SUBROUTINE PDORGQL( M, N, K, A, IA, JA, DESCA, TAU, 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 .. INTEGER IA, INFO, JA, K, LWORK, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ) DOUBLE PRECISION A( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PDORGQL generates an M-by-N real distributed matrix Q denoting * A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as * the last N columns of a product of K elementary reflectors of order M * * Q = H(k) . . . H(2) H(1) * * as returned by PDGEQLF. * * 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 * ========= * * M (global input) INTEGER * The number of rows to be operated on i.e the number of rows * of the distributed submatrix Q. M >= 0. * * N (global input) INTEGER * The number of columns to be operated on i.e the number of * columns of the distributed submatrix Q. M >= N >= 0. * * K (global input) INTEGER * The number of elementary reflectors whose product defines the * matrix Q. N >= K >= 0. * * A (local input/local output) DOUBLE PRECISION pointer into the * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). * On entry, the j-th column must contain the vector which * defines the elementary reflector H(j), JA+N-K <= j <= JA+N-1, * as returned by PDGEQLF in the K columns of its distributed * matrix argument A(IA:*,JA+N-K:JA+N-1). On exit, this array * contains the local pieces of the M-by-N distributed matrix Q. * * 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(JA+N-1) * This array contains the scalar factors TAU(j) of the * elementary reflectors H(j) as returned by PDGEQLF. * TAU is tied to the distributed matrix A. * * 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 * LWORK >= NB_A * ( NqA0 + MpA0 + NB_A ), where * * IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), * MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ), * NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), * * 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. * * ===================================================================== * * .. 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 ) DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY CHARACTER COLBTOP, ROWBTOP INTEGER IACOL, IAROW, ICTXT, IINFO, IPW, J, JB, JN, $ LWMIN, MPA0, MYCOL, MYROW, NPCOL, NPROW, NQA0 * .. * .. Local Arrays .. INTEGER IDUM1( 2 ), IDUM2( 2 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PDLARFB, $ PDLARFT, PDLASET, PDORG2L, PB_TOPGET, $ PB_TOPSET, PXERBLA * .. * .. External Functions .. INTEGER ICEIL, INDXG2P, NUMROC EXTERNAL ICEIL, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC DBLE, 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 = -(700+CTXT_) ELSE CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, INFO ) IF( INFO.EQ.0 ) THEN IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), $ NPCOL ) MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ), $ MYROW, IAROW, NPROW ) NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ), $ MYCOL, IACOL, NPCOL ) LWMIN = DESCA( NB_ ) * ( MPA0 + NQA0 + DESCA( NB_ ) ) * WORK( 1 ) = DBLE( LWMIN ) LQUERY = ( LWORK.EQ.-1 ) IF( N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -10 END IF END IF IDUM1( 1 ) = K IDUM2( 1 ) = 3 IF( LWORK.EQ.-1 ) THEN IDUM1( 2 ) = -1 ELSE IDUM1( 2 ) = 1 END IF IDUM2( 2 ) = 10 CALL PCHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, 2, IDUM1, IDUM2, $ INFO ) END IF IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PDORGQL', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * IPW = DESCA( NB_ )*DESCA( NB_ ) + 1 JN = MIN( ICEIL( JA+N-K, DESCA( NB_ ) )*DESCA( NB_ ), JA+N-1 ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'I-ring' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) * * Set A(ia+m-n+jn-ja+1:ia-m+1,ja:jn) to zero. * CALL PDLASET( 'All', N-JN+JA-1, JN-JA+1, ZERO, ZERO, A, $ IA+M-N+JN-JA+1, JA, DESCA ) * * Use unblocked code for the first or only block. * CALL PDORG2L( M-N+JN-JA+1, JN-JA+1, JN-JA-N+K+1, A, IA, JA, DESCA, $ TAU, WORK, LWORK, IINFO ) * * Use blocked code * DO 10 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * * Form the triangular factor of the block reflector * H = H(j+jb-1) . . . H(j+1) H(j) * CALL PDLARFT( 'Backward', 'Columnwise', M-N+J+JB-JA, JB, $ A, IA, J, DESCA, TAU, WORK, WORK( IPW ) ) * * Apply H to A(ia:ia+m-n+j+jb-ja-1,ja:j-1) from the left * CALL PDLARFB( 'Left', 'No transpose', 'Backward', $ 'Columnwise', M-N+J+JB-JA, J-JA, JB, A, IA, $ J, DESCA, WORK, A, IA, JA, DESCA, WORK( IPW ) ) * * Apply H to rows ia:m-k+i+ib-1 of current block * CALL PDORG2L( M-N+J+JB-JA, JB, JB, A, IA, J, DESCA, TAU, WORK, $ LWORK, IINFO ) * * Set rows ia+m-n+j+jb-ja:ia+m-1,j:j+jb-1 of current block to * zero * CALL PDLASET( 'All', N-J-JB+JA, JB, ZERO, ZERO, A, $ IA+M-N+J+JB-JA, J, DESCA ) * 10 CONTINUE * CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * WORK( 1 ) = DBLE( LWMIN ) * RETURN * * End of PDORGQL * END