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| <title>Matrix Expressions</title> |
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| <h1><img src="../../../../boost.png" align="middle" />Matrix Expressions</h1> |
| <div class="toc" id="toc"></div> |
| <h2><a name="matrix_expression"></a>Matrix Expression</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>matrix_expression<E></code> |
| is required to be a public base of all classes which model the Matrix Expression concept.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header expression_types.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>E</code></td> |
| <td>The type of the matrix expression.</td> |
| <td> </td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p>None. <u>Not a Matrix Expression</u>! |
| </p> |
| <h4>Type requirements</h4> |
| <p>None.</p> |
| <h4>Public base classes</h4> |
| <p>None.</p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>const expression_type &operator () () |
| const</code></td> |
| <td>Returns a <code>const</code> reference of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>expression_type &operator () ()</code></td> |
| <td>Returns a reference of the expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Notes</h4> |
| <p>The <code>operator[]</code>, <code>row</code>, <code>column</code>, <code>range</code>, <code>slice</code> and <code>project</code> functions have been removed. Use the free functions defined in <a href="matrix_proxy.htm">matrix proxy</a> instead.</p> |
| <h2><a name="matrix_container"></a>Matrix Container</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>matrix_container<C></code> |
| is required to be a public base of all classes which model the Matrix concept. |
| This includes the class <code>matrix</code> itself.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header expression_types.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>E</code></td> |
| <td>The type of the matrix expression.</td> |
| <td> </td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p>None. <u>Not a Matrix Expression OR Matrix</u>! |
| </p> |
| <h4>Type requirements</h4> |
| <p>None.</p> |
| <h4>Public base classes</h4> |
| <p><code>matrix_expression<C></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>const container_type &operator () () |
| const</code></td> |
| <td>Returns a <code>const</code> reference of the container.</td> |
| </tr> |
| <tr> |
| <td><code>container_type &operator () ()</code></td> |
| <td>Returns a reference of the container.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h2><a name="matrix_references"></a>Matrix References</h2> |
| <h3>Reference</h3> |
| <h4>Description</h4> |
| <p>The templated class <code>matrix_reference<E></code> |
| contains a reference to a matrix expression.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.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>E</code></td> |
| <td>The type of the matrix expression.</td> |
| <td> </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<matrix_reference<E> |
| ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>matrix_reference (expression_type &e)</code></td> |
| <td>Constructs a constant reference of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>void resize (size_type size1, size2)</code></td> |
| <td>Resizes the expression to hold at most <code>size1</code> rows |
| of <code>size2</code> elements.</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 the value 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>const_iterator1 begin1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 end1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the end of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 begin1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the beginning of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 end1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the end of the |
| expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 begin2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 end2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the end of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 begin2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the beginning of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 end2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the end of the |
| expression.</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 expression.</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 expression.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator1 rbegin1 ()</code></td> |
| <td>Returns a <code>reverse_iterator1</code> pointing to the |
| beginning of the reversed expression.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator1 rend1 ()</code></td> |
| <td>Returns a <code>reverse_iterator1</code> pointing to the end of |
| the reversed expression.</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 expression.</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 expression.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator2 rbegin2 ()</code></td> |
| <td>Returns a <code>reverse_iterator2</code> pointing to the |
| beginning of the reversed expression.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator2 rend2 ()</code></td> |
| <td>Returns a <code>reverse_iterator2</code> pointing to the end of |
| the reversed expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h2><a name="matrix_operations"></a>Matrix Operations</h2> |
| <h3>Unary Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated classes <code>matrix_unary1<E, F></code> and |
| <code>matrix_unary2<E, F></code> describe unary matrix |
