klu2_analyze.hpp

/* ========================================================================== */
/* === klu_analyze ========================================================== */
/* ========================================================================== */
// @HEADER
// *****************************************************************************
//                   KLU2: A Direct Linear Solver package
//
// Copyright 2011 NTESS and the KLU2 contributors.
// SPDX-License-Identifier: LGPL-2.1-or-later
// *****************************************************************************
// @HEADER
 
/* Order the matrix using BTF (or not), and then AMD, COLAMD, the natural
 * ordering, or the user-provided-function on the blocks.  Does not support
 * using a given ordering (use klu_analyze_given for that case). */
 
#ifndef KLU2_ANALYZE_HPP
#define KLU2_ANALYZE_HPP
 
#include "klu2_internal.h"
#include "klu2_analyze_given.hpp"
#include "klu2_memory.hpp"
 
/* ========================================================================== */
/* === analyze_worker ======================================================= */
/* ========================================================================== */
 
template <typename Entry, typename Int>
static Int analyze_worker       /* returns KLU_OK or < 0 if error */
(
    /* inputs, not modified */
    Int n,              /* A is n-by-n */
    Int Ap [ ],         /* size n+1, column pointers */
    Int Ai [ ],         /* size nz, row indices */
    Int nblocks,        /* # of blocks */
    Int Pbtf [ ],       /* BTF row permutation */
    Int Qbtf [ ],       /* BTF col permutation */
    Int R [ ],          /* size n+1, but only Rbtf [0..nblocks] is used */
    Int ordering,       /* what ordering to use (0, 1, or 3 for this routine) */
 
    /* output only, not defined on input */
    Int P [ ],          /* size n */
    Int Q [ ],          /* size n */
    double Lnz [ ],     /* size n, but only Lnz [0..nblocks-1] is used */
 
    /* workspace, not defined on input or output */
    Int Pblk [ ],       /* size maxblock */
    Int Cp [ ],         /* size maxblock+1 */
    Int Ci [ ],         /* size MAX (nz+1, Cilen) */
    Int Cilen,          /* nz+1, or COLAMD_recommend(nz,n,n) for COLAMD */
    Int Pinv [ ],       /* size maxblock */
 
    /* input/output */
    KLU_symbolic<Entry, Int> *Symbolic,
    KLU_common<Entry, Int> *Common
)
{
    double amd_Info [TRILINOS_AMD_INFO], lnz, lnz1, flops, flops1 ;
    Int k1, k2, nk, k, block, oldcol, pend, newcol, result, pc, p, newrow,
        maxnz, nzoff, cstats [TRILINOS_COLAMD_STATS], ok, err = KLU_INVALID ;
 
    /* ---------------------------------------------------------------------- */
    /* initializations */
    /* ---------------------------------------------------------------------- */
    for (k = 0 ; k < TRILINOS_AMD_INFO ; k++)
    {
        amd_Info[k] = 0;
    }
 
    /* compute the inverse of Pbtf */
#ifndef NDEBUGKLU2
    for (k = 0 ; k < n ; k++)
    {
        P [k] = AMESOS2_KLU2_EMPTY ;
        Q [k] = AMESOS2_KLU2_EMPTY ;
        Pinv [k] = AMESOS2_KLU2_EMPTY ;
    }
#endif
    for (k = 0 ; k < n ; k++)
    {
        ASSERT (Pbtf [k] >= 0 && Pbtf [k] < n) ;
        Pinv [Pbtf [k]] = k ;
    }
#ifndef NDEBUGKLU2
    for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != AMESOS2_KLU2_EMPTY) ;
#endif
    nzoff = 0 ;
    lnz = 0 ;
    maxnz = 0 ;
    flops = 0 ;
    Symbolic->symmetry = AMESOS2_KLU2_EMPTY ;        /* only computed by AMD */
 
