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<h1>SRC/zgsrfs.c File Reference</h1>Improves computed solution to a system of inear equations. <a href="#_details">More...</a>
<p>
<code>#include &lt;math.h&gt;</code><br>
<code>#include &quot;<a class="el" href="slu__zdefs_8h-source.html">slu_zdefs.h</a>&quot;</code><br>
<table border="0" cellpadding="0" cellspacing="0">
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<tr><td colspan="2"><br><h2>Defines</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">#define&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="zgsrfs_8c.html#3641b6d4c21b7a852dbb32c2b693302e">ITMAX</a>&nbsp;&nbsp;&nbsp;5</td></tr>

<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="zgsrfs_8c.html#c21acad54459e74738cbca9f7f20a73b">zgsrfs</a> (<a class="el" href="superlu__enum__consts_8h.html#0c4e17b2d5cea33f9991ccc6a6678d62">trans_t</a> trans, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *<a class="el" href="ilu__zdrop__row_8c.html#c900805a486cbb8489e3c176ed6e0d8e">A</a>, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *L, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *U, int *perm_c, int *perm_r, char *equed, double *R, double *C, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *B, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *X, double *ferr, double *berr, <a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> *stat, int *info)</td></tr>

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<hr><a name="_details"></a><h2>Detailed Description</h2>
<pre>
 -- SuperLU routine (version 3.0) --
 Univ. of California Berkeley, Xerox Palo Alto Research Center,
 and Lawrence Berkeley National Lab.
 October 15, 2003</pre><p>
<pre> Modified from lapack routine ZGERFS
 </pre> <hr><h2>Define Documentation</h2>
<a class="anchor" name="3641b6d4c21b7a852dbb32c2b693302e"></a><!-- doxytag: member="zgsrfs.c::ITMAX" ref="3641b6d4c21b7a852dbb32c2b693302e" args="" -->
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          <td class="memname">#define ITMAX&nbsp;&nbsp;&nbsp;5          </td>
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<hr><h2>Function Documentation</h2>
<a class="anchor" name="c21acad54459e74738cbca9f7f20a73b"></a><!-- doxytag: member="zgsrfs.c::zgsrfs" ref="c21acad54459e74738cbca9f7f20a73b" args="(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U, int *perm_c, int *perm_r, char *equed, double *R, double *C, SuperMatrix *B, SuperMatrix *X, double *ferr, double *berr, SuperLUStat_t *stat, int *info)" -->
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          <td class="memname">void zgsrfs           </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="superlu__enum__consts_8h.html#0c4e17b2d5cea33f9991ccc6a6678d62">trans_t</a>&nbsp;</td>
          <td class="paramname"> <em>trans</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> *&nbsp;</td>
          <td class="paramname"> <em>A</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> *&nbsp;</td>
          <td class="paramname"> <em>L</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> *&nbsp;</td>
          <td class="paramname"> <em>U</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>perm_c</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>perm_r</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">char *&nbsp;</td>
          <td class="paramname"> <em>equed</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>R</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>C</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> *&nbsp;</td>
          <td class="paramname"> <em>B</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> *&nbsp;</td>
          <td class="paramname"> <em>X</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>ferr</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>berr</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> *&nbsp;</td>
          <td class="paramname"> <em>stat</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>info</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td width="100%"></td>
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<p>
<pre>
   Purpose   
   =======</pre><p>
<pre>   ZGSRFS improves the computed solution to a system of linear   
   equations and provides error bounds and backward error estimates for 
   the solution.</pre><p>
<pre>   If equilibration was performed, the system becomes:
           (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.</pre><p>
<pre>   See <a class="el" href="supermatrix_8h.html" title="Defines matrix types.">supermatrix.h</a> for the definition of 'SuperMatrix' structure.</pre><p>
