Re: Random Number Generation : Is there a faster way of doing this ?
- To: mathgroup at smc.vnet.net
- Subject: [mg43194] Re: [mg43190] Random Number Generation : Is there a faster way of doing this ?
- From: jmt <jmt at dxdydz.net>
- Date: Mon, 18 Aug 2003 02:50:53 -0400 (EDT)
- References: <200308170828.EAA04316@smc.vnet.net>
- Reply-to: jmt at dxdydz.net
- Sender: owner-wri-mathgroup at wolfram.com
If n is the length of the sample list, and m the number of lists, your problem
is O(n m).
I have made timings on my machine (Pentium 350MHz, Mathematica 5.0), with n=m
10 -> 0.98s
25->5.85s
40->15.88s
80->62.77s
200->393.09s
I let you calculate the timing for n=10000 and m=5000.
I tried using a MathLink function, calling the GNU Scientific Library ; the
speed is roughly eight times better for short series, but longer series make
this code less efiicient - probably transfer times on the link.
Contact me directly if interested in this code.
On Sunday 17 August 2003 10:28, Christos Argyropoulos M.D. wrote:
> Hi,
>
> My problem is that I want to generate a large number of samples from
> Poisson distributions. Specifically the user has to supply a list of the
> parameters for a number of Poisson distributions and then generate a
> number of such samples. In the function below poissonparams is a list of
> the parameters of the Poisson distributions, and size is the number of
> samples. In my application (Analysis of counts of digital gene expression
> profiles), I supply a list of 10000 Poisson Parameters and have to
> generate a big sample of numbers drawn from the 10000 distributions.
> Typically > 1k such samples are required in order to establish a Log
> Likelihood statistic cutoff down the road.
> For the application at hand the poisson parameter can be zero (in this
> case the only point I can sample is the number zero) that is way I do not
> Map . My implementation shown below is ok, except for a small problem; it
> takes too long. In order to generate 5000 samples from each of the 10000
> distributions (this had to be repeated thrice, since I had to analyse 3
> profiles) i.e. total 150 million random numbers my system took close to
> 13 hours. The required overhead to periodically save the data to the HD
> is a very small fraction of the total processing time and given
> limitations of available RAM cannot be improved.
> The question is, is there a faster way of doing this in Mathematica or
> should I be prepared to move outside the kernel for the RNG part?
>
> I am using Mathematica 4.2 on a P4 at 2.2 GHz with 256 DDR RAM running
> Windows XP
>
> Simulate[poissonparams_List,size_Integer]:=
> Module[{},
> fnd[x_]:=
> Map[If[#\[Equal]0,0,Random[PoissonDistribution[#]]]&,
> poissonparams];
> Array[fnd,{size}]
> ]
>
> example of using the code :
>
> In[40]:=
> Simulate[{1,2,3,0.5,0},20]
>
> Out[40]=
> {{1,1,3,1,0},{1,1,3,1,0},{0,3,1,0,0},{3,4,5,0,0},{2,0,3,0,0},{4,4,3,0,0},
>{0, 2,
>
> 5,0,0},{2,1,2,1,0},{2,1,1,0,0},{2,2,2,2,0},{0,2,4,0,0},{0,2,1,0,0},{2,0,2
>,
>
> 1,0},{2,4,1,0,0},{0,2,6,2,0},{1,0,4,3,0},{0,2,1,0,0},{0,0,5,0,0},{1,0,3,0
>, 0},{1,1,3,0,0}}
>
> I.e. generates 20 samples from the 5 Poisson Distributions with
> Parameter lamda 1, 2, 3, 0.5, and zero
>
> Thanks In advance,
>
> Christos Argyropoulos
- References:
- Random Number Generation : Is there a faster way of doing this ?
- From: "Christos Argyropoulos M.D." <argchris@otenet.gr>
- Random Number Generation : Is there a faster way of doing this ?