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| <title>Vector Expressions</title> |
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| <body> |
| <h1><img src="../../../../boost.png" align="middle" />Vector Expressions</h1> |
| <div class="toc" id="toc"></div> |
| <h2><a name="vector_expression"></a>Vector Expression</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>vector_expression<E></code> |
| is required to be a public base of all classes which model the Vector 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 vector expression.</td> |
| <td> </td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p>None. <u>Not a Vector 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>range</code>, <code>slice</code> and <code>project</code> functions have been removed. Use the free functions defined in <a href="vector_proxy.htm">vector proxy</a> instead.</p> |
| |
| <h2><a name="vector_container"></a>Vector Container</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>vector_container<C></code> |
| is required to be a public base of all classes which model the Vector concept. |
| This includes the class <code>vector</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>C</code></td> |
| <td>The type of the vector container.</td> |
| <td> </td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p>None. <u>Not a Vector Expression OR Vector</u>! |
| </p> |
| <h4>Type requirements</h4> |
| <p>None.</p> |
| <h4>Public base classes</h4> |
| <p><code>vector_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="vector_references"></a>Vector References</h2> |
| <h3>Reference</h3> |
| <h4>Description</h4> |
| <p>The templated class <code>vector_reference<E></code> |
| contains a reference to a vector expression.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_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 vector expression.</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<vector_reference<E> |
| ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>vector_reference (expression_type &e)</code></td> |
| <td>Constructs a reference of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>void resize (size_type size)</code></td> |
| <td>Resizes the expression to hold at most <code>size</code> |
| elements.</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>reference operator () (size_type i)</code></td> |
| <td>Returns a reference 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>iterator begin ()</code></td> |
| <td>Returns a <code>iterator</code> pointing to the beginning of |
| the expression.</td> |
| </tr> |
| <tr> |
| <td><code>iterator end ()</code></td> |
| <td>Returns a <code>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> |
| <tr> |
| <td><code>reverse_iterator rbegin ()</code></td> |
| <td>Returns a <code>reverse_iterator</code> pointing to the |
| beginning of the reversed expression.</td> |
| </tr> |
| <tr> |
| <td><code>reverse_iterator rend ()</code></td> |
| <td>Returns a <code>reverse_iterator</code> pointing to the end of |
| the reversed expression.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h2><a name="vector_operations"></a>Vector Operations</h2> |
| <h3>Unary Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated class <code>vector_unary<E, F></code> |
| describes a unary vector operation.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_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 vector 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<vector_unary<E, F> |
| ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>vector_unary (const expression_type &e)</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>Unary Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E, class F> |
| struct vector_unary_traits { |
| typedef vector_unary<typename E::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (- v) [i] = - v [i] |
| template<class E> |
| typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::result_type |
| operator - (const vector_expression<E> &e); |
| |
| // (conj v) [i] = conj (v [i]) |
| template<class E> |
| typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type |
| conj (const vector_expression<E> &e); |
| |
| // (real v) [i] = real (v [i]) |
| template<class E> |
| typename vector_unary_traits<E, scalar_real<typename E::value_type> >::result_type |
| real (const vector_expression<E> &e); |
| |
| // (imag v) [i] = imag (v [i]) |
| template<class E> |
| typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::result_type |
| imag (const vector_expression<E> &e); |
| |
| // (trans v) [i] = v [i] |
| template<class E> |
| typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::result_type |
| trans (const vector_expression<E> &e); |
| |
| // (herm v) [i] = conj (v [i]) |
| template<class E> |
| typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type |
| herm (const vector_expression<E> &e);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>operator -</code> computes the additive inverse of a |
| vector expression. <code>conj</code> computes the complex conjugate |
| of a vector expression. <code>real</code> and <code>imag</code> |
| compute the real and imaginary parts of a vector expression. |
| <code>trans</code> computes the transpose of a vector expression. |
| <code>herm</code> computes the hermitian, i.e. the complex |
| conjugate of the transpose of a vector expression.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E</code> is a model of <a href= |
| "expression_concept.htm#vector_expression">Vector Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <p>None.</p> |
| <h4>Complexity</h4> |
| <p>Linear depending from the size of the vector expression.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/vector.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| vector<std::complex<double> > v (3); |
