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562 lines
18 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml">
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<!-- $Id$ -->
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<head>
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<meta name="generator" content=
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"HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" />
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<meta name="GENERATOR" content="Quanta Plus" />
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<link href="ublas.css" type="text/css" />
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<title>Types Overview</title>
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</head>
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<body>
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="middle" />
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Overview of Matrix- and Vector-Types </h1>
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<dl>
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<dt>Contents:</dt>
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<dd><a href="#vectors">Vectors</a></dd>
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<dd><a href="#vector_proxies">Vector Proxies</a></dd>
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<dd><a href="#matrices">Matrices</a></dd>
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<dd><a href="#matrix_proxies">Matrix Proxies</a></dd>
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<dd><a href="#storage_layout">Special Storage Layouts</a></dd>
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</dl>
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<h3>Notation:</h3>
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<table style="border: none;" summary="notation">
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<tr><td><code>T</code></td>
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<td>is the data type, e.g. <code>double, ...</code></td></tr>
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<tr><td><code>F</code></td>
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<td>is the orientation type (functor), either
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<code>row_major</code> or <code>column_major</code></td></tr>
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<tr><td><code>C</code></td> <td>is a container type, e.g. <code>std::vector,
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bounded_array, unbounded_array, ...</code></td></tr>
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<tr><td><code>TRI</code></td>
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<td>is a triangular functor: <code>lower,
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unit_lower, strict_lower, upper, unit_upper,
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strict_upper</code></td></tr>
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<tr><td><code>M, N</code></td>
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<td>are unsinged integer values
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(<code>std::size_t</code>)</td></tr>
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<tr><td><code>VEC</code></td>
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<td>is any vector type</td></tr>
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<tr><td><code>MAT</code> </td>
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<td>is any matrix type</td></tr>
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<tr><td><code>[...]</code></td>
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<td>denote optional arguments - for more details
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look at the section "storage layout".</td></tr>
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</table>
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<h2><a name="vectors">Vectors</a></h2>
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<table border="1" summary="vector types">
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<thead>
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<tr>
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<th width="30%">Definition</th>
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<th>Description</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td><code>vector<T [, C]> v(size);</code></td>
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<td>a dense vector of values of type <code>T</code> of arbitrary
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size - only depending on the underlying container type
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<code>C</code> which defaults to <code>unbounded_array</code>.</td>
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</tr>
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<tr>
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<td><code>bounded_vector<T, N> v;</code></td>
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<td>a dense vector of values of type <code>T</code> of maximal size
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<code>N</code>. The default contructor initialises <code>c</code>
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to a zero vector of size <code>N</code>.</td>
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</tr>
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<tr>
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<td><code>zero_vector<T> v(size);</code></td>
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<td>the zero vector of type <code>T</code> with arbitrary
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size.</td>
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</tr>
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<tr>
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<td><code>unit_vector<T> v(size, index);</code></td>
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<td>the unit vector of type <code>T</code> with arbitrary size. The
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vector is <code>v(i) = (i==index)?T(1):T()</code>.
