matlab随机函数rand使用中应注意的问题

matlab随机函数rand使用中应注意的问题(2009-04-06 15:49:33)

标签：杂谈

rand产生的是0到1(不包括1)的随机数.

matlab的rand函数生的是伪随机数,即由种子递推出来的,相同的种子,生成相同的随机数.

matlab刚运行起来时,种子都为初始值,因此每次第一次执行rand得到的随机数都是相同的.

1.多次运行,生成相同的随机数方法:

用rand('state',S)设定种子
S为35阶向量，最简单的设为0就好

例:

rand('state',0);rand(10)

2. 任何生成相同的随机数方法:

试着产生和时间相关的随机数,种子与当前时间有关.

rand('state',sum(100*clock))

即:

rand('state',sum(100*clock)) ;rand(10)

只要执行rand('state',sum(100*clock)) ;的当前计算机时间不现,生成的随机值就不现.

也就是如果时间相同,生成的随机数还是会相同.

在你计算机速度足够快的情况下,试运行一下:

rand('state',sum(100*clock));A=rand(5,5);rand('state',sum(100*clock));B=rand(5,5);

A和B是相同.

所以建议再增加一个随机变量,变成:

rand('state',sum(100*clock)*rand(1));

 

 

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据说matlab 的rand 函数还存在其它的根本性的问题,似乎是非随机性问题.

没具体研究及讨论,验证过,不感多言.

有兴趣的可以查阅:

<<A strong nonrandom pattern in Matlab default random number generator>>

 

Petr Savicky
Institute of Computer Science
Academy of Sciences of CR
Czech Republic
savicky@cs.cas.cz
September 16, 2006
Abstract
The default random number generator in Matlab versions between 5 and at least
7.3 (R2006b) has a strong dependence between the numbers zi+1, zi+16, zi+28 in the
generated sequence. In particular, there is no index i such that the inequalities
zi+1 < 1/4, 1/4 zi+16 < 1/2, and 1/2 zi+28 are satisfied simultaneously. This
fact is proved as a consequence of the recurrence relation defining the generator. A
random sequence satisfies the inequalities with probability 1/32. Another example
demonstrating the dependence is a simple function f with values −1 and 1, such that
the correlation between f(zi+1, zi+16) and sign(zi+28 − 1/2) is at least 0.416, while it
should be zero.
A simple distribution on three variables that closely approximates the joint
distribution of zi+1, zi+16, zi+28 is described. The region of zero density in the
approximating distribution has volume 4/21 in the three dimensional unit cube. For
every integer 1 k 10, there is a parallelepiped with edges 1/2k+1, 1/2k and 1/2k+1,
where the density of the distribution is 2k. Numerical simulation confirms that the
distribution of the original generator matches the approximation within small random
error corresponding to the sample size.