<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>GEN21</title>
<link rel="stylesheet" type="text/css" href="csound.css" />
<meta name="generator" content="DocBook XSL Stylesheets V1.76.1" />
<link rel="home" href="index.html" title="The Canonical Csound Reference Manual" />
<link rel="up" href="ScoregensTop.html" title="Score Statements and GEN Routines" />
<link rel="prev" href="GEN20.html" title="GEN20" />
<link rel="next" href="GEN23.html" title="GEN23" />
</head>
<body>
<div class="navheader">
<table width="100%" summary="Navigation header">
<tr>
<th colspan="3" align="center">GEN21</th>
</tr>
<tr>
<td width="20%" align="left"><a accesskey="p" href="GEN20.html">Prev</a> </td>
<th width="60%" align="center">Score Statements and GEN Routines</th>
<td width="20%" align="right"> <a accesskey="n" href="GEN23.html">Next</a></td>
</tr>
</table>
<hr />
</div>
<div class="refentry" title="GEN21">
<a id="GEN21"></a>
<div class="titlepage"></div>
<a id="IndexGEN21" class="indexterm"></a>
<div class="refnamediv">
<h2>
<span class="refentrytitle">GEN21</span>
</h2>
<p>GEN21 —
Generates tables of different random distributions.
</p>
</div>
<div class="refsect1" title="Description">
<a id="idp77917352"></a>
<h2>Description</h2>
<p>
This generates tables of different random distributions. (See also <a class="link" href="betarand.html" title="betarand"><em class="citetitle">betarand</em></a>, <a class="link" href="bexprnd.html" title="bexprnd"><em class="citetitle">bexprnd</em></a>, <a class="link" href="cauchy.html" title="cauchy"><em class="citetitle">cauchy</em></a>, <a class="link" href="exprand.html" title="exprand"><em class="citetitle">exprand</em></a>, <a class="link" href="gauss.html" title="gauss"><em class="citetitle">gauss</em></a>, <a class="link" href="linrand.html" title="linrand"><em class="citetitle">linrand</em></a>, <a class="link" href="pcauchy.html" title="pcauchy"><em class="citetitle">pcauchy</em></a>, <a class="link" href="poisson.html" title="poisson"><em class="citetitle">poisson</em></a>, <a class="link" href="trirand.html" title="trirand"><em class="citetitle">trirand</em></a>, <a class="link" href="unirand.html" title="unirand"><em class="citetitle">unirand</em></a>, and <a class="link" href="weibull.html" title="weibull"><em class="citetitle">weibull</em></a>)
</p>
</div>
<div class="refsect1" title="Syntax">
<a id="idp77978576"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 21 type level [arg1 [arg2]]</pre>
</div>
<div class="refsect1" title="Initialization">
<a id="idp77979624"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>time</em></span> and <span class="emphasis"><em>size</em></span> are the usual GEN function arguments. <span class="emphasis"><em>level</em></span> defines the amplitude. Note that GEN21 is not self-normalizing as are most other GEN functions. <span class="emphasis"><em>type</em></span> defines the distribution to be used as follow:
</p>
<div class="itemizedlist">
<ul class="itemizedlist" type="disc">
<li class="listitem">
<p>1 = Uniform (positive numbers only)</p>
</li>
<li class="listitem">
<p>2 = Linear (positive numbers only)</p>
</li>
<li class="listitem">
<p>3 = Triangular (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>4 = Exponential (positive numbers only)</p>
</li>
<li class="listitem">
<p>5 = Biexponential (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>6 = Gaussian (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>7 = Cauchy (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>8 = Positive Cauchy (positive numbers only)</p>
</li>
<li class="listitem">
<p>9 = Beta (positive numbers only)</p>
</li>
<li class="listitem">
<p>10 = Weibull (positive numbers only)</p>
</li>
<li class="listitem">
<p>11 = Poisson (positive numbers only)</p>
</li>
</ul>
</div>
<p>
Of all these cases only 9 (Beta) and 10 (Weibull) need extra arguments. Beta needs two arguments and Weibull one.
