xan/awips2
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions
awips2/pythonPackages/scientific/Doc/Reference/Scientific.Functions.Polynomial.Polynomial-class.html
root 8e80217e59 Initial revision of AWIPS2 11.9.0-7p5 
Former-commit-id: a02aeb236c [formerly 9f19e3f712] [formerly 06a8b51d6d [formerly 64fa9254b946eae7e61bbc3f513b7c3696c4f54f]]
Former-commit-id: 06a8b51d6d
Former-commit-id: 3360eb6c5f
2012-01-06 08:55:05 -06:00

498 lines
18 KiB
HTML
Executable file
Raw Blame History

<?xml version="1.0" encoding="ascii"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
<title>Scientific.Functions.Polynomial.Polynomial</title>
<link rel="stylesheet" href="epydoc.css" type="text/css" />
<script type="text/javascript" src="epydoc.js"></script>
</head>
<body bgcolor="white" text="black" link="blue" vlink="#204080"
alink="#204080">
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
bgcolor="#a0c0ff" cellspacing="0">
<tr valign="middle">
<!-- Home link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="Scientific-module.html">Home</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Tree link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Index link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Help link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Project homepage -->
<th class="navbar" align="right" width="100%">
<table border="0" cellpadding="0" cellspacing="0">
<tr><th class="navbar" align="center"
><a class="navbar" target="_top" href="http://dirac.cnrs-orleans.fr/ScientificPython/">Scientific Python</a></th>
</tr></table></th>
</tr>
</table>
<table width="100%" cellpadding="0" cellspacing="0">
<tr valign="top">
<td width="100%">
<span class="breadcrumbs">
<a href="Scientific-module.html">Package&nbsp;Scientific</a> ::
<a href="Scientific.Functions-module.html">Package&nbsp;Functions</a> ::
<a href="Scientific.Functions.Polynomial-module.html">Module&nbsp;Polynomial</a> ::
Class&nbsp;Polynomial
</span>
</td>
<td>
<table cellpadding="0" cellspacing="0">
<!-- hide/show private -->
<tr><td align="right"><span class="options"
>[<a href="frames.html" target="_top">frames</a
>]&nbsp;|&nbsp;<a href="Scientific.Functions.Polynomial.Polynomial-class.html"
target="_top">no&nbsp;frames</a>]</span></td></tr>
</table>
</td>
</tr>
</table>
<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class Polynomial</h1><p class="nomargin-top"></p>
<p><a name="index-Multivariate"></a><i class="indexterm">Multivariate</i>
<a name="index-polynomial"></a><i class="indexterm">polynomial</i></p>
<p>Instances of this class represent polynomials of any order and in any
number of variables. The coefficients and thus the values can be real or
complex. Polynomials can be evaluated like functions.</p>
<!-- ==================== INSTANCE METHODS ==================== -->
<a name="section-InstanceMethods"></a>
<table class="summary" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Instance Methods</span></td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__add__"></a><span class="summary-sig-name">__add__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#__call__" class="summary-sig-name">__call__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">*args</span>)</span><br />
Returns:
the value of the polynomial at the given point</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__coerce__"></a><span class="summary-sig-name">__coerce__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__div__"></a><span class="summary-sig-name">__div__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">coefficients</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__mul__"></a><span class="summary-sig-name">__mul__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__rdiv__"></a><span class="summary-sig-name">__rdiv__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__repr__"></a><span class="summary-sig-name">__repr__</span>(<span class="summary-sig-arg">self</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Polynomial</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#derivative" class="summary-sig-name">derivative</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">variable</span>=<span class="summary-sig-default">0</span>)</span><br />
Returns:
a polynomial of reduced order in one variable</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Polynomial</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#integral" class="summary-sig-name">integral</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">variable</span>=<span class="summary-sig-default">0</span>)</span><br />
Returns:
a polynomial of higher order in one variable</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><code>Numeric.array</code></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#zeros" class="summary-sig-name">zeros</a>(<span class="summary-sig-arg">self</span>)</span><br />
Find the <a name="index-zeros"></a><i class="indexterm">zeros</i> (<a
name="index-roots"></a><i class="indexterm">roots</i>) of the
polynomial by diagonalization of the associated Frobenius matrix.</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
</table>
<!-- ==================== CLASS VARIABLES ==================== -->
<a name="section-ClassVariables"></a>
