PROGRAM EXAMPLE1 * * Example Program solving Ax=b via ScaLAPACK routine PDGESV * * .. Parameters .. INTEGER DLEN_, IA, JA, IB, JB, M, N, MB, NB, RSRC, \$ CSRC, MXLLDA, MXLLDB, NRHS, NBRHS, NOUT, \$ MXLOCR, MXLOCC, MXRHSC PARAMETER ( DLEN_ = 9, IA = 1, JA = 1, IB = 1, JB = 1, \$ M = 9, N = 9, MB = 2, NB = 2, RSRC = 0, \$ CSRC = 0, MXLLDA = 5, MXLLDB = 5, NRHS = 1, \$ NBRHS = 1, NOUT = 6, MXLOCR = 5, MXLOCC = 4, \$ MXRHSC = 1 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER ICTXT, INFO, MYCOL, MYROW, NPCOL, NPROW DOUBLE PRECISION ANORM, BNORM, EPS, RESID, XNORM * .. * .. Local Arrays .. INTEGER DESCA( DLEN_ ), DESCB( DLEN_ ), \$ IPIV( MXLOCR+NB ) DOUBLE PRECISION A( MXLLDA, MXLOCC ), A0( MXLLDA, MXLOCC ), \$ B( MXLLDB, MXRHSC ), B0( MXLLDB, MXRHSC ), \$ WORK( MXLOCR ) * .. * .. External Functions .. DOUBLE PRECISION PDLAMCH, PDLANGE EXTERNAL PDLAMCH, PDLANGE * .. * .. External Subroutines .. EXTERNAL BLACS_EXIT, BLACS_GRIDEXIT, BLACS_GRIDINFO, \$ DESCINIT, MATINIT, PDGEMM, PDGESV, PDLACPY, \$ SL_INIT * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Data statements .. DATA NPROW / 2 / , NPCOL / 3 / * .. * .. Executable Statements .. * * INITIALIZE THE PROCESS GRID * CALL SL_INIT( ICTXT, NPROW, NPCOL ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * If I'm not in the process grid, go to the end of the program * IF( MYROW.EQ.-1 ) \$ GO TO 10 * * DISTRIBUTE THE MATRIX ON THE PROCESS GRID * Initialize the array descriptors for the matrices A and B * CALL DESCINIT( DESCA, M, N, MB, NB, RSRC, CSRC, ICTXT, MXLLDA, \$ INFO ) CALL DESCINIT( DESCB, N, NRHS, NB, NBRHS, RSRC, CSRC, ICTXT, \$ MXLLDB, INFO ) * * Generate matrices A and B and distribute to the process grid * CALL MATINIT( A, DESCA, B, DESCB ) * * Make a copy of A and B for checking purposes * CALL PDLACPY( 'All', N, N, A, 1, 1, DESCA, A0, 1, 1, DESCA ) CALL PDLACPY( 'All', N, NRHS, B, 1, 1, DESCB, B0, 1, 1, DESCB ) * * CALL THE SCALAPACK ROUTINE * Solve the linear system A * X = B * CALL PDGESV( N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB, DESCB, \$ INFO ) * IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN WRITE( NOUT, FMT = 9999 ) WRITE( NOUT, FMT = 9998 )M, N, NB WRITE( NOUT, FMT = 9997 )NPROW*NPCOL, NPROW, NPCOL WRITE( NOUT, FMT = 9996 )INFO END IF * * Compute residual ||A * X - B|| / ( ||X|| * ||A|| * eps * N ) * EPS = PDLAMCH( ICTXT, 'Epsilon' ) ANORM = PDLANGE( 'I', N, N, A, 1, 1, DESCA, WORK ) BNORM = PDLANGE( 'I', N, NRHS, B, 1, 1, DESCB, WORK ) CALL PDGEMM( 'N', 