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贴一个蒙特卡洛方法的matlab程序,供大家使用。* z: e1 F" d# Z) B
祝大家比赛都能取得好成绩
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% Example Monte Carlo Simulation in Matlab
8 J6 `6 G& f. }/ d o% Function: y = x2^2/x1 " _& M; X r, q! g' T: r
% ' r8 k2 R7 h; V% s0 H: r* ?
% Generate n samples from a normal distribution
0 z+ f2 }, B7 w/ f% r = ( randn(n,1) * sd ) + mu
: d# S# M' @$ E) H" E2 P, }1 l+ r% mu : mean - [+ u' d9 O4 _
% sd : standard deviation
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) {; g& d- x% m/ G% Generate n samples from a uniform distribution ! H) `2 h* u8 D' p
% r = a + rand(n,1) * (b-a) # [) C, r; f, p
% a : minimum
* d3 \1 h, s1 G- ]; ], e% b : maximum
) B8 t' m* U" ^/ u' n# Gn = 100000; % The number of function evaluations
' A2 X# O5 }& f1 x, ]' ?% --- Generate vectors of random inputs / o3 P' L% h" ?: V; L, A8 T
% x1 ~ Normal distribution N(mean=100,sd=5) + U, y8 z9 K4 L+ @( h' T
% x2 ~ Uniform distribution U(a=5,b=15) & O; u2 \6 F& L" ]: q- `, \$ _. i
x1 = ( randn(n,1) * 5 ) + 100;
8 r; v1 B1 X5 V' m# |- o# tx2 = 5 + rand(n,1) * ( 15 - 5 ); $ y/ a7 _+ r0 V b: L
% --- Run the simulation 1 U z3 G4 q5 i5 R+ @3 ?2 t% p
% Note the use of element-wise multiplication % f! x8 c! Z$ V% O6 ~( |1 X
y = x2.^2 ./ x1;
8 {$ ]6 ]5 L' d% O! M3 j% O r6 Z% --- Create a histogram of the results (50 bins) ! v5 l8 i! Z; w. {# V6 Y& j
hist(y,50);
3 K, X# h: n8 t$ C2 B8 u% E8 B% --- Calculate summary statistics
4 N2 y$ E! q5 {; V" t, m' cy_mean = mean(y) ( x: @7 _; J1 k4 N# B
y_std = std(y)
6 Q: V1 r7 S5 C$ M* g/ @. Q% s+ ?y_median = median(y) |
zan
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