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<meta content="text/html;charset=UTF-8" http-equiv="Content-Type">
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<title>SuperLU: SRC/cgstrf.c File Reference</title>
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<link href="doxygen.css" rel="stylesheet" type="text/css">
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Main Page
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Data Structures
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Files
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SRC/cgstrf.c File ReferenceComputes an LU factorization of a general sparse matrix. More...
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#include "slu_cdefs.h"
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Functions
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void cgstrf (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 cgstrf
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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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CGSTRF 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_C; 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_C, 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_C, 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 cpanel_dfs.c; marker2 is used for inner-factorization,
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see ccolumn_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 cpanel_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_cdefs.h.
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<address style="text-align: right;"><small>Generated on Mon Nov 22 10:23:47 2010 for SuperLU by </small></address>
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 1.5.5
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