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贴一个蒙特卡洛方法的matlab程序,供大家使用。
( D t) t& P3 F祝大家比赛都能取得好成绩
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& q7 F% d! f0 S% Example Monte Carlo Simulation in Matlab
+ _) g, [6 J# G8 s% {8 V: O% Function: y = x2^2/x1
4 k) `; T( s* @: J" v f% - I. @: e# x9 F! i( c4 ]" a
% Generate n samples from a normal distribution
1 ^3 [& ~7 {; z9 p- x% r = ( randn(n,1) * sd ) + mu
8 t4 H) L( ^3 ` g [1 S+ f! F* b" f K% mu : mean & g2 K7 ^1 d& A* ]7 B, {$ p
% sd : standard deviation
& q, {0 F$ ~# A: j4 `& u%
0 A$ u/ g& T9 b* P! m7 B2 B/ ^% Generate n samples from a uniform distribution
& u3 E) \9 [* Z- q% r = a + rand(n,1) * (b-a) # \: A4 l: {+ `9 P$ e
% a : minimum 0 p& p0 t) z0 j- b) r7 _
% b : maximum * q' ]8 w. ^* k1 d. r5 X I
n = 100000; % The number of function evaluations ) }3 i g6 h2 ]- i' { I
% --- Generate vectors of random inputs
/ n* K# R9 o7 z2 D0 I% x1 ~ Normal distribution N(mean=100,sd=5) ( {- E* K& Z8 s# }
% x2 ~ Uniform distribution U(a=5,b=15) + f! R x7 r) B) D2 }; ~( [* W9 g
x1 = ( randn(n,1) * 5 ) + 100; 7 V% v7 w) l' H' B
x2 = 5 + rand(n,1) * ( 15 - 5 );
$ W ]9 `( Y8 q& Y. a% --- Run the simulation
; W* f; K- g1 a2 H% Note the use of element-wise multiplication
' T; V, S9 c2 I; [" T1 Ly = x2.^2 ./ x1;
9 N- {2 I# l C( J& ?# G/ g2 W: Q% --- Create a histogram of the results (50 bins) & @/ f7 v1 J" H
hist(y,50);
2 _. X3 j& O8 t$ L% --- Calculate summary statistics ; C/ F- C9 e# w4 T% p
y_mean = mean(y) : I+ {; ]# m% @. H R( W6 v
y_std = std(y)
1 l) n% `4 n& r! yy_median = median(y) |
zan
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