数学建模社区-数学中国

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;' @. q# c: D' t- m# g
  2. k0 = 2*Pi/lamda;
    5 q: p7 w0 z. X# R5 b
  3. n1 = 1.4677;(*纤芯折射率*)
    6 h; k% f* J# U8 w
  4. n2 = 1.4628;(*包层折射率*)0 a3 M: {& E0 |8 o
  5. n3 = 0.469 + 9.32*I;(*银折射率*)) g4 l+ I. Q7 ~; V8 D- `: I
  6. a1 = 4.1 10^-6;(*纤芯半径*)* i1 p1 B* d5 W9 h8 j
  7. a2 = 62.5 10^-6;(*包层半径*)
    9 m' O. H4 n9 M
  8. d = 40 10^-9;(*金属厚度*)
    " \% E" Y: f. b/ k
  9. a3 = a2 + d;
    6 L! ^' d6 ^3 N( Y
  10. mu = Pi*4 10^-7;(*真空磁导率*)
      t0 m  |2 d/ f9 Y/ |+ Y6 V4 i
  11. epsi0 = 8.85 10^-12;(*介电常数*): y% x5 A* P6 C" k" j0 N
  12. ( N7 o) F9 r: H1 Y, k; W
  13. n4 = 1.330;
    & D2 Q$ v  P3 R

  14. * u  x$ E+ f! ]" F2 f$ L2 ]
  15. neffcl = neffclre + neffclim*I;
    ! _9 M8 K8 Z& {% S# k; p

  16. , ^, ?/ Y# K; g2 L$ v8 s, S
  17. betacl = k0*neffcl;
    . i1 Y- G& h' j, j! m
  18. omega = 2*Pi*299792458/lamda;/ V1 @% z' n8 Q4 W

  19. 0 m) X. y0 t; y: m" \
  20. epsi1 = n1^2*epsi0;
    3 i, {% ^0 R! m/ A3 h
  21. epsi2 = n2^2*epsi0;
    0 w# y# Z' O* f! A
  22. epsi3 = n3^2*epsi0;0 |1 u* w1 k( H9 X
  23. epsi4 = n4^2*epsi0;" B% t" e- m1 H' y, {8 T* ~1 j

  24. ) y- \) n# p+ m9 D" V- n' G% |
  25. u1 = k0*Sqrt[neffcl^2 - n1^2];+ d# x) G6 q' @% I( {# @
  26. u2 = k0*Sqrt[neffcl^2 - n2^2];
    ; x; }2 N7 E3 Z9 w) W9 c1 \
  27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    1 ^/ E4 ?0 d( U5 |. T' B/ H& E
  28. w4 = k0*Sqrt[neffcl^2 - n4^2];$ h( u9 v$ i7 f3 y8 H# C

  29. ' o7 O0 M/ d' B+ Y- P1 W; A
  30. Iua111 = BesselI[1, u1*a1];
    . V: ]9 f& ^; @& k% o
  31. Iua121 = BesselI[1, u2*a1];0 d, d. g; ]. G- c: F
  32. Iua122 = BesselI[1, u2*a2];' u" b1 J( |& _8 Y5 O; T7 l
  33. Iua132 = BesselI[1, u3*a2];! V3 j" D/ U1 N4 i0 v
  34. Iua133 = BesselI[1, u3*a3];/ ]; w8 B2 t- |
  35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;. h! N2 A: H4 _8 i4 S& J% f
  36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;% C9 H: x' G5 _0 Q
  37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    $ A: H$ W( s, `  G
  38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;
    ! y; k/ T. F6 }
  39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
    + Z. \3 e) r# D( y2 [7 R. @* \
  40. 5 P+ ^* f( O( h2 l1 ]
  41. Kua121 = BesselK [1, u2*a1];
    . c" m( E) P1 g' f# h8 h
  42. Kua122 = BesselK [1, u2*a2];
    , `/ A3 Z$ I5 e# i' Q* S
  43. Kua132 = BesselK [1, u3*a2];
    5 q; g3 z! E# D. j7 y2 t$ N
  44. Kua133 = BesselK [1, u3*a3];
    . N& J& |. p# n% A, b, q
  45. Kwa143 = BesselK [1, w4*a3];
    + y! D6 X' |2 g( h3 F6 T. S( I# {
  46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
    0 h7 }* |7 z$ p+ M9 r3 z
  47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;0 Z  [% }2 u& A9 z: }0 B: L
  48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
    $ t. p" f: _9 t) h
  49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;7 r- @& K9 ]% z2 L+ s
  50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;3 q- [0 G# }, ]8 N, p7 U" g4 A

