/*! \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 sp_preorder.c
 * \brief Permute and performs functions on columns of orginal matrix
 */
#include "slu_ddefs.h"


/*! \brief
 *
 * <pre>
 * 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.
 * </pre>
 */
void
sp_preorder(superlu_options_t *options,  SuperMatrix *A, int *perm_c, 
	    int *etree, SuperMatrix *AC)
{
    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));*/
    marker = (int *) malloc(n * sizeof(int));
    for (i = 0; i < n; ++i) marker[i] = 0;

    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;
}