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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
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