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| <h1>SRC/cgsrfs.c File Reference</h1>Improves computed solution to a system of inear equations. <a href="#_details">More...</a> |
| <p> |
| <code>#include <math.h></code><br> |
| <code>#include "<a class="el" href="slu__cdefs_8h-source.html">slu_cdefs.h</a>"</code><br> |
| <table border="0" cellpadding="0" cellspacing="0"> |
| <tr><td></td></tr> |
| <tr><td colspan="2"><br><h2>Defines</h2></td></tr> |
| <tr><td class="memItemLeft" nowrap align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="cgsrfs_8c.html#3641b6d4c21b7a852dbb32c2b693302e">ITMAX</a> 5</td></tr> |
| |
| <tr><td colspan="2"><br><h2>Functions</h2></td></tr> |
| <tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="cgsrfs_8c.html#45c3a69a2e1025c59b2d96be63f65b71">cgsrfs</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, float *R, float *C, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *B, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *X, float *ferr, float *berr, <a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> *stat, int *info)</td></tr> |
| |
| </table> |
| <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 CGERFS |
| </pre> <hr><h2>Define Documentation</h2> |
| <a class="anchor" name="3641b6d4c21b7a852dbb32c2b693302e"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">#define ITMAX 5 </td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| |
| <p> |
| |
| </div> |
| </div><p> |
| <hr><h2>Function Documentation</h2> |
| <a class="anchor" name="45c3a69a2e1025c59b2d96be63f65b71"></a> |
| <div class="memitem"> |
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| <td class="memname">void cgsrfs </td> |
| <td>(</td> |
| <td class="paramtype"><a class="el" href="superlu__enum__consts_8h.html#0c4e17b2d5cea33f9991ccc6a6678d62">trans_t</a> </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> * </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> * </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> * </td> |
| <td class="paramname"> <em>U</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int * </td> |
| <td class="paramname"> <em>perm_c</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int * </td> |
| <td class="paramname"> <em>perm_r</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">char * </td> |
| <td class="paramname"> <em>equed</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float * </td> |
| <td class="paramname"> <em>R</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float * </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> * </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> * </td> |
| <td class="paramname"> <em>X</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float * </td> |
| <td class="paramname"> <em>ferr</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float * </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> * </td> |
| <td class="paramname"> <em>stat</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int * </td> |
| <td class="paramname"> <em>info</em></td><td> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td><td width="100%"></td> |
| </tr> |
| </table> |
| </div> |
| <div class="memdoc"> |
| |
| <p> |
| <pre> |
| Purpose |
| =======</pre><p> |
| <pre> CGSRFS 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_C, 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_C, 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="cgstrf_8c.html#9c9f2ce12946612c7426a10352ac5984">cgstrf()</a>. Use column-wise storage scheme, |
| i.e., U has types: Stype = SLU_NC, Dtype = SLU_C, Mtype = SLU_TRU.</pre><p> |
| <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><p> |
| <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><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) float*, 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><p> |
| <pre> C (input) float*, 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><p> |
| <pre> B (input) SuperMatrix* |
| B has types: Stype = SLU_DN, Dtype = SLU_C, 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_C, Mtype = SLU_GE. |
| On entry, the solution matrix X, as computed by <a class="el" href="cgstrs_8c.html#19517b9d29e4faf9ae777ca6fb9d415b">cgstrs()</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) float*, 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><p> |
| <pre> BERR (output) float*, 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><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 |
| < 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> |
| </div> |
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