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NAME

       PDORMQR   -   overwrite   the   general   real  M-by-N  distributed  matrix  sub(  C  )  =
       C(IC:IC+M-1,JC:JC+N-1) with   SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

       SUBROUTINE PDORMQR( SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, C, IC, JC,  DESCC,  WORK,
                           LWORK, INFO )

           CHARACTER       SIDE, TRANS

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

           INTEGER         DESCA( * ), DESCC( * )

           DOUBLE          PRECISION A( * ), C( * ), TAU( * ), WORK( * )

PURPOSE

       PDORMQR   overwrites   the   general   real   M-by-N   distributed   matrix  sub(  C  )  =
       C(IC:IC+M-1,JC:JC+N-1) with TRANS = 'T':      Q**T * sub( C )       sub( C ) * Q**T

       where Q is a real orthogonal distributed matrix defined as the  product  of  k  elementary
       reflectors

             Q = H(1) H(2) . . . H(k)

       as returned by PDGEQRF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

       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

       SIDE    (global input) CHARACTER
               = 'L': apply Q or Q**T from the Left;
               = 'R': apply Q or Q**T from the Right.

       TRANS   (global input) CHARACTER
               = 'N':  No transpose, apply Q;
               = 'T':  Transpose, apply Q**T.

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

       K       (global input) INTEGER
               The number of elementary reflectors whose product defines the matrix Q.  If SIDE =
               'L', M >= K >= 0, if SIDE = 'R', N >= K >= 0.

       A       (local input) DOUBLE PRECISION pointer into the local memory
               to  an  array  of  dimension  (LLD_A,LOCc(JA+K-1)). On entry, the j-th column must
               contain the vector which defines the elemen- tary  reflector  H(j),  JA  <=  j  <=
               JA+K-1, as returned by PDGEQRF in the K columns of its distributed matrix argument
               A(IA:*,JA:JA+K-1). A(IA:*,JA:JA+K-1) is modified by the routine  but  restored  on
               exit.   If  SIDE  =  'L', LLD_A >= MAX( 1, LOCr(IA+M-1) ); if SIDE = 'R', LLD_A >=
               MAX( 1, LOCr(IA+N-1) ).

       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) DOUBLE PRECISION, array, dimension LOCc(JA+K-1).
               This array contains the scalar factors TAU(j) of the elementary reflectors H(j) as
               returned by PDGEQRF.  TAU is tied to the distributed matrix A.

       C       (local input/local output) DOUBLE PRECISION pointer into the
               local  memory  to an array of dimension (LLD_C,LOCc(JC+N-1)).  On entry, the local
               pieces of the distributed matrix sub(C).  On exit, sub(  C  )  is  overwritten  by
               Q*sub( C ) or Q'*sub( C ) or sub( C )*Q' or sub( C )*Q.

       IC      (global input) INTEGER
               The row index in the global array C indicating the first row of sub( C ).

       JC      (global input) INTEGER
               The column index in the global array C indicating the first column of sub( C ).

       DESCC   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix C.

       WORK    (local workspace/local output) DOUBLE PRECISION 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 If
               SIDE = 'L', LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) +  NB_A  *  NB_A
               else  if SIDE = 'R', LWORK >= MAX( (NB_A*(NB_A-1))/2, ( NqC0 + MAX( NpA0 + NUMROC(
               NUMROC( N+ICOFFC, NB_A, 0, 0, NPCOL ), NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) +  NB_A
               * NB_A end if

               where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),

               IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IAROW = INDXG2P( IA, MB_A,
               MYROW, RSRC_A, NPROW ), NpA0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ),

               IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ), ICROW = INDXG2P( IC, MB_C,
               MYROW,  RSRC_C, NPROW ), ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ), MpC0 =
               NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ),  NqC0  =  NUMROC(  N+ICOFFC,  NB_C,
               MYCOL, ICCOL, NPCOL ),

               ILCM,  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.

               Alignment requirements ======================

               The  distributed  submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1) must verify
               some alignment properties, namely the following expressions should be true:

               If SIDE = 'L', ( MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC  .AND.  IAROW.EQ.ICROW  )  If
               SIDE = 'R', ( MB_A.EQ.NB_C .AND. IROFFA.EQ.ICOFFC )