#include "stdafx.h"
/*
* -- SuperLU routine (version 2.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November 15, 1997
*
*/
#include "hnum_pdsp_defs.h"
#include "hnum_colamd.h"
#include "hnum_cblas.h"
namespace harlinn
{
namespace numerics
{
namespace SuperLU
{
void get_colamd(
const int m, /* number of rows in matrix A. */
const int n, /* number of columns in matrix A. */
const int nnz,/* number of nonzeros in matrix A. */
int *colptr, /* column pointer of size n+1 for matrix A. */
int *rowind, /* row indices of size nz for matrix A. */
int *perm_c /* out - the column permutation vector. */
)
{
int Alen, *A, i, info, *p;
double *knobs;
Alen = colamd_recommended(nnz, m, n);
if ( !(knobs = (double *) SUPERLU_MALLOC(COLAMD_KNOBS * sizeof(double))) )
SUPERLU_ABORT("Malloc fails for knobs");
colamd_set_defaults(knobs);
if (!(A = (int *) SUPERLU_MALLOC(Alen * sizeof(int))) )
SUPERLU_ABORT("Malloc fails for A[]");
if (!(p = (int *) SUPERLU_MALLOC((n+1) * sizeof(int))) )
SUPERLU_ABORT("Malloc fails for p[]");
for (i = 0; i <= n; ++i) p[i] = colptr[i];
for (i = 0; i < nnz; ++i) A[i] = rowind[i];
info = colamd(m, n, Alen, A, p, knobs);
if ( info == FALSE ) SUPERLU_ABORT("COLAMD failed");
for (i = 0; i < n; ++i) perm_c[p[i]] = i;
SUPERLU_FREE(knobs);
SUPERLU_FREE(A);
SUPERLU_FREE(p);
}
void
getata(
const int m, /* number of rows in matrix A. */
const int n, /* number of columns in matrix A. */
const int nz, /* number of nonzeros in matrix A */
int *colptr, /* column pointer of size n+1 for matrix A. */
int *rowind, /* row indices of size nz for matrix A. */
int *atanz, /* out - on exit, returns the actual number of
nonzeros in matrix A'*A. */
int **ata_colptr, /* out - size n+1 */
int **ata_rowind /* out - size *atanz */
)
/*
* Purpose
* =======
*
* Form the structure of A'*A. A is an m-by-n matrix in column oriented
* format represented by (colptr, rowind). The output A'*A is in column
* oriented format (symmetrically, also row oriented), represented by
* (ata_colptr, ata_rowind).
*
* This routine is modified from GETATA routine by Tim Davis.
* The complexity of this algorithm is: SUM_{i=1,m} r(i)^2,
* i.e., the sum of the square of the row counts.
*
* Questions
* =========
* o Do I need to withhold the *dense* rows?
* o How do I know the number of nonzeros in A'*A?
*
*/
{
register int i, j, k, col, num_nz, ti, trow;
int *marker, *b_colptr, *b_rowind;
int *t_colptr, *t_rowind; /* a column oriented form of T = A' */
if (!(marker = (int*)SUPERLU_MALLOC( (SUPERLU_MAX(m,n)+1) * sizeof(int)) ))
SUPERLU_ABORT("SUPERLU_MALLOC fails for marker[]");
if ( !(t_colptr = (int*) SUPERLU_MALLOC( (m+1) * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC t_colptr[]");
if ( !(t_rowind = (int*) SUPERLU_MALLOC( nz * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails for t_rowind[]");
/* Get counts of each column of T, and set up column pointers */
for (i = 0; i < m; ++i) marker[i] = 0;
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i)
++marker[rowind[i]];
}
t_colptr[0] = 0;
for (i = 0; i < m; ++i) {
t_colptr[i+1] = t_colptr[i] + marker[i];
marker[i] = t_colptr[i];
}
/* Transpose the matrix from A to T */
for (j = 0; j < n; ++j)
for (i = colptr[j]; i < colptr[j+1]; ++i) {
col = rowind[i];
t_rowind[marker[col]] = j;
++marker[col];
}
/* ----------------------------------------------------------------
compute B = T * A, where column j of B is:
Struct (B_*j) = UNION ( Struct (T_*k) )
A_kj != 0
do not include the diagonal entry
( Partition A as: A = (A_*1, ..., A_*n)
Then B = T * A = (T * A_*1, ..., T * A_*n), where
T * A_*j = (T_*1, ..., T_*m) * A_*j. )
---------------------------------------------------------------- */
/* Zero the diagonal flag */
for (i = 0; i < n; ++i) marker[i] = -1;
