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<title>Container Concepts</title>
</head>
<body>
<h1><img src="../../../../boost.png" align="middle" />Container Concepts</h1>
<div class="toc" id="toc"></div>
<h2><a name="vector"></a>Vector</h2>
<h4>Description</h4>
<p>A Vector describes common aspects of dense, packed and sparse
vectors.</p>
<h4>Refinement of</h4>
<p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
<a href="expression_concept.html#vector_expression">Vector Expression</a>
<a href="#vector_expression_note">[1]</a>.</p>
<h4>Associated types</h4>
<p>In addition to the types defined by <a href="expression_concept.html#vector_expression">Vector Expression</a></p>
<table border="1" summary="types">
<tbody>
<tr>
<td>Public base</td>
<td>vector_container&lt;V&gt;</td>
<td>V must be derived from this public base type.</td>
</tr>
<tr>
<td>Storage array</td>
<td>V::array_type</td>
<td>
Dense Vector ONLY. The type of underlying storage array used to store the elements. The array_type must model the
<a href="storage_concept.html"><b>Storage</b></a> concept.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0" summary="notation">
<tbody>
<tr>
<td><code>V</code></td>
<td>A type that is a model of Vector</td>
</tr>
<tr>
<td><code>v</code></td>
<td>Objects of type <code>V</code></td>
</tr>
<tr>
<td><code>n, i</code></td>
<td>Objects of a type convertible to <code>size_type</code></td>
</tr>
<tr>
<td><code>t</code></td>
<td>Object of a type convertible to <code>value_type</code></td>
</tr>
<tr>
<td><code>p</code></td>
<td>Object of a type convertible to <code>bool</code></td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined in <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
<a href="expression_concept.html#vector_expression">Vector Expression</a> the following expressions must be valid.</p>
<table border="1" summary="expressions">
<tbody>
<tr>
<th>Name</th>
<th>Expression</th>
<th>Type requirements</th>
<th>Return type</th>
</tr>
<tr>
<td>Sizing constructor</td>
<td><code>V v (n)</code></td>
<td>&nbsp;</td>
<td><code>V</code></td>
</tr>
<tr>
<td>Insert</td>
<td><code>v.insert_element (i, t)</code></td>
<td><code>v</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Erase</td>
<td><code>v.erase_element (i)</code></td>
<td><code>v</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Clear</td>
<td><code>v.clear ()</code></td>
<td><code>v</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Resize</td>
<td><code>v.resize (n)</code><br />
<code>v.resize (n, p)</code></td>
<td><code>v</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Storage</td>
<td><code>v.data()</code></td>
<td><code>v</code> is mutable and Dense.</td>
<td><code>array_type&amp;</code> if <code>v</code> is mutable, <code>const array_type&amp;</code> otherwise</td>
</tr>
</tbody>
</table>
<h4>Expression semantics</h4>
<p>Semantics of an expression is defined only where it differs
from, or is not defined in <a href=
"expression_concept.html#vector_expression">Vector Expression</a> .</p>
<table border="1" summary="semantics">
<tr>
<th>Name</th>
<th>Expression</th>
<th>Precondition</th>
<th>Semantics</th>
<th>Postcondition</th>
</tr>
<tr>
<td>Sizing constructor</td>
<td><code>V v (n)</code></td>
<td><code>n &gt;= 0</code></td>
<td>Allocates a vector of<code>n</code> elements.</td>
<td><code>v.size () == n</code>.</td>
</tr>
<tr>
<td>Element access <a href="#element_access_note">[2]</a></td>
<td><code>v[n]</code></td>
<td><code>0&lt;n&gt;v.size()</code></td>
<td>returns the n-th element in v</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Insert</td>
<td><code>v.insert_element (i, t)</code></td>
<td><code>0 &lt;= i &lt; v.size ()</code>.</td>
<td>Inserts an element at <code>v (i)</code> with value <code>t</code>.
