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<div class="title">MGBlockLanczosSolver< Field, Matrix > Class Template Reference</div> </div>
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<!-- doxytag: class="LinBox::MGBlockLanczosSolver" -->
<p>Block Lanczos iteration.
<a href="class_lin_box_1_1_m_g_block_lanczos_solver.html#details">More...</a></p>
<p><code>#include <mg-block-lanczos.h></code></p>
<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"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_m_g_block_lanczos_solver.html#ad1099c590dd29c9df13bbf307abcf820">MGBlockLanczosSolver</a> (const <a class="el" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html">Field</a> &F, const BlockLanczosTraits &traits)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor. <a href="#ad1099c590dd29c9df13bbf307abcf820"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_m_g_block_lanczos_solver.html#a80a571e17c804d860bbd9e5cd7e48f26">MGBlockLanczosSolver</a> (const <a class="el" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html">Field</a> &F, const BlockLanczosTraits &traits, typename Field::RandIter r)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor with a random iterator. <a href="#a80a571e17c804d860bbd9e5cd7e48f26"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Blackbox , class Vector > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_m_g_block_lanczos_solver.html#aab28bb034aa20c85c2be57451c5ceee6">solve</a> (const Blackbox &A, Vector &x, const Vector &b)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve the linear system Ax = b. <a href="#aab28bb034aa20c85c2be57451c5ceee6"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class Blackbox , class Matrix1 > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">unsigned int </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_lin_box_1_1_m_g_block_lanczos_solver.html#ad6ba66df44b9a83fc626c1c6982e83c9">sampleNullspace</a> (const Blackbox &A, Matrix1 &x)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Sample uniformly from the (right) nullspace of A. <a href="#ad6ba66df44b9a83fc626c1c6982e83c9"></a><br/></td></tr>
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<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><h3>template<class Field, class Matrix = DenseMatrixBase<typename Field::Element>><br/>
class LinBox::MGBlockLanczosSolver< Field, Matrix ></h3>
<p>Block Lanczos iteration. </p>
<p>This is a blocked version of the iteration given in <a class="el" href="class_lin_box_1_1_lanczos_solver.html">LanczosSolver</a>. The essential difference is that, rather than applying the black box $A$ to a single vector <img class="formulaInl" alt="$v$" src="form_12.png"/> during each iteration, the block box <img class="formulaInl" alt="$A$" src="form_5.png"/> is applied to an <img class="formulaInl" alt="$n\times N$" src="form_6.png"/> matrix <img class="formulaInl" alt="$V$" src="form_2.png"/> or, equivalently, to $N$ vectors <img class="formulaInl" alt="$v_1, \ldots, v_N$" src="form_8.png"/> Scalars in the original iteration become <img class="formulaInl" alt="$N\times N$" src="form_9.png"/> matrices in the blocked version. The resulting iteration is a natural extension of the basic theory of the original Lanczos iteration, c.f. (Montgomery 1995). This has the advantage of more flexible parallelization, and does not break down as often when used over small fields.</p>
<p>Currently, only dense vectors are supported for this iteration, and it is unlikely any other vector archetypes will be supported in the future. </p>
</div><hr/><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" id="ad1099c590dd29c9df13bbf307abcf820"></a><!-- doxytag: member="LinBox::MGBlockLanczosSolver::MGBlockLanczosSolver" ref="ad1099c590dd29c9df13bbf307abcf820" args="(const Field &F, const BlockLanczosTraits &traits)" -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_m_g_block_lanczos_solver.html">MGBlockLanczosSolver</a> </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html">Field</a> & </td>
<td class="paramname"><em>F</em>, </td>
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<td class="paramtype">const BlockLanczosTraits & </td>
<td class="paramname"><em>traits</em> </td>
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<td>)</td>
<td></td><td><code> [inline]</code></td>
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<p>Constructor. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">F</td><td>Field over which to operate </td></tr>
