贴一个蒙特卡洛方法的matlab程序,供大家使用。 % y/ p; |5 T) A5 k0 T: U祝大家比赛都能取得好成绩 ' t: J' m. d' q% Z/ T9 o2 W- c5 ^2 g: o5 O9 q& D9 Q
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% Example Monte Carlo Simulation in Matlab 2 u5 Z. Y P+ w1 S% Function: y = x2^2/x1 ! r, ^, n. t G2 p0 n8 R% 7 j3 B- ]9 |& u
% Generate n samples from a normal distribution $ |# T2 f3 b: P( _, o$ Q: S% r = ( randn(n,1) * sd ) + mu 2 Q B2 f( ]$ U% mu : mean 1 ~6 U1 A I. m% sd : standard deviation Z- y. L8 }& Y7 Y2 p
% + Y; u- m Q7 A) x1 p1 E9 N' y% Generate n samples from a uniform distribution \# X* ^5 t+ T: O- m% r = a + rand(n,1) * (b-a) ) z" z1 k7 B) d4 k2 h0 o) H% a : minimum - \( H" y D6 A+ D; E
% b : maximum , g6 c( N2 y' ^+ ~8 `% u @
n = 100000; % The number of function evaluations ; a$ ~7 d, I% k, o, E/ f
% --- Generate vectors of random inputs . [- S8 }- [+ [# Q0 i1 D6 u
% x1 ~ Normal distribution N(mean=100,sd=5) : C9 H7 O0 O+ j! \
% x2 ~ Uniform distribution U(a=5,b=15) + k6 ^' t9 t/ `; k
x1 = ( randn(n,1) * 5 ) + 100; 2 e, R2 O3 t/ Y S2 }; s' Ox2 = 5 + rand(n,1) * ( 15 - 5 ); ; R8 [# h. D! ^6 e% --- Run the simulation + F! t3 C% _: J! r$ F7 ?9 A% Note the use of element-wise multiplication 3 n$ }6 f, \/ u7 W
y = x2.^2 ./ x1; ) V4 u( h. j1 G( f1 B( z8 V, s% --- Create a histogram of the results (50 bins) 9 y/ u/ T$ V5 n! m, e
hist(y,50); & i& w! E( r, r2 Y4 I, _4 d% --- Calculate summary statistics 7 b* X# I8 t6 f" t+ a6 @y_mean = mean(y) & v o, E' ]5 C5 A2 U- My_std = std(y) 7 B- {- ?: N3 u: a( o% `y_median = median(y)