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<h1><img src="../../../../boost.png" align="middle" />Tensor Expressions</h1>
<div class="toc" id="toc"></div>


<h2><a name="tensor_expression"></a>Tensor Expression</h2>
<h4>Description</h4>
<p>The templated class <code>tensor_expression&lt;T,E&gt;</code>
is required to be a public base of all classes. There is no Tensor Expression concept defined.</p>
<h4>Definition</h4>
<p>Defined in the header tensor/expression.hpp.</p>
<h4>Model of</h4>
<p>None. <u>Not a Tensor Expression</u>!
</p>

<h4>Type requirements</h4>
<p>None.</p>
<h4>Public base classes</h4>
<p><code>ublas_expression&lt;E&gt;</code>.</p>

<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
</tr>
<tr>
<td><code>T</code></td>
<td>The type of the tensor.</td>
</tr>
<tr>
<td><code>E</code></td>
<td>The type of the tensor expression.</td>
</tr>
</tbody>
</table>

<h4>Member types</h4>
<table border="1" style="font-size:100%" summary="members">
<tbody style="font-size:100%" >
<tr>
<th>Member type</th>
<th>Description</th>
</tr>
<tr>
<td><code>expression_type</code></td>
<td>Type of the derived expression which is <code>E</code>.</td>
</tr>
<tr>
<td><code>type_category</code></td>
<td>Tag for categorization which is <code>tensor_tag</code>.</td>
</tr>
<tr>
<td><code>tensor_type</code></td>
<td>Reference type which is <code>T</code>.</td>
</tr>
</tbody>
</table>

<h4>Public Member Functions</h4>
<table border="1" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>const expression_type &amp;operator()() const</code></td>
<td>Returns a <code>const</code> reference to the derived expression.</td>
</tr>
</tbody>
</table>

<!--------------------- ---->
<br>
<br>

<h2><a name="entrywise_tensor_operations"></a>Entrywise Tensor Operations</h2>


<h3><a name="binary_tensor_expression"></a>Binary Tensor Expression</h3>

<h4>Description</h4>
<p>The templated class <code>binary_tensor_expression&lt;T,EL,ER,OP&gt;</code> contains a constant reference to a left and right expression that can be evaluated by using the access operator.</p>
<h4>Definition</h4>
<p>Defined in the header tensor/expression.hpp.</p>
<h4>Model of</h4>
<p>Tensor Expression</p>


<h4>Type requirements</h4>
<p>None.</p>

<h4>Public base classes</h4>
<p><code>tensor_expression&lt;T,binary_tensor_expression&lt;T,EL,ER,OP&gt;&gt;</code></p>

<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
</tr>
<tr>
<td><code>T</code></td>
<td>Type of the tensor.</td>
</tr>
<tr>
<td><code>EL</code></td>
<td>Type of the left binary tensor expression.</td>
</tr>
<tr>
<td><code>ER</code></td>
<td>Type of the right binary tensor expression.</td>
</tr>
<tr>
<td><code>OP</code></td>
<td>Type of the binary operation.</td>
</tr>
</tbody>
</table>

<h4>Member types</h4>
<table border="1" style="font-size:100%" summary="members">
<tbody style="font-size:100%" >
<tr>
<th>Member type</th>
<th>Description</th>
</tr>
<tr>
<td><code>expression_type_left</code></td>
<td>Type of the left expression which is <code>EL</code>.</td>
</tr>
<tr>
<td><code>expression_type_right</code></td>
<td>Type of the right expression which is <code>ER</code>.</td>
</tr>
<tr>
<td><code>tensor_type</code></td>
<td>Reference type which is <code>T</code>.</td>
</tr>
<tr>
<td><code>binary_operation</code></td>
<td>Type of the binary operation which is <code>OP</code>.</td>
</tr>
</tbody>
</table>

<h4>Public Member Functions</h4>
<table border="1" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>decltype(auto) operator()(std::size_t i) const </code></td>
<td>Returns a <code>const</code> reference to the i-th element of the expression.</td>
</tr>
</tbody>
</table>
<br>

<!--------------------- ---->

<h3><a name="unary_tensor_expression"></a>Unary Tensor Expression</h3>


<h4>Description</h4>
<p>The templated class <code>unary_tensor_expression&lt;T,E,OP&gt;</code> contains a constant reference to an expression that can be evaluated by using the access operator.</p>
<h4>Definition</h4>
<p>Defined in the header tensor/expression.hpp.</p>
<h4>Model of</h4>
<p>Tensor Expression</p>

<h4>Type requirements</h4>
<p>None.</p>

<h4>Public base classes</h4>
<p><code>tensor_expression&lt;T,unary_tensor_expression&lt;T,E,OP&gt;&gt; </code></p>

<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
</tr>
<tr>
<td><code>T</code></td>
<td>Type of the tensor.</td>
</tr>
<tr>
<td><code>E</code></td>
<td>Type of the unary tensor expression.</td>
</tr>
<tr>
<td><code>OP</code></td>
<td>Type of the unary operation.</td>
</tr>
</tbody>
</table>

<h4>Member types</h4>
<table border="1" style="font-size:100%" summary="members">
<tbody style="font-size:100%" >
<tr>
<th>Member type</th>
<th>Description</th>
</tr>
<tr>
<td><code>expression_type</code></td>
<td>Type of the expression which is <code>E</code>.</td>
</tr>
<tr>
<td><code>tensor_type</code></td>
<td>Reference type which is <code>T</code>.</td>
</tr>
<tr>
<td><code>unary_operation</code></td>
<td>Type of the unary operation which is <code>OP</code>.</td>
</tr>
</tbody>
</table>

<h4>Public Member Functions</h4>
<table border="1" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>decltype(auto) operator()(std::size_t i) const </code></td>
<td>Returns a <code>const</code> reference to the i-th element of the expression.</td>
</tr>
</tbody>
</table>

<hr />
<p>Copyright (&copy;) 2018 Cem Bassoy <br />
   Use, modification and distribution are subject to the
   Boost Software License, Version 1.0.
   (See accompanying file LICENSE_1_0.txt
   or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
      http://www.boost.org/LICENSE_1_0.txt
   </a>).
</p>
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