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<code>index</code> should be less than <code>size</code>.</td>
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</tr>
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<tr>
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<td><code>sparse_vector<T [, C]> v(size);</code></td>
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<td>a sparse vector of values of type <code>T</code> of arbitrary
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size. The container type can be <code>std::map<size_t,
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T></code> or <code>map_array<size_t, T></code>.</td>
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</tr>
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<tr>
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<td><code>compressed_vector<T [, C]> v(size);</code></td>
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<td>a sparse vector of values of type <code>T</code> of arbitrary
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size. The non zero values are stored as two seperate arrays - an
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index array and a value array. The index array is always sorted and
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the is at most one entry for each index.</td>
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</tr>
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<tr>
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<td><code>coordinate_vector<T [, C]> v(size);</code></td>
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<td>a sparse vector of values of type <code>T</code> of arbitrary
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size. The non zero values are stored as two seperate arrays - an
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index array and a value array. The arrays may be out of order with
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multiple entries for each vector element. If there are multiple
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values for the same index the sum of these values is the real
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value.</td>
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</tr>
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</tbody>
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</table>
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<p><em>Note:</em> the default types are defined in
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<code>boost/numeric/ublas/fwd.hpp</code>.</p>
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<h2><a name="vector_proxies">Vector Proxies</a></h2>
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<table border="1" summary="vector proxies">
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<thead>
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<tr>
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<th width="30%">Definition</th>
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<th>Description</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td><code>vector_range<VEC> vr(v, range);</code></td>
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<td>a vector referencing a continuous subvector of elements of
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vector <code>v</code> containing all elements specified by
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<code>range</code>.</td>
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</tr>
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<tr>
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<td><code>vector_slice<VEC> vs(v, slice);</code></td>
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<td>a vector referencing a non continuous subvector of elements of
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vector <code>v</code> containing all elements specified by
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<code>slice</code>.</td>
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</tr>
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<tr>
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<td><code>matrix_row<MAT> vr(m, index);</code></td>
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<td>a vector referencing the <code>index</code>-th row of matrix
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<code>m</code></td>
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</tr>
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<tr>
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<td><code>matrix_column<MAT> vc(m, index);</code></td>
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<td>a vector referencing the <code>index</code>-th column of matrix
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<code>m</code></td>
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</tr>
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</tbody>
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</table>
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<h2><a name="matrices">Matrices</a></h2>
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<table border="1" summary="matrix types">
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<thead>
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<tr>
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<th width="30%">Definition</th>
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<th>Description</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td><code>matrix<T [, F, C]> m(rows, columns);</code></td>
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<td>a dense matrix of values of type <code>T</code> of arbitrary
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size - only depending on the underlying container type
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<code>C</code> which defaults to <code>unbounded_array</code>. The
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orientation functor <code>F</code> defaults to
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<code>row_major</code>.</td>
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</tr>
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<tr>
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<td><code>bounded_matrix<T, M, N [, F]> m;</code></td>
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<td>a dense matrix of <code>M</code>-by-<code>N</code> values of
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type <code>T</code>. The orientation functor <code>F</code>
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defaults to <code>row_major</code>. The default constructor creates
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a <code>M</code>-by-<code>N</code> zero matrix.</td>
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</tr>
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<tr>
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<td><code>c_matrix<T, M, N> m(rows, columns);</code></td>
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<td>a dense matrix of values of type <code>T</code> of given size.
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The data is stored as a usual c array <code>T
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data_[N][M]</code></td>
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</tr>
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<tr>
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<td><code>vector_of_vector<T [, F, C]> m(rows,
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columns);</code></td>
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<td>a dense matrix of values of type <code>T</code> of given size.
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The data is stored as a vector of vectors. The orientation
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<code>F</code> defaults to <code>row_major</code>. The container
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type <code>C</code> defaults to
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<code>unbounded_array<unbounded_array<T> ></code></td>
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</tr>
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<tr>
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<td><code>zero_matrix<T> m(rows, columns);</code></td>
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<td>a zero matrix of type <code>T</code> of arbitrary size.</td>
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</tr>
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<tr>
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<td><code>identity_matrix<T> m(rows, columns);</code></td>
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<td>an identity matrix of type <code>T</code> of arbitrary size.