    /* ---------------------------------------------------------------------- */
    /* order each block */
    /* ---------------------------------------------------------------------- */
 
    for (block = 0 ; block < nblocks ; block++)
    {
 
        /* ------------------------------------------------------------------ */
        /* the block is from rows/columns k1 to k2-1 */
        /* ------------------------------------------------------------------ */
 
        k1 = R [block] ;
        k2 = R [block+1] ;
        nk = k2 - k1 ;
        PRINTF (("BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1, k2-1, nk)) ;
 
        /* ------------------------------------------------------------------ */
        /* construct the kth block, C */
        /* ------------------------------------------------------------------ */
 
        Lnz [block] = AMESOS2_KLU2_EMPTY ;
        pc = 0 ;
        for (k = k1 ; k < k2 ; k++)
        {
            newcol = k-k1 ;
            Cp [newcol] = pc ;
            oldcol = Qbtf [k] ;
            pend = Ap [oldcol+1] ;
            for (p = Ap [oldcol] ; p < pend ; p++)
            {
                newrow = Pinv [Ai [p]] ;
                if (newrow < k1)
                {
                    nzoff++ ;
                }
                else
                {
                    /* (newrow,newcol) is an entry in the block */
                    ASSERT (newrow < k2) ;
                    newrow -= k1 ;
                    Ci [pc++] = newrow ;
                }
            }
        }
        Cp [nk] = pc ;
        maxnz = MAX (maxnz, pc) ;
        ASSERT (KLU_valid (nk, Cp, Ci, NULL)) ;
 
        /* ------------------------------------------------------------------ */
        /* order the block C */
        /* ------------------------------------------------------------------ */
 
        if (nk <= 3)
        {
 
            /* -------------------------------------------------------------- */
            /* use natural ordering for tiny blocks (3-by-3 or less) */
            /* -------------------------------------------------------------- */
 
            for (k = 0 ; k < nk ; k++)
            {
                Pblk [k] = k ;
            }
            lnz1 = nk * (nk + 1) / 2 ;
            flops1 = nk * (nk - 1) / 2 + (nk-1)*nk*(2*nk-1) / 6 ;
            ok = TRUE ;
 
        }
        else if (ordering == 0)
        {
 
            /* -------------------------------------------------------------- */
            /* order the block with AMD (C+C') */
            /* -------------------------------------------------------------- */
 
            /*result = AMD_order (nk, Cp, Ci, Pblk, NULL, amd_Info) ;*/
            result = KLU_OrdinalTraits<Int>::amd_order (nk, Cp, Ci, Pblk, 
                        NULL, amd_Info) ;
            ok = (result >= TRILINOS_AMD_OK) ;
            if (result == TRILINOS_AMD_OUT_OF_MEMORY)
            {
                err = KLU_OUT_OF_MEMORY ;
            }
 
            /* account for memory usage in AMD */
            Common->mempeak = ( size_t) (MAX (Common->mempeak,
                Common->memusage + amd_Info [TRILINOS_AMD_MEMORY])) ;
 
            /* get the ordering statistics from AMD */
            lnz1 = (Int) (amd_Info [TRILINOS_AMD_LNZ]) + nk ;
            flops1 = 2 * amd_Info [TRILINOS_AMD_NMULTSUBS_LU] + amd_Info [TRILINOS_AMD_NDIV] ;
            if (pc == maxnz)
            {
                /* get the symmetry of the biggest block */
                Symbolic->symmetry = amd_Info [TRILINOS_AMD_SYMMETRY] ;
            }
 
        }
        else if (ordering == 1)
        {
 
            /* -------------------------------------------------------------- */
            /* order the block with COLAMD (C) */
            /* -------------------------------------------------------------- */
 
            /* order (and destroy) Ci, returning column permutation in Cp.
             * COLAMD "cannot" fail since the matrix has already been checked,
             * and Ci allocated. */
 
            /*ok = COLAMD (nk, nk, Cilen, Ci, Cp, NULL, cstats) ;*/
            ok = KLU_OrdinalTraits<Int>::colamd (nk, nk, Cilen, Ci, Cp, 
                                NULL, cstats) ;
            lnz1 = AMESOS2_KLU2_EMPTY ;
            flops1 = AMESOS2_KLU2_EMPTY ;
 
