436 lines
16 KiB
C
436 lines
16 KiB
C
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/*! @file cgstrf.c
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* \brief Computes an LU factorization of a general sparse matrix
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*
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* <pre>
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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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*
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* Copyright (c) 1994 by Xerox Corporation. All rights reserved.
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*
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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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*
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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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* </pre>
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*/
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#include "slu_cdefs.h"
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/*! \brief
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*
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* <pre>
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* Purpose
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* =======
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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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*
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* See supermatrix.h for the definition of 'SuperMatrix' structure.
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*
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* Arguments
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* =========
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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* ======================================================================
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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*
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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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* </pre>
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*/
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void
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cgstrf (superlu_options_t *options, SuperMatrix *A,
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int relax, int panel_size, int *etree, void *work, int lwork,
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int *perm_c, int *perm_r, SuperMatrix *L, SuperMatrix *U,
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SuperLUStat_t *stat, int *info)
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{
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/* Local working arrays */
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NCPformat *Astore;
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int *iperm_r = NULL; /* inverse of perm_r; used when
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options->Fact == SamePattern_SameRowPerm */
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int *iperm_c; /* inverse of perm_c */
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int *iwork;
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complex *cwork;
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int *segrep, *repfnz, *parent, *xplore;
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int *panel_lsub; /* dense[]/panel_lsub[] pair forms a w-wide SPA */
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int *xprune;
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int *marker;
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complex *dense, *tempv;
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int *relax_end;
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complex *a;
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int *asub;
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int *xa_begin, *xa_end;
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int *xsup, *supno;
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int *xlsub, *xlusup, *xusub;
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int nzlumax;
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float fill_ratio = sp_ienv(6); /* estimated fill ratio */
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static GlobalLU_t Glu; /* persistent to facilitate multiple factors. */
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/* Local scalars */
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fact_t fact = options->Fact;
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double diag_pivot_thresh = options->DiagPivotThresh;
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int pivrow; /* pivotal row number in the original matrix A */
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int nseg1; /* no of segments in U-column above panel row jcol */
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int nseg; /* no of segments in each U-column */
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register int jcol;
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register int kcol; /* end column of a relaxed snode */
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register int icol;
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register int i, k, jj, new_next, iinfo;
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int m, n, min_mn, jsupno, fsupc, nextlu, nextu;
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int w_def; /* upper bound on panel width */
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int usepr, iperm_r_allocated = 0;
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int nnzL, nnzU;
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int *panel_histo = stat->panel_histo;
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flops_t *ops = stat->ops;
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iinfo = 0;
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m = A->nrow;
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n = A->ncol;
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min_mn = SUPERLU_MIN(m, n);
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Astore = A->Store;
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a = Astore->nzval;
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asub = Astore->rowind;
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xa_begin = Astore->colbeg;
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xa_end = Astore->colend;
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/* Allocate storage common to the factor routines */
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*info = cLUMemInit(fact, work, lwork, m, n, Astore->nnz,
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panel_size, fill_ratio, L, U, &Glu, &iwork, &cwork);
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if ( *info ) return;
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xsup = Glu.xsup;
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supno = Glu.supno;
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xlsub = Glu.xlsub;
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xlusup = Glu.xlusup;
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xusub = Glu.xusub;
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SetIWork(m, n, panel_size, iwork, &segrep, &parent, &xplore,
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&repfnz, &panel_lsub, &xprune, &marker);
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cSetRWork(m, panel_size, cwork, &dense, &tempv);
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usepr = (fact == SamePattern_SameRowPerm);
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if ( usepr ) {
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/* Compute the inverse of perm_r */
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iperm_r = (int *) intMalloc(m);
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for (k = 0; k < m; ++k) iperm_r[perm_r[k]] = k;
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iperm_r_allocated = 1;
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}
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iperm_c = (int *) intMalloc(n);
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for (k = 0; k < n; ++k) iperm_c[perm_c[k]] = k;
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/* Identify relaxed snodes */
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relax_end = (int *) intMalloc(n);
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if ( options->SymmetricMode == YES ) {
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heap_relax_snode(n, etree, relax, marker, relax_end);
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} else {
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relax_snode(n, etree, relax, marker, relax_end);
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}
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ifill (perm_r, m, EMPTY);
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ifill (marker, m * NO_MARKER, EMPTY);
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supno[0] = -1;
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xsup[0] = xlsub[0] = xusub[0] = xlusup[0] = 0;
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w_def = panel_size;
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/*
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* Work on one "panel" at a time. A panel is one of the following:
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* (a) a relaxed supernode at the bottom of the etree, or
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* (b) panel_size contiguous columns, defined by the user
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*/
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for (jcol = 0; jcol < min_mn; ) {
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if ( relax_end[jcol] != EMPTY ) { /* start of a relaxed snode */
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kcol = relax_end[jcol]; /* end of the relaxed snode */
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panel_histo[kcol-jcol+1]++;
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/* --------------------------------------
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* Factorize the relaxed supernode(jcol:kcol)
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* -------------------------------------- */
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/* Determine the union of the row structure of the snode */
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if ( (*info = csnode_dfs(jcol, kcol, asub, xa_begin, xa_end,
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xprune, marker, &Glu)) != 0 )
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return;
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nextu = xusub[jcol];
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nextlu = xlusup[jcol];
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jsupno = supno[jcol];
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fsupc = xsup[jsupno];
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new_next = nextlu + (xlsub[fsupc+1]-xlsub[fsupc])*(kcol-jcol+1);
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nzlumax = Glu.nzlumax;
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while ( new_next > nzlumax ) {
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if ( (*info = cLUMemXpand(jcol, nextlu, LUSUP, &nzlumax, &Glu)) )
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return;
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}
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for (icol = jcol; icol<= kcol; icol++) {
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xusub[icol+1] = nextu;
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/* Scatter into SPA dense[*] */
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for (k = xa_begin[icol]; k < xa_end[icol]; k++)
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dense[asub[k]] = a[k];
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/* Numeric update within the snode */
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csnode_bmod(icol, jsupno, fsupc, dense, tempv, &Glu, stat);
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if ( (*info = cpivotL(icol, diag_pivot_thresh, &usepr, perm_r,
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iperm_r, iperm_c, &pivrow, &Glu, stat)) )
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if ( iinfo == 0 ) iinfo = *info;
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#ifdef DEBUG
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cprint_lu_col("[1]: ", icol, pivrow, xprune, &Glu);
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#endif
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}
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jcol = icol;
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} else { /* Work on one panel of panel_size columns */
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/* Adjust panel_size so that a panel won't overlap with the next
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* relaxed snode.