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The values are <code>v(i,j) = (i==j)?T(1):T()</code>.</td>
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</tr>
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<tr>
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<td><code>scalar_matrix<T> m(rows, columns,
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value);</code></td>
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<td>a matrix of type <code>T</code> of arbitrary size that has the
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value <code>value</code> everywhere.</td>
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</tr>
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<tr>
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<td><code>triangular_matrix<T [, TRI, F, C]>
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m(size);</code></td>
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<td>a triangular matrix of values of type <code>T</code> of
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arbitrary size. Only the nonzero elements are stored in the given
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order <code>F</code>. ("triangular packed storage") The triangular
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type <code>F</code> defaults to <code>lower</code>, the orientation
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type <code>F</code> defaults to <code>row_major</code>.</td>
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</tr>
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<tr>
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<td><code>banded_matrix<T [, F, C]> m(size1, size2, n_lower,
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n_upper);</code></td>
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<td>a banded matrix of values of type <code>T</code> of arbitrary
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size with <code>n_lower</code> sub diagonals and
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<code>n_upper</code> super diagonals. Only the nonzero elements are
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stored in the given order <code>F</code>. ("packed storage")</td>
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</tr>
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<tr>
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<td><code>symmetric_matrix<T [, TRI, F, C]>
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m(size);</code></td>
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<td>a symmetric matrix of values of type <code>T</code> of
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arbitrary size. Only the given triangular matrix is stored in the
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given order <code>F</code>.</td>
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</tr>
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<tr>
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<td><code>hermitian_matrix<T [, TRI, F, C]>
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m(size);</code></td>
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<td>a hermitian matrix of values of type <code>T</code> of
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arbitrary size. Only the given triangular matrix is stored using
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the order <code>F</code>.</td>
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</tr>
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<tr>
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<td><code>sparse_matrix<T, [F, C]> m(size1, size2 [,
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nnz]);</code></td>
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<td>a sparse matrix of values of type <code>T</code> of arbitrary
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size. The container type can be either <code>std::map<size_t,
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std::map<size_t, T> ></code> or
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<code>map_array<size_t, map_array<size_t,
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T> ></code>.</td>
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</tr>
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<tr>
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<td><code>sparse_vector_of_sparse_vector<T, [F, C]> m(size1,
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size2 [, nnz]);</code></td>
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<td>a sparse matrix of values of type <code>T</code> of arbitrary
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size.</td>
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</tr>
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<tr>
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<td><code>compressed_matrix<T, [F, IB, IA, TA]> m(size1,
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size2 [, nnz]);</code></td>
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<td>a sparse matrix of values of type <code>T</code> of arbitrary
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size. The values are stored in compressed row/column storage.</td>
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</tr>
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<tr>
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<td><code>coordinate_matrix<T, [F, IB, IA, TA]> m(size1,
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size2 [, nnz]);</code></td>
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<td>a sparse matrix of values of type <code>T</code> of arbitrary
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size. The values are stored in 3 parallel array as triples (i, j,
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value). More than one value for each pair of indices is possible,
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the real value is the sum of all.</td>
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</tr>
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<tr>
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<td><code>generalized_vector_of_vector<T, F, A> m(size1,
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size2 [, nnz]);</code></td>
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<td>a sparse matrix of values of type <code>T</code> of arbitrary
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size. The values are stored as a vector of sparse vectors, e.g.
