..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PSGGRQF computes a generalized RQ factorization of
  an M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1)
  and a P-by-N matrix sub( B ) = B(IB:IB+P-1,JB:JB+N-1):
              sub( A ) = R*Q,        sub( B ) = Z*T*Q,
  where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
  matrix, and R and T assume one of the forms:
  if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N,
                   N-M  M                           ( R21 ) N
                                                       N
  where R12 or R21 is upper triangular, and
  if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P,
                  (  0  ) P-N                         P   N-P
                     N
  where T11 is upper triangular.
  In particular, if sub( B ) is square and nonsingular, the GRQ
  factorization of sub( A ) and sub( B ) implicitly gives the RQ
  factorization of sub( A )*inv( sub( B ) ):
               sub( A )*inv( sub( B ) ) = (R*inv(T))*Z'
  where inv( sub( B ) ) denotes the inverse of the matrix sub( B ),
  and Z' denotes the transpose of matrix Z.
  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.
  P       (global input) INTEGER
          The number of rows to be operated on i.e the number of
          rows of the distributed submatrix sub( B ).  P >= 0.
  N       (global input) INTEGER
          The number of columns to be operated on i.e the number of
          columns of the distributed submatrices sub( A ) and sub( B ).
          N >= 0.
  A       (local input/local output) REAL 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, if M <= N, the
          upper triangle of A( IA:IA+M-1, JA+N-M:JA+N-1 ) contains the
          M by M upper triangular matrix R; if M >= N, the elements on
          and above the (M-N)-th subdiagonal contain the M by N upper
          trapezoidal matrix R; the remaining elements, with the array
          TAUA, represent the orthogonal matrix Q as a product of
          elementary reflectors (see Further Details).
  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.
  TAUA    (local output) REAL, array, dimension LOCr(IA+M-1)
          This array contains the scalar factors of the elementary
          reflectors which represent the orthogonal unitary matrix Q.
          TAUA is tied to the distributed matrix A (see Further
          Details).
  B       (local input/local output) REAL pointer into the
          local memory to an array of dimension (LLD_B, LOCc(JB+N-1)).
          On entry, the local pieces of the P-by-N distributed matrix
          sub( B ) which is to be factored.  On exit, the elements on
          and above the diagonal of sub( B ) contain the min(P,N) by N
          upper trapezoidal matrix T (T is upper triangular if P >= N);
          the elements below the diagonal, with the array TAUB,
          represent the orthogonal matrix Z as a product of elementary
          reflectors (see Further Details).
  IB      (global input) INTEGER
          The row index in the global array B indicating the first
          row of sub( B ).
  JB      (global input) INTEGER
          The column index in the global array B indicating the
          first column of sub( B ).
  DESCB   (global and local input) INTEGER array of dimension DLEN_.
          The array descriptor for the distributed matrix B.
  TAUB    (local output) REAL, array, dimension
          LOCc(JB+MIN(P,N)-1). This array contains the scalar factors
          TAUB of the elementary reflectors which represent the
          orthogonal matrix Z. TAUB is tied to the distributed matrix
          B (see Further Details).
  WORK    (local workspace/local output) REAL 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 >= MAX( MB_A * ( MpA0 + NqA0 + MB_A ),
                        MAX( (MB_A*(MB_A-1))/2, (PpB0 + NqB0)*MB_A ) +
                             MB_A * MB_A,
                        NB_B * ( PpB0 + NqB0 + NB_B ) ), where
          IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
          IAROW  = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
          IACOL  = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
          MpA0   = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
          NqA0   = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
          IROFFB = MOD( IB-1, MB_B ), ICOFFB = MOD( JB-1, NB_B ),
          IBROW  = INDXG2P( IB, MB_B, MYROW, RSRC_B, NPROW ),
          IBCOL  = INDXG2P( JB, NB_B, MYCOL, CSRC_B, NPCOL ),
          PpB0   = NUMROC( P+IROFFB, MB_B, MYROW, IBROW, NPROW ),
          NqB0   = NUMROC( N+ICOFFB, NB_B, MYCOL, IBCOL, 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 matrix Q is represented as a product of elementary reflectors
     Q = H(ia) H(ia+1) . . . H(ia+k-1), where k = min(m,n).
  Each H(i) has the form
     H(i) = I - taua * v * v'
  where taua is a real scalar, and v is a real vector with
  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
  A(ia+m-k+i-1,ja:ja+n-k+i-2), and taua in TAUA(ia+m-k+i-1).
  To form Q explicitly, use ScaLAPACK subroutine PSORGRQ.
  To use Q to update another matrix, use ScaLAPACK subroutine PSORMRQ.
  The matrix Z is represented as a product of elementary reflectors
     Z = H(jb) H(jb+1) . . . H(jb+k-1), where k = min(p,n).
  Each H(i) has the form
     H(i) = I - taub * v * v'
  where taub is a real scalar, and v is a real vector with
  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in
  B(ib+i:ib+p-1,jb+i-1), and taub in TAUB(jb+i-1).
  To form Z explicitly, use ScaLAPACK subroutine PSORGQR.
  To use Z to update another matrix, use ScaLAPACK subroutine PSORMQR.
  Alignment requirements
  ======================
  The distributed submatrices sub( A ) and sub( B ) must verify some
  alignment properties, namely the following expression should be true:
  ( NB_A.EQ.NB_B .AND. ICOFFA.EQ.ICOFFB .AND. IACOL.EQ.IBCOL )
  =====================================================================
     .. Parameters ..