454 lines
14 KiB
C
454 lines
14 KiB
C
/*
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* -- SuperLU routine (version 2.0) --
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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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* November 15, 1997
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*
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*/
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#include "ssp_defs.h"
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#include "colamd.h"
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extern int genmmd_(int *, int *, int *, int *, int *, int *, int *,
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int *, int *, int *, int *, int *);
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static void
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get_colamd(
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const int m, /* number of rows in matrix A. */
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const int n, /* number of columns in matrix A. */
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const int nnz,/* number of nonzeros in matrix A. */
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int *colptr, /* column pointer of size n+1 for matrix A. */
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int *rowind, /* row indices of size nz for matrix A. */
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int *perm_c /* out - the column permutation vector. */
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)
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{
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int Alen, *A, i, info, *p;
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double *knobs;
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Alen = colamd_recommended(nnz, m, n);
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if ( !(knobs = (double *) SUPERLU_MALLOC(COLAMD_KNOBS * sizeof(double))) )
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ABORT("Malloc fails for knobs");
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colamd_set_defaults(knobs);
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if (!(A = (int *) SUPERLU_MALLOC(Alen * sizeof(int))) )
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ABORT("Malloc fails for A[]");
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if (!(p = (int *) SUPERLU_MALLOC((n+1) * sizeof(int))) )
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ABORT("Malloc fails for p[]");
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for (i = 0; i <= n; ++i) p[i] = colptr[i];
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for (i = 0; i < nnz; ++i) A[i] = rowind[i];
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info = colamd(m, n, Alen, A, p, knobs);
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if ( info == FALSE ) ABORT("COLAMD failed");
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for (i = 0; i < n; ++i) perm_c[p[i]] = i;
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SUPERLU_FREE(knobs);
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SUPERLU_FREE(A);
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SUPERLU_FREE(p);
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}
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static void
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getata(
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const int m, /* number of rows in matrix A. */
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const int n, /* number of columns in matrix A. */
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const int nz, /* number of nonzeros in matrix A */
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int *colptr, /* column pointer of size n+1 for matrix A. */
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int *rowind, /* row indices of size nz for matrix A. */
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int *atanz, /* out - on exit, returns the actual number of
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nonzeros in matrix A'*A. */
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int **ata_colptr, /* out - size n+1 */
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int **ata_rowind /* out - size *atanz */
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)
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/*
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* Purpose
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* =======
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*
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* Form the structure of A'*A. A is an m-by-n matrix in column oriented
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* format represented by (colptr, rowind). The output A'*A is in column
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* oriented format (symmetrically, also row oriented), represented by
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* (ata_colptr, ata_rowind).
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*
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* This routine is modified from GETATA routine by Tim Davis.
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* The complexity of this algorithm is: SUM_{i=1,m} r(i)^2,
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* i.e., the sum of the square of the row counts.
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*
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* Questions
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* =========
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* o Do I need to withhold the *dense* rows?
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* o How do I know the number of nonzeros in A'*A?
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*
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*/
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{
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register int i, j, k, col, num_nz, ti, trow;
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int *marker, *b_colptr, *b_rowind;
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int *t_colptr, *t_rowind; /* a column oriented form of T = A' */
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if ( !(marker = (int*) SUPERLU_MALLOC((SUPERLU_MAX(m,n)+1)*sizeof(int))) )
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ABORT("SUPERLU_MALLOC fails for marker[]");
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if ( !(t_colptr = (int*) SUPERLU_MALLOC((m+1) * sizeof(int))) )
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ABORT("SUPERLU_MALLOC t_colptr[]");
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if ( !(t_rowind = (int*) SUPERLU_MALLOC(nz * sizeof(int))) )
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ABORT("SUPERLU_MALLOC fails for t_rowind[]");
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/* Get counts of each column of T, and set up column pointers */
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for (i = 0; i < m; ++i) marker[i] = 0;
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for (j = 0; j < n; ++j) {
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for (i = colptr[j]; i < colptr[j+1]; ++i)
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++marker[rowind[i]];
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}
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t_colptr[0] = 0;
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for (i = 0; i < m; ++i) {
