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<div class="title">MINRES< _MatrixType, _UpLo, _Preconditioner > 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<typename _MatrixType, int _UpLo = Lower, typename _Preconditioner = IdentityPreconditioner><br/>
class Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner ></h3>
<p>A minimal residual solver for sparse symmetric problems. </p>
<p>This class allows to solve for A.x = b sparse linear problems using the <a class="el" href="classEigen_1_1MINRES.html" title="A minimal residual solver for sparse symmetric problems. ">MINRES</a> algorithm of Paige and Saunders (1975). The sparse matrix A must be symmetric (possibly indefinite). The vectors x and b can be either dense or sparse.</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">_UpLo</td><td>the triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower. </td></tr>
<tr><td class="paramname">_Preconditioner</td><td>the type of the preconditioner. Default is DiagonalPreconditioner</td></tr>
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</dd>
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<p>The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.</p>
<p>This class can be used as the direct solver classes. Here is a typical usage example: </p>
<div class="fragment"><div class="line">* <span class="keywordtype">int</span> n = 10000;</div>
<div class="line">* VectorXd x(n), b(n);</div>
<div class="line">* SparseMatrix<double> A(n,n);</div>
<div class="line">* <span class="comment">// fill A and b</span></div>
<div class="line">* MINRES<SparseMatrix<double> > mr;</div>
<div class="line">* mr.compute(A);</div>
<div class="line">* x = mr.solve(b);</div>
<div class="line">* std::cout << <span class="stringliteral">"#iterations: "</span> << mr.iterations() << std::endl;</div>
<div class="line">* std::cout << <span class="stringliteral">"estimated error: "</span> << mr.error() << std::endl;</div>
<div class="line">* <span class="comment">// update b, and solve again</span></div>
<div class="line">* x = mr.solve(b);</div>
<div class="line">* </div>
</div><!-- fragment --><p>By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the <a class="el" href="classEigen_1_1MINRES.html#a4a42888f2c0db9ad90fc3b718ae582ca">solveWithGuess()</a> method. Here is a step by step execution example starting with a random guess and printing the evolution of the estimated error:</p>
<ul>
<li><div class="fragment"><div class="line">* x = VectorXd::Random(n);</div>
<div class="line">* mr.setMaxIterations(1);</div>
<div class="line">* <span class="keywordtype">int</span> i = 0;</div>
<div class="line">* <span class="keywordflow">do</span> {</div>
<div class="line">* x = mr.solveWithGuess(b,x);</div>
<div class="line">* std::cout << i << <span class="stringliteral">" : "</span> << mr.error() << std::endl;</div>
<div class="line">* ++i;</div>
<div class="line">* } <span class="keywordflow">while</span> (mr.info()!=Success && i<100);</div>
<div class="line">* </div>
</div><!-- fragment --> Note that such a step by step excution is slightly slower.</li>
</ul>
<dl class="section see"><dt>See Also</dt><dd>class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner </dd></dl>
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<p>Inherits IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >.</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:a659d9410353da2cd0805a8d8da66f7ef"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MINRES.html#a659d9410353da2cd0805a8d8da66f7ef">MINRES</a> ()</td></tr>
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<tr class="memitem:a0044acd402c536a32be6e9575da39141"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MINRES.html#a0044acd402c536a32be6e9575da39141">MINRES</a> (const MatrixType &A)</td></tr>
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<tr class="memitem:a4a42888f2c0db9ad90fc3b718ae582ca"><td class="memTemplParams" colspan="2">template<typename Rhs , typename Guess > </td></tr>
<tr class="memitem:a4a42888f2c0db9ad90fc3b718ae582ca"><td class="memTemplItemLeft" align="right" valign="top">const <br class="typebreak"/>
internal::solve_retval_with_guess<br class="typebreak"/>
< <a class="el" href="classEigen_1_1MINRES.html">MINRES</a>, Rhs, Guess > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1MINRES.html#a4a42888f2c0db9ad90fc3b718ae582ca">solveWithGuess</a> (const MatrixBase< Rhs > &b, const Guess &x0) const </td></tr>
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<tr class="memitem:a0ca81ac3b24c8216b3c526c1e454a40b"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MINRES.html#a0ca81ac3b24c8216b3c526c1e454a40b">~MINRES</a> ()</td></tr>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<p>Default constructor. </p>
<p>Referenced by <a class="el" href="classEigen_1_1MINRES.html#a4a42888f2c0db9ad90fc3b718ae582ca">MINRES< _MatrixType, _UpLo, _Preconditioner >::solveWithGuess()</a>.</p>
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<td class="paramname"><em>A</em></td><td>)</td>
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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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<p>Destructor. </p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname">const internal::solve_retval_with_guess<<a class="el" href="classEigen_1_1MINRES.html">MINRES</a>, Rhs, Guess> solveWithGuess </td>
<td>(</td>
<td class="paramtype">const MatrixBase< Rhs > & </td>
<td class="paramname"><em>b</em>, </td>
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<td class="paramtype">const Guess & </td>
<td class="paramname"><em>x0</em> </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_1MINRES.html#a659d9410353da2cd0805a8d8da66f7ef">MINRES< _MatrixType, _UpLo, _Preconditioner >::MINRES()</a>.</p>
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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="MINRES_8h_source.html">MINRES.h</a></li>
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