The storage requirement of the Vector may be increased.</td>
<td><code>v (i)</code> is equal to <code>t</code>.</td>
</tr>
<tr>
<td>Erase</td>
<td><code>v.erase_element (i)</code></td>
<td><code>0 &lt;= i &lt; v.size ()</code></td>
<td>Destroys the element as <code>v (i)</code> and replaces it with the default
<code>value_type ()</code>.
The storage requirement of the Vector may be decreased.</td>
<td><code>v (i)</code> is equal to <code>value_type ()</code>.</td>
</tr>
<tr>
<td>Clear</td>
<td><code>v.clear ()</code></td>
<td>&nbsp;</td>
<td>Equivalent to<br />
<code>for (i = 0; i &lt; v.size (); ++ i)</code><br />
&nbsp; <code>v.erase_element (i);</code></td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Resize</td>
<td><code>v.resize (n)
<br />v.resize (n, p)</code></td>
<td>&nbsp;</td>
<td>Reallocates the vector so that it can hold <code>n</code>
elements.<br />
Erases or appends elements in order to bring the vector to the prescribed size. Appended elements copies of <code>value_type()</code>.
<br />
When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the vector is in the same state as that after an equivalent sizing constructor.</td>
<td><code>v.size () == n</code>.</td>
</tr>
<tr>
<td>Storage</td>
<td><code>v.data()</code></td>
<td></td>
<td>Returns a reference to the underlying dense storage.</td>
<td>&nbsp;</td>
</tr>
</table>
<h4>Complexity guarantees</h4>
<p>The run-time complexity of the sizing constructor is linear in
the vector's size.</p>
<p>The run-time complexity of insert_element and erase_element is specific for the
Vector model and it depends on increases/decreases in storage requirements.</p>
<p>The run-time complexity of resize is linear in the vector's
size.</p>
<h4>Invariants</h4>
<h4>Models</h4>
<ul>
<li><code>vector</code>, <code>bounded_vector</code>, <code>c_vector</code></li>
<li><code>unit_vector</code>, <code>zero_vector</code>, <code>scalar_vector</code></li>
<li><code>mapped_vector;</code>, <code>compressed_vector</code>, <code>coordinate_vector</code></li>
</ul>
<h4>Notes</h4>
<p><a name="vector_expression_note">[1]</a>
As a user you need not care about <tt>Vector</tt> being a refinement of the VectorExpression. Being a refinement of the VectorExpression is only important for the template-expression engine but not the user.</p>
<p><a name="element_access_note">[2]</a>
The <code>operator[]</code> is added purely for convenience 
and compatibility with the <code>std::vector</code>. In uBLAS however, 
generally <code>operator()</code> is used for indexing because this can be
used for both vectors and matrices.</p>


<hr>

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

<h2><a name="matrix"></a>Matrix</h2>
<h4>Description</h4>
<p>A Matrix describes common aspects of dense, packed and sparse
matrices.</p>
<h4>Refinement of</h4>
<p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
<a href="expression_concept.html#matrix_expression">Matrix Expression</a>
<a href="#matrix_expression_note">[1]</a>
.</p>
<h4>Associated types</h4>
<p>In addition to the types defined by <a href="expression_concept.html#matrix_expression">Matrix Expression</a></p>
<table border="1" summary="types">
<tbody>
<tr>
<td>Public base</td>
<td>matrix_container&lt;M&gt;</td>
