Re[x];5 e( J% I' f, l: {; o4 U8 _
  147. x2 = Im[x];
    * N; j* `5 b% |4 Z5 n& \. X
  148. 2 {7 B( ]! K( G% ^0 G2 w6 u1 y& ^
  149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];7 N; L3 L/ q5 b& j
  150. ]
    * N) v1 g) d1 V) X, E

  151. + 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 yFindRoot::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.
) _4 J* X% x* o/ r
6 Z0 {: y9 Y/ L" T4 P: }请问是怎么回事?; @: K( C0 ?" V/ a3 @9 i/ f9 _/ K
: T" ?% W& a+ w/ A  f1 B2 L5 F




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