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<div class="title">BiCGSTAB< _MatrixType, _Preconditioner > Class Template Reference<div class="ingroups"><a class="el" href="group__IterativeLinearSolvers__Module.html">IterativeLinearSolvers module</a></div></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, typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar>><br/>
class Eigen::BiCGSTAB< _MatrixType, _Preconditioner ></h3>
<p>A bi conjugate gradient stabilized solver for sparse square problems. </p>
<p>This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient stabilized algorithm. 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">_Preconditioner</td><td>the type of the preconditioner. Default is <a class="el" href="classEigen_1_1DiagonalPreconditioner.html" title="A preconditioner based on the digonal entries. ">DiagonalPreconditioner</a></td></tr>
</table>
</dd>
</dl>
<p>The maximal number of iterations and tolerance value can be controlled via the <a class="el" href="classEigen_1_1IterativeSolverBase.html#ad9aa2f8ecfda11aba72cfd3c5eefae20">setMaxIterations()</a> and <a class="el" href="classEigen_1_1IterativeSolverBase.html#a39b43ecdc61211a15d1e986e28a03513">setTolerance()</a> 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">* <a class="code" href="group__matrixtypedefs.html#ga3da45e59796fbacf67fa568297927bd1">VectorXd</a> 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">* BiCGSTAB<SparseMatrix<double> > solver;</div>
<div class="line">* solver(A);</div>
<div class="line">* x = solver.solve(b);</div>
<div class="line">* std::cout << <span class="stringliteral">"#iterations: "</span> << solver.iterations() << std::endl;</div>
<div class="line">* std::cout << <span class="stringliteral">"estimated error: "</span> << solver.error() << std::endl;</div>
<div class="line">* <span class="comment">// update b, and solve again</span></div>
<div class="line">* x = solver.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_1BiCGSTAB.html#ac6991ac0f70dd889f55ebc0f287c04f2">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 = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">VectorXd::Random</a>(n);</div>
<div class="line">* solver.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 = solver.solveWithGuess(b,x);</div>
<div class="line">* std::cout << i << <span class="stringliteral">" : "</span> << solver.error() << std::endl;</div>
<div class="line">* ++i;</div>
<div class="line">* } <span class="keywordflow">while</span> (solver.info()!=<a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a> && 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 <a class="el" href="classEigen_1_1SimplicialCholesky.html">SimplicialCholesky</a>, <a class="el" href="classEigen_1_1DiagonalPreconditioner.html" title="A preconditioner based on the digonal entries. ">DiagonalPreconditioner</a>, <a class="el" href="classEigen_1_1IdentityPreconditioner.html" title="A naive preconditioner which approximates any matrix as the identity matrix. ">IdentityPreconditioner</a> </dd></dl>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for BiCGSTAB< _MatrixType, _Preconditioner >:</div>
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<div class="center"><img src="classEigen_1_1BiCGSTAB__inherit__graph.png" border="0" usemap="#BiCGSTAB_3_01__MatrixType_00_01__Preconditioner_01_4_inherit__map" alt="Inheritance graph"/></div>
<map name="BiCGSTAB_3_01__MatrixType_00_01__Preconditioner_01_4_inherit__map" id="BiCGSTAB_3_01__MatrixType_00_01__Preconditioner_01_4_inherit__map">
<area shape="rect" id="node2" href="classEigen_1_1IterativeSolverBase.html" title="{IterativeSolverBase\l\< BiCGSTAB\< _MatrixType,\l _Preconditioner \> \>\n|# m_analysisIsOk\l# m_error\l# m_factorizationIsOk\l# m_info\l# m_isInitialized\l# m_iterations\l# m_maxIterations\l# m_preconditioner\l# m_tolerance\l# mp_matrix\l|+ _solve_sparse()\l+ analyzePattern()\l+ cols()\l+ compute()\l+ derived()\l+ derived()\l+ error()\l+ factorize()\l+ info()\l+ iterations()\land 12 more...\l# init()\l}" alt="" coords="5,5,195,405"/></map>
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<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:ae044142449c071af13afc4fbbe633682"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, <br class="typebreak"/>
_Preconditioner > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#ae044142449c071af13afc4fbbe633682">analyzePattern</a> (const MatrixType &A)</td></tr>
<tr class="separator:ae044142449c071af13afc4fbbe633682"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:abda58f5b65579cb046bcb158cc356013"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1BiCGSTAB.html#abda58f5b65579cb046bcb158cc356013">BiCGSTAB</a> ()</td></tr>
<tr class="separator:abda58f5b65579cb046bcb158cc356013"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:abf2413ba65486c26becf303054d6ec12"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1BiCGSTAB.html#abf2413ba65486c26becf303054d6ec12">BiCGSTAB</a> (const MatrixType &A)</td></tr>
<tr class="separator:abf2413ba65486c26becf303054d6ec12"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a693a8142a905e7130bacd77586a6f6a0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, <br class="typebreak"/>
_Preconditioner > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute</a> (const MatrixType &A)</td></tr>
<tr class="separator:a693a8142a905e7130bacd77586a6f6a0"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a736349b3462f6ebf37c34b450db2ed18"><td class="memItemLeft" align="right" valign="top">RealScalar </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a736349b3462f6ebf37c34b450db2ed18">error</a> () const</td></tr>
<tr class="separator:a736349b3462f6ebf37c34b450db2ed18"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab837a9d99eea1f79dd4721727ef98d37"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, <br class="typebreak"/>
_Preconditioner > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#ab837a9d99eea1f79dd4721727ef98d37">factorize</a> (const MatrixType &A)</td></tr>
