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<div id="projectbrief">Linear Algebra in C++: matrices, vectors and numeric algorithms</div>
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<h1>boost::numeric::ublas::blas_1 Namespace Reference</h1> </div>
</div>
<div class="contents">
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="func-members"></a>
Functions</h2></td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a00465.html">type_traits</a>&lt; typename <br class="typebreak"/>
V::value_type &gt;::real_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a576c07d6b09c0b951eb5c8830de4b93a">amax</a> (const V &amp;v)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a00465.html">type_traits</a>&lt; typename <br class="typebreak"/>
V::value_type &gt;::real_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#ad7e35b223f5cac9878a04db6a6df6715">asum</a> (const V &amp;v)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class T , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#aabc7566ce5b699e5620e7d39b1de40fd">axpy</a> (V1 &amp;v1, const T &amp;t, const V2 &amp;v2)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V1 &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#aeb7460bec576eb9c5217050d6baa4f6f">copy</a> (V1 &amp;v1, const V2 &amp;v2)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a00364.html">promote_traits</a>&lt; typename <br class="typebreak"/>
V1::value_type, typename <br class="typebreak"/>
V2::value_type &gt;::promote_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a95dc5f5e3116c096ee78ed24d14f2b55">dot</a> (const V1 &amp;v1, const V2 &amp;v2)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a00465.html">type_traits</a>&lt; typename <br class="typebreak"/>
V::value_type &gt;::real_type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#ae7d8e65daedd8de344f4d169cfe22dc9">nrm2</a> (const V &amp;v)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class T1 , class V1 , class T2 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a69badeae884488668d2e31c387427da0">rot</a> (const T1 &amp;t1, V1 &amp;v1, const T2 &amp;t2, V2 &amp;v2)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V , class T &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">V &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a8e5af6ed9ca0d90e6daf640151c2b46a">scal</a> (V &amp;v, const T &amp;t)</td></tr>
<tr><td class="memTemplParams" colspan="2">template&lt;class V1 , class V2 &gt; </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00651.html#a7359c42bdbf22249101e062d45c8fec6">swap</a> (V1 &amp;v1, V2 &amp;v2)</td></tr>
</table>
<hr/><a name="_details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Interface and implementation of BLAS level 1 This includes functions which perform <b>vector-vector</b> operations. More information about BLAS can be found at <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> </p>
</div><hr/><h2>Function Documentation</h2>
<a class="anchor" id="ad7e35b223f5cac9878a04db6a6df6715"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::asum" ref="ad7e35b223f5cac9878a04db6a6df6715" args="(const V &amp;v)" -->
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class V &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="a00465.html">type_traits</a>&lt;typename V::value_type&gt;::real_type boost::numeric::ublas::blas_1::asum </td>
<td>(</td>
<td class="paramtype">const V &amp;&#160;</td>
<td class="paramname"><em>v</em></td><td>)</td>
<td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>1-Norm: <img class="formulaInl" alt="$\sum_i |x_i|$" src="form_12.png"/> (also called <img class="formulaInl" alt="$\mathcal{L}_1$" src="form_13.png"/> or Manhattan norm)</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v</td><td>a vector or vector expression </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>the 1-Norm with type of the vector's type</dd></dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V</td><td>type of the vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00034">34</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="ae7d8e65daedd8de344f4d169cfe22dc9"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::nrm2" ref="ae7d8e65daedd8de344f4d169cfe22dc9" args="(const V &amp;v)" -->
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class V &gt; </div>
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<td class="memname"><a class="el" href="a00465.html">type_traits</a>&lt;typename V::value_type&gt;::real_type boost::numeric::ublas::blas_1::nrm2 </td>
<td>(</td>
<td class="paramtype">const V &amp;&#160;</td>
<td class="paramname"><em>v</em></td><td>)</td>
<td></td>
</tr>
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<div class="memdoc">
<p>2-Norm: <img class="formulaInl" alt="$\sum_i |x_i|^2$" src="form_14.png"/> (also called <img class="formulaInl" alt="$\mathcal{L}_2$" src="form_15.png"/> or Euclidean norm)</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v</td><td>a vector or vector expression </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>the 2-Norm with type of the vector's type</dd></dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V</td><td>type of the vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00047">47</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="a576c07d6b09c0b951eb5c8830de4b93a"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::amax" ref="a576c07d6b09c0b951eb5c8830de4b93a" args="(const V &amp;v)" -->
