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C ----------------------------------------------------------------
C Programmer(s): Daniel R. Reynolds @ SMU
C Steve Smith, Eddy Banks and Alan C. Hindmarsh @ LLNL
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 This simple example problem for FIDA, due to Robertson, is from
c chemical kinetics, and consists of the following three equations:
c
c dy1/dt = -.04*y1 + 1.e4*y2*y3
c dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2
c 0 = y1 + y2 + y3 - 1
c
c on the interval from t = 0.0 to t = 4.e10, with initial
c conditions: y1 = 1, y2 = y3 = 0.
c
c While integrating the system, we also employ the rootfinding feature
c to find the points at which y1 = 1.e-4 or at which y3 = 0.01.
c
c The problem is solved using a dense linear solver, with a
c user-supplied Jacobian. Output is printed at
c t = .4, 4, 40, ..., 4e10.
c ----------------------------------------------------------------
c
program fidaRoberts_dns
c
implicit none
c
c The following declaration specification should match C type long int.
integer*8 neq, iout(25), ipar
integer ier, ierroot, info(2)
double precision rout(10), rpar
integer iatol, nout, jout, itask
integer nst, kused, hused, i
double precision t0, t1, rtol, tout, tret
double precision y(3), yp(3), atol(3)
c
data nst/3/, kused/9/, hused/2/
integer nthreads
nthreads = 4
c
c Initialize variables
c
neq = 3
nout = 12
rtol = 1.0d-4
t0 = 0.0d0
t1 = 0.4d0
iatol = 2
itask = 1
c
y(1) = 1.0d0
y(2) = 0.0d0
y(3) = 0.0d0
c
yp(1) = -0.04d0
yp(2) = 0.04d0
yp(3) = 0.0d0
c
atol(1) = 1.0d-6
atol(2) = 1.0d-10
atol(3) = 1.0d-6
c
c Initialize IDA vector environment
c
call fnvinitomp(2, neq, nthreads, ier)
if (ier .ne. 0) then
write(6,10) ier
10 format(///' SUNDIALS_ERROR: FNVINITS returned IER = ', i5)
stop
endif
c
call fidamalloc(t0, y, yp, iatol, rtol, atol,
& iout, rout, ipar, rpar, ier)
if (ier .ne. 0) then
write(6,20) ier
20 format(///' SUNDIALS_ERROR: FIDAMALLOC returned IER = ', i5)
stop
endif
c
c Initialize rootfinding problem
call fidarootinit(2, ier)
if (ier .ne. 0) then
write(6,25) ier
25 format(///' SUNDIALS_ERROR: FIDAROOTINIT returned IER = ', i5)
call fidafree
stop
endif
c
c Attach dense matrix and linear solver
c
call fsundensematinit(2, neq, neq, ier)
if (ier .ne. 0) then
write(6,30) ier
30 format(///' SUNDIALS_ERROR: FSUNDENSEMATINIT IER = ', i5)
call fidafree
stop
endif
call fsundenselinsolinit(2, ier)
if (ier .ne. 0) then
write(6,33) ier
33 format(///' SUNDIALS_ERROR: FSUNDENSELINSOLINIT IER = ', i5)
call fidafree
stop
endif
call fidalsinit(ier)
if (ier .ne. 0) then
write(6,35) ier
35 format(///' SUNDIALS_ERROR: FIDALSINIT returned IER = ', i5)
call fidafree
stop
endif
call fidadensesetjac(1, ier)
if (ier .ne. 0) then
write(6,37) ier
37 format(///' SUNDIALS_ERROR: FIDADENSESETJAC IER = ', i5)
call fidafree
stop
endif
c
c Print header
c
call prntintro(rtol, atol, y)
c
tout = t1
c
c
jout = 1
do while(jout .le. nout)
c
call fidasolve(tout, tret, y, yp, itask, ier)
c
write(6,40) tret, (y(i), i = 1,3), iout(nst), iout(kused),
& rout(hused)
40 format(e10.4, 3(1x,e12.4), i5, i3, e12.4)
c
if (ier .lt. 0) then
write(6,50) ier, iout(15)
50 format(///' SUNDIALS_ERROR: FIDASOLVE returned IER = ',i5,/,
1 ' Linear Solver returned IER = ',i5)
call fidarootfree
call fidafree
stop
endif
c
if (ier .eq. 2) then
call fidarootinfo(2, info, ierroot)
if (ierroot .lt. 0) then
write(6,55) ierroot
55 format(///' SUNDIALS_ERROR: FIDAROOTINFO returned IER = ',
1 i5)
call fidarootfree
call fidafree
stop
endif
write(6,60) (info(i), i = 1,2)
60 format(5x, 'Above is a root, INFO() = ', 2i3)
endif
c
if (ier .eq. 0) then
tout = tout * 10.0d0
jout = jout + 1
endif
c
ENDDO
c
c Print final statistics
c
call prntstats(iout)
c
c Free IDA memory
c
call fidarootfree
call fidafree
c
stop
end
c
c ==========
c
subroutine fidaresfun(tres, y, yp, res, ipar, rpar, reserr)
c
implicit none
c
c The following declaration specification should match C type long int.
