SUBROUTINE PZGELQF( M, N, 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, LWORK, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ) COMPLEX*16 A( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PZGELQF computes a LQ factorization of a complex distributed M-by-N * matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. * * 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 sub( A ). 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( A ). N >= 0. * * A (local input/local output) COMPLEX*16 pointer into the * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). * On entry, the local pieces of the M-by-N distributed matrix * sub( A ) which is to be factored. On exit, the elements on * and below the diagonal of sub( A ) contain the M by min(M,N) * lower trapezoidal matrix L (L is lower triangular if M <= N); * the elements above the diagonal, with the array TAU, repre- * sent the unitary matrix Q as a product of elementary * reflectors (see Further Details). * * 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 output) COMPLEX*16, array, dimension * LOCr(IA+MIN(M,N)-1). This array contains the scalar factors * of the elementary reflectors. TAU is tied to the distributed * matrix A. * * 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 * LWORK >= MB_A * ( Mp0 + Nq0 + MB_A ), where * * IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ), * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), * Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ), * Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ), * * and NUMROC, INDXG2P 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. * * Further Details * =============== * * The matrix Q is represented as a product of elementary reflectors * * Q = H(ia+k-1)' H(ia+k-2)' . . . H(ia)', where k = min(m,n). * * Each H(i) has the form * * H(i) = I - tau * v * v' * * where tau is a complex scalar, and v is a complex vector with * v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in * A(ia+i-1,ja+i:ja+n-1), and tau in TAU(ia+i-1). * * ===================================================================== * * .. 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 LQUERY CHARACTER COLBTOP, ROWBTOP INTEGER I, IACOL, IAROW, IB, ICTXT, IINFO, IN, IPW, $ IROFF, J, K, LWMIN, MP0, MYCOL, MYROW, NPCOL, $ NPROW, NQ0 * .. * .. Local Arrays .. INTEGER IDUM1( 1 ), IDUM2( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PB_TOPGET, $ PB_TOPSET, PXERBLA, PZGELQ2, PZLARFB, $ PZLARFT * .. * .. External Functions .. INTEGER ICEIL, INDXG2P, NUMROC EXTERNAL ICEIL, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, 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 = -(600+CTXT_) ELSE CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO ) IF( INFO.EQ.0 ) THEN IROFF = MOD( IA-1, DESCA( MB_ ) ) IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), $ NPCOL ) MP0 = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) NQ0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ), $ MYCOL, IACOL, NPCOL ) LWMIN = DESCA( MB_ ) * ( MP0 + NQ0 + DESCA( MB_ ) ) * WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) LQUERY = ( LWORK.EQ.-1 ) IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) $ INFO = -9 END IF IF( LWORK.EQ.-1 ) THEN IDUM1( 1 ) = -1 ELSE IDUM1( 1 ) = 1 END IF IDUM2( 1 ) = 9 CALL PCHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, 1, IDUM1, IDUM2, $ INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PZGELQF', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * K = MIN( M, N ) IPW = DESCA( MB_ ) * DESCA( MB_ ) + 1 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) * * Handle the first block of rows separately * IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 ) IB = IN - IA + 1 * * Compute the LQ factorization of the first block A(ia:in:ja:ja+n-1) * CALL PZGELQ2( IB, N, A, IA, JA, DESCA, TAU, WORK, LWORK, IINFO ) * IF( IA+IB.LE.IA+M-1 ) THEN * * Form the triangular factor of the block reflector * H = H(ia) H(ia+1) . . . H(in) * CALL PZLARFT( 'Forward', 'Rowwise', N, IB, A, IA, JA, DESCA, $ TAU, WORK, WORK( IPW ) ) * * Apply H to A(ia+ib:ia+m-1,ja:ja+n-1) from the right * CALL PZLARFB( 'Right', 'No transpose', 'Forward', 'Rowwise', $ M-IB, N, IB, A, IA, JA, DESCA, WORK, A, IA+IB, $ JA, DESCA, WORK( IPW ) ) END IF * * Loop over the remaining blocks of rows * DO 10 I = IN+1, IA+K-1, DESCA( MB_ ) IB = MIN( K-I+IA, DESCA( MB_ ) ) J = JA + I - IA * * Compute the LQ factorization of the current block * A(i:i+ib-1:j:ja+n-1) * CALL PZGELQ2( IB, N-I+IA, A, I, J, DESCA, TAU, WORK, LWORK, $ IINFO ) * IF( I+IB.LE.IA+M-1 ) THEN * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL PZLARFT( 'Forward', 'Rowwise', N-I+IA, IB, A, I, J, $ DESCA, TAU, WORK, WORK( IPW ) ) * * Apply H to A(i+ib:ia+m-1,j:ja+n-1) from the right * CALL PZLARFB( 'Right', 'No transpose', 'Forward', 'Rowwise', $ M-I-IB+IA, N-J+JA, IB, A, I, J, DESCA, WORK, $ A, I+IB, J, DESCA, WORK( IPW ) ) END IF * 10 CONTINUE * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) * RETURN * * End of PZGELQF * END