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<code>generalized_vector_of_vector<double, row_major,
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unbounded_array<coordinate_vector<double> > ></code></td>
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</tr>
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</tbody>
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</table>
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<p><em>Note:</em> the default types are defined in
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<code>boost/numeric/ublas/fwd.hpp</code>.</p>
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<h2><a name="matrix_proxies">Matrix Proxies</a></h2>
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<table border="1" summary="matrix proxies">
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<thead>
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<tr>
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<th width="30%">Definition</th>
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<th>Description</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td><code>triangular_adaptor<MAT, TRI> ta(m);</code></td>
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<td>a triangular matrix referencing a selection of elements of the
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matrix <code>m</code>.</td>
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</tr>
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<tr>
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<td><code>symmetric_adaptor<MAT, TRI> sa(m);</code></td>
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<td>a symmetric matrix referencing a selection of elements of the
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matrix <code>m</code>.</td>
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</tr>
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<tr>
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<td><code>hermitian_adaptor<MAT, TRI> ha(m);</code></td>
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<td>a hermitian matrix referencing a selection of elements of the
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matrix <code>m</code>.</td>
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</tr>
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<tr>
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<td><code>banded_adaptor<MAT> ba(m, n_lower,
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n_upper);</code></td>
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<td>a banded matrix referencing a selection of elements of the
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matrix <code>m</code>.</td>
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</tr>
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<tr>
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<td><code>matrix_range<MAT, TRI> mr(m, range1,
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range2);</code></td>
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<td>a matrix referencing a submatrix of elements in the matrix
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<code>m</code>.</td>
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</tr>
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<tr>
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<td><code>matrix_slice<MAT, TRI> ms(m, slice1,
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slice2);</code></td>
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<td>a matrix referencing a non continues submatrix of elements in
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the matrix <code>m</code>.</td>
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</tr>
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</tbody>
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</table>
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<h2><a name="storage_layout">Special Storage Layouts</a></h2>
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<p>The library supports conventional dense, packed and basic sparse
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vector and matrix storage layouts. The description of the most
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common constructions of vectors and matrices comes next.</p>
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<table border="1" summary="storage layouts">
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<tbody>
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<tr>
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<th width="30%">Construction</th>
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<th>Comment</th>
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</tr>
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<tr>
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<td><code>vector<T,<br />
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std::vector<T> ><br />
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v (size)</code></td>
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<td>Constructs a dense vector, storage is provided by a standard
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vector.<br />
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The storage layout usually is BLAS compliant.</td>
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</tr>
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<tr>
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<td><code>vector<T,<br />
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unbounded_array<T> ><br />
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v (size)</code></td>
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<td>Constructs a dense vector, storage is provided by a heap-based
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array.<br />
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The storage layout usually is BLAS compliant.</td>
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</tr>
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<tr>
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<td><code>vector<T,<br />
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bounded_array<T, N> ><br />
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v (size)</code></td>
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<td>Constructs a dense vector, storage is provided by a stack-based
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array.<br />
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The storage layout usually is BLAS compliant.</td>
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</tr>
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<tr>
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<td><code>sparse_vector<T,<br />
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std::map<std::size_t, T> ><br />
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v (size, non_zeros)</code></td>
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<td>Constructs a sparse vector, storage is provided by a standard
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map.</td>
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</tr>
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<tr>
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<td><code>sparse_vector<T,<br />
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map_array<std::size_t, T> ><br />
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v (size, non_zeros)</code></td>
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<td>Constructs a sparse vector, storage is provided by a map
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array.</td>
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</tr>
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<tr>
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<td><code>matrix<T,<br />
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row_major,<br />
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std::vector<T> ><br />
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m (size1, size2)</code></td>
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<td>Constructs a dense matrix, orientation is row major, storage is
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provided by a standard vector.</td>