            /* copy the permutation from Cp to Pblk */
            for (k = 0 ; k < nk ; k++)
            {
                Pblk [k] = Cp [k] ;
            }
 
        }
        else
        {
 
            /* -------------------------------------------------------------- */
            /* pass the block to the user-provided ordering function */
            /* -------------------------------------------------------------- */
 
            lnz1 = (Common->user_order) (nk, Cp, Ci, Pblk, Common) ;
            flops1 = AMESOS2_KLU2_EMPTY ;
            ok = (lnz1 != 0) ;
        }
 
        if (!ok)
        {
            return (err) ;  /* ordering method failed */
        }
 
        /* ------------------------------------------------------------------ */
        /* keep track of nnz(L) and flops statistics */
        /* ------------------------------------------------------------------ */
 
        Lnz [block] = lnz1 ;
        lnz = (lnz == AMESOS2_KLU2_EMPTY || lnz1 == AMESOS2_KLU2_EMPTY) ? AMESOS2_KLU2_EMPTY : (lnz + lnz1) ;
        flops = (flops == AMESOS2_KLU2_EMPTY || flops1 == AMESOS2_KLU2_EMPTY) ? AMESOS2_KLU2_EMPTY : (flops + flops1) ;
 
        /* ------------------------------------------------------------------ */
        /* combine the preordering with the BTF ordering */
        /* ------------------------------------------------------------------ */
 
        PRINTF (("Pblk, 1-based:\n")) ;
        for (k = 0 ; k < nk ; k++)
        {
            ASSERT (k + k1 < n) ;
            ASSERT (Pblk [k] + k1 < n) ;
            Q [k + k1] = Qbtf [Pblk [k] + k1] ;
        }
        for (k = 0 ; k < nk ; k++)
        {
            ASSERT (k + k1 < n) ;
            ASSERT (Pblk [k] + k1 < n) ;
            P [k + k1] = Pbtf [Pblk [k] + k1] ;
        }
    }
 
    PRINTF (("nzoff %d  Ap[n] %d\n", nzoff, Ap [n])) ;
    ASSERT (nzoff >= 0 && nzoff <= Ap [n]) ;
 
    /* return estimates of # of nonzeros in L including diagonal */
    Symbolic->lnz = lnz ;           /* AMESOS2_KLU2_EMPTY if COLAMD used */
    Symbolic->unz = lnz ;
    Symbolic->nzoff = nzoff ;
    Symbolic->est_flops = flops ;   /* AMESOS2_KLU2_EMPTY if COLAMD or user-ordering used */
    return (KLU_OK) ;
}
 
 
/* ========================================================================== */
/* === order_and_analyze ==================================================== */
/* ========================================================================== */
 
/* Orders the matrix with or with BTF, then orders each block with AMD, COLAMD,
 * or the user ordering function.  Does not handle the natural or given
 * ordering cases. */
 
template <typename Entry, typename Int>
static KLU_symbolic<Entry, Int> *order_and_analyze  /* returns NULL if error, or a valid
                                           KLU_symbolic object if successful */
(
    /* inputs, not modified */
    Int n,              /* A is n-by-n */
    Int Ap [ ],         /* size n+1, column pointers */
    Int Ai [ ],         /* size nz, row indices */
    /* --------------------- */
    KLU_common<Entry, Int> *Common
)
{
    double work ;
    KLU_symbolic<Entry, Int> *Symbolic ;
    double *Lnz ;
    Int *Qbtf, *Cp, *Ci, *Pinv, *Pblk, *Pbtf, *P, *Q, *R ;
    Int nblocks, nz, block, maxblock, k1, k2, nk, do_btf, ordering, k, Cilen,
        *Work ;
 
    /* ---------------------------------------------------------------------- */
    /* allocate the Symbolic object, and check input matrix */
    /* ---------------------------------------------------------------------- */
 