</p>
<p>
If <span class="emphasis"><em>type</em></span> = 6, the random numbers in the ftable follow a normal distribution centered
around 0.0 (mu = 0.0) with a variance (sigma) of <span class="emphasis"><em>level</em></span> / 3.83. Thus more than 99.99%
of the random values generated are in the range -<span class="emphasis"><em>level</em></span> to +<span class="emphasis"><em>level</em></span>.
The default value for <span class="emphasis"><em>level</em></span> is 1 (sigma = 0.261).
If a mean value different of 0.0 is desired, this mean value has to be added to the generated numbers.
</p>
</div>
<div class="refsect1" title="Examples">
<a id="idp77988056"></a>
<h2>Examples</h2>
<p>
</p>
<div class="informalexample">
<pre class="programlisting">
<span class="stamnt">f</span>1 0 1024 21 1 <span class="comment">; Uniform (white noise)</span>
<span class="stamnt">f</span>1 0 1024 21 6 <span class="comment">; Gaussian (mu=0.0, sigma=1/3.83=0.261)</span>
<span class="stamnt">f</span>1 0 1024 21 6 5.745 <span class="comment">; Gaussian (mu=0.0, sigma=5.745/3.83=1.5)</span>
<span class="stamnt">f</span>1 0 1024 21 9 1 1 2 <span class="comment">; Beta (note that level precedes arguments)</span>
<span class="stamnt">f</span>1 0 1024 21 10 1 2 <span class="comment">; Weibull</span></pre>
</div>
<p>
All of the above additions were designed by the author between May and December 1994, under the supervision of Dr. Richard Boulanger.
</p>
<p>
Here is a complete example of the GEN21 routine. It uses the file <a class="ulink" href="examples/gen21.csd" target="_top"><em class="citetitle">gen21.csd</em></a>.
</p>
<div class="example">
<a id="idp77993472"></a>
<p class="title">
<strong>Example 1057. Example of the GEN21 routine.</strong>
</p>
<div class="example-contents">
<p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
<pre class="programlisting">
<span class="csdtag"><CsoundSynthesizer></span>
<span class="csdtag"><CsOptions></span>
<span class="comment">; Select audio/midi flags here according to platform</span>
-odac <span class="comment">;;;realtime audio out</span>
<span class="comment">;-iadc ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o gen21.wav -W ;;; for file output any platform</span>
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">ksmps</span> <span class="op">=</span> 32
<span class="ohdr">nchnls</span> <span class="op">=</span> 2
<span class="ohdr">0dbfs</span> <span class="op">=</span> 1
<span class="oblock">instr</span> 1
ifn <span class="op">=</span> p4
isize <span class="op">=</span> <span class="opc">ftlen</span>(ifn)
<span class="opc">prints</span> "TABLE NUMBER<span class="op">:</span> <span class="op">%</span>d\n", ifn
<span class="opc">prints</span> "Index\tValue\n"
iindex <span class="op">=</span> 0 <span class="comment">;start loop</span>
<span class="olabel">begin_loop</span><span class="op">:</span>
ivalue <span class="opc">tab_i</span> iindex, ifn
<span class="opc">prints</span> "<span class="op">%</span>d<span class="op">:</span>\t<span class="op">%</span>f\n", iindex, ivalue
iindex <span class="op">=</span> iindex <span class="op">+</span> 1
<span class="octrl">if</span> (iindex <span class="op"><</span> isize) <span class="octrl">igoto</span> <span class="olabel">begin_loop</span>
<span class="comment">;produce sound - and repeat it 10 times so you can hear the patterns: </span>
aphase <span class="opc">phasor</span> 10<span class="op">/</span>10 <span class="comment">;play all 32 values 10x over 10 seconds</span>
aphase <span class="op">=</span> aphase<span class="op">*</span>isize <span class="comment">;step through table</span>
