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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;
    3 l% c: }' a/ g
  2. k0 = 2*Pi/lamda;$ z0 X, k7 U) Q! ^
  3. n1 = 1.4677;(*纤芯折射率*)
    9 ?! e$ [1 ~1 |  W& ]' O6 V# J" j/ z
  4. n2 = 1.4628;(*包层折射率*)' v4 V6 B; b- F4 M
  5. n3 = 0.469 + 9.32*I;(*银折射率*)
    " u8 e9 j$ Q( W7 o  y7 e5 {: d
  6. a1 = 4.1 10^-6;(*纤芯半径*)
    9 m3 s/ z! U; ^# a" v& l
  7. a2 = 62.5 10^-6;(*包层半径*)
    # l0 a5 Z; R/ M8 s/ h4 U7 S
  8. d = 40 10^-9;(*金属厚度*)
    % K2 w, b. J: O) j% ^
  9. a3 = a2 + d;
    1 n! }3 ~/ m0 j4 {# B, R5 V; g
  10. mu = Pi*4 10^-7;(*真空磁导率*)5 |. n% b- j9 {) T. L; u0 G! Y
  11. epsi0 = 8.85 10^-12;(*介电常数*)
      f* p# O. v& G: Z" H9 N: C0 ^* Q

  12. 7 B+ R5 G- J( x/ }) x
  13. n4 = 1.330;
    ) x/ T+ [9 U* E( w2 c7 P
  14. 2 T; g, w( b/ ]& l& n
  15. neffcl = neffclre + neffclim*I;: c% E7 _; w$ x9 k

  16. 9 J  u. q4 X, Y; [5 ?" f5 i
  17. betacl = k0*neffcl;$ U- h" J/ Z# j0 |( G+ q& W- r
  18. omega = 2*Pi*299792458/lamda;
    9 o9 @2 A* f; Z; @

  19. * @; E. C( ^5 y8 \$ m7 O- s! b' P
  20. epsi1 = n1^2*epsi0;% e: e; U$ k& X0 ]! |
  21. epsi2 = n2^2*epsi0;% X! I, ]3 }5 M; R( Q  |
  22. epsi3 = n3^2*epsi0;5 b# e2 M; r; ?7 C
  23. epsi4 = n4^2*epsi0;0 x8 y; Q4 P5 [% u" \

  24. 9 D/ N9 p9 r4 m* T  g+ Y  n. S
  25. u1 = k0*Sqrt[neffcl^2 - n1^2];+ w4 H( l- v: j; O" M- m
  26. u2 = k0*Sqrt[neffcl^2 - n2^2];5 V3 J! H4 K, A% A& H  J' D# _7 ^
  27. u3 = k0*Sqrt[neffcl^2 - n3^2];
    & c+ `5 z$ f% f. L8 e6 U: ^
  28. w4 = k0*Sqrt[neffcl^2 - n4^2];
    6 |7 ~+ `' @' G' g7 V7 I
  29. 2 v6 d* K6 C$ B( D, {! {! x
  30. Iua111 = BesselI[1, u1*a1];. {: U. y0 l9 F) ?
  31. Iua121 = BesselI[1, u2*a1];8 D* a- A5 P; D5 y- q" l. J2 P
  32. Iua122 = BesselI[1, u2*a2];
    3 A6 x' g. h" V1 b& l3 P
  33. Iua132 = BesselI[1, u3*a2];
    * t0 l9 t/ ]4 H0 T/ V/ l# U
  34. Iua133 = BesselI[1, u3*a3];
    9 P+ J9 p9 y7 R' J
  35. IIua111 = (BesselI[0, u1*a1] + BesselI [2, u1*a1])/2;2 g2 T2 n- ~# j2 o' {8 `4 C2 s
  36. IIua121 = (BesselI [0, u2*a1] + BesselI [2, u2*a1])/2;# l# r& m9 q$ f7 M9 B' a5 a1 e
  37. IIua122 = (BesselI[0, u2*a2] + BesselI[2, u2*a2])/2;
    ) t! E9 h6 p; S5 h
  38. IIua132 = (BesselI[0, u3*a2] + BesselI[2, u3*a2])/2;- c3 B1 M% i+ p% B: d, }
  39. IIua133 = (BesselI[0, u3*a3] + BesselI[2, u3*a3])/2;5 H4 i% q+ p) b( o1 \% j) D* o- B
  40. ( _% ^4 [& \, ?" h! }/ c7 E2 \
  41. Kua121 = BesselK [1, u2*a1];
    % P( P9 C$ B% U2 e9 _
  42. Kua122 = BesselK [1, u2*a2];
    ! n* \: G0 C$ P- s3 S6 s" a
  43. Kua132 = BesselK [1, u3*a2];  \: m& J/ C- `/ L
  44. Kua133 = BesselK [1, u3*a3];
    # l& i/ s! S3 N% u8 D! m! Z
  45. Kwa143 = BesselK [1, w4*a3];
    $ L/ R, a  ^% G: l( _( c3 H1 r
  46. KKua121 = -(BesselK [0, u2*a1] + BesselK [2, u2*a1])/2;+ I) i9 P! l! }7 Y: y
  47. KKua122 = -(BesselK [0, u2*a2] + BesselK [2, u2*a2])/2;5 S! [9 k- ]  v8 q
  48. KKua132 = -(BesselK [0, u3*a2] + BesselK [2, u3*a2])/2;
    " W  O% h8 N# M: F9 ~  e: Z4 I& F
  49. KKua133 = -(BesselK [0, u3*a3] + BesselK [2, u3*a3])/2;4 Y! d" b; k+ S4 `3 Z9 Q1 S2 x
  50. KKwa143 = -(BesselK [0, w4*a3] + BesselK [2, w4*a3])/2;
      `! a; y- P4 }4 o* z1 ^+ Z3 o  j