<tr><td class="paramname">traits</td><td><a class="el" href="struct_lin_box_1_1_solver_traits.html">SolverTraits</a> structure describing user options for the solver </td></tr>
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</dd>
</dl>
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<a class="anchor" id="a80a571e17c804d860bbd9e5cd7e48f26"></a><!-- doxytag: member="LinBox::MGBlockLanczosSolver::MGBlockLanczosSolver" ref="a80a571e17c804d860bbd9e5cd7e48f26" args="(const Field &F, const BlockLanczosTraits &traits, typename Field::RandIter r)" -->
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<td class="memname"><a class="el" href="class_lin_box_1_1_m_g_block_lanczos_solver.html">MGBlockLanczosSolver</a> </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html">Field</a> & </td>
<td class="paramname"><em>F</em>, </td>
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<td class="paramtype">const BlockLanczosTraits & </td>
<td class="paramname"><em>traits</em>, </td>
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<td class="paramtype">typename Field::RandIter </td>
<td class="paramname"><em>r</em> </td>
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<td>)</td>
<td></td><td><code> [inline]</code></td>
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<p>Constructor with a random iterator. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">F</td><td>Field over which to operate </td></tr>
<tr><td class="paramname">traits</td><td><a class="el" href="struct_lin_box_1_1_solver_traits.html">SolverTraits</a> structure describing user options for the solver </td></tr>
<tr><td class="paramname">r</td><td>Random iterator to use for randomization </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="aab28bb034aa20c85c2be57451c5ceee6"></a><!-- doxytag: member="LinBox::MGBlockLanczosSolver::solve" ref="aab28bb034aa20c85c2be57451c5ceee6" args="(const Blackbox &A, Vector &x, const Vector &b)" -->
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<td class="memname">bool solve </td>
<td>(</td>
<td class="paramtype">const Blackbox & </td>
<td class="paramname"><em>A</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">Vector & </td>
<td class="paramname"><em>x</em>, </td>
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<td></td>
<td class="paramtype">const Vector & </td>
<td class="paramname"><em>b</em> </td>
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<td>)</td>
<td></td><td><code> [inline]</code></td>
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<p>Solve the linear system Ax = b. </p>
<p>If the system is nonsingular, this method computes the unique solution to the system Ax = b. If the system is singular, it computes a random solution.</p>
<p>If the matrix A is nonsymmetric, this method preconditions the matrix A with the preconditioner D_1 A^T D_2 A D_1, where D_1 and D_2 are random nonsingular diagonal matrices. If the matrix A is symmetric, this method preconditions the system with A D, where D is a random diagonal matrix.</p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>Black box for the matrix A </td></tr>
<tr><td class="paramname">x</td><td>Vector in which to store solution </td></tr>
<tr><td class="paramname">b</td><td>Right-hand side of system </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>true on success and false on failure </dd></dl>
</div>
</div>
<a class="anchor" id="ad6ba66df44b9a83fc626c1c6982e83c9"></a><!-- doxytag: member="LinBox::MGBlockLanczosSolver::sampleNullspace" ref="ad6ba66df44b9a83fc626c1c6982e83c9" args="(const Blackbox &A, Matrix1 &x)" -->
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<td class="memname">unsigned int sampleNullspace </td>
<td>(</td>
<td class="paramtype">const Blackbox & </td>
<td class="paramname"><em>A</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">Matrix1 & </td>
<td class="paramname"><em>x</em> </td>
</tr>
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<td>)</td>
<td></td><td><code> [inline]</code></td>
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<p>Sample uniformly from the (right) nullspace of A. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>Black box for the matrix A </td></tr>
<tr><td class="paramname">x</td><td>Matrix into whose columns to store nullspace elements </td></tr>
</table>
</dd>
</dl>
<dl class="return"><dt><b>Returns:</b></dt><dd>Number of nullspace vectors found </dd></dl>
</div>
</div>
<hr/>The documentation for this class was generated from the following files:<ul>
<li>mg-block-lanczos.h</li>
<li>block-lanczos.inl</li>
<li>mg-block-lanczos.inl</li>
</ul>
</div>
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