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1034 lines
32 KiB
HTML
1034 lines
32 KiB
HTML
<html>
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<head>
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<meta http-equiv="Content-Type"
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content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR" content="Microsoft FrontPage Express 2.0">
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<title>Expression Concepts</title>
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</head>
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<body bgcolor="#FFFFFF">
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="center">Expression Concepts</h1>
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<h2><a name="scalar_expression"></a>Scalar Expression</h2>
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<h4>Description</h4>
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<p>A Scalar Expression is an expression convertible to a scalar
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type. </p>
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<h4>Refinement of </h4>
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<p>Default Constructible.</p>
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<h4>Associated types</h4>
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<table border="1">
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<tr>
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<td>Value type </td>
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<td><code>value_type</code> </td>
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<td>The type of the scalar expression. </td>
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</tr>
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</table>
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<h4>Notation</h4>
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<table border="0">
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<tr>
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<td><code>S</code> </td>
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<td>A type that is a model of Scalar Expression</td>
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</tr>
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</table>
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<h4>Definitions</h4>
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<h4>Valid expressions</h4>
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<p>In addition to the expressions defined in Default
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Constructible the following expressions must be valid. </p>
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<table border="1">
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<tr>
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<th>Name </th>
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<th>Expression </th>
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<th>Type requirements </th>
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<th>Return type </th>
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</tr>
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<tr>
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<td>Evaluation </td>
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<td><code>operator value_type () const</code></td>
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<td> </td>
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<td><code>value_type</code></td>
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</tr>
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</table>
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<h4>Expression semantics</h4>
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<p>Semantics of an expression is defined only where it differs
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from, or is not defined in Default Constructible.</p>
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<table border="1">
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<tr>
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<th>Name </th>
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<th>Expression </th>
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<th>Precondition </th>
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<th>Semantics </th>
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<th>Postcondition </th>
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</tr>
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<tr>
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<td>Evaluation </td>
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<td><code>operator value_type () const</code></td>
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<td> </td>
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<td> Evaluates the scalar expression.</td>
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<td> </td>
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</tr>
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</table>
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<h4>Complexity guarantees</h4>
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<p>The run-time complexity of the evaluation is specific for the
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evaluated scalar expression. </p>
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<h4>Invariants</h4>
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<h4>Models</h4>
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<ul>
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<li><code>vector_scalar_unary<E, F></code></li>
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<li><code>vector_scalar_binary<E1, E2, F></code></li>
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</ul>
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<h2><a name="vector_expression"></a>Vector Expression</h2>
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<h4>Description</h4>
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<p>A Vector Expression is an expression evaluatable to a vector.
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Vector Expression provides an <a
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href="iterator.htm#indexed_bidirectional_iterator">Indexed
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Bidirectional Iterator</a> or an <a
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href="iterator.htm#indexed_random_access_iterator">Indexed Random
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Access Iterator</a>.</p>
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<h4>Refinement of </h4>
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<p>Default Constructible.</p>
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<h4>Associated types</h4>
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<table border="1">
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<tr>
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<td>Value type </td>
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<td><code>value_type</code> </td>
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<td>The type of the vector expression. </td>
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</tr>
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<tr>
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<td>Const iterator type </td>
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<td><code>const_iterator</code> </td>
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<td>A type of iterator that may be used to examine a
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vector expression's elements. </td>
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</tr>
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<tr>
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<td>Iterator type </td>
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<td><code>iterator</code> </td>
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<td>A type of iterator that may be used to modify a
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vector expression's elements. </td>
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</tr>
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<tr>
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<td>Distance type </td>
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<td><code>difference_type</code> </td>
