PCUNMBR(3) ScaLAPACK routine of NEC Numeric Library Collection PCUNMBR(3)
NAME
PCUNMBR - VECT = 'Q', PCUNMBR overwrites the general complex dis-
tributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE =
'L' SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE PCUNMBR( 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 A( * ), C( * ), TAU( * ), WORK( * )
PURPOSE
If VECT = 'Q', PCUNMBR 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': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C
) sub( C ) * Q**H
If VECT = 'P', PCUNMBR 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
PCGEBRD 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 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
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 dis-
tributed matrix reduced by PCGEBRD. If VECT = 'P', the number
of rows in the original distributed matrix reduced by PCGEBRD.
K >= 0.
A (local input) COMPLEX 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 PCGEBRD. 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 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 ele-
mentary 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 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 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
ScaLAPACK routine 31 October 2017 PCUNMBR(3)