NAME¶

PCUNMHR - 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 PCUNMHR(

SIDE, TRANS, M, N, ILO, IHI, A, IA, JA, DESCA, TAU, C, IC, JC, DESCC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS INTEGER IA, IC, IHI, ILO, INFO, JA, JC, LWORK, M, N INTEGER DESCA( * ), DESCC( * ) COMPLEX A( * ), C( * ), TAU( * ), WORK( * )

PURPOSE¶

PCUNMHR overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with 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 IHI-ILO elementary reflectors, as returned by PCGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-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¶

SIDE (global input) CHARACTER

= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.

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.

ILO (global input) INTEGER

IHI (global input) INTEGER ILO and IHI must have the same values as in the previous call of PCGEHRD. Q is equal to the unit matrix except in the distributed submatrix Q(ia+ilo:ia+ihi-1,ia+ilo:ja+ihi-1). If SIDE = 'L', 1 <= ILO <= IHI <= max(1,M); if SIDE = 'R', 1 <= ILO <= IHI <= max(1,N); ILO and IHI are relative indexes.

A (local input) COMPLEX pointer into the local memory

to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L', and (LLD_A,LOCc(JA+N-1)) if SIDE = 'R'. The vectors which define the elementary reflectors, as returned by PCGEHRD.

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+M-2)

if SIDE = 'L', and LOCc(JA+N-2) if SIDE = 'R'. This array contains the scalar factors TAU(j) of the elementary reflectors H(j) as returned by PCGEHRD. 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

IAA = IA + ILO; JAA = JA+ILO-1; If SIDE = 'L', MI = IHI-ILO; NI = N; ICC = IC + ILO; JCC = JC; LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + NB_A * NB_A else if SIDE = 'R', MI = M; NI = IHI-ILO; ICC = IC; JCC = JC + ILO; 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 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 )