python vs octave random generator

问题

More specifically, numpy:

In [24]: a=np.random.RandomState(4)
In [25]: a.rand()
Out[25]: 0.9670298390136767
In [26]: a.get_state()
Out[26]: 
('MT19937',
 array([1248735455, ..., 1532921051], dtype=uint32),
 2,0,0.0)

octave:

octave:17> rand('state',4)
octave:18> rand()
ans =  0.23605
octave:19> rand('seed',4)
octave:20> rand()
ans =  0.12852

Octave claims to perform the same algorithm (Mersenne Twister with a period of 2^{19937-1})

Anybody know why the difference?

回答1:

Unfortunately the MT19937 generator in Octave does not allow you to initialise it using a single 32-bit integer as np.random.RandomState(4) does. If you use rand("seed",4) this actually switches to an earlier version of the PRNG used previously in Octave, which PRNG is not MT19937 at all, but rather the Fortran RANDLIB.

It is possible to get the same numbers in NumPy and Octave, but you have to hack around the random seed generation algorithm in Octave and write your own function to construct the state vector out of the initial 32-bit integer seed. I am not an Octave guru, but with several Internet searches on bit manipulation functions and integer classes in Octave/Matlab I was able to write the following crude script to implement the seeding:

function state = mtstate(seed)

state = uint32(zeros(625,1));

state(1) = uint32(seed);
for i=1:623,
   tmp = uint64(1812433253)*uint64(bitxor(state(i),bitshift(state(i),-30)))+i;
   state(i+1) = uint32(bitand(tmp,uint64(intmax('uint32'))));
end
state(625) = 1;

Use it like this:

octave:9> rand('state',mtstate(4));
octave:10> rand(1,5)
ans =

   0.96703   0.54723   0.97268   0.71482   0.69773

Just for comparison with NumPy:

>>> a = numpy.random.RandomState(4)
>>> a.rand(5)
array([ 0.96702984,  0.54723225,  0.97268436,  0.71481599,  0.69772882])

The numbers (or at least the first five of them) match.

Note that the default random number generator in Python, provided by the random module, is also MT19937, but it uses a different seeding algorithm, so random.seed(4) produces a completely different state vector and hence the PRN sequence is then different.

回答2:

If you look at the details of the Mersenne Twister algorithm, there are lots of parameters that affect the actual numbers produced. I don't think Python and Octave are trying to produce the same sequence of numbers.

回答3:

It looks like numpy is returning the raw random integers, whereas octave is normalising them to floats between 0 and 1.0.

来源：https://stackoverflow.com/questions/13735096/python-vs-octave-random-generator