<tr class="separator:ab837a9d99eea1f79dd4721727ef98d37"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0c06d5c2034ebb329c54235369643ad2"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a0c06d5c2034ebb329c54235369643ad2">info</a> () const</td></tr>
<tr class="separator:a0c06d5c2034ebb329c54235369643ad2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a07c5f1fe9fa1556edc79452b52839829"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a07c5f1fe9fa1556edc79452b52839829">iterations</a> () const</td></tr>
<tr class="separator:a07c5f1fe9fa1556edc79452b52839829"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9c020a2e26d3081eeff611b802962530"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a9c020a2e26d3081eeff611b802962530">maxIterations</a> () const</td></tr>
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<tr class="memitem:ae4bec7fa55f17f7bb64b6b2fc4039b58"><td class="memItemLeft" align="right" valign="top">Preconditioner & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#ae4bec7fa55f17f7bb64b6b2fc4039b58">preconditioner</a> ()</td></tr>
<tr class="separator:ae4bec7fa55f17f7bb64b6b2fc4039b58"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a11aed1f82ecbec6d7436915c6d804d7a"><td class="memItemLeft" align="right" valign="top">const Preconditioner & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a11aed1f82ecbec6d7436915c6d804d7a">preconditioner</a> () const</td></tr>
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<tr class="memitem:ad9aa2f8ecfda11aba72cfd3c5eefae20"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, <br class="typebreak"/>
_Preconditioner > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#ad9aa2f8ecfda11aba72cfd3c5eefae20">setMaxIterations</a> (int maxIters)</td></tr>
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<tr class="memitem:a39b43ecdc61211a15d1e986e28a03513"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, <br class="typebreak"/>
_Preconditioner > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a39b43ecdc61211a15d1e986e28a03513">setTolerance</a> (const RealScalar &<a class="el" href="classEigen_1_1IterativeSolverBase.html#aab135f12fadf495a511f20c71557e1aa">tolerance</a>)</td></tr>
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<tr class="memitem:acae1088225b7c746b16848d02d5e1c2a"><td class="memItemLeft" align="right" valign="top">const internal::solve_retval<br class="typebreak"/>
< <a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, <br class="typebreak"/>
_Preconditioner >, Rhs > </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#acae1088225b7c746b16848d02d5e1c2a">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>< Rhs > &b) const</td></tr>
<tr class="separator:acae1088225b7c746b16848d02d5e1c2a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7892f6fbc52bfa658e1324a63d376d1c"><td class="memItemLeft" align="right" valign="top">const <br class="typebreak"/>
internal::sparse_solve_retval<br class="typebreak"/>
< <a class="el" href="classEigen_1_1IterativeSolverBase.html">IterativeSolverBase</a>, Rhs > </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#a7892f6fbc52bfa658e1324a63d376d1c">solve</a> (const <a class="el" href="classEigen_1_1SparseMatrixBase.html">SparseMatrixBase</a>< Rhs > &b) const</td></tr>
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<tr class="memitem:ac6991ac0f70dd889f55ebc0f287c04f2"><td class="memTemplParams" colspan="2">template<typename Rhs , typename Guess > </td></tr>
<tr class="memitem:ac6991ac0f70dd889f55ebc0f287c04f2"><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_1BiCGSTAB.html">BiCGSTAB</a>, Rhs, Guess > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1BiCGSTAB.html#ac6991ac0f70dd889f55ebc0f287c04f2">solveWithGuess</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>< Rhs > &b, const Guess &x0) const </td></tr>
<tr class="separator:ac6991ac0f70dd889f55ebc0f287c04f2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aab135f12fadf495a511f20c71557e1aa"><td class="memItemLeft" align="right" valign="top">RealScalar </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterativeSolverBase.html#aab135f12fadf495a511f20c71557e1aa">tolerance</a> () const</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_1BiCGSTAB.html#ac6991ac0f70dd889f55ebc0f287c04f2">BiCGSTAB< _MatrixType, _Preconditioner >::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 <a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute()</a>.</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 <a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute()</a> 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"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, _Preconditioner > & analyzePattern </td>
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<td class="paramtype">const MatrixType & </td>
<td class="paramname"><em>A</em></td><td>)</td>
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<p>Initializes the iterative solver for the sparcity pattern of the matrix <em>A</em> for further solving <code>Ax=b</code> problems.</p>
<p>Currently, this function mostly call analyzePattern on the preconditioner. In the future we might, for instance, implement column reodering for faster matrix vector products. </p>
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<td class="memname"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, _Preconditioner > & compute </td>
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<td class="paramtype">const MatrixType & </td>
<td class="paramname"><em>A</em></td><td>)</td>
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<p>Initializes the iterative solver with the matrix <em>A</em> for further solving <code>Ax=b</code> problems.</p>
<p>Currently, this function mostly initialized/compute the preconditioner. In the future we might, for instance, implement column reodering for faster matrix vector products.</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 <a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute()</a> to update it with the new matrix A, or modify a copy of A. </dd></dl>
