SUBROUTINE PDORMRZ( SIDE, TRANS, M, N, K, L, A, IA, JA, DESCA,
$ TAU, C, IC, JC, DESCC, WORK, LWORK, INFO )
*
* -- ScaLAPACK routine (version 1.5) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER IA, IC, INFO, JA, JC, K, L, LWORK, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCC( * )
DOUBLE PRECISION A( * ), C( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PDORMRZ overwrites 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': Q * sub( C ) sub( C ) * Q
* 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 PDTZRZF. 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.
*
* L (global input) INTEGER
* The columns of the distributed submatrix sub( A ) containing
* the meaningful part of the Householder reflectors.
* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*
* A (local input) DOUBLE PRECISION 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', where
* LLD_A >= MAX(1,LOCr(IA+K-1)); On entry, the i-th row must
* contain the vector which defines the elementary reflector
* H(i), IA <= i <= IA+K-1, as returned by PDTZRZF in the
* K rows of its distributed matrix argument A(IA:IA+K-1,JA:*).
* A(IA:IA+K-1,JA:*) is modified by the routine but restored on
* exit.
*
* 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(IA+K-1).
* This array contains the scalar factors TAU(i) of the
* elementary reflectors H(i) as returned by PDTZRZF.
* 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( (MB_A*(MB_A-1))/2, ( MpC0 + MAX( MqA0 +
* NUMROC( NUMROC( M+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
*
* where LCMP = LCM / NPROW with LCM = ICLM( NPROW, NPCOL ),
*
* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
* MqA0 = NUMROC( M+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
*
* 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',
* ( NB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC )
* If SIDE = 'R',
* ( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL )
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
* ..
* .. Local Scalars ..
LOGICAL LEFT, LQUERY, NOTRAN
CHARACTER COLBTOP, ROWBTOP, TRANST
INTEGER I, I1, I2, I3, IACOL, IB, ICC, ICCOL, ICOFFA,
$ ICOFFC, ICROW, ICTXT, IINFO, IPW, IROFFC, JAA,
$ JCC, LCM, LCMP, LWMIN, MI, MPC0, MQA0, MYCOL,
$ MYROW, NI, NPCOL, NPROW, NQ, NQC0
* ..
* .. Local Arrays ..
INTEGER IDUM1( 5 ), IDUM2( 5 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PDLARZB,
$ PDLARZT, PDORMR3, PTOPGET, PTOPSET, PXERBLA
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ILCM, INDXG2P, NUMROC
EXTERNAL ICEIL, ILCM, INDXG2P, LSAME, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, ICHAR, MAX, MIN, MOD
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test the input parameters
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -(900+CTXT_)
ELSE
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
*
* NQ is the order of Q
*
IF( LEFT ) THEN
NQ = M
CALL CHK1MAT( K, 5, M, 3, IA, JA, DESCA, 10, INFO )
ELSE
NQ = N
CALL CHK1MAT( K, 5, N, 4, IA, JA, DESCA, 10, INFO )
END IF
CALL CHK1MAT( M, 3, N, 4, IC, JC, DESCC, 15, INFO )
IF( INFO.EQ.0 ) THEN
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
IROFFC = MOD( IC-1, DESCC( MB_ ) )
ICOFFC = MOD( JC-1, DESCC( NB_ ) )
IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL )
ICROW = INDXG2P( IC, DESCC( MB_ ), MYROW, DESCC( RSRC_ ),
$ NPROW )
ICCOL = INDXG2P( JC, DESCC( NB_ ), MYCOL, DESCC( CSRC_ ),
$ NPCOL )
MPC0 = NUMROC( M+IROFFC, DESCC( MB_ ), MYROW, ICROW, NPROW )
NQC0 = NUMROC( N+ICOFFC, DESCC( NB_ ), MYCOL, ICCOL, NPCOL )
*
IF( LEFT ) THEN
MQA0 = NUMROC( M+ICOFFA, DESCA( NB_ ), MYCOL, IACOL,
$ NPCOL )
LCM = ILCM( NPROW, NPCOL )
LCMP = LCM / NPROW
LWMIN = MAX( ( DESCA( MB_ ) * ( DESCA( MB_ ) - 1 ) )