  51. ' E& O9 ]/ t0 B# m
  52. H1 = (betacl*Kwa143*/ `3 q, G. h! J& N$ p
  53.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*+ [0 q  i8 ~% ]% c
  54.        Kua122 - u3^2/u2^2*Iua132*KKua122) - (betacl*Kwa143*
    4 O' H2 ^% ]8 x
  55.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*0 c' f% ~$ @- r  L+ B+ n: M0 o
  56.        Kua122 - u3^2/u2^2*Kua132*KKua122) + (betacl*Iua132*" I1 p1 W& B$ u; a
  57.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    1 X4 ^: b6 x. h( A7 C
  58.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*/ x1 \' y- p5 J
  59.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*! e2 N& U8 y& T
  60.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    ' D7 w. Z! D6 \

  61. ( K% w1 }3 N; b8 f# C, R, r/ f* J
  62. H2 = (betacl*Kwa143*
    2 m' ^+ P. b/ R' X$ v5 e
  63.       Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*IIua132*( Y& q2 ?( w' Z5 ]" U8 Y& ~
  64.        Iua122 - u3^2/u2^2*Iua132*IIua122) - (betacl*Kwa143*" P2 {- R; N8 L# c; a* d- X& P' |
  65.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3)*(u3/u2*KKua132*& p1 m7 K+ K5 H. m" `
  66.        Iua122 - u3^2/u2^2*Kua132*IIua122) + (betacl*Iua132*
    * l& c2 d; H. _# Y) S1 p7 b
  67.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*: j  C4 }: |9 C, t
  68.        Kua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (betacl*
    - G0 }; t* t$ m
  69.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(w4/u3*KKwa143*
    2 O) `8 d/ d5 R/ _! K0 n; R1 q8 Q3 c
  70.        Iua133 - w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);
    # N& n4 F) I! `9 ^6 j

  71. ! Q5 v( x3 Q. Y9 D) [, y
  72. H3 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*, o, F8 ^3 G: |. `% e' U. i
  73.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*2 H% E% ^2 \" E6 s1 m/ ^: ]
  74.       Kua132*Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*  z8 x5 L8 X( V
  75.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*
    8 p( Y+ d4 e3 g$ B  M8 t
  76.        Kua122 -
    : W: j' ~8 r4 B+ A3 ^
  77.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 -
    : F# T! M3 b- U( t
  78.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 - : h) B. x3 x$ g* T% r' H5 o
  79.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - , }2 o$ ?2 _# W  K1 I
  80.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);7 V# t/ H# ]% E- r, }5 a5 l8 M6 }
  81. ( a* ?2 r( w! ]
  82. H4 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*
    " q' d9 v; k1 W
  83.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) - (betacl*: c6 N' r# H6 p( X: D
  84.       Kua132*Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(betacl*Kwa143*
    2 w& a1 _  a" K, A2 L4 _* r
  85.       Iua133*(w4^2/u3^2 - 1)/omega/epsi4/u3/a3) + (u3/u2*IIua132*0 u9 v# c: g: ]5 A' O4 \
  86.        Iua122 -
    4 v0 f) d( s" n# ^
  87.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - : v- \4 ^" [+ a, s' a' g. _, b$ I
  88.       w4^2*epsi3/u3^2/epsi4*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    3 Y0 Z8 x$ _5 l0 V7 G/ \
  89.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    9 c% I. Z3 Q5 T5 h
  90.       w4^2*epsi3/u3^2/epsi4*Kwa143*IIua133);6 e9 z# F  ~1 k& ?2 p; p