  51. " X6 y$ ]1 a# l. |+ ^
  52. H1 = (betacl*Kwa143*
    + y  f% N3 l. E) `
  53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
    ( C& b: w" y# x( W
  54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
    9 l; O3 q  G: G/ ?% |3 X) @
  55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    4 G/ {5 a# t  N
  56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*
      b) g9 q7 y/ B
  57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    $ a5 i: x/ N- B
  58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    % R$ G8 m* f( p8 U3 ]
  59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*% Z6 h- \. [' Q/ i
  60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);) h* H5 I' u& O" O

  61. . L) [% b, e; i3 D
  62. H2 = (betacl*Kwa143*
    5 {* S# S: h" ^* P0 L% D
  63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*& D/ t) V# ^' H# ?
  64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*8 L' O1 ]8 R$ P2 l9 A, q
  65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*) o4 U% B" y; b& h1 y; A$ H
  66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*& u* G$ f$ G+ x
  67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    # a7 ^$ K: o5 J
  68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    * h% T& c3 l. \, ^! n! G7 }
  69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    + C# k+ q2 j+ _7 I3 h# t
  70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    " R9 ]" l! D; n" I+ {# v
  71. 8 b: O7 I9 e" R( G9 S3 K
  72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*# v) v" i& s! _
  73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*/ O2 ?* y% M% R( l
  74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*9 V9 I. y, W5 Y3 c# g; Z; H8 @) c
  75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    ' r; i2 p& I1 T' j  x" e! G! I  d
  76.        Kua122 -
    1 t) X5 I$ {+ x  i
  77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    # v4 ]: N; d: P7 Q' @' L# _/ U
  78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - . \" N  I4 S; @( _7 V4 J( F
  79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 6 x) j* K0 g7 @$ }0 o& _
  80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    ' D% i, b6 a: j5 d9 h

  81. - R; m3 T$ n& n& G+ Z7 Y# |1 _+ Y
  82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    " i7 R, F- w5 `: w$ f; m
  83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*, {  G  p( T3 G' k
  84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    6 O( h2 C( b$ ?) v
  85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    . S9 J- M4 W6 R- S9 A8 Y4 K# N
  86.        Iua122 - 7 ~. k4 f- r" p( U2 D
  87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - - v1 f* I& Y* g; F' \( U4 i4 s9 a: j
  88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    * W6 M, k% p5 Y* [4 t; s7 _5 ]
  89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    9 ]1 S7 j7 ~* o+ {' S
  90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    # D. u; r+ O6 X/ j+ J2 I; H

  91. & h& b9 y% A! c; }. o) R& l
  92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl** P! X" t. Z4 u( Q: H' r
  93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*. a0 ~4 \* f& L( A" T7 F) e
  94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*- O2 c+ ]& Z4 {$ F- x$ k$ r% c2 m) U  N
  95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    - \3 K& F4 w, o( ?0 Z) z  i! N
  96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    * s# e( O$ w+ M* G/ ~7 p
  97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - , A0 S& X& J# g% k0 @2 }
  98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 5 K8 R# @7 X0 i* x
  99.       w4^2/u3^2*Kwa143*IIua133);
    4 r) _: C& W* u% ^% @1 F$ Z$ K7 |$ E

  100. ) A/ F3 {* o: V: I& h- X
  101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*  q% i! l* F, t5 N+ [8 A0 q+ g
  102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
      L" `2 a: ^  j
  103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*  p( H0 s! B; I! ~3 y4 L
  104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
    , A; c: T% h8 k8 V: Y' P
  105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - 9 U  \" p) J' l. U+ y  ~. a9 O
  106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - / f# }: ?9 H7 {9 t, o* i
  107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    # a9 T3 l2 a# h0 f3 D# }8 z5 f
  108.       w4^2/u3^2*Kwa143*IIua133);
    2 l2 E/ A% V: ?+ V

