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<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Signals-module.html">Package Signals</a> ::
<a href="Scientific.Signals.Models-module.html">Module Models</a> ::
Class AutoRegressiveModel
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class AutoRegressiveModel</h1><p class="nomargin-top"></p>
<dl><dt>Known Subclasses:</dt>
<dd>
<ul class="subclass-list">
<li><a href="Scientific.Signals.Models.AveragedAutoRegressiveModel-class.html">AveragedAutoRegressiveModel</a></li> </ul>
</dd></dl>
<hr />
<p>Auto-regressive model for stochastic process</p>
<p>This implementation uses the Burg algorithm to obtain the coefficients
of the AR model.</p>
<!-- ==================== INSTANCE METHODS ==================== -->
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<td align="left" colspan="2" class="table-header">
<span class="table-header">Instance Methods</span></td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">order</span>,
<span class="summary-sig-arg">data</span>,
<span class="summary-sig-arg">delta_t</span>=<span class="summary-sig-default">1</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.Interpolation.InterpolatingFunction-class.html"
class="link">Scientific.Functions.Interpolation.InterpolatingFunction</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#correlation" class="summary-sig-name">correlation</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">nsteps</span>)</span><br />
Returns:
the autocorrelation function of the process as estimated from the AR
model</td>
<td align="right" valign="top">
</td>
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</table>
</td>
</tr>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
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<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#frictionConstant" class="summary-sig-name">frictionConstant</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the friction constant of the process, i.e.</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.Interpolation.InterpolatingFunction-class.html"
class="link">Scientific.Functions.Interpolation.InterpolatingFunction</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#memoryFunction" class="summary-sig-name">memoryFunction</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">nsteps</span>)</span><br />
Returns:
the memory function of the process as estimated from the AR model</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.Rational.RationalFunction-class.html"
class="link">Scientific.Function.Rational.RationalFunction</a></span>
</td><td class="summary">
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<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#memoryFunctionZ" class="summary-sig-name">memoryFunctionZ</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the <i class="math">z</i>-transform of the process' memory function</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.Rational.RationalFunction-class.html"
class="link">Scientific.Function.Rational.RationalFunction</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#memoryFunctionZapprox" class="summary-sig-name">memoryFunctionZapprox</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">den_order</span>)</span><br />
Returns:
an approximation to the <i class="math">z</i>-transform of the
process' memory function that correponds to an expansion of the
denominator up to order den_order</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> of <code>complex</code></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#poles" class="summary-sig-name">poles</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the poles of the model in the complex <i class="math">z</i>-plane</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>float</code> or <code>complex</code></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#predictStep" class="summary-sig-name">predictStep</a>(<span class="summary-sig-arg">self</span>)</span><br />
Calculates the linear prediction of the next step in the series.</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> of <code>float</code></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Signals.Models.AutoRegressiveModel-class.html#spectrum" class="summary-sig-name">spectrum</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">omega</span>)</span><br />
Returns:
the frequency spectrum of the process</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</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="__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">order</span>,
<span class="sig-arg">data</span>,
<span class="sig-arg">delta_t</span>=<span class="sig-default">1</span>)</span>
<br /><em class="fname">(Constructor)</em>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>order</code></strong> (<code>int</code>) - the order of the model</li>
<li><strong class="pname"><code>data</code></strong> (sequence of <code>float</code> or <code>complex</code>) - the time series</li>
<li><strong class="pname"><code>delta_t</code></strong> (<code>float</code>) - the sampling interval for the time series</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="correlation"></a>
<div>
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cellspacing="0" width="100%" bgcolor="white">
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<h3 class="epydoc"><span class="sig"><span class="sig-name">correlation</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">nsteps</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>nsteps</code></strong> (<code>int</code>) - the number of time steps for which the autocorrelation function
is to be evaluated</li>
</ul></dd>
<dt>Returns: <a
href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html"
class="link">Scientific.Functions.Interpolation.InterpolatingFunction</a></dt>
<dd>the autocorrelation function of the process as estimated from the
AR model</dd>
</dl>
</td></tr></table>
</div>
<a name="frictionConstant"></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">frictionConstant</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns:</dt>
<dd>the friction constant of the process, i.e. the integral over the
memory function</dd>
</dl>
</td></tr></table>
</div>
<a name="memoryFunction"></a>
<div>
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cellspacing="0" width="100%" bgcolor="white">
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<h3 class="epydoc"><span class="sig"><span class="sig-name">memoryFunction</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">nsteps</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>nsteps</code></strong> (<code>int</code>) - the number of time steps for which the memory function is to be
evaluated</li>
</ul></dd>
<dt>Returns: <a
href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html"
class="link">Scientific.Functions.Interpolation.InterpolatingFunction</a></dt>
<dd>the memory function of the process as estimated from the AR model</dd>
</dl>
</td></tr></table>
</div>
<a name="memoryFunctionZ"></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">memoryFunctionZ</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: <a href="Scientific.Functions.Rational.RationalFunction-class.html"
class="link">Scientific.Function.Rational.RationalFunction</a></dt>
<dd>the <i class="math">z</i>-transform of the process' memory
function</dd>
</dl>
</td></tr></table>
</div>
<a name="memoryFunctionZapprox"></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">memoryFunctionZapprox</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">den_order</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>den_order</code></strong> (<code>int</code>)</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Functions.Rational.RationalFunction-class.html"
class="link">Scientific.Function.Rational.RationalFunction</a></dt>
<dd>an approximation to the <i class="math">z</i>-transform of the
process' memory function that correponds to an expansion of the
denominator up to order den_order</dd>
</dl>
</td></tr></table>
</div>
<a name="poles"></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">poles</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: <code>Numeric.array</code> of <code>complex</code></dt>
<dd>the poles of the model in the complex <i class="math">z</i>-plane</dd>
</dl>
</td></tr></table>
</div>
<a name="predictStep"></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">predictStep</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Calculates the linear prediction of the next step in the series. This
step is appended internally to the current trajectory, making it
possible to call this method repeatedly in order to obtain a sequence of
predicted steps.</p>
<dl class="fields">
<dt>Returns: <code>float</code> or <code>complex</code></dt>
<dd>the predicted step</dd>
</dl>
</td></tr></table>
</div>
<a name="spectrum"></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">spectrum</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">omega</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>omega</code></strong> (<code>Numeric.array</code> of <code>float</code>) - the angular frequencies at which the spectrum is to be evaluated</li>
</ul></dd>
<dt>Returns: <code>Numeric.array</code> of <code>float</code></dt>
<dd>the frequency spectrum of the process</dd>
</dl>
</td></tr></table>
</div>
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