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| <title>Types Overview</title> |
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| <body> |
| <h1><img src="../../../../boost.png" align="middle" />Overview of Matrix- and Vector-Types </h1> |
| <div class="toc" id="toc"></div> |
| |
| <dl> |
| <dt>Contents:</dt> |
| <dd><a href="#vectors">Vectors</a></dd> |
| <dd><a href="#vector_proxies">Vector Proxies</a></dd> |
| <dd><a href="#matrices">Matrices</a></dd> |
| <dd><a href="#matrix_proxies">Matrix Proxies</a></dd> |
| <dd><a href="#storage_layout">Special Storage Layouts</a></dd> |
| </dl> |
| |
| |
| <h2>Notation</h2> |
| |
| <table style="border: none;" summary="notation"> |
| <tr><td><code>T</code></td> |
| <td>is the data type. For general linear algebra operations this will be a real type e.g. <code>double</code>, ...</td></tr> |
| <tr><td><code>F</code></td> |
| <td>is the orientation type (functor), either |
| <code>row_major</code> or <code>column_major</code></td></tr> |
| <tr><td><code>A, IA, TA</code></td> <td>is an array storage type, e.g. <code>std::vector, |
| bounded_array, unbounded_array, ...</code></td></tr> |
| <tr><td><code>TRI</code></td> |
| <td>is a triangular functor: <code>lower, |
| unit_lower, strict_lower, upper, unit_upper, |
| strict_upper</code></td></tr> |
| <tr><td><code>M, N</code></td> |
| <td>are unsigned integer sizes |
| (<code>std::size_t</code>)</td></tr> |
| <tr><td><code>IB</code></td> |
| <td>is an index base |
| (<code>std::size_t</code>)</td></tr> |
| <tr><td><code>VEC</code></td> |
| <td>is any vector type</td></tr> |
| <tr><td><code>MAT</code> </td> |
| <td>is any matrix type</td></tr> |
| <tr><td><code>[...]</code></td> |
| <td>denote optional arguments - for more details |
| look at the section "storage layout".</td></tr> |
| </table> |
| |
| <h2><a id="vectors">Vectors</a></h2> |
| <table border="1" summary="vector types"> |
| <thead> |
| <tr> |
| <th width="30%">Definition</th> |
| <th>Description</th> |
| </tr> |
| </thead> |
| <tbody> |
| <tr> |
| <td><code>vector<T [, A]><br /> v(size);</code></td> |
| <td>a dense vector of values of type <code>T</code> of variable |
| size. A storage type <code>A</code> can be specified |
| which defaults to <code>unbounded_array</code>. |
| Elements are constructed by <code>A</code>, which need not initialise their value.</td> |
| |
| </tr> |
| <tr> |
| <td><code>bounded_vector<T, N><br /> v;</code></td> |
| <td>a dense vector of values of type <code>T</code> of variable size but with maximum |
| <code>N</code>. The default constructor creates <code>v</code> |
| with size <code>N</code>. |
| Elements are constructed by the storage type <code>bounded_array</code>, which need not initialise their value.</td> |
| </tr> |
| <tr> |
| <td><code>c_vector<T, M><br /> v(size);</code></td> |
| <td>a dense vector of values of type <code>T</code> with the given size. |
| The data is stored as an ordinary C++ array <code>T |
| data_[M]</code></td> |
| </tr> |
| <tr> |
| <td><code>zero_vector<T><br /> v(size);</code></td> |
| <td>the zero vector of type <code>T</code> with the given |
| size.</td> |
| </tr> |
| <tr> |
| <td><code>unit_vector<T><br /> v(size, index);</code></td> |
| <td>the unit vector of type <code>T</code> with the given size. The |
| vector is zero other then a single specified element. |
| <br/><code>index</code> should be less than <code>size</code>.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_vector<T [, S]><br /> v(size);</code></td> |
| <td>a sparse vector of values of type <code>T</code> of variable |
| size. The sparse storage type <code>S</code> can be <code>std::map<size_t, |
| T></code> or <code>map_array<size_t, T></code>.</td> |
| </tr> |
| <tr> |
| <td><code>compressed_vector<T [,IB, IA, TA]><br /> v(size);</code></td> |
| <td>a sparse vector of values of type <code>T</code> of variable |
| size. The non zero values are stored as two seperate arrays - an |
| index array and a value array. The index array is always sorted and |
| there is at most one entry for each index.</td> |
| </tr> |
| <tr> |
| <td><code>coordinate_vector<T [,IB, IA, TA]><br /> v(size);</code></td> |
| <td>a sparse vector of values of type <code>T</code> of variable |
| size. The non zero values are stored as two seperate arrays - an |
| index array and a value array. The arrays may be out of order with |
| multiple entries for each vector element. If there are multiple |
| values for the same index the sum of these values is the real |
