PCUNMTR(3)    ScaLAPACK routine of NEC Numeric Library Collection   PCUNMTR(3)



NAME
       PCUNMTR  - overwrite the general complex 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 PCUNMTR( SIDE, UPLO, TRANS, M, N, A, IA, JA, DESCA, TAU,  C,
                           IC, JC, DESCC, WORK, LWORK, INFO )

           CHARACTER       SIDE, TRANS, UPLO

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

           INTEGER         DESCA( * ), DESCC( * )

           COMPLEX         A( * ), C( * ), TAU( * ), WORK( * )

PURPOSE
       PCUNMTR overwrites the general complex M-by-N distributed matrix sub( C
       ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q  *
       sub(  C ) sub( C ) * Q TRANS = 'C':      Q**H * sub( C )       sub( C )
       * Q**H

       where Q is a complex unitary distributed matrix of order nq, with nq  =
       m  if  SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product
       of nq-1 elementary reflectors, as returned by PCHETRD:

       if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

       if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).


       Notes
       =====

       Each global data object is described by an associated description  vec-
       tor.  This vector stores the information required to establish the map-
       ping 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 col-
       umn.
       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**H from the Left;
               = 'R': apply Q or Q**H from the Right.

       UPLO    (global input) CHARACTER
               = 'U':  Upper  triangle  of  A(IA:*,JA:*)  contains  elementary
               reflectors  from PCHETRD; = 'L': Lower triangle of A(IA:*,JA:*)
               contains elementary reflectors from PCHETRD.

       TRANS   (global input) CHARACTER
               = 'N':  No transpose, apply Q;
               = 'C':  Conjugate transpose, apply Q**H.

       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.

       A       (local input) COMPLEX pointer into the local memory
               to an array of dimension (LLD_A,LOCc(JA+M-1)) if  SIDE='L',  or
               (LLD_A,LOCc(JA+N-1))  if  SIDE  = 'R'. The vectors which define
               the elementary reflectors, as returned by PCHETRD.  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) COMPLEX array, dimension LTAU, where
               if SIDE = 'L' and UPLO = 'U', LTAU = LOCc(M_A), if SIDE  =  'L'
               and  UPLO  = 'L', LTAU = LOCc(JA+M-2), if SIDE = 'R' and UPLO =
               'U', LTAU = LOCc(N_A), if SIDE = 'R' and UPLO  =  'L',  LTAU  =
               LOCc(JA+N-2).   TAU(i)  must  contain  the scalar factor of the
               elementary reflector H(i), as returned by PCHETRD. TAU is  tied
               to the distributed matrix A.

       C       (local input/local output) COMPLEX 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) COMPLEX 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 UPLO = 'U', IAA = IA, JAA = JA+1, ICC = IC, JCC =  JC;  else
               UPLO  =  'L',  IAA = IA+1, JAA = JA; if SIDE = 'L', ICC = IC+1;
               JCC = JC; else ICC = IC; JCC = JC+1; end if end if

               If  SIDE  =  'L',  MI  =  M-1;  NI   =   N;   LWORK   >=   MAX(
               (NB_A*(NB_A-1))/2,  (NqC0  + MpC0)*NB_A ) + NB_A * NB_A else if
               SIDE = 'R', MI = M; MI = N-1; LWORK >= MAX(  (NB_A*(NB_A-1))/2,
               (  NqC0  +  MAX(  NpA0 + NUMROC( NUMROC( NI+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( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ), IAROW
               = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ),  NpA0  =  NUMROC(
               NI+IROFFA, MB_A, MYROW, IAROW, NPROW ),

               IROFFC = MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ), ICROW
               = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ), ICCOL =  INDXG2P(
               JCC,  NB_C,  MYCOL,  CSRC_C, NPCOL ), MpC0 = NUMROC( MI+IROFFC,
               MB_C, MYROW, ICROW, NPROW ), NqC0 =  NUMROC(  NI+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 subrou-
               tine 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 )



ScaLAPACK routine               31 October 2017                     PCUNMTR(3)