SUBROUTINE PCLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, IV, $ JV, DESCV, T, C, IC, JC, DESCC, WORK ) * * -- ScaLAPACK auxiliary routine (version 2.0.2) -- * Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver * May 1 2012 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, DIRECT, STOREV INTEGER IC, IV, JC, JV, K, M, N * .. * .. Array Arguments .. INTEGER DESCC( * ), DESCV( * ) COMPLEX C( * ), T( * ), V( * ), WORK( * ) * .. * * Purpose * ======= * * PCLARFB applies a complex block reflector Q or its conjugate * transpose Q**H to a complex M-by-N distributed matrix sub( C ) * denoting C(IC:IC+M-1,JC:JC+N-1), from the left or the right. * * 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. * * DIRECT (global input) CHARACTER * Indicates how Q is formed from a product of elementary * reflectors * = 'F': Q = H(1) H(2) . . . H(k) (Forward) * = 'B': Q = H(k) . . . H(2) H(1) (Backward) * * STOREV (global input) CHARACTER * Indicates how the vectors which define the elementary * reflectors are stored: * = 'C': Columnwise * = 'R': Rowwise * * 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 order of the matrix T (= the number of elementary * reflectors whose product defines the block reflector). * * V (local input) COMPLEX pointer into the local memory * to an array of dimension ( LLD_V, LOCc(JV+K-1) ) if * STOREV = 'C', ( LLD_V, LOCc(JV+M-1)) if STOREV = 'R' and * SIDE = 'L', ( LLD_V, LOCc(JV+N-1) ) if STOREV = 'R' and * SIDE = 'R'. It contains the local pieces of the distributed * vectors V representing the Householder transformation. * See further details. * If STOREV = 'C' and SIDE = 'L', LLD_V >= MAX(1,LOCr(IV+M-1)); * if STOREV = 'C' and SIDE = 'R', LLD_V >= MAX(1,LOCr(IV+N-1)); * if STOREV = 'R', LLD_V >= LOCr(IV+K-1). * * IV (global input) INTEGER * The row index in the global array V indicating the first * row of sub( V ). * * JV (global input) INTEGER * The column index in the global array V indicating the * first column of sub( V ). * * DESCV (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix V. * * T (local input) COMPLEX array, dimension MB_V by MB_V * if STOREV = 'R' and NB_V by NB_V if STOREV = 'C'. The trian- * gular matrix T in the representation of the block reflector. * * 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 M-by-N 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) COMPLEX array, dimension (LWORK) * If STOREV = 'C', * if SIDE = 'L', * LWORK >= ( NqC0 + MpC0 ) * K * else if SIDE = 'R', * LWORK >= ( NqC0 + MAX( NpV0 + NUMROC( NUMROC( N+ICOFFC, * NB_V, 