'N', N, NRHS, N, ONE, A0, 1, 1, DESCA, B, 1, 1, \$ DESCB, -ONE, B0, 1, 1, DESCB ) XNORM = PDLANGE( 'I', N, NRHS, B0, 1, 1, DESCB, WORK ) RESID = XNORM / ( ANORM*BNORM*EPS*DBLE( N ) ) * IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN IF( RESID.LT.10.0D+0 ) THEN WRITE( NOUT, FMT = 9995 ) WRITE( NOUT, FMT = 9993 )RESID ELSE WRITE( NOUT, FMT = 9994 ) WRITE( NOUT, FMT = 9993 )RESID END IF END IF * * RELEASE THE PROCESS GRID * Free the BLACS context * CALL BLACS_GRIDEXIT( ICTXT ) 10 CONTINUE * * Exit the BLACS * CALL BLACS_EXIT( 0 ) * 9999 FORMAT( / 'ScaLAPACK Example Program #1 -- May 1, 1997' ) 9998 FORMAT( / 'Solving Ax=b where A is a ', I3, ' by ', I3, \$ ' matrix with a block size of ', I3 ) 9997 FORMAT( 'Running on ', I3, ' processes, where the process grid', \$ ' is ', I3, ' by ', I3 ) 9996 FORMAT( / 'INFO code returned by PDGESV = ', I3 ) 9995 FORMAT( / \$ 'According to the normalized residual the solution is correct.' \$ ) 9994 FORMAT( / \$ 'According to the normalized residual the solution is incorrect.' \$ ) 9993 FORMAT( / '||A*x - b|| / ( ||x||*||A||*eps*N ) = ', 1P, E16.8 ) STOP END SUBROUTINE MATINIT( AA, DESCA, B, DESCB ) * * MATINIT generates and distributes matrices A and B (depicted in * Figures 2.5 and 2.6) to a 2 x 3 process grid * * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ) DOUBLE PRECISION AA( * ), B( * ) * .. * .. Parameters .. INTEGER CTXT_, LLD_ PARAMETER ( CTXT_ = 2, LLD_ = 9 ) * .. * .. Local Scalars .. INTEGER ICTXT, MXLLDA, MYCOL, MYROW, NPCOL, NPROW DOUBLE PRECISION A, C, K, L, P, S * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO * .. * .. Executable Statements .. * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * S = 19.0D0 C = 3.0D0 A = 1.0D0 L = 12.0D0 P = 16.0D0 K = 11.0D0 * MXLLDA = DESCA( LLD_ ) * IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN AA( 1 ) = S AA( 2 ) = -S AA( 3 ) = -S AA( 4 ) = -S AA( 5 ) = -S AA( 1+MXLLDA ) = C AA( 2+MXLLDA ) = C AA( 3+MXLLDA ) = -C AA( 4+MXLLDA ) = -C AA( 5+MXLLDA ) = -C AA( 1+2*MXLLDA ) = A AA( 2+2*MXLLDA ) = A AA( 3+2*MXLLDA ) = A AA( 4+2*MXLLDA ) = A AA( 5+2*MXLLDA ) = -A AA( 1+3*MXLLDA ) = C AA( 2+3*MXLLDA ) = C AA( 3+3*MXLLDA ) = C AA( 4+3*MXLLDA ) = C AA( 5+3*MXLLDA ) = -C B( 1 ) = 0.0D0 B( 2 ) = 0.0D0 B( 3 ) = 0.0D0 B( 4 ) = 0.0D0 B( 5 ) = 0.0D0 ELSE IF( MYROW.EQ.0 .AND. MYCOL.EQ.1 ) THEN AA( 1 ) = A AA( 2 ) = A AA( 3 ) = -A AA( 4 ) = -A AA( 5 ) = -A AA( 1+MXLLDA ) = L AA( 2+MXLLDA ) = L AA( 3+MXLLDA ) = -L AA( 4+MXLLDA ) = -L AA( 5+MXLLDA ) = -L AA( 1+2*MXLLDA ) = K