Provided by: scalapack-doc_1.5-11_all bug

NAME

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

SYNOPSIS

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

           CHARACTER       SIDE, TRANS, VECT

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

           INTEGER         DESCA( * ), DESCC( * )

           COMPLEX*16      A( * ), C( * ), TAU( * ), WORK( * )

PURPOSE

       If VECT = 'Q', PZUNMBR overwrites the general complex distributed M-by-N matrix sub( C ) =
       C(IC:IC+M-1,JC:JC+N-1) with TRANS = 'C':      Q**H * sub( C )       sub( C ) * Q**H

       If VECT = 'P', PZUNMBR overwrites sub( C ) with

                            SIDE = 'L'           SIDE = 'R'
       TRANS = 'N':      P * sub( C )          sub( C ) * P
       TRANS = 'C':      P**H * sub( C )       sub( C ) * P**H

       Here Q and P**H are the unitary distributed matrices determined by PZGEBRD when reducing a
       complex distributed matrix A(IA:*,JA:*) to bidiagonal form: A(IA:*,JA:*) = Q * B * P**H. Q
       and P**H are defined as products of elementary reflectors H(i) and G(i) respectively.

       Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the  order  of  the  unitary
       matrix Q or P**H that is applied.

       If VECT = 'Q', A(IA:*,JA:*) is assumed to have been an NQ-by-K matrix:
       if nq >= k, Q = H(1) H(2) . . . H(k);
       if nq < k, Q = H(1) H(2) . . . H(nq-1).

       If VECT = 'P', A(IA:*,JA:*) is assumed to have been a K-by-NQ matrix:
       if k < nq, P = G(1) G(2) . . . G(k);
       if k >= nq, P = G(1) G(2) . . . G(nq-1).

       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

       VECT    (global input) CHARACTER
               = 'Q': apply Q or Q**H;
               = 'P': apply P or P**H.

       SIDE    (global input) CHARACTER
               = 'L': apply Q, Q**H, P or P**H from the Left;
               = 'R': apply Q, Q**H, P or P**H from the Right.

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

       K       (global input) INTEGER
               If VECT = 'Q', the number of columns in the original distributed matrix reduced by
               PZGEBRD.   If  VECT  =  'P', the number of rows in the original distributed matrix
               reduced by PZGEBRD.  K >= 0.

       A       (local input) COMPLEX*16 pointer into the local memory
               to  an  array  of  dimension   (LLD_A,LOCc(JA+MIN(NQ,K)-1))   if   VECT='Q',   and
               (LLD_A,LOCc(JA+NQ-1))  if  VECT = 'P'. NQ = M if SIDE = 'L', and NQ = N otherwise.
               The vectors which define the elementary reflectors H(i) and G(i),  whose  products
               determine  the  matrices Q and P, as returned by PZGEBRD.  If VECT = 'Q', LLD_A >=
               max(1,LOCr(IA+NQ-1)); if VECT = 'P', LLD_A >= max(1,LOCr(IA+MIN(NQ,K)-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*16 array, dimension
               LOCc(JA+MIN(NQ,K)-1) if VECT = 'Q', LOCr(IA+MIN(NQ,K)-1) if  VECT  =  'P',  TAU(i)
               must  contain  the  scalar factor of the elementary  reflector H(i) or G(i), which
               determines Q or P, as returned by PDGEBRD in its array argument TAUQ or TAUP.  TAU
               is tied to the distributed matrix A.

       C       (local input/local output) COMPLEX*16 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,  if  VECT='Q',  sub(  C  )  is
               overwritten by Q*sub( C ) or Q'*sub( C ) or sub( C )*Q' or sub( C )*Q; if VECT='P,
               sub( C ) is overwritten by P*sub( C ) or P'*sub( C ) or sub( C )*P or sub( C )*P'.

       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*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  If
               SIDE  =  'L',  NQ = M; if( (VECT = 'Q' and NQ >= K) or (VECT <> 'Q' and NQ > K) ),
               IAA=IA; JAA=JA; MI=M; NI=N; ICC=IC; JCC=JC; else IAA=IA+1; JAA=JA;  MI=M-1;  NI=N;
               ICC=IC+1;  JCC=JC; end if else if SIDE = 'R', NQ = N; if( (VECT = 'Q' and NQ >= K)
               or (VECT <> 'Q' and NQ > K) ), IAA=IA; JAA=JA; MI=M; NI=N;  ICC=IC;  JCC=JC;  else
               IAA=IA; JAA=JA+1; MI=M; NI=N-1; ICC=IC; JCC=JC+1; end if end if

               If  VECT = 'Q', 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( NI+ICOFFC, NB_A, 0, 0, NPCOL ), NB_A, 0, 0, LCMQ ), MpC0 )
               )*NB_A ) + NB_A * NB_A end if else if VECT <> 'Q', if SIDE = 'L',  LWORK  >=  MAX(
               (MB_A*(MB_A-1))/2,  (  MpC0  +  MAX( MqA0 + NUMROC( NUMROC( MI+IROFFC, MB_A, 0, 0,
               NPROW ), MB_A, 0, 0, LCMP ), NqC0 ) )*MB_A ) + MB_A * MB_A else  if  SIDE  =  'R',
               LWORK >= MAX( (MB_A*(MB_A-1))/2, (MpC0 + NqC0)*MB_A ) + MB_A * MB_A end if end if

               where LCMP = LCM / NPROW, 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 ), IACOL = INDXG2P( JAA, NB_A, MYCOL, CSRC_A, NPCOL  ),
               MqA0  =  NUMROC( MI+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), 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 ),

               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 VECT = 'Q',  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 ) else If
               SIDE = 'L', ( MB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC ) If SIDE = 'R', (  NB_A.EQ.NB_C
               .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL ) end if