$ / 2, ( MPC0 + MAX( MQA0 + NUMROC( NUMROC(
$ M+IROFFC, DESCA( MB_ ), 0, 0, NPROW ),
$ DESCA( MB_ ), 0, 0, LCMP ), NQC0 ) ) *
$ DESCA( MB_ ) ) + DESCA( MB_ ) * DESCA( MB_ )
ELSE
LWMIN = MAX( ( DESCA( MB_ ) * ( DESCA( MB_ ) - 1 ) ) / 2,
$ ( MPC0 + NQC0 ) * DESCA( MB_ ) ) +
$ DESCA( MB_ ) * DESCA( MB_ )
END IF
*
WORK( 1 ) = DBLE( LWMIN )
LQUERY = ( LWORK.EQ.-1 )
IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
INFO = -2
ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
INFO = -5
ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
INFO = -6
ELSE IF( LEFT .AND. DESCA( NB_ ).NE.DESCC( MB_ ) ) THEN
INFO = -(1000+NB_)
ELSE IF( LEFT .AND. ICOFFA.NE.IROFFC ) THEN
INFO = -13
ELSE IF( .NOT.LEFT .AND. ICOFFA.NE.ICOFFC ) THEN
INFO = -14
ELSE IF( .NOT.LEFT .AND. IACOL.NE.ICCOL ) THEN
INFO = -14
ELSE IF( .NOT.LEFT .AND. DESCA( NB_ ).NE.DESCC( NB_ ) ) THEN
INFO = -(1500+NB_)
ELSE IF( ICTXT.NE.DESCC( CTXT_ ) ) THEN
INFO = -(1500+CTXT_)
ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -17
END IF
END IF
IF( LEFT ) THEN
IDUM1( 1 ) = ICHAR( 'L' )
ELSE
IDUM1( 1 ) = ICHAR( 'R' )
END IF
IDUM2( 1 ) = 1
IF( NOTRAN ) THEN
IDUM1( 2 ) = ICHAR( 'N' )
ELSE
IDUM1( 2 ) = ICHAR( 'T' )
END IF
IDUM2( 2 ) = 2
IDUM1( 3 ) = K
IDUM2( 3 ) = 5
IDUM1( 4 ) = L
IDUM2( 4 ) = 6
IF( LWORK.EQ.-1 ) THEN
IDUM1( 5 ) = -1
ELSE
IDUM1( 5 ) = 1
END IF
IDUM2( 5 ) = 17
IF( LEFT ) THEN
CALL PCHK2MAT( K, 5, M, 3, IA, JA, DESCA, 10, M, 3, N, 4,
$ IC, JC, DESCC, 15, 5, IDUM1, IDUM2, INFO )
ELSE
CALL PCHK2MAT( K, 5, N, 4, IA, JA, DESCA, 10, M, 3, N, 4,
$ IC, JC, DESCC, 15, 5, IDUM1, IDUM2, INFO )
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PDORMRZ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
$ RETURN
*
CALL PTOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
*
IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
I1 = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 )
$ + 1
I2 = IA + K - 1
I3 = DESCA( MB_ )
ELSE
I1 = MAX( ( (IA+K-2) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA )
I2 = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 )
$ + 1
I3 = -DESCA( MB_ )
END IF
*
IF( LEFT ) THEN
NI = N
JCC = JC
JAA = JA + M - L
ELSE
MI = M
ICC = IC
JAA = JA + N - L
CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' )
IF( NOTRAN ) THEN
CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' )
ELSE
CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', 'D-ring' )
END IF
END IF
*
IF( NOTRAN ) THEN
TRANST = 'T'
ELSE
TRANST = 'N'
END IF
*
IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
IB = I1 - IA
IF( LEFT ) THEN
MI = M
ELSE
NI = N
END IF
CALL PDORMR3( SIDE, TRANS, MI, NI, IB, L, A, IA, JA, DESCA,
$ TAU, C, IC, JC, DESCC, WORK, LWORK, IINFO )
END IF
*
IPW = DESCA( MB_ )*DESCA( MB_ ) + 1
DO 10 I = I1, I2, I3
IB = MIN( DESCA( MB_ ), K-I+IA )
*
* Form the triangular factor of the block reflector
* H = H(i+ib-1) . . . H(i+1) H(i)
*
CALL PDLARZT( 'Backward', 'Rowwise', L, IB, A, I, JAA, DESCA,
$ TAU, WORK, WORK( IPW ) )
IF( LEFT ) THEN
*
* H or H' is applied to C(ic+i-ia:ic+m-1,jc:jc+n-1)
*
MI = M - I + IA
ICC = IC + I - IA
ELSE
*
* H or H' is applied to C(ic:ic+m-1,jc+i-ia:jc+n-1)
*
NI = N - I + IA
JCC = JC + I - IA
END IF
*
* Apply H or H'
*
CALL PDLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, IB,
$ L, A, I, JAA, DESCA, WORK, C, ICC, JCC, DESCC,
$ WORK( IPW ) )
10 CONTINUE
*
IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
IB = I2 - IA
IF( LEFT ) THEN
MI = M
ELSE
NI = N
END IF
CALL PDORMR3( SIDE, TRANS, MI, NI, IB, L, A, IA, JA, DESCA,
$ TAU, C, IC, JC, DESCC, WORK, LWORK, IINFO )
END IF
*
CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
*
WORK( 1 ) = DBLE( LWMIN )
*
RETURN
*
* End of PDORMRZ
*
END