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#include "ssp_defs.h"
void
sp_preorder(superlu_options_t *options, SuperMatrix *A, int *perm_c,
int *etree, SuperMatrix *AC)
{
/*
* Purpose
* =======
*
* sp_preorder() permutes the columns of the original matrix. It performs
* the following steps:
*
* 1. Apply column permutation perm_c[] to A's column pointers to form AC;
*
* 2. If options->Fact = DOFACT, then
* (1) Compute column elimination tree etree[] of AC'AC;
* (2) Post order etree[] to get a postordered elimination tree etree[],
* and a postorder permutation post[];
* (3) Apply post[] permutation to columns of AC;
* (4) Overwrite perm_c[] with the product perm_c * post.
*
* Arguments
* =========
*
* options (input) superlu_options_t*
* Specifies whether or not the elimination tree will be re-used.
* If options->Fact == DOFACT, this means first time factor A,
* etree is computed, postered, and output.
* Otherwise, re-factor A, etree is input, unchanged on exit.
*
* A (input) SuperMatrix*
* Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
* of the linear equations is A->nrow. Currently, the type of A can be:
* Stype = NC or SLU_NCP; Mtype = SLU_GE.
* In the future, more general A may be handled.
*
* perm_c (input/output) int*
* Column permutation vector of size A->ncol, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
* If options->Fact == DOFACT, perm_c is both input and output.
* On output, it is changed according to a postorder of etree.
* Otherwise, perm_c is input.
*
* etree (input/output) int*
* Elimination tree of Pc'*A'*A*Pc, dimension A->ncol.
* If options->Fact == DOFACT, etree is an output argument,
* otherwise it is an input argument.
* 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.
*
* AC (output) SuperMatrix*
* The resulting matrix after applied the column permutation
* perm_c[] to matrix A. The type of AC can be:
* Stype = SLU_NCP; Dtype = A->Dtype; Mtype = SLU_GE.
*
*/
NCformat *Astore;
NCPformat *ACstore;
int *iwork, *post;
register int n, i;
n = A->ncol;
/* Apply column permutation perm_c to A's column pointers so to
obtain NCP format in AC = A*Pc. */
AC->Stype = SLU_NCP;
AC->Dtype = A->Dtype;
AC->Mtype = A->Mtype;
AC->nrow = A->nrow;
AC->ncol = A->ncol;
Astore = A->Store;
ACstore = AC->Store = (void *) SUPERLU_MALLOC( sizeof(NCPformat) );
if ( !ACstore ) ABORT("SUPERLU_MALLOC fails for ACstore");
ACstore->nnz = Astore->nnz;
ACstore->nzval = Astore->nzval;
ACstore->rowind = Astore->rowind;
ACstore->colbeg = (int*) SUPERLU_MALLOC(n*sizeof(int));
if ( !(ACstore->colbeg) ) ABORT("SUPERLU_MALLOC fails for ACstore->colbeg");
ACstore->colend = (int*) SUPERLU_MALLOC(n*sizeof(int));
if ( !(ACstore->colend) ) ABORT("SUPERLU_MALLOC fails for ACstore->colend");
#ifdef DEBUG
print_int_vec("pre_order:", n, perm_c);
check_perm("Initial perm_c", n, perm_c);
#endif
for (i = 0; i < n; i++) {
ACstore->colbeg[perm_c[i]] = Astore->colptr[i];
ACstore->colend[perm_c[i]] = Astore->colptr[i+1];
}
if ( options->Fact == DOFACT ) {
#undef ETREE_ATplusA
#ifdef ETREE_ATplusA
/*--------------------------------------------
COMPUTE THE ETREE OF Pc*(A'+A)*Pc'.
--------------------------------------------*/
int *b_colptr, *b_rowind, bnz, j;
int *c_colbeg, *c_colend;
/*printf("Use etree(A'+A)\n");*/
/* Form B = A + A'. */
at_plus_a(n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
/* Form C = Pc*B*Pc'. */
c_colbeg = (int*) SUPERLU_MALLOC(2*n*sizeof(int));
c_colend = c_colbeg + n;
if (!c_colbeg ) ABORT("SUPERLU_MALLOC fails for c_colbeg/c_colend");
for (i = 0; i < n; i++) {
c_colbeg[perm_c[i]] = b_colptr[i];
c_colend[perm_c[i]] = b_colptr[i+1];
}
for (j = 0; j < n; ++j) {
for (i = c_colbeg[j]; i < c_colend[j]; ++i) {
b_rowind[i] = perm_c[b_rowind[i]];
}
}
/* Compute etree of C. */
sp_symetree(c_colbeg, c_colend, b_rowind, n, etree);
SUPERLU_FREE(b_colptr);
if ( bnz ) SUPERLU_FREE(b_rowind);
SUPERLU_FREE(c_colbeg);
#else
/*--------------------------------------------
COMPUTE THE COLUMN ELIMINATION TREE.
--------------------------------------------*/
sp_coletree(ACstore->colbeg, ACstore->colend, ACstore->rowind,
A->nrow, A->ncol, etree);
#endif
#ifdef DEBUG
print_int_vec("etree:", n, etree);
#endif
/* In symmetric mode, do not do postorder here. */
if ( options->SymmetricMode == NO ) {
/* Post order etree */
post = (int *) TreePostorder(n, etree);
/* for (i = 0; i < n+1; ++i) inv_post[post[i]] = i;
iwork = post; */
#ifdef DEBUG
print_int_vec("post:", n+1, post);
check_perm("post", n, post);
#endif
iwork = (int*) SUPERLU_MALLOC((n+1)*sizeof(int));
if ( !iwork ) ABORT("SUPERLU_MALLOC fails for iwork[]");
/* Renumber etree in postorder */
for (i = 0; i < n; ++i) iwork[post[i]] = post[etree[i]];
for (i = 0; i < n; ++i) etree[i] = iwork[i];
#ifdef DEBUG
print_int_vec("postorder etree:", n, etree);
#endif
/* Postmultiply A*Pc by post[] */
for (i = 0; i < n; ++i) iwork[post[i]] = ACstore->colbeg[i];
for (i = 0; i < n; ++i) ACstore->colbeg[i] = iwork[i];
for (i = 0; i < n; ++i) iwork[post[i]] = ACstore->colend[i];
for (i = 0; i < n; ++i) ACstore->colend[i] = iwork[i];
for (i = 0; i < n; ++i)
iwork[i] = post[perm_c[i]]; /* product of perm_c and post */
for (i = 0; i < n; ++i) perm_c[i] = iwork[i];
#ifdef DEBUG
print_int_vec("Pc*post:", n, perm_c);
check_perm("final perm_c", n, perm_c);
#endif
SUPERLU_FREE (post);
SUPERLU_FREE (iwork);
} /* end postordering */
} /* if options->Fact == DOFACT ... */
}
int check_perm(char *what, int n, int *perm)
{
register int i;
int *marker;
marker = (int *) calloc(n, sizeof(int));
for (i = 0; i < n; ++i) {
if ( marker[perm[i]] == 1 || perm[i] >= n ) {
printf("%s: Not a valid PERM[%d] = %d\n", what, i, perm[i]);
ABORT("check_perm");
} else {
marker[perm[i]] = 1;
}
}
SUPERLU_FREE(marker);
return 0;
}
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