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t_colptr[i+1] = t_colptr[i] + marker[i];
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marker[i] = t_colptr[i];
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}
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/* Transpose the matrix from A to T */
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for (j = 0; j < n; ++j)
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for (i = colptr[j]; i < colptr[j+1]; ++i) {
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col = rowind[i];
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t_rowind[marker[col]] = j;
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++marker[col];
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}
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/* ----------------------------------------------------------------
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compute B = T * A, where column j of B is:
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Struct (B_*j) = UNION ( Struct (T_*k) )
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A_kj != 0
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do not include the diagonal entry
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( Partition A as: A = (A_*1, ..., A_*n)
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Then B = T * A = (T * A_*1, ..., T * A_*n), where
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T * A_*j = (T_*1, ..., T_*m) * A_*j. )
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---------------------------------------------------------------- */
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/* Zero the diagonal flag */
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for (i = 0; i < n; ++i) marker[i] = -1;
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/* First pass determines number of nonzeros in B */
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num_nz = 0;
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for (j = 0; j < n; ++j) {
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/* Flag the diagonal so it's not included in the B matrix */
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marker[j] = j;
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for (i = colptr[j]; i < colptr[j+1]; ++i) {
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/* A_kj is nonzero, add pattern of column T_*k to B_*j */
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k = rowind[i];
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for (ti = t_colptr[k]; ti < t_colptr[k+1]; ++ti) {
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trow = t_rowind[ti];
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if ( marker[trow] != j ) {
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marker[trow] = j;
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num_nz++;
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}
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}
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}
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}
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*atanz = num_nz;
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/* Allocate storage for A'*A */
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if ( !(*ata_colptr = (int*) SUPERLU_MALLOC( (n+1) * sizeof(int)) ) )
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ABORT("SUPERLU_MALLOC fails for ata_colptr[]");
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if ( *atanz ) {
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if ( !(*ata_rowind = (int*) SUPERLU_MALLOC( *atanz * sizeof(int)) ) )
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ABORT("SUPERLU_MALLOC fails for ata_rowind[]");
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}
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b_colptr = *ata_colptr; /* aliasing */
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b_rowind = *ata_rowind;
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/* Zero the diagonal flag */
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for (i = 0; i < n; ++i) marker[i] = -1;
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/* Compute each column of B, one at a time */
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num_nz = 0;
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for (j = 0; j < n; ++j) {
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b_colptr[j] = num_nz;
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/* Flag the diagonal so it's not included in the B matrix */
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marker[j] = j;
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for (i = colptr[j]; i < colptr[j+1]; ++i) {
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/* A_kj is nonzero, add pattern of column T_*k to B_*j */
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k = rowind[i];
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for (ti = t_colptr[k]; ti < t_colptr[k+1]; ++ti) {
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trow = t_rowind[ti];
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if ( marker[trow] != j ) {
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marker[trow] = j;
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b_rowind[num_nz++] = trow;
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}
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}
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}
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}
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b_colptr[n] = num_nz;
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SUPERLU_FREE(marker);
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SUPERLU_FREE(t_colptr);
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SUPERLU_FREE(t_rowind);
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}
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static void
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at_plus_a(
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const int n, /* number of columns in matrix A. */
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const int nz, /* number of nonzeros in matrix A */
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int *colptr, /* column pointer of size n+1 for matrix A. */
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int *rowind, /* row indices of size nz for matrix A. */
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int *bnz, /* out - on exit, returns the actual number of
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nonzeros in matrix A'*A. */
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int **b_colptr, /* out - size n+1 */
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int **b_rowind /* out - size *bnz */
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)
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{
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/*
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* Purpose
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* =======
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*
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* Form the structure of A'+A. A is an n-by-n matrix in column oriented
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* format represented by (colptr, rowind). The output A'+A is in column
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* oriented format (symmetrically, also row oriented), represented by
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* (b_colptr, b_rowind).
