// CSparse/Source/cs_sqr: ordering and symbolic analysis for sparse QR
// CSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
#include "cs.h"
/* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */
static csi cs_vcount (const cs *A, css *S)
{
    csi i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head,
        *tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ;
    S->pinv = pinv = cs_malloc (m+n, sizeof (csi)) ;        /* allocate pinv, */
    S->leftmost = leftmost = cs_malloc (m, sizeof (csi)) ;  /* and leftmost */
    w = cs_malloc (m+3*n, sizeof (csi)) ;   /* get workspace */
    if (!pinv || !w || !leftmost)
    {
        cs_free (w) ;                       /* pinv and leftmost freed later */
        return (0) ;                        /* out of memory */
    }
    next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ;
    for (k = 0 ; k < n ; k++) head [k] = -1 ;   /* queue k is empty */
    for (k = 0 ; k < n ; k++) tail [k] = -1 ;
    for (k = 0 ; k < n ; k++) nque [k] = 0 ;
    for (i = 0 ; i < m ; i++) leftmost [i] = -1 ;
    for (k = n-1 ; k >= 0 ; k--)
    {
        for (p = Ap [k] ; p < Ap [k+1] ; p++)
        {
            leftmost [Ai [p]] = k ;         /* leftmost[i] = min(find(A(i,:)))*/
        }
    }
    for (i = m-1 ; i >= 0 ; i--)            /* scan rows in reverse order */
    {
        pinv [i] = -1 ;                     /* row i is not yet ordered */
        k = leftmost [i] ;
        if (k == -1) continue ;             /* row i is empty */
        if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */
        next [i] = head [k] ;               /* put i at head of queue k */
        head [k] = i ;
    }
    S->lnz = 0 ;
    S->m2 = m ;
    for (k = 0 ; k < n ; k++)               /* find row permutation and nnz(V)*/
    {
        i = head [k] ;                      /* remove row i from queue k */
        S->lnz++ ;                          /* count V(k,k) as nonzero */
        if (i < 0) i = S->m2++ ;            /* add a fictitious row */
        pinv [i] = k ;                      /* associate row i with V(:,k) */
        if (--nque [k] <= 0) continue ;     /* skip if V(k+1:m,k) is empty */
        S->lnz += nque [k] ;                /* nque [k] is nnz (V(k+1:m,k)) */
        if ((pa = parent [k]) != -1)        /* move all rows to parent of k */
        {
            if (nque [pa] == 0) tail [pa] = tail [k] ;
            next [tail [k]] = head [pa] ;
            head [pa] = next [i] ;
            nque [pa] += nque [k] ;
        }
    }
    for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ;
    cs_free (w) ;
    return (1) ;
}

/* symbolic ordering and analysis for QR or LU */
css *cs_sqr (csi order, const cs *A, csi qr)
{
    csi n, k, ok = 1, *post ;
    css *S ;
    if (!CS_CSC (A)) return (NULL) ;        /* check inputs */
    n = A->n ;
    S = cs_calloc (1, sizeof (css)) ;       /* allocate result S */
    if (!S) return (NULL) ;                 /* out of memory */
    S->q = cs_amd (order, A) ;              /* fill-reducing ordering */
    if (order && !S->q) return (cs_sfree (S)) ;
    if (qr)                                 /* QR symbolic analysis */
    {
        cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ;
        S->parent = cs_etree (C, 1) ;       /* etree of C'*C, where C=A(:,q) */
        post = cs_post (S->parent, n) ;
        S->cp = cs_counts (C, S->parent, post, 1) ;  /* col counts chol(C'*C) */
        cs_free (post) ;
        ok = C && S->parent && S->cp && cs_vcount (C, S) ;
        if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ;
        if (order) cs_spfree (C) ;
    }
    else
    {
        S->unz = 4*(A->p [n]) + n ;         /* for LU factorization only, */
        S->lnz = S->unz ;                   /* guess nnz(L) and nnz(U) */
    }
    return (ok ? S : cs_sfree (S)) ;        /* return result S */
}