| value.</td> |
| </tr> |
| </tbody> |
| </table> |
| <p><em>Note:</em> the default types are defined in |
| <code>boost/numeric/ublas/fwd.hpp</code>.</p> |
| |
| <h2><a id="vector_proxies">Vector Proxies</a></h2> |
| |
| <table border="1" summary="vector proxies"> |
| <thead> |
| <tr> |
| <th width="30%">Definition</th> |
| <th>Description</th> |
| </tr> |
| </thead> |
| <tbody> |
| <tr> |
| <td><code>vector_range<VEC><br /> vr(v, range);</code></td> |
| <td>a vector referencing a continuous subvector of elements of |
| vector <code>v</code> containing all elements specified by |
| <code>range</code>.</td> |
| </tr> |
| <tr> |
| <td><code>vector_slice<VEC><br /> vs(v, slice);</code></td> |
| <td>a vector referencing a non continuous subvector of elements of |
| vector <code>v</code> containing all elements specified by |
| <code>slice</code>.</td> |
| </tr> |
| <tr> |
| <td><code>matrix_row<MAT><br /> vr(m, index);</code></td> |
| <td>a vector referencing the <code>index</code>-th row of matrix |
| <code>m</code></td> |
| </tr> |
| <tr> |
| <td><code>matrix_column<MAT><br /> vc(m, index);</code></td> |
| <td>a vector referencing the <code>index</code>-th column of matrix |
| <code>m</code></td> |
| </tr> |
| </tbody> |
| </table> |
| |
| <h2><a id="matrices">Matrices</a></h2> |
| |
| <table border="1" summary="matrix types"> |
| <thead> |
| <tr> |
| <th width="30%">Definition</th> |
| <th>Description</th> |
| </tr> |
| </thead> |
| <tbody> |
| <tr> |
| <td><code>matrix<T [, F, A]><br /> m(size1, size2);</code></td> |
| <td>a dense matrix of values of type <code>T</code> of variable |
| size. A storage type <code>A</code> can be specified |
| which defaults to <code>unbounded_array</code>. |
| The orientation functor <code>F</code> defaults to |
| <code>row_major</code>. |
| Elements are constructed by <code>A</code>, which need not initialise their value.</td> |
| </tr> |
| <tr> |
| <td><code>bounded_matrix<T, M, N [, F]><br /> m;</code></td> |
| <td>a dense matrix of type <code>T</code> with variable size with maximum <code>M</code>-by-<code>N</code>. The orientation functor <code>F</code> |
| defaults to <code>row_major</code>. The default constructor creates |
| <code>m</code> with size <code>M</code>-by-<code>N</code>. |
| Elements are constructed by the storage type <code>bounded_array</code>, which need not initialise their value.</td> |
| </tr> |
| <tr> |
| <td><code>c_matrix<T, M, N><br /> m(size1, size2);</code></td> |
| <td>a dense matrix of values of type <code>T</code> with the given size. |
| The data is stored as an ordinary C++ array <code>T |
| data_[N][M]</code></td> |
| </tr> |
| <tr> |
| <td><code>vector_of_vector<T [, F, A]><br /> m(size1, |
| size2);</code></td> |
| <td>a dense matrix of values of type <code>T</code> with the given size. |
| The data is stored as a vector of vectors. The orientation |
| <code>F</code> defaults to <code>row_major</code>. The storage |
| type <code>S</code> defaults to |
| <code>unbounded_array<unbounded_array<T> ></code></td> |
| </tr> |
| <tr> |
| <td><code>zero_matrix<T><br /> m(size1, size2);</code></td> |
| <td>a zero matrix of type <code>T</code> with the given size.</td> |
| </tr> |
| <tr> |
| <td><code>identity_matrix<T><br /> m(size1, size2);</code></td> |
| <td>an identity matrix of type <code>T</code> with the given size. |
| The values are <code>v(i,j) = (i==j)?T(1):T()</code>.</td> |
| </tr> |
| <tr> |
| <td><code>scalar_matrix<T><br /> m(size1, size2, |
| value);</code></td> |
| <td>a matrix of type <code>T</code> with the given size that has the |
| value <code>value</code> everywhere.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix<T [, TRI, F, A]><br /> |
| m(size);</code></td> |
| <td>a triangular matrix of values of type <code>T</code> of |
| variable size. Only the nonzero elements are stored in the given |
| order <code>F</code>. ("triangular packed storage") The triangular |
| type <code>F</code> defaults to <code>lower</code>, the orientation |
| type <code>F</code> defaults to <code>row_major</code>.</td> |
| </tr> |
| <tr> |
| <td><code>banded_matrix<T [, F, A]><br /> m(size1, size2, n_lower, |
| n_upper);</code></td> |
| <td>a banded matrix of values of type <code>T</code> of variable |
| size with <code>n_lower</code> sub diagonals and |
| <code>n_upper</code> super diagonals. Only the nonzero elements are |
| stored in the given order <code>F</code>. ("packed storage")</td> |
| </tr> |
| <tr> |
