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<p>Computes an ILU factorization of a general sparse matrix.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include "<a class="el" href="slu__cdefs_8h_source.html">slu_cdefs.h</a>"</code><br />
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Functions</h2></td></tr>
<tr class="memitem:a9bf92a834b43a4e163a5ae5c32a9ea4c"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="cgsitrf_8c.html#a9bf92a834b43a4e163a5ae5c32a9ea4c">cgsitrf</a> (<a class="el" href="structsuperlu__options__t.html">superlu_options_t</a> *options, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *<a class="el" href="ilu__zdrop__row_8c.html#ac900805a486cbb8489e3c176ed6e0d8e">A</a>, int relax, int panel_size, int *etree, void *work, int lwork, int *perm_c, int *perm_r, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *L, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *U, <a class="el" href="structGlobalLU__t.html">GlobalLU_t</a> *Glu, <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 4.1) --
Lawrence Berkeley National Laboratory.
June 30, 2009</pre><pre></pre> </div><h2 class="groupheader">Function Documentation</h2>
<a id="a9bf92a834b43a4e163a5ae5c32a9ea4c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9bf92a834b43a4e163a5ae5c32a9ea4c">◆ </a></span>cgsitrf()</h2>
<div class="memitem">
<div class="memproto">
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<tr>
<td class="memname">void cgsitrf </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structsuperlu__options__t.html">superlu_options_t</a> * </td>
<td class="paramname"><em>options</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">int </td>
<td class="paramname"><em>relax</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>panel_size</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>etree</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">void * </td>
<td class="paramname"><em>work</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>lwork</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>
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<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"><a class="el" href="structGlobalLU__t.html">GlobalLU_t</a> * </td>
<td class="paramname"><em>Glu</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>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<pre>
Purpose
=======</pre><pre>CGSITRF computes an ILU factorization of a general sparse m-by-n
matrix A using partial pivoting with row interchanges.
The factorization has the form
Pr * A = L * U
where Pr is a row permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if A->nrow > A->ncol), and U is upper
triangular (upper trapezoidal if A->nrow < A->ncol).</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>options (input) superlu_options_t*
The structure defines the input parameters to control
how the ILU decomposition will be performed.</pre><pre>A (input) SuperMatrix*
Original matrix A, permuted by columns, of dimension
(A->nrow, A->ncol). The type of A can be:
Stype = SLU_NCP; Dtype = SLU_C; Mtype = SLU_GE.</pre><pre>relax (input) int
To control degree of relaxing supernodes. If the number
of nodes (columns) in a subtree of the elimination tree is less
than relax, this subtree is considered as one supernode,
regardless of the row structures of those columns.</pre><pre>panel_size (input) int
A panel consists of at most panel_size consecutive columns.</pre><pre>etree (input) int*, dimension (A->ncol)
Elimination tree of A'*A.
Note: etree is a vector of parent pointers for a forest whose
vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.
On input, the columns of A should be permuted so that the
etree is in a certain postorder.</pre><pre>work (input/output) void*, size (lwork) (in bytes)
User-supplied work space and space for the output data structures.
Not referenced if lwork = 0;</pre><pre>lwork (input) int
Specifies the size of work array in bytes.
= 0: allocate space internally by system malloc;
> 0: use user-supplied work array of length lwork in bytes,
returns error if space runs out.
= -1: the routine guesses the amount of space needed without
performing the factorization, and returns it in
*info; no other side effects.</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.
When searching for diagonal, perm_c[*] is applied to the
row subscripts of A, so that diagonal threshold pivoting
can find the diagonal of A, rather than that of A*Pc.</pre><pre>perm_r (input/output) 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.
If options->Fact = SamePattern_SameRowPerm, the pivoting routine
will try to use the input perm_r, unless a certain threshold
criterion is violated. In that case, perm_r is overwritten by
a new permutation determined by partial pivoting or diagonal
threshold pivoting.
