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贴一个蒙特卡洛方法的matlab程序,供大家使用。
) t5 L# H, Y8 x1 `& ]祝大家比赛都能取得好成绩
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% Example Monte Carlo Simulation in Matlab
! D% o3 Y" G, @( }& y% Function: y = x2^2/x1 : g1 i$ y; h. C9 ^' G
% 3 _0 _: q: `" w' i m
% Generate n samples from a normal distribution
3 u9 V( e( ~; Z! k% r = ( randn(n,1) * sd ) + mu # V4 }7 u/ V( X$ W
% mu : mean
6 [! R' [' Q2 R: _5 o% sd : standard deviation
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) g* F/ }' m$ L, |. E% Generate n samples from a uniform distribution
0 e; X9 o+ U7 G# W- X% r = a + rand(n,1) * (b-a) ! n9 O+ v1 Y: u
% a : minimum $ j+ o6 J4 D6 t- {/ Q
% b : maximum
. H- A- }5 u! U9 j* E2 Tn = 100000; % The number of function evaluations
: j5 N' {5 M0 j2 [% --- Generate vectors of random inputs
& I- B* S9 y' G% x1 ~ Normal distribution N(mean=100,sd=5)
% i4 Z. n1 }' u& Q# C1 u% x2 ~ Uniform distribution U(a=5,b=15)
3 y. _: P6 c( {" sx1 = ( randn(n,1) * 5 ) + 100; ! V; q" G4 \# o, U) S; I
x2 = 5 + rand(n,1) * ( 15 - 5 );
+ F6 w4 M1 i1 ^8 I. S1 J% --- Run the simulation
) `6 A' _6 S; j8 N" r8 B" ^# C; x% Note the use of element-wise multiplication 1 K9 j. n) K5 r a
y = x2.^2 ./ x1;
1 K' H/ z; n# c6 X. _( ]0 r% Q% --- Create a histogram of the results (50 bins)
* v/ W4 Y2 F! M5 ~8 `3 @; `. t2 S$ Dhist(y,50);
+ p$ ^3 b+ Z6 z/ A, o" g4 A% --- Calculate summary statistics
0 |. Q2 }1 G' M0 Z8 a% gy_mean = mean(y)
0 A7 k$ E8 | }( }y_std = std(y)
1 t3 C1 z7 ^. W- h3 q! G6 zy_median = median(y) |
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