Computes an ILU factorization of a general sparse matrix. More...
#include "slu_sdefs.h"
Functions | |
| void | sgsitrf (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, GlobalLU_t *Glu, SuperLUStat_t *stat, int *info) |
Computes an ILU factorization of a general sparse matrix.
-- SuperLU routine (version 4.1) -- Lawrence Berkeley National Laboratory. June 30, 2009
| void sgsitrf | ( | 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, | |||
| GlobalLU_t * | Glu, | |||
| SuperLUStat_t * | stat, | |||
| int * | info | |||
| ) |
Purpose =======
SGSITRF 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).See supermatrix.h for the definition of 'SuperMatrix' structure.
Arguments =========
options (input) superlu_options_t* The structure defines the input parameters to control how the ILU decomposition will be performed.
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_S; Mtype = SLU_GE.
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.
panel_size (input) int A panel consists of at most panel_size consecutive columns.
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.
work (input/output) void*, size (lwork) (in bytes) User-supplied work space and space for the output data structures. Not referenced if lwork = 0;
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.
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.
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;
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_S, Mtype = SLU_TRLU.
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_S, Mtype = SLU_TRU.
Glu (input/output) GlobalLU_t * 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.
stat (output) SuperLUStat_t* Record the statistics on runtime and floating-point operation count. See slu_util.h for the definition of 'SuperLUStat_t'.
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.
======================================================================
Local Working Arrays: ====================== m = number of rows in the matrix n = number of columns in the matrix
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_)dpanel_dfs.c; marker2 is used for inner-factorization, see (ilu)_dcolumn_dfs.c; marker_relax(has its own space) is used for relaxed supernodes.
parent[0:m-1]: parent vector used during dfs Storage: relative to new row subscripts
xplore[0:m-1]: xplore[i] gives the location of the next (dfs) unexplored neighbor of i in lsub[*]
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.
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.
panel_lsub[0:W*m-1]: temporary for the nonzeros row indices below the panel diagonal. These are filled in during dpanel_dfs(), 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.
dense[0:W*m-1]: sparse accumulating (SPA) vector for intermediate values; NOTE: there are W of them.
tempv[0:*]: real temporary used for dense numeric kernels; The size of this array is defined by NUM_TEMPV() in slu_util.h. It is also used by the dropping routine ilu_ddrop_row().
1.6.1