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NAME

       PSORGRQ  -  generate  an  M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1)
       with orthonormal rows, which is defined as the last M rows of a product  of  K  elementary
       reflectors of order N   Q = H(1) H(2)

SYNOPSIS

       SUBROUTINE PSORGRQ( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, INFO )

           INTEGER         IA, INFO, JA, K, LWORK, M, N

           INTEGER         DESCA( * )

           REAL            A( * ), TAU( * ), WORK( * )

PURPOSE

       PSORGRQ generates an M-by-N real distributed matrix Q denoting A(IA:IA+M-1,JA:JA+N-1) with
       orthonormal rows, which is defined as the last  M  rows  of  a  product  of  K  elementary
       reflectors of order N

       as returned by PSGERQF.

       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 Q. M >= 0.

       N       (global input) INTEGER
               The  number  of  columns  to  be  operated  on  i.e  the  number of columns of the
               distributed submatrix Q.  N >= M >= 0.

       K       (global input) INTEGER
               The number of elementary reflectors whose product defines the matrix Q. M >= K  >=
               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 i-th
               row must contain the vector which defines the elementary reflector H(i), IA+M-K <=
               i  <=  IA+M-1,  as  returned  by  PSGERQF  in the K rows of its distributed matrix
               argument A(IA+M-K:IA+M-1,JA:*). On exit, this array contains the local  pieces  of
               the M-by-N distributed matrix Q.

       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 input) REAL, array, dimension LOCr(IA+M-1)
               This array contains the scalar factors TAU(i) of the elementary reflectors H(i) as
               returned by PSGERQF.  TAU is tied to the distributed matrix A.

       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
               >= MB_A * ( MpA0 + NqA0 + MB_A ), 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 ),

               INDXG2P and NUMROC 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.