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<td>A signed integral type used to represent the distance
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between two of the vector expression's iterators. </td>
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</tr>
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<tr>
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<td>Size type </td>
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<td><code>size_type</code> </td>
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<td>An unsigned integral type that can represent any
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nonnegative value of the vector expression's distance
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type. </td>
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</tr>
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<tr>
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<td>Const reverse iterator type </td>
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<td><code>const_reverse_iterator</code> </td>
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<td>A Reverse Iterator adaptor whose base iterator type
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is the vector expression's const iterator type. </td>
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</tr>
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<tr>
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<td>Reverse iterator type </td>
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<td><code>reverse_iterator</code> </td>
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<td>A Reverse Iterator adaptor whose base iterator type
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is the vector expression's iterator type. </td>
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</tr>
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</table>
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<h4>Notation</h4>
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<table border="0">
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<tr>
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<td><code>V</code> </td>
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<td>A type that is a model of Vector Expression</td>
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</tr>
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<tr>
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<td><code>v, v1, v2</code></td>
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<td>Object of type <code>V</code> </td>
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</tr>
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<tr>
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<td><code>i</code></td>
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<td>Object of a type convertible to <code>size_type</code>
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</td>
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</tr>
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<tr>
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<td><code>t</code></td>
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<td>Object of a type convertible to <code>value_type</code></td>
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</tr>
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</table>
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<h4>Definitions</h4>
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<h4>Valid expressions</h4>
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<p>In addition to the expressions defined in Default
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Constructible the following expressions must be valid. </p>
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<table border="1">
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<tr>
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<th>Name </th>
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<th>Expression </th>
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<th>Type requirements </th>
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<th>Return type </th>
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</tr>
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<tr>
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<td rowspan="2">Beginning of range </td>
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<td><code>v.begin ()</code> </td>
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<td> </td>
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<td><code>const_iterator</code></td>
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</tr>
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<tr>
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<td><code>v.begin ()</code></td>
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<td><code>v</code> is mutable. </td>
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<td><code>iterator</code></td>
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</tr>
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<tr>
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<td rowspan="2">End of range </td>
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<td><code>v.end ()</code> </td>
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<td> </td>
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<td><code>const_iterator</code></td>
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</tr>
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<tr>
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<td><code>v.end ()</code> </td>
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<td><code>v</code> is mutable.</td>
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<td><code>iterator</code></td>
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</tr>
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<tr>
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<td>Size </td>
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<td><code>v.size ()</code> </td>
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<td> </td>
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<td><code>size_type</code> </td>
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</tr>
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<tr>
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<td>Swap </td>
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<td><code>v1.swap (v2)</code> </td>
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<td><code>v1</code> and <code>v2</code> are mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td rowspan="2">Beginning of reverse range </td>
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<td><code>v.rbegin ()</code> </td>
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<td> </td>
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<td><code>const_reverse_iterator</code></td>
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</tr>
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<tr>
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<td><code>v.rbegin ()</code> </td>
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<td><code>v</code> is mutable.</td>
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<td><code>reverse_iterator</code></td>
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</tr>
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<tr>
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<td rowspan="2">End of reverse range </td>
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<td><code>v.rend ()</code> </td>
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<td> </td>
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<td><code>const_reverse_iterator</code></td>
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</tr>
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<tr>
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<td><code>v.rend ()</code> </td>
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<td><code>v</code> is mutable.</td>
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<td><code>reverse_iterator</code></td>
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</tr>
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<tr>
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<td>Element access </td>
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<td><code>v (i)</code> </td>
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<td><code>i</code> is convertible to <code>size_type</code>.
