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<div class="title">GaussDomain< _Field > Class Template Reference</div> </div>
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<!-- doxytag: class="LinBox::GaussDomain" -->
<p>Repository of functions for rank by elimination on sparse matrices.
<a href="class_lin_box_1_1_gauss_domain.html#details">More...</a></p>
<p><code>#include <gauss.h></code></p>
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<img id="dynsection-0-trigger" src="closed.png"/> Inheritance diagram for GaussDomain< _Field >:</div>
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<area href="class_lin_box_1_1_power_gauss_domain.html" title="Repository of functions for rank modulo a prime power by elimination on sparse matrices." alt="PowerGaussDomain< _Field >" shape="rect" coords="0,56,184,80"/>
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<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a62be6cb3661a2942ff2b438f42fac160"></a><!-- doxytag: member="LinBox::GaussDomain::GaussDomain" ref="a62be6cb3661a2942ff2b438f42fac160" args="(const Field &F)" -->
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_gauss_domain.html#a62be6cb3661a2942ff2b438f42fac160">GaussDomain</a> (const Field &F)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">The field parameter is the domain over which to perform computations. <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a66be394bace6f92c18729a119581d7bd"></a><!-- doxytag: member="LinBox::GaussDomain::field" ref="a66be394bace6f92c18729a119581d7bd" args="() const " -->
const Field & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_gauss_domain.html#a66be394bace6f92c18729a119581d7bd">field</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">accessor for the field of computation <br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Matrix , class Perm > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_gauss_domain.html#a10e9e1d9eed55ae330cc605fc871dedc">QLUPin</a> (unsigned long &rank, Element &determinant, Perm &Q, Matrix &L, Matrix &U, Perm &P, unsigned long Ni, unsigned long Nj) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Sparse in place Gaussian elimination with reordering to reduce fill-in. <a href="#a10e9e1d9eed55ae330cc605fc871dedc"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_gauss_domain.html#a15fc04b8a7f8f60d3bcc25fc665bc658">NoReordering</a> (unsigned long &rank, Element &determinant, Matrix &LigneA, unsigned long Ni, unsigned long Nj) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Sparse Gaussian elimination without reordering. <a href="#a15fc04b8a7f8f60d3bcc25fc665bc658"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_gauss_domain.html#a016d14c820675ea91cee3455936ad5e3">LUin</a> (unsigned long &rank, Matrix &A) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Dense in place LU factorization without reordering. <a href="#a016d14c820675ea91cee3455936ad5e3"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_gauss_domain.html#a0ea789427aaeba698016d75673f35bd5">upperin</a> (unsigned long &rank, Matrix &A) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Dense in place Gaussian elimination without reordering. <a href="#a0ea789427aaeba698016d75673f35bd5"></a><br/></td></tr>
<tr><td colspan="2"><div class="groupHeader">rank</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p>Callers of the different rank routines\</p>
<p>-/ The "in" suffix indicates in place computation\ -/ Without Ni, Nj, the Matrix parameter must be a vector of sparse row vectors, NOT storing any zero.\ -/ Calls <a class="el" href="">rankinLinearPivoting</a> (by default) or <a class="el" href="">rankinNoReordering</a> </p>
</div></td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="ade463e97ffaf17a2fe758e3f3f12dfa2"></a><!-- doxytag: member="LinBox::GaussDomain::rankin" ref="ade463e97ffaf17a2fe758e3f3f12dfa2" args="(unsigned long &rank, Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><b>rankin</b> (unsigned long &rank, Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a05d5a66398c68f4deb7d1804be3a07b2"></a><!-- doxytag: member="LinBox::GaussDomain::rankin" ref="a05d5a66398c68f4deb7d1804be3a07b2" args="(unsigned long &rank, Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><b>rankin</b> (unsigned long &rank, Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a931951c1218b6c2e0a94c17a83b690f6"></a><!-- doxytag: member="LinBox::GaussDomain::rank" ref="a931951c1218b6c2e0a94c17a83b690f6" args="(unsigned long &rank, const Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><b>rank</b> (unsigned long &rank, const Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a19985139fabda161db318610e5f4c8d4"></a><!-- doxytag: member="LinBox::GaussDomain::rank" ref="a19985139fabda161db318610e5f4c8d4" args="(unsigned long &rank, const Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned long & </td><td class="memTemplItemRight" valign="bottom"><b>rank</b> (unsigned long &rank, const Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
<tr><td colspan="2"><div class="groupHeader">det</div></td></tr>
<tr><td colspan="2"><div class="groupText"><p>Callers of the different determinant routines\</p>
<p>-/ The "in" suffix indicates in place computation\ -/ Without Ni, Nj, the Matrix parameter must be a vector of sparse row vectors, NOT storing any zero.\ -/ Calls <a class="el" href="">LinearPivoting</a> (by default) or <a class="el" href="class_lin_box_1_1_gauss_domain.html#a15fc04b8a7f8f60d3bcc25fc665bc658">NoReordering</a> </p>
</div></td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="adaddd90073e31b6149b4809b1d200502"></a><!-- doxytag: member="LinBox::GaussDomain::detin" ref="adaddd90073e31b6149b4809b1d200502" args="(Element &determinant, Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">Element & </td><td class="memTemplItemRight" valign="bottom"><b>detin</b> (Element &determinant, Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a5d103446dc42c24666b9dc26e668fa85"></a><!-- doxytag: member="LinBox::GaussDomain::detin" ref="a5d103446dc42c24666b9dc26e668fa85" args="(Element &determinant, Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">Element & </td><td class="memTemplItemRight" valign="bottom"><b>detin</b> (Element &determinant, Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a6a3a26bb18b79063f081fc45aabe9fe0"></a><!-- doxytag: member="LinBox::GaussDomain::det" ref="a6a3a26bb18b79063f081fc45aabe9fe0" args="(Element &determinant, const Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">Element & </td><td class="memTemplItemRight" valign="bottom"><b>det</b> (Element &determinant, const Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
