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<div class="header">
  <div class="summary">
<a href="classEigen_1_1DGMRES-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pro-methods">Protected Member Functions</a>  </div>
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<div class="title">DGMRES&lt; _MatrixType, _Preconditioner &gt; Class Template Reference</div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename _MatrixType, typename _Preconditioner = DiagonalPreconditioner&lt;typename _MatrixType::Scalar&gt;&gt;<br/>
class Eigen::DGMRES&lt; _MatrixType, _Preconditioner &gt;</h3>

<p>A Restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> with deflation. This class implements a modification of the <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> solver for sparse linear systems. The basis is built with modified Gram-Schmidt. At each restart, a few approximated eigenvectors corresponding to the smallest eigenvalues are used to build a preconditioner for the next cycle. This preconditioner for deflation can be combined with any other preconditioner, the IncompleteLUT for instance. The preconditioner is applied at right of the matrix and the combination is multiplicative. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">_MatrixType</td><td>the type of the sparse matrix A, can be a dense or a sparse matrix. </td></tr>
    <tr><td class="paramname">_Preconditioner</td><td>the type of the preconditioner. Default is DiagonalPreconditioner Typical usage : <div class="fragment"><div class="line">* SparseMatrix&lt;double&gt; A;</div>
<div class="line">* VectorXd x, b; </div>
<div class="line">* <span class="comment">//Fill A and b ...</span></div>
<div class="line">* DGMRES&lt;SparseMatrix&lt;double&gt; &gt; solver;</div>
<div class="line">* solver.set_restart(30); <span class="comment">// Set restarting value</span></div>
<div class="line">* solver.setEigenv(1); <span class="comment">// Set the number of eigenvalues to deflate</span></div>
<div class="line">* solver.compute(A);</div>
<div class="line">* x = solver.solve(b);</div>
<div class="line">* </div>
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<p>References : [1] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, In Press, <a href="http://dx.doi.org/10.1016/j.compfluid.2012.03.023">http://dx.doi.org/10.1016/j.compfluid.2012.03.023</a> [2] K. Burrage and J. Erhel, On the performance of various adaptive preconditioned <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> strategies, 5(1998), 101-121. [3] J. Erhel, K. Burrage and B. Pohl, Restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996), 303-318. </p>
</div>
<p>Inherits IterativeSolverBase&lt; DGMRES&lt; _MatrixType, _Preconditioner &gt; &gt;.</p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a62f9d64844caff6007cabecc997fbad1"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a62f9d64844caff6007cabecc997fbad1">deflSize</a> ()</td></tr>
<tr class="separator:a62f9d64844caff6007cabecc997fbad1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acebe7001a430de6ff6059e42a2c3d7e1"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#acebe7001a430de6ff6059e42a2c3d7e1">DGMRES</a> ()</td></tr>
<tr class="separator:acebe7001a430de6ff6059e42a2c3d7e1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a13ee3911a809ab56f9d207f4201134ad"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a13ee3911a809ab56f9d207f4201134ad">DGMRES</a> (const MatrixType &amp;A)</td></tr>
<tr class="separator:a13ee3911a809ab56f9d207f4201134ad"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae246359e104d63520158c26329caac80"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80">restart</a> ()</td></tr>
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<tr class="memitem:a88b3d18c69eccbd4b1c68a5713a05bb3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3">set_restart</a> (const int <a class="el" href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80">restart</a>)</td></tr>
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<tr class="memitem:a16852b8c7e2b1a8154937d392d342051"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a16852b8c7e2b1a8154937d392d342051">setEigenv</a> (const int neig)</td></tr>
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<tr class="memitem:afed207f423f44020219ac444b982dcf9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#afed207f423f44020219ac444b982dcf9">setMaxEigenv</a> (const int maxNeig)</td></tr>
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<tr class="memitem:a3ceaab72040862ca224adc3984eed08c"><td class="memTemplParams" colspan="2">template&lt;typename Rhs , typename Guess &gt; </td></tr>
<tr class="memitem:a3ceaab72040862ca224adc3984eed08c"><td class="memTemplItemLeft" align="right" valign="top">const <br class="typebreak"/>
internal::solve_retval_with_guess<br class="typebreak"/>
&lt; <a class="el" href="classEigen_1_1DGMRES.html">DGMRES</a>, Rhs, Guess &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a3ceaab72040862ca224adc3984eed08c">solveWithGuess</a> (const MatrixBase&lt; Rhs &gt; &amp;b, const Guess &amp;x0) const </td></tr>
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Protected Member Functions</h2></td></tr>
<tr class="memitem:ac77967ca048597f4b4cba3a6bf00b0a4"><td class="memTemplParams" colspan="2">template&lt;typename Rhs , typename Dest &gt; </td></tr>
<tr class="memitem:ac77967ca048597f4b4cba3a6bf00b0a4"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#ac77967ca048597f4b4cba3a6bf00b0a4">dgmres</a> (const MatrixType &amp;mat, const Rhs &amp;rhs, Dest &amp;x, const Preconditioner &amp;precond) const </td></tr>
<tr class="memdesc:ac77967ca048597f4b4cba3a6bf00b0a4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Perform several cycles of restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> with modified Gram Schmidt,.  <a href="#ac77967ca048597f4b4cba3a6bf00b0a4">More...</a><br/></td></tr>
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<tr class="memitem:ad56b61782bcd392b88b807c9e6099e02"><td class="memTemplParams" colspan="2">template&lt;typename Dest &gt; </td></tr>
<tr class="memitem:ad56b61782bcd392b88b807c9e6099e02"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#ad56b61782bcd392b88b807c9e6099e02">dgmresCycle</a> (const MatrixType &amp;mat, const Preconditioner &amp;precond, Dest &amp;x, DenseVector &amp;r0, RealScalar &amp;beta, const RealScalar &amp;normRhs, int &amp;nbIts) const </td></tr>
<tr class="memdesc:ad56b61782bcd392b88b807c9e6099e02"><td class="mdescLeft">&#160;</td><td class="mdescRight">Perform one restart cycle of <a class="el" href="classEigen_1_1DGMRES.html" title="A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse...">DGMRES</a>.  <a href="#ad56b61782bcd392b88b807c9e6099e02">More...</a><br/></td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<p>Default constructor. </p>