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</td>
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<td>Convertible to <code>value_type</code>.</td>
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</tr>
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<tr>
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<td rowspan="2">Assignment</td>
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<td><code>v2 = v1</code></td>
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<td><code>v2</code> is mutable and <code>v1</code> is
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convertible to <code>V</code>. </td>
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<td><code>V &</code></td>
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</tr>
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<tr>
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<td><code>v2.assign (v1)</code></td>
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<td><code>v2</code> is mutable and <code>v1</code> is
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convertible to <code>V</code>.</td>
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<td><code>V &</code></td>
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</tr>
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<tr>
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<td rowspan="5">Computed assignment</td>
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<td><code>v2 += v1</code></td>
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<td><code>v2</code> is mutable and <code>v1</code> is
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convertible to <code>V</code>.</td>
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<td><code>V &</code></td>
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</tr>
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<tr>
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<td><code>v2.plus_assign (v1)</code></td>
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<td><code>v2</code> is mutable and <code>v1</code> is
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convertible to <code>V</code>.</td>
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<td><code>V &</code></td>
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</tr>
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<tr>
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<td><code>v2 -= v1</code></td>
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<td><code>v2</code> is mutable and <code>v1</code> is
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convertible to <code>V</code>.</td>
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<td><code>V &</code></td>
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</tr>
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<tr>
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<td><code>v2.minus_assign (v1)</code></td>
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<td><code>v2</code> is mutable and <code>v1</code> is
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convertible to <code>V</code>.</td>
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<td><code>V &</code></td>
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</tr>
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<tr>
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<td><code>v *= t</code></td>
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<td><code>v</code> is mutable and <code>t</code> is
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convertible to <code>value_type</code>.</td>
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<td><code>V &</code></td>
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</tr>
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</table>
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<h4>Expression semantics</h4>
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<p>Semantics of an expression is defined only where it differs
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from, or is not defined in Default Constructible.</p>
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<table border="1">
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<tr>
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<th>Name </th>
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<th>Expression </th>
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<th>Precondition </th>
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<th>Semantics </th>
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<th>Postcondition </th>
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</tr>
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<tr>
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<td>Beginning of range </td>
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<td><code>v.begin ()</code> </td>
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<td> </td>
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<td>Returns an iterator pointing to the first element in
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the vector expression. </td>
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<td><code>v.begin ()</code> is either dereferenceable or
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past-the-end. It is past-the-end if and only if <code>v.size
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() == 0</code>. </td>
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</tr>
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<tr>
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<td>End of range </td>
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<td><code>v.end ()</code> </td>
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<td> </td>
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<td>Returns an iterator pointing one past the last
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element in the vector expression. </td>
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<td><code>v.end ()</code> is past-the-end. </td>
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</tr>
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<tr>
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<td>Size </td>
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<td><code>v.size ()</code> </td>
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<td> </td>
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<td>Returns the size of the vector expression, that is,
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its number of elements. </td>
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<td><code>v.size () >= 0 </code></td>
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</tr>
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<tr>
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<td>Swap </td>
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<td><code>v1.swap (v2)</code> </td>
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<td> </td>
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<td>Equivalent to <code>swap (v1, v2)</code>. </td>
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<td> </td>
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</tr>
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<tr>
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<td>Beginning of reverse range </td>
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<td><code>v.rbegin ()</code> </td>
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<td> </td>
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<td>Equivalent to <code>reverse_iterator (v.end ())</code>.
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</td>
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<td><code>v.rbegin ()</code> is either dereferenceable or
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past-the-end. It is past-the-end if and only if <code>v.size
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() == 0</code>. </td>
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</tr>
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<tr>
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<td>End of reverse range </td>
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<td><code>v.rend ()</code> </td>