0, 0, NPCOL ), NB_V, 0, 0, LCMQ ), * MpC0 ) ) * K * end if * else if STOREV = 'R', * if SIDE = 'L', * LWORK >= ( MpC0 + MAX( MqV0 + NUMROC( NUMROC( M+IROFFC, * MB_V, 0, 0, NPROW ), MB_V, 0, 0, LCMP ), * NqC0 ) ) * K * else if SIDE = 'R', * LWORK >= ( MpC0 + NqC0 ) * K * end if * end if * * where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ), * * IROFFV = MOD( IV-1, MB_V ), ICOFFV = MOD( JV-1, NB_V ), * IVROW = INDXG2P( IV, MB_V, MYROW, RSRC_V, NPROW ), * IVCOL = INDXG2P( JV, NB_V, MYCOL, CSRC_V, NPCOL ), * MqV0 = NUMROC( M+ICOFFV, NB_V, MYCOL, IVCOL, NPCOL ), * NpV0 = NUMROC( N+IROFFV, MB_V, MYROW, IVROW, NPROW ), * * 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 ), * NpC0 = NUMROC( N+ICOFFC, 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. * * Alignment requirements * ====================== * * The distributed submatrices V(IV:*, JV:*) and C(IC:IC+M-1,JC:JC+N-1) * must verify some alignment properties, namely the following * expressions should be true: * * If STOREV = 'Columnwise' * If SIDE = 'Left', * ( MB_V.EQ.MB_C .AND. IROFFV.EQ.IROFFC .AND. IVROW.EQ.ICROW ) * If SIDE = 'Right', * ( MB_V.EQ.NB_C .AND. IROFFV.EQ.ICOFFC ) * else if STOREV = 'Rowwise' * If SIDE = 'Left', * ( NB_V.EQ.MB_C .AND. ICOFFV.EQ.IROFFC ) * If SIDE = 'Right', * ( NB_V.EQ.NB_C .AND. ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL ) * end if * * ===================================================================== * * .. 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 ) COMPLEX ONE, ZERO PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), $ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL FORWARD CHARACTER COLBTOP, ROWBTOP, TRANST, UPLO INTEGER HEIGHT, IBASE, ICCOL, ICOFFC, ICOFFV, ICROW, $ ICTXT, II, IIBEG, IIC, IIEND, IINXT, IIV, $ ILASTCOL, ILASTROW, ILEFT, IOFF, IOFFC, IOFFV, $ IPT, IPV, IPW, IPW1, IRIGHT, IROFFC, IROFFV, $ ITOP, IVCOL, IVROW, JJ, JJBEG, JJC, JJEND, $ JJNXT, JJV, KP, KQ, LDC, LDV, LV, LW, MBV, MPC, $ MPC0, MQV, MQV0, MYCOL, MYDIST, MYROW, NBV, $ NPV, NPV0, NPCOL, NPROW, NQC, NQC0, WIDE * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CGEBR2D, CGEBS2D,CGEMM, $ CGSUM2D, CLAMOV, CLASET, CTRBR2D, $ CTRBS2D, CTRMM, INFOG1L, INFOG2L, PB_TOPGET, $ PBCTRAN * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, MOD * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL, NUMROC EXTERNAL ICEIL, LSAME, NUMROC * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 .OR. K.LE.0 ) $ RETURN * * Get grid parameters * ICTXT = DESCC( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'C' ELSE