<td>M must be derived from this public base type.</td>
</tr>
<tr>
<td>Storage array</td>
<td>M::array_type</td>
<td>Dense Matrix ONLY. The type of underlying storage array used to store the elements. The array_type must model
the <a href="storage_concept.html"><b>Storage</b></a> concept.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0" summary="notation">
<tbody>
<tr>
<td><code>M</code></td>
<td>A type that is a model of Matrix</td>
</tr>
<tr>
<td><code>m</code></td>
<td>Objects of type <code>M</code></td>
</tr>
<tr>
<td><code>n1, n2, i, j</code></td>
<td>Objects of a type convertible to <code>size_type</code></td>
</tr>
<tr>
<td><code>t</code></td>
<td>Object of a type convertible to <code>value_type</code></td>
</tr>
<tr>
<td><code>p</code></td>
<td>Object of a type convertible to <code>bool</code></td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined in <a href=
"expression_concept.html#matrix_expression">Matrix Expression</a> the
following expressions must be valid.</p>
<table border="1" summary="expressions">
<tbody>
<tr>
<th>Name</th>
<th>Expression</th>
<th>Type requirements</th>
<th>Return type</th>
</tr>
<tr>
<td>Sizing constructor</td>
<td><code>M m (n1, n2)</code></td>
<td>&nbsp;</td>
<td><code>M</code></td>
</tr>
<tr>
<td>Insert</td>
<td><code>m.insert_element (i, j, t)</code></td>
<td><code>m</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Erase</td>
<td><code>m.erase_element (i, j)</code></td>
<td><code>m</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Clear</td>
<td><code>m.clear ()</code></td>
<td><code>m</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Resize</td>
<td><code>m.resize (n1, n2)</code><br />
<code>m.resize (n1, n2, p)</code></td>
<td><code>m</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Storage</td>
<td><code>m.data()</code></td>
<td><code>m</code> is mutable and Dense.</td>
<td><code>array_type&amp;</code> if <code>m</code> is mutable, <code>const array_type&amp;</code> otherwise</td>
</tr>
</tbody>
</table>
<h4>Expression semantics</h4>
<p>Semantics of an expression is defined only where it differs
from, or is not defined in <a href=
"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
<table border="1" summary="semantics">
<tbody>
<tr>
<th>Name</th>
<th>Expression</th>
<th>Precondition</th>
<th>Semantics</th>
<th>Postcondition</th>
</tr>
<tr>
<td>Sizing constructor</td>
<td><code>M m (n1, n2)</code></td>
<td><code>n1 &gt;= 0</code> and <code>n2 &gt;= 0</code></td>
<td>Allocates a matrix of <code>n1</code> rows and <code>n2</code>
columns.</td>
<td><code>m.size1 () == n1</code> and <code>m.size2 () ==
n2</code>.</td>
</tr>
<tr>
<td>Insert</td>
<td><code>m.insert_element (i, j, t)</code></td>
<td><code>0 &lt;= i &lt; m.size1 ()</code>,<br />
<code>0 &lt;= j &lt; m.size2 ()</code>.</td>
<td>Inserts an element at <code>m (i, j)</code> with value <code>t</code>.
The storage requirement of the Matrix may be increased.</td>
<td><code>m (i, j)</code> is equal to <code>t</code>.</td>
</tr>
<tr>
<td>Erase</td>
<td><code>m.erase_element (i, j)</code></td>
<td><code>0 &lt;= i &lt; m.size1 ()</code>and <code><br />
0 &lt;= j &lt; m.size2</code></td>
<td>Destroys the element as <code>m (i, j)</code> and replaces it with the default
<code>value_type ()</code>.
