SUBROUTINE INTEGRATE( NSENSIT, Y, TIN, TOUT ) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' INTEGER NSENSIT 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 ROS2_DDM(NVAR,NSENSIT,TIN,TOUT,STEPMIN,STEPMAX, + STEPMIN,Y,ATOL,RTOL, + Info,FUNC_CHEM,JAC_CHEM) RETURN END SUBROUTINE ROS2_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 C Ros2 with direct-decoupled calculation of sensitivities C 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 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, December 2001 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) KPP_REAL DFDT(NVAR*(NSENSIT+1)) KPP_REAL DFDP(NVAR*NSENSIT+1), DFDPDT(NVAR*NSENSIT+1) KPP_REAL DJDP(NVAR*NSENSIT+1) KPP_REAL F1(NVAR), F2(NVAR) KPP_REAL JAC(LU_NONZERO), AJAC(LU_NONZERO) KPP_REAL DJDT(LU_NONZERO) KPP_REAL HESS(NHESS) KPP_REAL Hmin,Hmax,Hnew,Hstart,ghinv,uround KPP_REAL AbsTol(NVAR), RelTol(NVAR) KPP_REAL T, Tnext, H, Hold, Tplus, e KPP_REAL ERR, factor, facmax, dround, elo, tau, gam INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier INTEGER Info(5) LOGICAL IsReject,Autonomous,Embed3 EXTERNAL FUNC_CHEM, JAC_CHEM, HESS_CHEM LOGICAL negative KPP_REAL gamma, m1, m2, alpha, beta, delta, theta, w KPP_REAL gamma3, d1, d2, d3, beta1, beta2 KPP_REAL c31, c32, c34 c Initialization of counters, etc. Autonomous = Info(1) .EQ. 1 Embed3 = Info(2) .EQ. 1 uround = 1.d-15 dround = 1.0d-7 ! DSQRT(uround) H = DMAX1(1.d-8, Hstart) Tplus = T IsReject = .false. Naccept = 0 Nreject = 0 Nfcn = 0 Njac = 0 gamma = 1.d0 + 1.d0/DSQRT(2.0d0) c31 = -1.0D0/gamma**2*(1.0D0-7.0D0*gamma+9.0D0*gamma**2) & /(-1.0D0+2.0D0*gamma) c32 = -1.0D0/gamma**2*(1.0D0-6.0D0*gamma+6.0D0*gamma**2) & /(-1.0D0+2.0D0*gamma)/2 gamma3 = 0.5D0 - 2*gamma d1 = ((-9.0D0*gamma+8.0D0*gamma**2+2.0D0)/gamma**2/ & (-1.0D0+2*gamma))/6.0D0 d2 = ((-1.0D0+3.0D0*gamma)/gamma**2/ & (-1.0D0+2.0D0*gamma))/6.0D0 d3 = -1.0D0/(3.0D0*gamma) m1 = -3.d0/(2.d0*gamma) m2 = -1.d0/(2.d0*gamma) C === Starting the time loop === 10 CONTINUE Tplus = T + H IF ( Tplus .gt. Tnext ) THEN H = Tnext - T Tplus = Tnext END IF C Initial Function, Jacobian, and Hessian Values CALL FUNC_CHEM(NVAR, T, y, F1) CALL JAC_CHEM(NVAR, T, y, JAC) CALL HESS_CHEM( NVAR, T, y, HESS ) IF (DDMTYPE .EQ. 1) THEN CALL DFUNDPAR(NVAR, NSENSIT, T, y, DFDP) END IF C Estimate the time derivatives in non-autonomous case IF (.not. Autonomous) THEN tau = DSIGN(dround*DMAX1( 1.0d0, DABS(T) ), T) CALL FUNC_CHEM(NVAR, T+tau, y, K2) nfcn=nfcn+1 CALL JAC_CHEM(NVAR, T+tau, y, AJAC) njac=njac+1 DO 20 j = 1,NVAR DFDT(j) = ( K2(j)-F1(j) )/tau 20 CONTINUE 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 ! .not. Autonomous Njac = Njac+1 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)) = JAC(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 C ----- STAGE 1 ----- delta = gamma*H DO 70 j = 1,NVAR K1(j) = F1(j) 70 CONTINUE IF (.NOT. Autonomous) THEN DO 80 j = 1,NVAR K1(j) = K1(j) + delta*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 120 i=1,NSENSIT CALL Jac_SP_Vec (JAC,y(i*NVAR+1),K1(i*NVAR+1)) CALL Hess_Vec ( HESS, K1(1), y(i*NVAR+1), F2 ) DO 90 j=1,NVAR K1(i*NVAR+j) = K1(i*NVAR+j) + gHinv*F2(j) 90 