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<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Geometry-module.html">Package Geometry</a> ::
Class Tensor
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class Tensor</h1><p class="nomargin-top"></p>
<p>Tensor in 3D space</p>
<p>Tensors support the usual arithmetic operations ('t1', 't2': tensors,
'v': vector, 's': scalar):</p>
<ul>
<li>
't1+t2' (addition)
</li>
<li>
't1-t2' (subtraction)
</li>
<li>
't1*t2' (tensorial (outer) product)
</li>
<li>
't1*v' (contraction with a vector, same as
t1.dot(v.asTensor()))
</li>
<li>
's*t1', 't1*s' (multiplication with a scalar)
</li>
<li>
't1/s' (division by a scalar)
</li>
</ul>
<p>The coordinates can be extracted by indexing; a tensor of rank N can
be indexed like an array of dimension N.</p>
<p>Tensors are <i>immutable</i>, i.e. their elements cannot be
changed.</p>
<p>Tensor elements can be any objects on which the standard arithmetic
operations are defined. However, eigenvalue calculation is supported only
for float elements.</p>
<!-- ==================== INSTANCE METHODS ==================== -->
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<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 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>
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</td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__cmp__"></a><span class="summary-sig-name">__cmp__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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<span class="summary-type"> </span>
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<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>
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</td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__getitem__"></a><span class="summary-sig-name">__getitem__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">index</span>)</span></td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a href="Scientific.Geometry.Tensor-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">elements</span>,
<span class="summary-sig-arg">nocheck</span>=<span class="summary-sig-default">None</span>)</span></td>
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</td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__len__"></a><span class="summary-sig-name">__len__</span>(<span class="summary-sig-arg">self</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>
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<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>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__neg__"></a><span class="summary-sig-name">__neg__</span>(<span class="summary-sig-arg">self</span>)</span></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">
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<tr>
<td><span class="summary-sig"><a name="__radd__"></a><span class="summary-sig-name">__radd__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></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">
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<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>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
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<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>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__rmul__"></a><span class="summary-sig-name">__rmul__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></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">
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<td><span class="summary-sig"><a name="__rsub__"></a><span class="summary-sig-name">__rsub__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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</td>
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<span class="summary-type"> </span>
</td><td class="summary">
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<td><span class="summary-sig"><a name="__str__"></a><span class="summary-sig-name">__str__</span>(<span class="summary-sig-arg">self</span>)</span></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>
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</table>
</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</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.Tensor-class.html#asVector" class="summary-sig-name">asVector</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
an equivalent vector object</td>
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</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"><a href="Scientific.Geometry.Tensor-class.html"
class="link">Tensor</a></span>
</td><td class="summary">
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<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Tensor-class.html#asymmetricalPart" class="summary-sig-name">asymmetricalPart</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the asymmetrical part of the tensor</td>
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</td>
</tr>
</table>
</td>
</tr>
<tr>
<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="diagonal"></a><span class="summary-sig-name">diagonal</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">axis1</span>=<span class="summary-sig-default">0</span>,
<span class="summary-sig-arg">axis2</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">(<code>Numeric.array</code>, <a
href="Scientific.Geometry.Tensor-class.html" class="link">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.Tensor-class.html#diagonalization" class="summary-sig-name">diagonalization</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the eigenvalues of the tensor and a tensor representing the rotation
matrix to the diagonal form</td>
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</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">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.Tensor-class.html#dot" class="summary-sig-name">dot</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span><br />
Returns:
the contraction with other</td>
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</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.Geometry.Tensor-class.html#eigenvalues" class="summary-sig-name">eigenvalues</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the eigenvalues of the tensor</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">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.Tensor-class.html#inverse" class="summary-sig-name">inverse</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the inverse of the tensor</td>
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</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">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.Tensor-class.html#symmetricalPart" class="summary-sig-name">symmetricalPart</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the symmetrical part of the tensor</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">type of tensor elements</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Tensor-class.html#trace" class="summary-sig-name">trace</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">axis1</span>=<span class="summary-sig-default">0</span>,
<span class="summary-sig-arg">axis2</span>=<span class="summary-sig-default">1</span>)</span><br />
Returns:
the trace of the tensor</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">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.Tensor-class.html#transpose" class="summary-sig-name">transpose</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the transposed (index reversed) tensor</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"> </span>
</td><td class="summary">
<a name="is_tensor"></a><span class="summary-name">is_tensor</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="__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">elements</span>,
<span class="sig-arg">nocheck</span>=<span class="sig-default">None</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>elements</code></strong> (<code>Numeric.array</code> or <code>list</code>) - 2D array or nested list specifying the nine tensor components
[[xx, xy, xz], [yx, yy, yz], [zx, zy, zz]]</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="asVector"></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">asVector</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.Vector-class.html"
class="link">Scientific.Geometry.Vector</a></dt>
<dd>an equivalent vector object</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if rank > 1</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="asymmetricalPart"></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">asymmetricalPart</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">Tensor</a></dt>
<dd>the asymmetrical part of the tensor</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if rank !=2</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="diagonalization"></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">diagonalization</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>, <a
href="Scientific.Geometry.Tensor-class.html" class="link">Tensor</a>)</dt>
<dd>the eigenvalues of the tensor and a tensor representing the
rotation matrix to the diagonal form</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if rank !=2</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="dot"></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">dot</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">other</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">Tensor</a></dt>
<dd>the contraction with other</dd>
</dl>
</td></tr></table>
</div>
<a name="eigenvalues"></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">eigenvalues</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></dt>
<dd>the eigenvalues of the tensor</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if rank !=2</li>
</ul></dd>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">inverse</span>(<span class="sig-arg">self</span>)</span>
</h3>
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<dl class="fields">
<dt>Returns: <a href="Scientific.Geometry.Tensor-class.html"
class="link">Tensor</a></dt>
<dd>the inverse of the tensor</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if rank !=2</li>
</ul></dd>
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<a name="symmetricalPart"></a>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">symmetricalPart</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
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</td>
</tr></table>
<dl class="fields">
<dt>Returns: <a href="Scientific.Geometry.Tensor-class.html"
class="link">Tensor</a></dt>
<dd>the symmetrical part of the tensor</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if rank !=2</li>
</ul></dd>
</dl>
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<a name="trace"></a>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">trace</span>(<span class="sig-arg">self</span>,
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</h3>
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</td>
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<dl class="fields">
<dt>Returns: type of tensor elements</dt>
<dd>the trace of the tensor</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if rank !=2</li>
</ul></dd>
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<dl class="fields">
<dt>Returns: <a href="Scientific.Geometry.Tensor-class.html"
class="link">Tensor</a></dt>
<dd>the transposed (index reversed) tensor</dd>
</dl>
</td></tr></table>
</div>
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