<table class="summary" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Class Variables</span></td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">&nbsp;</span>
</td><td class="summary">
<a name="is_polynomial"></a><span class="summary-name">is_polynomial</span> = <code title="1">1</code>
</td>
</tr>
</table>
<!-- ==================== METHOD DETAILS ==================== -->
<a name="section-MethodDetails"></a>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Method Details</span></td>
</tr>
</table>
<a name="__call__"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">__call__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">*args</span>)</span>
<br /><em class="fname">(Call operator)</em>
</h3>
</td><td align="right" valign="top"
>&nbsp;
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>args</code></strong> (<code>tuple</code> of numbers) - tuple of values, one for each variable of the polynomial</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the value of the polynomial at the given point</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>TypeError</strong></code> - if the number of arguments is not equal to the number of variable
of the polynomial</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="__init__"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">__init__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">coefficients</span>)</span>
<br /><em class="fname">(Constructor)</em>
</h3>
</td><td align="right" valign="top"
>&nbsp;
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>coefficients</code></strong> (<code>Numeric.array</code> or nested list of numbers) - an <i class="math">N</i>-dimnesional array for a polynomial in <i
class="math">N</i> variables. <code>coeffcients[i, j, ...]</code>
is the coefficient of <i class="math">x_1^i x_2^j ...</i></li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="derivative"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">derivative</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">variable</span>=<span class="sig-default">0</span>)</span>
</h3>
</td><td align="right" valign="top"
>&nbsp;
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>variable</code></strong> (<code>int</code>) - the index of the variable with respect to which the <a
name="index-derivative"></a><i class="indexterm">derivative</i>
is taken</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Polynomial</a></dt>
<dd>a polynomial of reduced order in one variable</dd>
</dl>
</td></tr></table>
</div>
<a name="integral"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">integral</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">variable</span>=<span class="sig-default">0</span>)</span>
</h3>
</td><td align="right" valign="top"
>&nbsp;
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>variable</code></strong> (<code>int</code>) - the index of the variable with respect to which the <a
name="index-integral"></a><i class="indexterm">integral</i> is
computed</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Polynomial</a></dt>
<dd>a polynomial of higher order in one variable</dd>
</dl>
</td></tr></table>
</div>
<a name="zeros"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">zeros</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>&nbsp;
</td>
</tr></table>
<p>Find the <a name="index-zeros"></a><i class="indexterm">zeros</i> (<a
name="index-roots"></a><i class="indexterm">roots</i>) of the polynomial
by diagonalization of the associated Frobenius matrix.</p>
<dl class="fields">
<dt>Returns: <code>Numeric.array</code></dt>
<dd>an array containing the zeros</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - is the polynomial has more than one variable</li>
</ul></dd>
</dl>
<div class="fields"> <p><strong>Note:</strong>
this is defined only for polynomials in one variable
</p>
</div></td></tr></table>
</div>
<br />
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
bgcolor="#a0c0ff" cellspacing="0">
<tr valign="middle">
<!-- Home link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="Scientific-module.html">Home</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Tree link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Index link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Help link -->
<th>&nbsp;&nbsp;&nbsp;<a
href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>
<!-- Project homepage -->
<th class="navbar" align="right" width="100%">
<table border="0" cellpadding="0" cellspacing="0">
<tr><th class="navbar" align="center"
><a class="navbar" target="_top" href="http://dirac.cnrs-orleans.fr/ScientificPython/">Scientific Python</a></th>
</tr></table></th>
</tr>
</table>
<table border="0" cellpadding="0" cellspacing="0" width="100%%">
<tr>
<td align="left" class="footer">
Generated by Epydoc 3.0 on Tue Oct 28 14:16:03 2008
</td>
<td align="right" class="footer">
<a target="mainFrame" href="http://epydoc.sourceforge.net"
>http://epydoc.sourceforge.net</a>
</td>
</tr>
</table>
<script type="text/javascript">
<!--
// Private objects are initially displayed (because if
// javascript is turned off then we want them to be
// visible); but by default, we want to hide them. So hide
// them unless we have a cookie that says to show them.
checkCookie();
// -->
</script>
</body>
</html>
Reference in a new issue View git blame Copy permalink