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<td> </td>
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<td>Equivalent to <code>reverse_iterator (v.begin ())</code>.
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</td>
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<td><code>v.rend ()</code> is past-the-end.</td>
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</tr>
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<tr>
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<td>Element access </td>
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<td><code>v (i)</code> </td>
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<td><code>0 <= i < v.size ()</code> </td>
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<td>Returns the <code>i</code>-th element of the vector
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expression. </td>
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<td> </td>
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</tr>
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<tr>
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<td rowspan="2">Assignment</td>
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<td><code>v2 = v1</code></td>
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<td><code>v1.size () == v2.size ()</code></td>
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<td>Assigns every element of the evaluated vector
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expression <code>v1</code> to the corresponding element
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of <code>v2</code>.</td>
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<td> </td>
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</tr>
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<tr>
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<td><code>v2.assign (v1)</code></td>
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<td><code>v1.size () == v2.size ()</code></td>
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<td>Assigns every element of <code>v1 </code>to the
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corresponding element of <code>v2</code>.</td>
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<td> </td>
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</tr>
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<tr>
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<td rowspan="5">Computed assignment</td>
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<td><code>v2 += v1</code></td>
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<td><code>v1.size () == v2.size ()</code></td>
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<td>Adds every element of the evaluated vector expression
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<code>v1</code> to the corresponding element of <code>v2</code>.</td>
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<td> </td>
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</tr>
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<tr>
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<td><code>v2.plus_assign (v1)</code></td>
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<td><code>v1.size () == v2.size ()</code></td>
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<td>Adds every element of <code>v1</code> to the
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corresponding element of <code>v2</code>.</td>
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<td> </td>
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</tr>
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<tr>
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<td><code>v2 -= v1</code></td>
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<td><code>v1.size () == v2.size ()</code></td>
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<td>Subtracts every element of the evaluated vector
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expression <code>v1</code> from the corresponding element
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of <code>v2</code>.</td>
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<td> </td>
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</tr>
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||
<tr>
|
||
<td><code>v2.minus_assign (v1)</code></td>
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<td><code>v1.size () == v2.size ()</code></td>
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<td>Subtracts every element of <code>v1</code> from the
|
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corresponding element of <code>v2</code>.</td>
|
||
<td> </td>
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||
</tr>
|
||
<tr>
|
||
<td><code>v *= t</code></td>
|
||
<td> </td>
|
||
<td>Multiplies every element of <code>v</code> with <code>t</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Complexity guarantees</h4>
|
||
|
||
<p>The run-time complexity of <code>begin () </code>and <code>end
|
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() </code>is specific for the evaluated vector expression,
|
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typically amortized constant time.</p>
|
||
|
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<p>The run-time complexity of <code>size ()</code> is constant
|
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time. </p>
|
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|
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<p>The run-time complexity of <code>swap ()</code> is specific
|
||
for the evaluated vector expression, typically constant time. </p>
|
||
|
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<p>The run-time complexity of <code>rbegin ()</code> and <code>rend
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()</code> is specific for the evaluated vector expression,
|
||
typically amortized constant time.</p>
|
||
|
||
<p>The run-time complexity of the element access is specific for
|
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the evaluated vector expression, typically amortized constant
|
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time for the dense and logarithmic for the sparse case.</p>
|
||
|
||
<p>The run-time complexity of the arithmetic operations is
|
||
specific for the evaluated vector expressions, typically linear
|
||
in the size of the expressions.</p>
|
||
|
||
<h4>Invariants</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<td>Valid range </td>
|
||
<td>For any vector expression <code>v</code>, <code>[v.begin
|
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(), v.end ())</code> is a valid range. </td>
|
||
</tr>
|
||
<tr>
|
||
<td>Completeness </td>
|
||
<td>An algorithm that iterates through the range <code>[v.begin
|
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(), v.end ())</code> will pass through every element of <code>v</code>.
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Valid reverse range </td>
|
||
<td><code>[v.rbegin (), v.rend ())</code> is a valid
|
||
range. </td>
|
||
</tr>
|
||
<tr>
|
||
<td>Equivalence of ranges </td>
|
||
<td>The distance from <code>v.begin ()</code> to <code>v.end
|
||
()</code> is the same as the distance from <code>v.rbegin
|
||
()</code> to <code>v.rend ()</code>. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Models</h4>
|
||
|
||
<ul>
|
||
<li><code>vector_range<V></code></li>
|
||
<li><code>vector_slice<V></code></li>
|
||
<li><code>matrix_row<M></code></li>
|
||
<li><code>matrix_column<M></code></li>
|
||
<li><code>matrix_vector_range<M></code></li>
|
||
<li><code>matrix_vector_slice<M></code></li>
|
||
<li><code>vector_unary<E, F></code></li>
|
||
<li><code>vector_binary<E1, E2, F></code></li>
|
||
<li><code>vector_binary_scalar1<E1, E2, F></code></li>
|
||
<li><code>vector_binary_scalar2<E1, E2, F></code></li>
|
||
<li><code>matrix_vector_unary1<E></code></li>
|
||
<li><code>matrix_vector_unary2<E></code></li>
|
||
<li><code>matrix_vector_binary1<E1, E2, F></code></li>
|
||
<li><code>matrix_vector_binary2<E1, E2, F></code></li>
|
||
</ul>
|
||
|
||
<h2><a name="matrix_expression"></a>Matrix Expression</h2>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>A Matrix Expression is an expression evaluatable to a matrix.
