/*! \brief
*
* <pre>
* Purpose
* =======
*
* GET_PERM_C_DIST obtains a permutation matrix Pc, by applying the multiple
* minimum degree ordering code by Joseph Liu to matrix A'*A or A+A',
* or using approximate minimum degree column ordering by Davis et. al.
* The LU factorization of A*Pc tends to have less fill than the LU
* factorization of A.
*
* Arguments
* =========
*
* ispec (input) colperm_t
* Specifies what type of column permutation to use to reduce fill.
* = NATURAL: natural ordering (i.e., Pc = I)
* = MMD_AT_PLUS_A: minimum degree ordering on structure of A'+A
* = MMD_ATA: minimum degree ordering on structure of A'*A
* = METIS_AT_PLUS_A: MeTis on A'+A
*
* 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 = SLU_NC; Dtype = SLU_D; Mtype = SLU_GE.
* In the future, more general A can be handled.
*
* perm_c (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.
* </pre>
*/
void
get_perm_c_dist(int_t pnum, int_t ispec, SuperMatrix *A, int_t *perm_c)
{
NCformat *Astore = A->Store;
int_t m, n, bnz = 0, *b_colptr, *b_rowind, i;
int_t delta, maxint, nofsub, *invp;
int_t *dhead, *qsize, *llist, *marker;
double t, SuperLU_timer_();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(pnum, "Enter get_perm_c_dist()");
#endif
m = A->nrow;
n = A->ncol;
t = SuperLU_timer_();
switch ( ispec ) {
case NATURAL: /* Natural ordering */
for (i = 0; i < n; ++i) perm_c[i] = i;
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use natural column ordering\n");
#endif
return;
case MMD_AT_PLUS_A: /* Minimum degree ordering on A'+A */
if ( m != n ) ABORT("Matrix is not square");
at_plus_a_dist(n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
t = SuperLU_timer_() - t;
/*printf("Form A'+A time = %8.3f\n", t);*/
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use minimum degree ordering on A'+A.\n");
#endif
break;
case MMD_ATA: /* Minimum degree ordering on A'*A */
getata_dist(m, n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
t = SuperLU_timer_() - t;
/*printf("Form A'*A time = %8.3f\n", t);*/
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use minimum degree ordering on A'*A\n");
#endif
break;
case METIS_AT_PLUS_A: /* METIS ordering on A'+A */
if ( m != n ) ABORT("Matrix is not square");
at_plus_a_dist(n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
if ( bnz ) { /* non-empty adjacency structure */
get_metis(n, bnz, b_colptr, b_rowind, perm_c);
} else { /* e.g., diagonal matrix */
for (i = 0; i < n; ++i) perm_c[i] = i;
SUPERLU_FREE(b_colptr);
/* b_rowind is not allocated in this case */
}
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use METIS ordering on A'+A\n");
#endif
return;
default:
ABORT("Invalid ISPEC");
}
if ( bnz ) {
t = SuperLU_timer_();
/* Initialize and allocate storage for GENMMD. */
delta = 0; /* DELTA is a parameter to allow the choice of nodes
whose degree <= min-degree + DELTA. */
maxint = 2147483647; /* 2**31 - 1 */
invp = (int_t *) SUPERLU_MALLOC((n+delta)*sizeof(int_t));
if ( !invp ) ABORT("SUPERLU_MALLOC fails for invp.");
dhead = (int_t *) SUPERLU_MALLOC((n+delta)*sizeof(int_t));
if ( !dhead ) ABORT("SUPERLU_MALLOC fails for dhead.");
qsize = (int_t *) SUPERLU_MALLOC((n+delta)*sizeof(int_t));
if ( !qsize ) ABORT("SUPERLU_MALLOC fails for qsize.");
llist = (int_t *) SUPERLU_MALLOC(n*sizeof(int_t));
if ( !llist ) ABORT("SUPERLU_MALLOC fails for llist.");
marker = (int_t *) SUPERLU_MALLOC(n*sizeof(int_t));
if ( !marker ) ABORT("SUPERLU_MALLOC fails for marker.");
/* Transform adjacency list into 1-based indexing required by GENMMD.*/
for (i = 0; i <= n; ++i) ++b_colptr[i];
for (i = 0; i < bnz; ++i) ++b_rowind[i];
genmmd_dist_(&n, b_colptr, b_rowind, perm_c, invp, &delta, dhead,
qsize, llist, marker, &maxint, &nofsub);
/* Transform perm_c into 0-based indexing. */
for (i = 0; i < n; ++i) --perm_c[i];
SUPERLU_FREE(invp);
SUPERLU_FREE(dhead);
SUPERLU_FREE(qsize);
SUPERLU_FREE(llist);
SUPERLU_FREE(marker);
SUPERLU_FREE(b_rowind);
t = SuperLU_timer_() - t;
/* printf("call GENMMD time = %8.3f\n", t);*/
} else { /* Empty adjacency structure */
for (i = 0; i < n; ++i) perm_c[i] = i;
}
SUPERLU_FREE(b_colptr);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(pnum, "Exit get_perm_c_dist()");
#endif
} /* get_perm_c_dist */
void
get_perm_c_dist(int_t pnum, int_t ispec, SuperMatrix *A, int_t *perm_c)
/*
* Purpose
* =======
*
* GET_PERM_C_DIST obtains a permutation matrix Pc, by applying the multiple
* minimum degree ordering code by Joseph Liu to matrix A'*A or A+A',
* or using approximate minimum degree column ordering by Davis et. al.