<pre>   Arguments   
   =========</pre><p>
<pre> trans   (input) trans_t
          Specifies the form of the system of equations:
          = NOTRANS: A * X = B  (No transpose)
          = TRANS:   A'* X = B  (Transpose)
          = CONJ:    A**H * X = B  (Conjugate transpose)</pre><p>
<pre>   A       (input) SuperMatrix*
           The original matrix A in the system, or the scaled A if
           equilibration was done. The type of A can be:
           Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_GE.</pre><p>
<pre>   L       (input) SuperMatrix*
	     The factor L from the factorization Pr*A*Pc=L*U. Use
           compressed row subscripts storage for supernodes, 
           i.e., L has types: Stype = SLU_SC, Dtype = SLU_Z, Mtype = SLU_TRLU.</pre><p>
<pre>   U       (input) SuperMatrix*
           The factor U from the factorization Pr*A*Pc=L*U as computed by
           <a class="el" href="slu__zdefs_8h.html#58d722a16a6f114a94cb2f59c8b08df4">zgstrf()</a>. Use column-wise storage scheme, 
           i.e., U has types: Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_TRU.</pre><p>
<pre>   perm_c  (input) int*, dimension (A-&gt;ncol)
	     Column permutation vector, which defines the 
           permutation matrix Pc; perm_c[i] = j means column i of A is 
           in position j in A*Pc.</pre><p>
<pre>   perm_r  (input) int*, dimension (A-&gt;nrow)
           Row permutation vector, which defines the permutation matrix Pr;
           perm_r[i] = j means row i of A is in position j in Pr*A.</pre><p>
<pre>   equed   (input) Specifies the form of equilibration that was done.
           = 'N': No equilibration.
           = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
           = 'C': Column equilibration, i.e., A was postmultiplied by
                  diag(C).
           = 'B': Both row and column equilibration, i.e., A was replaced 
                  by diag(R)*A*diag(C).</pre><p>
<pre>   R       (input) double*, dimension (A-&gt;nrow)
           The row scale factors for A.
           If equed = 'R' or 'B', A is premultiplied by diag(R).
           If equed = 'N' or 'C', R is not accessed.</pre><p>
<pre>   C       (input) double*, dimension (A-&gt;ncol)
           The column scale factors for A.
           If equed = 'C' or 'B', A is postmultiplied by diag(C).
           If equed = 'N' or 'R', C is not accessed.</pre><p>
<pre>   B       (input) SuperMatrix*
           B has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
           The right hand side matrix B.
           if equed = 'R' or 'B', B is premultiplied by diag(R).</pre><p>
<pre>   X       (input/output) SuperMatrix*
           X has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
           On entry, the solution matrix X, as computed by <a class="el" href="slu__zdefs_8h.html#1b74304cd437572bbec487bc29422a90">zgstrs()</a>.
           On exit, the improved solution matrix X.
           if *equed = 'C' or 'B', X should be premultiplied by diag(C)
               in order to obtain the solution to the original system.</pre><p>
<pre>   FERR    (output) double*, dimension (B-&gt;ncol)   
           The estimated forward error bound for each solution vector   
           X(j) (the j-th column of the solution matrix X).   
           If XTRUE is the true solution corresponding to X(j), FERR(j) 
           is an estimated upper bound for the magnitude of the largest 
           element in (X(j) - XTRUE) divided by the magnitude of the   
           largest element in X(j).  The estimate is as reliable as   
           the estimate for RCOND, and is almost always a slight   
           overestimate of the true error.</pre><p>
<pre>   BERR    (output) double*, dimension (B-&gt;ncol)   
           The componentwise relative backward error of each solution   
           vector X(j) (i.e., the smallest relative change in   
           any element of A or B that makes X(j) an exact solution).</pre><p>
<pre>   stat     (output) SuperLUStat_t*
            Record the statistics on runtime and floating-point operation count.
            See util.h for the definition of 'SuperLUStat_t'.</pre><p>
<pre>   info    (output) int*   
           = 0:  successful exit   
            &lt; 0:  if INFO = -i, the i-th argument had an illegal value</pre><p>
<pre>    Internal Parameters   
    ===================</pre><p>
<pre>    ITMAX is the maximum number of steps of iterative refinement.</pre><p>
<pre> </pre> 
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