SUBROUTINE PDGETRF( M, N, A, IA, JA, DESCA, IPIV, INFO )
*
* -- ScaLAPACK routine (version 1.0) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* February 28, 1995
*
* .. Scalar Arguments ..
INTEGER IA, INFO, JA, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), IPIV( * )
DOUBLE PRECISION A( * )
* ..
*
* Purpose
* =======
*
* PDGETRF 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
* =====
*
* A description vector is associated with each 2D block-cyclicly dis-
* tributed matrix. This vector stores the information required to
* establish the mapping between a matrix entry and its corresponding
* process and memory location.
*
* In the following comments, the character _ should be read as
* "of the distributed matrix". Let A be a generic term for any 2D
* block cyclicly distributed matrix. Its description vector is DESCA:
*
* NOTATION STORED IN EXPLANATION
* --------------- ---------- ------------------------------------------
* M_A (global) DESCA( 1 ) The number of rows in the distributed
* matrix.
* N_A (global) DESCA( 2 ) The number of columns in the distributed
* matrix.
* MB_A (global) DESCA( 3 ) The blocking factor used to distribute
* the rows of the matrix.
* NB_A (global) DESCA( 4 ) The blocking factor used to distribute
* the columns of the matrix.
* RSRC_A (global) DESCA( 5 ) The process row over which the first row
* of the matrix is distributed.
* CSRC_A (global) DESCA( 6 ) The process column over which the first
* column of the matrix is distributed.
* CTXT_A (global) DESCA( 7 ) The BLACS context handle, indicating the
* BLACS process grid A is distributed over.
* The context itself is global, but the handle
* (the integer value) may vary.
* LLD_A (local) DESCA( 8 ) The leading dimension of the local array
* storing the local blocks of the distri-
* buted matrix A. LLD_A >= MAX(1,LOCp(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.
* LOCp( 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, LOCq( 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 LOCp() and LOCq() may be determined via a call to the
* ScaLAPACK tool function, NUMROC:
* LOCp( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
* LOCq( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
*
* 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) DOUBLE PRECISION pointer into the
* local memory to an array of dimension (LLD_A, LOCq(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
* A's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JA (global input) INTEGER
* A's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCA (global and local input) INTEGER array of dimension 8
* The array descriptor for the distributed matrix A.
*
* IPIV (local output) INTEGER array, dimension ( LOCp(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 ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
CHARACTER COLBTOP, COLCTOP, ROWBTOP
INTEGER I, ICOFF, ICTXT, IINFO, IROFF, J, JB, JN, MN,
$ MYCOL, MYROW, NPCOL, NPROW
* ..
* .. Local Arrays ..
INTEGER IDUM1( 1 ), IDUM2( 1 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, IGAMN2D, PCHK1MAT,
$ PTOPGET, PTOPSET, PDGEMM, PDGETF2,
$ PDLASWP, PDTRSM, PXERBLA
* ..
* .. External Functions ..
INTEGER ICEIL, INDXG2P, NUMROC
EXTERNAL ICEIL, INDXG2P, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( 7 )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test the input parameters
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -607
ELSE
CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO )
IF( INFO.EQ.0 ) THEN
IROFF = MOD( IA-1, DESCA( 3 ) )
ICOFF = MOD( JA-1, DESCA( 4 ) )
IF( IROFF.NE.0 ) THEN
INFO = -4
ELSE IF( ICOFF.NE.0 ) THEN
INFO = -5
ELSE IF( DESCA( 3 ).NE.DESCA( 4 ) ) THEN
INFO = -604
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, 'PDGETRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( DESCA( 1 ).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 PTOPGET( 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPGET( 'Broadcast', 'Columnwise', COLBTOP )
CALL PTOPGET( 'Combine', 'Columnwise', COLCTOP )
CALL PTOPSET( 'Broadcast', 'Rowwise', 'S-ring' )
CALL PTOPSET( 'Broadcast', 'Columnwise', ' ' )
CALL PTOPSET( 'Combine', 'Columnwise', ' ' )
*
* Handle the first block of columns separately
*
MN = MIN( M, N )
JN = MIN( ICEIL( JA, DESCA( 4 ) )*DESCA( 4 ), JA+MN-1 )
JB = JN - JA + 1
*
* Factor diagonal and subdiagonal blocks and test for exact
* singularity.
*
CALL PDGETF2( M, JB, A, IA, JA, DESCA, IPIV, INFO )
*
IF( JB+1.LE.N ) THEN
*
* Apply interchanges to columns JA+JB:JA+N-1.
*
CALL PDLASWP( 'Forward', 'Rows', N-JB, A, IA, JA+JB, DESCA,
$ IA, IA+JB-1, IPIV )
*
* Compute block row of U.
*
CALL PDTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
$ N-JB, ONE, A, IA, JA, DESCA, A, IA, JA+JB, DESCA )
*
IF( JB+1.LE.M ) THEN
*
* Update trailing submatrix.
*
CALL PDGEMM( 'No transpose', 'No transpose', M-JB, N-JB, JB,
$ -ONE, A, IA+JB, JA, DESCA, A, IA, JA+JB, DESCA,
$ ONE, A, IA+JB, JA+JB, DESCA )
*
END IF
END IF
*
* Loop over the remaining blocks of columns.
*
DO 10 J = JN+1, JA+MN-1, DESCA( 4 )
JB = MIN( MN-J+JA, DESCA( 4 ) )
I = IA + J - JA
*
* Factor diagonal and subdiagonal blocks and test for exact
* singularity.
*
CALL PDGETF2( 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 PDLASWP( '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 PDLASWP( 'Forward', 'Rowwise', N-J-JB+JA, A, IA, J+JB,
$ DESCA, I, I+JB-1, IPIV )
*
* Compute block row of U.
*
CALL PDTRSM( '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 PDGEMM( '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 PTOPSET( 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPSET( 'Broadcast', 'Columnwise', COLBTOP )
CALL PTOPSET( 'Combine', 'Columnwise', COLCTOP )
*
RETURN
*
* End of PDGETRF
*
END