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<title>SuperLU: SRC/zgstrf.c File Reference</title>
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    SRC/zgstrf.c File Reference

    Computes an LU factorization of a general sparse matrix. More...
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    #include "slu_zdefs.h"
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    Functions

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    void zgstrf (superlu_options_t *options, SuperMatrix *A, int relax, int panel_size, int *etree, void *work, int lwork, int *perm_c, int *perm_r, SuperMatrix *L, SuperMatrix *U, SuperLUStat_t *stat, int *info)
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    Detailed Description

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     -- SuperLU routine (version 3.0) --
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     Univ. of California Berkeley, Xerox Palo Alto Research Center,
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     and Lawrence Berkeley National Lab.
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     October 15, 2003

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     Copyright (c) 1994 by Xerox Corporation.  All rights reserved.

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     THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
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     EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.

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     Permission is hereby granted to use or copy this program for any
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     purpose, provided the above notices are retained on all copies.
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     Permission to modify the code and to distribute modified code is
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     granted, provided the above notices are retained, and a notice that
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     the code was modified is included with the above copyright notice.
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    Function Documentation

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              void zgstrf           
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              (
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              superlu_options_t
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               options, 
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              SuperMatrix
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               A, 
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              int 
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               relax, 
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              int 
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               panel_size, 
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              int * 
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               etree, 
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              void * 
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               work, 
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              int 
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               lwork, 
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              int * 
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               perm_c, 
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              int * 
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               perm_r, 
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              SuperMatrix
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               L, 
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              SuperMatrix
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               U, 
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              SuperLUStat_t
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               stat, 
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              int * 
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               info 
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              )
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     Purpose
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     =======

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     ZGSTRF computes an LU factorization of a general sparse m-by-n
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     matrix A using partial pivoting with row interchanges.
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     The factorization has the form
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         Pr * A = L * U
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     where Pr is a row permutation matrix, L is lower triangular with unit
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     diagonal elements (lower trapezoidal if A->nrow > A->ncol), and U is upper 
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     triangular (upper trapezoidal if A->nrow < A->ncol).

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     See supermatrix.h for the definition of 'SuperMatrix' structure.

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     Arguments
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     =========

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     options (input) superlu_options_t*
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             The structure defines the input parameters to control
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             how the LU decomposition will be performed.

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     A        (input) SuperMatrix*
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    	    Original matrix A, permuted by columns, of dimension
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              (A->nrow, A->ncol). The type of A can be:
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              Stype = SLU_NCP; Dtype = SLU_Z; Mtype = SLU_GE.

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     relax    (input) int
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              To control degree of relaxing supernodes. If the number
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              of nodes (columns) in a subtree of the elimination tree is less
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              than relax, this subtree is considered as one supernode,
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              regardless of the row structures of those columns.

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     panel_size (input) int
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              A panel consists of at most panel_size consecutive columns.

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     etree    (input) int*, dimension (A->ncol)
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              Elimination tree of A'*A.
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              Note: etree is a vector of parent pointers for a forest whose
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              vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.
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              On input, the columns of A should be permuted so that the
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              etree is in a certain postorder.

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     work     (input/output) void*, size (lwork) (in bytes)
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              User-supplied work space and space for the output data structures.
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              Not referenced if lwork = 0;

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     lwork   (input) int
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             Specifies the size of work array in bytes.
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             = 0:  allocate space internally by system malloc;
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             > 0:  use user-supplied work array of length lwork in bytes,
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                   returns error if space runs out.
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             = -1: the routine guesses the amount of space needed without
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                   performing the factorization, and returns it in
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                   *info; no other side effects.

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     perm_c   (input) int*, dimension (A->ncol)
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    	    Column permutation vector, which defines the 
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              permutation matrix Pc; perm_c[i] = j means column i of A is 
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              in position j in A*Pc.
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              When searching for diagonal, perm_c[*] is applied to the
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              row subscripts of A, so that diagonal threshold pivoting
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              can find the diagonal of A, rather than that of A*Pc.