* The LU factorization of A*Pc tends to have less fill than the LU
* factorization of A.
*
* Arguments
* =========
*
* ispec (input) colperm_t
* Specifies what type of column permutation to use to reduce fill.
* = NATURAL: natural ordering (i.e., Pc = I)
* = MMD_AT_PLUS_A: minimum degree ordering on structure of A'+A
* = MMD_ATA: minimum degree ordering on structure of A'*A
* = METIS_AT_PLUS_A: MeTis on A'+A
*
* 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 = SLU_NC; Dtype = SLU_D; Mtype = SLU_GE.
* In the future, more general A can be handled.
*
* perm_c (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.
*
*/
{
NCformat *Astore = A->Store;
int_t m, n, bnz = 0, *b_colptr, *b_rowind, i;
int_t delta, maxint, nofsub, *invp;
int_t *dhead, *qsize, *llist, *marker;
double t, SuperLU_timer_();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(pnum, "Enter get_perm_c_dist()");
#endif
m = A->nrow;
n = A->ncol;
t = SuperLU_timer_();
switch ( ispec ) {
case NATURAL: /* Natural ordering */
for (i = 0; i < n; ++i) perm_c[i] = i;
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use natural column ordering\n");
#endif
return;
case MMD_AT_PLUS_A: /* Minimum degree ordering on A'+A */
if ( m != n ) ABORT("Matrix is not square");
at_plus_a_dist(n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
t = SuperLU_timer_() - t;
/*printf("Form A'+A time = %8.3f\n", t);*/
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use minimum degree ordering on A'+A.\n");
#endif
break;
case MMD_ATA: /* Minimum degree ordering on A'*A */
getata_dist(m, n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
t = SuperLU_timer_() - t;
/*printf("Form A'*A time = %8.3f\n", t);*/
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use minimum degree ordering on A'*A\n");
#endif
break;
case METIS_AT_PLUS_A: /* METIS ordering on A'+A */
if ( m != n ) ABORT("Matrix is not square");
at_plus_a_dist(n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
get_metis(n, bnz, b_colptr, b_rowind, perm_c);
#if ( PRNTlevel>=1 )
if ( !pnum ) printf(".. Use METIS ordering on A'+A\n");
#endif
return;
default:
ABORT("Invalid ISPEC");
}
if ( bnz ) {
t = SuperLU_timer_();
/* Initialize and allocate storage for GENMMD. */
delta = 0; /* DELTA is a parameter to allow the choice of nodes
whose degree <= min-degree + DELTA. */
maxint = 2147483647; /* 2**31 - 1 */
invp = (int_t *) SUPERLU_MALLOC((n+delta)*sizeof(int_t));
if ( !invp ) ABORT("SUPERLU_MALLOC fails for invp.");
dhead = (int_t *) SUPERLU_MALLOC((n+delta)*sizeof(int_t));
if ( !dhead ) ABORT("SUPERLU_MALLOC fails for dhead.");
qsize = (int_t *) SUPERLU_MALLOC((n+delta)*sizeof(int_t));
if ( !qsize ) ABORT("SUPERLU_MALLOC fails for qsize.");
llist = (int_t *) SUPERLU_MALLOC(n*sizeof(int_t));
if ( !llist ) ABORT("SUPERLU_MALLOC fails for llist.");
marker = (int_t *) SUPERLU_MALLOC(n*sizeof(int_t));
if ( !marker ) ABORT("SUPERLU_MALLOC fails for marker.");
/* Transform adjacency list into 1-based indexing required by GENMMD.*/
for (i = 0; i <= n; ++i) ++b_colptr[i];
for (i = 0; i < bnz; ++i) ++b_rowind[i];
genmmd_dist_(&n, b_colptr, b_rowind, perm_c, invp, &delta, dhead,
qsize, llist, marker, &maxint, &nofsub);
/* Transform perm_c into 0-based indexing. */
for (i = 0; i < n; ++i) --perm_c[i];
SUPERLU_FREE(invp);
SUPERLU_FREE(dhead);
SUPERLU_FREE(qsize);
SUPERLU_FREE(llist);
SUPERLU_FREE(marker);
SUPERLU_FREE(b_rowind);
t = SuperLU_timer_() - t;
/* printf("call GENMMD time = %8.3f\n", t);*/
} else { /* Empty adjacency structure */
for (i = 0; i < n; ++i) perm_c[i] = i;
}
SUPERLU_FREE(b_colptr);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(pnum, "Exit get_perm_c_dist()");
#endif
} /* get_perm_c_dist */