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<div class="titlepage"><div><div><h5 class="title">
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx"></a><a class="link" href="ggesx.html" title="ggesx">ggesx</a>
</h5></div></div></div>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.prototype"></a><h6>
<a name="id809835"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.prototype">Prototype</a>
</h6>
<p>
There are two prototypes of <code class="computeroutput"><span class="identifier">ggesx</span></code>
available, please see below.
</p>
<pre class="programlisting"><span class="identifier">ggesx</span><span class="special">(</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvsl</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvsr</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sort</span><span class="special">,</span>
<span class="identifier">external_fp</span> <span class="identifier">selctg</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sense</span><span class="special">,</span> <span class="identifier">MatrixA</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">MatrixB</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
<span class="identifier">int_t</span><span class="special">&</span> <span class="identifier">sdim</span><span class="special">,</span> <span class="identifier">VectorALPHAR</span><span class="special">&</span> <span class="identifier">alphar</span><span class="special">,</span> <span class="identifier">VectorALPHAI</span><span class="special">&</span> <span class="identifier">alphai</span><span class="special">,</span>
<span class="identifier">VectorBETA</span><span class="special">&</span> <span class="identifier">beta</span><span class="special">,</span> <span class="identifier">MatrixVSL</span><span class="special">&</span> <span class="identifier">vsl</span><span class="special">,</span> <span class="identifier">MatrixVSR</span><span class="special">&</span> <span class="identifier">vsr</span><span class="special">,</span>
<span class="identifier">VectorRCONDE</span><span class="special">&</span> <span class="identifier">rconde</span><span class="special">,</span> <span class="identifier">VectorRCONDV</span><span class="special">&</span> <span class="identifier">rcondv</span> <span class="special">);</span>
</pre>
<p>
</p>
<p>
</p>
<pre class="programlisting"><span class="identifier">ggesx</span><span class="special">(</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvsl</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvsr</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sort</span><span class="special">,</span>
<span class="identifier">external_fp</span> <span class="identifier">selctg</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sense</span><span class="special">,</span> <span class="identifier">MatrixA</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">MatrixB</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
<span class="identifier">int_t</span><span class="special">&</span> <span class="identifier">sdim</span><span class="special">,</span> <span class="identifier">VectorALPHA</span><span class="special">&</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">VectorBETA</span><span class="special">&</span> <span class="identifier">beta</span><span class="special">,</span>
<span class="identifier">MatrixVSL</span><span class="special">&</span> <span class="identifier">vsl</span><span class="special">,</span> <span class="identifier">MatrixVSR</span><span class="special">&</span> <span class="identifier">vsr</span><span class="special">,</span> <span class="identifier">VectorRCONDE</span><span class="special">&</span> <span class="identifier">rconde</span><span class="special">,</span>
<span class="identifier">VectorRCONDV</span><span class="special">&</span> <span class="identifier">rcondv</span> <span class="special">);</span>
</pre>
<p>
</p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.description"></a><h6>
<a name="id810576"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.description">Description</a>
</h6>
<p>
<code class="computeroutput"><span class="identifier">ggesx</span></code> (short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SGGESX, DGGESX, CGGESX, and
ZGGESX. <code class="computeroutput"><span class="identifier">ggesx</span></code> computes
for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized
eigenvalues, the complex Schur form (S,T), and, optionally, the left
and/or right matrices of Schur vectors (VSL and VSR). This gives the
generalized Schur factorization
</p>
<p>
(A,B) = ( (VSL) S (VSR)<span class="bold"><strong>*H, (VSL) T (VSR)</strong></span>*H
)
</p>
<p>
where (VSR)**H is the conjugate-transpose of VSR.
</p>
<p>
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper triangular
matrix S and the upper triangular matrix T; computes a reciprocal condition
number for the average of the selected eigenvalues (RCONDE); and computes
a reciprocal condition number for the right and left deflating subspaces
corresponding to the selected eigenvalues (RCONDV). The leading columns
of VSL and VSR then form an orthonormal basis for the corresponding left
and right eigenspaces (deflating subspaces).