<tr><td class="memTemplParams" colspan="2"><a class="anchor" id="a171047f30a7b31c80c3d04871129fb6f"></a><!-- doxytag: member="LinBox::GaussDomain::det" ref="a171047f30a7b31c80c3d04871129fb6f" args="(Element &determinant, const Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const " -->
template<class Matrix > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">Element & </td><td class="memTemplItemRight" valign="bottom"><b>det</b> (Element &determinant, const Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><h3>template<class _Field><br/>
class LinBox::GaussDomain< _Field ></h3>
<p>Repository of functions for rank by elimination on sparse matrices. </p>
<p>Several versions allow for adjustment of the pivoting strategy and for choosing in-place elimination or for not modifying the input matrix. Also an LU interface is offered. </p>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a10e9e1d9eed55ae330cc605fc871dedc"></a><!-- doxytag: member="LinBox::GaussDomain::QLUPin" ref="a10e9e1d9eed55ae330cc605fc871dedc" args="(unsigned long &rank, Element &determinant, Perm &Q, Matrix &L, Matrix &U, Perm &P, unsigned long Ni, unsigned long Nj) const " -->
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<td class="memname">unsigned long & QLUPin </td>
<td>(</td>
<td class="paramtype">unsigned long & </td>
<td class="paramname"><em>rank</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>determinant</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Perm & </td>
<td class="paramname"><em>Q</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Matrix & </td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Matrix & </td>
<td class="paramname"><em>U</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Perm & </td>
<td class="paramname"><em>P</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long </td>
<td class="paramname"><em>Ni</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long </td>
<td class="paramname"><em>Nj</em> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
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<div class="memdoc">
<p>Sparse in place Gaussian elimination with reordering to reduce fill-in. </p>
<p>Pivots are chosen in sparsest column of sparsest row. This runs in linear overhead. It is similar in spirit but different from Markovitz' approach.</p>
<dl class="pre"><dt><b>Precondition:</b></dt><dd>Using : SparseFindPivot(..., density) for sparsest column, and eliminate (..., density)</dd></dl>
<p>The Matrix parameter must meet the <a class="el" href="namespace_lin_box.html" title="Namespace in which all linbox code resides.">LinBox</a> sparse matrix interface. [check details]. The computedet indicates whether the algorithm must compute the determionant as it goes</p>
<dl class="bib"><dt><b><a class="el" href="bib.html#_bib000007">Bibliography:</a></b></dt><dd></dd></dl>
<p>- Jean-Guillaume Dumas and Gilles Villard, <em>Computing the rank of sparse matrices over finite fields</em>. In Ganzha et~al. CASC'2002, pages 47--62. </p>
</div>
</div>
<a class="anchor" id="a15fc04b8a7f8f60d3bcc25fc665bc658"></a><!-- doxytag: member="LinBox::GaussDomain::NoReordering" ref="a15fc04b8a7f8f60d3bcc25fc665bc658" args="(unsigned long &rank, Element &determinant, Matrix &LigneA, unsigned long Ni, unsigned long Nj) const " -->
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<td class="memname">unsigned long & NoReordering </td>
<td>(</td>
<td class="paramtype">unsigned long & </td>
<td class="paramname"><em>rank</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Element & </td>
<td class="paramname"><em>determinant</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Matrix & </td>
<td class="paramname"><em>LigneA</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long </td>
<td class="paramname"><em>Ni</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long </td>
<td class="paramname"><em>Nj</em> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
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<div class="memdoc">
<p>Sparse Gaussian elimination without reordering. </p>
<p>Gaussian elimination is done on a copy of the matrix. Using : SparseFindPivot eliminate</p>
<p>Requirements : SLA is an array of sparse rows WARNING : NOT IN PLACE, THERE IS A COPY. Without reordering (Pivot is first non-zero in row) </p>
</div>
</div>
<a class="anchor" id="a016d14c820675ea91cee3455936ad5e3"></a><!-- doxytag: member="LinBox::GaussDomain::LUin" ref="a016d14c820675ea91cee3455936ad5e3" args="(unsigned long &rank, Matrix &A) const " -->
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<div class="memproto">
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<td class="memname">unsigned long & LUin </td>
<td>(</td>
<td class="paramtype">unsigned long & </td>
<td class="paramname"><em>rank</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Matrix & </td>
<td class="paramname"><em>A</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Dense in place LU factorization without reordering. </p>
<p>Using : FindPivot and LU </p>
</div>
</div>
<a class="anchor" id="a0ea789427aaeba698016d75673f35bd5"></a><!-- doxytag: member="LinBox::GaussDomain::upperin" ref="a0ea789427aaeba698016d75673f35bd5" args="(unsigned long &rank, Matrix &A) const " -->
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<td class="memname">unsigned long & upperin </td>
<td>(</td>
<td class="paramtype">unsigned long & </td>
<td class="paramname"><em>rank</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Matrix & </td>
<td class="paramname"><em>A</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [inline]</code></td>
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</div>
<div class="memdoc">
<p>Dense in place Gaussian elimination without reordering. </p>
<p>Using : FindPivot and LU </p>
</div>
</div>
<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="gauss_8h.html">gauss.h</a></li>
<li>gauss-det.inl</li>
<li>gauss-elim.inl</li>
<li>gauss-nullspace.inl</li>
<li>gauss-pivot.inl</li>
<li>gauss-rank.inl</li>
<li>gauss-solve.inl</li>
<li>gauss.inl</li>
</ul>
</div>
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