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<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Geometry-module.html">Package Geometry</a> ::
<a href="Scientific.Geometry.TensorAnalysis-module.html">Module TensorAnalysis</a> ::
Class TensorField
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class TensorField</h1><p class="nomargin-top"></p>
<pre class="base-tree">
<a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html">Functions.Interpolation.InterpolatingFunction</a> --+
|
<strong class="uidshort">TensorField</strong>
</pre>
<dl><dt>Known Subclasses:</dt>
<dd>
<ul class="subclass-list">
<li><a href="Scientific.Geometry.TensorAnalysis.ScalarField-class.html">ScalarField</a></li><li>, <a href="Scientific.Geometry.TensorAnalysis.VectorField-class.html">VectorField</a></li> </ul>
</dd></dl>
<hr />
<p>Tensor field of arbitrary rank</p>
<p>A tensor field is described by a tensor at each point of a
three-dimensional rectangular grid. The grid spacing must be uniform.
Tensor fields are implemented as a subclass of InterpolatingFunction from
the module Scientific.Functions.Interpolation and thus share all methods
defined in that class.</p>
<p>Evaluation:</p>
<ul>
<li>
'tensorfield(x, y, z)' (three coordinates)
</li>
<li>
'tensorfield(coordinates)' (sequence containing three coordinates)
</li>
</ul>
<!-- ==================== 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>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
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<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>
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</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
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<td><span class="summary-sig"><a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html#__call__" class="summary-sig-name">__call__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">*points</span>)</span><br />
Returns:
the function value obtained by linear interpolation</td>
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</td>
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</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">InterpolatingFunction</a> or number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html#__getitem__" class="summary-sig-name">__getitem__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">index</span>)</span><br />
Returns:
an InterpolatingFunction whose number of variables is reduced, or a
number if no variable is left</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"> </span>
</td><td class="summary">
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<td><span class="summary-sig"><a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">rank</span>,
<span class="summary-sig-arg">axes</span>,
<span class="summary-sig-arg">values</span>,
<span class="summary-sig-arg">default</span>=<span class="summary-sig-default">None</span>,
<span class="summary-sig-arg">period</span>=<span class="summary-sig-default"><code class="variable-group">(</code>None<code class="variable-op">, </code>None<code class="variable-op">, </code>None<code class="variable-group">)</code></span>,
<span class="summary-sig-arg">check</span>=<span class="summary-sig-default">True</span>)</span></td>
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</td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__sub__"></a><span class="summary-sig-name">__sub__</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">(<a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a>, <a
href="Scientific.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a>, <a
href="Scientific.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a>)</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html#allDerivatives" class="summary-sig-name">allDerivatives</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
all three derivatives (x, y, z) on equal-sized grids</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.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html#derivative" class="summary-sig-name">derivative</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">variable</span>)</span><br />
Returns:
the derivative with respect to 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.Geometry.Tensor-class.html"
class="link">Scientifc.Geometry.Tensor</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html#zero" class="summary-sig-name">zero</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
a tensor of the same rank as the field values with all elements equal
to zero</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td colspan="2" class="summary">
<p class="indent-wrapped-lines"><b>Inherited from <code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html">Functions.Interpolation.InterpolatingFunction</a></code></b>:
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#__abs__">__abs__</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#__getattr__">__getattr__</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#__getslice__">__getslice__</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#__len__">__len__</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#arccos">arccos</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#arcsin">arcsin</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#arctan">arctan</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#cos">cos</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#cosh">cosh</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#definiteIntegral">definiteIntegral</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#exp">exp</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#fitPolynomial">fitPolynomial</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#integral">integral</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#log">log</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#selectInterval">selectInterval</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#sin">sin</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#sinh">sinh</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#sqrt">sqrt</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#tan">tan</a></code>,