| for (unsigned i = 0; i < v.size (); ++ i) |
| v (i) = std::complex<double> (i, i); |
| |
| std::cout << - v << std::endl; |
| std::cout << conj (v) << std::endl; |
| std::cout << real (v) << std::endl; |
| std::cout << imag (v) << std::endl; |
| std::cout << trans (v) << std::endl; |
| std::cout << herm (v) << std::endl; |
| } |
| </pre> |
| <h3>Binary Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated class <code>vector_binary<E1, E2, F></code> |
| describes a binary vector operation.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_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 vector expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>E2</code></td> |
| <td>The type of the second vector 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<vector_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>vector_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 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 E1, class E2, class F> |
| struct vector_binary_traits { |
| typedef vector_binary<typename E1::const_closure_type, |
| typename E2::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (v1 + v2) [i] = v1 [i] + v2 [i] |
| template<class E1, class E2> |
| typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type, |
| typename E2::value_type> >::result_type |
| operator + (const vector_expression<E1> &e1, |
| const vector_expression<E2> &e2); |
| |
| // (v1 - v2) [i] = v1 [i] - v2 [i] |
| template<class E1, class E2> |
| typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type, |
| typename E2::value_type> >::result_type |
| operator - (const vector_expression<E1> &e1, |
| const vector_expression<E2> &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>operator +</code> computes the sum of two vector |
| expressions. <code>operator -</code> computes the difference of two |
| vector expressions.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E1</code> is a model of <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> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <ul> |
| <li><code>e1 ().size () == e2 ().size ()</code></li> |
| </ul> |
| <h4>Complexity</h4> |
| <p>Linear depending from the size of the vector expressions.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/vector.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| vector<double> v1 (3), v2 (3); |
| for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i) |
| v1 (i) = v2 (i) = i; |
| |
| std::cout << v1 + v2 << std::endl; |
| std::cout << v1 - v2 << std::endl; |
| } |
| </pre> |
| <h3>Binary Outer Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated class <code>vector_matrix_binary<E1, E2, |
| F></code> describes a binary outer vector 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 vector expression.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>E2</code></td> |
| <td>The type of the second vector 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<vector_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>vector_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 Outer Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E1, class E2, class F> |
| struct vector_matrix_binary_traits { |
| typedef vector_matrix_binary<typename E1::const_closure_type, |
| typename E2::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (outer_prod (v1, v2)) [i] [j] = v1 [i] * v2 [j] |
| template<class E1, class E2> |
| typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type |
| outer_prod (const vector_expression<E1> &e1, |
| const vector_expression<E2> &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>outer_prod</code> computes the outer product of two vector |
| 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#vector_expression">Vector Expression</a> .</li> |
| <li><code>E2</code> is a model of <a href= |
| "expression_concept.htm#vector_expression">Vector Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <p>None.</p> |
| <h4>Complexity</h4> |
| <p>Quadratic depending from the size of the vector 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; |
| vector<double> v1 (3), v2 (3); |
| for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i) |
| v1 (i) = v2 (i) = i; |
| |
| std::cout << outer_prod (v1, v2) << std::endl; |
| } |
| </pre> |
| <h3>Scalar Vector Operation Description</h3> |
| <h4>Description</h4> |
| <p>The templated classes <code>vector_binary_scalar1<E1, E2, |
| F></code> and <code>vector_binary_scalar2<E1, E2, |
| F></code> describe binary operations between a scalar and a |
| vector.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_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 vector 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<vector_binary_scalar1<E1, E2, |
| F> ></code> and |
| <code>vector_expression<vector_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>vector_binary_scalar1 (const expression1_type &e1, |
| const expression2_type &e2)</code></td> |
| <td>Constructs a description of the expression.</td> |
| </tr> |
| <tr> |
| <td><code>vector_binary_scalar2 (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>Scalar Vector Operations</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class T1, class E2, class F> |
| struct vector_binary_scalar1_traits { |
| typedef vector_binary_scalar1<scalar_const_reference<T1>, |
| typename E2::const_closure_type, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (t * v) [i] = t * v [i] |
| template<class T1, class E2> |
| typename vector_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type |
| operator * (const T1 &e1, |
| const vector_expression<E2> &e2); |
| |
| template<class E1, class T2, class F> |
| struct vector_binary_scalar2_traits { |
| typedef vector_binary_scalar2<typename E1::const_closure_type, |
| scalar_const_reference<T2>, F> expression_type; |
| typedef expression_type result_type; |
| }; |
| |