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     perm_r   (input/output) int*, dimension (A->nrow)
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              Row permutation vector which defines the permutation matrix Pr,
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              perm_r[i] = j means row i of A is in position j in Pr*A.
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              If options->Fact = SamePattern_SameRowPerm, the pivoting routine
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                 will try to use the input perm_r, unless a certain threshold
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                 criterion is violated. In that case, perm_r is overwritten by
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                 a new permutation determined by partial pivoting or diagonal
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                 threshold pivoting.
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              Otherwise, perm_r is output argument;

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     L        (output) SuperMatrix*
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              The factor L from the factorization Pr*A=L*U; use compressed row 
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              subscripts storage for supernodes, i.e., L has type: 
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              Stype = SLU_SC, Dtype = SLU_Z, Mtype = SLU_TRLU.

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     U        (output) SuperMatrix*
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    	    The factor U from the factorization Pr*A*Pc=L*U. Use column-wise
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              storage scheme, i.e., U has types: Stype = SLU_NC, 
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              Dtype = SLU_Z, Mtype = SLU_TRU.

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     stat     (output) SuperLUStat_t*
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              Record the statistics on runtime and floating-point operation count.
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              See slu_util.h for the definition of 'SuperLUStat_t'.

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     info     (output) int*
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              = 0: successful exit
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              < 0: if info = -i, the i-th argument had an illegal value
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              > 0: if info = i, and i is
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                 <= A->ncol: U(i,i) is exactly zero. The factorization has
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                    been completed, but the factor U is exactly singular,
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                    and division by zero will occur if it is used to solve a
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                    system of equations.
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                 > A->ncol: number of bytes allocated when memory allocation
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                    failure occurred, plus A->ncol. If lwork = -1, it is
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                    the estimated amount of space needed, plus A->ncol.

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     ======================================================================

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     Local Working Arrays: 
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     ======================
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       m = number of rows in the matrix
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       n = number of columns in the matrix

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       xprune[0:n-1]: xprune[*] points to locations in subscript 
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    	vector lsub[*]. For column i, xprune[i] denotes the point where 
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    	structural pruning begins. I.e. only xlsub[i],..,xprune[i]-1 need 
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    	to be traversed for symbolic factorization.

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       marker[0:3*m-1]: marker[i] = j means that node i has been 
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    	reached when working on column j.
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    	Storage: relative to original row subscripts
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    	NOTE: There are 3 of them: marker/marker1 are used for panel dfs, 
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    	      see zpanel_dfs.c; marker2 is used for inner-factorization,
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                see zcolumn_dfs.c.

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       parent[0:m-1]: parent vector used during dfs
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          Storage: relative to new row subscripts

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       xplore[0:m-1]: xplore[i] gives the location of the next (dfs) 
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    	unexplored neighbor of i in lsub[*]

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       segrep[0:nseg-1]: contains the list of supernodal representatives
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    	in topological order of the dfs. A supernode representative is the 
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    	last column of a supernode.
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          The maximum size of segrep[] is n.

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       repfnz[0:W*m-1]: for a nonzero segment U[*,j] that ends at a 
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    	supernodal representative r, repfnz[r] is the location of the first 
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    	nonzero in this segment.  It is also used during the dfs: repfnz[r]>0
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    	indicates the supernode r has been explored.
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    	NOTE: There are W of them, each used for one column of a panel.

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       panel_lsub[0:W*m-1]: temporary for the nonzeros row indices below 
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          the panel diagonal. These are filled in during zpanel_dfs(), and are
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          used later in the inner LU factorization within the panel.
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    	panel_lsub[]/dense[] pair forms the SPA data structure.
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    	NOTE: There are W of them.

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       dense[0:W*m-1]: sparse accumulating (SPA) vector for intermediate values;
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    	    	   NOTE: there are W of them.

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       tempv[0:*]: real temporary used for dense numeric kernels;
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    	The size of this array is defined by NUM_TEMPV() in slu_zdefs.h.
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