..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix
  sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper triangular form by means
  of unitary transformations.
  The upper trapezoidal matrix sub( A ) is factored as
     sub( A ) = ( R  0 ) * Z,
  where Z is an N-by-N unitary matrix and R is an M-by-M upper
  triangular matrix.
  Notes
  =====
  Each global data object is described by an associated description
  vector.  This vector stores the information required to establish
  the mapping between an object element and its corresponding process
  and memory location.
  Let A be a generic term for any 2D block cyclicly distributed array.
  Such a global array has an associated description vector DESCA.
  In the following comments, the character _ should be read as
  "of the global array".
  NOTATION        STORED IN      EXPLANATION
  --------------- -------------- --------------------------------------
  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                                 DTYPE_A = 1.
  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                                 the BLACS process grid A is distribu-
                                 ted over. The context itself is glo-
                                 bal, but the handle (the integer
                                 value) may vary.
  M_A    (global) DESCA( M_ )    The number of rows in the global
                                 array A.
  N_A    (global) DESCA( N_ )    The number of columns in the global
                                 array A.
  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                                 the rows of the array.
  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                                 the columns of the array.
  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                                 row of the array A is distributed.
  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                                 first column of the array A is
                                 distributed.
  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
  Let K be the number of rows or columns of a distributed matrix,
  and assume that its process grid has dimension p x q.
  LOCr( K ) denotes the number of elements of K that a process
  would receive if K were distributed over the p processes of its
  process column.
  Similarly, LOCc( K ) denotes the number of elements of K that a
  process would receive if K were distributed over the q processes of
  its process row.
  The values of LOCr() and LOCc() may be determined via a call to the
  ScaLAPACK tool function, NUMROC:
          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
  An upper bound for these quantities may be computed by:
          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
  Arguments
  =========
  M       (global input) INTEGER
          The number of rows to be operated on, i.e. the number of rows
          of the distributed submatrix sub( A ). M >= 0.
  N       (global input) INTEGER
          The number of columns to be operated on, i.e. the number of
          columns of the distributed submatrix sub( A ). N >= 0.
  A       (local input/local output) COMPLEX*16 pointer into the
          local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
          On entry, the local pieces of the M-by-N distributed matrix
          sub( A ) which is to be factored. On exit, the leading M-by-M
          upper triangular part of sub( A ) contains the upper trian-
          gular matrix R, and elements M+1 to N of the first M rows of
          sub( A ), with the array TAU, represent the unitary matrix Z
          as a product of M elementary reflectors.
  IA      (global input) INTEGER
          The row index in the global array A indicating the first
          row of sub( A ).
  JA      (global input) INTEGER
          The column index in the global array A indicating the
          first column of sub( A ).
  DESCA   (global and local input) INTEGER array of dimension DLEN_.
          The array descriptor for the distributed matrix A.
  TAU     (local output) COMPLEX*16, array, dimension LOCr(IA+M-1)
          This array contains the scalar factors of the elementary
          reflectors. TAU is tied to the distributed matrix A.
  WORK    (local workspace/local output) COMPLEX*16 array,
                                                    dimension (LWORK)
          On exit, WORK(1) returns the minimal and optimal LWORK.
  LWORK   (local or global input) INTEGER
          The dimension of the array WORK.
          LWORK is local input and must be at least
          LWORK >= MB_A * ( Mp0 + Nq0 + MB_A ), where
          IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ),
          IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
          IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
          Mp0   = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ),
          Nq0   = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ),
          and NUMROC, INDXG2P are ScaLAPACK tool functions;
          MYROW, MYCOL, NPROW and NPCOL can be determined by calling
          the subroutine BLACS_GRIDINFO.
          If LWORK = -1, then LWORK is global input and a workspace
          query is assumed; the routine only calculates the minimum
          and optimal size for all work arrays. Each of these
          values is returned in the first entry of the corresponding
          work array, and no error message is issued by PXERBLA.
  INFO    (global output) INTEGER
          = 0:  successful exit
          < 0:  If the i-th argument is an array and the j-entry had
                an illegal value, then INFO = -(i*100+j), if the i-th
                argument is a scalar and had an illegal value, then
                INFO = -i.
  Further Details
  ===============
  The  factorization is obtained by Householder's method.  The kth
  transformation matrix, Z( k ), whose conjugate transpose is used to
  introduce zeros into the (m - k + 1)th row of sub( A ), is given in
  the form
     Z( k ) = ( I     0   ),
              ( 0  T( k ) )
  where
     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
                                                 (   0    )
                                                 ( z( k ) )
  tau is a scalar and z( k ) is an ( n - m ) element vector.
  tau and z( k ) are chosen to annihilate the elements of the kth row
  of sub( A ).
  The scalar tau is returned in the kth element of TAU and the vector
  u( k ) in the kth row of sub( A ), such that the elements of z( k )
  are in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned
  in the upper triangular part of sub( A ).
  Z is given by
     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
  =====================================================================
     .. Parameters ..