The storage requirement of the Matrix may be decreased.</td>
<td><code>m (i, j)</code> is equal to <code>value_type ()</code>.</td>
</tr>
<tr>
<td>Clear</td>
<td><code>m.clear ()</code></td>
<td>&nbsp;</td>
<td>Equivalent to<br />
<code>for (i = 0; i &lt; m.size1 (); ++ i)</code><br />
&nbsp; <code>for (j = 0; j &lt; m.size2 (); ++ j)</code><br />
&nbsp; &nbsp; <code>m.erase_element (i, j);</code></td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Resize</td>
<td><code>m.resize (n1, n2)
<br />
m.resize (n1, n2, p)
</code></td>
<td>&nbsp;</td>
<td>Reallocate the matrix so that it can hold <code>n1</code> rows
and <code>n2</code> columns.<br />
Erases or appends elements in order to bring the matrix to the
prescribed size. Appended elements are <code>value_type()</code>
copies.<br />
When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the matrix is in the same state as that after an equivalent sizing constructor.</td>
<td><code>m.size1 () == n1</code> and <code>m.size2 () == n2</code>.</td>
</tr>
<tr>
<td>Storage</td>
<td><code>m.data()</code></td>
<td></td>
<td>Returns a reference to the underlying dense storage.</td>
<td>&nbsp;</td>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The run-time complexity of the sizing constructor is quadratic
in the matrix's size.</p>
<p>The run-time complexity of insert_element and erase_element is specific for the
Matrix model and it depends on increases/decreases in storage requirements.</p>
<p>The run-time complexity of resize is quadratic in the matrix's
size.</p>
<h4>Invariants</h4>
<h4>Models</h4>
<ul>
<li><code>matrix</code>, <code>bounded_matrix</code>, <code>c_matrix</code></li>
<li><code>identity_matrix</code> , <code>zero_matrix</code> , <code>scalar_matrix</code></li>
<li><code>triangular_matrix</code> , <code>symmetric_matrix</code> , <code>banded_matrix</code></li>
<li><code>mapped_matrix</code> , <code>compressed_matrix</code> , <code>coordinate_matrix</code></li>
</ul>
<h4>Notes</h4>
<p><a name="matrix_expression_note">[1]</a>
As a user you need not care about <tt>Matrix</tt> being a refinement of the MatrixExpression. Being a refinement of the MatrixExpression is only important for the template-expression engine but not the user.</p>

<hr>

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

<h2><a name="tensor"></a>Tensor</h2>
<h4>Description</h4>
<p>A Tensor describes common aspects of dense multidimensional arrays.</p>
<h4>Refinement of</h4>
<p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
<a href="expression_concept.html#tensor_expression">Tensor Expression</a>
<a href="#tensor_expression_note">[1]</a>
.</p>
<h4>Associated types</h4>
<p>In addition to the types defined by <a href="expression_concept.html#tensor_expression">Tensor Expression</a></p>
<table border="1" summary="types">
<tbody>
<tr>
<td>Public base</td>
<td><code>tensor_container&lt;tensor_t&gt;</code></td>
<td><code>tensor_t</code> must be derived from this public base type.</td>
</tr>
<tr>
<td>Storage array</td>
<td><code>tensor_t::array_type<code></td>
<td>Dense tensor ONLY. The type of underlying storage array used to store the elements. The array_type must model
the <a href="storage_concept.html"><b>Storage</b></a> concept.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0" summary="notation">
<tbody>
<tr>
<td><code>tensor_t</code></td>
<td>A type that is a model of Tensor</td>
</tr>
<tr>
<td><code>t</code></td>
<td>Objects of type <code>tensor_t</code></td>
</tr>
<tr>
<td><code>n1, n2, np, m1, m2, mq </code></td>
<td>Dimension objects of a type convertible to <code>size_type</code></td>
</tr>
<tr>
<td><code>i1, i2, ip, j, k </code></td>
<td>Index objects of a type convertible to <code>size_type</code></td>
</tr>
<tr>
<td><code>v</code></td>
<td>Object of a type convertible to <code>value_type</code></td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined in <a href=
