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| <title>Triangular Matrix</title> |
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| <h1><img src="../../../../boost.png" align="middle" />Triangular Matrix</h1> |
| <div class="toc" id="toc"></div> |
| <h2><a name="triangular_matrix"></a>Triangular Matrix</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>triangular_matrix<T, F1, F2, |
| A></code> is the base container adaptor for triangular matrices. |
| For a <em>(n x n</em> )-dimensional lower triangular matrix and |
| <em>0 <= i < n</em>,<em>0 <= j < n</em> holds |
| <em>t</em><sub><em>i, j</em></sub> <em>= 0</em> , if <em>i > |
| j</em>. If furthermore holds t<sub><em>i, i</em></sub><em>= 1</em> |
| the matrix is called unit lower triangular. For a <em>(n x n</em> |
| )-dimensional lower triangular matrix and <em>0 <= i < |
| n</em>,<em>0 <= j < n</em> holds <em>t</em><sub><em>i, |
| j</em></sub> <em>= 0</em> , if <em>i < j</em>. If furthermore |
| holds t<sub><em>i, i</em></sub><em>= 1</em> the matrix is called |
| unit lower triangular. The storage of triangular matrices is |
| packed.</p> |
| <h4>Example</h4> |
| <pre> |
| #include <boost/numeric/ublas/triangular.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| triangular_matrix<double, lower> ml (3, 3); |
| for (unsigned i = 0; i < ml.size1 (); ++ i) |
| for (unsigned j = 0; j <= i; ++ j) |
| ml (i, j) = 3 * i + j; |
| std::cout << ml << std::endl; |
| triangular_matrix<double, upper> mu (3, 3); |
| for (unsigned i = 0; i < mu.size1 (); ++ i) |
| for (unsigned j = i; j < mu.size2 (); ++ j) |
| mu (i, j) = 3 * i + j; |
| std::cout << mu << std::endl; |
| } |
| </pre> |
| <p>Please read the <a href="samples/ex_triangular.cpp">full triangular example</a> for more details.</p> |
| |
| <h4>Definition</h4> |
| <p>Defined in the header triangular.hpp.</p> |
| <h4>Template parameters</h4> |
| <table border="1" summary="parameters"> |
| <tbody> |
| <tr> |
| <th>Parameter</th> |
| <th>Description</th> |
| <th>Default</th> |
| </tr> |
| <tr> |
| <td><code>T</code></td> |
| <td>The type of object stored in the matrix.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F1</code></td> |
| <td>Functor describing the type of the triangular matrix. <a href= |
| "#triangular_matrix_1">[1]</a></td> |
| <td><code>lower</code></td> |
| </tr> |
| <tr> |
| <td><code>F2</code></td> |
| <td>Functor describing the storage organization. <a href= |
| "#triangular_matrix_2">[2]</a></td> |
| <td><code>row_major</code></td> |
| </tr> |
| <tr> |
| <td><code>A</code></td> |
| <td>The type of the adapted array. <a href= |
| "#triangular_matrix_3">[3]</a></td> |
| <td><code>unbounded_array<T></code></td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p><a href="container_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Type requirements</h4> |
| <p>None, except for those imposed by the requirements of <a href= |
| "container_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Public base classes</h4> |
| <p><code>matrix_container<triangular_matrix<T, F1, F2, A> |
| ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix ()</code></td> |
| <td>Allocates an uninitialized <code>triangular_matrix</code> that |
| holds zero rows of zero elements.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix (size_type size1, size_type |
| size2)</code></td> |
| <td>Allocates an uninitialized <code>triangular_matrix</code> that |
| holds <code>size1</code> rows of <code>size2</code> elements.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix (const triangular_matrix |
| &m)</code></td> |
| <td>The copy constructor.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_matrix (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>The extended copy constructor.</td> |
| </tr> |
| <tr> |
| <td><code>void resize (size_type size1, size_type size2, bool |
| preserve = true)</code></td> |
| <td>Reallocates a <code>triangular_matrix</code> to hold |
| <code>size1</code> rows of <code>size2</code> elements. The |
| existing elements of the <code>triangular_matrix</code> are |
| preseved when specified.</td> |
| </tr> |
| <tr> |
| <td><code>size_type size1 () const</code></td> |
| <td>Returns the number of rows.</td> |
| </tr> |
| <tr> |
| <td><code>size_type size2 () const</code></td> |
| <td>Returns the number of columns.</td> |
| </tr> |
| <tr> |
| <td><code>const_reference operator () (size_type i, size_type j) |
| const</code></td> |
| <td>Returns a <code>const</code> reference of the <code>j</code> |
| -th element in the <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>reference operator () (size_type i, size_type |
| j)</code></td> |
| <td>Returns a reference of the <code>j</code>-th element in the |
| <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix &operator = (const |
| triangular_matrix &m)</code></td> |
| <td>The assignment operator.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_matrix &assign_temporary |
| (triangular_matrix &m)</code></td> |
| <td>Assigns a temporary. May change the triangular matrix |
| <code>m</code>.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_matrix &operator = (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>The extended assignment operator.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_matrix &assign (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>Assigns a matrix expression to the triangular matrix. Left and |
| right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_matrix &operator += (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>A computed assignment operator. Adds the matrix expression to |
| the triangular matrix.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_matrix &plus_assign (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>Adds a matrix expression to the triangular matrix. Left and |
| right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_matrix &operator -= (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>A computed assignment operator. Subtracts the matrix expression |
