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<h2>
<span class="refentrytitle">gauss</span>
</h2>
<p>gauss —
Gaussian distribution random number generator.
</p>
</div>
<div class="refsect1">
<a id="idm281472927869096"></a>
<h2>Description</h2>
<p>
Gaussian distribution random number generator. This is an x-class noise generator.
</p>
</div>
<div class="refsect1">
<a id="idm281472927796616"></a>
<h2>Syntax</h2>
<pre class="synopsis">ares <span class="command"><strong>gauss</strong></span> krange</pre>
<pre class="synopsis">ires <span class="command"><strong>gauss</strong></span> krange</pre>
<pre class="synopsis">kres <span class="command"><strong>gauss</strong></span> krange</pre>
</div>
<div class="refsect1">
<a id="idm281472927791656"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>krange</em></span> -- the range of the random numbers (-<span class="emphasis"><em>krange</em></span> to +<span class="emphasis"><em>krange</em></span>). Outputs both positive and negative numbers.
</p>
<p>
<span class="emphasis"><em>gauss</em></span> returns random numbers following a normal distribution centered around 0.0 (mu = 0.0) with a variance (sigma) of <span class="emphasis"><em>krange</em></span> / 3.83. Thus more than 99.99%
of the random values generated are in the range -<span class="emphasis"><em>krange</em></span> to +<span class="emphasis"><em>krange</em></span>. If a mean value different of 0.0 is desired, this mean value has to
be added to the generated numbers (see example below).
</p>
<p>
For more detailed explanation of these distributions, see:
</p>
<div class="orderedlist">
<ol class="orderedlist" type="1">
<li class="listitem">
<p>C. Dodge - T.A. Jerse 1985. Computer music. Schirmer books. pp.265 - 286</p>
</li>
<li class="listitem">
<p>D. Lorrain. A panoply of stochastic cannons. In C. Roads, ed. 1989. Music machine . Cambridge, Massachusetts: MIT press, pp. 351 - 379.</p>
</li>
</ol>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472927783544"></a>
<h2>Examples</h2>
<p>
Here is an example of the gauss opcode. It uses the file <a class="ulink" href="examples/gauss.csd" target="_top"><em class="citetitle">gauss.csd</em></a>.
</p>
<div class="example">
<a id="idm281472927781688"></a>
<p class="title">
<strong>Example 371. Example of the gauss opcode.</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>
<div class="refsect1">
<a id="idm281472757923848"></a>
<pre class="programlisting">
<span class="nt"><CsoundSynthesizer></span>
<span class="nt"><CsOptions></span>
-d -o dac
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="kd">instr</span> <span class="nf">1</span>
i<span class="n">range</span> <span class="o">=</span> <span class="nb">p4</span>
i<span class="n">mu</span> <span class="o">=</span> <span class="nb">p5</span>
i<span class="n">samples</span> <span class="o">=</span> <span class="nb">p6</span>
i<span class="n">ndx</span> <span class="o">=</span> <span class="mi">0</span>
i<span class="n">count</span> <span class="o">=</span> <span class="mi">1</span>
i<span class="n">x</span> <span class="o">=</span> <span class="mf">0.0</span>
i<span class="n">x2</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="nl">loop</span><span class="p">:</span>
i<span class="n">1</span> <span class="nb">gauss</span> i<span class="n">range</span>
i<span class="n">1</span> <span class="o">=</span> i<span class="n">1</span> <span class="o">+</span> i<span class="n">mu</span>
i<span class="n">x</span> <span class="o">=</span> i<span class="n">x</span> <span class="o">+</span> i<span class="n">1</span>
i<span class="n">x2</span> <span class="o">=</span> i<span class="n">x2</span> <span class="o">+</span> i<span class="n">1</span><span class="o">*</span>i<span class="n">1</span>
<span class="k">if</span> i<span class="n">1</span> <span class="o">>=</span> <span class="o">-</span><span class="p">(</span>i<span class="n">range</span><span class="o">+</span>i<span class="n">mu</span><span class="p">)</span> <span class="o">&&</span> i<span class="n">1</span> <span class="o"><=</span> <span class="p">(</span>i<span class="n">range</span><span class="o">+</span>i<span class="n">mu</span><span class="p">)</span> <span class="k">then</span>
i<span class="n">count</span> <span class="o">=</span> i<span class="n">count</span><span class="o">+</span><span class="mi">1</span>
<span class="k">endif</span>
<span class="k">loop_lt</span> i<span class="n">ndx</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> i<span class="n">samples</span><span class="p">,</span> <span class="nl">loop</span>
i<span class="n">mean</span> <span class="o">=</span> i<span class="n">x</span> <span class="o">/</span> i<span class="n">samples</span> <span class="c1">;mean value</span>
i<span class="n">std</span> <span class="o">=</span> <span class="nb">sqrt</span><span class="p">(</span>i<span class="n">x2</span><span class="o">/</span>i<span class="n">samples</span> <span class="o">-</span> i<span class="n">mean</span><span class="o">*</span>i<span class="n">mean</span><span class="p">)</span> <span class="c1">;standard deviation</span>
<span class="nb">prints</span> <span class="s">"mean = %3.3f, std = %3.3f, "</span><span class="p">,</span> i<span class="n">mean</span><span class="p">,</span> i<span class="n">std</span>
<span class="nb">prints</span> <span class="s">"samples inside the given range: %3.3f\%</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> i<span class="n">count</span><span class="o">*</span><span class="mf">100.0</span><span class="o">/</span>i<span class="n">samples</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mf">0.1</span> <span class="mf">1.0</span> <span class="mi">0</span> <span class="mi">100000</span> <span class="c1">; range = 1, mu = 0.0, sigma = 1/3.83 = 0.261</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mf">0.1</span> <span class="mf">0.1</span> <span class="mf">3.83</span> <span class="mi">0</span> <span class="mi">100000</span> <span class="c1">; range = 3.83, mu = 0.0, sigma = 1</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mf">0.2</span> <span class="mf">0.1</span> <span class="mf">5.745</span> <span class="mf">2.7</span> <span class="mi">100000</span> <span class="c1">; range = 5.745, mu = 2.7, sigma = 5.745/3.83 = 1.5</span>
<span class="nt"></CsScore></span>
<span class="nt"></CsoundSynthesizer></span>
</pre>
</div>
</div>
</div>
<p><br class="example-break" />
Its output should include lines like this:
</p>
<pre class="screen">
mean = 0.000, std = 0.260, samples inside the given range: 99.993%
mean = 0.005, std = 0.999, samples inside the given range: 99.998%
mean = 2.700, std = 1.497, samples inside the given range: 100.000%</pre>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472927776472"></a>
<h2>See Also</h2>
<p>
<a class="link" href="seed.html" title="seed"><em class="citetitle">seed</em></a>,
<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="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>,
<a class="link" href="weibull.html" title="weibull"><em class="citetitle">weibull</em></a>
</p>
</div>
<div class="refsect1">
<a id="idm281472927764792"></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>Precisions about mu and sigma added by François Pinot after a discussion with
Joachim Heintz on the Csound List, December 2010.</p>
<p>Example written by François Pinot, adapted from a csd file by Joachim Heintz, December 2010.</p>
<p>Existed in 3.30</p>
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