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class V &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="a00465.html">type_traits</a>&lt;typename V::value_type&gt;::real_type boost::numeric::ublas::blas_1::amax </td>
<td>(</td>
<td class="paramtype">const V &amp;&#160;</td>
<td class="paramname"><em>v</em></td><td>)</td>
<td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Infinite-norm: <img class="formulaInl" alt="$\max_i |x_i|$" src="form_16.png"/> (also called <img class="formulaInl" alt="$\mathcal{L}_\infty$" src="form_17.png"/> norm)</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v</td><td>a vector or vector expression </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>the Infinite-Norm with type of the vector's type</dd></dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V</td><td>type of the vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00060">60</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="a95dc5f5e3116c096ee78ed24d14f2b55"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::dot" ref="a95dc5f5e3116c096ee78ed24d14f2b55" args="(const V1 &amp;v1, const V2 &amp;v2)" -->
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class V1 , class V2 &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="a00364.html">promote_traits</a>&lt;typename V1::value_type, typename V2::value_type&gt;::promote_type boost::numeric::ublas::blas_1::dot </td>
<td>(</td>
<td class="paramtype">const V1 &amp;&#160;</td>
<td class="paramname"><em>v1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const V2 &amp;&#160;</td>
<td class="paramname"><em>v2</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Inner product of vectors <img class="formulaInl" alt="$v_1$" src="form_18.png"/> and <img class="formulaInl" alt="$v_2$" src="form_19.png"/></p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v1</td><td>first vector of the inner product </td></tr>
<tr><td class="paramname">v2</td><td>second vector of the inner product </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>the inner product of the type of the most generic type of the 2 vectors</dd></dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V1</td><td>type of first vector (not needed by default) </td></tr>
<tr><td class="paramname">V2</td><td>type of second vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00075">75</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="aeb7460bec576eb9c5217050d6baa4f6f"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::copy" ref="aeb7460bec576eb9c5217050d6baa4f6f" args="(V1 &amp;v1, const V2 &amp;v2)" -->
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class V1 , class V2 &gt; </div>
<table class="memname">
<tr>
<td class="memname">V1&amp; boost::numeric::ublas::blas_1::copy </td>
<td>(</td>
<td class="paramtype">V1 &amp;&#160;</td>
<td class="paramname"><em>v1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const V2 &amp;&#160;</td>
<td class="paramname"><em>v2</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Copy vector <img class="formulaInl" alt="$v_2$" src="form_19.png"/> to <img class="formulaInl" alt="$v_1$" src="form_18.png"/></p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v1</td><td>target vector </td></tr>
<tr><td class="paramname">v2</td><td>source vector </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>a reference to the target vector</dd></dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V1</td><td>type of first vector (not needed by default) </td></tr>
<tr><td class="paramname">V2</td><td>type of second vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00089">89</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="a7359c42bdbf22249101e062d45c8fec6"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::swap" ref="a7359c42bdbf22249101e062d45c8fec6" args="(V1 &amp;v1, V2 &amp;v2)" -->
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class V1 , class V2 &gt; </div>
<table class="memname">
<tr>
<td class="memname">void boost::numeric::ublas::blas_1::swap </td>
<td>(</td>
<td class="paramtype">V1 &amp;&#160;</td>
<td class="paramname"><em>v1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">V2 &amp;&#160;</td>
<td class="paramname"><em>v2</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Swap vectors <img class="formulaInl" alt="$v_1$" src="form_18.png"/> and <img class="formulaInl" alt="$v_2$" src="form_19.png"/></p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v1</td><td>first vector </td></tr>
<tr><td class="paramname">v2</td><td>second vector</td></tr>
</table>
</dd>
</dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V1</td><td>type of first vector (not needed by default) </td></tr>
<tr><td class="paramname">V2</td><td>type of second vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00103">103</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="a8e5af6ed9ca0d90e6daf640151c2b46a"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::scal" ref="a8e5af6ed9ca0d90e6daf640151c2b46a" args="(V &amp;v, const T &amp;t)" -->
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class V , class T &gt; </div>