TRANST = 'N' END IF FORWARD = LSAME( DIRECT, 'F' ) IF( FORWARD ) THEN UPLO = 'U' ELSE UPLO = 'L' END IF * CALL INFOG2L( IV, JV, DESCV, NPROW, NPCOL, MYROW, MYCOL, IIV, JJV, $ IVROW, IVCOL ) CALL INFOG2L( IC, JC, DESCC, NPROW, NPCOL, MYROW, MYCOL, IIC, JJC, $ ICROW, ICCOL ) LDC = DESCC( LLD_ ) LDV = DESCV( LLD_ ) IIC = MIN( IIC, LDC ) IIV = MIN( IIV, LDV ) IROFFC = MOD( IC-1, DESCC( MB_ ) ) ICOFFC = MOD( JC-1, DESCC( NB_ ) ) MBV = DESCV( MB_ ) NBV = DESCV( NB_ ) IROFFV = MOD( IV-1, MBV ) ICOFFV = MOD( JV-1, NBV ) MPC = NUMROC( M+IROFFC, DESCC( MB_ ), MYROW, ICROW, NPROW ) NQC = NUMROC( N+ICOFFC, DESCC( NB_ ), MYCOL, ICCOL, NPCOL ) IF( MYCOL.EQ.ICCOL ) $ NQC = NQC - ICOFFC IF( MYROW.EQ.ICROW ) $ MPC = MPC - IROFFC JJC = MIN( JJC, MAX( 1, JJC+NQC-1 ) ) JJV = MIN( JJV, MAX( 1, NUMROC( DESCV( N_ ), NBV, MYCOL, $ DESCV( CSRC_ ), NPCOL ) ) ) IOFFC = IIC + ( JJC-1 ) * LDC IOFFV = IIV + ( JJV-1 ) * LDV * IF( LSAME( STOREV, 'C' ) ) THEN * * V is stored columnwise * IF( LSAME( SIDE, 'L' ) ) THEN * * Form Q*sub( C ) or Q'*sub( C ) * * Locally V( IOFFV ) is MPV x K, C( IOFFC ) is MPC x NQC * WORK( IPV ) is MPC x K = V( IOFFV ), MPC = MPV * WORK( IPW ) is NQC x K = C( IOFFC )' * V( IOFFV ) * IPV = 1 IPW = IPV + MPC * K LV = MAX( 1, MPC ) LW = MAX( 1, NQC ) * * Broadcast V to the other process columns. * CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) IF( MYCOL.EQ.IVCOL ) THEN CALL CGEBS2D( ICTXT, 'Rowwise', ROWBTOP, MPC, K, $ V( IOFFV ), LDV ) IF( MYROW.EQ.IVROW ) $ CALL CTRBS2D( ICTXT, 'Rowwise', ROWBTOP, UPLO, $ 'Non unit', K, K, T, NBV ) CALL CLAMOV( 'All', MPC, K, V( IOFFV ), LDV, WORK( IPV ), $ LV ) ELSE CALL CGEBR2D( ICTXT, 'Rowwise', ROWBTOP, MPC, K, $ WORK( IPV ), LV, MYROW, IVCOL ) IF( MYROW.EQ.IVROW ) $ CALL CTRBR2D( ICTXT, 'Rowwise', ROWBTOP, UPLO, $ 'Non unit', K, K, T, NBV, MYROW, IVCOL ) END IF * IF( FORWARD ) THEN * * WORK(IPV) = ( V1 ) where V1 is unit lower triangular, * ( V2 ) zeroes upper triangular part of V1 * MYDIST = MOD( MYROW-IVROW+NPROW, NPROW ) ITOP = MAX( 0, MYDIST*MBV - IROFFV ) IIBEG = IIV IIEND = IIBEG + MPC - 1 IINXT = MIN( ICEIL( IIBEG, MBV )*MBV, IIEND ) * 10 CONTINUE IF( K-ITOP .GT.0 ) THEN CALL CLASET( 'Upper', IINXT-IIBEG+1, K-ITOP, ZERO, $ ONE, WORK( IPV+IIBEG-IIV+ITOP*LV ), LV ) MYDIST = MYDIST + NPROW ITOP = MYDIST * MBV - IROFFV IIBEG = IINXT + 1 IINXT = MIN( IINXT+MBV, IIEND ) GO TO 10 END IF * ELSE * * WORK(IPV) = ( V1 ) where V2 is unit upper triangular, * ( V2 ) zeroes lower triangular part of V2 * JJ = JJV IOFF = MOD( IV+M-K-1, MBV ) CALL INFOG1L( IV+M-K, MBV, NPROW, MYROW, DESCV( RSRC_ ), $ II, ILASTROW ) KP = NUMROC( K+IOFF, MBV, MYROW, ILASTROW, NPROW ) IF( MYROW.EQ.ILASTROW ) $ KP = KP - IOFF MYDIST = MOD( MYROW-ILASTROW+NPROW, NPROW ) ITOP = MYDIST * MBV - IOFF IBASE = MIN( ITOP+MBV, K ) ITOP = MIN( MAX( 0, ITOP ), K ) * 20 CONTINUE IF( JJ.LE.