| operations.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.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>E</code></td> |
| <td>The type of the matrix expression.</td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>The type of the operation.</td> |
| <td> </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<matrix_unary1<E, F> ></code> |
| and <code>matrix_expression<matrix_unary2<E, F> |
| ></code> resp.</p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>matrix_unary1 (const expression_type &e)</code></td> |
| <td>Constructs a description of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>matrix_unary2 (const expression_type &e)</code></td> |
| <td>Constructs a description of the expression.</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 the value of the <code>j</code>-th element in the |
| <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 begin1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 end1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the end of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 begin2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 end2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the end of |
| the expression.</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 expression.</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 expression.</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 expression.</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 expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h3>Unary Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E, class F> |
| struct matrix_unary1_traits { |
| typedef matrix_unary1<typename E::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (- m) [i] [j] = - m [i] [j] |
| template<class E> |
| typename matrix_unary1_traits<E, scalar_negate<typename E::value_type> >::result_type |
| operator - (const matrix_expression<E> &e); |
| |
| // (conj m) [i] [j] = conj (m [i] [j]) |
| template<class E> |
| typename matrix_unary1_traits<E, scalar_conj<typename E::value_type> >::result_type |
| conj (const matrix_expression<E> &e); |
| |
| // (real m) [i] [j] = real (m [i] [j]) |
| template<class E> |
| typename matrix_unary1_traits<E, scalar_real<typename E::value_type> >::result_type |
| real (const matrix_expression<E> &e); |
| |
| // (imag m) [i] [j] = imag (m [i] [j]) |
| template<class E> |
| typename matrix_unary1_traits<E, scalar_imag<typename E::value_type> >::result_type |
| imag (const matrix_expression<E> &e); |
| |
| template<class E, class F> |
| struct matrix_unary2_traits { |
| typedef matrix_unary2<typename E::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (trans m) [i] [j] = m [j] [i] |
| template<class E> |
| typename matrix_unary2_traits<E, scalar_identity<typename E::value_type> >::result_type |
| trans (const matrix_expression<E> &e); |
| |
| // (herm m) [i] [j] = conj (m [j] [i]) |
| template<class E> |
| typename matrix_unary2_traits<E, scalar_conj<typename E::value_type> >::result_type |
| herm (const matrix_expression<E> &e);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>operator -</code> computes the additive inverse of a |
| matrix expression. <code>conj</code> computes the complex conjugate |
| of a matrix expression. <code>real</code> and <code>imag</code> |
| compute the real and imaginary parts of a matrix expression. |
| <code>trans</code> computes the transpose of a matrix expression. |
| <code>herm</code> computes the hermitian, i.e. the complex |
| conjugate of the transpose of a matrix expression.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <p>None.</p> |
| <h4>Complexity</h4> |
| <p>Quadratic depending from the size of the matrix expression.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/matrix.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| matrix<std::complex<double> > m (3, 3); |
| for (unsigned i = 0; i < m.size1 (); ++ i) |
| for (unsigned j = 0; j < m.size2 (); ++ j) |
| m (i, j) = std::complex<double> (3 * i + j, 3 * i + j); |
| |
| std::cout << - m << std::endl; |
| std::cout << conj (m) << std::endl; |
| std::cout << real (m) << std::endl; |
| std::cout << imag (m) << std::endl; |
| std::cout << trans (m) << std::endl; |
| std::cout << herm (m) << std::endl; |
| } |
| </pre> |
| <h3>Binary Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated class <code>matrix_binary<E1, E2, F></code> |
| describes a binary matrix operation.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.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>E1</code></td> |
| <td>The type of the first matrix expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>E2</code></td> |
| <td>The type of the second matrix expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>The type of the operation.</td> |
| <td></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<matrix_binary<E1, E2, F> |
| ></code>.</p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>matrix_binary (const expression1_type &e1, const |
| expression2_type &e2)</code></td> |
| <td>Constructs a description of the expression.</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 the value of the <code>j</code>-th element in the |
| <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 begin1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 end1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the end of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 begin2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 end2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the end of |
| the expression.</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 expression.</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 expression.</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 expression.</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 expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h3>Binary Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E1, class E2, class F> |
