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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;* @* I7 [7 |- X$ Q2 ]  y& v
  2. k0 = 2*Pi/lamda;
    # l7 ]; a$ h, f& Z* O
  3. n1 = 1.4677;(*纤芯折射率*)& _/ z/ j- z# e, L9 U9 a
  4. n2 = 1.4628;(*包层折射率*)
    7 E* s6 {1 c1 K7 V
  5. n3 = 0.469 + 9.32*I;(*银折射率*)  {: D8 t! f3 `0 M* `- L8 L
  6. a1 = 4.1 10^-6;(*纤芯半径*)
    ! w9 w3 l' |( m7 S7 D
  7. a2 = 62.5 10^-6;(*包层半径*)
    + O4 v) h( y8 ^
  8. d = 40 10^-9;(*金属厚度*)
    + O( |7 T/ k, c
  9. a3 = a2 + d;
    ' o) [6 a/ ~1 {+ S5 b, p
  10. mu = Pi*4 10^-7;(*真空磁导率*)" o. r7 u8 q( R( @
  11. epsi0 = 8.85 10^-12;(*介电常数*)2 C/ K/ A( S$ Y: ^
  12. : l9 `! k+ w, v% |" y
  13. n4 = 1.330;
    8 ^  y. k6 ]9 D: ~! F+ F/ Q

  14. * l* L; c' i3 o. k
  15. neffcl = neffclre + neffclim*I;5 P0 A* E$ g3 s% ^
  16. 9 `5 ]+ F' j0 C2 i* G- ~) N- M; Y
  17. betacl = k0*neffcl;
    * p$ d- s3 \1 k* W; |
  18. omega = 2*Pi*299792458/lamda;+ [) [2 \9 y5 o0 ~6 X

  19. - K& ^- {) u: ^5 z: W7 A
  20. epsi1 = n1^2*epsi0;
    . K# L: f- i6 ^1 R, A
  21. epsi2 = n2^2*epsi0;; R7 c) [8 |. @+ s
  22. epsi3 = n3^2*epsi0;" l( ^# l/ x' S  T
  23. epsi4 = n4^2*epsi0;7 T& i( {- _# q! `5 C

  24. 8 }( z& O/ K/ t8 a4 J
  25. u1 = k0*Sqrt[neffcl^2 - n1^2];
    + I) ?& ^) \/ G1 o. s
  26. u2 = k0*Sqrt[neffcl^2 - n2^2];* E: l% {) j- R8 p3 k
  27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    " e" Z) o8 M4 }: J4 G) f
  28. w4 = k0*Sqrt[neffcl^2 - n4^2];% j: i2 U- p5 @4 Z# W. U+ J
  29. $ G! H1 K9 ~5 R$ {) q* g  n9 v
  30. Iua111 = BesselI[1, u1*a1];; a5 g1 l2 N2 v* i8 ^4 T5 G* M7 B
  31. Iua121 = BesselI[1, u2*a1];
    . C' H9 ?. \& L2 f
  32. Iua122 = BesselI[1, u2*a2];, x0 j5 s! m/ g' ?3 U9 C
  33. Iua132 = BesselI[1, u3*a2];6 d, L' V2 Q# p( S* x5 \# m
  34. Iua133 = BesselI[1, u3*a3];2 n. L5 a) J$ Y: l; X  y
  35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;' E, O; T! x6 ^: G
  36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;8 ^+ m6 e0 A! ~  g0 n: F8 O4 X( Y; V% _
  37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    $ r/ q0 h: j; @4 Y0 ^' L7 o
  38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;( L8 x! A8 U/ K' y% |4 H+ ^" j
  39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;
    + \* b) ~; d& _

