/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required 
approvals from U.S. Dept. of Energy) 

All rights reserved. 

The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/
/*! @file get_perm_c.c
 * \brief Matrix permutation operations
 *
 * <pre>
 * -- SuperLU routine (version 3.1) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * August 1, 2008
 * </pre>
 */
#include "slu_ddefs.h"
#include "colamd.h"

extern int  genmmd_(int *, int *, int *, int *, int *, int *, int *, 
		    int *, int *, int *, int *, int *);

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[COLAMD_KNOBS];
    int stats[COLAMD_STATS];

    Alen = colamd_recommended(nnz, m, n);

    colamd_set_defaults(knobs);

    if (!(A = (int *) SUPERLU_MALLOC(Alen * sizeof(int))) )
        ABORT("Malloc fails for A[]");
    if (!(p = (int *) SUPERLU_MALLOC((n+1) * sizeof(int))) )
        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, stats);
    if ( info == FALSE ) ABORT("COLAMD failed");

    for (i = 0; i < n; ++i) perm_c[p[i]] = i;

    SUPERLU_FREE(A);
    SUPERLU_FREE(p);
}
/*! \brief
 *
 * <pre>
 * 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?
 * </pre>
 */
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 */
       )
{
    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))) )
	ABORT("SUPERLU_MALLOC fails for marker[]");
    if ( !(t_colptr = (int*) SUPERLU_MALLOC((m+1) * sizeof(int))) )
	ABORT("SUPERLU_MALLOC t_colptr[]");
    if ( !(t_rowind = (int*) SUPERLU_MALLOC(nz * sizeof(int))) )
	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)) ) )
	ABORT("SUPERLU_MALLOC fails for ata_colptr[]");
    if ( *atanz ) {
	if ( !(*ata_rowind = (int*) SUPERLU_MALLOC( *atanz * sizeof(int)) ) )
	    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);
}


/*! \brief
 *
 * <pre>
 * 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).
 * </pre>
 */
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 */
	  )
{
    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)) ) )
	ABORT("SUPERLU_MALLOC fails for marker[]");
    if ( !(t_colptr = (int*) SUPERLU_MALLOC( (n+1) * sizeof(int)) ) )
	ABORT("SUPERLU_MALLOC fails for t_colptr[]");
    if ( !(t_rowind = (int*) SUPERLU_MALLOC( nz * sizeof(int)) ) )
	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)) ) )
	ABORT("SUPERLU_MALLOC fails for b_colptr[]");
    if ( *bnz) {
      if ( !(*b_rowind = (int*) SUPERLU_MALLOC( *bnz * sizeof(int)) ) )
	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);
}

/*! \brief
 *
 * <pre>
 * 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.
 * </pre>
 */
void
get_perm_c(int ispec, SuperMatrix *A, int *perm_c)
{
    NCformat *Astore = A->Store;
    int m, n, bnz = 0, *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 (NATURAL): /* Natural ordering */
	for (i = 0; i < n; ++i) perm_c[i] = i;
#if ( PRNTlevel>=1 )
	printf("Use natural column ordering.\n");
#endif
	return;
    case (MMD_ATA): /* Minimum degree ordering on A'*A */
	getata(m, n, Astore->nnz, Astore->colptr, Astore->rowind,
		     &bnz, &b_colptr, &b_rowind);
#if ( PRNTlevel>=1 )
	printf("Use minimum degree ordering on A'*A.\n");
#endif
	t = SuperLU_timer_() - t;
	/*printf("Form A'*A time = %8.3f\n", t);*/
	break;
    case (MMD_AT_PLUS_A): /* Minimum degree ordering on A'+A */
	if ( m != n ) ABORT("Matrix is not square");
	at_plus_a(n, Astore->nnz, Astore->colptr, Astore->rowind,
		  &bnz, &b_colptr, &b_rowind);
#if ( PRNTlevel>=1 )
	printf("Use minimum degree ordering on A'+A.\n");
#endif
	t = SuperLU_timer_() - t;
	/*printf("Form A'+A time = %8.3f\n", t);*/
	break;
    case (COLAMD): /* Approximate minimum degree column ordering. */
	get_colamd(m, n, Astore->nnz, Astore->colptr, Astore->rowind, perm_c);
#if ( PRNTlevel>=1 )
	printf(".. Use approximate minimum degree column ordering.\n");
#endif
	return; 
    default:
	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 ) ABORT("SUPERLU_MALLOC fails for invp.");
	dhead = (int *) SUPERLU_MALLOC((n+delta)*sizeof(int));
	if ( !dhead ) ABORT("SUPERLU_MALLOC fails for dhead.");
	qsize = (int *) SUPERLU_MALLOC((n+delta)*sizeof(int));
	if ( !qsize ) ABORT("SUPERLU_MALLOC fails for qsize.");
	llist = (int *) SUPERLU_MALLOC(n*sizeof(int));
	if ( !llist ) ABORT("SUPERLU_MALLOC fails for llist.");
	marker = (int *) SUPERLU_MALLOC(n*sizeof(int));
	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_(&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);
}