SUBROUTINE INTEGRATE( NSENSIT, Y, TIN, TOUT ) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' C TIN - Start Time KPP_REAL TIN C TOUT - End Time KPP_REAL TOUT C Y - Concentrations and Sensitivities KPP_REAL Y(NVAR*(NSENSIT+1)) C --- Note: Y contains: (1:NVAR) concentrations, followed by C --- (1:NVAR) sensitivities w.r.t. first parameter, followed by C --- etc., followed by C --- (1:NVAR) sensitivities w.r.t. NSENSIT's parameter INTEGER INFO(5) EXTERNAL FUNC_CHEM, JAC_CHEM INFO(1) = Autonomous CALL ROS3_DDM(NVAR,NSENSIT,TIN,TOUT,STEPMIN,STEPMAX, + STEPMIN,Y,ATOL,RTOL, + Info,FUNC_CHEM,JAC_CHEM) RETURN END SUBROUTINE ROS3_DDM(N,NSENSIT,T,Tnext,Hmin,Hmax,Hstart, + y,AbsTol,RelTol, + Info,FUNC_CHEM,JAC_CHEM) IMPLICIT NONE INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' INCLUDE 'KPP_ROOT_sparse.h' C L-stable Rosenbrock 3(2), with C strongly A-stable embedded formula for error control. C C Direct decoupled computation of sensitivities. C The global variable DDMTYPE distinguishes between: C DDMTYPE = 0 : sensitivities w.r.t. initial values C DDMTYPE = 1 : sensitivities w.r.t. parameters C C All the arguments aggree with the KPP syntax. C C INPUT ARGUMENTS: C y = Vector of: (1:NVAR) concentrations, followed by C (1:NVAR) sensitivities w.r.t. first parameter, followed by C etc., followed by C (1:NVAR) sensitivities w.r.t. NSENSIT's parameter C (y contains initial values at input, final values at output) C [T, Tnext] = the integration interval C Hmin, Hmax = lower and upper bounds for the selected step-size. C Note that for Step = Hmin the current computed C solution is unconditionally accepted by the error C control mechanism. C AbsTol, RelTol = (NVAR) dimensional vectors of C componentwise absolute and relative tolerances. C FUNC_CHEM = name of routine of derivatives. KPP syntax. C See the header below. C JAC_CHEM = name of routine that computes the Jacobian, in C sparse format. KPP syntax. See the header below. C Info(1) = 1 for Autonomous system C = 0 for nonAutonomous system C C OUTPUT ARGUMENTS: C y = the values of concentrations at TEND. C T = equals TEND on output. C Info(2) = # of FUNC_CHEM calls. C Info(3) = # of JAC_CHEM calls. C Info(4) = # of accepted steps. C Info(5) = # of rejected steps. C C Adrian Sandu, April 1996 C The Center for Global and Regional Environmental Research INTEGER NSENSIT KPP_REAL y(NVAR*(NSENSIT+1)), ynew(NVAR*(NSENSIT+1)) KPP_REAL K1(NVAR*(NSENSIT+1)) KPP_REAL K2(NVAR*(NSENSIT+1)) KPP_REAL K3(NVAR*(NSENSIT+1)) KPP_REAL DFDT(NVAR*(NSENSIT+1)) KPP_REAL DFDP(NVAR*NSENSIT), DFDPDT(NVAR*NSENSIT) KPP_REAL DJDP(NVAR*NSENSIT) KPP_REAL JAC(LU_NONZERO), AJAC(LU_NONZERO) KPP_REAL DJDT(LU_NONZERO) KPP_REAL Fv(NVAR), Hv(NVAR) KPP_REAL HESS(NHESS) KPP_REAL Hmin,Hmax,Hstart,ghinv,uround KPP_REAL AbsTol(NVAR), RelTol(NVAR) KPP_REAL T, Tnext, Tplus, H, Hnew, elo KPP_REAL ERR, factor, facmax INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier INTEGER Info(5) LOGICAL IsReject,Autonomous EXTERNAL FUNC_CHEM, JAC_CHEM, HESS_CHEM KPP_REAL