  40. + `0 r( Z8 ^0 E: A5 r" e+ `
  41. Kua121 = BesselK [1, u2*a1];
    . |- t  \; S! v! {
  42. Kua122 = BesselK [1, u2*a2];
    ) @" Y+ W+ G/ h: P9 g
  43. Kua132 = BesselK [1, u3*a2];* a8 L: p$ U3 h/ e" a
  44. Kua133 = BesselK [1, u3*a3];. j- U# A6 x4 q
  45. Kwa143 = BesselK [1, w4*a3];* ?! @3 ^2 O% p, O
  46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;
    / i' W7 {* z7 w* _3 O4 w; a- i
  47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;/ o- D" A. E6 D% H: e  `3 e
  48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;6 Z. K. h1 l- L
  49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;
    + r7 ^3 {( \2 T, x- ?$ J2 I4 I
  50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;$ [; b4 [, V: P- C
  51. / J! c5 ~  P0 i
  52. H1 = (betacl*Kwa143*+ J6 v( O6 o: H$ ?4 }' Z7 A
  53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*
    1 t* H; N" A0 i* _
  54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
    + N  `, g2 B) a- v! ^
  55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*7 N5 g1 \6 E. ]8 L& n) c  g
  56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*. m( u( I5 v8 q0 g) i5 Y2 t  Q# x
  57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    * i) `4 K3 g7 E) V8 H6 R# B
  58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*) Q) K; T5 Y9 x+ V
  59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*8 j3 O* j* s- K8 `4 H
  60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    1 O8 f$ k) H; z, D7 v, {! ^/ @2 _+ l
  61. * ?6 Y6 p. s0 |# E
  62. H2 = (betacl*Kwa143*
    7 m& {; Q7 e  d7 D6 S
  63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*; l- D9 c% V9 C8 p' |  V* I' j
  64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143** ?; H, X" s0 m( C0 l+ L
  65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*+ ^$ T3 t1 z7 |+ d
  66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*9 d7 K& ~) Z+ B
  67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*) ]: q# X4 Z$ o
  68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*0 ?5 Z  S9 B' _* E9 n; u+ s
  69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    ) s& O. {) Q: V2 c) e
  70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    ; ]  d8 g, ?: v" Y5 O
  71. 7 O/ y. u* D) f0 {! i
  72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    0 F' A# x5 A) S: a/ W9 p
  73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*- P9 W: ?9 w& a/ o7 Z
  74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    / G$ x6 l, x  ~, q2 s
  75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*2 f) c) D* a/ \0 ?; k& ]) D
  76.        Kua122 - $ y$ H% C5 }- R7 x; e
  77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - % x5 e6 C( L7 Q. Y% K0 l
  78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    ) }, L/ p& V: S( {
  79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 -
    : g# {0 L2 x5 l
  80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);! W1 @- l0 o' g* J7 e" }' k2 d! t# C
  81. ) m# J% P* n6 B3 Y4 V
  82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*! m& a  r$ U2 E, @0 v- ~) H: n
  83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*7 k$ o! j/ u1 I- i2 ?! V
  84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*  L1 S' g  M2 a: k( ^/ ]
  85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*; q2 @0 K( j- T2 [$ M
  86.        Iua122 -
    / J+ ]8 n. A) X. \4 G2 I% o9 c
  87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    6 F* s( T, v8 [" P/ Q7 l
  88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    + U0 S! Z" l" v
  89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    4 a- A" V  S7 F; M" p1 O6 b" ]
  90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    - Y- n" Z  V& ^2 j9 ~

  91. ) _7 `' |3 Z  I2 _- J& ~
  92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    7 ^# ^, Y& y, \* `1 B4 y
  93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*+ P- J- y5 j0 b, C
  94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*
    $ G+ R1 _' b* g5 _' e8 R
  95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    1 V8 ]  H& F" _
  96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - * W& R7 R& P4 D+ m* M4 k9 D
  97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    8 e0 v4 |6 L& _# m1 t' A
  98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 4 \( t4 i" b; W( \& [
  99.       w4^2/u3^2*Kwa143*IIua133);  N, ]- m0 a, }3 u5 R3 W

