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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;
    : d. G: ?, p0 z" I( ]
  2. k0 = 2*Pi/lamda;0 _  j9 A9 A( \, a. M
  3. n1 = 1.4677;(*纤芯折射率*)* q3 P! n) M) q3 O1 F. T$ E& q
  4. n2 = 1.4628;(*包层折射率*)
    " c; S& r1 I/ }: }& ?
  5. n3 = 0.469 + 9.32*I;(*银折射率*)
    & U$ D; B  r+ `* c
  6. a1 = 4.1 10^-6;(*纤芯半径*)
    8 L0 Q0 o+ w& \2 F/ i
  7. a2 = 62.5 10^-6;(*包层半径*)
    . M! X5 h6 [, G- h+ t6 t6 c
  8. d = 40 10^-9;(*金属厚度*)
    # V# j7 V3 ?- X; ]3 g- q$ o8 s& _
  9. a3 = a2 + d;& T# y$ N* @4 G( g" n
  10. mu = Pi*4 10^-7;(*真空磁导率*)* p+ f% r! y" x. t. u: d4 E
  11. epsi0 = 8.85 10^-12;(*介电常数*)5 Q; m2 F, [# m7 t  r( {+ f

  12. & O+ c! F- i; f% x
  13. n4 = 1.330;
    + d' Q0 k8 T4 P; _4 `/ W0 P( H# r0 v( E

  14. ) `2 q" }8 D  F  }5 j( q) h  `
  15. neffcl = neffclre + neffclim*I;
    * Z8 F: y! `# S4 ?  O% K$ }
  16. ( O- ~( z4 E0 Z) e) Y: C
  17. betacl = k0*neffcl;
    ) O% A( a4 i- b# @4 V: v
  18. omega = 2*Pi*299792458/lamda;; ~9 a5 c; v- f! L1 I0 [

  19. 8 s! O" H/ I6 ~: t* g: a4 g) U" B& Z
  20. epsi1 = n1^2*epsi0;  v3 I7 S7 z  w$ N7 @
  21. epsi2 = n2^2*epsi0;% M& {: j* ~/ O
  22. epsi3 = n3^2*epsi0;; p4 d$ _0 u/ R# }; ~
  23. epsi4 = n4^2*epsi0;
    7 s: h7 S" o- l( ~$ g

  24. # U+ e4 C( W# \8 o' a
  25. u1 = k0*Sqrt[neffcl^2 - n1^2];9 {- }4 {7 l/ D
  26. u2 = k0*Sqrt[neffcl^2 - n2^2];
    + \7 L* U4 A# B1 v% K  L( h
  27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    , F! e/ e, `& _1 J' z% `+ M
  28. w4 = k0*Sqrt[neffcl^2 - n4^2];
    3 g1 \; S% w1 S3 x1 k. g  C' n

  29. & G: q. @* w$ u0 Y- \! b
  30. Iua111 = BesselI[1, u1*a1];( ^* ~5 p% u) w# H7 ?( M
  31. Iua121 = BesselI[1, u2*a1];
    $ h; E8 S) {7 u% I, V7 ]
  32. Iua122 = BesselI[1, u2*a2];' I$ ^8 o8 \3 q
  33. Iua132 = BesselI[1, u3*a2];
    2 {% k: ?8 M& a7 z! D9 ~
  34. Iua133 = BesselI[1, u3*a3];) @" V4 T4 K+ q# a7 J) u
  35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;
    $ K+ Y, T; E' I8 W
  36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;
    1 {2 d, e  A& `4 i  H
  37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    % w: J, |7 W8 P' q. q* ~1 [1 r% }4 k
  38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;  j  U# [+ ]8 e% a; o2 b/ C
  39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;; k/ q! q- J9 U" _$ f6 _' V+ U

