SUBROUTINE PZTZRZF( 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 * ======= * * PZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix * sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper triangular form by means * of unitary transformations. * * The upper trapezoidal matrix sub( A ) is factored as * * sub( A ) = ( R 0 ) * Z, * * where Z is an N-by-N unitary matrix and R is an M-by-M upper * triangular matrix. * * 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 leading M-by-M * upper triangular part of sub( A ) contains the upper trian- * gular matrix R, and elements M+1 to N of the first M rows of * sub( A ), with the array TAU, represent the unitary matrix Z * as a product of M elementary reflectors. * * 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+M-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 factorization is obtained by Householder's method. The kth * transformation matrix, Z( k ), whose conjugate transpose is used to * introduce zeros into the (m - k + 1)th row of sub( A ), is given in * the form * * Z( k ) = ( I 0 ), * ( 0 T( k ) ) * * where * * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), * ( 0 ) * ( z( k ) ) * * tau is a scalar and z( k ) is an ( n - m ) element vector. * tau and z( k ) are chosen to annihilate the elements of the kth row * of sub( A ). * * The scalar tau is returned in the kth element of TAU and the vector * u( k ) in the kth row of sub( A ), such that the elements of z( k ) * are in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned * in the upper triangular part of sub( A ). * * Z is given by * * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). * * ===================================================================== * * .. 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*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY CHARACTER COLBTOP, ROWBTOP INTEGER I, IACOL, IAROW, IB, ICTXT, IIA, IL, IN, IPW, $ IROFFA, J, JM1, L, LWMIN, MP0, MYCOL, MYROW, $ NPCOL, NPROW, NQ0 * .. * .. Local Arrays .. INTEGER IDUM1( 1 ), IDUM2( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, INFOG1L, PCHK1MAT, $ PB_TOPGET, PB_TOPSET, PXERBLA, PZLATRZ, $ PZLARZB, PZLARZT * .. * .. External Functions .. INTEGER ICEIL, INDXG2P, NUMROC EXTERNAL ICEIL, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, 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 = -(600+CTXT_) ELSE CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO ) IF( INFO.EQ.0 ) THEN IROFFA = 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+IROFFA, 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( N.LT.M ) THEN INFO = -2 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -9 END IF END IF IF( LQUERY ) 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, 'PZTZRZF', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * IF( M.EQ.N ) THEN * CALL INFOG1L( IA, DESCA( MB_ ), NPROW, MYROW, DESCA( RSRC_ ), $ IIA, IAROW ) IF( MYROW.EQ.IAROW ) $ MP0 = MP0 - IROFFA DO 10 I = IIA, IIA+MP0-1 TAU( I ) = ZERO 10 CONTINUE * ELSE * L = N-M JM1 = JA + MIN( M+1, N ) - 1 IPW = DESCA( MB_ ) * DESCA( MB_ ) + 1 IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+M-1 ) IL = MAX( ( (IA+M-2) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA ) 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', 'D-ring' ) * * Use blocked code initially * DO 20 I = IL, IN+1, -DESCA( MB_ ) IB = MIN( IA+M-I, DESCA( MB_ ) ) J = JA + I - IA * * Compute the complete orthogonal factorization of the current * block A(i:i+ib-1,j:ja+n-1) * CALL PZLATRZ( IB, JA+N-J, L, A, I, J, DESCA, TAU, WORK ) * IF( I.GT.IA ) THEN * * Form the triangular factor of the block reflector * H = H(i+ib-1) . . . H(i+1) H(i) * CALL PZLARZT( 'Backward', 'Rowwise', L, IB, A, I, JM1, $ DESCA, TAU, WORK, WORK( IPW ) ) * * Apply H to A(ia:i-1,j:ja+n-1) from the right * CALL PZLARZB( 'Right', 'No transpose', 'Backward', $ 'Rowwise', I-IA, JA+N-J, IB, L, A, I, JM1, $ DESCA, WORK, A, IA, J, DESCA, WORK( IPW ) ) END IF * 20 CONTINUE * * Use unblocked code to factor the last or only block * CALL PZLATRZ( IN-IA+1, N, N-M, A, IA, JA, DESCA, TAU, WORK ) * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * END IF * WORK( 1 ) = DCMPLX( DBLE( LWMIN ) ) * RETURN * * End of PZTZRZF * END