| struct matrix_binary_traits { |
| typedef matrix_binary<typename E1::const_closure_type, |
| typename E2::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (m1 + m2) [i] [j] = m1 [i] [j] + m2 [i] [j] |
| template<class E1, class E2> |
| typename matrix_binary_traits<E1, E2, scalar_plus<typename E1::value_type, |
| typename E2::value_type> >::result_type |
| operator + (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2); |
| |
| // (m1 - m2) [i] [j] = m1 [i] [j] - m2 [i] [j] |
| template<class E1, class E2> |
| typename matrix_binary_traits<E1, E2, scalar_minus<typename E1::value_type, |
| typename E2::value_type> >::result_type |
| operator - (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>operator +</code> computes the sum of two matrix |
| expressions. <code>operator -</code> computes the difference of two |
| matrix expressions.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E1</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| <li><code>E2</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <ul> |
| <li><code>e1 ().size1 () == e2 ().size1 ()</code></li> |
| <li><code>e1 ().size2 () == e2 ().size2 ()</code></li> |
| </ul> |
| <h4>Complexity</h4> |
| <p>Quadratic depending from the size of the matrix expressions.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/matrix.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| matrix<double> m1 (3, 3), m2 (3, 3); |
| for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i) |
| for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j) |
| m1 (i, j) = m2 (i, j) = 3 * i + j; |
| |
| std::cout << m1 + m2 << std::endl; |
| std::cout << m1 - m2 << std::endl; |
| } |
| </pre> |
| <h3>Scalar Matrix Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated classes <code>matrix_binary_scalar1<E1, E2, |
| F></code> and <code>matrix_binary_scalar2<E1, E2, |
| F></code> describe binary operations between a scalar and a |
| matrix.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.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>E1/E2</code></td> |
| <td>The type of the scalar expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>E2/E1</code></td> |
| <td>The type of the matrix expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>The type of the operation.</td> |
| <td></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<matrix_binary_scalar1<E1, E2, |
| F> ></code> and |
| <code>matrix_expression<matrix_binary_scalar2<E1, E2, F> |
| ></code> resp.</p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>matrix_binary_scalar1 (const expression1_type &e1, |
| const expression2_type &e2)</code></td> |
| <td>Constructs a description of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>matrix_binary_scalar1 (const expression1_type &e1, |
| const expression2_type &e2)</code></td> |
| <td>Constructs a description of the expression.</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 the value of the <code>j</code>-th element in the |
| <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 begin1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 end1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the end of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 begin2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 end2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the end of |
| the expression.</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 expression.</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 expression.</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 expression.</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 expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h3>Scalar Matrix Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class T1, class E2, class F> |
| struct matrix_binary_scalar1_traits { |
| typedef matrix_binary_scalar1<scalar_const_reference<T1>, |
| typename E2::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (t * m) [i] [j] = t * m [i] [j] |
| template<class T1, class E2> |
| typename matrix_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type |
| operator * (const T1 &e1, |
| const matrix_expression<E2> &e2); |
| |
| template<class E1, class T2, class F> |
| struct matrix_binary_scalar2_traits { |
| typedef matrix_binary_scalar2<typename E1::const_closure_type, |
| scalar_const_reference<T2>, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (m * t) [i] [j] = m [i] [j] * t |
| template<class E1, class T2> |
| typename matrix_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type |
| operator * (const matrix_expression<E1> &e1, |
| const T2 &e2); |
| |
| // (m / t) [i] [j] = m [i] [j] / t |
| template<class E1, class T2> |
| typename matrix_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type |
| operator / (const matrix_expression<E1> &e1, |
| const T2 &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>operator *</code> computes the product of a scalar and a |
| matrix expression. <code>operator /</code> multiplies the matrix |
| with the reciprocal of the scalar.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>T1/T2</code> is a model of <a href= |
| "expression_concept.htm#scalar_expression">Scalar Expression</a> .</li> |
| <li><code>E2/E1</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <p>None.</p> |
| <h4>Complexity</h4> |
| <p>Quadratic depending from the size of the matrix expression.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/matrix.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| matrix<double> m (3, 3); |
| for (unsigned i = 0; i < m.size1 (); ++ i) |