  109. : I: {3 k1 ]% x/ M/ [
  110. M3 = (betacl*Kwa143*
    9 [/ N& r! k" z  [* K. F; F4 T* S
  111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - 0 E8 N* y4 O% n+ M& l
  112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
    0 l$ M. v' ?0 _! ~( b7 }4 P2 h
  113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
    ( j& F# A7 B! L8 [
  114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*1 |* z- i4 S. ~' G5 J+ B; z
  115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 0 B  ^' T+ r: s
  116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
    " S0 X; [3 N9 d# A
  117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - 6 r, U) K2 K0 G' l7 e1 o) a& }) j
  118.       w4^2/u3^2*Kwa143*IIua133);: J. `9 v1 U1 @# f+ ]

  119. * V7 I( L! {) Y8 U. s+ o
  120. M4 = (betacl*Kwa143*
    - C; L: s6 [8 k5 |9 P
  121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 6 X0 O' p. {& ?1 b
  122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
    ! d; ~4 @8 G# X% S( p# l9 W9 M
  123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 -
    3 _, g& v6 A. a5 C5 T8 z. h
  124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*) O' V% n& O2 p0 m1 t
  125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - . s" {/ y0 ?) F5 I! b
  126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*. g' M* r! u3 D) F
  127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - ) {3 W* ^7 J3 D& ]8 }1 C
  128.       w4^2/u3^2*Kwa143*IIua133);, Q' B/ D7 X$ @4 E: D& E

  129. ! M" D/ V6 h2 ]- f6 T/ U$ M
  130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;: ~( W$ T6 Z, Q4 a+ c" Z% E+ p$ s
  131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
    6 O" R7 O/ C* H0 L/ i4 s5 a
  132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
    4 o3 M9 i/ B& A; P8 e
  133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;+ Y. M4 I2 ^0 M3 e3 _
  134. - G- c' T0 n1 G
  135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
    , F! I, ]. r! y0 X2 I  p( a
  136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;  R. g) i: Z3 Y1 J! Z
  137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
    - v* n! h" R- `7 }1 a
  138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;7 N0 d5 t) M" V, J# c5 X5 g  l& K9 M

  139. & L, |6 B# X  b) v0 }7 a
  140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
    $ N6 d% X8 T, {$ l
  141.      V1*M4);
    4 u4 l) b' d# m* \6 N) W1 @
  142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + " [3 ?, c, g( O
  143.      V2*M2);' k4 {- @" z, `2 O% \
  144. ! f& Z$ w& a1 E, s3 h
  145. x = xicl1 - xicl2;5 S( `! N9 {# N! \' P
  146. x1 = Re[x];
    2 E# V1 C% K+ f+ N2 L% P: B# D7 p
  147. x2 = Im[x];3 t' K3 G' O8 u: U: C# q

  148. # K& S/ H1 t: u4 B% a9 [
  149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
    & T9 [+ j/ K, d
  150. ]
    ! e/ G! }  k1 g; `8 b
  151. ) z: b' Z& r4 h7 G
复制代码
代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
+ W& U6 ^& P# J3 G; R但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
! h" S1 g8 D( j. Y& q换成) e4 \' f9 m0 R
For[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
7 [" F7 |+ G/ N7 i: T8 P FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];; [, |# t6 N! m, n; Z) ?
]
* }: E9 T$ ]- z4 ~2 Q就会出现  o" i5 B) _. E' k. u
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.
+ c9 k# C, ^# @6 |3 S% L' d
$ d- J! I/ _5 M5 V, T, ~$ {请问是怎么回事?* S7 o- }3 z+ e9 I% `/ _
2 W3 D3 ]; I6 l4 J6 Y9 J5 d0 u8 u7 B




欢迎光临 数学建模社区-数学中国 (http://www.madio.net/) Powered by Discuz! X2.5