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贴一个蒙特卡洛方法的matlab程序,供大家使用。5 e+ {1 s$ } I+ D8 D5 w
祝大家比赛都能取得好成绩 % w2 m/ f1 @ F( Q, N( V
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% Example Monte Carlo Simulation in Matlab * l& I1 Z- ]/ I% N
% Function: y = x2^2/x1
" \2 b# t1 M, F% D5 q% v% 2 _# g! V5 a" z% Q ~
% Generate n samples from a normal distribution
- G1 t: }* g1 R! w. q# q/ P0 {8 a% r = ( randn(n,1) * sd ) + mu
* ?5 j9 _9 @; [% mu : mean 9 [! {0 y+ f" h3 ~- T
% sd : standard deviation
* H( h, ]# n. e# x8 y% 6 p/ i. O) _9 G& p# h
% Generate n samples from a uniform distribution
4 I; x- x- i* ?9 `; H- u. T3 s% r = a + rand(n,1) * (b-a)
g) D+ v5 M C: d% a : minimum
7 X; R+ j! o7 C0 J( E& s' }/ c" B; M& u% b : maximum
% l" e6 X3 O a) o, E, k) z! Ln = 100000; % The number of function evaluations
/ c" o. Y6 C6 W0 n8 W% --- Generate vectors of random inputs g) E2 V2 B; J/ Q/ _
% x1 ~ Normal distribution N(mean=100,sd=5) % X/ B8 s: g1 h4 N1 F: e
% x2 ~ Uniform distribution U(a=5,b=15)
& V- o7 G: h: d+ B* Ox1 = ( randn(n,1) * 5 ) + 100; # R2 i9 _: C+ [3 S. e5 w" J
x2 = 5 + rand(n,1) * ( 15 - 5 ); " ^1 M$ F0 V }2 A, ?
% --- Run the simulation
* @- H) e6 d' P& \( @' E X! D; \% Note the use of element-wise multiplication 2 t1 |! \' A5 u4 @+ Z7 e, [
y = x2.^2 ./ x1;
: j0 C1 `/ s* `" B: x* V5 B% --- Create a histogram of the results (50 bins) 0 U5 S5 J, N9 t- c& Z5 c
hist(y,50); 5 {) |7 d! \4 B% W( `7 q
% --- Calculate summary statistics
3 [7 W% s. j* S- Dy_mean = mean(y) 3 L6 X" d/ i& _8 C4 |
y_std = std(y)
4 n; o1 Q9 }2 @0 gy_median = median(y) |
zan
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