/* First pass determines number of nonzeros in B */
num_nz = 0;
for (j = 0; j < n; ++j) {
/* Flag the diagonal so it's not included in the B matrix */
marker[j] = j;
for (i = colptr[j]; i < colptr[j+1]; ++i) {
/* A_kj is nonzero, add pattern of column T_*k to B_*j */
k = rowind[i];
for (ti = t_colptr[k]; ti < t_colptr[k+1]; ++ti) {
trow = t_rowind[ti];
if ( marker[trow] != j ) {
marker[trow] = j;
num_nz++;
}
}
}
}
*atanz = num_nz;
/* Allocate storage for A'*A */
if ( !(*ata_colptr = (int*) SUPERLU_MALLOC( (n+1) * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails for ata_colptr[]");
if ( *atanz ) {
if ( !(*ata_rowind = (int*) SUPERLU_MALLOC( *atanz * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails for ata_rowind[]");
}
b_colptr = *ata_colptr; /* aliasing */
b_rowind = *ata_rowind;
/* Zero the diagonal flag */
for (i = 0; i < n; ++i) marker[i] = -1;
/* Compute each column of B, one at a time */
num_nz = 0;
for (j = 0; j < n; ++j) {
b_colptr[j] = num_nz;
/* Flag the diagonal so it's not included in the B matrix */
marker[j] = j;
for (i = colptr[j]; i < colptr[j+1]; ++i) {
/* A_kj is nonzero, add pattern of column T_*k to B_*j */
k = rowind[i];
for (ti = t_colptr[k]; ti < t_colptr[k+1]; ++ti) {
trow = t_rowind[ti];
if ( marker[trow] != j ) {
marker[trow] = j;
b_rowind[num_nz++] = trow;
}
}
}
}
b_colptr[n] = num_nz;
SUPERLU_FREE(marker);
SUPERLU_FREE(t_colptr);
SUPERLU_FREE(t_rowind);
}
void
at_plus_a(
const int n, /* number of columns in matrix A. */
const int nz, /* number of nonzeros in matrix A */
int *colptr, /* column pointer of size n+1 for matrix A. */
int *rowind, /* row indices of size nz for matrix A. */
int *bnz, /* out - on exit, returns the actual number of
nonzeros in matrix A'*A. */
int **b_colptr, /* out - size n+1 */
int **b_rowind /* out - size *bnz */
)
{
/*
* Purpose
* =======
*
* Form the structure of A'+A. A is an n-by-n matrix in column oriented
* format represented by (colptr, rowind). The output A'+A is in column
* oriented format (symmetrically, also row oriented), represented by
* (b_colptr, b_rowind).
*
*/
register int i, j, k, col, num_nz;
int *t_colptr, *t_rowind; /* a column oriented form of T = A' */
int *marker;
if ( !(marker = (int*) SUPERLU_MALLOC( n * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails for marker[]");
if ( !(t_colptr = (int*) SUPERLU_MALLOC( (n+1) * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails for t_colptr[]");
if ( !(t_rowind = (int*) SUPERLU_MALLOC( nz * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails t_rowind[]");
/* Get counts of each column of T, and set up column pointers */
for (i = 0; i < n; ++i) marker[i] = 0;
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i)
++marker[rowind[i]];
}
t_colptr[0] = 0;
for (i = 0; i < n; ++i) {
t_colptr[i+1] = t_colptr[i] + marker[i];
marker[i] = t_colptr[i];
}
/* Transpose the matrix from A to T */
for (j = 0; j < n; ++j)
for (i = colptr[j]; i < colptr[j+1]; ++i) {
col = rowind[i];
t_rowind[marker[col]] = j;
++marker[col];
}
/* ----------------------------------------------------------------
compute B = A + T, where column j of B is:
Struct (B_*j) = Struct (A_*k) UNION Struct (T_*k)
do not include the diagonal entry
---------------------------------------------------------------- */
/* Zero the diagonal flag */
for (i = 0; i < n; ++i) marker[i] = -1;
/* First pass determines number of nonzeros in B */
num_nz = 0;
for (j = 0; j < n; ++j) {
/* Flag the diagonal so it's not included in the B matrix */
marker[j] = j;
/* Add pattern of column A_*k to B_*j */
for (i = colptr[j]; i < colptr[j+1]; ++i) {
k = rowind[i];
if ( marker[k] != j ) {
marker[k] = j;
++num_nz;
}
}
/* Add pattern of column T_*k to B_*j */
for (i = t_colptr[j]; i < t_colptr[j+1]; ++i) {
