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209 lines
8 KiB
HTML
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209 lines
8 KiB
HTML
Executable file
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<a href="Scientific-module.html">Package Scientific</a> ::
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<a href="Scientific.Functions-module.html">Package Functions</a> ::
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Module FindRoot
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>[<a href="frames.html" target="_top">frames</a
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target="_top">no frames</a>]</span></td></tr>
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<!-- ==================== MODULE DESCRIPTION ==================== -->
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<h1 class="epydoc">Module FindRoot</h1><p class="nomargin-top"></p>
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<p>Newton-Raphson for numerical root finding</p>
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<p>Example:</p>
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<pre class="literalblock">
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>>>from Scientific.Functions.FindRoot import newtonRaphson
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>>>from Scientific.N import pi, sin, cos
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>>>def func(x):
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>>> return (2*x*cos(x) - sin(x))*cos(x) - x + pi/4.0
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>>>newtonRaphson(func, 0.0, 1.0, 1.0e-12)
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yields 0.952847864655.
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</pre>
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<!-- ==================== FUNCTIONS ==================== -->
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<a name="section-Functions"></a>
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<table class="summary" border="1" cellpadding="3"
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cellspacing="0" width="100%" bgcolor="white">
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<tr bgcolor="#70b0f0" class="table-header">
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<td align="left" colspan="2" class="table-header">
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<span class="table-header">Functions</span></td>
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</tr>
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<tr>
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<td width="15%" align="right" valign="top" class="summary">
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<span class="summary-type"><code>float</code></span>
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</td><td class="summary">
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<table width="100%" cellpadding="0" cellspacing="0" border="0">
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<tr>
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<td><span class="summary-sig"><a href="Scientific.Functions.FindRoot-module.html#newtonRaphson" class="summary-sig-name">newtonRaphson</a>(<span class="summary-sig-arg">function</span>,
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<span class="summary-sig-arg">lox</span>,
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<span class="summary-sig-arg">hix</span>,
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<span class="summary-sig-arg">xacc</span>)</span><br />
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<a name="index-Newton_Raphson"></a><i
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class="indexterm">Newton-Raphson</i> algorithm for <a
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name="index-root"></a><i class="indexterm">root</i> finding.</td>
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<td align="right" valign="top">
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</td>
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</tr>
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</table>
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</td>
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</table>
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<!-- ==================== FUNCTION DETAILS ==================== -->
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<a name="section-FunctionDetails"></a>
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<table class="details" border="1" cellpadding="3"
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cellspacing="0" width="100%" bgcolor="white">
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<td align="left" colspan="2" class="table-header">
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<span class="table-header">Function Details</span></td>
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</tr>
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</table>
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<a name="newtonRaphson"></a>
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<div>
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<table class="details" border="1" cellpadding="3"
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cellspacing="0" width="100%" bgcolor="white">
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<tr><td>
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<tr valign="top"><td>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">newtonRaphson</span>(<span class="sig-arg">function</span>,
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<span class="sig-arg">lox</span>,
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<span class="sig-arg">hix</span>,
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<span class="sig-arg">xacc</span>)</span>
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</h3>
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</td><td align="right" valign="top"
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>
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</td>
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</tr></table>
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<p><a name="index-Newton_Raphson"></a><i
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class="indexterm">Newton-Raphson</i> algorithm for <a
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name="index-root"></a><i class="indexterm">root</i> finding. The
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algorithm used is a safe version of Newton-Raphson (see page 366 of
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Numerical Recipes in C, 2ed).</p>
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<dl class="fields">
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<dt>Parameters:</dt>
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<dd><ul class="nomargin-top">
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<li><strong class="pname"><code>function</code></strong> (callable) - function of one numerical variable that uses only those
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operations that are defined for DerivVar objects in the module
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<a href="Scientific.Functions.FirstDerivatives-module.html"
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class="link">Scientific.Functions.FirstDerivatives</a></li>
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<li><strong class="pname"><code>lox</code></strong> (<code>float</code>) - lower limit of the search interval</li>
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<li><strong class="pname"><code>hix</code></strong> (C[{loat}) - upper limit of the search interval</li>
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<li><strong class="pname"><code>xacc</code></strong> (<code>float</code>) - requested absolute precision of the root</li>
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</ul></dd>
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<dt>Returns: <code>float</code></dt>
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<dd>a root of function between lox and hix</dd>
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<dt>Raises:</dt>
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<dd><ul class="nomargin-top">
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<li><code><strong class='fraise'>ValueError</strong></code> - if <code>function(lox)</code> and <code>function(hix)</code> have
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the same sign, or if there is no convergence after 500 iterations</li>
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</ul></dd>
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</dl>
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