<table class="memname">
<tr>
<td class="memname">V&amp; boost::numeric::ublas::blas_1::scal </td>
<td>(</td>
<td class="paramtype">V &amp;&#160;</td>
<td class="paramname"><em>v</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const T &amp;&#160;</td>
<td class="paramname"><em>t</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>scale vector <img class="formulaInl" alt="$v$" src="form_20.png"/> with scalar <img class="formulaInl" alt="$t$" src="form_21.png"/></p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v</td><td>vector to be scaled </td></tr>
<tr><td class="paramname">t</td><td>the scalar </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd><code>t*v</code> </dd></dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V</td><td>type of the vector (not needed by default) </td></tr>
<tr><td class="paramname">T</td><td>type of the scalar (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00118">118</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="aabc7566ce5b699e5620e7d39b1de40fd"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::axpy" ref="aabc7566ce5b699e5620e7d39b1de40fd" args="(V1 &amp;v1, const T &amp;t, const V2 &amp;v2)" -->
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template&lt;class V1 , class T , class V2 &gt; </div>
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<td class="memname">V1&amp; boost::numeric::ublas::blas_1::axpy </td>
<td>(</td>
<td class="paramtype">V1 &amp;&#160;</td>
<td class="paramname"><em>v1</em>, </td>
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<td class="paramtype">const T &amp;&#160;</td>
<td class="paramname"><em>t</em>, </td>
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<td class="paramtype">const V2 &amp;&#160;</td>
<td class="paramname"><em>v2</em>&#160;</td>
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<td>)</td>
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<p>Compute <img class="formulaInl" alt="$v_1= v_1 + t.v_2$" src="form_22.png"/></p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">v1</td><td>target and first vector </td></tr>
<tr><td class="paramname">t</td><td>the scalar </td></tr>
<tr><td class="paramname">v2</td><td>second vector </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>a reference to the first and target vector</dd></dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">V1</td><td>type of the first vector (not needed by default) </td></tr>
<tr><td class="paramname">T</td><td>type of the scalar (not needed by default) </td></tr>
<tr><td class="paramname">V2</td><td>type of the second vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00135">135</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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<a class="anchor" id="a69badeae884488668d2e31c387427da0"></a><!-- doxytag: member="boost::numeric::ublas::blas_1::rot" ref="a69badeae884488668d2e31c387427da0" args="(const T1 &amp;t1, V1 &amp;v1, const T2 &amp;t2, V2 &amp;v2)" -->
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<td class="memname">void boost::numeric::ublas::blas_1::rot </td>
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<td class="paramtype">const T1 &amp;&#160;</td>
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<td class="paramname"><em>v1</em>, </td>
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<td></td>
<td class="paramtype">const T2 &amp;&#160;</td>
<td class="paramname"><em>t2</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">V2 &amp;&#160;</td>
<td class="paramname"><em>v2</em>&#160;</td>
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<p>Performs rotation of points in the plane and assign the result to the first vector</p>
<p>Each point is defined as a pair <code>v1(i)</code> and <code>v2(i)</code>, being respectively the <img class="formulaInl" alt="$x$" src="form_23.png"/> and <img class="formulaInl" alt="$y$" src="form_24.png"/> coordinates. The parameters <code>t1</code> and are respectively the cosine and sine of the angle of the rotation. Results are not returned but directly written into <code>v1</code>.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">t1</td><td>cosine of the rotation </td></tr>
<tr><td class="paramname">v1</td><td>vector of <img class="formulaInl" alt="$x$" src="form_23.png"/> values </td></tr>
<tr><td class="paramname">t2</td><td>sine of the rotation </td></tr>
<tr><td class="paramname">v2</td><td>vector of <img class="formulaInl" alt="$y$" src="form_24.png"/> values</td></tr>
</table>
</dd>
</dl>
<dl><dt><b>Template Parameters:</b></dt><dd>
<table class="">
<tr><td class="paramname">T1</td><td>type of the cosine value (not needed by default) </td></tr>
<tr><td class="paramname">V1</td><td>type of the <img class="formulaInl" alt="$x$" src="form_23.png"/> vector (not needed by default) </td></tr>
<tr><td class="paramname">T2</td><td>type of the sine value (not needed by default) </td></tr>
<tr><td class="paramname">V2</td><td>type of the <img class="formulaInl" alt="$y$" src="form_24.png"/> vector (not needed by default) </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="a00598_source.html#l00158">158</a> of file <a class="el" href="a00598_source.html">blas.hpp</a>.</p>
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