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|
<!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 href="ublas.css" type="text/css" />
<title>Vector Expressions</title>
</head>
<body>
<h1><img src="../../../../boost.png" align="middle" />
Vector Expressions</h1>
<h2><a name="vector_expression" id="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" id="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" id="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" id="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" id="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 />
Permission to copy, use, modify, sell and distribute this document
is granted provided this copyright notice appears in all copies.
This document is provided ``as is'' without express or implied
warranty, and with no claim as to its suitability for any
purpose.</p>
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