    Symbolic = KLU_alloc_symbolic (n, Ap, Ai, Common) ;
    if (Symbolic == NULL)
    {
        return (NULL) ;
    }
    P = Symbolic->P ;
    Q = Symbolic->Q ;
    R = Symbolic->R ;
    Lnz = Symbolic->Lnz ;
    nz = Symbolic->nz ;
 
    ordering = Common->ordering ;
    if (ordering == 1)
    {
        /* COLAMD TODO : Should call the right version of COLAMD and other 
         external functions below */
        /*Cilen = COLAMD_recommended (nz, n, n) ;*/
        Cilen = KLU_OrdinalTraits<Int>::colamd_recommended (nz, n, n) ;
    }
    else if (ordering == 0 || (ordering == 3 && Common->user_order != NULL))
    {
        /* AMD or user ordering function */
        Cilen = nz+1 ;
    }
    else
    {
        /* invalid ordering */
        Common->status = KLU_INVALID ;
        KLU_free_symbolic (&Symbolic, Common) ;
        return (NULL) ;
    }
 
    /* AMD memory management routines */
    trilinos_amd_malloc  = Common->malloc_memory ;
    trilinos_amd_free    = Common->free_memory ;
    trilinos_amd_calloc  = Common->calloc_memory ;
    trilinos_amd_realloc = Common->realloc_memory ;
 
    /* ---------------------------------------------------------------------- */
    /* allocate workspace for BTF permutation */
    /* ---------------------------------------------------------------------- */
 
    Pbtf = (Int *) KLU_malloc (n, sizeof (Int), Common) ;
    Qbtf = (Int *) KLU_malloc (n, sizeof (Int), Common) ;
    if (Common->status < KLU_OK)
    {
        KLU_free (Pbtf, n, sizeof (Int), Common) ;
        KLU_free (Qbtf, n, sizeof (Int), Common) ;
        KLU_free_symbolic (&Symbolic, Common) ;
        return (NULL) ;
    }
 
    /* ---------------------------------------------------------------------- */
    /* get the common parameters for BTF and ordering method */
    /* ---------------------------------------------------------------------- */
 
    do_btf = Common->btf ;
    do_btf = (do_btf) ? TRUE : FALSE ;
    Symbolic->ordering = ordering ;
    Symbolic->do_btf = do_btf ;
    Symbolic->structural_rank = AMESOS2_KLU2_EMPTY ;
 
    /* ---------------------------------------------------------------------- */
    /* find the block triangular form (if requested) */
    /* ---------------------------------------------------------------------- */
 
    Common->work = 0 ;
    work = 0;
 
    if (do_btf)
    {
        Work = (Int *) KLU_malloc (5*n, sizeof (Int), Common) ;
        if (Common->status < KLU_OK)
        {
            /* out of memory */
            KLU_free (Pbtf, n, sizeof (Int), Common) ;
            KLU_free (Qbtf, n, sizeof (Int), Common) ;
            KLU_free_symbolic (&Symbolic, Common) ;
            return (NULL) ;
        }
 
        /* TODO : Correct version of BTF */
        /*nblocks = BTF_order (n, Ap, Ai, Common->maxwork, &work, Pbtf, Qbtf, R,
                &(Symbolic->structural_rank), Work) ;*/
        nblocks = KLU_OrdinalTraits<Int>::btf_order (n, Ap, Ai, 
                Common->maxwork, &work, Pbtf, Qbtf, R, 
                &(Symbolic->structural_rank), Work) ;
        Common->structural_rank = Symbolic->structural_rank ;
        Common->work += work ;
 
        KLU_free (Work, 5*n, sizeof (Int), Common) ;
 
        /* unflip Qbtf if the matrix does not have full structural rank */
        if (Symbolic->structural_rank < n)
        {
            for (k = 0 ; k < n ; k++)
            {
                Qbtf [k] = TRILINOS_BTF_UNFLIP (Qbtf [k]) ;
            }
        }
 
        /* find the size of the largest block */
        maxblock = 1 ;
        for (block = 0 ; block < nblocks ; block++)
        {
            k1 = R [block] ;
            k2 = R [block+1] ;
            nk = k2 - k1 ;
            PRINTF (("block %d size %d\n", block, nk)) ;
            maxblock = MAX (maxblock, nk) ;
        }
    }
    else
    {
        /* BTF not requested */
        nblocks = 1 ;
        maxblock = n ;
        R [0] = 0 ;
        R [1] = n ;
        for (k = 0 ; k < n ; k++)
        {
            Pbtf [k] = k ;
            Qbtf [k] = k ;
        }
    }
 
