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贴一个蒙特卡洛方法的matlab程序,供大家使用。* `: x6 }4 d0 \5 H: i3 D
祝大家比赛都能取得好成绩
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% Example Monte Carlo Simulation in Matlab
5 A6 h3 |# @- |: [% Function: y = x2^2/x1
; G) r- c3 g* k0 a, a% 3 g; v! _2 L8 b) {! |% B
% Generate n samples from a normal distribution : Q2 k& L+ z) d. M) P7 D. H& r
% r = ( randn(n,1) * sd ) + mu
, O; N6 z# y4 @1 P; h4 f/ z" b! Z' z% mu : mean # n8 Z6 }. d$ c! l* ?
% sd : standard deviation
" I: ^6 E* g+ J* R/ h* i; p# S%
b$ ]( q, ^5 G ?3 M$ M- _% Generate n samples from a uniform distribution
( n, o0 D3 c& p. _8 B% r = a + rand(n,1) * (b-a)
/ w# c3 s% c: F* r! p# S" v7 k5 n- [% a : minimum
0 Y. n3 q U! R% b : maximum
6 b! V9 t6 d- bn = 100000; % The number of function evaluations
8 [5 h' X, @2 p+ p/ u8 Y% i3 q% --- Generate vectors of random inputs
6 r' Y' \: G5 O% h+ a% x1 ~ Normal distribution N(mean=100,sd=5) 8 ^2 D; S! `# K( O; e, `
% x2 ~ Uniform distribution U(a=5,b=15) / B; P. ]7 Z0 U5 g
x1 = ( randn(n,1) * 5 ) + 100; 7 Q! E# J- V4 E" g* T' C
x2 = 5 + rand(n,1) * ( 15 - 5 );
, d" Q# y1 Y( m$ Q: B1 P% --- Run the simulation + m* L4 A* q! L3 _ h
% Note the use of element-wise multiplication
# X1 V& U& J9 M* U) ^, ly = x2.^2 ./ x1;
/ r7 n5 m. k( M3 v7 J) ?2 M7 L% --- Create a histogram of the results (50 bins) " G" a4 J! V& S3 B
hist(y,50); 4 L( K2 S( o* p' X
% --- Calculate summary statistics : \2 u/ [- g% F# \4 p" n% r
y_mean = mean(y)
1 |+ N1 \6 A: V, R6 }y_std = std(y) 4 X% b; H& e" ]( R5 w( c
y_median = median(y) |
zan
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