CONTINUE IF (.NOT. Autonomous) THEN DO 100 j = 1,NVAR K1(i*NVAR+j) = K1(i*NVAR+j) + delta*DFDT(i*NVAR+j) 100 CONTINUE END IF C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN DO 110 j = 1,NVAR K1(i*NVAR+j) = K1(i*NVAR+j) + DFDP((i-1)*NVAR+j) & + DJDP((i-1)*NVAR+j) 110 CONTINUE END IF C --- End of derivative w.r.t. parameters CALL KppSolve (AJAC, K1(i*NVAR+1)) 120 CONTINUE C ----- STAGE 2 ----- alpha = - 1.d0/gamma DO 130 j = 1,NVAR*(NSENSIT+1) ynew(j) = y(j) + alpha*K1(j) 130 CONTINUE CALL FUNC_CHEM(NVAR, T+H, ynew, F1) IF (DDMTYPE.EQ.1) THEN CALL DFUNDPAR(NVAR, NSENSIT, T+H, ynew, DFDP) END IF nfcn=nfcn+1 beta1 = 2.d0/(gamma*H) delta = -gamma*H DO 140 j = 1,NVAR K2(j) = F1(j) + beta1*K1(j) 140 CONTINUE IF (.NOT. Autonomous) THEN DO 150 j = 1,NVAR K2(j) = K2(j) + delta*DFDT(j) 150 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+H, Ynew, JAC) njac=njac+1 DO 190 i=1,NSENSIT CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K2(i*NVAR+1)) CALL Jac_SP_Vec (DJDT,y(i*NVAR+1),F1) CALL Hess_Vec ( HESS, K2(1), y(i*NVAR+1), F2 ) DO 160 j = 1,NVAR K2(i*NVAR+j) = K2(i*NVAR+j) + beta1*K1(i*NVAR+j) & + gHinv*F2(j) 160 CONTINUE IF (.NOT. Autonomous) THEN DO 170 j = 1,NVAR K2(i*NVAR+j) = K2(i*NVAR+j) + delta*DFDT(i*NVAR+j) 170 CONTINUE END IF C --- If derivative w.r.t. parameters IF (DDMTYPE .EQ. 1) THEN DO 180 j = 1,NVAR K2(i*NVAR+j) = K2(i*NVAR+j) + DFDP((i-1)*NVAR+j) & + DJDP((i-1)*NVAR+j) 180 CONTINUE END IF C --- End of derivative w.r.t. parameters CALL KppSolve (AJAC, K2(i*NVAR+1)) 190 CONTINUE C ----- STAGE 3 for error control only ----- IF (Embed3) THEN beta1 = -c31/H beta2 = -c32/H delta = gamma3*H DO 195 j = 1,NVAR K3(j) = F1(j) + beta1*K1(j) + beta2*K2(j) 195 CONTINUE IF (.NOT. Autonomous) THEN DO 196 j = 1,NVAR K3(j) = K3(j) + delta*DFDT(j) 196 CONTINUE END IF CALL KppSolve (AJAC, K3) END IF C ---- The Solution --- DO 200 j = 1,NVAR*(NSENSIT+1) ynew(j) = y(j) + m1*K1(j) + m2*K2(j) 200 CONTINUE C ====== Error estimation for concentrations only; this can be easily adapted to C estimate the sensitivity error too ======== ERR=0.d0 DO 210 i=1,NVAR w = AbsTol(i) + RelTol(i)*DMAX1(DABS(y(i)),DABS(ynew(i))) IF (Embed3) THEN e = d1*K1(i) + d2*K2(i) + d3*K3(i) ELSE e = (1.d0/(2.d0*gamma))*(K1(i)+K2(i)) END IF ERR = ERR + ( e/w )**2 210 CONTINUE ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) C ======= Choose the stepsize =============================== IF (Embed3) THEN elo = 3.0D0 ! estimator local order ELSE elo = 2.0D0 END IF 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 ELSE DO 300 i=1,NVAR*(NSENSIT+1) y(i) = ynew(i) 300 CONTINUE T = Tplus IF (.NOT.IsReject) THEN H = Hnew ! Do not increase stepsize if previous 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 RETURN END SUBROUTINE FUNC_CHEM(N, T, Y, P) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' 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 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 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 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 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 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