/*
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
 * \brief Permute and performs functions on columns of original matrix
 *
 * \ingroup Common
 */
#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(const superlu_options_t* options, SuperMatrix* A, int* perm_c, int* etree, SuperMatrix* AC) {
    NCformat* Astore;
    NCPformat* ACstore;
    int *iwork, *post;
    register int n, i;
    extern void check_perm(const char* what, int n, const int* perm);

    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 = intMalloc(n);
    if(!(ACstore->colbeg)) ABORT("SUPERLU_MALLOC fails for ACstore->colbeg");
    ACstore->colend = intMalloc(n);
    if(!(ACstore->colend)) ABORT("SUPERLU_MALLOC fails for ACstore->colend");

#if (DEBUGlevel >= 1)
    check_perm("Initial perm_c", n, perm_c);
#endif
#if (DEBUGlevel >= 2)
    print_int_vec("pre_order:", 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
#if (DEBUGlevel >= 2)
        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; */

#if (DEBUGlevel >= 1)
            check_perm("post", n, post);
#endif
#if (DEBUGlevel >= 2)
            print_int_vec("post:", n + 1, 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];

#if (DEBUGlevel >= 2)
            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];

#if (DEBUGlevel >= 1)
            check_perm("final perm_c", n, perm_c);
#endif
#if (DEBUGlevel >= 2)
            print_int_vec("Pc*post:", n, perm_c);
#endif
            SUPERLU_FREE(post);
            SUPERLU_FREE(iwork);
        } /* end postordering */

    } /* if options->Fact == DOFACT ... */
}