  100. ; t8 R& t+ ?6 Y% Z  F6 E5 Q
  101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*; Z4 z  j: }8 N5 A9 `( a$ ]
  102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*$ S4 I3 I$ i& G) O6 O2 P& Q, W' s( M
  103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*% N8 R. E# g+ w8 S: U8 @
  104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -
    ' E7 q  w) e4 [0 n$ K* B; e/ _, [
  105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 -
    8 d# \; b. Z) H- y: [" J& Q2 S
  106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 - 6 I/ a; E# `4 Z. D8 U9 F
  107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 - : _# h, V9 |* s  g+ h! n% [
  108.       w4^2/u3^2*Kwa143*IIua133);
    3 u3 Z% o1 }$ x/ V) M: Z
  109. ! e. m% I0 G4 o, D
  110. M3 = (betacl*Kwa143*: F) j% U* ]. L5 K  ~
  111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 - * h# c, u6 v) H8 `0 b' x0 z& d5 f  o4 m
  112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*2 F7 t8 e# G3 I" _2 b, e
  113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 -
    9 M0 y$ G( R: N* l  I5 j- e5 m
  114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*9 e4 z8 @0 b$ k1 Q! n0 }' h
  115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 2 |9 ]% E7 I; d7 N5 ~4 M( o
  116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*" H3 G; j% ~" K. v1 Z( I5 {0 f
  117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - , h1 p! {# X/ Q- K/ H
  118.       w4^2/u3^2*Kwa143*IIua133);4 A# ^8 T; n5 k& G+ O
  119. + `# |% q+ J% K( G4 s6 Y# h
  120. M4 = (betacl*Kwa143*
    : [1 d# C2 {0 G  D0 \3 a
  121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 - & ?4 L6 t: _5 Q& I5 s$ s4 a
  122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*. D" u2 _; m7 e& r" G4 i
  123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - % R- F, D- L/ e( [
  124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*. R4 Z! F- B: G! l5 R# n1 G+ Z
  125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
    9 Y$ q3 M% q9 n. H
  126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*) Y( k/ m- C. L) H' h% M* l
  127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    - T: N; \0 j$ M& i1 z& I+ o
  128.       w4^2/u3^2*Kwa143*IIua133);  _1 s! \- a+ d" \

  129. / k* B! P- Y5 a, M- j( k4 q6 X
  130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;- r3 Y2 k$ P. e7 W! f
  131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;# ]% G! e, a& k4 _9 {8 q6 a
  132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;4 q8 N; E* c3 i/ Y# ~9 E1 a7 d
  133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;
    3 H5 r7 i' o- B0 z/ f0 E( |3 u

  134. $ b8 A, f/ Z* \3 x) T+ [+ r1 Y2 Z
  135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;% F5 _( U. R) k8 x
  136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
    # s$ D( E& c/ P# }
  137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;1 {- w7 J! A" f) ~, i( ~
  138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;
    8 J6 _) Q4 U5 O$ B: {" K; J$ B
  139. 0 u9 i% {! h( \5 T4 O  b
  140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
    ' l5 d+ \7 \6 x9 F) s1 A7 g
  141.      V1*M4);$ {- n6 l- K' f! J
  142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 4 l0 k* h. n4 t5 p% ]
  143.      V2*M2);
    3 U) j! |2 }3 J8 g8 B/ b& `
  144. ; k9 s8 {( y3 b/ Y* v: E, K, e4 U
  145. x = xicl1 - xicl2;4 a/ M# \! y5 _
  146. x1 = Re[x];0 m- D/ w5 V, X  O
  147. x2 = Im[x];; _8 L. c! Q+ M
  148. , A4 d' m1 d5 `) \* x
  149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];9 O% `0 o; j/ _; e
  150. ]
    8 ]' F; b% J* N9 A% A* T3 |

  151.   f8 F( _& c% I3 g
复制代码
代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}
0 |6 c+ P% _: a% B但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
' g6 x8 d+ @) |2 ^5 r% }7 v% @" G换成
0 ?0 n1 {) D& v3 WFor[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
: B: V% _$ l; X- H FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];; O+ t5 ?& z5 M) y7 ]9 {
]
6 e4 `" M7 E  E' l* [8 K就会出现
8 }8 Y) A6 O5 _# y+ |3 CFindRoot::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.
: e$ H4 N4 ^2 N$ M& V8 ]. z' P* a' m6 t% S
请问是怎么回事?  T. y7 u7 S$ @9 r; b1 k
0 c% g" @, e, g- i# ^0 S+ _0 h




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