( JJV+K-1 ) ) THEN HEIGHT = IBASE - ITOP CALL CLASET( 'All', KP, ITOP-JJ+JJV, ZERO, ZERO, $ WORK( IPV+II-IIV+(JJ-JJV)*LV ), LV ) CALL CLASET( 'Lower', KP, HEIGHT, ZERO, ONE, $ WORK( IPV+II-IIV+ITOP*LV ), LV ) KP = MAX( 0, KP - HEIGHT ) II = II + HEIGHT JJ = JJV + IBASE MYDIST = MYDIST + NPROW ITOP = MYDIST * MBV - IOFF IBASE = MIN( ITOP + MBV, K ) ITOP = MIN( ITOP, K ) GO TO 20 END IF * END IF * * WORK( IPW ) = C( IOFFC )' * V (NQC x MPC x K) -> NQC x K * IF( MPC.GT.0 ) THEN CALL CGEMM( 'Conjugate transpose', 'No transpose', NQC, $ K, MPC, ONE, C( IOFFC ), LDC, WORK( IPV ), LV, $ ZERO, WORK( IPW ), LW ) ELSE CALL CLASET( 'All', NQC, K, ZERO, ZERO, WORK( IPW ), LW ) END IF * CALL CGSUM2D( ICTXT, 'Columnwise', ' ', NQC, K, WORK( IPW ), $ LW, IVROW, MYCOL ) * IF( MYROW.EQ.IVROW ) THEN * * WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T * CALL CTRMM( 'Right', UPLO, TRANST, 'Non unit', NQC, K, $ ONE, T, NBV, WORK( IPW ), LW ) CALL CGEBS2D( ICTXT, 'Columnwise', ' ', NQC, K, $ WORK( IPW ), LW ) ELSE CALL CGEBR2D( ICTXT, 'Columnwise', ' ', NQC, K, $ WORK( IPW ), LW, IVROW, MYCOL ) END IF * * C C - V * W' * C( IOFFC ) = C( IOFFC ) - WORK( IPV ) * WORK( IPW )' * MPC x NQC MPC x K K x NQC * CALL CGEMM( 'No transpose', 'Conjugate transpose', MPC, NQC, $ K, -ONE, WORK( IPV ), LV, WORK( IPW ), LW, ONE, $ C( IOFFC ), LDC ) * ELSE * * Form sub( C )*Q or sub( C )*Q' * * ICOFFC = IROFFV is required by the current transposition * routine PBCTRAN * NPV0 = NUMROC( N+IROFFV, MBV, MYROW, IVROW, NPROW ) IF( MYROW.EQ.IVROW ) THEN NPV = NPV0 - IROFFV ELSE NPV = NPV0 END IF IF( MYCOL.EQ.ICCOL ) THEN NQC0 = NQC + ICOFFC ELSE NQC0 = NQC END IF * * Locally V( IOFFV ) is NPV x K C( IOFFC ) is MPC x NQC * WORK( IPV ) is K x NQC0 = [ . V( IOFFV ) ]' * WORK( IPW ) is NPV0 x K = [ . V( IOFFV )' ]' * WORK( IPT ) is the workspace for PBCTRAN * IPV = 1 IPW = IPV + K * NQC0 IPT = IPW + NPV0 * K LV = MAX( 1, K ) LW = MAX( 1, NPV0 ) * IF( MYCOL.EQ.IVCOL ) THEN IF( MYROW.EQ.IVROW ) THEN CALL CLASET( 'All', IROFFV, K, ZERO, ZERO, $ WORK( IPW ), LW ) IPW1 = IPW + IROFFV CALL CLAMOV( 'All', NPV, K, V( IOFFV ), LDV, $ WORK( IPW1 ), LW ) ELSE IPW1 = IPW CALL CLAMOV( 'All', NPV, K, V( IOFFV ), LDV, $ WORK( IPW1 ), LW ) END IF * IF( FORWARD ) THEN * * WORK(IPW) = ( . V1' V2' )' where V1 is unit lower * triangular, zeroes upper triangular part of V1 * MYDIST = MOD( MYROW-IVROW+NPROW, NPROW ) ITOP = MAX( 0, MYDIST*MBV - IROFFV ) IIBEG = IIV IIEND = IIBEG + NPV - 1 IINXT = MIN( ICEIL( IIBEG, MBV )*MBV, IIEND ) * 30 CONTINUE IF( ( K-ITOP ).GT.0 ) THEN CALL CLASET( 'Upper', IINXT-IIBEG+1, K-ITOP, ZERO, $ ONE, WORK( IPW1+IIBEG-IIV+ITOP*LW ), $ LW ) MYDIST = MYDIST + NPROW ITOP = MYDIST * MBV - IROFFV IIBEG = IINXT + 1 IINXT = MIN( IINXT+MBV, IIEND ) GO TO 30 END IF * ELSE * * WORK( IPW ) = ( . V1' V2' )' where V2 is unit upper * triangular, zeroes lower triangular part of V2. * JJ = JJV CALL INFOG1L( IV+N-K, MBV, NPROW, MYROW, $ DESCV( RSRC_ ), II, ILASTROW ) IOFF = MOD( IV+N-K-1, MBV ) KP = NUMROC( K+IOFF, MBV, MYROW, ILASTROW, NPROW ) IF( MYROW.EQ.ILASTROW ) $ KP = KP - IOFF MYDIST = MOD( MYROW-ILASTROW+NPROW, NPROW ) ITOP = MYDIST * MBV - IOFF IBASE = MIN( ITOP+MBV, K ) ITOP = MIN( MAX( 0, ITOP ), K ) * 40 CONTINUE IF( JJ.LE.( JJV+K-1 ) ) THEN HEIGHT = IBASE - ITOP CALL CLASET( 'All', KP, ITOP-JJ+JJV, ZERO, ZERO, $ WORK( IPW1+II-IIV+(JJ-JJV)*LW ), LW ) CALL CLASET( 'Lower', KP, HEIGHT, ZERO, ONE, $ WORK( IPW1+II-IIV+ITOP*LW ), LW ) KP = MAX( 0, KP - HEIGHT ) II = II + HEIGHT JJ = JJV + IBASE MYDIST = MYDIST + NPROW ITOP = MYDIST * MBV - IOFF IBASE = MIN( ITOP + MBV, K ) ITOP = MIN( ITOP, K ) GO TO 40 END IF END IF END IF * CALL PBCTRAN( ICTXT, 'Columnwise', 'Conjugate transpose', $ N+IROFFV, K, MBV, WORK( IPW ), LW, ZERO, $ WORK( IPV ), LV, IVROW, IVCOL, -1, ICCOL, $ WORK( IPT ) ) * * WORK( IPV ) = ( . V' ) -> WORK( IPV ) = V' is K x NQC * IF( MYCOL.EQ.ICCOL ) $ IPV = IPV + ICOFFC * LV * * WORK( IPW ) becomes MPC x K = C( IOFFC ) * V * WORK( IPW ) = C( IOFFC ) * V (MPC x NQC x K) -> MPC x K * LW = MAX( 1, MPC ) * IF( NQC.GT.0 ) THEN CALL CGEMM( 'No transpose', 'Conjugate transpose', MPC, $ K, NQC, ONE, C( IOFFC ), LDC, WORK( IPV ), $ LV, ZERO, WORK( IPW ), LW ) ELSE CALL CLASET( 'All', MPC, K, ZERO, ZERO, WORK( IPW ), LW ) END IF * CALL CGSUM2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ), $ LW, MYROW, IVCOL ) * * WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T * IF( MYCOL.EQ.IVCOL ) THEN IF( MYROW.EQ.IVROW ) THEN * * Broadcast the block reflector to the other rows. * CALL CTRBS2D( ICTXT, 'Columnwise', ' ', UPLO, $ 'Non unit', K, K, T, NBV ) ELSE CALL CTRBR2D( ICTXT, 'Columnwise', ' ', UPLO, $ 'Non unit', K, K, T, NBV, IVROW, MYCOL ) END IF CALL CTRMM( 'Right', UPLO, TRANS, 'Non unit', MPC, K, $ ONE, T, NBV, WORK( IPW ), LW ) * CALL