    Symbolic->nblocks = nblocks ;
 
    PRINTF (("maxblock size %d\n", maxblock)) ;
    Symbolic->maxblock = maxblock ;
 
    /* ---------------------------------------------------------------------- */
    /* allocate more workspace, for analyze_worker */
    /* ---------------------------------------------------------------------- */
 
    Pblk = (Int *) KLU_malloc (maxblock, sizeof (Int), Common) ;
    Cp   = (Int *) KLU_malloc (maxblock + 1, sizeof (Int), Common) ;
    Ci   = (Int *) KLU_malloc (MAX (Cilen, nz+1), sizeof (Int), Common) ;
    Pinv = (Int *) KLU_malloc (n, sizeof (Int), Common) ;
 
    /* ---------------------------------------------------------------------- */
    /* order each block of the BTF ordering, and a fill-reducing ordering */
    /* ---------------------------------------------------------------------- */
 
    if (Common->status == KLU_OK)
    {
        PRINTF (("calling analyze_worker\n")) ;
        Common->status = analyze_worker (n, Ap, Ai, nblocks, Pbtf, Qbtf, R,
            ordering, P, Q, Lnz, Pblk, Cp, Ci, Cilen, Pinv, Symbolic, Common) ;
        PRINTF (("analyze_worker done\n")) ;
    }
 
    /* ---------------------------------------------------------------------- */
    /* free all workspace */
    /* ---------------------------------------------------------------------- */
 
    KLU_free (Pblk, maxblock, sizeof (Int), Common) ;
    KLU_free (Cp, maxblock+1, sizeof (Int), Common) ;
    KLU_free (Ci, MAX (Cilen, nz+1), sizeof (Int), Common) ;
    KLU_free (Pinv, n, sizeof (Int), Common) ;
    KLU_free (Pbtf, n, sizeof (Int), Common) ;
    KLU_free (Qbtf, n, sizeof (Int), Common) ;
 
    /* ---------------------------------------------------------------------- */
    /* return the symbolic object */
    /* ---------------------------------------------------------------------- */
 
    if (Common->status < KLU_OK)
    {
        KLU_free_symbolic (&Symbolic, Common) ;
    }
    return (Symbolic) ;
}
 
 
/* ========================================================================== */
/* === KLU_analyze ========================================================== */
/* ========================================================================== */
 
template <typename Entry, typename Int>
KLU_symbolic<Entry, Int> *KLU_analyze       /* returns NULL if error, or a valid
                                   KLU_symbolic object if successful */
(
    /* inputs, not modified */
    Int n,              /* A is n-by-n */
    Int Ap [ ],         /* size n+1, column pointers */
    Int Ai [ ],         /* size nz, row indices */
    /* -------------------- */
    KLU_common<Entry, Int> *Common
)
{
 
    /* ---------------------------------------------------------------------- */
    /* get the control parameters for BTF and ordering method */
    /* ---------------------------------------------------------------------- */
 
    if (Common == NULL)
    {
        return (NULL) ;
    }
    Common->status = KLU_OK ;
    Common->structural_rank = AMESOS2_KLU2_EMPTY ;
 
    /* ---------------------------------------------------------------------- */
    /* order and analyze */
    /* ---------------------------------------------------------------------- */
 
    if (Common->ordering == 2)
    {
        /* natural ordering */
        /* TODO : c++ sees Ap, Ai as int *& Why ? */
        /* TODO : c++ does not allow NULL to be passed directly */
        Int *dummy = NULL ;
        return (KLU_analyze_given (n, Ap, Ai, dummy, dummy, Common)) ;
    }
    else
    {
        /* order with P and Q */
        return (order_and_analyze (n, Ap, Ai, Common)) ;
    }
}
 
#endif