SUBROUTINE PCLAUUM( 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 A( * ) * .. * * Purpose * ======= * * PCLAUUM 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 distributed 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 blocked form of the algorithm, calling Level 3 PBLAS. * * 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 * distributed 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 triangular factor U or L. N >= 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 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 ) REAL ONE PARAMETER ( ONE = 1.0E+0 ) COMPLEX CONE PARAMETER ( CONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J, JB, JN * .. * .. External Subroutines .. EXTERNAL PCGEMM, PCHERK, PCLAUU2, PCTRMM * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL EXTERNAL ICEIL, LSAME * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) IF( LSAME( UPLO, 'U' ) ) THEN * * Compute the product U * U'. * * Handle first block separately * JB = JN-JA+1 CALL PCLAUU2( 'Upper', JB, A, IA, JA, DESCA ) IF( JB.LE.N-1 ) THEN CALL PCHERK( 'Upper', 'No transpose', JB, N-JB, ONE, A, IA, $ JA+JB, DESCA, ONE, A, IA, JA, DESCA ) END IF * * Loop over remaining block of columns * DO 10 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( N-J+JA, DESCA( NB_ ) ) I = IA + J - JA CALL PCTRMM( 'Right', 'Upper', 'Conjugate transpose', $ 'Non-unit', J-JA, JB, CONE, A, I, J, DESCA, $ A, IA, J, DESCA ) CALL PCLAUU2( 'Upper', JB, A, I, J, DESCA ) IF( J+JB.LE.JA+N-1 ) THEN CALL PCGEMM( 'No transpose', 'Conjugate transpose', $ J-JA, JB, N-J-JB+JA, CONE, A, IA, J+JB, $ DESCA, A, I, J+JB, DESCA, CONE, A, IA, $ J, DESCA ) CALL PCHERK( 'Upper', 'No transpose', JB, N-J-JB+JA, ONE, $ A, I, J+JB, DESCA, ONE, A, I, J, DESCA ) END IF 10 CONTINUE ELSE * * Compute the product L' * L. * * Handle first block separately * JB = JN-JA+1 CALL PCLAUU2( 'Lower', JB, A, IA, JA, DESCA ) IF( JB.LE.N-1 ) THEN CALL PCHERK( 'Lower', 'Conjugate transpose', JB, N-JB, ONE, $ A, IA+JB, JA, DESCA, ONE, A, IA, JA, DESCA ) END IF * * Loop over remaining block of columns * DO 20 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( N-J+JA, DESCA( NB_ ) ) I = IA + J - JA CALL PCTRMM( 'Left', 'Lower', 'Conjugate Transpose', $ 'Non-unit', JB, J-JA, CONE, A, I, J, DESCA, A, $ I, JA, DESCA ) CALL PCLAUU2( 'Lower', JB, A, I, J, DESCA ) IF( J+JB.LE.JA+N-1 ) THEN CALL PCGEMM( 'Conjugate transpose', 'No transpose', JB, $ J-JA, N-J-JB+JA, CONE, A, I+JB, J, DESCA, $ A, I+JB, JA, DESCA, CONE, A, I, JA, DESCA ) CALL PCHERK( 'Lower', 'Conjugate transpose', JB, $ N-J-JB+JA, ONE, A, I+JB, J, DESCA, ONE, $ A, I, J, DESCA ) END IF 20 CONTINUE END IF * RETURN * * End of PCLAUUM * END