  91. ( W) p% t8 X( M/ r- Z
  92. M1 = (betacl*Iua132*Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    & U0 I) H5 S6 C: L, a* I
  93.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    : s3 u1 T9 l$ v) b# U
  94.       Kua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*, j8 D2 i/ C2 Q5 o  \1 A7 i2 Z2 J
  95.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Kua122 -
    , i; f$ B8 i& \
  96.        u3^2/u2^2*Iua132*KKua122)*(w4/u3*KKwa143*Kua133 - . z. r. M+ M2 z; F: y
  97.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Kua122 -
    4 \# g6 H7 S$ G, I
  98.       u3^2/u2^2*Kua132*KKua122)*(w4/u3*KKwa143*Iua133 - 7 m5 t2 q7 g$ U- @+ N& ~) h
  99.       w4^2/u3^2*Kwa143*IIua133);( H* u* H. X8 D" a
  100. ( e9 k( Z1 O5 }; v
  101. M2 = (betacl*Iua132*Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*
    8 V4 h& s2 ?9 x9 C4 `
  102.       Kwa143*Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) - (betacl*Kua132*
    # y% R0 [6 X; M- }' p8 {5 ^
  103.       Iua122*(u3^2/u2^2 - 1)/omega/epsi3/u2/a2)*(betacl*Kwa143*  X# d' d5 R" Q. B% s3 @
  104.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3) + (u3/u2*IIua132*Iua122 -0 J9 g3 `, q% M2 K. ^6 ?4 `1 v$ D
  105.        u3^2/u2^2*Iua132*IIua122)*(w4/u3*KKwa143*Kua133 - , n4 S$ _- L8 t
  106.       w4^2/u3^2*Kwa143*KKua133) - (u3/u2*KKua132*Iua122 -
    + g" e% X& \* U! N. r: y
  107.       u3^2/u2^2*Kua132*IIua122)*(w4/u3*KKwa143*Iua133 -
    / ~# r$ Q2 G' |7 h
  108.       w4^2/u3^2*Kwa143*IIua133);
    " N; N1 `7 |' u) F* n5 `! ^$ V6 r
  109. 0 j  g+ W- V* R- x2 g6 h  ~7 v3 E7 }
  110. M3 = (betacl*Kwa143*6 g8 r; t* U' I- n% e
  111.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Kua122 -
    9 u# B# k) z9 r9 t; f
  112.       u3^2*epsi2/u2^2/epsi3*Iua132*KKua122) - (betacl*Kwa143*! t3 m! c6 K3 x. B' v
  113.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Kua122 - 1 n# P8 ]: g# x3 Q  F
  114.       u3^2*epsi2/u2^2/epsi3*Kua132*KKua122) + (betacl*Iua132*
    1 U. ]# N- P5 j1 y
  115.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 - 4 b" n+ ~2 z0 n$ A& X$ V
  116.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
    0 @! v& O, ^' l$ d+ h, m& F8 [% ]
  117.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 -
    " o: E" K6 H" s, `! o" J4 {
  118.       w4^2/u3^2*Kwa143*IIua133);
    8 W8 H; i5 x; L( G$ B; v
  119. 3 W0 v; B3 U7 ~8 _& G0 l
  120. M4 = (betacl*Kwa143*
    ! J! [. x0 g+ y/ K2 ]( D
  121.       Kua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*IIua132*Iua122 -
    ; u$ _2 t( I7 ]5 D- j3 M) |% h0 Q( I
  122.       u3^2*epsi2/u2^2/epsi3*Iua132*IIua122) - (betacl*Kwa143*8 U; K7 t; u$ P, Y: M! [+ M
  123.       Iua133*(w4^2/u3^2 - 1)/omega/mu/u3/a3)*(u3/u2*KKua132*Iua122 - - h" s) v7 K- Y( B+ Z! R
  124.       u3^2*epsi2/u2^2/epsi3*Kua132*IIua122) + (betacl*Iua132*
    # e4 Q. y# k5 q' M
  125.       Kua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Kua133 -
    # }. s/ a4 k1 X
  126.       w4^2/u3^2*Kwa143*KKua133) - (betacl*Kua132*
    ! @, a0 u  z+ m2 C/ S
  127.       Iua122*(u3^2/u2^2 - 1)/omega/mu/u2/a2)*(w4/u3*KKwa143*Iua133 - / v  C+ v0 _2 i4 D' ]8 Z. q
  128.       w4^2/u3^2*Kwa143*IIua133);- O4 e1 W% C" q: v
  129.   t  D) ]" a! v9 w3 H  d6 v' x8 P4 V
  130. R1 = u2^2/u1^2*Iua121*IIua111 - u2/u1*IIua121*Iua111;' L4 |- g. }8 V+ @% w
  131. T1 = u2^2/u1^2*Kua121*IIua111 - u2/u1*KKua121*Iua111;2 y; L2 e% @( N' ^7 A
  132. U1 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;9 h( l8 G2 x) i- Z+ C
  133. V1 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/epsi2/u1/a1;6 f2 \% m' j! ]& X' z
  134. ) d! f2 O$ x/ M! c  \! `+ a
  135. R2 = u2^2/u1^2*epsi1/epsi2*Iua121*IIua111 - u2/u1*IIua121*Iua111;
    & D6 ~+ ~; {0 V  t$ g
  136. T2 = u2^2/u1^2*epsi1/epsi2*Kua121*IIua111 - u2/u1*KKua121*Iua111;
    5 W+ ?! W+ e1 k! w# O6 r
  137. U2 = betacl*Iua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;" }, M- _( `- }& m+ G
  138. V2 = betacl*Kua121*Iua111*(u2^2/u1^2 - 1)/omega/mu/u1/a1;4 a# u4 M( S+ v" ]