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*
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*/
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register int i, j, k, col, num_nz;
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int *t_colptr, *t_rowind; /* a column oriented form of T = A' */
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int *marker;
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if ( !(marker = (int*) SUPERLU_MALLOC( n * sizeof(int)) ) )
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ABORT("SUPERLU_MALLOC fails for marker[]");
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if ( !(t_colptr = (int*) SUPERLU_MALLOC( (n+1) * sizeof(int)) ) )
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ABORT("SUPERLU_MALLOC fails for t_colptr[]");
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if ( !(t_rowind = (int*) SUPERLU_MALLOC( nz * sizeof(int)) ) )
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ABORT("SUPERLU_MALLOC fails t_rowind[]");
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/* Get counts of each column of T, and set up column pointers */
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for (i = 0; i < n; ++i) marker[i] = 0;
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for (j = 0; j < n; ++j) {
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for (i = colptr[j]; i < colptr[j+1]; ++i)
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++marker[rowind[i]];
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}
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t_colptr[0] = 0;
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for (i = 0; i < n; ++i) {
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t_colptr[i+1] = t_colptr[i] + marker[i];
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marker[i] = t_colptr[i];
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}
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/* Transpose the matrix from A to T */
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for (j = 0; j < n; ++j)
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for (i = colptr[j]; i < colptr[j+1]; ++i) {
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col = rowind[i];
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t_rowind[marker[col]] = j;
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++marker[col];
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}
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/* ----------------------------------------------------------------
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compute B = A + T, where column j of B is:
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Struct (B_*j) = Struct (A_*k) UNION Struct (T_*k)
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do not include the diagonal entry
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---------------------------------------------------------------- */
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/* Zero the diagonal flag */
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for (i = 0; i < n; ++i) marker[i] = -1;
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/* First pass determines number of nonzeros in B */
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num_nz = 0;
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for (j = 0; j < n; ++j) {
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/* Flag the diagonal so it's not included in the B matrix */
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marker[j] = j;
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/* Add pattern of column A_*k to B_*j */
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for (i = colptr[j]; i < colptr[j+1]; ++i) {
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k = rowind[i];
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if ( marker[k] != j ) {
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marker[k] = j;
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++num_nz;
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}
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}
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/* Add pattern of column T_*k to B_*j */
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for (i = t_colptr[j]; i < t_colptr[j+1]; ++i) {
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k = t_rowind[i];
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if ( marker[k] != j ) {
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marker[k] = j;
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++num_nz;
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}
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}
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}
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*bnz = num_nz;
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/* Allocate storage for A+A' */
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if ( !(*b_colptr = (int*) SUPERLU_MALLOC( (n+1) * sizeof(int)) ) )
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ABORT("SUPERLU_MALLOC fails for b_colptr[]");
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if ( *bnz) {
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if ( !(*b_rowind = (int*) SUPERLU_MALLOC( *bnz * sizeof(int)) ) )
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ABORT("SUPERLU_MALLOC fails for b_rowind[]");
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}
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/* Zero the diagonal flag */
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for (i = 0; i < n; ++i) marker[i] = -1;
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/* Compute each column of B, one at a time */
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num_nz = 0;
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for (j = 0; j < n; ++j) {
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(*b_colptr)[j] = num_nz;
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/* Flag the diagonal so it's not included in the B matrix */
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marker[j] = j;
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/* Add pattern of column A_*k to B_*j */
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for (i = colptr[j]; i < colptr[j+1]; ++i) {
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k = rowind[i];
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if ( marker[k] != j ) {
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marker[k] = j;
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(*b_rowind)[num_nz++] = k;
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}
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}
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/* Add pattern of column T_*k to B_*j */
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for (i = t_colptr[j]; i < t_colptr[j+1]; ++i) {
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k = t_rowind[i];
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if ( marker[k] != j ) {
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marker[k] = j;
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(*b_rowind)[num_nz++] = k;
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}
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}
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}
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(*b_colptr)[n] = num_nz;
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SUPERLU_FREE(marker);
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SUPERLU_FREE(t_colptr);
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SUPERLU_FREE(t_rowind);
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}
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void
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get_perm_c(int ispec, SuperMatrix *A, int *perm_c)
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/*
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* Purpose
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* =======
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*
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* GET_PERM_C obtains a permutation matrix Pc, by applying the multiple
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* minimum degree ordering code by Joseph Liu to matrix A'*A or A+A'.
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* or using approximate minimum degree column ordering by Davis et. al.
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* The LU factorization of A*Pc tends to have less fill than the LU
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* factorization of A.
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*
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* Arguments
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* =========
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*
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* ispec (input) int
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* Specifies the type of column ordering to reduce fill:
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* = 1: minimum degree on the structure of A^T * A
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* = 2: minimum degree on the structure of A^T + A
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* = 3: approximate minimum degree for unsymmetric matrices
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* If ispec == 0, the natural ordering (i.e., Pc = I) is returned.