CGEBS2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ), $ LW ) ELSE CALL CGEBR2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ), $ LW, MYROW, IVCOL ) END IF * * C C - W * V' * C( IOFFC ) = C( IOFFC ) - WORK( IPW ) * WORK( IPV ) * MPC x NQC MPC x K K x NQC * CALL CGEMM( 'No transpose', 'No transpose', MPC, NQC, K, $ -ONE, WORK( IPW ), LW, WORK( IPV ), LV, ONE, $ C( IOFFC ), LDC ) END IF * ELSE * * V is stored rowwise * IF( LSAME( SIDE, 'L' ) ) THEN * * Form Q*sub( C ) or Q'*sub( C ) * * IROFFC = ICOFFV is required by the current transposition * routine PBCTRAN * MQV0 = NUMROC( M+ICOFFV, NBV, MYCOL, IVCOL, NPCOL ) IF( MYCOL.EQ.IVCOL ) THEN MQV = MQV0 - ICOFFV ELSE MQV = MQV0 END IF IF( MYROW.EQ.ICROW ) THEN MPC0 = MPC + IROFFC ELSE MPC0 = MPC END IF * * Locally V( IOFFV ) is K x MQV, C( IOFFC ) is MPC x NQC * WORK( IPV ) is MPC0 x K = [ . V( IOFFV ) ]' * WORK( IPW ) is K x MQV0 = [ . V( IOFFV ) ] * WORK( IPT ) is the workspace for PBCTRAN * IPV = 1 IPW = IPV + MPC0 * K IPT = IPW + K * MQV0 LV = MAX( 1, MPC0 ) LW = MAX( 1, K ) * IF( MYROW.EQ.IVROW ) THEN IF( MYCOL.EQ.IVCOL ) THEN CALL CLASET( 'All', K, ICOFFV, ZERO, ZERO, $ WORK( IPW ), LW ) IPW1 = IPW + ICOFFV * LW CALL CLAMOV( 'All', K, MQV, V( IOFFV ), LDV, $ WORK( IPW1 ), LW ) ELSE IPW1 = IPW CALL CLAMOV( 'All', K, MQV, V( IOFFV ), LDV, $ WORK( IPW1 ), LW ) END IF * IF( FORWARD ) THEN * * WORK( IPW ) = ( . V1 V2 ) where V1 is unit upper * triangular, zeroes lower triangular part of V1 * MYDIST = MOD( MYCOL-IVCOL+NPCOL, NPCOL ) ILEFT = MAX( 0, MYDIST * NBV - ICOFFV ) JJBEG = JJV JJEND = JJV + MQV - 1 JJNXT = MIN( ICEIL( JJBEG, NBV ) * NBV, JJEND ) * 50 CONTINUE IF( ( K-ILEFT ).GT.0 ) THEN CALL CLASET( 'Lower', K-ILEFT, JJNXT-JJBEG+1, ZERO, $ ONE, $ WORK( IPW1+ILEFT+(JJBEG-JJV)*LW ), $ LW ) MYDIST = MYDIST + NPCOL ILEFT = MYDIST * NBV - ICOFFV JJBEG = JJNXT + 1 JJNXT = MIN( JJNXT+NBV, JJEND ) GO TO 50 END IF * ELSE * * WORK( IPW ) = ( . V1 V2 ) where V2 is unit lower * triangular, zeroes upper triangular part of V2. * II = IIV CALL INFOG1L( JV+M-K, NBV, NPCOL, MYCOL, $ DESCV( CSRC_ ), JJ, ILASTCOL ) IOFF = MOD( JV+M-K-1, NBV ) KQ = NUMROC( K+IOFF, NBV, MYCOL, ILASTCOL, NPCOL ) IF( MYCOL.EQ.ILASTCOL ) $ KQ = KQ - IOFF MYDIST = MOD( MYCOL-ILASTCOL+NPCOL, NPCOL ) ILEFT = MYDIST * NBV - IOFF IRIGHT = MIN( ILEFT+NBV, K ) ILEFT = MIN( MAX( 0, ILEFT ), K ) * 60 CONTINUE IF( II.LE.