SUBROUTINE PDORMTR( SIDE, UPLO, TRANS, M, N, 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 1, 1997 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, UPLO INTEGER IA, IC, INFO, JA, JC, LWORK, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCC( * ) DOUBLE PRECISION A( * ), C( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PDORMTR 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 of order nq, with * nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the * product of nq-1 elementary reflectors, as returned by PDSYTRD: * * if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); * * if UPLO = 'L', Q = H(1) H(2) . . . H(nq-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**T from the Left; * = 'R': apply Q or Q**T from the Right. * * UPLO (global input) CHARACTER * = 'U': Upper triangle of A(IA:*,JA:*) contains elementary * reflectors from PDSYTRD; * = 'L': Lower triangle of A(IA:*,JA:*) contains elementary * reflectors from PDSYTRD. * * 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. * * A (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L', * or (LLD_A,LOCc(JA+N-1)) if SIDE = 'R'. The vectors which * define the elementary reflectors, as returned by PDSYTRD. * If SIDE = 'L', LLD_A >= max(1,LOCr(IA+M-1)); * if SIDE = 'R', LLD_A >= max(1,LOCr(IA+N-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) DOUBLE PRECISION array, dimension LTAU, where * if SIDE = 'L' and UPLO = 'U', LTAU = LOCc(M_A), * if SIDE = 'L' and UPLO = 'L', LTAU = LOCc(JA+M-2), * if SIDE = 'R' and UPLO = 'U', LTAU = LOCc(N_A), * if SIDE = 'R' and UPLO = 'L', LTAU = LOCc(JA+N-2). * TAU(i) must contain the scalar factor of the elementary * reflector H(i), as returned by PDSYTRD. 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 UPLO = 'U', * IAA = IA, JAA = JA+1, ICC = IC, JCC = JC; * else UPLO = 'L', * IAA = IA+1, JAA = JA; * if SIDE = 'L', * ICC = IC+1; JCC = JC; * else * ICC = IC; JCC = JC+1; * end if * end if * * If SIDE = 'L', * MI = M-1; NI = N; * LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + * NB_A * NB_A * else if SIDE = 'R', * MI = M; MI = N-1; * 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 ) * * ===================================================================== * * .. 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, UPPER INTEGER IAA, IAROW, ICC, ICCOL, ICOFFC, ICROW, ICTXT, $ IINFO, IROFFA, IROFFC, JAA, JCC, LCM, LCMQ, $ LWMIN, MI, MPC0, MYCOL, MYROW, NI, NPA0, NPCOL, $ NPROW, NQ, NQC0 * .. * .. Local Arrays .. INTEGER IDUM1( 4 ), IDUM2( 4 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PDORMQL, $ PDORMQR, PXERBLA * .. * .. External Functions .. LOGICAL LSAME INTEGER ILCM, INDXG2P, NUMROC EXTERNAL ILCM, INDXG2P, LSAME, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC DBLE, ICHAR, MAX, 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' ) UPPER = LSAME( UPLO, 'U' ) * IF( UPPER ) THEN IAA = IA JAA = JA+1 ICC = IC JCC = JC ELSE IAA = IA+1 JAA = JA IF( LEFT ) THEN ICC = IC + 1 JCC = JC ELSE ICC = IC JCC = JC + 1 END IF END IF * * NQ is the order of Q * IF( LEFT ) THEN NQ = M MI = M - 1 NI = N CALL CHK1MAT( MI, 4, NQ-1, 4, IAA, JAA, DESCA, 9, INFO ) ELSE NQ = N MI = M NI = N - 1 CALL CHK1MAT( NI, 5, NQ-1, 5, IAA, JAA, DESCA, 9, INFO ) END IF CALL CHK1MAT( MI, 4, NI, 5, ICC, JCC, DESCC, 14, INFO ) IF( INFO.EQ.0 ) THEN IROFFA = MOD( IAA-1, DESCA( MB_ ) ) IROFFC = MOD( ICC-1, DESCC( MB_ ) ) ICOFFC = MOD( JCC-1, DESCC( NB_ ) ) IAROW = INDXG2P( IAA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) ICROW = INDXG2P( ICC, DESCC( MB_ ), MYROW, DESCC( RSRC_ ), $ NPROW ) ICCOL = INDXG2P( JCC, DESCC( NB_ ), MYCOL, DESCC( CSRC_ ), $ NPCOL ) MPC0 = NUMROC( MI+IROFFC, DESCC( MB_ ), MYROW, ICROW, $ NPROW ) NQC0 = NUMROC( NI+ICOFFC, DESCC( NB_ ), MYCOL, ICCOL, $ NPCOL ) * IF( LEFT ) THEN LWMIN = MAX( ( DESCA( NB_ ) * ( DESCA( NB_ ) - 1 ) ) / 2, $ ( MPC0 + NQC0 ) * DESCA( NB_ ) ) + $ DESCA( NB_ ) * DESCA( NB_ ) ELSE NPA0 = NUMROC( NI+IROFFA, DESCA( MB_ ), MYROW, IAROW, $ NPROW ) LCM = ILCM( NPROW, NPCOL ) LCMQ = LCM / NPCOL LWMIN = MAX( ( DESCA( NB_ ) * ( DESCA( NB_ ) - 1 ) ) $ / 2, ( NQC0 + MAX( NPA0 + NUMROC( NUMROC( $ NI+ICOFFC, DESCA( NB_ ), 0, 0, NPCOL ), $ DESCA( NB_ ), 0, 0, LCMQ ), MPC0 ) ) * $ DESCA( NB_ ) ) + DESCA( NB_ ) * DESCA( NB_ ) END IF * WORK( 1 ) = DBLE( LWMIN ) LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. $ .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -3 ELSE IF( .NOT.LEFT .AND. DESCA( MB_ ).NE.DESCC( NB_ ) ) THEN INFO = -(900+NB_) ELSE IF( LEFT .AND. IROFFA.NE.IROFFC ) THEN INFO = -12 ELSE IF( LEFT .AND. IAROW.NE.ICROW ) THEN INFO = -12 ELSE IF( .NOT.LEFT .AND. IROFFA.NE.ICOFFC ) THEN INFO = -13 ELSE IF( LEFT .AND. DESCA( MB_ ).NE.DESCC( MB_ ) ) THEN INFO = -(1400+MB_) 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( UPPER ) THEN IDUM1( 2 ) = ICHAR( 'U' ) ELSE IDUM1( 2 ) = ICHAR( 'L' ) END IF IDUM2( 2 ) = 2 IF( NOTRAN ) THEN IDUM1( 3 ) = ICHAR( 'N' ) ELSE IDUM1( 3 ) = ICHAR( 'T' ) END IF IDUM2( 3 ) = 3 IF( LWORK.EQ.-1 ) THEN IDUM1( 4 ) = -1 ELSE IDUM1( 4 ) = 1 END IF IDUM2( 4 ) = 16 IF( LEFT ) THEN CALL PCHK2MAT( MI, 4, NQ-1, 4, IAA, JAA, DESCA, 9, MI, 4, $ NI, 5, ICC, JCC, DESCC, 14, 4, IDUM1, IDUM2, $ INFO ) ELSE CALL PCHK2MAT( NI, 5, NQ-1, 5, IAA, JAA, DESCA, 9, MI, 4, $ NI, 5, ICC, JCC, DESCC, 14, 4, IDUM1, IDUM2, $ INFO ) END IF END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PDORMTR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) $ RETURN * IF( UPPER ) THEN * * Q was determined by a call to PDSYTRD with UPLO = 'U' * CALL PDORMQL( SIDE, TRANS, MI, NI, NQ-1, A, IAA, JAA, DESCA, $ TAU, C, ICC, JCC, DESCC, WORK, LWORK, IINFO ) * ELSE * * Q was determined by a call to PDSYTRD with UPLO = 'L' * CALL PDORMQR( SIDE, TRANS, MI, NI, NQ-1, A, IAA, JAA, DESCA, $ TAU, C, ICC, JCC, DESCC, WORK, LWORK, IINFO ) * END IF * WORK( 1 ) = DBLE( LWMIN ) * RETURN * * End of PDORMTR * END