text: /* +---------------------------------------------------------------------------+
     |                     Mobile Robot Programming Toolkit (MRPT)               |
     |                          https://www.mrpt.org/                            |
     |                                                                           |
     | Copyright (c) 2005-2022, Individual contributors, see AUTHORS file        |
     | See: https://www.mrpt.org/Authors - All rights reserved.                  |
     | Released under BSD License. See details in https://www.mrpt.org/License   |
     +---------------------------------------------------------------------------+ */
  #include "cs.h"
  /* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */
  static int cs_vcount (const cs *A, css *S)
  {
      int 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 (int)) ;        /* allocate pinv, */
      S->leftmost = leftmost = cs_malloc (m, sizeof (int)) ;  /* and leftmost */
      w = cs_malloc (m+3*n, sizeof (int)) ;   /* 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 (int order, const cs *A, int qr)
  {
      int 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] ;
          ok = ok && S->lnz >= 0 && S->unz >= 0 ;     /* int overflow guard */
          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 */
  }
  