  40. ; P: a+ [+ W  ]/ H- c2 \7 K. Y4 V- z
  41. Kua121 = BesselK [1, u2*a1];
      r3 H0 r% b5 r( ^) A2 h* ?3 `
  42. Kua122 = BesselK [1, u2*a2];
    4 l5 b. ^% q5 u- ?/ t4 T; ~% ^
  43. Kua132 = BesselK [1, u3*a2];
    2 K, s" M5 N6 ]; t. A! e$ U
  44. Kua133 = BesselK [1, u3*a3];% l$ B& a% d3 h+ Y& s
  45. Kwa143 = BesselK [1, w4*a3];
    4 Z" b- y: E' R0 [' I  C
  46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;) e) m  C. j# u% ]$ S
  47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;( }& C+ l0 c6 W: `5 k
  48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;1 j. u! H' B: t' c9 j8 S8 H! z1 m
  49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    3 C+ f( y) f# V2 r) F& j+ ?
  50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;4 f7 z. P7 x/ V" ]- @+ n* `$ l
  51.   w4 @4 n2 a( u, t% y
  52. H1 = (betacl*Kwa143*! O8 p+ [" Y; a& Y
  53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
    2 X! T. t0 q) y* o
  54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*& g# e2 v7 Y; }/ H; Y, y% ^9 p
  55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    1 i& W1 O% c" h0 w0 ~
  56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*/ @% ?" @5 m5 v% w2 L
  57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*; \* {) A2 n4 ~+ e
  58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*% x% M/ m5 D% ~
  59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*: [" h, O0 U6 ]5 Z
  60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    $ M9 U8 ~) i& C  c: o% ]# N& G/ P
  61. % W  d' y+ s) |7 z* y& o# u* q
  62. H2 = (betacl*Kwa143*6 e. d% l0 b4 F' d, M$ K; D
  63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*  J5 ?+ j; l, C7 u: A
  64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*
    & J; y) l+ f3 A) x
  65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*
    : P  d7 n3 l  s
  66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*8 Y7 Z4 B" L% ~9 z% e
  67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    # _) q% }4 a, y
  68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    . M, A" v/ @5 |* p  j( _
  69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    - ~0 u4 Q  i4 U0 J1 ^% ~
  70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    , @- v& K' L4 i: d( k7 j1 h

  71.   g: O5 ~. v- X
  72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*& K7 l6 E0 b( ^9 H6 K# b
  73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*
    % e' ^( Y9 A2 a; g
  74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
      s# A3 i6 [/ b( a4 q! W8 Z
  75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    6 L9 y* l. u% A0 I
  76.        Kua122 -
    ; g8 R! O8 a0 u( a' c$ U, U
  77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    ( u4 c# y1 f2 ~* K
  78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - ( ~( L7 r* ?( _( ~5 q4 \" N* A
  79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    * i# `* A9 k( h6 i( V
  80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    9 z9 U6 Z5 O& G% l) Y" A
  81. 9 y' o/ e+ h1 s
  82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    ( d7 v, |( H2 Q
  83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*. ]- S- N* O, V: d! }3 E
  84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143** t4 g: D* [' y  d$ P; S
  85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    , v5 N+ H& g: d$ A+ O4 o9 f( k, Q
  86.        Iua122 - : c9 O6 U( I0 h6 j. p- A4 j
  87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - ! U* D# U2 M( x& n: [' ]) q& m) [
  88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - : K  ~" v" j7 ?5 h. |
  89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    7 o" X- Z; r2 a4 X0 {: \0 p
  90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    2 s" L, e8 ^+ N3 t. C& c

  91. ; u! A/ c" x. t2 F) ?* T
  92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*6 n8 c0 v  ?2 T
  93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*' S( g6 }4 M3 k
  94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
    * B, A( Z" K# k# m& C. A
  95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    % Z; B6 s3 s6 K9 i0 F
  96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - 0 u! s/ F5 h+ w7 ]- G, q
  97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    / G2 S- t! J& ~" f+ t9 {
  98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    8 |! X" h" L% N) Y  Y9 r$ s2 l
  99.       w4^2/u3^2*Kwa143*IIua133);
    1 `' u) m* A! {4 H; ^4 a6 {

