Random Number Generation

From: tylersc111 (scott.tyler_at_[hidden])
Date: 2003-07-23 18:14:16

I've got three questions/comments regarding the Random Number Library:

Question (1) ---------------------------------------------------------

How about including a facility for generating 
"antithetic random variates"?
(Do a google search if the term is unfamiliar).

A partial implementation might be something like the following,
(I haven't tried compiling this, so please pardon any syntax 
errors...):

template< class URNG > // Uniform Random Number Generator
class antithetic
{
private:
   URNG urng;

public:
   explicit antithetic( s ) { urng.seed(s); }
   // Perhaps not quite right (see question (2) below)
   typename URNG::result_type operator()() 
      { return URNG::max_value - urng(); }  
};

Then one would be able to construct two antithetic variates (rng1 & 
rng2) as follows:

mt19937 rng1(seed);
antithetic<mt19937> rng2(seed);

Question (2) --------------------------------------------------------

Regarding the "uniform_01" generator (and a possible bug 
in "uniform_in_sphere").
The interval generated by uniform_01 is designed to be the 
"half-open" interval [0,1).
The asymmetry seems unnecessary.
How about using the open interval (0,1).
I can appreciate that perhaps efficiency is the reason for 
using the interval [0,1) if one is generating the random floating 
point numbers by setting the mantissa with a random bit stream.
But, consider the following advantage to using (0,1):
You would avoid a possible zerodivide in the "uniform_in_sphere" 
class.
Here's my reasoning:
Using the current "uniform_01" generator with the half open interval 
[0,1) the normal_distribution::operator() can return zero.
Using my proposed "uniform_01" generator with the open interval (1,1) 
the normal_distribution::operator() will never return exactly zero.
The "zero" return from normal_distribution::operator() could 
conceivably cause a zerodivide in "uniform_in_sphere".

Question (3) --------------------------------------------------------

How about having a boost random number generator whose output would 
match that of Matlab's random number generator
(both uniform and gaussian)?
This would be useful in doing sanity tests when porting code to/from 
Matlab.
Here's a link which gives some info on their generators:
http://www.mathworks.com/support/solutions/data/8542.shtml