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<title>tgsyl</title>
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<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsyl"></a><a class="link" href="tgsyl.html" title="tgsyl">tgsyl</a>
</h5></div></div></div>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.prototype"></a><h6>
<a name="id1069951"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.prototype">Prototype</a>
</h6>
<p>
There is one prototype of <code class="computeroutput"><span class="identifier">tgsyl</span></code>
available, please see below.
</p>
<pre class="programlisting"><span class="identifier">tgsyl</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">int_t</span> <span class="identifier">ijob</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MatrixA</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MatrixB</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span>
<span class="identifier">MatrixC</span><span class="special">&</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MatrixD</span><span class="special">&</span> <span class="identifier">d</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">MatrixE</span><span class="special">&</span> <span class="identifier">e</span><span class="special">,</span> <span class="identifier">MatrixF</span><span class="special">&</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">Scalar</span> <span class="special">>,</span>
<span class="identifier">Scalar</span> <span class="special">></span> <span class="special">);</span>
</pre>
<p>
</p>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.description"></a><h6>
<a name="id1070226"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.description">Description</a>
</h6>
<p>
<code class="computeroutput"><span class="identifier">tgsyl</span></code> (short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines STGSYL, DTGSYL, CTGSYL, and
ZTGSYL. <code class="computeroutput"><span class="identifier">tgsyl</span></code> solves
the generalized Sylvester equation:
</p>
<p>
A * R - L * B = scale * C (1) D * R - L * E = scale * F
</p>
<p>
where R and L are unknown m-by-n matrices, (A, D), (B, E) and (C, F)
are given matrix pairs of size m-by-m, n-by-n and m-by-n, respectively,
with complex entries. A, B, D and E are upper triangular (i.e., (A,D)
and (B,E) in generalized Schur form).
</p>
<p>
The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output
scaling factor chosen to avoid overflow.
</p>
<p>
In matrix notation (1) is equivalent to solve Zx = scale*b, where Z is
defined as
</p>
<p>
Z = [ kron(In, A) -kron(B', Im) ] (2) [ kron(In, D) -kron(E', Im) ],
</p>
<p>
Here Ix is the identity matrix of size x and X' is the conjugate transpose
of X. Kron(X, Y) is the Kronecker product between the matrices X and
Y.
</p>
<p>
If TRANS = 'C', y in the conjugate transposed system Z'*y = scale*b is
solved for, which is equivalent to solve for R and L in
</p>
<p>
A' * R + D' * L = scale * C (3) R * B' + L * E' = scale * -F
</p>
<p>
This case (TRANS = 'C') is used to compute an one-norm-based estimate
of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) and
(B,E), using ZLACON.
</p>
<p>
If IJOB >= 1, <code class="computeroutput"><span class="identifier">tgsyl</span></code>
computes a Frobenius norm-based estimate of Dif[(A,D),(B,E)]. That is,
the reciprocal of a lower bound on the reciprocal of the smallest singular
value of Z.
</p>
<p>
This is a level-3 BLAS algorithm.
</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.computational_routines.tgsyl.dispatching_of_tgsyl"></a><p class="title"><b>Table 1.338. Dispatching of tgsyl</b></p>
<div class="table-contents"><table class="table" summary="Dispatching of tgsyl">
<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>
STGSYL
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">double</span></code>
</p>
</td>
<td>
<p>
DTGSYL
</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>
CTGSYL
</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>
ZTGSYL
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.definition"></a><h6>
<a name="id1070641"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.definition">Definition</a>
</h6>
<p>
Defined in header <code class="computeroutput">boost/numeric/bindings/lapack/computational/tgsyl.hpp</code>.
</p>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.parameters_or_requirements_on_types"></a><h6>
<a name="id1070682"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.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.computational_routines.tgsyl.complexity"></a><h6>
<a name="id1070769"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.complexity">Complexity</a>
</h6>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.example"></a><h6>
<a name="id1070795"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.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">computational</span><span class="special">/</span><span class="identifier">tgsyl</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">tgsyl</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.computational_routines.tgsyl.notes"></a><h6>
<a name="id1071079"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.notes">Notes</a>
</h6>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.see_also"></a><h6>
<a name="id1071105"></a>
<a class="link" href="tgsyl.html#boost_numeric_bindings.reference.lapack.computational_routines.tgsyl.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/stgsyl.f" target="_top">stgsyl.f</a>,
<a href="http://www.netlib.org/lapack/double/dtgsyl.f" target="_top">dtgsyl.f</a>,
<a href="http://www.netlib.org/lapack/complex/ctgsyl.f" target="_top">ctgsyl.f</a>,
and <a href="http://www.netlib.org/lapack/complex16/ztgsyl.f" target="_top">ztgsyl.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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