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贴一个蒙特卡洛方法的matlab程序,供大家使用。
4 [4 ` r; Y, n6 F! A9 W. I4 ~6 N m祝大家比赛都能取得好成绩
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+ m+ ~! r2 T4 l* P/ ]4 \& x
$ W% f! r7 p5 Q! u& T! O' g% Example Monte Carlo Simulation in Matlab * U& ?8 }9 d" f2 K4 ]! ^2 [. @
% Function: y = x2^2/x1
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6 x* d6 l3 n' u, _2 }1 C% Generate n samples from a normal distribution
0 u) ]5 t4 \ a( B+ r8 F/ s& ~% r = ( randn(n,1) * sd ) + mu
, W3 _* |9 P- j) r+ y: x6 e% mu : mean 2 a9 w8 I- X1 \+ l& c( Z
% sd : standard deviation 8 s2 m6 ~" {* y6 o
%
4 `5 v. B% x' m! ]) r- X% Generate n samples from a uniform distribution , I9 x& ~% @; |4 M$ @+ ]9 A
% r = a + rand(n,1) * (b-a)
9 T6 l! x7 p8 H0 e! N% a : minimum
: C2 x# d- W* a% [! N& Q- e% b : maximum ; i7 j+ [5 ^3 [+ T- x7 _
n = 100000; % The number of function evaluations I5 x) B$ q9 M f5 A
% --- Generate vectors of random inputs + Y/ V" P/ Z- R+ d- U- x {; D
% x1 ~ Normal distribution N(mean=100,sd=5)
# d0 s$ U2 m$ A; ^% x2 ~ Uniform distribution U(a=5,b=15) 5 ~4 j' [' S' ^1 T3 k
x1 = ( randn(n,1) * 5 ) + 100;
3 C. O% z& \- \4 N, X" p8 Wx2 = 5 + rand(n,1) * ( 15 - 5 );
: ^: H( D6 A, }; G; l* v% --- Run the simulation
: P* e% b0 G4 P$ ?& V% q% Note the use of element-wise multiplication ! c0 ^! f, t3 y% _
y = x2.^2 ./ x1;
3 k3 T* W# O( A, J( i$ |8 Y1 B5 p$ Y% --- Create a histogram of the results (50 bins) ( {& @% ` Z' N" c1 w
hist(y,50);
) G1 L" E4 `5 H3 o$ m% --- Calculate summary statistics
( y8 }# _% Y- Y6 [, my_mean = mean(y)
/ l0 A. p; G5 G: X- {y_std = std(y)
! I' w, z. h; H3 ?( Vy_median = median(y) |
zan
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