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<H1><A NAME="SECTION001300000000000000000">
Random Numbers</A>
</H1>
Adevs has two classes that work together to generate random numbers. These classes are the <B>random_seq</B> class and the <B>rv</B> class. The <B>random_seq</B> class provides uniformly distributed random numbers to the <B>rv</B> class. The <B>rv</B> class transforms these uniform random numbers into a variety of random number distributions.

<P>
The <B>random_seq</B> class is the interface for a random number generator. Its derived classes produce uniformly distributed pseudo-random numbers. The underlying random number stream is accessed with two methods. The method <B><I>next_long</I></B> returns a random number as an unsigned long. The method <B><I>next_dlb</I></B> refines the <B><I>next_long</I></B> method by reducing that random number to a double precision number in the interval <IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img59.png"
 ALT="$ [0,1]$">
. The random number sequence is initialized with the <B><I>set_seed</I></B> method, and the entire random number generator can be copied with the <B><I>copy</I></B> method. To summarize, the <B>random_seq</B> class has four virtual methods
<PRE>
void set_seed(unsigned long seed) 
double next_dbl() 
random_seq* copy() const 
unsigned long next_long()
</PRE>
that must be implemented by any derived class.

<P>
Adevs comes with two implementations of the <B>random_seq</B> class: the <B>crand</B> class and the <B>mtrand</B> class. The <B>crand</B> class uses the rand function from the standard C library to implement the required methods. Its implementation is trivial. I've listed it below as an example of how to implement the <B>random_seq</B> interface.
<PRE>
class crand: public random_seq {
    public:
        /// Create a generator with the default seed
        crand(){}
        /// Create a generator with the given seed
        crand(unsigned long seed) { srand (seed); }
        /// Set the seed for the random number generator
        void set_seed(unsigned long seed) { srand (seed); }
        /// Get the next double uniformly distributed in [0, 1]
        double next_dbl() { return (double)rand()/(double)RAND_MAX; } 
        /// Copy the random number generator
        unsigned long next_long() { return (unsigned long)rand(); }

        random_seq* copy() const { return new crand (); }
        /// Destructor
        ~crand(){}
};
</PRE>

<P>
The <B>mtrand</B> class implements the Mersenne Twister random number generator<A NAME="tex2html30"
  HREF="footnode.html#foot3019"><SUP>12.1</SUP></A>. This code is based on their open source implementation of the Mersenne Twister. Aside from its potential advantages as a random number generator, the <B>mtrand</B> class differs from the <B>crand</B> class by its ability to make deep copies. Every instance of the <B>mtrand</B> class has its own random number stream.

<P>
The <B>rv</B> class uses the uniform random numbers provided by a <B>random_seq</B> object to produce several different random number distributions: triangular, uniform, normal, exponential, lognormal, Poisson, Weibull, binomial, and many others. Every instance of the <B>rv</B> class is created with a <B>random_seq</B>. The default is an <B>mtrand</B> object, but any type of <B>random_seq</B> object can be passed to the <B>rv</B> constructor. The different random distributions are sampled by calling the appropriate method: <B><I>triangular</I></B> for a triangular distribution, <B><I>exponential</I></B> for an exponential distribution, <B><I>poisson</I></B> for a Poisson distribution, etc. Because Adevs is open source software, if a new distribution is needed then you can add a method that implements it to the <B>rv</B> class (and, I hope, contribute the expansion to the Adevs project).
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2013-06-18
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