|
||
Matrix Expression provides an <a
|
||
href="iterator.htm#indexed_bidirectional_cr_iterator">Indexed
|
||
Bidirectional Column/Row Iterator</a> or an <a
|
||
href="iterator.htm#indexed_random_access_cr_iterator">Indexed
|
||
Random Access Column/Row Iterator</a>.</p>
|
||
|
||
<h4>Refinement of </h4>
|
||
|
||
<p>Default Constructible.</p>
|
||
|
||
<h4>Associated types</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<td>Value type </td>
|
||
<td><code>value_type</code> </td>
|
||
<td>The type of the matrix expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Const iterator types </td>
|
||
<td><code>const_iterator1</code> </td>
|
||
<td>A type of column iterator that may be used to examine
|
||
a matrix expression's elements. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator2</code></td>
|
||
<td>A type of row iterator that may be used to examine a
|
||
matrix expression's elements. </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Iterator types </td>
|
||
<td><code>iterator1</code> </td>
|
||
<td>A type of column iterator that may be used to modify
|
||
a matrix expression's elements. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>iterator2</code></td>
|
||
<td>A type of row iterator that may be used to modify a
|
||
matrix expression's elements. </td>
|
||
</tr>
|
||
<tr>
|
||
<td>Distance type </td>
|
||
<td><code>difference_type</code> </td>
|
||
<td>A signed integral type used to represent the distance
|
||
between two of the matrix expression's iterators. </td>
|
||
</tr>
|
||
<tr>
|
||
<td>Size type </td>
|
||
<td><code>size_type</code> </td>
|
||
<td>An unsigned integral type that can represent any
|
||
nonnegative value of the matrix expression's distance
|
||
type. </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Const reverse iterator types </td>
|
||
<td><code>const_reverse_iterator1</code> </td>
|
||
<td>A Reverse Iterator adaptor whose base iterator type
|
||
is the matrix expression's const column iterator type. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator2</code> </td>
|
||
<td>A Reverse Iterator adaptor whose base iterator type
|
||
is the matrix expression's const row iterator type. </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Reverse iterator types </td>
|
||
<td><code>reverse_iterator1</code> </td>
|
||
<td>A Reverse Iterator adaptor whose base iterator type
|
||
is the matrix expression's column iterator type. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>reverse_iterator2</code> </td>
|
||
<td>A Reverse Iterator adaptor whose base iterator type
|
||
is the matrix expression's row iterator type. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Notation</h4>
|
||
|
||
<table border="0">
|
||
<tr>
|
||
<td><code>M</code> </td>
|
||
<td>A type that is a model of Matrix Expression</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m, m1, m2</code></td>
|
||
<td>Object of type <code>M</code> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>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>
|
||
</table>
|
||
|
||
<h4>Definitions</h4>
|
||
|
||
<h4>Valid expressions</h4>
|
||
|
||
<p>In addition to the expressions defined in Default
|
||
Constructible the following expressions must be valid. </p>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Name </th>
|
||
<th>Expression </th>
|
||
<th>Type requirements </th>
|
||
<th>Return type </th>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="4">Beginning of range </td>
|
||
<td><code>m.begin1 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.begin2 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.begin1 ()</code> </td>
|
||
<td><code>m</code> is mutable. </td>
|
||
<td><code>iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.begin2 ()</code> </td>
|
||
<td><code>m</code> is mutable.</td>
|
||
<td><code>iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="4">End of range </td>
|
||
<td><code>m.end1 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.end2 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.end1 ()</code> </td>
|
||
<td><code>m</code> is mutable. </td>
|
||
<td><code>iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.end2 ()</code> </td>
|
||
<td><code>m</code> is mutable.</td>
|
||
<td><code>iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Size </td>
|
||
<td><code>m.size1 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>size_type</code> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.size2 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>size_type</code> </td>
|
||
</tr>
|
||
<tr>
|
||
<td>Swap </td>
|
||
<td><code>m1.swap (m2)</code></td>
|
||
<td><code>m1</code> and <code>m2</code> are
|
||
mutable. </td>
|
||
<td><code>void</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="4">Beginning of reverse range </td>
|
||
<td><code>m.rbegin1 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_reverse_iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rbegin2 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_reverse_iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rbegin1 ()</code> </td>
|
||
<td><code>m</code> is mutable. </td>
|
||
<td><code>reverse_iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rbegin2 ()</code> </td>
|
||
<td><code>m</code> is mutable.</td>
|
||
<td><code>reverse_iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="4">End of reverse range </td>
|
||
<td><code>m.rend1 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_reverse_iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rend2 ()</code> </td>
|
||
<td> </td>
|
||
<td><code>const_reverse_iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rend1 ()</code> </td>
|
||
<td><code>m</code> is mutable.</td>
|
||
<td><code>reverse_iterator1</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rend2 ()</code></td>
|
||
<td><code>m</code> is mutable.</td>
|
||
<td><code>reverse_iterator2</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Element access </td>
|
||
<td><code>m (i, j)</code> </td>
|
||
<td><code>i</code> and <code>j </code>are convertible to <code>size_type</code>.
