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<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Geometry-module.html">Package Geometry</a> ::
Class Vector
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class Vector</h1><p class="nomargin-top"></p>
<p>Vector in 3D space</p>
<p>Constructor:</p>
<p>Vectors support the usual arithmetic operations ('v1', 'v2': vectors,
's': scalar):</p>
<ul>
<li>
'v1+v2' (addition)
</li>
<li>
'v1-v2' (subtraction)
</li>
<li>
'v1*v2' (scalar product)
</li>
<li>
's*v1', 'v1*s' (multiplication with a scalar)
</li>
<li>
'v1/s' (division by a scalar)
</li>
</ul>
<p>The three coordinates can be extracted by indexing.</p>
<p>Vectors are <b>immutable</b>, i.e. their elements cannot be
changed.</p>
<p>Vector elements can be any objects on which the standard arithmetic
operations plus the functions sqrt and arccos are defined.</p>
<!-- ==================== INSTANCE METHODS ==================== -->
<a name="section-InstanceMethods"></a>
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<span class="table-header">Instance Methods</span></td>
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<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="__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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</td>
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<tr>
<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="__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>
<td align="right" valign="top">
</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="__copy__"></a><span class="summary-sig-name">__copy__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">memo</span>=<span class="summary-sig-default">None</span>)</span></td>
<td align="right" valign="top">
</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="__deepcopy__"></a><span class="summary-sig-name">__deepcopy__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">memo</span>=<span class="summary-sig-default">None</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="__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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</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="__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>
<td align="right" valign="top">
</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="__getstate__"></a><span class="summary-sig-name">__getstate__</span>(<span class="summary-sig-arg">self</span>)</span></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.Geometry.Vector-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">x</span>=<span class="summary-sig-default">None</span>,
<span class="summary-sig-arg">y</span>=<span class="summary-sig-default">None</span>,
<span class="summary-sig-arg">z</span>=<span class="summary-sig-default">None</span>)</span><br />
There are two supported calling patterns:</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"> </span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<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>
<td align="right" valign="top">
</td>
</tr>
</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">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<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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</table>
</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="__neg__"></a><span class="summary-sig-name">__neg__</span>(<span class="summary-sig-arg">self</span>)</span></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 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>
<td align="right" valign="top">
</td>
</tr>
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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="__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>
</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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<tr>
<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>
<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">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<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>
<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">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<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>
<td align="right" valign="top">
</td>
</tr>
</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">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="__setstate__"></a><span class="summary-sig-name">__setstate__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">state</span>)</span></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="__str__"></a><span class="summary-sig-name">__str__</span>(<span class="summary-sig-arg">self</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"> </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>
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</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><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.Geometry.Vector-class.html#angle" class="summary-sig-name">angle</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span><br />
Returns:
the angle to 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"><a href="Scientific.Geometry.Tensor-class.html"
class="link">Scientific.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.Vector-class.html#asTensor" class="summary-sig-name">asTensor</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
an equivalent rank-1 tensor object</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.Vector-class.html"
class="link">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.Vector-class.html#cross" class="summary-sig-name">cross</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span><br />
Returns:
cross product with other</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">Scientific.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.Vector-class.html#dyadicProduct" class="summary-sig-name">dyadicProduct</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span><br />
Returns:
the dyadic product with other</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 vector 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.Vector-class.html#length" class="summary-sig-name">length</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the length (norm) of the vector</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.Vector-class.html"
class="link">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.Vector-class.html#normal" class="summary-sig-name">normal</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
a normalized (length 1) copy of the vector</td>
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</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">type of vector 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.Vector-class.html#x" class="summary-sig-name">x</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the x coordinate</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 vector 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.Vector-class.html#y" class="summary-sig-name">y</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the y coordinate</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 vector 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.Vector-class.html#z" class="summary-sig-name">z</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the z coordinate</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_vector"></a><span class="summary-name">is_vector</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">x</span>=<span class="sig-default">None</span>,
<span class="sig-arg">y</span>=<span class="sig-default">None</span>,
<span class="sig-arg">z</span>=<span class="sig-default">None</span>)</span>
<br /><em class="fname">(Constructor)</em>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>There are two supported calling patterns:</p>
<ol start="1">
<li>
<code>Vector(x, y, z)</code> (from three coordinates)
</li>
<li>
<code>Vector(coordinates)</code> (from any sequence containing three
coordinates)
</li>
</ol>
<dl class="fields">
</dl>
</td></tr></table>
</div>
<a name="angle"></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">angle</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>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>other</code></strong> (<a href="Scientific.Geometry.Vector-class.html"
class="link">Vector</a>) - a vector</li>
</ul></dd>
<dt>Returns: <code>float</code></dt>
<dd>the angle to other</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>TypeError</strong></code> - if other is not a vector</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="asTensor"></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">asTensor</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">Scientific.Geometry.Tensor</a></dt>
<dd>an equivalent rank-1 tensor object</dd>
</dl>
</td></tr></table>
</div>
<a name="cross"></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">cross</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>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>other</code></strong> (<a href="Scientific.Geometry.Vector-class.html"
class="link">Vector</a>) - a vector</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Geometry.Vector-class.html"
class="link">Vector</a></dt>
<dd>cross product with other</dd>
</dl>
</td></tr></table>
</div>
<a name="dyadicProduct"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
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<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">dyadicProduct</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>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>other</code></strong> (<a href="Scientific.Geometry.Vector-class.html"
class="link">Vector</a> or <a
href="Scientific.Geometry.Tensor-class.html"
class="link">Scientific.Geometry.Tensor</a>) - a vector or a tensor</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Geometry.Tensor-class.html"
class="link">Scientific.Geometry.Tensor</a></dt>
<dd>the dyadic product with other</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>TypeError</strong></code> - if other is not a vector or a tensor</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="length"></a>
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cellspacing="0" width="100%" bgcolor="white">
<tr><td>
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<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">length</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: type of vector elements</dt>
<dd>the length (norm) of the vector</dd>
</dl>
</td></tr></table>
</div>
<a name="normal"></a>
<div>
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<tr><td>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">normal</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">Vector</a></dt>
<dd>a normalized (length 1) copy of the vector</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ZeroDivisionError</strong></code> - if vector length is zero</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="x"></a>
<div>
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cellspacing="0" width="100%" bgcolor="white">
<tr><td>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">x</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: type of vector elements</dt>
<dd>the x coordinate</dd>
</dl>
</td></tr></table>
</div>
<a name="y"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
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<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">y</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: type of vector elements</dt>
<dd>the y coordinate</dd>
</dl>
</td></tr></table>
</div>
<a name="z"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
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<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">z</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: type of vector elements</dt>
<dd>the z coordinate</dd>
</dl>
</td></tr></table>
</div>
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