afrq <span class="opc">table</span> aphase, p4 <span class="comment">;read table number</span>
asig <span class="opc">poscil</span> .5, (afrq<span class="op">*</span>500)<span class="op">+</span>1000,10 <span class="comment">;scale values of table 500 times, add 1000 Hz</span>
<span class="opc">outs</span> asig , asig <span class="comment">;so we can distinguish the different tables </span>
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="stamnt">f</span>1 0 32 21 1 <span class="comment">;Uniform (white noise)</span>
<span class="stamnt">f</span>2 0 32 21 6 <span class="comment">;Gaussian (mu=0.0, sigma=1/3.83=0.261)</span>
<span class="stamnt">f</span>3 0 32 21 6 5.745 <span class="comment">;Gaussian (mu=0.0, sigma=5.745/3.83=1.5)</span>
<span class="stamnt">f</span>4 0 32 21 9 1 1 2 <span class="comment">;Beta (note that level precedes arguments)</span>
<span class="stamnt">f</span>5 0 32 21 10 1 2 <span class="comment">;Weibull</span>
<span class="stamnt">f</span>10 0 8192 10 1 <span class="comment">;Sine wave</span>
<span class="stamnt">i</span> 1 0 10 1
<span class="stamnt">i</span> 1 11 10 2
<span class="stamnt">i</span> 1 22 10 3
<span class="stamnt">i</span> 1 33 10 4
<span class="stamnt">i</span> 1 44 10 5
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
</div>
</div>
<p><br class="example-break" />
<span>These are the diagrams of the waveforms of the GEN21 routines, as used in the example:</span>
</p>
<div class="mediaobject">
<img src="images/gen21_1.png" alt="f 1 0 32 21 1 - positive numbers only" />
<div class="caption">
<p>f 1 0 32 21 1 - positive numbers only</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_2.png" alt="f 2 0 32 21 6" />
<div class="caption">
<p>f 2 0 32 21 6</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_3.png" alt="f 3 0 32 21 6 5.745" />
<div class="caption">
<p>f 3 0 32 21 6 5.745</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_4.png" alt="f 4 0 32 21 9 1 1 2 - positive numbers only" />
<div class="caption">
<p>f 4 0 32 21 9 1 1 2 - positive numbers only</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_5.png" alt="f 5 0 32 21 10 1 2 - positive numbers only" />
<div class="caption">
<p>f 5 0 32 21 10 1 2 - positive numbers only</p>
</div>
</div>
<p>
</p>
</div>
<div class="refsect1" title="Credits">
<a id="idp78004304"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Paris Smaragdis</td>
</tr>
<tr>
<td>MIT, Cambridge</td>
</tr>
<tr>
<td>1995</td>
</tr>
</table>
<p>
</p>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: John ffitch</td>
</tr>
<tr>
<td>University of Bath/Codemist Ltd.</td>
</tr>
<tr>
<td>Bath, UK</td>
</tr>
</table>
<p>
</p>
<p>Precisions about mu and sigma added by François Pinot after a discussion with
Joachim Heintz on the Csound List, December 2010.</p>
<p>New in Csound version 3.2</p>
</div>
</div>
<div class="navfooter">
<hr />
<table width="100%" summary="Navigation footer">
<tr>
<td width="40%" align="left"><a accesskey="p" href="GEN20.html">Prev</a> </td>
<td width="20%" align="center">
<a accesskey="u" href="ScoregensTop.html">Up</a>
</td>
<td width="40%" align="right"> <a accesskey="n" href="GEN23.html">Next</a></td>
</tr>
<tr>
<td width="40%" align="left" valign="top">GEN20 </td>
<td width="20%" align="center">
<a accesskey="h" href="index.html">Home</a>
</td>
<td width="40%" align="right" valign="top"> GEN23</td>
</tr>
</table>
</div>
</body>
</html>
distrib
>
Mageia
>
5
>
x86_64
>
media
>
core-release
>
by-pkgid
>
b707d9a4ee443103660a75ccb6e51334
>
files
>
141