|
||
</td>
|
||
<td>Convertible to <code>value_type</code>.</td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Assignment</td>
|
||
<td><code>m2 = m1</code></td>
|
||
<td><code>m2</code> is mutable and <code>m1</code> is
|
||
convertible to <code>M</code>.</td>
|
||
<td><code>M &</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2.assign (m1)</code></td>
|
||
<td><code>m2</code> is mutable and <code>m1</code> is
|
||
convertible to <code>M</code>.</td>
|
||
<td><code>M &</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="5">Computed assignment</td>
|
||
<td><code>m2 += m1</code></td>
|
||
<td><code>m2</code> is mutable and <code>m1</code> is
|
||
convertible to <code>M</code>.</td>
|
||
<td><code>M &</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2.plus_assign (m1)</code></td>
|
||
<td><code>m2</code> is mutable and <code>m1</code> is
|
||
convertible to <code>M</code>.</td>
|
||
<td><code>M &</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2 -= m1</code></td>
|
||
<td><code>m2</code> is mutable and <code>m1</code> is
|
||
convertible to <code>M</code>.</td>
|
||
<td><code>M &</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2.minus_assign (m1)</code></td>
|
||
<td><code>m2</code> is mutable and <code>m1</code> is
|
||
convertible to <code>M</code>.</td>
|
||
<td><code>M &</code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m *= t</code></td>
|
||
<td><code>m</code> is mutable and <code>t</code> is
|
||
convertible to <code>value_type</code>.</td>
|
||
<td><code>M &</code></td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Expression semantics</h4>
|
||
|
||
<p>Semantics of an expression is defined only where it differs
|
||
from, or is not defined in Default Constructible.</p>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Name </th>
|
||
<th>Expression </th>
|
||
<th>Precondition </th>
|
||
<th>Semantics </th>
|
||
<th>Postcondition </th>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Beginning of range </td>
|
||
<td><code>m.begin1 ()</code> </td>
|
||
<td> </td>
|
||
<td>Returns an iterator pointing to the first element in
|
||
the first column of a matrix expression. </td>
|
||
<td><code>m.begin1 ()</code> is either dereferenceable or
|
||
past-the-end. It is past-the-end if and only if <code>m.size1
|
||
() == 0</code>. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.begin2 ()</code> </td>
|
||
<td> </td>
|
||
<td>Returns an iterator pointing to the first element in
|
||
the first row of a matrix expression. </td>
|
||
<td><code>m.begin2 ()</code> is either dereferenceable or
|
||
past-the-end. It is past-the-end if and only if <code>m.size2
|
||
() == 0</code>. </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">End of range </td>
|
||
<td><code>m.end1 ()</code> </td>
|
||
<td> </td>
|
||
<td>Returns an iterator pointing one past the last
|
||
element in the matrix expression. </td>
|
||
<td><code>m.end1 ()</code> is past-the-end. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.end2 ()</code> </td>
|
||
<td> </td>
|
||
<td>Returns an iterator pointing one past the last
|
||
element in the matrix expression. </td>
|
||
<td><code>m.end2 ()</code> is past-the-end. </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Size </td>
|
||
<td><code>m.size1 ()</code> </td>
|
||
<td> </td>
|
||
<td>Returns the number of rows of the matrix expression. </td>
|
||
<td><code>m.size1 () >= 0 </code></td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.size2 ()</code> </td>
|
||
<td> </td>
|
||
<td>Returns the number of columns of the matrix
|
||
expression. </td>
|
||
<td><code>m.size2 () >= 0 </code></td>
|
||
</tr>
|
||
<tr>
|
||
<td>Swap </td>
|
||
<td><code>m1.swap (m2)</code> </td>
|
||
<td> </td>
|
||
<td>Equivalent to <code>swap (m1, m2)</code>. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Beginning of reverse range </td>
|
||
<td><code>m.rbegin1 ()</code> </td>
|
||
<td> </td>
|
||
<td>Equivalent to <code>reverse_iterator1 (m.end1 ())</code>.
