SUBROUTINE PZUNMLQ( SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, $ C, IC, JC, DESCC, WORK, LWORK, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 25, 2001 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER IA, IC, INFO, JA, JC, K, LWORK, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCC( * ) COMPLEX*16 A( * ), C( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PZUNMLQ overwrites 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': Q * sub( C ) sub( C ) * Q * TRANS = 'C': Q**H * sub( C sub( C ) * Q**H * * where Q is a complex unitary distributed matrix defined as the * product of K elementary reflectors * * Q = H(k)' . . . H(2)' H(1)' * * as returned by PZGELQF. 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**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. * * 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. * * A (local input) COMPLEX*16 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 PZGELQF 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) COMPLEX*16, array, dimension LOCc(IA+K-1). * This array contains the scalar factors TAU(i) of the * elementary reflectors H(i) as returned by PZGELQF. * 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, 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*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', * 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, JCC, $ LCM, LCMP, LWMIN, MI, MPC0, MQA0, MYCOL, MYROW, $ NI, NPCOL, NPROW, NQ, NQC0 * .. * .. Local Arrays .. INTEGER IDUM1( 4 ), IDUM2( 4 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PB_TOPGET, $ PB_TOPSET, PXERBLA, PZLARFB, PZLARFT, $ PZUNML2 * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL, ILCM, INDXG2P, NUMROC EXTERNAL ICEIL, ILCM, INDXG2P, LSAME, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, 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, 9, INFO ) ELSE NQ = N CALL CHK1MAT( K, 5, N, 4, IA, JA, DESCA, 9, INFO ) END IF CALL CHK1MAT( M, 3, N, 4, IC, JC, DESCC, 14, 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 ) = DCMPLX( 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, 'C' ) ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LEFT .AND. DESCA( NB_ ).NE.DESCC( MB_ ) ) THEN INFO = -(900+NB_) ELSE IF( LEFT .AND. ICOFFA.NE.IROFFC ) THEN INFO = -12 ELSE IF( .NOT.LEFT .AND. ICOFFA.NE.ICOFFC ) THEN INFO = -13 ELSE IF( .NOT.LEFT .AND. IACOL.NE.ICCOL ) THEN INFO = -13 ELSE IF( .NOT.LEFT .AND. DESCA( NB_ ).NE.DESCC( NB_ ) ) THEN INFO = -(1400+NB_) ELSE IF( ICTXT.NE.DESCC( CTXT_ ) ) THEN INFO = -(1400+CTXT_) ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -16 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( 'C' ) END IF IDUM2( 2 ) = 2 IDUM1( 3 ) = K IDUM2( 3 ) = 5 IF( LWORK.EQ.-1 ) THEN IDUM1( 4 ) = -1 ELSE IDUM1( 4 ) = 1 END IF IDUM2( 4 ) = 16 IF( LEFT ) THEN CALL PCHK2MAT( K, 5, M, 3, IA, JA, DESCA, 9, M, 3, N, 4, IC, $ JC, DESCC, 14, 4, IDUM1, IDUM2, INFO ) ELSE CALL PCHK2MAT( K, 5, N, 4, IA, JA, DESCA, 9, M, 3, N, 4, IC, $ JC, DESCC, 14, 4, IDUM1, IDUM2, INFO ) END IF END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PZUNMLQ', -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 PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * IF( ( LEFT .AND. NOTRAN ) .OR. $ ( .NOT.LEFT .AND. .NOT.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 ELSE MI = M ICC = IC CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) IF( NOTRAN ) THEN CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'D-ring' ) ELSE CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) END IF END IF * IF( NOTRAN ) THEN TRANST = 'C' ELSE TRANST = 'N' END IF * IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) $ CALL PZUNML2( SIDE, TRANS, M, N, I1-IA, A, IA, JA, DESCA, TAU, $ C, IC, JC, DESCC, WORK, LWORK, IINFO ) * 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) H(i+1) . . . H(i+ib-1) * CALL PZLARFT( 'Forward', 'Rowwise', NQ-I+IA, IB, A, I, JA+I-IA, $ 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 PZLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, $ A, I, JA+I-IA, DESCA, WORK, C, ICC, JCC, DESCC, $ WORK( IPW ) ) 10 CONTINUE * IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. ( .NOT.LEFT .AND. NOTRAN ) ) $ CALL PZUNML2( SIDE, TRANS, M, N, I2-IA, A, IA, JA, DESCA, TAU, $ C, IC, JC, DESCC, WORK, LWORK, IINFO ) * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) * RETURN * * End of PZUNMLQ * END