gamma, c21, c31,c32,b1,b2,b3,d1,d2,d3,a21,a31,a32 KPP_REAL alpha2, alpha3, g1, g2, g3, x1, x2, x3, ytol KPP_REAL dround, tau gamma= .43586652150845899941601945119356d+00 c21= -.10156171083877702091975600115545d+01 c31= .40759956452537699824805835358067d+01 c32= .92076794298330791242156818474003d+01 b1= .10000000000000000000000000000000d+01 b2= .61697947043828245592553615689730d+01 b3= -.42772256543218573326238373806514d+00 d1= .50000000000000000000000000000000d+00 d2= -.29079558716805469821718236208017d+01 d3= .22354069897811569627360909276199d+00 a21 = 1.d0 a31 = 1.d0 a32 = 0.d0 alpha2 = gamma g1= .43586652150845899941601945119356d+00 g2= .24291996454816804366592249683314d+00 g3= .21851380027664058511513169485832d+01 c Initialization of counters, etc. Autonomous = Info(1) .EQ. 1 uround = 1.d-15 dround = DSQRT(uround) IF (Hmax.le.0.D0) THEN Hmax = DABS(Tnext-T) END IF H = DMAX1(1.d-8, Hstart) Tplus = T IsReject = .false. Naccept = 0 Nreject = 0 Nfcn = 0 Njac = 0 C === Starting the time loop === 10 CONTINUE C ====== Initial Function, Jacobian, and Hessian values =============== CALL FUNC_CHEM(NVAR, T, y, Fv) Nfcn = Nfcn + 1 CALL JAC_CHEM(NVAR, T, y, JAC) Njac = Njac + 1 CALL HESS_CHEM( NVAR, T, y, HESS ) IF (DDMTYPE .EQ. 1) THEN CALL DFUNDPAR(NVAR, NSENSIT, T, y, DFDP) END IF C ====== Time derivatives for NONAutonomousous CASE =============== IF (.not. Autonomous) THEN tau = DSIGN(dround*DMAX1( 1.0d-6, DABS(T) ), T) CALL FUNC_CHEM(NVAR, T+tau, y, K2) nfcn=nfcn+1 DO 20 j = 1,NVAR DFDT(j) = ( K2(j)-Fv(j) )/tau 20 CONTINUE CALL JAC_CHEM(NVAR, T+tau, y, AJAC) DO 30 j = 1,LU_NONZERO DJDT(j) = ( AJAC(j)-JAC(j) )/tau 30 CONTINUE DO 40 i=1,NSENSIT CALL Jac_SP_Vec (DJDT,y(i*NVAR+1),DFDT(i*NVAR+1)) 40 CONTINUE END IF Tplus = T + H IF ( Tplus .gt. Tnext ) then H = Tnext - T Tplus = Tnext END IF gHinv = 1.0d0/(gamma*H) DO 50 j=1,LU_NONZERO AJAC(j) = -JAC(j) 50 CONTINUE DO 60 j=1,NVAR AJAC(LU_DIAG(j)) = AJAC(LU_DIAG(j)) + gHinv 60 CONTINUE CALL KppDecomp (AJAC, ier) IF (ier.NE.0) THEN IF ( H.GT.Hmin) THEN H = 5.0d-1*H GO TO 10 ELSE PRINT *,'IER <> 0, H=',H STOP END IF END IF Autonomous = .true. C ------------------------------- STAGE 1 -------------------------------------- DO 70 j = 1,NVAR K1(j) = Fv(j) 70 CONTINUE IF (.NOT.Autonomous) THEN x1 = gamma*H DO 80 j = 1,NVAR K1(j) = K1(j) + x1*DFDT(j) 80 CONTINUE END IF CALL KppSolve (AJAC, K1) C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN CALL DJACDPAR(NVAR, NSENSIT, T, y, K1(1), DJDP) END IF C --- End of derivative w.r.t. parameters DO 110 i=1,NSENSIT CALL Jac_SP_Vec (JAC,y(i*NVAR+1),K1(i*NVAR+1)) CALL Hess_Vec ( HESS, y(i*NVAR+1), K1(1), Hv ) DO 90 j=1,NVAR K1(i*NVAR+j) = K1(i*NVAR+j) + Hv(j) 90 CONTINUE IF (.NOT. Autonomous) THEN DO 100 j=1,NVAR K1(i*NVAR+j) = K1(i*NVAR+j) + x1*DFDT(i*NVAR+j) 100 CONTINUE END IF C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN DO 44 j = 1,NVAR K1(i*NVAR+j) = K1(i*NVAR+j) + DFDP((i-1)*NVAR+j) & + DJDP((i-1)*NVAR+j) 44 CONTINUE END IF C --- End of derivative w.r.t. parameters CALL KppSolve (AJAC, K1(i*NVAR+1)) 110 CONTINUE C ------------------------------- STAGE 2 -------------------------------------- DO 120 j = 1,NVAR*(NSENSIT+1) ynew(j) = y(j) + a21*K1(j) 120 CONTINUE CALL FUNC_CHEM(NVAR, T + alpha2*H, ynew, Fv) IF (DDMTYPE .EQ. 1) THEN CALL DFUNDPAR(NVAR, NSENSIT, T+alpha3*H, ynew, DFDP) END IF nfcn=nfcn+1 x1 = c21/H DO 130 j = 1,NVAR K2(j) = Fv(j) + x1*K1(j) 130 CONTINUE IF (.NOT.Autonomous) THEN x2 = g2*H DO 140 j = 1,NVAR K2(j) = K2(j) + x2*DFDT(j) 140 CONTINUE END IF CALL KppSolve (AJAC, K2) C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN CALL DJACDPAR(NVAR, NSENSIT, T, y, K2(1), DJDP) END IF C --- End of derivative w.r.t. parameters CALL JAC_CHEM(NVAR, T+alpha2*H, ynew, JAC) njac=njac+1 DO 170 i=1,NSENSIT CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K2(i*NVAR+1)) CALL Hess_Vec ( HESS, y(i*NVAR+1), K2(1), Hv ) DO 150 j = 1,NVAR K2(i*NVAR+j) = K2(i*NVAR+j) + x1*K1(i*NVAR+j) & + Hv(j) 150 CONTINUE IF (.NOT. Autonomous) THEN DO 160 j=1,NVAR K2(i*NVAR+j) = K2(i*NVAR+j) + x2*DFDT(i*NVAR+j) 160 CONTINUE END IF C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN DO 165 j = 1,NVAR K2(i*NVAR+j) = K2(i*NVAR+j) + DFDP((i-1)*NVAR+j) & + DJDP((i-1)*NVAR+j) 165 CONTINUE END IF C --- End of derivative w.r.t. parameters CALL KppSolve (AJAC, K2(i*NVAR+1)) 170 CONTINUE C ------------------------------- STAGE 3 -------------------------------------- x1 = c31/H x2 = c32/H DO 180 j = 1,NVAR K3(j) = Fv(j) + x1*K1(j) + x2*K2(j) 180 CONTINUE IF (.NOT.Autonomous) THEN x3 = g3*H DO 190 j = 1,NVAR K3(j) = K3(j) + x3*DFDT(j) 190 CONTINUE END IF CALL KppSolve (AJAC, K3) C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN CALL DJACDPAR(NVAR, NSENSIT, T, y, K3(1), DJDP) END IF C --- End of derivative w.r.t. parameters DO 220 i=1,NSENSIT CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K3(i*NVAR+1)) CALL Hess_Vec ( HESS, y(i*NVAR+1), K3(1), Hv ) DO 200 j = 1,NVAR K3(i*NVAR+j) = K3(i*NVAR+j) +x1*K1(i*NVAR+j) & + x2*K2(i*NVAR+j) + Hv(j) 200 CONTINUE IF (.NOT. Autonomous) THEN DO 210 j=1,NVAR K3(i*NVAR+j) = K3(i*NVAR+j) + x3*DFDT(i*NVAR+j) 210 CONTINUE END IF C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN DO 215 j = 1,NVAR K3(i*NVAR+j) = K3(i*NVAR+j) + DFDP((i-1)*NVAR+j) & + DJDP((i-1)*NVAR+j) 215 CONTINUE END IF C --- End of derivative w.r.t. parameters CALL KppSolve (AJAC, K3(i*NVAR+1)) 220 CONTINUE C ------------------------------ The Solution --- DO 230 j = 1,NVAR*(NSENSIT+1) ynew(j) = y(j) + b1*K1(j) + b2*K2(j) + b3*K3(j) 230 CONTINUE C ====== Error estimation ======== ERR=0.d0 DO 240 i=1,NVAR ytol = AbsTol(i) + RelTol(i)*DABS(ynew(i)) ERR=ERR+((d1*K1(i)+d2*K2(i)+d3*K3(i))/ytol)**2 240 CONTINUE ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) C ======= Choose the stepsize =============================== elo = 3.0D0 ! estimator local order factor = DMAX1(2.0D-1,DMIN1(6.0D0,ERR**(1.0D0/elo)/.9D0)) Hnew = DMIN1(Hmax,DMAX1(Hmin, H/factor)) C ======= Rejected/Accepted Step ============================ IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN IsReject = .true. H = DMIN1(H/10,Hnew) Nreject = Nreject+1 GO TO 10 ELSE DO 250 j=1,NVAR*(NSENSIT+1) y(j) = ynew(j) 250 CONTINUE T = Tplus IF (.NOT.IsReject) THEN H = Hnew ! Do not increase stepsize IF previos step was rejected END IF IsReject = .false. Naccept = Naccept+1 END IF C ======= End of the time loop =============================== IF ( T .lt. Tnext ) GO TO 10 C ======= Output Information ================================= Info(2) = Nfcn Info(3) = Njac Info(4) = Naccept Info(5) = Nreject Hstart = H RETURN END SUBROUTINE FUNC_CHEM(N, T, Y, P) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' INTEGER N KPP_REAL T, Told KPP_REAL Y(NVAR), P(NVAR) Told = TIME TIME = T CALL Update_SUN() CALL Update_RCONST() CALL Fun( Y, FIX, RCONST, P ) TIME = Told RETURN END SUBROUTINE DFUNDPAR(N, NSENSIT, T, Y, P) C --- Computes the partial derivatives of FUNC_CHEM w.r.t. parameters INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients INTEGER N INTEGER NCOEFF, JCOEFF(NREACT) COMMON /DDMRCOEFF/ NCOEFF, JCOEFF KPP_REAL T, Told KPP_REAL Y(NVAR), P(NVAR*NSENSIT) Told = TIME TIME = T CALL Update_SUN() CALL Update_RCONST() C IF (DDMTYPE .EQ. 0) THEN C --- Note: the values below are for sensitivities w.r.t. initial values; C --- they may have to be changed for other applications DO j=1,NSENSIT DO i=1,NVAR P(i+NVAR*(j-1)) = 0.0D0 END DO END DO ELSE C --- Example: the call below is for sensitivities w.r.t. rate coefficients; C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients C --- w.r.t. which one differentiates CALL dFun_dRcoeff( Y, FIX, NCOEFF, JCOEFF, P ) END IF TIME = Told RETURN END SUBROUTINE JAC_CHEM(N, T, Y, J) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' INTEGER N KPP_REAL Told, T KPP_REAL Y(NVAR), J(LU_NONZERO) Told = TIME TIME = T CALL Update_SUN() CALL Update_RCONST() CALL Jac_SP( Y, FIX, RCONST, J ) TIME = Told RETURN END SUBROUTINE DJACDPAR(N, NSENSIT, T, Y, U, P) C --- Computes the partial derivatives of JAC w.r.t. parameters times user vector U INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients INTEGER N INTEGER NCOEFF, JCOEFF(NREACT) COMMON /DDMRCOEFF/ NCOEFF, JCOEFF KPP_REAL T, Told KPP_REAL Y(NVAR), U(NVAR) KPP_REAL P(NVAR*NSENSIT) Told = TIME TIME = T CALL Update_SUN() CALL Update_RCONST() C IF (DDMTYPE .EQ. 0) THEN C --- Note: the values below are for sensitivities w.r.t. initial values; C --- they may have to be changed for other applications DO j=1,NSENSIT DO i=1,NVAR P(i+NVAR*(j-1)) = 0.0D0 END DO END DO ELSE C --- Example: the call below is for sensitivities w.r.t. rate coefficients; C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients C --- w.r.t. which one differentiates CALL dJac_dRcoeff( Y, FIX, U, NCOEFF, JCOEFF, P ) END IF TIME = Told RETURN END SUBROUTINE HESS_CHEM(N, T, Y, HESS) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' INTEGER N KPP_REAL Told, T KPP_REAL Y(NVAR), HESS(NHESS) Told = TIME TIME = T CALL Update_SUN() CALL Update_RCONST() CALL Hessian( Y, FIX, RCONST, HESS ) TIME = Told RETURN END