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<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="boost_numeric_bindings.reference.lapack.computational_routines.ggrqf"></a><a class="link" href="ggrqf.html" title="ggrqf">ggrqf</a>
</h5></div></div></div>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.prototype"></a><h6>
<a name="id911979"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.prototype">Prototype</a>
          </h6>
<p>
            There is one prototype of <code class="computeroutput"><span class="identifier">ggrqf</span></code>
            available, please see below. 
</p>
<pre class="programlisting"><span class="identifier">ggrqf</span><span class="special">(</span> <span class="identifier">MatrixA</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">VectorTAUA</span><span class="special">&amp;</span> <span class="identifier">taua</span><span class="special">,</span> <span class="identifier">MatrixB</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">VectorTAUB</span><span class="special">&amp;</span> <span class="identifier">taub</span> <span class="special">);</span>
</pre>
<p>
          </p>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.description"></a><h6>
<a name="id912132"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.description">Description</a>
          </h6>
<p>
            <code class="computeroutput"><span class="identifier">ggrqf</span></code> (short for $FRIENDLY_NAME)
            provides a C++ interface to LAPACK routines SGGRQF, DGGRQF, CGGRQF, and
            ZGGRQF. <code class="computeroutput"><span class="identifier">ggrqf</span></code> computes
            a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix
            B:
          </p>
<p>
            A = R*Q, B = Z*T*Q,
          </p>
<p>
            where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, and
            R and T assume one of the forms:
          </p>
<p>
            if M &lt;= N, R = ( 0 R12 ) M, or if M &gt; N, R = ( R11 ) M-N, N-M M
            ( R21 ) N N
          </p>
<p>
            where R12 or R21 is upper triangular, and
          </p>
<p>
            if P &gt;= N, T = ( T11 ) N , or if P &lt; N, T = ( T11 T12 ) P, ( 0
            ) P-N P N-P N
          </p>
<p>
            where T11 is upper triangular.
          </p>
<p>
            In particular, if B is square and nonsingular, the GRQ factorization
            of A and B implicitly gives the RQ factorization of A*inv(B):
          </p>
<p>
            A*inv(B) = (R*inv(T))*Z'
          </p>
<p>
            where inv(B) denotes the inverse of the matrix B, and Z' denotes the
            conjugate transpose of the matrix Z.
          </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">&lt;</span><span class="identifier">MatrixA</span><span class="special">&gt;::</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.ggrqf.dispatching_of_ggrqf"></a><p class="title"><b>Table&#160;1.191.&#160;Dispatching of ggrqf</b></p>
<div class="table-contents"><table class="table" summary="Dispatching of ggrqf">
<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>
                      SGGRQF
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="keyword">double</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      DGGRQF
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      CGGRQF
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      ZGGRQF
                    </p>
                  </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.definition"></a><h6>
<a name="id912513"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.definition">Definition</a>
          </h6>
<p>
            Defined in header <code class="computeroutput">boost/numeric/bindings/lapack/computational/ggrqf.hpp</code>.
          </p>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.parameters_or_requirements_on_types"></a><h6>
<a name="id912553"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.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.ggrqf.complexity"></a><h6>
<a name="id912641"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.complexity">Complexity</a>
          </h6>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.example"></a><h6>
<a name="id912666"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.example">Example</a>
          </h6>
<p>
            
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</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">ggrqf</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</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">ggrqf</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.ggrqf.notes"></a><h6>
<a name="id912949"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.notes">Notes</a>
          </h6>
<a name="boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.see_also"></a><h6>
<a name="id912974"></a>
            <a class="link" href="ggrqf.html#boost_numeric_bindings.reference.lapack.computational_routines.ggrqf.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/sggrqf.f" target="_top">sggrqf.f</a>,
                <a href="http://www.netlib.org/lapack/double/dggrqf.f" target="_top">dggrqf.f</a>,
                <a href="http://www.netlib.org/lapack/complex/cggrqf.f" target="_top">cggrqf.f</a>,
                and <a href="http://www.netlib.org/lapack/complex16/zggrqf.f" target="_top">zggrqf.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 &#169; 2002 -2009 Rutger ter Borg, Kre&#353;imir 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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