SUBROUTINE PZLAUU2( UPLO, N, A, IA, JA, DESCA ) * * -- ScaLAPACK auxiliary routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER IA, JA, N * .. * .. Array Arguments .. INTEGER DESCA( * ) COMPLEX*16 A( * ) * .. * * Purpose * ======= * * PZLAUU2 computes the product U * U' or L' * L, where the triangular * factor U or L is stored in the upper or lower triangular part of * the matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). * * If UPLO = 'U' or 'u' then the upper triangle of the result is stored, * overwriting the factor U in sub( A ). * If UPLO = 'L' or 'l' then the lower triangle of the result is stored, * overwriting the factor L in sub( A ). * * This is the unblocked form of the algorithm, calling Level 2 BLAS. * No communication is performed by this routine, the matrix to operate * on should be strictly local to one process. * * 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 * ========= * * UPLO (global input) CHARACTER*1 * Specifies whether the triangular factor stored in the matrix * sub( A ) is upper or lower triangular: * = 'U': Upper triangular, * = 'L': Lower triangular. * * N (global input) INTEGER * The number of rows and columns to be operated on, i.e. the * order of the order of the triangular factor U or L. 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 triangular factor L or U. * On exit, if UPLO = 'U', the upper triangle of the distributed * matrix sub( A ) is overwritten with the upper triangle of the * product U * U'; if UPLO = 'L', the lower triangle of sub( A ) * is overwritten with the lower triangle of the product L' * L. * * 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. * * ===================================================================== * * .. 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 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER IACOL, IAROW, ICURR, IDIAG, IIA, IOFFA, JJA, $ LDA, MYCOL, MYROW, NA, NPCOL, NPROW DOUBLE PRECISION AII * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, INFOG2L, ZDSCAL, ZGEMV, $ ZLACGV * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX, DBLE * .. * .. Executable Statements .. * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Get grid parameters and compute local indexes * CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) * IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN * LDA = DESCA( LLD_ ) IDIAG = IIA + ( JJA - 1 ) * LDA IOFFA = IDIAG * IF( LSAME( UPLO, 'U' ) ) THEN * * Compute the product U * U'. * DO 10 NA = N-1, 1, -1 AII = A( IDIAG ) ICURR = IDIAG + LDA A( IDIAG ) = AII*AII + DBLE( ZDOTC( NA, A( ICURR ), LDA, $ A( ICURR ), LDA ) ) CALL ZLACGV( NA, A( ICURR ), LDA ) CALL ZGEMV( 'No transpose', N-NA-1, NA, ONE, $ A( IOFFA+LDA ), LDA, A( ICURR ), LDA, $ DCMPLX( AII ), A( IOFFA ), 1 ) CALL ZLACGV( NA, A( ICURR ), LDA ) IDIAG = IDIAG + LDA + 1 IOFFA = IOFFA + LDA 10 CONTINUE AII = A( IDIAG ) CALL ZDSCAL( N, AII, A( IOFFA ), 1 ) * ELSE * * Compute the product L' * L. * DO 20 NA = 1, N-1 AII = A( IDIAG ) ICURR = IDIAG + 1 A( IDIAG ) = AII*AII + DBLE( ZDOTC( N-NA, A( ICURR ), 1, $ A( ICURR ), 1 ) ) CALL ZLACGV( NA-1, A( IOFFA ), LDA ) CALL ZGEMV( 'Conjugate transpose', N-NA, NA-1, ONE, $ A( IOFFA+1 ), LDA, A( ICURR ), 1, $ DCMPLX( AII ), A( IOFFA ), LDA ) CALL ZLACGV( NA-1, A( IOFFA ), LDA ) IDIAG = IDIAG + LDA + 1 IOFFA = IOFFA + 1 20 CONTINUE AII = A( IDIAG ) CALL ZDSCAL( N, AII, A( IOFFA ), LDA ) * END IF * END IF * RETURN * * End of PZLAUU2 * END