SUBROUTINE PDGESV( N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB,
$ DESCB, 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, IB, INFO, JA, JB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCB( * ), IPIV( * )
DOUBLE PRECISION A( * ), B( * )
* ..
*
* Purpose
* =======
*
* PDGESV computes the solution to a real system of linear equations
*
* sub( A ) * X = sub( B ),
*
* where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed
* matrix and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS
* distributed matrices.
*
* The LU decomposition with partial pivoting and row interchanges is
* used to factor sub( A ) as sub( A ) = P * L * U, where P is a permu-
* tation matrix, L is unit lower triangular, and U is upper triangular.
* L and U are stored in sub( A ). The factored form of sub( A ) is then
* used to solve the system of equations sub( A ) * X = sub( B ).
*
* 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
* =========
*
* N (global input) INTEGER
* The number of rows and columns to be operated on, i.e. the
* order of the distributed submatrix sub( A ). N >= 0.
*
* NRHS (global input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the distributed submatrix sub( A ). NRHS >= 0.
*
* A (local input/local output) DOUBLE PRECISION pointer into the
* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
* On entry, the local pieces of the N-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 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.
*
* B (local input/local output) DOUBLE PRECISION pointer into the
* local memory to an array of dimension
* (LLD_B,LOCc(JB+NRHS-1)). On entry, the right hand side
* distributed matrix sub( B ). On exit, if INFO = 0, sub( B )
* is overwritten by the solution distributed matrix X.
*
* IB (global input) INTEGER
* The row index in the global array B indicating the first
* row of sub( B ).
*
* JB (global input) INTEGER
* The column index in the global array B indicating the
* first column of sub( B ).
*
* DESCB (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix B.
*
* 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, so the solution could not be
* computed.
*
* =====================================================================
*
* .. 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 )
* ..
* .. Local Scalars ..
INTEGER IAROW, IBROW, ICOFFA, ICTXT, IROFFA, IROFFB,
$ MYCOL, MYROW, NPCOL, NPROW
* ..
* .. Local Arrays ..
INTEGER IDUM1( 1 ), IDUM2( 1 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PDGETRF,
$ PDGETRS, PXERBLA
* ..
* .. External Functions ..
INTEGER INDXG2P
EXTERNAL INDXG2P
* ..
* .. Intrinsic Functions ..
INTRINSIC 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( N, 1, N, 1, IA, JA, DESCA, 6, INFO )
CALL CHK1MAT( N, 1, NRHS, 2, IB, JB, DESCB, 11, INFO )
IF( INFO.EQ.0 ) THEN
IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
$ NPROW )
IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),
$ NPROW )
IROFFA = MOD( IA-1, DESCA( MB_ ) )
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
IROFFB = MOD( IB-1, DESCB( MB_ ) )
IF( IROFFA.NE.0 ) THEN
INFO = -4
ELSE IF( ICOFFA.NE.0 ) THEN
INFO = -5
ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -(600+NB_)
ELSE IF( IBROW.NE.IAROW .OR. ICOFFA.NE.IROFFB ) THEN
INFO = -9
ELSE IF( DESCB( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -(1100+NB_)
ELSE IF( ICTXT.NE.DESCB( CTXT_ ) ) THEN
INFO = -(1100+CTXT_)
END IF
END IF
CALL PCHK2MAT( N, 1, N, 1, IA, JA, DESCA, 6, N, 1, NRHS, 2,
$ IB, JB, DESCB, 11, 0, IDUM1, IDUM2, INFO )
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PDGESV', -INFO )
RETURN
END IF
*
* Compute the LU factorization of sub( A ).
*
CALL PDGETRF( N, N, A, IA, JA, DESCA, IPIV, INFO )
*
IF( INFO.EQ.0 ) THEN
*
* Solve the system sub( A ) * X = sub( B ), overwriting sub( B )
* with X.
*
CALL PDGETRS( 'No transpose', N, NRHS, A, IA, JA, DESCA, IPIV,
$ B, IB, JB, DESCB, INFO )
*
END IF
*
RETURN
*
* End of PDGESV
*
END