Otherwise, perm_r is output argument;</pre><pre>L (output) SuperMatrix*
The factor L from the factorization Pr*A=L*U; use compressed row
subscripts storage for supernodes, i.e., L has type:
Stype = SLU_SC, Dtype = SLU_C, Mtype = SLU_TRLU.</pre><pre>U (output) SuperMatrix*
The factor U from the factorization Pr*A*Pc=L*U. Use column-wise
storage scheme, i.e., U has types: Stype = SLU_NC,
Dtype = SLU_C, Mtype = SLU_TRU.</pre><pre>Glu (input/output) <a class="el" href="structGlobalLU__t.html">GlobalLU_t</a> *
If options->Fact == SamePattern_SameRowPerm, it is an input;
The matrix A will be factorized assuming that a
factorization of a matrix with the same sparsity pattern
and similar numerical values was performed prior to this one.
Therefore, this factorization will reuse both row and column
scaling factors R and C, both row and column permutation
vectors perm_r and perm_c, and the L & U data structures
set up from the previous factorization.
Otherwise, it is an output.</pre><pre>stat (output) SuperLUStat_t*
Record the statistics on runtime and floating-point operation count.
See <a class="el" href="slu__util_8h.html" title="Utility header file.">slu_util.h</a> 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
> 0: if info = i, and i is
<= A->ncol: number of zero pivots. They are replaced by small
entries according to options->ILU_FillTol.
> A->ncol: number of bytes allocated when memory allocation
failure occurred, plus A->ncol. If lwork = -1, it is
the estimated amount of space needed, plus A->ncol.</pre><pre>======================================================================</pre><pre>Local Working Arrays:
======================
m = number of rows in the matrix
n = number of columns in the matrix</pre><pre> marker[0:3*m-1]: marker[i] = j means that node i has been
reached when working on column j.
Storage: relative to original row subscripts
NOTE: There are 4 of them:
marker/marker1 are used for panel dfs, see (ilu_)<a class="el" href="dpanel__dfs_8c.html" title="Peforms a symbolic factorization on a panel of symbols.">dpanel_dfs.c</a>;
marker2 is used for inner-factorization, see (ilu)_dcolumn_dfs.c;
marker_relax(has its own space) is used for relaxed supernodes.</pre><pre> parent[0:m-1]: parent vector used during dfs
Storage: relative to new row subscripts</pre><pre> xplore[0:m-1]: xplore[i] gives the location of the next (dfs)
unexplored neighbor of i in lsub[*]</pre><pre> segrep[0:nseg-1]: contains the list of supernodal representatives
in topological order of the dfs. A supernode representative is the
last column of a supernode.
The maximum size of segrep[] is n.</pre><pre> repfnz[0:W*m-1]: for a nonzero segment U[*,j] that ends at a
supernodal representative r, repfnz[r] is the location of the first
nonzero in this segment. It is also used during the dfs: repfnz[r]>0
indicates the supernode r has been explored.
NOTE: There are W of them, each used for one column of a panel.</pre><pre> panel_lsub[0:W*m-1]: temporary for the nonzeros row indices below
the panel diagonal. These are filled in during <a class="el" href="dpanel__dfs_8c.html#a2a809488b87d2c1a9b2a574b726e8517">dpanel_dfs()</a>, and are
used later in the inner LU factorization within the panel.
panel_lsub[]/dense[] pair forms the SPA data structure.
NOTE: There are W of them.</pre><pre> dense[0:W*m-1]: sparse accumulating (SPA) vector for intermediate values;
NOTE: there are W of them.</pre><pre> tempv[0:*]: real temporary used for dense numeric kernels;
The size of this array is defined by <a class="el" href="slu__util_8h.html#a06193b28f40a4779ae7737711642eb45">NUM_TEMPV()</a> in <a class="el" href="slu__util_8h.html" title="Utility header file.">slu_util.h</a>.
It is also used by the dropping routine <a class="el" href="ilu__ddrop__row_8c.html#a380317801e05b11930fd1e094db34179">ilu_ddrop_row()</a>.
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