SUBROUTINE PCUNGR2( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK, $ INFO ) * * -- ScaLAPACK routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. INTEGER IA, INFO, JA, K, LWORK, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ) COMPLEX A( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PCUNGR2 generates an M-by-N complex distributed matrix Q denoting * A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as the * last M rows of a product of K elementary reflectors of order N * * Q = H(1)' H(2)' . . . H(k)' * * as returned by PCGERQF. * * 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. N >= M >= 0. * * K (global input) INTEGER * The number of elementary reflectors whose product defines the * matrix Q. M >= K >= 0. * * A (local input/local output) COMPLEX pointer into the * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). * On entry, the i-th row must contain the vector which defines * the elementary reflector H(i), IA+M-K <= i <= IA+M-1, as * returned by PCGERQF in the K rows of its distributed * matrix argument A(IA+M-K:IA+M-1,JA:*). 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) COMPLEX, array, dimension LOCr(IA+M-1) * This array contains the scalar factors TAU(i) of the * elementary reflectors H(i) as returned by PCGERQF. * TAU is tied to the distributed matrix A. * * WORK (local workspace/local output) COMPLEX 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 >= NqA0 + MAX( 1, MpA0 ), 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 (local 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 ) COMPLEX ONE, ZERO PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), $ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY CHARACTER COLBTOP, ROWBTOP INTEGER IACOL, IAROW, I, ICTXT, II, LWMIN, MP, MPA0, $ MYCOL, MYROW, NPCOL, NPROW, NQA0 COMPLEX TAUI * .. * .. External Subroutines .. EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, PCELSET, $ PCLACGV, PCLARFC, PCLASET, PCSCAL, $ PTOPGET, PTOPSET, PXERBLA * .. * .. External Functions .. INTEGER INDXG2L, INDXG2P, NUMROC EXTERNAL INDXG2L, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, CONJG, MAX, MIN, MOD, REAL * .. * .. 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 = NQA0 + MAX( 1, MPA0 ) * WORK( 1 ) = CMPLX( REAL( LWMIN ) ) LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN INFO = -3 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -10 END IF END IF END IF IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PCUNGR2', -INFO ) CALL BLACS_ABORT( ICTXT, 1 ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.LE.0 ) $ RETURN * CALL PTOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PTOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) * IF( K.LT.M ) THEN * * Initialise rows ia:ia+m-k-1 to rows of the unit matrix * CALL PCLASET( 'All', M-K, N-M, ZERO, ZERO, A, IA, JA, DESCA ) CALL PCLASET( 'All', M-K, M, ZERO, ONE, A, IA, JA+N-M, DESCA ) * END IF * TAUI = ZERO MP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) * DO 10 I = IA+M-K, IA+M-1 * * Apply H(i)' to A(ia:i,ja:ja+n-m+i-ia) from the right * CALL PCLACGV( I-IA+N-M, A, I, JA, DESCA, DESCA( M_ ) ) CALL PCELSET( A, I, JA+N-M+I-IA, DESCA, ONE ) CALL PCLARFC( 'Right', I-IA, I-IA+N-M+1, A, I, JA, DESCA, $ DESCA( M_ ), TAU, A, IA, JA, DESCA, WORK ) II = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) TAUI = TAU( MIN( II, MP ) ) CALL PCSCAL( I-IA+N-M, -TAUI, A, I, JA, DESCA, DESCA( M_ ) ) CALL PCLACGV( I-IA+N-M, A, I, JA, DESCA, DESCA( M_ ) ) CALL PCELSET( A, I, JA+N-M+I-IA, DESCA, ONE-CONJG( TAUI ) ) * * Set A(i,ja+n-m+i-ia+1:ja+n-1) to zero * CALL PCLASET( 'All', 1, IA+M-1-I, ZERO, ZERO, A, I, $ JA+N-M+I-IA+1, DESCA ) * 10 CONTINUE * CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * WORK( 1 ) = CMPLX( REAL( LWMIN ) ) * RETURN * * End of PCUNGR2 * END