SUBROUTINE PCGETF2( M, N, A, IA, JA, DESCA, IPIV, INFO ) * * -- ScaLAPACK routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. INTEGER IA, INFO, JA, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ), IPIV( * ) COMPLEX A( * ) * .. * * Purpose * ======= * * PCGETF2 computes an LU factorization of a general M-by-N * distributed matrix sub( A ) = 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 * elements (lower trapezoidal if m > n), and U is upper triangular * (upper trapezoidal if m < n). * * This is the right-looking Parallel Level 2 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 N <= NB_A-MOD(JA-1, NB_A) and 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 ). * NB_A-MOD(JA-1, NB_A) >= 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, this array contains the local pieces of the M-by-N * distributed matrix sub( A ). On exit, this array contains * the local pieces of the factors L and U from the factoriza- * tion sub( A ) = P*L*U; the unit diagonal elements 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 (local 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 ) COMPLEX ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. CHARACTER ROWBTOP INTEGER I, IACOL, IAROW, ICOFF, ICTXT, IIA, IROFF, J, $ JJA, MN, MYCOL, MYROW, NPCOL, NPROW COMPLEX GMAX * .. * .. External Subroutines .. EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, IGEBR2D, $ IGEBS2D, INFOG2L, PCAMAX, PCGERU, $ PCSCAL, PCSWAP, PTOPGET, PXERBLA * .. * .. 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( N+ICOFF.GT.DESCA( NB_ ) ) THEN INFO = -2 ELSE 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 END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PCGETF2', -INFO ) CALL BLACS_ABORT( ICTXT, 1 ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * MN = MIN( M, N ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) CALL PTOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) * IF( MYCOL.EQ.IACOL ) THEN DO 10 J = JA, JA+MN-1 I = IA + J - JA * * Find pivot and test for singularity. * CALL PCAMAX( M-J+JA, GMAX, IPIV( IIA+J-JA ), A, I, J, $ DESCA, 1 ) IF( GMAX.NE.ZERO ) THEN * * Apply the row interchanges to columns JA:JA+N-1 * CALL PCSWAP( N, A, I, JA, DESCA, DESCA( M_ ), A, $ IPIV( IIA+J-JA ), JA, DESCA, DESCA( M_ ) ) * * Compute elements I+1:IA+M-1 of J-th column. * IF( J-JA+1.LT.M ) $ CALL PCSCAL( M-J+JA-1, ONE / GMAX, A, I+1, J, $ DESCA, 1 ) ELSE IF( INFO.EQ.0 ) THEN INFO = J - JA + 1 END IF * * Update trailing submatrix * IF( J-JA+1.LT.MN ) THEN CALL PCGERU( M-J+JA-1, N-J+JA-1, -ONE, A, I+1, J, DESCA, $ 1, A, I, J+1, DESCA, DESCA( M_ ), A, I+1, $ J+1, DESCA ) END IF 10 CONTINUE * CALL IGEBS2D( ICTXT, 'Rowwise', ROWBTOP, MN, 1, IPIV( IIA ), $ MN ) * ELSE * CALL IGEBR2D( ICTXT, 'Rowwise', ROWBTOP, MN, 1, IPIV( IIA ), $ MN, MYROW, IACOL ) * END IF * RETURN * * End of PCGETF2 * END