<code><a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#tanh">tanh</a></code>
</p>
</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">*points</span>)</span>
<br /><em class="fname">(Call operator)</em>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: number</dt>
<dd>the function value obtained by linear interpolation</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>TypeError</strong></code> - if the number of arguments (<code>len(points)</code>) does not
match the number of variables of the function</li>
<li><code><strong class='fraise'>ValueError</strong></code> - if the evaluation point is outside of the domain of definition and
no default value is defined</li>
</ul></dd>
<dt>Overrides:
<a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#__call__">Functions.Interpolation.InterpolatingFunction.__call__</a>
<dd><em class="note">(inherited documentation)</em></dd>
</dt>
</dl>
</td></tr></table>
</div>
<a name="__getitem__"></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">__getitem__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">index</span>)</span>
<br /><em class="fname">(Indexing operator)</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>i</code></strong> - any indexing expression possible for <code>N.array</code> that
does not use <code>N.NewAxis</code></li>
</ul></dd>
<dt>Returns: <a
href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html"
class="link">InterpolatingFunction</a> or number</dt>
<dd>an InterpolatingFunction whose number of variables is reduced, or
a number if no variable is left</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>TypeError</strong></code> - if i is not an allowed index expression</li>
</ul></dd>
<dt>Overrides:
<a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#__getitem__">Functions.Interpolation.InterpolatingFunction.__getitem__</a>
<dd><em class="note">(inherited documentation)</em></dd>
</dt>
</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">rank</span>,
<span class="sig-arg">axes</span>,
<span class="sig-arg">values</span>,
<span class="sig-arg">default</span>=<span class="sig-default">None</span>,
<span class="sig-arg">period</span>=<span class="sig-default"><code class="variable-group">(</code>None<code class="variable-op">, </code>None<code class="variable-op">, </code>None<code class="variable-group">)</code></span>,
<span class="sig-arg">check</span>=<span class="sig-default">True</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>rank</code></strong> (<code>int</code>) - the tensor rank</li>
<li><strong class="pname"><code>axes</code></strong> (sequence of <code>Numeric.array</code> of rank 1) - three arrays specifying the axis ticks for the three axes</li>
<li><strong class="pname"><code>values</code></strong> (<code>Numeric.array</code> of rank+3 dimensions) - an array containing the field values. Its first three dimensions
correspond to the x, y, z directions and must have lengths
compatible with the axis arrays. The remaining dimensions must
have length 3.</li>
<li><strong class="pname"><code>default</code></strong> (<a href="Scientific.Geometry.Tensor-class.html"
class="link">Scientific.Geometry.Tensor</a> or
<code>NoneType</code>) - the value of the field for points outside the grid. A value of
'None' means that an exception will be raised for an attempt to
evaluate the field outside the grid. Any other value must a
tensor of the correct rank.</li>
<li><strong class="pname"><code>period</code></strong> (sequence of length three) - the period for each of the variables, or <code>None</code> for
variables in which the function is not periodic.</li>
</ul></dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if the arguments are not consistent</li>
</ul></dd>
<dt>Overrides:
<a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#__init__">Functions.Interpolation.InterpolatingFunction.__init__</a>
</dt>
</dl>
</td></tr></table>
</div>
<a name="allDerivatives"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
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<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">allDerivatives</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.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a>, <a
href="Scientific.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a>, <a
href="Scientific.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a>)</dt>
<dd>all three derivatives (x, y, z) on equal-sized grids</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>
</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>variable</code></strong> (<code>int</code>) - 0 for x, 1 for y, 2 for z</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Geometry.TensorAnalysis.TensorField-class.html"
class="link">TensorField</a></dt>
<dd>the derivative with respect to variable</dd>
<dt>Overrides:
<a href="Scientific.Functions.Interpolation.InterpolatingFunction-class.html#derivative">Functions.Interpolation.InterpolatingFunction.derivative</a>
</dt>
</dl>
</td></tr></table>
</div>
<a name="zero"></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">zero</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.Geometry.Tensor-class.html"
class="link">Scientifc.Geometry.Tensor</a></dt>
<dd>a tensor of the same rank as the field values with all elements
equal to zero</dd>
</dl>
</td></tr></table>
</div>
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