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贴一个蒙特卡洛方法的matlab程序,供大家使用。
" ~! z1 K A5 `4 A4 H6 O祝大家比赛都能取得好成绩
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% Example Monte Carlo Simulation in Matlab + ?( q' |- v% w, V0 Z
% Function: y = x2^2/x1
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2 P. R; `5 ?" r% Generate n samples from a normal distribution
% [* w, U6 ]) }& ~; g8 u' n; d% r = ( randn(n,1) * sd ) + mu 8 S( [% N! m) u
% mu : mean
% @7 X$ p( y8 k8 U# g6 o: ^% c% sd : standard deviation
3 y4 q( H, W/ G) C+ g& l2 Q& q%
8 t; t7 H# k( M) {4 [2 s5 o3 B% Generate n samples from a uniform distribution
5 v/ P8 n7 l5 O- S- J% r = a + rand(n,1) * (b-a)
* `" R8 m/ g8 G- F5 i4 B% a : minimum $ r& ] J0 M" b- {; E' }# W
% b : maximum 5 q+ N" k+ u: F; g
n = 100000; % The number of function evaluations ; P6 s o/ y& I2 n( |5 H
% --- Generate vectors of random inputs
# l# M7 `2 B" @) ~5 G% x1 ~ Normal distribution N(mean=100,sd=5)
- ?+ \1 u1 M: U- H, ]. d5 D$ V% s% x2 ~ Uniform distribution U(a=5,b=15)
6 J; c* s. d4 _8 i8 q2 e( r8 lx1 = ( randn(n,1) * 5 ) + 100;
( K; M9 q& y' u2 H" Sx2 = 5 + rand(n,1) * ( 15 - 5 );
# H$ h0 h9 M: S5 U$ N5 d' G- @% --- Run the simulation ' @* m z/ u0 W0 u! k$ h
% Note the use of element-wise multiplication - t0 f6 Z# I: H% L6 Z
y = x2.^2 ./ x1;
+ u- P+ ~0 n% z& x% --- Create a histogram of the results (50 bins)
9 g6 ]$ T/ I1 J# t+ D- chist(y,50); 4 L2 ~: d; ^2 D' U! a2 j' T; f8 `
% --- Calculate summary statistics
, B$ n6 a. y; r' C. R# m8 K Qy_mean = mean(y)
; T1 r9 s6 a" J0 q$ \' E# R: m3 Py_std = std(y) M" v, V3 O% K7 C5 y1 ]
y_median = median(y) |
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