|
||
</td>
|
||
<td><code>m.rbegin1 ()</code> is either dereferenceable
|
||
or past-the-end. It is past-the-end if and only if <code>m.size1
|
||
() == 0</code>. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rbegin2 ()</code> </td>
|
||
<td> </td>
|
||
<td>Equivalent to <code>reverse_iterator2 (m.end2 ())</code>.
|
||
</td>
|
||
<td><code>m.rbegin2 ()</code> is either dereferenceable
|
||
or past-the-end. It is past-the-end if and only if <code>m.size2
|
||
() == 0</code>. </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">End of reverse range </td>
|
||
<td><code>m.rend1 ()</code> </td>
|
||
<td> </td>
|
||
<td>Equivalent to <code>reverse_iterator1 (m.begin1 ())</code>.
|
||
</td>
|
||
<td><code>m.rend1 ()</code> is past-the-end.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m.rend2 ()</code> </td>
|
||
<td> </td>
|
||
<td>Equivalent to <code>reverse_iterator2 (m.begin2 ())</code>.
|
||
</td>
|
||
<td><code>m.rend2 ()</code> is past-the-end.</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Element access </td>
|
||
<td><code>m (i, j)</code> </td>
|
||
<td><code>0 <= i < m.size1 ()</code> and <code>0
|
||
<= j < m.size2 ()</code> </td>
|
||
<td>Returns the <code>j</code>-th element of the <code>i</code>-th
|
||
row of the matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="2">Assignment</td>
|
||
<td><code>m2 = m1</code></td>
|
||
<td><code>m1.size1 () == m2.size1 ()</code> and <code><br>
|
||
m1.size2 () == m2.size2 ()</code> </td>
|
||
<td>Assigns every element of the evaluated matrix
|
||
expression <code>m1</code> to the corresponding element
|
||
of <code>m2</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2.assign (m1)</code></td>
|
||
<td><code>m1.size1 () == m2.size1 ()</code> and <code><br>
|
||
m1.size2 () == m2.size2 ()</code> </td>
|
||
<td>Assigns every element of <code>m1 </code>to the
|
||
corresponding element of <code>m2</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td rowspan="5">Computed assignment</td>
|
||
<td><code>m2 += m1</code></td>
|
||
<td><code>m1.size1 () == m2.size1 ()</code> and <code><br>
|
||
m1.size2 () == m2.size2 ()</code> </td>
|
||
<td>Adds every element of the evaluated matrix expression
|
||
<code>m1</code> to the corresponding element of <code>m2</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2.plus_assign (m1)</code></td>
|
||
<td><code>m1.size1 () == m2.size1 ()</code> and <code><br>
|
||
m1.size2 () == m2.size2 ()</code> </td>
|
||
<td>Adds every element of <code>m1</code> to the
|
||
corresponding element of <code>m2</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2 -= m1</code></td>
|
||
<td><code>m1.size1 () == m2.size1 ()</code> and <code><br>
|
||
m1.size2 () == m2.size2 ()</code> </td>
|
||
<td>Subtracts every element of the evaluated matrix
|
||
expression <code>m1</code> from the corresponding element
|
||
of <code>m2</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m2.minus_assign (m1)</code></td>
|
||
<td><code>m1.size1 () == m2.size1 ()</code> and <code><br>
|
||
m1.size2 () == m2.size2 ()</code> </td>
|
||
<td>Subtracts every element of <code>m1</code> from the
|
||
corresponding element of <code>m2</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>m *= t</code></td>
|
||
<td> </td>
|
||
<td>Multiplies every element of <code>m</code> with <code>t</code>.</td>
|
||
<td> </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Complexity guarantees</h4>
|
||
