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贴一个蒙特卡洛方法的matlab程序,供大家使用。
5 e5 y* y! A4 [" P& ~( ^/ d祝大家比赛都能取得好成绩 " X! |8 y+ y# s0 i8 [+ W' j
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% Example Monte Carlo Simulation in Matlab + C% x6 B, m3 u( U9 v
% Function: y = x2^2/x1
- s- r! G1 u, V% n! i; f: ]3 m% : @! \2 C( f7 Q2 R i
% Generate n samples from a normal distribution 0 q( d/ a: U; v6 s) G X
% r = ( randn(n,1) * sd ) + mu ( z( @. Q2 G9 Q: a* }
% mu : mean
% W, l. u( j- B& @% sd : standard deviation 5 N4 X0 U; R: w8 A
%
% X2 a2 J! q, w+ b/ r% Generate n samples from a uniform distribution 8 l3 u) W4 i t: u
% r = a + rand(n,1) * (b-a)
/ d( x7 b% { I5 O/ A- ?% t% a : minimum
" J# o* F4 G T+ ?% b : maximum $ G2 ^& d, v) V# Y
n = 100000; % The number of function evaluations ( S3 U* v* t ~6 r# M% G% f, k
% --- Generate vectors of random inputs
7 F" d1 T* z; {& F% a% A* u3 M2 q) C% x1 ~ Normal distribution N(mean=100,sd=5)
6 U) S% L# z1 _/ @2 s) }2 K1 k% x2 ~ Uniform distribution U(a=5,b=15) 7 n/ L8 s% D1 J8 {3 M2 ^2 ]! f
x1 = ( randn(n,1) * 5 ) + 100;
6 l* d' ]) Q( G2 jx2 = 5 + rand(n,1) * ( 15 - 5 );
+ L/ C' x2 x) Y4 ]6 {& b4 \" z9 c8 a: I% --- Run the simulation
+ e H4 N3 \( W2 a3 n. a4 j3 r+ [% Note the use of element-wise multiplication
" i$ j. i! E& S" ly = x2.^2 ./ x1;
- o( A* R! `. c0 o+ Z6 L$ H% --- Create a histogram of the results (50 bins)
8 X Z. u' a( w4 q9 g3 t; vhist(y,50); ! T- q' i, X7 M4 L) K$ X7 t( v
% --- Calculate summary statistics
8 A( H$ u5 n+ ^y_mean = mean(y) 1 m( s9 |: e' n8 ?1 J
y_std = std(y)
6 D/ |4 q+ R( Ky_median = median(y) |
zan
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