stocc.htm

很好用的随机数产生器

    <br>
    If you want to call the same stochastic functions from more than one thread
    in a multi-threaded program then you have to make these functions re-entrant. There are two ways to do
    this:<br>
    <br>
    Method 1. Find all static local variables in the non-uniform random variate
    generating functions in stoc1.cpp and stoc3.cpp. Make these variables non-static and make the setup in these
    functions non-conditional. Don't use <code>StochasticLib2</code> and
    stoc2.cpp.<br>
    <br>
    Method 2. Find all static local variables in the non-uniform random variate
    generating functions in stoc1.cpp, stoc2.cpp and stoc3.cpp. Make all these variables
    non-static members of the respective class. Those variables that need to be
    initialized to <code>-1</code>  (names ending in <code>_last</code>) must be so in the constructor.<br>
    <br>
    Whether you use method 1 or 2, you have to give each thread its own instance
    of the class and make sure they don't have the same seed. A difference of 1
    in the seeds is sufficient.</li>
  <li>See <a href="randomc.htm">randomc.htm</a> for more portability issues.</li>
</ol>
<h2>Function descriptions</h2>
<dl>
  <dt>int Bernoulli(double p)</dt>
  <dd>Bernoulli distribution with probability parameter p.<br>
    Returns 1 with probability p, or 0 with probability 1-p.<br>
    Error conditions:<br>
    Gives error message if p &lt; 0 or p &gt; 1.</dd>
  <dt>double Normal(double m, double s)</dt>
  <dd>Normal distribution with mean m and standard deviation s.<br>
    This distribution simulates the sum of many random factors.<br>
    Definition:<br>
    f(x) = (2*pi*s<SUP>2</SUP>)<sup>-0.5</sup>*exp(-0.5*s<sup>-2</sup>*(x-m)<sup>2</sup>)<br>
    Error conditions:<br>
    None.</dd>
  <dt>long int Poisson (double L)</dt>
  <dd>Poisson distribution with mean L.<br>
    This is the distribution of the number of events in a given time span or a
    given geographical area when these events are randomly scattered in time or
    space.<br>
    Definition:<br>
    f(x) = L<sup>x</sup>/x! * exp(-L)<br>
    Error conditions:<br>
    Gives error message if L &lt; 0 or L &gt; 2*10<sup>9</sup>.</dd>
  <dt>long int Binomial (long int n, double p)</dt>
  <dd>Binomial distribution with parameters n and p.<br>
    This is the distribution of the number of red balls you get when drawing n
    balls <i>with replacement</i> from an urn where p is the fraction of red
    balls in the urn.<br>
    Definition:<br>
    f(x) = B(n,x) * p<sup>x </sup>* (1-p)<sup>n-x</sup>,<br>
    where the binomial coefficient B(a,b) = a! / (b! * (a-b)!).<br>
    Error conditions:<br>
    Gives error message if n &lt; 0 or p &lt; 0 or p &gt; 1.</dd>
  <dt>long int Hypergeometric (long int n, long int m, long int N)</dt>
  <dd>Hypergeometric distribution with parameters n, m, N. (Note the order of
    the parameters).<br>
    This is the distribution of the number of red balls you get when drawing n
    balls <i>without replacement</i> from an urn where the urn contains N balls,
    where m balls are red and N-m balls are white.<br>
    Definition:<br>
    f(x) = B(m,x) * B(N-m,n-x) / B(N,n),<br>
    where the binomial coefficient B(a,b) = a! / (b! * (a-b)!).<br>
    Error conditions:<br>
    Gives error message if any parameter is negative or n &gt; N or m &gt; N.</dd>
  <dt>long int WalleniusNCHyp(long int n, long int m, long int N, double
    odds)</dt>
  <dd>The Wallenius noncentral hypergeometric distribution is the same as the hypergeometric distribution, but with bias. The bias can be seen
    as an odds ratio. A bias &gt; 1 will favor the red balls, a bias &lt; 1 will
    favor the white balls.<br>
    When bias = 1 we have the hypergeometric distribution.<br>
    Error conditions:<br>
    Gives error message if any parameter is negative or n &gt; N or m &gt; N.</dd>
  <dt>long int FishersNCHyp(long int n, long int m, long int N, double
    odds)</dt>
  <dd>The Fisher's noncentral hypergeometric distribution is a conditional binomial
    distribution resembling the Wallenius noncentral hypergeometric distribution. See the
    file <A HREF="distrib.pdf">distrib.pdf</A> for a definition. Execution may
    be slow and inexact when N is high and bias is far from 1.<br>
    Error conditions:<br>
    Gives error message if any parameter is negative or n &gt; N or m &gt; N.</dd>
  <dt>void Multinomial (long int * destination, double * source, long int n, int colors)<br>
    void Multinomial (long int * destination, long int * source, long int n, int colors)</dt>
  <dd>Multivariate binomial distribution.<br>
    This is the distribution you get when drawing n balls from an urn <i>with
    replacement</i>, where there can be any number of colors. This is the same
    as the binomial distribution when <code>colors</code> = 2.<br>
    The number of balls of each color is returned in <code>destination</code>,
    which must be an array with <code>colors</code> places. <code>source</code>
    contains the number or fraction of balls of each color in the urn. <code>source</code>
