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C --------------------------------------------------------------------
C SUNDIALS Copyright Start
C Copyright (c) 2002-2022, Lawrence Livermore National Security
C and Southern Methodist University.
C All rights reserved.
C
C See the top-level LICENSE and NOTICE files for details.
C
C SPDX-License-Identifier: BSD-3-Clause
C SUNDIALS Copyright End
C --------------------------------------------------------------------
C Diagonal ODE example. Nonstiff case: alpha = 10/NEQ.
C --------------------------------------------------------------------
C
C Include MPI-Fortran header file for MPI_COMM_WORLD, MPI types.
C
IMPLICIT NONE
C
INCLUDE "mpif.h"
C
C The following declaration specification should match C type long int.
INTEGER*8 NLOCAL, NEQ, I, IOUT(25), IPAR(2)
PARAMETER (NLOCAL=2)
C
INTEGER*4 IER, MYPE, NPES, NOUT, LNST, LNFE, LNNI, LNCF, LNETF
INTEGER*4 METH, IATOL, ITASK, JOUT
INTEGER*8 NST, NFE, NNI, NCFN, NETF
DOUBLE PRECISION Y(128), ROUT(10), RPAR(1)
DOUBLE PRECISION ATOL, RTOL, DTOUT, T, ALPHA, TOUT
DOUBLE PRECISION ERMAX, ERRI, GERMAX
C
DATA ATOL/1.0D-10/, RTOL/1.0D-5/, DTOUT/0.1D0/, NOUT/10/
DATA LNST/3/, LNFE/4/, LNNI/7/, LNCF/6/, LNETF/5/
C
C Get NPES and MYPE. Requires initialization of MPI.
CALL MPI_INIT(IER)
IF (IER .NE. 0) THEN
WRITE(6,5) IER
5 FORMAT(///' MPI_ERROR: MPI_INIT returned IER = ', I5)
STOP
ENDIF
CALL MPI_COMM_SIZE(MPI_COMM_WORLD, NPES, IER)
IF (IER .NE. 0) THEN
WRITE(6,6) IER
6 FORMAT(///' MPI_ERROR: MPI_COMM_SIZE returned IER = ', I5)
CALL MPI_ABORT(MPI_COMM_WORLD, 1, IER)
STOP
ENDIF
CALL MPI_COMM_RANK(MPI_COMM_WORLD, MYPE, IER)
IF (IER .NE. 0) THEN
WRITE(6,7) IER
7 FORMAT(///' MPI_ERROR: MPI_COMM_RANK returned IER = ', I5)
CALL MPI_ABORT(MPI_COMM_WORLD, 1, IER)
STOP
ENDIF
C
C Set input arguments.
NEQ = NPES * NLOCAL
T = 0.0D0
METH = 1
IATOL = 1
ITASK = 1
c Set parameter ALPHA
ALPHA = 10.0D0 / NEQ
C
C Load IPAR and RPAR
IPAR(1) = NLOCAL
IPAR(2) = MYPE
RPAR(1) = ALPHA
C
DO 10 I = 1, NLOCAL
10 Y(I) = 1.0D0
C
IF (MYPE .EQ. 0) THEN
WRITE(6,11) NEQ, ALPHA
11 FORMAT('Diagonal test problem:'//' NEQ = ', I3, /
1 ' parameter alpha = ', F8.3)
WRITE(6,12)
12 FORMAT(' ydot_i = -alpha*i * y_i (i = 1,...,NEQ)')
WRITE(6,13) RTOL, ATOL
13 FORMAT(' RTOL, ATOL = ', 2E10.1)
WRITE(6,14)
14 FORMAT(' Method is ADAMS/FIXEDPOINT')
WRITE(6,15) NPES
15 FORMAT(' Number of processors = ', I3//)
ENDIF
C
CALL FNVINITP(MPI_COMM_WORLD, 1, NLOCAL, NEQ, IER)
C
IF (IER .NE. 0) THEN
WRITE(6,20) IER
20 FORMAT(///' SUNDIALS_ERROR: FNVINITP returned IER = ', I5)
CALL MPI_FINALIZE(IER)
STOP
ENDIF
C
CALL FCVMALLOC(T, Y, METH, IATOL, RTOL, ATOL,
1 IOUT, ROUT, IPAR, RPAR, IER)
C
IF (IER .NE. 0) THEN
WRITE(6,30) IER
30 FORMAT(///' SUNDIALS_ERROR: FCVMALLOC returned IER = ', I5)
CALL MPI_ABORT(MPI_COMM_WORLD, 1, IER)
STOP
ENDIF
C
C Create Fixed Point Solver
CALL FSUNFIXEDPOINTINIT(1, 0, IER)
C
IF (IER .NE. 0) THEN
WRITE(6,31) IER
31 FORMAT(
1 ///' SUNDIALS_ERROR: FSUNFIXEDPOINTINIT returned IER = ', I5)
CALL MPI_ABORT(MPI_COMM_WORLD, 1, IER)
STOP
ENDIF
C
C Attach Fixed Point Solver
CALL FCVNLSINIT(IER)
C
IF (IER .NE. 0) THEN
WRITE(6,32) IER
32 FORMAT(///' SUNDIALS_ERROR: FCVNLSINIT returned IER = ', I5)
CALL MPI_ABORT(MPI_COMM_WORLD, 1, IER)
STOP
ENDIF
C
C Loop through tout values, call solver, print output, test for failure.