<p>Referenced by <a class="el" href="classEigen_1_1DGMRES.html#a3ceaab72040862ca224adc3984eed08c">DGMRES&lt; _MatrixType, _Preconditioner &gt;::solveWithGuess()</a>.</p>

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<p>Initialize the solver with matrix <em>A</em> for further <code>Ax=b</code> solving.</p>
<p>This constructor is a shortcut for the default constructor followed by a call to compute().</p>
<dl class="section warning"><dt>Warning</dt><dd>this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if <em>A</em> is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A. </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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          <td class="memname">int deflSize </td>
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<p>Get the size of the deflation subspace size </p>

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          <td class="memname">void dgmres </td>
          <td>(</td>
          <td class="paramtype">const MatrixType &amp;&#160;</td>
          <td class="paramname"><em>mat</em>, </td>
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<p>Perform several cycles of restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> with modified Gram Schmidt,. </p>
<p>A right preconditioner is used combined with deflation. </p>

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<p>Perform one restart cycle of <a class="el" href="classEigen_1_1DGMRES.html" title="A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse...">DGMRES</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">mat</td><td>The coefficient matrix </td></tr>
    <tr><td class="paramname">precond</td><td>The preconditioner </td></tr>
    <tr><td class="paramname">x</td><td>the new approximated solution </td></tr>
    <tr><td class="paramname">r0</td><td>The initial residual vector </td></tr>
    <tr><td class="paramname">beta</td><td>The norm of the residual computed so far </td></tr>
    <tr><td class="paramname">normRhs</td><td>The norm of the right hand side vector </td></tr>
    <tr><td class="paramname">nbIts</td><td>The number of iterations </td></tr>
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<p>Get the restart value </p>

<p>Referenced by <a class="el" href="classEigen_1_1DGMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3">DGMRES&lt; _MatrixType, _Preconditioner &gt;::set_restart()</a>.</p>

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          <td class="memname">void set_restart </td>
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<p>Set the restart value (default is 30) </p>

<p>References <a class="el" href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80">DGMRES&lt; _MatrixType, _Preconditioner &gt;::restart()</a>.</p>

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<p>Set the number of eigenvalues to deflate at each restart </p>

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<p>Set the maximum size of the deflation subspace </p>

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          <td class="memname">const internal::solve_retval_with_guess&lt;<a class="el" href="classEigen_1_1DGMRES.html">DGMRES</a>, Rhs, Guess&gt; solveWithGuess </td>
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<dl class="section return"><dt>Returns</dt><dd>the solution x of <img class="formulaInl" alt="$ A x = b $" src="form_64.png"/> using the current decomposition of A <em>x0</em> as an initial solution.</dd></dl>
<dl class="section see"><dt>See Also</dt><dd>compute() </dd></dl>

<p>References <a class="el" href="classEigen_1_1DGMRES.html#acebe7001a430de6ff6059e42a2c3d7e1">DGMRES&lt; _MatrixType, _Preconditioner &gt;::DGMRES()</a>.</p>

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