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贴一个蒙特卡洛方法的matlab程序,供大家使用。 n; s! V5 s- Z) P) _8 ~
祝大家比赛都能取得好成绩 & |- O) d5 C. H( w6 K7 @8 Q+ G' n
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% Example Monte Carlo Simulation in Matlab
* h! d4 t8 I: H8 g: R% Function: y = x2^2/x1
( O5 _" h" I y% ( U% o- E' J* F- U
% Generate n samples from a normal distribution
5 w8 u: F/ g2 Y1 Z$ ~- `% r = ( randn(n,1) * sd ) + mu
, J( W$ F* y- F' E+ A% mu : mean 5 o) ^1 H6 A) o# H: q# e
% sd : standard deviation
2 o7 H3 t3 u7 d! z6 \/ [ R/ }/ _ A4 A% % z- | f" F; r) o- L. s; t
% Generate n samples from a uniform distribution
3 Q2 Y0 t* y" {, u! M9 K7 f3 |' h5 U% r = a + rand(n,1) * (b-a) : A: Z4 u1 b; U0 l5 j/ k, Y, A2 Y
% a : minimum , n9 V3 @# \9 O) D- E- J
% b : maximum 6 Y3 p. }7 ~9 t* }' W6 F
n = 100000; % The number of function evaluations
0 I6 d9 |& T, X2 o% --- Generate vectors of random inputs
7 C! r( G2 F- S7 ~% x1 ~ Normal distribution N(mean=100,sd=5)
0 E, U0 Y* {5 ]" g% x2 ~ Uniform distribution U(a=5,b=15) 5 a5 L5 ]& f0 |& ~
x1 = ( randn(n,1) * 5 ) + 100; % c% U7 m0 a5 @- P" ~3 R0 M! |
x2 = 5 + rand(n,1) * ( 15 - 5 );
. i0 s% G% E) T! K7 ^* Y% --- Run the simulation , w) ^) m$ p/ p2 e" A1 o4 p
% Note the use of element-wise multiplication , h4 V1 \4 n6 ~
y = x2.^2 ./ x1; 6 K* H0 y: w( L( _
% --- Create a histogram of the results (50 bins)
: A$ u. x) }9 O' L* lhist(y,50);
L" E' ~ G+ C7 Z& b9 {1 r% --- Calculate summary statistics & J# x; f L' p' A k' `
y_mean = mean(y) 7 p5 E5 i" A+ j4 x/ o+ y
y_std = std(y)
- X9 r/ R5 u6 i9 Hy_median = median(y) |
zan
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