| <td><code>symmetric_matrix<T [, TRI, F, A]><br /> |
| m(size);</code></td> |
| <td>a symmetric matrix of values of type <code>T</code> of |
| variable size. Only the given triangular matrix is stored in the |
| given order <code>F</code>.</td> |
| </tr> |
| <tr> |
| <td><code>hermitian_matrix<T [, TRI, F, A]><br /> |
| m(size);</code></td> |
| <td>a hermitian matrix of values of type <code>T</code> of |
| variable size. Only the given triangular matrix is stored using |
| the order <code>F</code>.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix<T, [F, S]><br /> m(size1, size2 [, |
| non_zeros]);</code></td> |
| <td>a sparse matrix of values of type <code>T</code> of variable |
| size. The sparse storage type <code>S</code> can be either <code>std::map<size_t, |
| std::map<size_t, T> ></code> or |
| <code>map_array<size_t, map_array<size_t, |
| T> ></code>.</td> |
| </tr> |
| <tr> |
| <td><code>sparse_vector_of_sparse_vector<T, [F, C]><br /> m(size1, |
| size2 [, non_zeros]);</code></td> |
| <td>a sparse matrix of values of type <code>T</code> of variable |
| size.</td> |
| </tr> |
| <tr> |
| <td><code>compressed_matrix<T, [F, IB, IA, TA]><br /> m(size1, |
| size2 [, non_zeros]);</code></td> |
| <td>a sparse matrix of values of type <code>T</code> of variable |
| size. The values are stored in compressed row/column storage.</td> |
| </tr> |
| <tr> |
| <td><code>coordinate_matrix<T, [F, IB, IA, TA]><br /> m(size1, |
| size2 [, non_zeros]);</code></td> |
| <td>a sparse matrix of values of type <code>T</code> of variable |
| size. The values are stored in 3 parallel array as triples (i, j, |
| value). More than one value for each pair of indices is possible, |
| the real value is the sum of all.</td> |
| </tr> |
| <tr> |
| <td><code>generalized_vector_of_vector<T, F, A><br /> m(size1, |
| size2 [, non_zeros]);</code></td> |
| <td>a sparse matrix of values of type <code>T</code> of variable |
| size. The values are stored as a vector of sparse vectors, e.g. |
| <code>generalized_vector_of_vector<double, row_major, |
| unbounded_array<coordinate_vector<double> > ></code></td> |
| </tr> |
| </tbody> |
| </table> |
| <p><em>Note:</em> the default types are defined in |
| <code>boost/numeric/ublas/fwd.hpp</code>.</p> |
| |
| <h2><a id="matrix_proxies">Matrix Proxies</a></h2> |
| |
| <table border="1" summary="matrix proxies"> |
| <thead> |
| <tr> |
| <th width="30%">Definition</th> |
| <th>Description</th> |
| </tr> |
| </thead> |
| <tbody> |
| <tr> |
| <td><code>triangular_adaptor<MAT, TRI><br /> ta(m);</code></td> |
| <td>a triangular matrix referencing a selection of elements of the |
| matrix <code>m</code>.</td> |
| </tr> |
| <tr> |
| <td><code>symmetric_adaptor<MAT, TRI><br /> sa(m);</code></td> |
| <td>a symmetric matrix referencing a selection of elements of the |
| matrix <code>m</code>.</td> |
| </tr> |
| <tr> |
| <td><code>hermitian_adaptor<MAT, TRI><br /> ha(m);</code></td> |
| <td>a hermitian matrix referencing a selection of elements of the |
| matrix <code>m</code>.</td> |
| </tr> |
| <tr> |
| <td><code>banded_adaptor<MAT><br /> ba(m, n_lower, |
| n_upper);</code></td> |
| <td>a banded matrix referencing a selection of elements of the |
| matrix <code>m</code>.</td> |
| </tr> |
| <tr> |
| <td><code>matrix_range<MAT, TRI><br /> mr(m, range1, |
| range2);</code></td> |
| <td>a matrix referencing a submatrix of elements in the matrix |
| <code>m</code>.</td> |
| </tr> |
| <tr> |
| <td><code>matrix_slice<MAT, TRI><br /> ms(m, slice1, |
| slice2);</code></td> |
| <td>a matrix referencing a non continues submatrix of elements in |
| the matrix <code>m</code>.</td> |
| </tr> |
| </tbody> |
| </table> |
| |
| |
| |
| <h2><a id="storage_layout">Special Storage Layouts</a></h2> |
| |
| |
| <p>The library supports conventional dense, packed and basic sparse |
| vector and matrix storage layouts. The description of the most |
| common constructions of vectors and matrices comes next.</p> |
| |
| <table border="1" summary="storage layouts"> |
| <tbody> |
| <tr> |
| <th width="30%">Construction</th> |
| <th>Comment</th> |
| </tr> |
| <tr> |
| <td><code>vector<T,<br /> |
| std::vector<T> ><br /> |
| v (size)</code></td> |
| <td>a dense vector, storage is provided by a standard |
| vector.<br /> |
| The storage layout usually is BLAS compliant.</td> |
| </tr> |
| <tr> |
| <td><code>vector<T,<br /> |
| unbounded_array<T> ><br /> |
| v (size)</code></td> |
| <td>a dense vector, storage is provided by a heap-based |