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<td class="memname">RealScalar error </td>
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<td> const</td>
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<dl class="section return"><dt>Returns</dt><dd>the tolerance error reached during the last solve </dd></dl>
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<td class="memname"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, _Preconditioner > & factorize </td>
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<td class="paramtype">const MatrixType & </td>
<td class="paramname"><em>A</em></td><td>)</td>
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<p>Initializes the iterative solver with the numerical values of the matrix <em>A</em> for further solving <code>Ax=b</code> problems.</p>
<p>Currently, this function mostly call factorize on the preconditioner.</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 <a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute()</a> to update it with the new matrix A, or modify a copy of A. </dd></dl>
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<td class="memname"><a class="el" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> info </td>
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<dl class="section return"><dt>Returns</dt><dd>Success if the iterations converged, and NoConvergence otherwise. </dd></dl>
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<td class="memname">int iterations </td>
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<dl class="section return"><dt>Returns</dt><dd>the number of iterations performed during the last solve </dd></dl>
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<td class="memname">int maxIterations </td>
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<dl class="section return"><dt>Returns</dt><dd>the max number of iterations </dd></dl>
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<td class="memname">Preconditioner& preconditioner </td>
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<dl class="section return"><dt>Returns</dt><dd>a read-write reference to the preconditioner for custom configuration. </dd></dl>
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<td class="memname">const Preconditioner& preconditioner </td>
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<dl class="section return"><dt>Returns</dt><dd>a read-only reference to the preconditioner. </dd></dl>
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<td class="memname"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, _Preconditioner > & setMaxIterations </td>
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<td class="paramname"><em>maxIters</em></td><td>)</td>
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<p>Sets the max number of iterations </p>
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<td class="memname"><a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, _Preconditioner > & setTolerance </td>
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<td class="paramtype">const RealScalar & </td>
<td class="paramname"><em>tolerance</em></td><td>)</td>
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<p>Sets the tolerance threshold used by the stopping criteria </p>
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<td class="memname">const internal::solve_retval<<a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>< _MatrixType, _Preconditioner > , Rhs> solve </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>< Rhs > & </td>
<td class="paramname"><em>b</em></td><td>)</td>
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<dl class="section return"><dt>Returns</dt><dd>the solution x of <img class="formulaInl" alt="$ A x = b $" src="form_3.png"/> using the current decomposition of A.</dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute()</a> </dd></dl>
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<td class="memname">const internal::sparse_solve_retval<<a class="el" href="classEigen_1_1IterativeSolverBase.html">IterativeSolverBase</a>, Rhs> solve </td>
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<td class="paramtype">const <a class="el" href="classEigen_1_1SparseMatrixBase.html">SparseMatrixBase</a>< Rhs > & </td>
<td class="paramname"><em>b</em></td><td>)</td>
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<dl class="section return"><dt>Returns</dt><dd>the solution x of <img class="formulaInl" alt="$ A x = b $" src="form_3.png"/> using the current decomposition of A.</dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute()</a> </dd></dl>
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<td class="memname">const internal::solve_retval_with_guess<<a class="el" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>, Rhs, Guess> solveWithGuess </td>
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<dl class="section return"><dt>Returns</dt><dd>the solution x of <img class="formulaInl" alt="$ A x = b $" src="form_3.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><a class="el" href="classEigen_1_1IterativeSolverBase.html#a693a8142a905e7130bacd77586a6f6a0">compute()</a> </dd></dl>
<p>References <a class="el" href="classEigen_1_1BiCGSTAB.html#abda58f5b65579cb046bcb158cc356013">BiCGSTAB< _MatrixType, _Preconditioner >::BiCGSTAB()</a>.</p>
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<td class="memname">RealScalar tolerance </td>
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<dl class="section return"><dt>Returns</dt><dd>the tolerance threshold used by the stopping criteria </dd></dl>
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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="BiCGSTAB_8h_source.html">BiCGSTAB.h</a></li>
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