|
||
<p>The run-time complexity of <code>begin1 ()</code>,<code>
|
||
begin2 ()</code>,<code> end1 () </code>and <code>end2 () </code>is
|
||
specific for the evaluated matrix expression.</p>
|
||
|
||
<p>The run-time complexity of <code>size1 () </code>and <code>size2
|
||
() </code>is constant time. </p>
|
||
|
||
<p>The run-time complexity of <code>swap () </code>is specific
|
||
for the evaluated matrix expression, typically constant time. </p>
|
||
|
||
<p>The run-time complexity of <code>rbegin1 ()</code>,<code>
|
||
rbegin2 ()</code>,<code> rend1 () </code>and <code>rend2 () </code>is
|
||
specific for the evaluated matrix expression.</p>
|
||
|
||
<p>The run-time complexity of the element access is specific for
|
||
the evaluated matrix expression, typically amortized constant
|
||
time for the dense and logarithmic for the sparse case.</p>
|
||
|
||
<p>The run-time complexity of the arithmetic operations is
|
||
specific for the evaluated matrix expressions, typically
|
||
quadratic in the size of the proxies.</p>
|
||
|
||
<h4>Invariants</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<td>Valid range </td>
|
||
<td>For any matrix expression <code>m</code>, <code>[m.begin1
|
||
(), m.end1 ())</code> and <code>[m.begin2 (), m.end2 ())</code>
|
||
are valid ranges. </td>
|
||
</tr>
|
||
<tr>
|
||
<td>Completeness </td>
|
||
<td>An algorithm that iterates through the range <code>[m.begin1
|
||
(), m.end1 ())</code> will pass through every row of <code>m</code>,
|
||
an algorithm that iterates through the range <code>[m.begin2
|
||
(), m.end2 ())</code> will pass through every column of <code>m</code>.</td>
|
||
</tr>
|
||
<tr>
|
||
<td>Valid reverse range </td>
|
||
<td><code>[m.rbegin1 (), m.rend1 ())</code> and <code>[m.rbegin2
|
||
(), m.rend2 ())</code> are valid ranges. </td>
|
||
</tr>
|
||
<tr>
|
||
<td>Equivalence of ranges </td>
|
||
<td>The distance from <code>m.begin1 ()</code> to <code>m.end1
|
||
()</code> is the same as the distance from <code>m.rbegin1
|
||
()</code> to <code>m.rend1 ()</code> and the distance
|
||
from <code>m.begin2 ()</code> to <code>m.end2 ()</code>
|
||
is the same as the distance from <code>m.rbegin2 ()</code>
|
||
to <code>m.rend2 ()</code>. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Models</h4>
|
||
|
||
<ul>
|
||
<li><code>matrix_range<M></code></li>
|
||
<li><code>matrix_slice<M></code></li>
|
||
<li><code>triangular_adaptor<M, F></code></li>
|
||
<li><code>symmetric_adaptor<M, F></code></li>
|
||
<li><code>banded_adaptor<M></code></li>
|
||
<li><code>vector_matrix_binary<E1, E2, F></code></li>
|
||
<li><code>matrix_unary1<E, F></code></li>
|
||
<li><code>matrix_unary2<E, F></code></li>
|
||
<li><code>matrix_binary<E1, E2, F></code></li>
|
||
<li><code>matrix_binary_scalar1<E1, E2, F></code></li>
|
||
<li><code>matrix_binary_scalar2<E1, E2, F></code></li>
|
||
<li><code>matrix_matrix_binary<E1, E2, F></code></li>
|
||
</ul>
|
||
|
||
<hr>
|
||
|
||
<p>Copyright (<28>) 2000-2002 Joerg Walter, Mathias Koch <br>
|
||
Permission to copy, use, modify, sell and distribute this document is granted
|
||
provided this copyright notice appears in all copies. This document is provided
|
||
``as is'' without express or implied warranty, and with no claim as to its suitability
|
||
for any purpose.</p>
|
||
|
||
<p>Last revised: 8/3/2002</p>
|
||
|
||
</body>
|
||
</html>
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