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贴一个蒙特卡洛方法的matlab程序,供大家使用。; O3 z9 d3 v4 @1 }: y
祝大家比赛都能取得好成绩 6 e" C& j' ^, h Y/ x
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: W X6 x' j; P2 q/ `6 P1 W) Z$ |. {% Example Monte Carlo Simulation in Matlab
: ~1 Q. a4 c ]- ^9 z5 i8 V& D% Function: y = x2^2/x1 7 s1 f0 y: v/ I7 Q6 N0 ~7 O
% ) T, m: M3 z- M. S1 s8 C: W
% Generate n samples from a normal distribution
" @. a5 z3 q4 N/ w; T: ^# u% r = ( randn(n,1) * sd ) + mu 6 H2 J4 n, M F) c/ k \- `$ O
% mu : mean 7 Z1 \8 a4 @' L1 s" K/ m* N6 B
% sd : standard deviation 5 z( p2 f2 g+ {8 W6 l7 M
% : H; ?0 e& f8 Y5 @# g; x+ k
% Generate n samples from a uniform distribution
% E9 K/ r# Z% i% D+ O* o$ R% r = a + rand(n,1) * (b-a) " h% N3 N% Q8 J
% a : minimum ! n5 d* _, _, I# N% t: ]' e/ |
% b : maximum
+ @* `3 [( B6 |8 K2 vn = 100000; % The number of function evaluations ( s4 H3 ~: K4 Q3 [ p! U; d
% --- Generate vectors of random inputs
" \6 ^8 t9 m: F0 H1 R6 v3 S% x1 ~ Normal distribution N(mean=100,sd=5)
, g5 _# A. L) o1 u; @% x2 ~ Uniform distribution U(a=5,b=15) . `& |0 d. u/ U4 f
x1 = ( randn(n,1) * 5 ) + 100; ( C, l7 B; C* V$ c
x2 = 5 + rand(n,1) * ( 15 - 5 );
0 ?* @8 w" I% |, Z5 H6 `$ ?, {% --- Run the simulation
! i) O, t2 b( G u% M% Note the use of element-wise multiplication
. r) t* v7 z$ D1 V" T8 i& Uy = x2.^2 ./ x1;
3 z& t: ]# Z6 a, N% --- Create a histogram of the results (50 bins)
! l" s1 W' A! ?* Y2 e! J; c5 ~6 jhist(y,50); 3 n' k5 B- M6 }. e
% --- Calculate summary statistics
1 a5 f3 w" o, g% @. py_mean = mean(y) & w# P9 E1 z* m1 l' c9 K0 \
y_std = std(y) ; M! v2 {. N5 t: d/ e+ g6 y( J9 t4 i
y_median = median(y) |
zan
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