  139. # [6 D. J, ^- s+ [) h" s' Z
  140. xicl1 = (-R1*H1 + T1*H2 + U1*H3 - V1*H4)/(R1*M1 - T1*M2 - U1*M3 +
    ! [' W7 z) }( p/ N9 j
  141.      V1*M4);
    " T7 E: x9 N2 t2 h! F' r
  142. xicl2 = (-R2*H3 + T2*H4 + U2*H1 - V2*H2)/(R2*M3 - T2*M4 - U2*M1 + 7 ?- ]9 H* j; A% R0 X* [5 \) k* O
  143.      V2*M2);
    4 b4 C6 b% q9 ^0 {8 w2 I
  144. 7 V$ v9 r7 S- f# C
  145. x = xicl1 - xicl2;1 [' v  w# l" h9 |" U* k, A; j
  146. x1 = Re[x];
    & }6 \  N* U: Z
  147. x2 = Im[x];( B0 q# ?# a  r( z2 v7 M

  148.   D1 U% V, i) f
  149. FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];& }: G9 @7 C8 T. h+ [7 ~9 V
  150. ]# x: I. {. U* n# E7 x; @

  151. 9 t# {: m7 _* {$ D
复制代码
代码如上，结果是{neffclre -> 1.33017, neffclim -> 0.0000172055}2 ?$ G( U9 G( D/ p& u
但我把FindRoot[{x1,x2},{{neffclre,1.333},{neffclim,0.00001}}];
7 }) N, }# a: m5 |* o8 w换成$ Z% z% m' P# l: V0 P
For[i = 1, i < 133, i++, neffclbase = 1.330 + 0.001*i;
) s* e, |* l' N  t2 K0 C FindRoot[{x1, x2}, {{neffclre, neffclbase}, {neffclim, 0.00001}}];: y  C, i3 |8 |! U
]
# O6 R# B7 I( S% B& \就会出现
0 e5 O/ M! z% N0 _2 w$ XFindRoot::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.! @. w7 r# F  F- R5 J9 Z% w$ h7 T

$ e6 }, s% v- o7 U8 b7 W请问是怎么回事?0 X  b2 w" P- n6 _& z
+ I6 @8 g! K- u: g




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