"expression_concept.html#tensor_expression">Tensor Expression</a> the
following expressions must be valid.</p>
<table border="1" summary="expressions">
<tbody>
<tr>
<th>Name</th>
<th>Expression</th>
<th>Type requirements</th>
<th>Return type</th>
</tr>
<tr>
<td>Sizing constructor</td>
<td><code>T t(n1, n2, ..., np)</code></td>
<td>&nbsp;</td>
<td><code>T</code></td>
</tr>
<tr>
<td>Write</td>
<td><code>t.at(i1, i2, ..., ip)</code></td>
<td><code>t</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Read</td>
<td><code>t.at(i1, i2, ..., ip)</code></td>
<td><code>t</code> is mutable.</td>
<td><code>v</code></td>
</tr>
<tr>
<td>Clear</td>
<td><code>t.clear ()</code></td>
<td><code>t</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Resize</td>
<td><code>t.resize(m1, m2, ... , mq)</code></td>
<td><code>t</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Storage</td>
<td><code>t.data()</code></td>
<td><code>t</code> is mutable and dense.</td>
<td><code>pointer</code> if <code>t</code> is mutable, <code>const_pointer</code> otherwise</td>
</tr>
</tbody>
</table>
<h4>Expression semantics</h4>
<p>Semantics of an expression is defined only where it differs
from, or is not defined in <a href=
"expression_concept.html#tensor_expression">Tensor Expression</a> .</p>
<table border="1" summary="semantics">
<tbody>
<tr>
<th>Name</th>
<th>Expression</th>
<th>Precondition</th>
<th>Semantics</th>
<th>Postcondition</th>
</tr>
<tr>
<td>Sizing constructor</td>
<td><code>T t(n1, n2, ..., np)</code></td>
<td>$n_r \geq 1$ for $1\leq 1 \leq p $</code></td>
<td>Allocates a <code>p</code>-order tensor with dimension extents $n_1,n_2,\dots,n_p$.</td>
<td><code>t.size(r)==nr</code> for $1\leq r \leq p$.</td>
</tr>
<tr>
<td>Write</td>
<td><code>t.at(i1,i2,...,ip)=v</code></td>
<td>$0 \leq i_r < n_r$ for $1 \leq r \leq p$.</td>
<td>Writes an element at multi-index position $i_1,i_2,\dots,i_p$ with value <code>v</code>.</td>
<td><code>t(i1,i2,...,ip)</code> is equal to <code>v</code>.</td>
<tr>
<td>Read</td>
<td><code>v=t.at(i1,i2,...,ip)</code></td>
<td>$0 \leq i_r < n_r$ for $1 \leq r \leq p$.</td>
<td>Reads the element at multi-index position $(i_1,i2_,\dots,i_p)$ and returns a value <code>v</code>.</td>
<td><code>t(i1,i2,...,ip)</code> is equal to <code>v</code>.</td>
</tr>
<tr>
<td>Clear</td>
<td><code>t.clear()</code></td>
<td>&nbsp;</td>
<td>Removes all elements from the container.</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Resize</td>
<td><code>t.resize(m1, m2, ..., mq)</code></td>
<td>$m_r \geq 1$ for $1\leq 1 \leq q $</code></td>
<td>Reallocate the matrix so that it can hold $m_1\times m_2\times \cdots \times m_q$ elements.<br />
Erases or appends elements in order to bring the matrix to the
prescribed size. Appended elements are <code>value_type()</code>
copies.</td>
<td><code>t.size(r) == mr</code> for $1\leq r \leq q$.</td>
</tr>
<tr>
<td>Storage</td>
<td><code>m.data()</code></td>
<td></td>
<td>Returns a reference to the underlying dense storage.</td>
<td>&nbsp;</td>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The run-time complexity of contructor is linear in the tensor's size $n_1 \times n_2 \times \cdots \times n_p$.</p>
<p>The run-time complexity of <code>write()</code> and <code>read()</code> is linear in the order of the tensor.</p>
<p>The run-time complexity of resize is at most linear in the tensor's size $m_1 \times m_2 \times \cdots \times n_q$.</p>
<h4>Invariants</h4>
<h4>Models</h4>
<ul>
<li><code>tensor</code></li>
</ul>

<h4>Notes</h4>
<p><a name="tensor_expression_note">[1]</a>
As a user you need not care about <tt>Tensor</tt> being a refinement of the TensorExpression. Being a refinement of the TensorExpression is only important for the template-expression engine but not the user.</p>


<hr />
<p>
Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
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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