SUBROUTINE PZLATRZ( M, N, L, A, IA, JA, DESCA, TAU, WORK ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * December 31, 1998 * * .. Scalar Arguments .. INTEGER IA, JA, L, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ) COMPLEX*16 A( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PZLATRZ reduces the M-by-N ( M<=N ) complex upper trapezoidal * matrix sub( A ) = [A(IA:IA+M-1,JA:JA+M-1) A(IA:IA+M-1,JA+N-L: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. * * L (global input) INTEGER * The columns of the distributed submatrix sub( A ) containing * the meaningful part of the Householder reflectors. L > 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 N-L+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) COMPLEX*16 array, dimension (LWORK) * LWORK >= Nq0 + MAX( 1, Mp0 ), 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. * * 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 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, IAROW, ICTXT, II, J, J1, MP, MYCOL, MYROW, $ NPCOL, NPROW COMPLEX*16 AII * .. * .. Local Arrays .. INTEGER DESCTAU( DLEN_ ) * .. * .. External Subroutines .. EXTERNAL DESCSET, INFOG1L, PZELSET, PZLACGV, $ PZLARFG, PZLARZ * .. * .. External Functions .. INTEGER NUMROC EXTERNAL NUMROC * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * MP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) * CALL DESCSET( DESCTAU, DESCA( M_ ), 1, DESCA( MB_ ), 1, $ DESCA( RSRC_ ), MYCOL, ICTXT, MAX( 1, MP ) ) * IF( M.EQ.N ) THEN * CALL INFOG1L( IA, DESCA( MB_ ), NPROW, MYROW, DESCA( RSRC_ ), $ II, IAROW ) DO 10 I = II, MP TAU( I ) = ZERO 10 CONTINUE * ELSE * AII = ZERO * J1 = JA + N - L DO 20 I = IA+M-1, IA, -1 J = JA + I - IA * * Generate elementary reflector H(i) to annihilate * [ A(i, j) A(i,j1:ja+n-1) ] * CALL PZLACGV( 1, A, I, J, DESCA, DESCA( M_ ) ) CALL PZLACGV( L, A, I, J1, DESCA, DESCA( M_ ) ) CALL PZLARFG( L+1, AII, I, J, A, I, J1, DESCA, DESCA( M_ ), $ TAU ) * * Apply H(i) to A(ia:i-1,j:ja+n-1) from the right * CALL PZLARZ( 'Right', I-IA, JA+N-J, L, A, I, J1, DESCA, $ DESCA( M_ ), TAU, A, IA, J, DESCA, WORK ) CALL PZELSET( A, I, J, DESCA, DCONJG( AII ) ) * 20 CONTINUE * CALL PZLACGV( M, TAU, IA, 1, DESCTAU, 1 ) * END IF * RETURN * * End of PZLATRZ * END