| array.<br /> |
| The storage layout usually is BLAS compliant.</td> |
| </tr> |
| <tr> |
| <td><code>vector<T,<br /> |
| bounded_array<T, N> ><br /> |
| v (size)</code></td> |
| <td>a dense vector, storage is provided by a stack-based |
| array.<br /> |
| The storage layout usually is BLAS compliant.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_vector<T,<br /> |
| std::map<std::size_t, T> ><br /> |
| v (size, non_zeros)</code></td> |
| <td>a sparse vector, storage is provided by a standard |
| map.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_vector<T,<br /> |
| map_array<std::size_t, T> ><br /> |
| v (size, non_zeros)</code></td> |
| <td>a sparse vector, storage is provided by a map |
| array.</td> |
| </tr> |
| <tr> |
| <td><code>matrix<T,<br /> |
| row_major,<br /> |
| std::vector<T> ><br /> |
| m (size1, size2)</code></td> |
| <td>a dense matrix, orientation is row major, storage is |
| provided by a standard vector.</td> |
| </tr> |
| <tr> |
| <td><code>matrix<T,<br /> |
| column_major,<br /> |
| std::vector<T> ><br /> |
| m (size1, size2)</code></td> |
| <td>a dense matrix, orientation is column major, storage |
| is provided by a standard vector.<br /> |
| The storage layout usually is BLAS compliant.</td> |
| </tr> |
| <tr> |
| <td><code>matrix<T,<br /> |
| row_major,<br /> |
| unbounded_array<T> ><br /> |
| m (size1, size2)</code></td> |
| <td>a dense matrix, orientation is row major, storage is |
| provided by a heap-based array.</td> |
| </tr> |
| <tr> |
| <td><code>matrix<T,<br /> |
| column_major,<br /> |
| unbounded_array<T> ><br /> |
| m (size1, size2)</code></td> |
| <td>a dense matrix, orientation is column major, storage |
| is provided by a heap-based array.<br /> |
| The storage layout usually is BLAS compliant.</td> |
| </tr> |
| <tr> |
| <td><code>matrix<T,<br /> |
| row_major,<br /> |
| bounded_array<T, N1 * N2> ><br /> |
| m (size1, size2)</code></td> |
| <td>a dense matrix, orientation is row major, storage is |
| provided by a stack-based array.</td> |
| </tr> |
| <tr> |
| <td><code>matrix<T,<br /> |
| column_major,<br /> |
| bounded_array<T, N1 * N2> ><br /> |
| m (size1, size2)</code></td> |
| <td>a dense matrix, orientation is column major, storage |
| is provided by a stack-based array.<br /> |
| The storage layout usually is BLAS compliant.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix<T,<br /> |
| row_major, F, A><br /> |
| m (size)</code></td> |
| <td>a packed triangular matrix, orientation is row |
| major.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix<T,<br /> |
| column_major, F, A><br /> |
| m (size)</code></td> |
| <td>a packed triangular matrix, orientation is column |
| major.<br /> |
| 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>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>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>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>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>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>a packed hermitian matrix, orientation is column |
| major.<br /> |
| The storage layout usually is BLAS compliant.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix<T,<br /> |
| row_major,<br /> |
| std::map<std::size_t, T> ><br /> |
| m (size1, size2, non_zeros)</code></td> |
| <td>a sparse matrix, orientation is row major, storage |
| is provided by a standard map.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix<T,<br /> |
| column_major,<br /> |
| std::map<std::size_t, T> ><br /> |
| m (size1, size2, non_zeros)</code></td> |
| <td>a sparse matrix, orientation is column major, |
| storage is provided by a standard map.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix<T,<br /> |
| row_major,<br /> |
| map_array<std::size_t, T> ><br /> |
| m (size1, size2, non_zeros)</code></td> |
| <td>a sparse matrix, orientation is row major, storage |
| is provided by a map array.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix<T,<br /> |
| column_major,<br /> |
| map_array<std::size_t, T> ><br /> |
| m (size1, size2, non_zeros)</code></td> |
| <td>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>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>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>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>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 /> |
| 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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