</p>
<p>
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or
a ratio alpha/beta = w, such that A - w*B is singular. It is usually
represented as the pair (alpha,beta), as there is a reasonable interpretation
for beta=0 or for both being zero.
</p>
<p>
A pair of matrices (S,T) is in generalized complex Schur form if T is
upper triangular with non-negative diagonal and S is upper triangular.
</p>
<p>
The selection of the LAPACK routine is done during compile-time, and
is determined by the type of values contained in type <code class="computeroutput"><span class="identifier">MatrixA</span></code>.
The type of values is obtained through the <code class="computeroutput"><span class="identifier">value_type</span></code>
meta-function <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special"><</span><span class="identifier">MatrixA</span><span class="special">>::</span><span class="identifier">type</span></code>. The dispatching table below illustrates
to which specific routine the code path will be generated.
</p>
<div class="table">
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.dispatching_of_ggesx"></a><p class="title"><b>Table 1.103. Dispatching of ggesx</b></p>
<div class="table-contents"><table class="table" summary="Dispatching of ggesx">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Value type of MatrixA
</p>
</th>
<th>
<p>
LAPACK routine
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">float</span></code>
</p>
</td>
<td>
<p>
SGGESX
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">double</span></code>
</p>
</td>
<td>
<p>
DGGESX
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span></code>
</p>
</td>
<td>
<p>
CGGESX
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>
</p>
</td>
<td>
<p>
ZGGESX
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.definition"></a><h6>
<a name="id810956"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.definition">Definition</a>
</h6>
<p>
Defined in header <code class="computeroutput">boost/numeric/bindings/lapack/driver/ggesx.hpp</code>.
</p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.parameters_or_requirements_on_types"></a><h6>
<a name="id810996"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.parameters_or_requirements_on_types">Parameters
or Requirements on Types</a>
</h6>
<div class="variablelist">
<p class="title"><b>Parameters</b></p>
<dl>
<dt><span class="term">MatrixA</span></dt>
<dd><p>
The definition of term 1
</p></dd>
<dt><span class="term">MatrixB</span></dt>
<dd><p>
The definition of term 2
</p></dd>
<dt><span class="term">MatrixC</span></dt>
<dd>
<p>
The definition of term 3.
</p>
<p>
Definitions may contain paragraphs.
</p>
</dd>
</dl>
</div>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.complexity"></a><h6>
<a name="id811083"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.complexity">Complexity</a>
</h6>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.example"></a><h6>
<a name="id811110"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.example">Example</a>
</h6>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">bindings</span><span class="special">/</span><span class="identifier">lapack</span><span class="special">/</span><span class="identifier">driver</span><span class="special">/</span><span class="identifier">ggesx</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bindings</span><span class="special">;</span>
<span class="identifier">lapack</span><span class="special">::</span><span class="identifier">ggesx</span><span class="special">(</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">z</span> <span class="special">);</span>
</pre>
<p>
</p>
<p>
this will output
</p>
<p>
</p>
<pre class="programlisting"><span class="special">[</span><span class="number">5</span><span class="special">]</span> <span class="number">0</span> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span> <span class="number">4</span> <span class="number">5</span>
</pre>
<p>
</p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.notes"></a><h6>
<a name="id811393"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.notes">Notes</a>
</h6>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggesx.see_also"></a><h6>
<a name="id811418"></a>
<a class="link" href="ggesx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggesx.see_also">See
Also</a>
</h6>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
Originating Fortran source files <a href="http://www.netlib.org/lapack/single/sggesx.f" target="_top">sggesx.f</a>,
<a href="http://www.netlib.org/lapack/double/dggesx.f" target="_top">dggesx.f</a>,
<a href="http://www.netlib.org/lapack/complex/cggesx.f" target="_top">cggesx.f</a>,
and <a href="http://www.netlib.org/lapack/complex16/zggesx.f" target="_top">zggesx.f</a>
at Netlib.
</li></ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2002 -2009 Rutger ter Borg, Krešimir Fresl, Thomas Klimpel,
Toon Knapen, Karl Meerbergen<p>
Distributed under 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" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
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