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<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Functions-module.html">Package Functions</a> ::
Module FindRoot
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<!-- ==================== MODULE DESCRIPTION ==================== -->
<h1 class="epydoc">Module FindRoot</h1><p class="nomargin-top"></p>
<p>Newton-Raphson for numerical root finding</p>
<p>Example:</p>
<pre class="literalblock">
>>>from Scientific.Functions.FindRoot import newtonRaphson
>>>from Scientific.N import pi, sin, cos
>>>def func(x):
>>> return (2*x*cos(x) - sin(x))*cos(x) - x + pi/4.0
>>>newtonRaphson(func, 0.0, 1.0, 1.0e-12)
yields 0.952847864655.
</pre>
<!-- ==================== FUNCTIONS ==================== -->
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<span class="summary-type"><code>float</code></span>
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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>,
<span class="summary-sig-arg">lox</span>,
<span class="summary-sig-arg">hix</span>,
<span class="summary-sig-arg">xacc</span>)</span><br />
<a name="index-Newton_Raphson"></a><i
class="indexterm">Newton-Raphson</i> algorithm for <a
name="index-root"></a><i class="indexterm">root</i> finding.</td>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">newtonRaphson</span>(<span class="sig-arg">function</span>,
<span class="sig-arg">lox</span>,
<span class="sig-arg">hix</span>,
<span class="sig-arg">xacc</span>)</span>
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<p><a name="index-Newton_Raphson"></a><i
class="indexterm">Newton-Raphson</i> algorithm for <a
name="index-root"></a><i class="indexterm">root</i> finding. The
algorithm used is a safe version of Newton-Raphson (see page 366 of
Numerical Recipes in C, 2ed).</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>function</code></strong> (callable) - function of one numerical variable that uses only those
operations that are defined for DerivVar objects in the module
<a href="Scientific.Functions.FirstDerivatives-module.html"
class="link">Scientific.Functions.FirstDerivatives</a></li>
<li><strong class="pname"><code>lox</code></strong> (<code>float</code>) - lower limit of the search interval</li>
<li><strong class="pname"><code>hix</code></strong> (C[{loat}) - upper limit of the search interval</li>
<li><strong class="pname"><code>xacc</code></strong> (<code>float</code>) - requested absolute precision of the root</li>
</ul></dd>
<dt>Returns: <code>float</code></dt>
<dd>a root of function between lox and hix</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if <code>function(lox)</code> and <code>function(hix)</code> have
the same sign, or if there is no convergence after 500 iterations</li>
</ul></dd>
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