/* ========================================================================== */
  /* === umfpack_qsymbolic ==================================================== */
  /* ========================================================================== */
  
  /* -------------------------------------------------------------------------- */
  /* UMFPACK Copyright (c) Timothy A. Davis, CISE,                              */
  /* Univ. of Florida.  All Rights Reserved.  See ../Doc/License for License.   */
  /* web: http://www.cise.ufl.edu/research/sparse/umfpack                       */
  /* -------------------------------------------------------------------------- */
  
  int umfpack_di_qsymbolic
  (
      int n_row,
      int n_col,
      const int Ap [ ],
      const int Ai [ ],
      const double Ax [ ],
      const int Qinit [ ],
      void **Symbolic,
      const double Control [UMFPACK_CONTROL],
      double Info [UMFPACK_INFO]
  ) ;
  
  UF_long umfpack_dl_qsymbolic
  (
      UF_long n_row,
      UF_long n_col,
      const UF_long Ap [ ],
      const UF_long Ai [ ],
      const double Ax [ ],
      const UF_long Qinit [ ],
      void **Symbolic,
      const double Control [UMFPACK_CONTROL],
      double Info [UMFPACK_INFO]
  ) ;
  
  int umfpack_zi_qsymbolic
  (
      int n_row,
      int n_col,
      const int Ap [ ],
      const int Ai [ ],
      const double Ax [ ], const double Az [ ],
      const int Qinit [ ],
      void **Symbolic,
      const double Control [UMFPACK_CONTROL],
      double Info [UMFPACK_INFO]
  ) ;
  
  UF_long umfpack_zl_qsymbolic
  (
      UF_long n_row,
      UF_long n_col,
      const UF_long Ap [ ],
      const UF_long Ai [ ],
      const double Ax [ ], const double Az [ ],
      const UF_long Qinit [ ],
      void **Symbolic,
      const double Control [UMFPACK_CONTROL],
      double Info [UMFPACK_INFO]
  ) ;
  
  /*
  double int Syntax:
  
      #include "umfpack.h"
      void *Symbolic ;
      int n_row, n_col, *Ap, *Ai, *Qinit, status ;
      double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
      status = umfpack_di_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit,
  	&Symbolic, Control, Info) ;
  
  double UF_long Syntax:
  
      #include "umfpack.h"
      void *Symbolic ;
      UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ;
      double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
      status = umfpack_dl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit,
  	&Symbolic, Control, Info) ;
  
  complex int Syntax:
  
      #include "umfpack.h"
      void *Symbolic ;
      int n_row, n_col, *Ap, *Ai, *Qinit, status ;
      double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
      status = umfpack_zi_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit,
  	&Symbolic, Control, Info) ;
  
  complex UF_long Syntax:
  
      #include "umfpack.h"
      void *Symbolic ;
      UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ;
      double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
      status = umfpack_zl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit,
  	&Symbolic, Control, Info) ;
  
  packed complex Syntax:
  
      Same as above, except Az is NULL.
  
  Purpose:
  
      Given the nonzero pattern of a sparse matrix A in column-oriented form, and
      a sparsity preserving column pre-ordering Qinit, umfpack_*_qsymbolic
      performs the symbolic factorization of A*Qinit (or A (:,Qinit) in MATLAB
      notation).  This is identical to umfpack_*_symbolic, except that neither
      COLAMD nor AMD are called and the user input column order Qinit is used
      instead.  Note that in general, the Qinit passed to umfpack_*_qsymbolic
      can differ from the final Q found in umfpack_*_numeric.  The unsymmetric
      strategy will perform a column etree postordering done in
      umfpack_*_qsymbolic and sparsity-preserving modifications are made within
      each frontal matrix during umfpack_*_numeric.  The symmetric and 2-by-2
      strategies will preserve Qinit, unless the matrix is structurally singular.
  
      See umfpack_*_symbolic for more information.
  
      *** WARNING ***  A poor choice of Qinit can easily cause umfpack_*_numeric
      to use a huge amount of memory and do a lot of work.  The "default" symbolic
      analysis method is umfpack_*_symbolic, not this routine.  If you use this
      routine, the performance of UMFPACK is your responsibility;  UMFPACK will
      not try to second-guess a poor choice of Qinit.
  
  Returns:
  
      The value of Info [UMFPACK_STATUS]; see umfpack_*_symbolic.
      Also returns UMFPACK_ERROR_invalid_permuation if Qinit is not a valid
      permutation vector.
  
  Arguments:
  
      All arguments are the same as umfpack_*_symbolic, except for the following:
  
      Int Qinit [n_col] ;		Input argument, not modified.
  
  	The user's fill-reducing initial column pre-ordering.  This must be a
  	permutation of 0..n_col-1.  If Qinit [k] = j, then column j is the kth
  	column of the matrix A (:,Qinit) to be factorized.  If Qinit is an
  	(Int *) NULL pointer, then COLAMD or AMD are called instead.
  
      double Control [UMFPACK_CONTROL] ;	Input argument, not modified.
  
  	If Qinit is not NULL, then only two strategies are recognized:
  	the unsymmetric strategy and the symmetric strategy.
  	If Control [UMFPACK_STRATEGY] is UMFPACK_STRATEGY_SYMMETRIC,
  	then the symmetric strategy is used.  Otherwise the unsymmetric
  	strategy is used.
  */