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</tr>
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<tr>
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<td><code>matrix<T,<br />
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column_major,<br />
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std::vector<T> ><br />
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m (size1, size2)</code></td>
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<td>Constructs a dense matrix, orientation is column major, storage
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is provided by a standard vector.<br />
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The storage layout usually is BLAS compliant.</td>
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</tr>
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<tr>
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<td><code>matrix<T,<br />
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row_major,<br />
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unbounded_array<T> ><br />
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m (size1, size2)</code></td>
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<td>Constructs a dense matrix, orientation is row major, storage is
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provided by a heap-based array.</td>
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</tr>
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<tr>
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<td><code>matrix<T,<br />
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column_major,<br />
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unbounded_array<T> ><br />
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m (size1, size2)</code></td>
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<td>Constructs a dense matrix, orientation is column major, storage
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is provided by a heap-based array.<br />
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The storage layout usually is BLAS compliant.</td>
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</tr>
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<tr>
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<td><code>matrix<T,<br />
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row_major,<br />
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bounded_array<T, N1 * N2> ><br />
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m (size1, size2)</code></td>
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<td>Constructs a dense matrix, orientation is row major, storage is
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provided by a stack-based array.</td>
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</tr>
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<tr>
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<td><code>matrix<T,<br />
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column_major,<br />
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bounded_array<T, N1 * N2> ><br />
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m (size1, size2)</code></td>
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<td>Constructs a dense matrix, orientation is column major, storage
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is provided by a stack-based array.<br />
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The storage layout usually is BLAS compliant.</td>
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</tr>
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<tr>
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<td><code>triangular_matrix<T,<br />
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row_major, F, A><br />
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m (size)</code></td>
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<td>Constructs a packed triangular matrix, orientation is row
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major.</td>
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</tr>
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<tr>
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<td><code>triangular_matrix<T,<br />
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column_major, F, A><br />
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m (size)</code></td>
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<td>Constructs a packed triangular matrix, orientation is column
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major.<br />
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The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>banded_matrix<T,<br />
|
|
row_major, A><br />
|
|
m (size1, size2, lower, upper)</code></td>
|
|
<td>Constructs a packed banded matrix, orientation is row
|
|
major.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>banded_matrix<T,<br />
|
|
column_major, A><br />
|
|
m (size1, size2, lower, upper)</code></td>
|
|
<td>Constructs a packed banded matrix, orientation is column
|
|
major.<br />
|
|
The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>symmetric_matrix<T,<br />
|
|
row_major, F, A><br />
|
|
m (size)</code></td>
|
|
<td>Constructs a packed symmetric matrix, orientation is row
|
|
major.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>symmetric_matrix<T,<br />
|
|
column_major, F, A><br />
|
|
m (size)</code></td>
|
|
<td>Constructs a packed symmetric matrix, orientation is column
|
|
major.<br />
|
|
The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>hermitian_matrix<T,<br />
|
|
row_major, F, A><br />
|
|
m (size)</code></td>
|
|
<td>Constructs a packed hermitian matrix, orientation is row
|
|
major.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>hermitian_matrix<T,<br />
|
|
column_major, F, A><br />
|
|
m (size)</code></td>
|
|
<td>Constructs a packed hermitian matrix, orientation is column
|
|
major.<br />
|
|
The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>sparse_matrix<T,<br />
|
|
row_major,<br />
|
|
std::map<std::size_t, T> ><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a sparse matrix, orientation is row major, storage
|
|
is provided by a standard map.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>sparse_matrix<T,<br />
|
|
column_major,<br />
|
|
std::map<std::size_t, T> ><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a sparse matrix, orientation is column major,
|
|
storage is provided by a standard map.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>sparse_matrix<T,<br />
|
|
row_major,<br />
|
|
map_array<std::size_t, T> ><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a sparse matrix, orientation is row major, storage
|
|
is provided by a map array.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>sparse_matrix<T,<br />
|
|
column_major,<br />
|
|
map_array<std::size_t, T> ><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a sparse matrix, orientation is column major,
|
|
storage is provided by a map array.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>compressed_matrix<T,<br />
|
|
row_major><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a compressed matrix, orientation is row major.<br />
|
|
The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>compressed_matrix<T,<br />
|
|
column_major><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a compressed matrix, orientation is column
|
|
major.<br />
|
|
The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>coordinate_matrix<T,<br />
|
|
row_major><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a coordinate matrix, orientation is row major.<br />
|
|
The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>coordinate_matrix<T,<br />
|
|
column_major><br />
|
|
m (size1, size2, non_zeros)</code></td>
|
|
<td>Constructs a coordinate matrix, orientation is column
|
|
major.<br />
|
|
The storage layout usually is BLAS compliant.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
|
|
|
|
<hr />
|
|
<p>Copyright (©) 2000-2004 Joerg Walter, Mathias Koch, Gunter
|
|
Winkler, Michael Stevens<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: 2004-07-05</p>
|
|
</body>
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</html>
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