TOUT = DTOUT
DO 70 JOUT = 1, NOUT
C
CALL FCVODE(TOUT, T, Y, ITASK, IER)
C
IF (MYPE .EQ. 0) WRITE(6,40) T, IOUT(LNST), IOUT(LNFE)
40 FORMAT(' t = ', D10.2, 5X, 'no. steps = ', I5,
& ' no. f-s = ', I5)
C
IF (IER .NE. 0) THEN
WRITE(6,60) IER, IOUT(15)
60 FORMAT(///' SUNDIALS_ERROR: FCVODE returned IER = ', I5, /,
& ' Linear Solver returned IER = ', I5)
CALL MPI_ABORT(MPI_COMM_WORLD, 1, IER)
STOP
ENDIF
C
TOUT = TOUT + DTOUT
70 CONTINUE
C
C Get max. absolute error in the local vector.
ERMAX = 0.0D0
DO 75 I = 1, NLOCAL
ERRI = Y(I) - EXP(-ALPHA * (MYPE * NLOCAL + I) * T)
ERMAX = MAX(ERMAX, ABS(ERRI))
75 CONTINUE
C Get global max. error from MPI_REDUCE call.
CALL MPI_REDUCE(ERMAX, GERMAX, 1, MPI_DOUBLE_PRECISION, MPI_MAX,
1 0, MPI_COMM_WORLD, IER)
IF (IER .NE. 0) THEN
WRITE(6,80) IER
80 FORMAT(///' MPI_ERROR: MPI_REDUCE returned IER = ', I5)
CALL MPI_ABORT(MPI_COMM_WORLD, 1, IER)
STOP
ENDIF
IF (MYPE .EQ. 0) WRITE(6,85) GERMAX
85 FORMAT(/'Max. absolute error is ', E10.2/)
C
C Print final statistics.
NST = IOUT(LNST)
NFE = IOUT(LNFE)
NNI = IOUT(LNNI)
NCFN = IOUT(LNCF)
NETF = IOUT(LNETF)
IF (MYPE .EQ. 0) WRITE (6,90) NST, NFE, NNI, NCFN, NETF
90 FORMAT(/'Final statistics:'//
& ' number of steps = ', I5, 5X, /,
& ' number of f evals. = ', I5/
& ' number of nonlinear iters. = ', I5/
& ' number of nonlinear conv. failures = ', I3/
& ' number of error test failures = ', I3)
C
C Free the memory and finalize MPI.
CALL FCVFREE
CALL MPI_FINALIZE(IER)
IF (IER .NE. 0) THEN
WRITE(6,95) IER
95 FORMAT(///' MPI_ERROR: MPI_FINALIZE returned IER = ', I5)
STOP
ENDIF
C
STOP
END
C
C ------------------------------------------------------------------------
C
SUBROUTINE FCVFUN(T, Y, YDOT, IPAR, RPAR, IER)
C Routine for right-hand side function f
C
IMPLICIT NONE
C
C The following declaration specification should match C type long int.
INTEGER*8 IPAR(*), MYPE, I, NLOCAL
INTEGER*4 IER
DOUBLE PRECISION T, Y(*), YDOT(*), RPAR(*)
DOUBLE PRECISION ALPHA
C
NLOCAL = IPAR(1)
MYPE = IPAR(2)
ALPHA = RPAR(1)
C
DO I = 1, NLOCAL
YDOT(I) = -ALPHA * (MYPE * NLOCAL + I) * Y(I)
ENDDO
C
IER = 0
C
RETURN
END
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