| // (v * t) [i] = v [i] * t |
| template<class E1, class T2> |
| typename vector_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type |
| operator * (const vector_expression<E1> &e1, |
| const T2 &e2); |
| |
| // (v / t) [i] = v [i] / t |
| template<class E1, class T2> |
| typename vector_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type |
| operator / (const vector_expression<E1> &e1, |
| const T2 &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>operator *</code> computes the product of a scalar and a |
| vector expression. <code>operator /</code> multiplies the vector |
| with the reciprocal of the scalar.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_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#vector_expression">Vector Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <p>None.</p> |
| <h4>Complexity</h4> |
| <p>Linear depending from the size of the vector expression.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/vector.hpp> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| vector<double> v (3); |
| for (unsigned i = 0; i < v.size (); ++ i) |
| v (i) = i; |
| |
| std::cout << 2.0 * v << std::endl; |
| std::cout << v * 2.0 << std::endl; |
| } |
| </pre> |
| <h2><a name="vector_reductions"></a>Vector Reductions</h2> |
| <h3>Unary Reductions</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E, class F> |
| struct vector_scalar_unary_traits { |
| typedef typename F::result_type result_type; |
| }; |
| |
| // sum v = sum (v [i]) |
| template<class E> |
| typename vector_scalar_unary_traits<E, vector_sum<typename E::value_type> >::result_type |
| sum (const vector_expression<E> &e); |
| |
| // norm_1 v = sum (abs (v [i])) |
| template<class E> |
| typename vector_scalar_unary_traits<E, vector_norm_1<typename E::value_type> >::result_type |
| norm_1 (const vector_expression<E> &e); |
| |
| // norm_2 v = sqrt (sum (v [i] * v [i])) |
| template<class E> |
| typename vector_scalar_unary_traits<E, vector_norm_2<typename E::value_type> >::result_type |
| norm_2 (const vector_expression<E> &e); |
| |
| // norm_inf v = max (abs (v [i])) |
| template<class E> |
| typename vector_scalar_unary_traits<E, vector_norm_inf<typename E::value_type> >::result_type |
| norm_inf (const vector_expression<E> &e); |
| |
| // index_norm_inf v = min (i: abs (v [i]) == max (abs (v [i]))) |
| template<class E> |
| typename vector_scalar_unary_traits<E, vector_index_norm_inf<typename E::value_type> >::result_type |
| index_norm_inf (const vector_expression<E> &e);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>sum</code> computes the sum of the vector expression's |
| elements. <code>norm_1</code>, <code>norm_2</code> and |
| <code>norm_inf</code> compute the corresponding |
| <em>||.||</em><sub><em>1</em></sub>, |
| <em>||.||</em><sub><em>2</em></sub> and |
| <em>||.||</em><sub><em>inf</em></sub> vector norms. |
| <code>index_norm_1</code> computes the index of the vector |
| expression's first element having maximal absolute value.</p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E</code> is a model of <a href= |
| "#vector_expression">Vector Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <p>None.</p> |
| <h4>Complexity</h4> |
| <p>Linear depending from the size of the vector expression.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/vector.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| vector<double> v (3); |
| for (unsigned i = 0; i < v.size (); ++ i) |
| v (i) = i; |
| |
| std::cout << sum (v) << std::endl; |
| std::cout << norm_1 (v) << std::endl; |
| std::cout << norm_2 (v) << std::endl; |
| std::cout << norm_inf (v) << std::endl; |
| std::cout << index_norm_inf (v) << std::endl; |
| } |
| </pre> |
| <h3>Binary Reductions</h3> |
| <h4>Prototypes</h4> |
| <pre> |
| <code>template<class E1, class E2, class F> |
| struct vector_scalar_binary_traits { |
| typedef typename F::result_type result_type; |
| }; |
| |
| // inner_prod (v1, v2) = sum (v1 [i] * v2 [i]) |
| template<class E1, class E2> |
| typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type, |
| typename E2::value_type, |
| typename promote_traits<typename E1::value_type, |
| typename E2::value_type>::promote_type> >::result_type |
| inner_prod (const vector_expression<E1> &e1, |
| const vector_expression<E2> &e2); |
| |
| template<class E1, class E2> |
| typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type, |
| typename E2::value_type, |
| typename type_traits<typename promote_traits<typename E1::value_type, |
| typename E2::value_type>::promote_type>::precision_type> >::result_type |
| prec_inner_prod (const vector_expression<E1> &e1, |
| const vector_expression<E2> &e2);</code> |
| </pre> |
| <h4>Description</h4> |
| <p><code>inner_prod</code> computes the inner product of the vector |
| expressions. <code>prec_inner_prod</code> computes the double |
| precision inner product of the vector expressions<code>.</code></p> |
| <h4>Definition</h4> |
| <p>Defined in the header vector_expression.hpp.</p> |
| <h4>Type requirements</h4> |
| <ul> |
| <li><code>E1</code> is a model of <a href= |
| "#vector_expression">Vector Expression</a> .</li> |
| <li><code>E2</code> is a model of <a href= |
| "#vector_expression">Vector Expression</a> .</li> |
| </ul> |
| <h4>Preconditions</h4> |
| <ul> |
| <li><code>e1 ().size () == e2 ().size ()</code></li> |
| </ul> |
| <h4>Complexity</h4> |
| <p>Linear depending from the size of the vector expressions.</p> |
| <h4>Examples</h4> |
| <pre> |
| #include <boost/numeric/ublas/vector.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| vector<double> v1 (3), v2 (3); |
| for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i) |
| v1 (i) = v2 (i) = i; |
| |
| std::cout << inner_prod (v1, v2) << 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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