  100. 1 n0 {  n( c: M/ B  }
  101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    0 R6 c+ H. b3 m' N
  102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    ) @$ C( K2 ~  ?, L0 ~1 H7 \0 Y
  103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
    2 `, x  H" g, Q! K9 b4 Z9 o8 p
  104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
    2 ~% P( ?( |' B: h5 N
  105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - # ~% i+ i3 S2 m) ~& ~3 O3 |
  106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    ( L, _" Y: g( g
  107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    ) }  _, i( m0 m4 ~1 W4 G2 f( w( v
  108.       w4^2/u3^2*Kwa143*IIua133);
    $ E6 s+ O* @5 ?$ a( |

  109. 9 N7 x) {( z6 t0 H
  110. M3 = (betacl*Kwa143*  K# M; W7 ?" p( d' Z8 n
  111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
    ' t' Y$ U9 ^! `7 u& ?. ?
  112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*
    9 g7 e4 Z1 ?* k6 l7 b
  113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - ! e; ?; Z; W% I. e; ]0 y3 H
  114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*2 F1 a/ r! p+ t9 i3 e
  115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
    : x6 Z; M9 ]3 J: m
  116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*9 T2 W  U1 A, o/ n/ i
  117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    - }4 s: {0 r/ q% F; p: B9 w2 ^
  118.       w4^2/u3^2*Kwa143*IIua133);
    , U* R2 T0 |' ~* J5 z/ r# @

  119. % v5 h' N$ a: P2 @/ O& ]
  120. M4 = (betacl*Kwa143*( [& V3 q  U2 H0 X5 f
  121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - 4 g9 r* K9 n, J' B1 r1 b  e* r- W
  122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*
    4 U4 q+ B) M2 Y9 I4 Q
  123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - / P' j3 Z5 \' Y% B
  124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
    : [; V+ E# e; w4 _2 x: G
  125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 4 l, z3 e( m4 e! D
  126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
    % W4 v# [$ h% P7 n) a, T
  127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    ( x$ a0 t( B# G; d) K/ o0 X
  128.       w4^2/u3^2*Kwa143*IIua133);
    $ L3 w! Z0 K( L' w* D

  129. 8 n4 N- t: c: f  e: l" P
  130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;. t2 }" \. C! `2 `5 }
  131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;/ @: g. X. Z( a0 l
  132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
    / g+ Q: Y5 Y" C% E3 h
  133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
    , a2 ?. V7 [7 h5 `2 h$ n5 t$ N0 |
  134. * G4 O2 A! r% r
  135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;) w3 m6 l( p, b( s; Y. T- V
  136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;* Q+ T2 G% ^, g% h
  137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
    / `$ N8 U  M2 u: }6 H+ }" x, h
  138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
    ( `  q* u6 [, O

  139. 3 I6 n& V. k7 N0 w8 q+ J
  140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 + % d7 h+ c7 l. T# B, b
  141.      V1*M4);
    7 b! l0 P) |; P' t8 O
  142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 +
    $ z2 l' s) L' L
  143.      V2*M2);
    8 a' S. N, Q% B  s% h% `1 c0 e
  144. , D* h/ c1 L  g9 o7 o2 j2 f
  145. x = xicl1 - xicl2;% G' @- H" x5 z  M  r# ?( D( D
  146. x1 = Re[x];
    % b  k/ c: L9 r' Y7 o, G
  147. x2 = Im[x];
    5 n* O1 H( I! @6 D
  148. * S1 w) }& U! j6 P) [: ^2 W* P& o- V& Q
  149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];2 R4 ^& O: K- m
  150. ]
    . u% ]$ X$ U- V1 z) J5 e$ }* m

  151. , E% N; s6 w, x9 M
复制代码
代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}* |! y" O' _. n
但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
, d8 w: F3 \( |3 n0 y1 D换成
& C' i! p8 f6 i( d& YFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
. K: W1 q/ B9 _* A% b FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];9 U8 F+ X5 H7 P
]
% @1 j( N: R. C2 R2 W( z0 O! z就会出现( w) [) n- ?' {" e. @3 C4 ?
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.
; w% T; y$ I! R9 P  D( H, {# j& J2 G" i7 V; x# X! [! G& m1 N
请问是怎么回事?7 V1 h8 n" c, D6 R
) k* f3 A/ x& ~" u5 ?; o9 \8 Q5 J




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