| for (unsigned j = 0; j < m.size2 (); ++ j) |
| m (i, j) = 3 * i + j; |
| |
| std::cout << 2.0 * m << std::endl; |
| std::cout << m * 2.0 << std::endl; |
| } |
| </pre> |
| <h2><a name="matrix_vector_operations"></a>Matrix Vector Operations</h2> |
| <h3>Binary Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated classes <code>matrix_vector_binary1<E1, E2, |
| F></code> and <code>matrix_vector_binary2<E1, E2, |
| F></code> describe binary matrix vector operations.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.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>E1</code></td> |
| <td>The type of the matrix or vector expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>E2</code></td> |
| <td>The type of the vector or matrix expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>The type of the operation.</td> |
| <td></td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p><a href="expression_concept.htm#vector_expression">Vector Expression</a> |
| .</p> |
| <h4>Type requirements</h4> |
| <p>None, except for those imposed by the requirements of <a href= |
| "expression_concept.htm#vector_expression">Vector Expression</a> .</p> |
| <h4>Public base classes</h4> |
| <p><code>vector_expression<matrix_vector_binary1<E1, E2, |
| F> ></code> and |
| <code>vector_expression<matrix_vector_binary2<E1, E2, F> |
| ></code> resp.</p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>matrix_vector_binary1 (const expression1_type &e1, |
| const expression2_type &e2)</code></td> |
| <td>Constructs a description of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>matrix_vector_binary2 (const expression1_type &e1, |
| const expression2_type &e2)</code></td> |
| <td>Constructs a description of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>size_type size () const</code></td> |
| <td>Returns the size of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_reference operator () (size_type i) |
| const</code></td> |
| <td>Returns the value of the <code>i</code>-th element.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator begin () const</code></td> |
| <td>Returns a <code>const_iterator</code> pointing to the beginning |
| of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator end () const</code></td> |
| <td>Returns a <code>const_iterator</code> pointing to the end of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator rbegin () const</code></td> |
| <td>Returns a <code>const_reverse_iterator</code> pointing to the |
| beginning of the reversed expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_reverse_iterator rend () const</code></td> |
| <td>Returns a <code>const_reverse_iterator</code> pointing to the |
| end of the reversed expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h3>Binary Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class T1, class E1, class T2, class E2> |
| struct matrix_vector_binary1_traits { |
| typedef row_major_tag dispatch_category; |
| typedef typename promote_traits<T1, T2>::promote_type promote_type; |
| typedef matrix_vector_binary1<typename E1::const_closure_type, |
| typename E2::const_closure_type, |
| matrix_vector_prod1<T1, T2, promote_type> > expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| template<class E1, class E2> |
| typename matrix_vector_binary1_traits<typename E1::value_type, E1, |
| typename E2::value_type, E2>::result_type |
| prod (const matrix_expression<E1> &e1, |
| const vector_expression<E2> &e2, |
| row_major_tag); |
| |
| // Dispatcher |
| template<class E1, class E2> |
| typename matrix_vector_binary1_traits<typename E1::value_type, E1, |
| typename E2::value_type, E2>::result_type |
| prod (const matrix_expression<E1> &e1, |
| const vector_expression<E2> &e2); |
| |
| template<class E1, class E2> |
| typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1, |
| typename type_traits<typename E2::value_type>::precision_type, E2>::result_type |
| prec_prod (const matrix_expression<E1> &e1, |
| const vector_expression<E2> &e2, |
| row_major_tag); |
| |
| // Dispatcher |
| template<class E1, class E2> |
| typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1, |
| typename type_traits<typename E2::value_type>::precision_type, E2>::result_type |
| prec_prod (const matrix_expression<E1> &e1, |
| const vector_expression<E2> &e2); |
| |
| template<class V, class E1, class E2> |
| V |
| prod (const matrix_expression<E1> &e1, |
| const vector_expression<E2> &e2); |
| |
| template<class V, class E1, class E2> |
| V |
| prec_prod (const matrix_expression<E1> &e1, |
| const vector_expression<E2> &e2); |
| |
| template<class T1, class E1, class T2, class E2> |
| struct matrix_vector_binary2_traits { |
| typedef column_major_tag dispatch_category; |
| typedef typename promote_traits<T1, T2>::promote_type promote_type; |
| typedef matrix_vector_binary2<typename E1::const_closure_type, |
| typename E2::const_closure_type, |
| matrix_vector_prod2<T1, T2, promote_type> > expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| template<class E1, class E2> |
| typename matrix_vector_binary2_traits<typename E1::value_type, E1, |
| typename E2::value_type, E2>::result_type |
| prod (const vector_expression<E1> &e1, |
| const matrix_expression<E2> &e2, |
| column_major_tag); |
| |
| // Dispatcher |
| template<class E1, class E2> |
| typename matrix_vector_binary2_traits<typename E1::value_type, E1, |
| typename E2::value_type, E2>::result_type |
| prod (const vector_expression<E1> &e1, |
| const matrix_expression<E2> &e2); |
| |
| template<class E1, class E2> |
| typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1, |
| typename type_traits<typename E2::value_type>::precision_type, E2>::result_type |
| prec_prod (const vector_expression<E1> &e1, |