AA( 2+2*MXLLDA ) = K AA( 3+2*MXLLDA ) = K AA( 4+2*MXLLDA ) = K AA( 5+2*MXLLDA ) = K ELSE IF( MYROW.EQ.0 .AND. MYCOL.EQ.2 ) THEN AA( 1 ) = A AA( 2 ) = A AA( 3 ) = A AA( 4 ) = -A AA( 5 ) = -A AA( 1+MXLLDA ) = P AA( 2+MXLLDA ) = P AA( 3+MXLLDA ) = P AA( 4+MXLLDA ) = P AA( 5+MXLLDA ) = -P ELSE IF( MYROW.EQ.1 .AND. MYCOL.EQ.0 ) THEN AA( 1 ) = -S AA( 2 ) = -S AA( 3 ) = -S AA( 4 ) = -S AA( 1+MXLLDA ) = -C AA( 2+MXLLDA ) = -C AA( 3+MXLLDA ) = -C AA( 4+MXLLDA ) = C AA( 1+2*MXLLDA ) = A AA( 2+2*MXLLDA ) = A AA( 3+2*MXLLDA ) = A AA( 4+2*MXLLDA ) = -A AA( 1+3*MXLLDA ) = C AA( 2+3*MXLLDA ) = C AA( 3+3*MXLLDA ) = C AA( 4+3*MXLLDA ) = C B( 1 ) = 1.0D0 B( 2 ) = 0.0D0 B( 3 ) = 0.0D0 B( 4 ) = 0.0D0 ELSE IF( MYROW.EQ.1 .AND. MYCOL.EQ.1 ) THEN AA( 1 ) = A AA( 2 ) = -A AA( 3 ) = -A AA( 4 ) = -A AA( 1+MXLLDA ) = L AA( 2+MXLLDA ) = L AA( 3+MXLLDA ) = -L AA( 4+MXLLDA ) = -L AA( 1+2*MXLLDA ) = K AA( 2+2*MXLLDA ) = K AA( 3+2*MXLLDA ) = K AA( 4+2*MXLLDA ) = K ELSE IF( MYROW.EQ.1 .AND. MYCOL.EQ.2 ) THEN AA( 1 ) = A AA( 2 ) = A AA( 3 ) = -A AA( 4 ) = -A AA( 1+MXLLDA ) = P AA( 2+MXLLDA ) = P AA( 3+MXLLDA ) = -P AA( 4+MXLLDA ) = -P END IF RETURN END SUBROUTINE SL_INIT( ICTXT, NPROW, NPCOL ) * * .. Scalar Arguments .. INTEGER ICTXT, NPCOL, NPROW * .. * * Purpose * ======= * * SL_INIT initializes an NPROW x NPCOL process grid using a row-major * ordering of the processes. This routine retrieves a default system * context which will include all available processes. In addition it * spawns the processes if needed. * * Arguments * ========= * * ICTXT (global output) INTEGER * ICTXT specifies the BLACS context handle identifying the * created process grid. The context itself is global. * * NPROW (global input) INTEGER * NPROW specifies the number of process rows in the grid * to be created. * * NPCOL (global input) INTEGER * NPCOL specifies the number of process columns in the grid * to be created. * * ===================================================================== * * .. Local Scalars .. INTEGER IAM, NPROCS * .. * .. External Subroutines .. EXTERNAL BLACS_GET, BLACS_GRIDINIT, BLACS_PINFO, \$ BLACS_SETUP * .. * .. Executable Statements .. * * Get starting information * CALL BLACS_PINFO( IAM, NPROCS ) * * If machine needs additional set up, do it now * IF( NPROCS.LT.1 ) THEN IF( IAM.EQ.0 ) \$ NPROCS = NPROW*NPCOL CALL BLACS_SETUP( IAM, NPROCS ) END IF * * Define process grid * CALL BLACS_GET( -1, 0, ICTXT ) CALL BLACS_GRIDINIT( ICTXT, 'Row-major', NPROW, NPCOL ) * RETURN * * End of SL_INIT * END