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<HTML><HEAD><TITLE> Random Variate Generation Routines </TITLE></HEAD><BODY><H1> Random Variate Generation Routines </H1><P>This module provides facilities for basic pseudo-random number generation,and for generation of random variates from various common distributions.<P>All the random generation procedures use the same underlying"stream" of random numbers. This stream is generated using the<TT>nrand48</TT> pseudo-random generation procedure found on most Unixsystems, with the output being combined with a limited supply of realrandom numbers from the file "randfile" in the sourcedirectory for this software, in order to reduce the chances that thepseudo-random numbers aren't random enough.<P>A pseudo-random number stream is determined by an integer<I>seed</I>, which is typically set by the user for each experimentalrun (eg, to 1, 2, 3, etc. for successive runs). The state of therandom number stream can be saved in a structure of type<TT>rand_state</TT>, and later restored. For example, the state couldbe saved in a file at the end of a run, and restored if it is laterdecided that the run should be continued for longer.<P>The methods for generating random variates from various distributionsare mostly taken from the following reference:<BLOCKQUOTE> Devroye, L. (1986) <I>Non-Uniform Random Variate Generation</I>, New York: Springer-Verlag.</BLOCKQUOTE>The methods used here are not necessarily the fastest available. They wereselected to be reasonably fast while also being easy to write.<P><B>Header file required</B>: <TT>rand.h</TT><A NAME="get-set-sec"><P><HR><CENTER><BIG>Setting and saving the state</BIG></CENTER></A><A NAME="seed"><HR><B>rand_seed</B>: Set the state from an integer seed.</A><BLOCKQUOTE><PRE>void rand_seed( int seed; /* Seed to set state based on */)</PRE></BLOCKQUOTE> <P>Sets the random number generator to a state that is determined fromthe integer <TT>seed</TT>. Setting the seed the same on two occasions,and then calling exactly the same sequence of random generationprocedures, should produce exactly the same sequence of randomvariates. (Note: this may not be true, however, if computers withdifferent architectures are used on the two occasions.)<P>Sequential seeds should produce streams that are pretty muchindependent (unlike the situation for some pseudo-random numbergenerators). Setting the seed randomly according to the time or day,or some such, without recording what it was, is <B>not</B>recommended, since the results are then not reproducible.<P><A NAME="get_state"><HR><B>rand_get_state</B>: Get a pointer to the current state.</A><BLOCKQUOTE><PRE>rand_state *rand_get_state (void)</PRE></BLOCKQUOTE>Returns a pointer to the current state of the random number generator,which is a structure of type <TT>rand_state</TT>. The only use for thispointer is to use it to save a copy of the current state someplace.<P><A NAME="use_state"><HR><B>rand_use_state</B>: Set the state to use from now on.</A><BLOCKQUOTE><PRE>void rand_use_state ( rand_state *state /* Pointer to a previously saved state */)</PRE></BLOCKQUOTE>Sets the random number generator to the state pointed to by the argument.This state must be valid. The only way to get a valid state is by using<TT>rand_get_state</TT>.<A NAME="uniform-sec"><P><HR><CENTER><BIG>Generating uniform random variates</BIG></CENTER></A><A NAME="uniform"><HR><B>rand_uniform</B>: Generate uniformly from [0,1).</A><BLOCKQUOTE><PRE>double rand_uniform (void)</PRE></BLOCKQUOTE>Returns a random number that is uniformly distributed between 0 and 1,with a value of exactly 0 being possible, but with a value of exactly 1not being possible.<P><A NAME="uniopen"><HR><B>rand_uniopen</B>: Generate uniformly from (0,1).</A><BLOCKQUOTE><PRE>double rand_uniopen (void)</PRE></BLOCKQUOTE>Returns a random number that is uniformly distributed between 0 and 1,with neither a value of exactly 0 nor a value of exactly 1being possible.<A NAME="discrete-sec"><P><HR><CENTER><BIG>Generating discrete random variates</BIG></CENTER></A><A NAME="int"><HR><B>rand_int</B>: Pick an integer uniformly from <I>0</I> to <I>n-1</I>.