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*
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* A (input) SuperMatrix*
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* Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
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* of the linear equations is A->nrow. Currently, the type of A
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* can be: Stype = NC; Dtype = _D; Mtype = GE. In the future,
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* more general A can be handled.
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*
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* perm_c (output) int*
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* Column permutation vector of size A->ncol, 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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*
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*/
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{
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NCformat *Astore = A->Store;
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int m, n, bnz, *b_colptr, i;
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int delta, maxint, nofsub, *invp;
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int *b_rowind, *dhead, *qsize, *llist, *marker;
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double t, SuperLU_timer_();
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m = A->nrow;
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n = A->ncol;
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t = SuperLU_timer_();
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switch ( ispec ) {
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case 0: /* Natural ordering */
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for (i = 0; i < n; ++i) perm_c[i] = i;
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#if ( PRNTlevel>=1 )
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printf("Use natural column ordering.\n");
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#endif
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return;
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case 1: /* Minimum degree ordering on A'*A */
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getata(m, n, Astore->nnz, Astore->colptr, Astore->rowind,
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&bnz, &b_colptr, &b_rowind);
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#if ( PRNTlevel>=1 )
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printf("Use minimum degree ordering on A'*A.\n");
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#endif
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t = SuperLU_timer_() - t;
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/*printf("Form A'*A time = %8.3f\n", t);*/
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break;
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case 2: /* Minimum degree ordering on A'+A */
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if ( m != n ) ABORT("Matrix is not square");
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at_plus_a(n, Astore->nnz, Astore->colptr, Astore->rowind,
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&bnz, &b_colptr, &b_rowind);
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#if ( PRNTlevel>=1 )
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printf("Use minimum degree ordering on A'+A.\n");
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#endif
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t = SuperLU_timer_() - t;
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/*printf("Form A'+A time = %8.3f\n", t);*/
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break;
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case 3: /* Approximate minimum degree column ordering. */
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get_colamd(m, n, Astore->nnz, Astore->colptr, Astore->rowind,
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perm_c);
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#if ( PRNTlevel>=1 )
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printf(".. Use approximate minimum degree column ordering.\n");
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#endif
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return;
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default:
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ABORT("Invalid ISPEC");
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}
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if ( bnz != 0 ) {
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t = SuperLU_timer_();
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/* Initialize and allocate storage for GENMMD. */
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delta = 1; /* DELTA is a parameter to allow the choice of nodes
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whose degree <= min-degree + DELTA. */
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maxint = 2147483647; /* 2**31 - 1 */
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invp = (int *) SUPERLU_MALLOC((n+delta)*sizeof(int));
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if ( !invp ) ABORT("SUPERLU_MALLOC fails for invp.");
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dhead = (int *) SUPERLU_MALLOC((n+delta)*sizeof(int));
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if ( !dhead ) ABORT("SUPERLU_MALLOC fails for dhead.");
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qsize = (int *) SUPERLU_MALLOC((n+delta)*sizeof(int));
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if ( !qsize ) ABORT("SUPERLU_MALLOC fails for qsize.");
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llist = (int *) SUPERLU_MALLOC(n*sizeof(int));
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if ( !llist ) ABORT("SUPERLU_MALLOC fails for llist.");
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marker = (int *) SUPERLU_MALLOC(n*sizeof(int));
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if ( !marker ) ABORT("SUPERLU_MALLOC fails for marker.");
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/* Transform adjacency list into 1-based indexing required by GENMMD.*/
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for (i = 0; i <= n; ++i) ++b_colptr[i];
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for (i = 0; i < bnz; ++i) ++b_rowind[i];
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genmmd_(&n, b_colptr, b_rowind, perm_c, invp, &delta, dhead,
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qsize, llist, marker, &maxint, &nofsub);
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/* Transform perm_c into 0-based indexing. */
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for (i = 0; i < n; ++i) --perm_c[i];
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SUPERLU_FREE(b_colptr);
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SUPERLU_FREE(b_rowind);
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SUPERLU_FREE(invp);
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SUPERLU_FREE(dhead);
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SUPERLU_FREE(qsize);
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SUPERLU_FREE(llist);
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SUPERLU_FREE(marker);
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t = SuperLU_timer_() - t;
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/* printf("call GENMMD time = %8.3f\n", t);*/
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} else { /* Empty adjacency structure */
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for (i = 0; i < n; ++i) perm_c[i] = i;
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}
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}
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