| const matrix_expression<E2> &e2, |
| column_major_tag); |
| |
| // Dispatcher |
| template<class E1, class E2> |
| typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1, |
| typename type_traits<typename E2::value_type>::precision_type, E2>::result_type |
| prec_prod (const vector_expression<E1> &e1, |
| const matrix_expression<E2> &e2); |
| |
| template<class V, class E1, class E2> |
| V |
| prod (const vector_expression<E1> &e1, |
| const matrix_expression<E2> &e2); |
| |
| template<class V, class E1, class E2> |
| V |
| prec_prod (const vector_expression<E1> &e1, |
| const matrix_expression<E2> &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>prod</code> computes the product of the matrix and the |
| vector expression. <code>prec_prod</code> computes the double |
| precision product of the matrix and the vector expression.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E1</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> or |
| <a href="expression_concept.htm#vector_expression">Vector Expression</a> |
| .</li> |
| <li><code>E2</code> is a model of <a href= |
| "expression_concept.htm#vector_expression">Vector Expression</a> or |
| <a href="expression_concept.htm#matrix_expression">Matrix Expression</a> |
| .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <ul> |
| <li><code>e1 ().size2 () == e2 ().size ()</code></li> |
| <li><code>e1 ().size () == e2 ().size1 ()</code></li> |
| </ul> |
| <h4>Complexity</h4> |
| <p>Quadratic depending from the size of the matrix expression.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/matrix.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| matrix<double> m (3, 3); |
| vector<double> v (3); |
| for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) { |
| for (unsigned j = 0; j < m.size2 (); ++ j) |
| m (i, j) = 3 * i + j; |
| v (i) = i; |
| } |
| |
| std::cout << prod (m, v) << std::endl; |
| std::cout << prod (v, m) << std::endl; |
| } |
| </pre> |
| <h3>Triangular Solver</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E1, class E2> |
| struct matrix_vector_solve_traits { |
| typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type; |
| typedef vector<promote_type> result_type; |
| }; |
| |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| lower_tag, |
| vector_tag); |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| upper_tag, |
| vector_tag); |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| unit_lower_tag, |
| vector_tag); |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| unit_upper_tag, |
| vector_tag); |
| |
| template<class E1, class E2, class C> |
| typename matrix_vector_solve_traits<E1, E2>::result_type |
| solve (const matrix_expression<E1> &e1, |
| const vector_expression<E2> &e2, |
| C); |
| |
| template<class E1, class E2> |
| void inplace_solve (E1 &e1, |
| const matrix_expression<E2> &e2, |
| vector_tag, |
| lower_tag); |
| template<class E1, class E2> |
| void inplace_solve (E1 &e1, |
| const matrix_expression<E2> &e2, |
| vector_tag, |
| upper_tag); |
| template<class E1, class E2> |
| void inplace_solve (E1 &e1, |
| const matrix_expression<E2> &e2, |
| vector_tag, |
| unit_lower_tag); |
| template<class E1, class E2> |
| void inplace_solve (E1 &e1, |
| const matrix_expression<E2> &e2, |
| vector_tag, |
| unit_upper_tag); |
| |
| template<class E1, class E2, class C> |
| typename matrix_vector_solve_traits<E1, E2>::result_type |
| solve (const vector_expression<E1> &e1, |
| const matrix_expression<E2> &e2, |
| C);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>solve</code> solves a linear equation for lower or upper |
| (unit) triangular matrices.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header triangular.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E1</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> or |
| <a href="expression_concept.htm#vector_expression">Vector Expression</a> |
| .</li> |
| <li><code>E2</code> is a model of <a href= |
| "expression_concept.htm#vector_expression">Vector Expression</a> or |
| <a href="expression_concept.htm#matrix_expression">Matrix Expression</a> |
| .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <ul> |
| <li><code>e1 ().size1 () == e1 ().size2 ()</code></li> |
| <li><code>e1 ().size2 () == e2 ().size ()</code></li> |
| <li><code>e1 ().size () == e2 ().size1 ()</code></li> |
| <li><code>e2 ().size1 () == e2 ().size2 ()</code></li> |
| </ul> |
| <h4>Complexity</h4> |
| <p>Quadratic depending from the size of the matrix expression.</p> |
| <h4>Examples</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); |
| vector<double> v (3); |
| for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) { |
| for (unsigned j = 0; j <= i; ++ j) |
| m (i, j) = 3 * i + j + 1; |
| v (i) = i; |
| } |
| |
| std::cout << solve (m, v, lower_tag ()) << std::endl; |
| std::cout << solve (v, m, lower_tag ()) << std::endl; |
| } |
| </pre> |
| <h2><a name="matrix_matrix_operations"></a>Matrix Matrix Operations</h2> |
| <h3>Binary Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated class <code>matrix_matrix_binary<E1, E2, |
| F></code> describes a binary matrix operation.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.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>E1</code></td> |
| <td>The type of the first matrix expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>E2</code></td> |
| <td>The type of the second matrix expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>The type of the operation.</td> |
| <td></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<matrix_matrix_binary<E1, E2, F> |
| ></code> .</p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>matrix_matrix_binary (const expression1_type &e1, |
