SUBROUTINE PSGETRF( M, N, A, IA, JA, DESCA, IPIV, 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, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ), IPIV( * ) REAL A( * ) * .. * * Purpose * ======= * * PSGETRF computes an LU factorization of a general M-by-N distributed * matrix sub( A ) = (IA:IA+M-1,JA:JA+N-1) using partial pivoting with * row interchanges. * * The factorization has the form sub( A ) = P * L * U, where P is a * permutation matrix, L is lower triangular with unit diagonal ele- * ments (lower trapezoidal if m > n), and U is upper triangular * (upper trapezoidal if m < n). L and U are stored in sub( A ). * * This is the right-looking Parallel Level 3 BLAS version of the * algorithm. * * 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 * * This routine requires square block decomposition ( MB_A = 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) REAL pointer into the * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). * On entry, this array contains the local pieces of the M-by-N * distributed matrix sub( A ) to be factored. On exit, this * array contains the local pieces of the factors L and U from * the factorization sub( A ) = P*L*U; the unit diagonal ele- * ments of L are not stored. * * 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. * * IPIV (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A ) * This array contains the pivoting information. * IPIV(i) -> The global row local row i was swapped with. * This array is tied to the distributed matrix A. * * 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. * > 0: If INFO = K, U(IA+K-1,JA+K-1) is exactly zero. * The factorization has been completed, but the factor U * is exactly singular, and division by zero will occur if * it is used to solve a system of equations. * * ===================================================================== * * .. 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 ) * .. * .. Local Scalars .. CHARACTER COLBTOP, COLCTOP, ROWBTOP INTEGER I, ICOFF, ICTXT, IINFO, IN, IROFF, J, JB, JN, $ MN, MYCOL, MYROW, NPCOL, NPROW * .. * .. Local Arrays .. INTEGER IDUM1( 1 ), IDUM2( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, IGAMN2D, PCHK1MAT, $ PB_TOPGET, PB_TOPSET, PSGEMM, PSGETF2, $ PSLASWP, PSTRSM, PXERBLA * .. * .. External Functions .. INTEGER ICEIL EXTERNAL ICEIL * .. * .. Intrinsic Functions .. INTRINSIC 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 IROFF = MOD( IA-1, DESCA( MB_ ) ) ICOFF = MOD( JA-1, DESCA( NB_ ) ) IF( IROFF.NE.0 ) THEN INFO = -4 ELSE IF( ICOFF.NE.0 ) THEN INFO = -5 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(600+NB_) END IF END IF CALL PCHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, 0, IDUM1, $ IDUM2, INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PSGETRF', -INFO ) RETURN END IF * * Quick return if possible * IF( DESCA( M_ ).EQ.1 ) THEN IPIV( 1 ) = 1 RETURN ELSE IF( M.EQ.0 .OR. N.EQ.0 ) THEN RETURN END IF * * Split-ring topology for the communication along process rows * CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PB_TOPGET( ICTXT, 'Combine', 'Columnwise', COLCTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'S-ring' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', ' ' ) * * Handle the first block of columns separately * MN = MIN( M, N ) IN = MIN( ICEIL( IA, DESCA( MB_ ) )*DESCA( MB_ ), IA+M-1 ) JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA( NB_ ), JA+MN-1 ) JB = JN - JA + 1 * * Factor diagonal and subdiagonal blocks and test for exact * singularity. * CALL PSGETF2( M, JB, A, IA, JA, DESCA, IPIV, INFO ) * IF( JB+1.LE.N ) THEN * * Apply interchanges to columns JN+1:JA+N-1. * CALL PSLASWP( 'Forward', 'Rows', N-JB, A, IA, JN+1, DESCA, $ IA, IN, IPIV ) * * Compute block row of U. * CALL PSTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, $ N-JB, ONE, A, IA, JA, DESCA, A, IA, JN+1, DESCA ) * IF( JB+1.LE.M ) THEN * * Update trailing submatrix. * CALL PSGEMM( 'No transpose', 'No transpose', M-JB, N-JB, JB, $ -ONE, A, IN+1, JA, DESCA, A, IA, JN+1, DESCA, $ ONE, A, IN+1, JN+1, DESCA ) * END IF END IF * * Loop over the remaining blocks of columns. * DO 10 J = JN+1, JA+MN-1, DESCA( NB_ ) JB = MIN( MN-J+JA, DESCA( NB_ ) ) I = IA + J - JA * * Factor diagonal and subdiagonal blocks and test for exact * singularity. * CALL PSGETF2( M-J+JA, JB, A, I, J, DESCA, IPIV, IINFO ) * IF( INFO.EQ.0 .AND. IINFO.GT.0 ) $ INFO = IINFO + J - JA * * Apply interchanges to columns JA:J-JA. * CALL PSLASWP( 'Forward', 'Rowwise', J-JA, A, IA, JA, DESCA, $ I, I+JB-1, IPIV ) * IF( J-JA+JB+1.LE.N ) THEN * * Apply interchanges to columns J+JB:JA+N-1. * CALL PSLASWP( 'Forward', 'Rowwise', N-J-JB+JA, A, IA, J+JB, $ DESCA, I, I+JB-1, IPIV ) * * Compute block row of U. * CALL PSTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, $ N-J-JB+JA, ONE, A, I, J, DESCA, A, I, J+JB, $ DESCA ) * IF( J-JA+JB+1.LE.M ) THEN * * Update trailing submatrix. * CALL PSGEMM( 'No transpose', 'No transpose', M-J-JB+JA, $ N-J-JB+JA, JB, -ONE, A, I+JB, J, DESCA, A, $ I, J+JB, DESCA, ONE, A, I+JB, J+JB, DESCA ) * END IF END IF * 10 CONTINUE * IF( INFO.EQ.0 ) $ INFO = MN + 1 CALL IGAMN2D( ICTXT, 'Rowwise', ' ', 1, 1, INFO, 1, IDUM1, IDUM2, $ -1, -1, MYCOL ) IF( INFO.EQ.MN+1 ) $ INFO = 0 * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', COLCTOP ) * RETURN * * End of PSGETRF * END