k = t_rowind[i];
if ( marker[k] != j ) {
marker[k] = j;
++num_nz;
}
}
}
*bnz = num_nz;
/* Allocate storage for A+A' */
if ( !(*b_colptr = (int*) SUPERLU_MALLOC( (n+1) * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails for b_colptr[]");
if ( *bnz) {
if ( !(*b_rowind = (int*) SUPERLU_MALLOC( *bnz * sizeof(int)) ) )
SUPERLU_ABORT("SUPERLU_MALLOC fails for b_rowind[]");
}
/* Zero the diagonal flag */
for (i = 0; i < n; ++i) marker[i] = -1;
/* Compute each column of B, one at a time */
num_nz = 0;
for (j = 0; j < n; ++j) {
(*b_colptr)[j] = num_nz;
/* Flag the diagonal so it's not included in the B matrix */
marker[j] = j;
/* Add pattern of column A_*k to B_*j */
for (i = colptr[j]; i < colptr[j+1]; ++i) {
k = rowind[i];
if ( marker[k] != j ) {
marker[k] = j;
(*b_rowind)[num_nz++] = k;
}
}
/* Add pattern of column T_*k to B_*j */
for (i = t_colptr[j]; i < t_colptr[j+1]; ++i) {
k = t_rowind[i];
if ( marker[k] != j ) {
marker[k] = j;
(*b_rowind)[num_nz++] = k;
}
}
}
(*b_colptr)[n] = num_nz;
SUPERLU_FREE(marker);
SUPERLU_FREE(t_colptr);
SUPERLU_FREE(t_rowind);
}
void
get_perm_c(int ispec, SuperMatrix *A, int *perm_c)
/*
* Purpose
* =======
*
* GET_PERM_C 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) int
* Specifies the type of column ordering to reduce fill:
* = 1: minimum degree on the structure of A^T * A
* = 2: minimum degree on the structure of A^T + A
* = 3: approximate minimum degree for unsymmetric matrices
* If ispec == 0, the natural ordering (i.e., Pc = I) is returned.
*
* 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; Dtype = _D; Mtype = 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 = (NCformat *)A->Store;
int m, n, bnz, *b_colptr, i;
int delta, maxint, nofsub, *invp;
int *b_rowind, *dhead, *qsize, *llist, *marker;
double t, SuperLU_timer_();
m = A->nrow;
n = A->ncol;
t = SuperLU_timer_();
switch ( ispec ) {
case 0: /* Natural ordering */
for (i = 0; i < n; ++i) perm_c[i] = i;
printf("Use natural column ordering.\n");
return;
case 1: /* Minimum degree ordering on A'*A */
getata(m, n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
printf("Use minimum degree ordering on A'*A.\n");
t = SuperLU_timer_() - t;
/*printf("Form A'*A time = %8.3f\n", t);*/
break;
case 2: /* Minimum degree ordering on A'+A */
if ( m != n ) SUPERLU_ABORT("Matrix is not square");
at_plus_a(n, Astore->nnz, Astore->colptr, Astore->rowind,
&bnz, &b_colptr, &b_rowind);
printf("Use minimum degree ordering on A'+A.\n");
t = SuperLU_timer_() - t;
/*printf("Form A'+A time = %8.3f\n", t);*/
break;
case 3: /* Approximate minimum degree column ordering. */
get_colamd(m, n, Astore->nnz, Astore->colptr, Astore->rowind,
perm_c);
printf(".. Use approximate minimum degree column ordering.\n");
return;
default:
SUPERLU_ABORT("Invalid ISPEC");
}
if ( bnz != 0 ) {
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 *) SUPERLU_MALLOC((n+delta)*sizeof(int));
if ( !invp ) SUPERLU_ABORT("SUPERLU_MALLOC fails for invp.");
dhead = (int *) SUPERLU_MALLOC((n+delta)*sizeof(int));
if ( !dhead ) SUPERLU_ABORT("SUPERLU_MALLOC fails for dhead.");
qsize = (int *) SUPERLU_MALLOC((n+delta)*sizeof(int));
if ( !qsize ) SUPERLU_ABORT("SUPERLU_MALLOC fails for qsize.");
llist = (int *) SUPERLU_MALLOC(n*sizeof(int));
if ( !llist ) SUPERLU_ABORT("SUPERLU_MALLOC fails for llist.");
marker = (int *) SUPERLU_MALLOC(n*sizeof(int));
if ( !marker ) SUPERLU_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_(&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(b_colptr);
SUPERLU_FREE(b_rowind);
SUPERLU_FREE(invp);
SUPERLU_FREE(dhead);
SUPERLU_FREE(qsize);
SUPERLU_FREE(llist);
SUPERLU_FREE(marker);
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;
}
}
};
};
};
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