    must be a <code>double</code> or <code>long int</code> array with <code>colors</code> places.<br>
    The sum of the values in <code>source</code> does not have to be 1, but it
    must be positive.&nbsp;The probability that a ball has color <code>i</code>
    is <code>source[i]</code> divided by the sum of all values in <code>source</code>.<br>
    Error conditions:<br>
    Gives an error message if any parameter is negative or if the sum of the
    values in <code>source</code> is zero. The behavior is unpredictable if <code>source</code>
    or <code>destination</code>  has less than <code>colors</code> places.</dd>
  <dt>void MultiHypergeo (long int * destination, long int * source, long int n, int colors)</dt>
  <dd>Multivariate hypergeometric distribution.<br>
    This is the distribution you get when drawing n balls from an urn <i>without
    replacement</i>, where there can be any number of colors. This is the same
    as the hypergeometric distribution when <code>colors</code> = 2.<br>
    The number of balls of each color is returned in <code>destination</code>,
    which must be an array with <code>colors</code> places. <code>source</code>
    contains the number of balls of each color in the urn. <code>source</code>
    must be an array with <code>colors</code> places.<br>
    Error conditions:<br>
    Gives an error message if any parameter is negative or if the sum of the
    values in <code>source</code> is less than n. The behavior is unpredictable
    if <code>source</code> or <code>destination</code>  has less than <code>colors</code>
    places.</dd>
  <dt>void MultiWalleniusNCHyp(long int * destination, long int * source, double * weights, long int n, int
    colors)</dt>
  <dd>Multivariate Wallenius noncentral hypergeometric distribution. This is the
    distribution you get when drawing colored balls from un urn <i>without
    replacement</i>, <i>with bias</i>. <code>weights</code>
    is an array with <code>colors</code> places containing the odds for each
    color. The probability of drawing a particular ball is proportional to its
    weight. The other parameters are the same as above.<BR>
    This function may be inexact, but uses an approximation with an accuracy that
    is better than 1% in almost all cases.<br>
    Error conditions:<br>
    Gives an error message if any parameter is negative or if the total number
    of balls with nonzero weight is less than n. The behavior is unpredictable
    if any of the arrays has less than <code>colors</code>
    places.</dd>
  <dt>void MultiFishersNCHyp(long int * destination, long int * source, double * weights, long int n, int
    colors)</dt>
  <dd>The multivariate Fisher's noncentral hypergeometric distribution is a conditional
    binomial distribution resembling the multivariate Wallenius noncentral hypergeometric
    distribution. See the file <A HREF="distrib.pdf">distrib.pdf</A> for a
    definition.<br>
    This function may be inexact, but uses an approximation with an accuracy that
    is better than 1% in most cases. The precision can be tuned at the expense
    of higher calculation times.<br>
    Error conditions:<br>
    Gives an error message if any parameter is negative or if the total number
    of balls with nonzero weight is less than n. The behavior is unpredictable
    if any of the arrays has less than <code>colors</code>
    places.</dd>
  <dt>void Shuffle(int * list, int min, int n)</dt>
  <dd>This function makes a list of the n numbers from&nbsp; <code>min</code>&nbsp;
    to&nbsp; <code>min+n-1</code>&nbsp; in random order.<br>
    The result is returned in <code>list</code>, which must be an array with n elements.<br>
   The array index goes from <code> 0</code> to <code>n-1</code>.<br>
   If you want to shuffle something else than integers then use the   integers in
    <code> list</code> as an index into a table of the items you want to shuffle.<br>
    Error conditions: none. The behavior is unpredictable if the size of the
    array <code>list</code> is less than <code>n</code>.</dd>
  <dt>static double LnFac(long int n)</dt>
  <dd>Log factorial. Mainly used internally.<br>
    Definition:<br>
    LnFac(n) = log<sub>e</sub>(n!).<br>
    This function uses a table when n &lt; 1024 and Stirling's approximation for
    larger n. The table is generated by the constructor.<br>
    Error conditions:<br>
    Gives an error message if n &lt; 0.</dd>
</dl>
<h2>Theory</h2>
<p>These distributions are defined in the file <A HREF="distrib.pdf">distrib.pdf</A>.
The methods used for generating variates with these distributions are described
in the file <A HREF="sampmet.pdf">sampmet.pdf</A>.</p>
<p>A theoretical description of the univariate and multivariate Wallenius and
Fisher's noncentral hypergeometric distributions, including calculation methods and
sampling methods, is given in <A HREF="http://www.agner.org/random/theory/nchyp.pdf">nchyp.pdf</A>.</p>
<p>Examples showing how to simulate biological evolution using this class
library can be found in <a href="evolc.zip">evolc.zip</a>.</p>
<H2>General public license</H2>
<P>