integer*8 ipar(*)
integer reserr
double precision tres, rpar(*)
double precision y(*), yp(*), res(*)
c
res(1) = -0.04d0*y(1)+1.0d4*y(2)*y(3)
res(2) = -res(1)-3.0d7*y(2)*y(2)-yp(2)
res(1) = res(1)-yp(1)
res(3) = y(1)+y(2)+y(3)-1.0d0
c
reserr = 0
c
return
end
c
c ==========
c
subroutine fidadjac(neq, t, y, yp, r, jac, cj, ewt, h,
1 ipar, rpar, wk1, wk2, wk3, djacerr)
c
implicit none
c
c The following declaration specification should match C type long int.
integer*8 neq, ipar(*)
integer djacerr
double precision t, h, cj, rpar(*)
double precision y(*), yp(*), r(*), ewt(*), jac(neq,neq)
double precision wk1(*), wk2(*), wk3(*)
c
jac(1,1) = -0.04d0-cj
jac(2,1) = 0.04d0
jac(3,1) = 1.0d0
jac(1,2) = 1.0d4*y(3)
jac(2,2) = -1.0d4*y(3)-6.0d7*y(2)-cj
jac(3,2) = 1.0d0
jac(1,3) = 1.0d4*y(2)
jac(2,3) = -1.0d4*y(2)
jac(3,3) = 1.0d0
c
djacerr = 0
return
end
c
c ==========
c
subroutine fidarootfn(t, y, yp, g, ipar, rpar, ier)
c Fortran routine for rootfinding
implicit none
c
c The following declaration specification should match C type long int.
integer*8 ipar(*)
integer ier
double precision t, y(*), yp(*), g(*), rpar(*)
c
g(1) = y(1) - 1.0d-4
g(2) = y(3) - 1.0d-2
ier = 0
return
end
c
c ==========
c
subroutine prntintro(rtol, atol, y)
c
implicit none
c
integer i
double precision rtol, atol(*), y(*)
c
write(6,60) rtol, (atol(i), i = 1,3), (y(i), i = 1,3)
60 format(/'fidaRoberts_dns: Robertson kinetics DAE serial example',
& 'problem for IDA', /,' Three equation chemical',
& 'kinetics problem.', //,
& 'Tolerance parameters: rtol = ', e8.2,
& ' atol = ', 3(1x,e8.2), /,
& 'Initial conditions y0 = (', 3(1x,e8.2), ')', //,
& ' t y1 y2 y3 nst',
& ' k h')
c
return
end
c
c ==========
c
subroutine prntstats(iout)
c
implicit none
c
c The following declaration specification should match C type long int.
integer*8 iout(25)
integer nst, reseval, jaceval, nni, ncf, netf, nge
c
data nst/3/, reseval/4/, jaceval/17/, nni/7/, netf/5/,
& ncf/6/, nge/12/
c
write(6,70) iout(nst), iout(reseval), iout(jaceval),
& iout(nni), iout(netf), iout(ncf), iout(nge)
70 format(/'Final Run Statistics:', //,
& 'Number of steps = ', i3, /,
& 'Number of residual evaluations = ', i3, /,
& 'Number of Jacobian evaluations = ', i3, /,
& 'Number of nonlinear iterations = ', i3, /,
& 'Number of error test failures = ', i3, /,
& 'Number of nonlinear conv. failures = ', i3, /,
& 'Number of root function evals. = ', i3)
c
return
end
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