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<p>Example #2 showing how to use ILU to precondition GMRES.
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<div class="textblock"><code>#include "<a class="el" href="slu__zdefs_8h_source.html">slu_zdefs.h</a>"</code><br />
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Include dependency graph for zitersol1.c:</div>
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Functions</h2></td></tr>
<tr class="memitem:ae970280d13c1a6f41e71834f00776082"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="zitersol1_8c.html#ae970280d13c1a6f41e71834f00776082">zpsolve</a> (int n, <a class="el" href="structdoublecomplex.html">doublecomplex</a> x[], <a class="el" href="structdoublecomplex.html">doublecomplex</a> y[])</td></tr>
<tr class="memdesc:ae970280d13c1a6f41e71834f00776082"><td class="mdescLeft"> </td><td class="mdescRight">Performs ZGSISX with original matrix A. <a href="zitersol1_8c.html#ae970280d13c1a6f41e71834f00776082">More...</a><br /></td></tr>
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<tr class="memitem:a4e1543e740b505ad649e15bddd2c60ca"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="zitersol1_8c.html#a4e1543e740b505ad649e15bddd2c60ca">zmatvec_mult</a> (<a class="el" href="structdoublecomplex.html">doublecomplex</a> alpha, <a class="el" href="structdoublecomplex.html">doublecomplex</a> x[], <a class="el" href="structdoublecomplex.html">doublecomplex</a> beta, <a class="el" href="structdoublecomplex.html">doublecomplex</a> y[])</td></tr>
<tr class="memdesc:a4e1543e740b505ad649e15bddd2c60ca"><td class="mdescLeft"> </td><td class="mdescRight">Performs matrix-vector multipliation sp_zgemv with original matrix A. <a href="zitersol1_8c.html#a4e1543e740b505ad649e15bddd2c60ca">More...</a><br /></td></tr>
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<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="zitersol1_8c.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
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Variables</h2></td></tr>
<tr class="memitem:a869338b25a186a486edd0cf1850a7fbb"><td class="memItemLeft" align="right" valign="top">char * </td><td class="memItemRight" valign="bottom"><a class="el" href="zitersol1_8c.html#a869338b25a186a486edd0cf1850a7fbb">GLOBAL_EQUED</a></td></tr>
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<tr class="memitem:a8cb83de814c7fbf89011ba08bb602ce0"><td class="memItemLeft" align="right" valign="top">double * </td><td class="memItemRight" valign="bottom"><a class="el" href="zitersol1_8c.html#a8cb83de814c7fbf89011ba08bb602ce0">GLOBAL_R</a></td></tr>
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<tr class="memitem:ac5dce1561e620f6a6f6b6f17d82df4e8"><td class="memItemLeft" align="right" valign="top">double * </td><td class="memItemRight" valign="bottom"><a class="el" href="zitersol1_8c.html#ac5dce1561e620f6a6f6b6f17d82df4e8">GLOBAL_C</a></td></tr>
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<tr class="memitem:afbcb1904a71d92b04c1aef1cede6c4b1"><td class="memItemLeft" align="right" valign="top">int * </td><td class="memItemRight" valign="bottom"><a class="el" href="zitersol1_8c.html#afbcb1904a71d92b04c1aef1cede6c4b1">GLOBAL_PERM_C</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >This example shows that ILU is computed from the equilibrated matrix, but the preconditioned GMRES is applied to the original system. The driver routine ZGSISX is called twice to perform factorization and apply preconditioner separately.</p>
<p >Note that ZGSISX performs the following factorization: Pr*Dr*A*Dc*Pc^T ~= LU with Pr being obtained from MC64 statically then partial pivoting dynamically. On return, A is overwritten as A1 = Dr*A*Dc.</p>
<p >We need to save a copy of the original matrix A, then solve the original system, A*x = B, using FGMRES. Each GMRES step requires requires 2 procedures: 1) Apply preconditioner M^{-1} = Dc*Pc^T*U^{-1}*L^{-1}*Pr*Dr 2) Matrix-vector multiplication: w = A*v </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">◆ </a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramname"><em>argc</em>, </td>
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<td class="paramtype">char * </td>
<td class="paramname"><em>argv</em>[] </td>
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<h2 class="memtitle"><span class="permalink"><a href="#a4e1543e740b505ad649e15bddd2c60ca">◆ </a></span>zmatvec_mult()</h2>
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<td class="memname">void zmatvec_mult </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structdoublecomplex.html">doublecomplex</a> </td>
<td class="paramname"><em>alpha</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structdoublecomplex.html">doublecomplex</a> </td>
<td class="paramname"><em>x</em>[], </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structdoublecomplex.html">doublecomplex</a> </td>
<td class="paramname"><em>beta</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structdoublecomplex.html">doublecomplex</a> </td>
<td class="paramname"><em>y</em>[] </td>
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<td></td>
<td>)</td>
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<p >The operations is y := alpha*A*x + beta*y. See documentation of sp_zgemv for further details.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">alpha</td><td>Scalar factor for A*x </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>Vector to multiply with A </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">beta</td><td>Scalar factor for y </td></tr>
<tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>Vector to add to to matrix-vector multiplication and storage for result. </td></tr>
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<h2 class="memtitle"><span class="permalink"><a href="#ae970280d13c1a6f41e71834f00776082">◆ </a></span>zpsolve()</h2>
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<td class="memname">void zpsolve </td>
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<td class="paramtype">int </td>
<td class="paramname"><em>n</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structdoublecomplex.html">doublecomplex</a> </td>
<td class="paramname"><em>x</em>[], </td>
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<td></td>
<td class="paramtype"><a class="el" href="structdoublecomplex.html">doublecomplex</a> </td>
<td class="paramname"><em>y</em>[] </td>
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<td>)</td>
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<p >See documentation of zgsisx for more details.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>Dimension of matrices </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">x</td><td>Solution </td></tr>
<tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>Right-hand side </td></tr>
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<h2 class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a64b516645b16ef03c6fd0d692e6eb277">◆ </a></span>GLOBAL_OPTIONS</h2>
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<td class="memname"><a class="el" href="structsuperlu__options__t.html">superlu_options_t</a>* GLOBAL_OPTIONS</td>
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<h2 class="memtitle"><span class="permalink"><a href="#afbcb1904a71d92b04c1aef1cede6c4b1">◆ </a></span>GLOBAL_PERM_C</h2>
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<td class="memname">int* GLOBAL_PERM_C</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a5a42ee721355f1c852f770661834be93">◆ </a></span>GLOBAL_PERM_R</h2>
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<td class="memname">int * GLOBAL_PERM_R</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a8cb83de814c7fbf89011ba08bb602ce0">◆ </a></span>GLOBAL_R</h2>
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<td class="memname">double* GLOBAL_R</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a96a062252c26544370e8feae987c6d16">◆ </a></span>GLOBAL_STAT</h2>
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<td class="memname"><a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a>* GLOBAL_STAT</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a000ad5c2198e4309802b4478ed08a98c">◆ </a></span>GLOBAL_U</h2>
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<td class="memname"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * GLOBAL_U</td>
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