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*/
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panel_size = w_def;
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for (k = jcol + 1; k < SUPERLU_MIN(jcol+panel_size, min_mn); k++)
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if ( relax_end[k] != EMPTY ) {
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panel_size = k - jcol;
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break;
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}
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if ( k == min_mn ) panel_size = min_mn - jcol;
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panel_histo[panel_size]++;
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/* symbolic factor on a panel of columns */
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cpanel_dfs(m, panel_size, jcol, A, perm_r, &nseg1,
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dense, panel_lsub, segrep, repfnz, xprune,
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marker, parent, xplore, &Glu);
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/* numeric sup-panel updates in topological order */
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cpanel_bmod(m, panel_size, jcol, nseg1, dense,
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tempv, segrep, repfnz, &Glu, stat);
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/* Sparse LU within the panel, and below panel diagonal */
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for ( jj = jcol; jj < jcol + panel_size; jj++) {
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k = (jj - jcol) * m; /* column index for w-wide arrays */
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nseg = nseg1; /* Begin after all the panel segments */
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if ((*info = ccolumn_dfs(m, jj, perm_r, &nseg, &panel_lsub[k],
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segrep, &repfnz[k], xprune, marker,
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parent, xplore, &Glu)) != 0) return;
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/* Numeric updates */
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if ((*info = ccolumn_bmod(jj, (nseg - nseg1), &dense[k],
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tempv, &segrep[nseg1], &repfnz[k],
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jcol, &Glu, stat)) != 0) return;
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/* Copy the U-segments to ucol[*] */
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if ((*info = ccopy_to_ucol(jj, nseg, segrep, &repfnz[k],
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perm_r, &dense[k], &Glu)) != 0)
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return;
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if ( (*info = cpivotL(jj, diag_pivot_thresh, &usepr, perm_r,
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iperm_r, iperm_c, &pivrow, &Glu, stat)) )
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if ( iinfo == 0 ) iinfo = *info;
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/* Prune columns (0:jj-1) using column jj */
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cpruneL(jj, perm_r, pivrow, nseg, segrep,
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&repfnz[k], xprune, &Glu);
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/* Reset repfnz[] for this column */
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resetrep_col (nseg, segrep, &repfnz[k]);
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#ifdef DEBUG
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cprint_lu_col("[2]: ", jj, pivrow, xprune, &Glu);
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#endif
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}
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jcol += panel_size; /* Move to the next panel */
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} /* else */
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} /* for */
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*info = iinfo;
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if ( m > n ) {
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k = 0;
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for (i = 0; i < m; ++i)
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if ( perm_r[i] == EMPTY ) {
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perm_r[i] = n + k;
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++k;
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}
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}
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countnz(min_mn, xprune, &nnzL, &nnzU, &Glu);
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fixupL(min_mn, perm_r, &Glu);
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cLUWorkFree(iwork, cwork, &Glu); /* Free work space and compress storage */
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if ( fact == SamePattern_SameRowPerm ) {
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/* L and U structures may have changed due to possibly different
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pivoting, even though the storage is available.
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There could also be memory expansions, so the array locations
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may have changed, */
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((SCformat *)L->Store)->nnz = nnzL;
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((SCformat *)L->Store)->nsuper = Glu.supno[n];
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((SCformat *)L->Store)->nzval = Glu.lusup;
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((SCformat *)L->Store)->nzval_colptr = Glu.xlusup;
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((SCformat *)L->Store)->rowind = Glu.lsub;
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((SCformat *)L->Store)->rowind_colptr = Glu.xlsub;
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((NCformat *)U->Store)->nnz = nnzU;
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((NCformat *)U->Store)->nzval = Glu.ucol;
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((NCformat *)U->Store)->rowind = Glu.usub;
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((NCformat *)U->Store)->colptr = Glu.xusub;
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} else {
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cCreate_SuperNode_Matrix(L, A->nrow, min_mn, nnzL, Glu.lusup,
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Glu.xlusup, Glu.lsub, Glu.xlsub, Glu.supno,
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Glu.xsup, SLU_SC, SLU_C, SLU_TRLU);
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cCreate_CompCol_Matrix(U, min_mn, min_mn, nnzU, Glu.ucol,
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Glu.usub, Glu.xusub, SLU_NC, SLU_C, SLU_TRU);
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}
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ops[FACT] += ops[TRSV] + ops[GEMV];
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stat->expansions = --(Glu.num_expansions);
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if ( iperm_r_allocated ) SUPERLU_FREE (iperm_r);
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SUPERLU_FREE (iperm_c);
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SUPERLU_FREE (relax_end);
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}
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