<?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>polynomial</title>
<link rel="stylesheet" href="csound.css" type="text/css" />
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2" />
<link rel="home" href="index.html" title="The Canonical Csound Reference Manual" />
<link rel="up" href="OpcodesTop.html" title="Orchestra Opcodes and Operators" />
<link rel="prev" href="polyaft.html" title="polyaft" />
<link rel="next" href="pop.html" title="pop" />
</head>
<body>
<div class="navheader">
<table width="100%" summary="Navigation header">
<tr>
<th colspan="3" align="center">polynomial</th>
</tr>
<tr>
<td width="20%" align="left"><a accesskey="p" href="polyaft.html">Prev</a> </td>
<th width="60%" align="center">Orchestra Opcodes and Operators</th>
<td width="20%" align="right"> <a accesskey="n" href="pop.html">Next</a></td>
</tr>
</table>
<hr />
</div>
<div class="refentry" title="polynomial">
<a id="polynomial"></a>
<div class="titlepage"></div>
<a id="IndexPolynomial" class="indexterm"></a>
<div class="refnamediv">
<h2>
<span class="refentrytitle">polynomial</span>
</h2>
<p>polynomial —
Efficiently evaluates a polynomial of arbitrary order.
</p>
</div>
<div class="refsect1" title="Description">
<a id="id3107287"></a>
<h2>Description</h2>
<p>
The <span class="emphasis"><em>polynomial</em></span> opcode calculates a polynomial with a single a-rate input variable. The polynomial is a sum of any number of terms in the form <span class="emphasis"><em>kn*x^n</em></span> where <span class="emphasis"><em>kn</em></span> is the nth coefficient of the expression. These coefficients are k-rate values.
</p>
</div>
<div class="refsect1" title="Syntax">
<a id="id3108122"></a>
<h2>Syntax</h2>
<pre class="synopsis">aout <span class="command"><strong>polynomial</strong></span> ain, k0 [, k1 [, k2 [...]]]</pre>
</div>
<div class="refsect1" title="Performance">
<a id="id3108140"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>ain</em></span> -- the input signal used as the independent variable of the polynomial ("x").
</p>
<p>
<span class="emphasis"><em>aout</em></span> -- the output signal ("y").
</p>
<p>
<span class="emphasis"><em>k0, k1, k2, ...</em></span> -- the coefficients for each term of the polynomial.
</p>
<p>
If we consider the input parameter <span class="emphasis"><em>ain</em></span> to be "x" and the output <span class="emphasis"><em>aout</em></span> to be "y", then the <span class="emphasis"><em>polynomial</em></span> opcode calculates the following equation:
</p>
<div class="literallayout">
<p><br />
y = k0 + k1*x + k2*x^2 + k3*x^3 + ...<br />
</p>
</div>
<p>
</p>
</div>
<div class="refsect1" title="Examples">
<a id="id3108195"></a>
<h2>Examples</h2>
<p>
Here is an example of the polynomial opcode. It uses the file <a class="ulink" href="examples/polynomial.csd" target="_top"><em class="citetitle">polynomial.csd</em></a>.
</p>
<div class="example">
<a id="id3108212"></a>
<p class="title">
<b>Example 445. Example of the polynomial opcode.</b>
</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">; no sound output</span>
-n
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100 <span class="comment">; audio rate is not important</span>
<span class="ohdr">kr</span> <span class="op">=</span> 10 <span class="comment">; execute the statements in instr 1 ten times per second</span>
<span class="oblock">instr</span> 1
<span class="comment">; ax will vary from 1 to 10</span>
ax <span class="opc">init</span> 1
<span class="comment">; ay = ax^3 + 2ax^2 + 3ax + 4</span>
ay <span class="opc">polynomial</span> ax, 4, 3, 2, 1
<span class="comment">; convert our a-rate signals to k-rate values so that we can print</span>
ky <span class="opc">downsamp</span> ay
kx <span class="opc">downsamp</span> ax
<span class="opc">printf</span> "<span class="op">%</span>d<span class="op">:</span> <span class="op">%</span>d\n", kx, kx, ky
ax <span class="op">=</span> ax <span class="op">+</span> 1
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="stamnt">i</span>1 0 1
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
</div>
</div>
<p><br class="example-break" />
</p>
</div>
<div class="refsect1" title="See Also">
<a id="id3108250"></a>
<h2>See Also</h2>
<p>
<a class="link" href="chebyshevpoly.html" title="chebyshevpoly"><em class="citetitle">chebyshevpoly</em></a>,
<a class="link" href="mac.html" title="mac"><em class="citetitle">mac</em></a>
<a class="link" href="maca.html" title="maca"><em class="citetitle">maca</em></a>
</p>
</div>
<div class="refsect1" title="Credits">
<a id="id3108282"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Anthony Kozar</td>
</tr>
<tr>
<td>January 2008</td>
</tr>
</table>
<p>
</p>
<p>New in Csound version 5.08</p>
</div>
</div>
<div class="navfooter">
<hr />
<table width="100%" summary="Navigation footer">
<tr>
<td width="40%" align="left"><a accesskey="p" href="polyaft.html">Prev</a> </td>
<td width="20%" align="center">
<a accesskey="u" href="OpcodesTop.html">Up</a>
</td>
<td width="40%" align="right"> <a accesskey="n" href="pop.html">Next</a></td>
</tr>
<tr>
<td width="40%" align="left" valign="top">polyaft </td>
<td width="20%" align="center">
<a accesskey="h" href="index.html">Home</a>
</td>
<td width="40%" align="right" valign="top"> pop</td>
</tr>
</table>
</div>
</body>
</html>