( IIV+K-1 ) ) THEN WIDE = IRIGHT - ILEFT CALL CLASET( 'All', ILEFT-II+IIV, KQ, ZERO, ZERO, $ WORK( IPW1+II-IIV+(JJ-JJV)*LW ), LW ) CALL CLASET( 'Upper', WIDE, KQ, ZERO, ONE, $ WORK( IPW1+ILEFT+(JJ-JJV)*LW ), LW ) KQ = MAX( 0, KQ - WIDE ) II = IIV + IRIGHT JJ = JJ + WIDE MYDIST = MYDIST + NPCOL ILEFT = MYDIST * NBV - IOFF IRIGHT = MIN( ILEFT + NBV, K ) ILEFT = MIN( ILEFT, K ) GO TO 60 END IF END IF END IF * * WORK( IPV ) = WORK( IPW )' (replicated) is MPC0 x K * CALL PBCTRAN( ICTXT, 'Rowwise', 'Conjugate transpose', K, $ M+ICOFFV, NBV, WORK( IPW ), LW, ZERO, $ WORK( IPV ), LV, IVROW, IVCOL, ICROW, -1, $ WORK( IPT ) ) * * WORK( IPV ) = ( . V )' -> WORK( IPV ) = V' is MPC x K * IF( MYROW.EQ.ICROW ) $ IPV = IPV + IROFFC * * WORK( IPW ) becomes NQC x K = C( IOFFC )' * V' * WORK( IPW ) = C( IOFFC )' * V' (NQC x MPC x K) -> NQC x K * LW = MAX( 1, NQC ) * IF( MPC.GT.0 ) THEN CALL CGEMM( 'Conjugate transpose', 'No transpose', NQC, $ K, MPC, ONE, C( IOFFC ), LDC, WORK( IPV ), $ LV, ZERO, WORK( IPW ), LW ) ELSE CALL CLASET( 'All', NQC, K, ZERO, ZERO, WORK( IPW ), LW ) END IF * CALL CGSUM2D( ICTXT, 'Columnwise', ' ', NQC, K, WORK( IPW ), $ LW, IVROW, MYCOL ) * * WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T * IF( MYROW.EQ.IVROW ) THEN IF( MYCOL.EQ.IVCOL ) THEN * * Broadcast the block reflector to the other columns. * CALL CTRBS2D( ICTXT, 'Rowwise', ' ', UPLO, 'Non unit', $ K, K, T, MBV ) ELSE CALL CTRBR2D( ICTXT, 'Rowwise', ' ', UPLO, 'Non unit', $ K, K, T, MBV, MYROW, IVCOL ) END IF CALL CTRMM( 'Right', UPLO, TRANST, 'Non unit', NQC, K, $ ONE, T, MBV, WORK( IPW ), LW ) * CALL CGEBS2D( ICTXT, 'Columnwise', ' ', NQC, K, $ WORK( IPW ), LW ) ELSE CALL CGEBR2D( ICTXT, 'Columnwise', ' ', NQC, K, $ WORK( IPW ), LW, IVROW, MYCOL ) END IF * * C C - V' * W' * C( IOFFC ) = C( IOFFC ) - WORK( IPV ) * WORK( IPW )' * MPC x NQC MPC x K K x NQC * CALL CGEMM( 'No transpose', 'Conjugate transpose', MPC, NQC, $ K, -ONE, WORK( IPV ), LV, WORK( IPW ), LW, ONE, $ C( IOFFC ), LDC ) * ELSE * * Form Q*sub( C ) or Q'*sub( C ) * * Locally V( IOFFV ) is K x NQV, C( IOFFC ) is MPC x NQC * WORK( IPV ) is K x NQV = V( IOFFV ), NQV = NQC * WORK( IPW ) is MPC x K = C( IOFFC ) * V( IOFFV )' * IPV = 1 IPW = IPV + K * NQC LV = MAX( 1, K ) LW = MAX( 1, MPC ) * * Broadcast V to the other process rows. * CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) IF( MYROW.EQ.IVROW ) THEN CALL CGEBS2D( ICTXT, 'Columnwise', COLBTOP, K, NQC, $ V( IOFFV ), LDV ) IF( MYCOL.EQ.IVCOL ) $ CALL CTRBS2D( ICTXT, 'Columnwise', COLBTOP, UPLO, $ 'Non unit', K, K, T, MBV ) CALL CLAMOV( 'All', K, NQC, V( IOFFV ), LDV, WORK( IPV ), $ LV ) ELSE CALL CGEBR2D( ICTXT, 'Columnwise', COLBTOP, K, NQC, $ WORK( IPV ), LV, IVROW, MYCOL ) IF( MYCOL.EQ.IVCOL ) $ CALL CTRBR2D( ICTXT, 'Columnwise', COLBTOP, UPLO, $ 'Non unit', K, K, T, MBV, IVROW, MYCOL ) END IF * IF( FORWARD ) THEN * * WORK(IPW) = ( V1 V2 ) where V1 is unit upper * triangular, zeroes lower triangular part of V1 * MYDIST = MOD( MYCOL-IVCOL+NPCOL, NPCOL ) ILEFT = MAX( 0, MYDIST * NBV - ICOFFV ) JJBEG = JJV JJEND = JJV + NQC - 1 JJNXT = MIN( ICEIL( JJBEG, NBV ) * NBV, JJEND ) * 70 CONTINUE IF( ( K-ILEFT ).GT.0 ) THEN CALL CLASET( 'Lower', K-ILEFT, JJNXT-JJBEG+1, ZERO, $ ONE, WORK( IPV+ILEFT+(JJBEG-JJV)*LV ), $ LV ) MYDIST = MYDIST + NPCOL ILEFT = MYDIST * NBV - ICOFFV JJBEG = JJNXT + 1 JJNXT = MIN( JJNXT+NBV, JJEND ) GO TO 70 END IF * ELSE * * WORK( IPW ) = ( . V1 V2 ) where V2 is unit lower * triangular, zeroes upper triangular part of V2. * II = IIV CALL INFOG1L( JV+N-K, NBV, NPCOL, MYCOL, DESCV( CSRC_ ), $ JJ, ILASTCOL ) IOFF = MOD( JV+N-K-1, NBV ) KQ = NUMROC( K+IOFF, NBV, MYCOL, ILASTCOL, NPCOL ) IF( MYCOL.EQ.ILASTCOL ) $ KQ = KQ - IOFF MYDIST = MOD( MYCOL-ILASTCOL+NPCOL, NPCOL ) ILEFT = MYDIST * NBV - IOFF IRIGHT = MIN( ILEFT+NBV, K ) ILEFT = MIN( MAX( 0, ILEFT ), K ) * 80 CONTINUE IF( II.LE.( IIV+K-1 ) ) THEN WIDE = IRIGHT - ILEFT CALL CLASET( 'All', ILEFT-II+IIV, KQ, ZERO, ZERO, $ WORK( IPV+II-IIV+(JJ-JJV)*LV ), LV ) CALL CLASET( 'Upper', WIDE, KQ, ZERO, ONE, $ WORK( IPV+ILEFT+(JJ-JJV)*LV ), LV ) KQ = MAX( 0, KQ - WIDE ) II = IIV + IRIGHT JJ = JJ + WIDE MYDIST = MYDIST + NPCOL ILEFT = MYDIST * NBV - IOFF IRIGHT = MIN( ILEFT + NBV, K ) ILEFT = MIN( ILEFT, K ) GO TO 80 END IF * END IF * * WORK( IPV ) is K x NQC = V = V( IOFFV ) * WORK( IPW ) = C( IOFFC ) * V' (MPC x NQC x K) -> MPC x K * IF( NQC.GT.0 ) THEN CALL CGEMM( 'No transpose', 'Conjugate transpose', MPC, $ K, NQC, ONE, C( IOFFC ), LDC, WORK( IPV ), $ LV, ZERO, WORK( IPW ), LW ) ELSE CALL CLASET( 'All', MPC, K, ZERO, ZERO, WORK( IPW ), LW ) END IF * CALL CGSUM2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ), $ LW, MYROW, IVCOL ) * * WORK( IPW ) = WORK( IPW ) * T' or WORK( IPW ) * T * IF( MYCOL.EQ.IVCOL ) THEN CALL CTRMM( 'Right', UPLO, TRANS, 'Non unit', MPC, K, $ ONE, T, MBV, WORK( IPW ), LW ) CALL CGEBS2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ), $ LW ) ELSE CALL CGEBR2D( ICTXT, 'Rowwise', ' ', MPC, K, WORK( IPW ), $ LW, MYROW, IVCOL ) END IF * * C C - W * V * C( IOFFC ) = C( IOFFC ) - WORK( IPW ) * WORK( IPV ) * MPC x NQC MPC x K K x NQC * CALL CGEMM( 'No transpose', 'No transpose', MPC, NQC, K, $ -ONE, WORK( IPW ), LW, WORK( IPV ), LV, ONE, $ C( IOFFC ), LDC ) * END IF * END IF * RETURN * * End of PCLARFB * END