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<p>Improves computed solution to a system of inear equations.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include <math.h></code><br />
<code>#include "<a class="el" href="slu__zdefs_8h_source.html">slu_zdefs.h</a>"</code><br />
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<tr class="memitem:a3641b6d4c21b7a852dbb32c2b693302e"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="zgsrfs_8c.html#a3641b6d4c21b7a852dbb32c2b693302e">ITMAX</a>   5</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ac21acad54459e74738cbca9f7f20a73b"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="zgsrfs_8c.html#ac21acad54459e74738cbca9f7f20a73b">zgsrfs</a> (<a class="el" href="superlu__enum__consts_8h.html#a0c4e17b2d5cea33f9991ccc6a6678d62">trans_t</a> trans, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *<a class="el" href="ilu__zdrop__row_8c.html#ac900805a486cbb8489e3c176ed6e0d8e">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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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)</p>
<p>All rights reserved.</p>
<p>The source code is distributed under BSD license, see the file License.txt at the top-level directory.</p>
<pre>
-- SuperLU routine (version 5.1) --
Univ. of California Berkeley, Xerox Palo Alto Research Center,
and Lawrence Berkeley National Lab.
October 15, 2003</pre><pre>Modified from lapack routine ZGERFS
Last modified: December 3, 2015
</pre> </div><h2 class="groupheader">Macro Definition Documentation</h2>
<a id="a3641b6d4c21b7a852dbb32c2b693302e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3641b6d4c21b7a852dbb32c2b693302e">◆ </a></span>ITMAX</h2>
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<td class="memname">#define ITMAX   5</td>
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<h2 class="groupheader">Function Documentation</h2>
<a id="ac21acad54459e74738cbca9f7f20a73b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac21acad54459e74738cbca9f7f20a73b">◆ </a></span>zgsrfs()</h2>
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<td class="memname">void zgsrfs </td>
<td>(</td>
<td class="paramtype"><a class="el" href="superlu__enum__consts_8h.html#a0c4e17b2d5cea33f9991ccc6a6678d62">trans_t</a> </td>
<td class="paramname"><em>trans</em>, </td>
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<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>A</em>, </td>
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<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>L</em>, </td>
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<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>U</em>, </td>
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<td class="paramtype">int * </td>
<td class="paramname"><em>perm_c</em>, </td>
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<td class="paramtype">int * </td>
<td class="paramname"><em>perm_r</em>, </td>
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<td class="paramtype">char * </td>
<td class="paramname"><em>equed</em>, </td>
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<td class="paramtype">double * </td>
<td class="paramname"><em>R</em>, </td>
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<td class="paramtype">double * </td>
<td class="paramname"><em>C</em>, </td>
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<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>B</em>, </td>
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<td class="paramname"><em>X</em>, </td>
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<td class="paramtype">double * </td>
<td class="paramname"><em>ferr</em>, </td>
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<td class="paramtype">double * </td>
<td class="paramname"><em>berr</em>, </td>
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<td class="paramtype"><a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> * </td>
<td class="paramname"><em>stat</em>, </td>
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<td class="paramtype">int * </td>
<td class="paramname"><em>info</em> </td>
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<td>)</td>
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<pre>
Purpose
=======</pre><pre> ZGSRFS improves the computed solution to a system of linear
equations and provides error bounds and backward error estimates for
the solution.</pre><pre> If equilibration was performed, the system becomes:
(diag(R)*A_original*diag(C)) * X = diag(R)*B_original.</pre><pre> See <a class="el" href="supermatrix_8h.html" title="Matrix type definitions.">supermatrix.h</a> for the definition of '<a class="el" href="structSuperMatrix.html">SuperMatrix</a>' structure.</pre><pre> Arguments
=========</pre><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><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><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><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#a2590dbb66d39c3055f88292f5f093be7">zgstrf()</a>. Use column-wise storage scheme,
i.e., U has types: Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_TRU.</pre><pre> perm_c (input) int*, dimension (A->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><pre> perm_r (input) int*, dimension (A->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><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><pre> R (input) double*, dimension (A->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><pre> C (input) double*, dimension (A->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><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><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#a1b74304cd437572bbec487bc29422a90">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><pre> FERR (output) double*, dimension (B->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><pre> BERR (output) double*, dimension (B->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><pre> stat (output) SuperLUStat_t*
Record the statistics on runtime and floating-point operation count.
See util.h for the definition of '<a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a>'.</pre><pre> info (output) int*
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value</pre><pre> Internal Parameters
===================</pre><pre> ITMAX is the maximum number of steps of iterative refinement.</pre><pre></pre> <div class="dynheader">
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