| from the triangular matrix.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_matrix &minus_assign (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>Subtracts a matrix expression from the triangular matrix. Left |
| and right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AT><br /> |
| triangular_matrix &operator *= (const AT &at)</code></td> |
| <td>A computed assignment operator. Multiplies the triangular |
| matrix with a scalar.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AT><br /> |
| triangular_matrix &operator /= (const AT &at)</code></td> |
| <td>A computed assignment operator. Divides the triangular matrix |
| through a scalar.</td> |
| </tr> |
| <tr> |
| <td><code>void swap (triangular_matrix &m)</code></td> |
| <td>Swaps the contents of the triangular matrices.</td> |
| </tr> |
| <tr> |
| <td><code>void insert (size_type i, size_type j, const_reference |
| t)</code></td> |
| <td>Inserts the value <code>t</code> at the <code>j</code>-th |
| element of the <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>void erase (size_type i, size_type j)</code></td> |
| <td>Erases the value at the <code>j</code>-th elemenst of the |
| <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>void clear ()</code></td> |
| <td>Clears the matrix.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 begin1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the |
| beginning of the <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 end1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the end of |
| the <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 begin1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the beginning of |
| the <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 end1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the end of the |
| <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 begin2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the |
| beginning of the <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 end2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the end of |
| the <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 begin2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the beginning of |
| the <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 end2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the end of the |
| <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator1 rbegin1 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator1</code> pointing to the |
| beginning of the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator1 rend1 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator1</code> pointing to the |
| end of the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator1 rbegin1 ()</code></td> |
| <td>Returns a <code>reverse_iterator1</code> pointing to the |
| beginning of the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator1 rend1 ()</code></td> |
| <td>Returns a <code>reverse_iterator1</code> pointing to the end of |
| the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator2 rbegin2 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator2</code> pointing to the |
| beginning of the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator2 rend2 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator2</code> pointing to the |
| end of the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator2 rbegin2 ()</code></td> |
| <td>Returns a <code>reverse_iterator2</code> pointing to the |
| beginning of the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator2 rend2 ()</code></td> |
| <td>Returns a <code>reverse_iterator2</code> pointing to the end of |
| the reversed <code>triangular_matrix</code>.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Notes</h4> |
| <p><a name="triangular_matrix_1">[1]</a> |
| Supported parameters for the type of the triangular matrix are |
| <code>lower</code> , <code>unit_lower</code>, <code>upper</code> |
| and <code>unit_upper</code> .</p> |
| <p><a name="triangular_matrix_2">[2]</a> |
| Supported parameters for the storage organization are |
| <code>row_major</code> and <code>column_major</code>.</p> |
| <p><a name="triangular_matrix_3">[3]</a> |
| Supported parameters for the adapted array are |
| <code>unbounded_array<T></code> , |
| <code>bounded_array<T></code> and |
| <code>std::vector<T></code> .</p> |
| <h2><a name="triangular_adaptor"></a>Triangular Adaptor</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>triangular_adaptor<M, F></code> |
| is a triangular matrix adaptor for other matrices.</p> |
| <h4>Example</h4> |
| <pre> |
| #include <boost/numeric/ublas/triangular.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| matrix<double> m (3, 3); |
| triangular_adaptor<matrix<double>, lower> tal (m); |
| for (unsigned i = 0; i < tal.size1 (); ++ i) |
| for (unsigned j = 0; j <= i; ++ j) |
| tal (i, j) = 3 * i + j; |
| std::cout << tal << std::endl; |
| triangular_adaptor<matrix<double>, upper> tau (m); |
| for (unsigned i = 0; i < tau.size1 (); ++ i) |
| for (unsigned j = i; j < tau.size2 (); ++ j) |
| tau (i, j) = 3 * i + j; |
| std::cout << tau << std::endl; |
| } |
| </pre> |
| <p>Please read the <a href="samples/ex_triangular.cpp">full triangular example</a> for more details.</p> |
| |
| <h4>Definition</h4> |
| <p>Defined in the header triangular.hpp.</p> |
| <h4>Template parameters</h4> |
| <table border="1" summary="parameters"> |
| <tbody> |
| <tr> |
| <th>Parameter</th> |
| <th>Description</th> |
| <th>Default</th> |
| </tr> |
| <tr> |
| <td><code>M</code></td> |
| <td>The type of the adapted matrix.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>Functor describing the type of the triangular adaptor. <a href= |
| "#triangular_adaptor_1">[1]</a></td> |
| <td><code>lower</code></td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p><a href="expression_concept.htm#matrix_expression">Matrix Expression</a> |
| .</p> |
| <h4>Type requirements</h4> |
| <p>None, except for those imposed by the requirements of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</p> |
| <h4>Public base classes</h4> |
| <p><code>matrix_expression<triangular_adaptor<M, F> |
| ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>triangular_adaptor (matrix_type &data)</code></td> |
| <td>Constructs a <code>triangular_adaptor</code> of a matrix.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_adaptor (const triangular_adaptor |
| &m)</code></td> |
| <td>The copy constructor.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_adaptor (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>The extended copy constructor.</td> |
| </tr> |
| <tr> |
| <td><code>size_type size1 () const</code></td> |
| <td>Returns the number of rows.</td> |
| </tr> |
| <tr> |
| <td><code>size_type size2 () const</code></td> |
| <td>Returns the number of columns.</td> |
| </tr> |
| <tr> |
| <td><code>const_reference operator () (size_type i, size_type j) |
| const</code></td> |
| <td>Returns a <code>const</code> reference of the <code>j</code> |
| -th element in the <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>reference operator () (size_type i, size_type |
| j)</code></td> |
| <td>Returns a reference of the <code>j</code>-th element in the |
| <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_adaptor &operator = (const |
| triangular_adaptor &m)</code></td> |
| <td>The assignment operator.</td> |
| </tr> |
| <tr> |
| <td><code>triangular_adaptor &assign_temporary |
| (triangular_adaptor &m)</code></td> |
| <td>Assigns a temporary. May change the triangular adaptor |
| <code>m</code>.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_adaptor &operator = (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>The extended assignment operator.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_adaptor &assign (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>Assigns a matrix expression to the triangular adaptor. Left and |
| right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_adaptor &operator += (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>A computed assignment operator. Adds the matrix expression to |
| the triangular adaptor.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_adaptor &plus_assign (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>Adds a matrix expression to the triangular adaptor. Left and |
| right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_adaptor &operator -= (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>A computed assignment operator. Subtracts the matrix expression |
| from the triangular adaptor.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| triangular_adaptor &minus_assign (const |
| matrix_expression<AE> &ae)</code></td> |
| <td>Subtracts a matrix expression from the triangular adaptor. Left |
| and right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AT><br /> |
| triangular_adaptor &operator *= (const AT &at)</code></td> |
| <td>A computed assignment operator. Multiplies the triangular |
| adaptor with a scalar.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AT><br /> |
| triangular_adaptor &operator /= (const AT &at)</code></td> |
| <td>A computed assignment operator. Divides the triangular adaptor |
| through a scalar.</td> |
| </tr> |
| <tr> |
| <td><code>void swap (triangular_adaptor &m)</code></td> |
| <td>Swaps the contents of the triangular adaptors.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 begin1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the |
| beginning of the <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 end1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the end of |
| the <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 begin1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the beginning of |
| the <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 end1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the end of the |
| <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 begin2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the |
| beginning of the <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 end2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the end of |
| the <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 begin2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the beginning of |
| the <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 end2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the end of the |
| <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator1 rbegin1 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator1</code> pointing to the |
| beginning of the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator1 rend1 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator1</code> pointing to the |
| end of the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator1 rbegin1 ()</code></td> |
| <td>Returns a <code>reverse_iterator1</code> pointing to the |
| beginning of the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator1 rend1 ()</code></td> |
| <td>Returns a <code>reverse_iterator1</code> pointing to the end of |
| the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator2 rbegin2 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator2</code> pointing to the |
| beginning of the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator2 rend2 () const</code></td> |
| <td>Returns a <code>const_reverse_iterator2</code> pointing to the |
| end of the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator2 rbegin2 ()</code></td> |
| <td>Returns a <code>reverse_iterator2</code> pointing to the |
| beginning of the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator2 rend2 ()</code></td> |
| <td>Returns a <code>reverse_iterator2</code> pointing to the end of |
| the reversed <code>triangular_adaptor</code>.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Notes</h4> |
| <p><a name="triangular_adaptor_1">[1]</a> |
| Supported parameters for the type of the triangular adaptor are |
| <code>lower</code> , <code>unit_lower</code>, <code>upper</code> |
| and <code>unit_upper</code> .</p> |
| <hr /> |
| <p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<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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