</A><BLOCKQUOTE><PRE>int rand_int ( int n /* Number of integers (from 0) to pick from */)</PRE></BLOCKQUOTE><P>Randomly picks an integer from the set { <TT>0, 1, ..., n-1</TT> },with each integer being equally probable. The probabilities maybecome somewhat unequal, however, if <TT>n</TT> is very large,approaching 2<SUP><SMALL>31</SMALL></SUP>.<P><A NAME="pickd"><HR><B>rand_pickd</B>: Pick an integer from <I>0</I>to <I>n-1</I> with given probabilities (as doubles).</A><BLOCKQUOTE><PRE>int rand_pickd( double *p, /* Array of probabilities, of length n */ int n /* Number of integers (from 0) to pick from */)</PRE></BLOCKQUOTE><P>Randomly picks an integer from the set { <TT>0, 1, ..., n-1</TT> },with probabilities given by the array of double-precision numberspassed as the first argument. These numbers need not sum to one, but theymust be non-negative, and must not all be zero. The actualprobabilities used are obtained by dividing each number in this arrayby the sum of all the numbers. <P>If one of the probabilities is exactly zero, it is guaranteed thatthe corresponding integer will not be picked.<P><A NAME="pickf"><HR><B>rand_pickf</B>: Pick an integer from <I>0</I>to <I>n-1</I> with given probabilities (as floats).</A><BLOCKQUOTE><PRE>int rand_pickf( float *p, /* Array of probabilities, of length n */ int n /* Number of integers (from 0) to pick from */)</PRE></BLOCKQUOTE><P>This procedure is the same as <A HREF="#pickd"><TT>rand_pickd</TT></A>except that the array giving the probabilities is an array of single-precisionfloating point numbers, rather than double-precision.<A NAME="continuous-sec"><P><HR><CENTER><BIG>Generating continuous random variates</BIG></CENTER></A><A NAME="gaussian"><HR><B>rand_gaussian</B>: Generate a standard Gaussian (normal) random variate.</A><BLOCKQUOTE><PRE>double rand_gaussian (void)</PRE></BLOCKQUOTE><P>Generates a random value drawn from the Gaussian (normal) distributionwith mean zero and standard deviation one, whose density function is proportional to exp(-<I>x<SUP><SMALL>2</SMALL></SUP></I>/2), with <I>x</I>being any real value.<A NAME="logistic"><HR><B>rand_logistic</B>: Generate a logistic random variate.</A><BLOCKQUOTE><PRE>double rand_logistic (void)</PRE></BLOCKQUOTE><P>Generates a random value drawn from the logistic distribution withlocation parameter zero and width parameter one, whose densityfunction is proportional to exp(-<I>x</I>) / [1 + exp(-<I>x</I>)]<SUP><SMALL>2</SMALL></SUP>, with <I>x</I> being any real value.<P><A NAME="cauchy"><HR><B>rand_cauchy</B>:Generate a Cauchy random variate.</A><BLOCKQUOTE><PRE>double rand_cauchy (void)</PRE></BLOCKQUOTE><P>Generates a random value drawn from the Cauchy distribution with centreat zero and width one, whose density function is proportional to 1 / (1+<I>x<SUP><SMALL>2</SMALL></SUP></I>), with <I>x</I> being any real value.<P><A NAME="gamma"><HR><B>rand_gamma</B>:Generate a gamma-distributed random variate.</A><BLOCKQUOTE><PRE>double rand_gamma( double A /* Shape parameter */)</PRE></BLOCKQUOTE><P>Generates a random value drawn from the gamma distribution withpositive shape parameter <I>A</I>, whose density function is proportionalto <I>x<SUP><SMALL>A-1</SMALL></SUP></I> exp(-<I>x</I>), with <I>x</I>being any positive real. This procedure will never return a value that isexactly zero.<P><A NAME="exp"><HR><B>rand_exp</B>:Generate an exponentially-distributed random variate.</A><BLOCKQUOTE><PRE>double rand_exponential (void)</PRE></BLOCKQUOTE><P>Generates a random value drawn from the exponential distribution with mean one, whose density function is exp(-<I>x</I>), with <I>x</I> beingany positive real. This procedure will never return a value that isexactly zero. <P>Note: This is a common special case of the gamma distribution.<P><A NAME="beta"><HR><B>rand_beta</B>:Generate a beta-distributed random variate.</A><BLOCKQUOTE><PRE>double rand_beta( double A, /* Parameters of distribution */ double B)</PRE></BLOCKQUOTE><P>Generates a random value drawn from the beta distribution with positiveparameters <I>A</I> and <I>B</I>, whose density function is proportionalto <I>x<SUP><SMALL>A-1</SMALL></SUP>(1-x)<SUP><SMALL>B-1</SMALL></SUP></I>,with <I>x</I> being any real in the interval (0,1). This procedurewill never return a value that is exactly zero or exactly one.<HR><A HREF="index.html">Back to index for LDPC software</A></BODY></HTML>⌨️ 快捷键说明
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