boost-react-native-bundle

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta name="generator" content= "HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" /> <meta http-equiv="Content-Type" content= "text/html; charset=us-ascii" /> <link rel="stylesheet" href="../../../../boost.css" type="text/css"/> <link rel="stylesheet" href="ublas.css" type="text/css" /> <script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script> <script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script> <title>Matrix Expressions</title> </head> <body> <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.html">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.html#matrix_expression">Matrix Expression</a> .</p> <h4>Type requirements</h4> <p>None, except for those imposed by the requirements of <a href= "expression_concept.html#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.html#matrix_expression">Matrix Expression</a> .</p> <h4>Type requirements</h4> <p>None, except for those imposed by the requirements of <a href= "expression_concept.html#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.html#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.html#matrix_expression">Matrix Expression</a> .</p> <h4>Type requirements</h4> <p>None, except for those imposed by the requirements of <a href= "expression_concept.html#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.html#matrix_expression">Matrix Expression</a> .</li> <li><code>E2</code> is a model of <a href= "expression_concept.html#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.html#matrix_expression">Matrix Expression</a> .</p> <h4>Type requirements</h4> <p>None, except for those imposed by the requirements of <a href= "expression_concept.html#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.html#scalar_expression">Scalar Expression</a> .</li> <li><code>E2/E1</code> is a model of <a href= "expression_concept.html#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.html#vector_expression">Vector Expression</a> .</p> <h4>Type requirements</h4> <p>None, except for those imposed by the requirements of <a href= "expression_concept.html#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.html#matrix_expression">Matrix Expression</a> or <a href="expression_concept.html#vector_expression">Vector Expression</a> .</li> <li><code>E2</code> is a model of <a href= "expression_concept.html#vector_expression">Vector Expression</a> or <a href="expression_concept.html#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.html#matrix_expression">Matrix Expression</a> or <a href="expression_concept.html#vector_expression">Vector Expression</a> .</li> <li><code>E2</code> is a model of <a href= "expression_concept.html#vector_expression">Vector Expression</a> or <a href="expression_concept.html#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.html#matrix_expression">Matrix Expression</a> .</p> <h4>Type requirements</h4> <p>None, except for those imposed by the requirements of <a href= "expression_concept.html#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.html#matrix_expression">Matrix Expression</a> .</li> <li><code>E2</code> is a model of <a href= "expression_concept.html#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.html#matrix_expression">Matrix Expression</a> .</li> <li><code>E2</code> is a model of <a href= "expression_concept.html#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,