| const expression2_type &e2)</code></td> |
| <td>Constructs a description of the expression.</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 the value of the <code>j</code>-th element in the |
| <code>i</code>-th row.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 begin1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator1 end1 () const</code></td> |
| <td>Returns a <code>const_iterator1</code> pointing to the end of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 begin2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the |
| beginning of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>const_iterator2 end2 () const</code></td> |
| <td>Returns a <code>const_iterator2</code> pointing to the end of |
| the expression.</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 expression.</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 expression.</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 expression.</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 expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h3>Binary Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class T1, class E1, class T2, class E2> |
| struct matrix_matrix_binary_traits { |
| typedef unknown_orientation_tag dispatch_category; |
| typedef typename promote_traits<T1, T2>::promote_type promote_type; |
| typedef matrix_matrix_binary<typename E1::const_closure_type, |
| typename E2::const_closure_type, |
| matrix_matrix_prod<T1, T2, promote_type> > expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| template<class E1, class E2> |
| typename matrix_matrix_binary_traits<typename E1::value_type, E1, |
| typename E2::value_type, E2>::result_type |
| prod (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2, |
| unknown_orientation_tag); |
| |
| // Dispatcher |
| template<class E1, class E2> |
| typename matrix_matrix_binary_traits<typename E1::value_type, E1, |
| typename E2::value_type, E2>::result_type |
| prod (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2); |
| |
| template<class E1, class E2> |
| typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1, |
| typename type_traits<typename E2::value_type>::precision_type, E2>::result_type |
| prec_prod (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2, |
| unknown_orientation_tag); |
| |
| // Dispatcher |
| template<class E1, class E2> |
| typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1, |
| typename type_traits<typename E2::value_type>::precision_type, E2>::result_type |
| prec_prod (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2); |
| |
| template<class M, class E1, class E2> |
| M |
| prod (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2); |
| |
| template<class M, class E1, class E2> |
| M |
| prec_prod (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>prod</code> computes the product of the matrix |
| expressions. <code>prec_prod</code> computes the double precision |
| product of the matrix expressions.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E1</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| <li><code>E2</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <ul> |
| <li><code>e1 ().size2 () == e2 ().size1 ()</code></li> |
| </ul> |
| <h4>Complexity</h4> |
| <p>Cubic depending from the size of the matrix expression.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/matrix.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| matrix<double> m1 (3, 3), m2 (3, 3); |
| for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i) |
| for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j) |
| m1 (i, j) = m2 (i, j) = 3 * i + j; |
| |
| std::cout << prod (m1, m2) << std::endl; |
| } |
| </pre> |
| <h3>Triangular Solvers</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E1, class E2> |
| struct matrix_matrix_solve_traits { |
| typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type; |
| typedef matrix<promote_type> result_type; |
| }; |
| |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| lower_tag, |
| matrix_tag); |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| upper_tag, |
| matrix_tag); |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| unit_lower_tag, |
| matrix_tag); |
| template<class E1, class E2> |
| void inplace_solve (const matrix_expression<E1> &e1, |
| E2 &e2, |
| unit_upper_tag, |
| matrix_tag); |
| |
| template<class E1, class E2, class C> |
| typename matrix_matrix_solve_traits<E1, E2>::result_type |
| solve (const matrix_expression<E1> &e1, |
| const matrix_expression<E2> &e2, |
| C);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>solve</code> solves a linear equation for lower or upper |
| (unit) triangular matrices.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header triangular.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E1</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| <li><code>E2</code> is a model of <a href= |
| "expression_concept.htm#matrix_expression">Matrix Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <ul> |
| <li><code>e1 ().size1 () == e1 ().size2 ()</code></li> |
| <li><code>e1 ().size2 () == e2 ().size1 ()</code></li> |
| </ul> |
| <h4>Complexity</h4> |
| <p>Cubic depending from the size of the matrix expressions.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/triangular.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| matrix<double> m1 (3, 3), m2 (3, 3); |
| for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i) |
| for (unsigned j = 0; j <= i; ++ j) |
| m1 (i, j) = m2 (i, j) = 3 * i + j + 1; |
| |
| std::cout << solve (m1, m2, lower_tag ()) << std::endl; |
| } |
| </pre> |
| <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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