!==================================================================================================================================! !()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()! !==================================================================================================================================! !> !!### Synopsis !! !! _DLSODE_ solves the initial-value problem for stiff or !! nonstiff systems of first-order ODE's, !!```text !! dy/dt = f(t,y), or, in component form, !! dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(N)), i=1,...,N. !!``` !! !! **NOTE**: The "Usage" and "Arguments" sections treat only a subset of !! available options, in condensed fashion. The options !! covered and the information supplied will support most !! standard uses of DLSODE. !! !! For more sophisticated uses, full details on all options are !! given in the concluding section, headed "Long Description." !! A synopsis of the DLSODE Long Description is provided at the !! beginning of that section; general topics covered are: !! !! + Elements of the call sequence; optional input and output !! + Optional supplemental routines in the DLSODE package !! + internal COMMON block !! !!------------------------------------------------------------------------ !!### Usage !! Communication between the user and the DLSODE package, for normal !! situations, is summarized here. This summary describes a subset !! of the available options. See "Long Description" for complete !! details, including optional communication, nonstandard options, !! and instructions for special situations. !! !! A sample program is given in the "Examples" section. !! !! Refer to the argument descriptions for the definitions of the !! quantities that appear in the following sample declarations. !! !! For MF = 10, !!```fortran !! PARAMETER (LRW = 20 + 16*NEQ, LIW = 20) !!``` !! For MF = 21 or 22, !!```fortran !! PARAMETER (LRW = 22 + 9*NEQ + NEQ**2, LIW = 20 + NEQ) !!``` !! For MF = 24 or 25, !!```fortran !! PARAMETER (LRW = 22 + 10*NEQ + (2*ML+MU)*NEQ, !! & LIW = 20 + NEQ) !! !! EXTERNAL F, JAC !! INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK(LIW), !! & LIW, MF !! DOUBLE PRECISION Y(NEQ), T, TOUT, RTOL, ATOL(ntol), RWORK(LRW) !! !! CALL DLSODE (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, !! & ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) !!``` !!### Arguments !! !! F (external) !! !! ; Name of subroutine for right-hand-side vector f. !! This name must be declared EXTERNAL in calling !! program. The form of F must be: !!```fortran !! SUBROUTINE F (NEQ, T, Y, YDOT) !! INTEGER NEQ !! DOUBLE PRECISION T, Y(*), YDOT(*) !!``` !! The inputs are NEQ, T, Y. F is to set !!```text !! YDOT(i) = f(i,T,Y(1),Y(2),...,Y(NEQ)), i = 1, ..., NEQ . !!``` !! !! NEQ (intent IN) !! !! : Number of first-order ODE's. !! !! Y (intent INOUT) !! !! : Array of values of the y(t) vector, of length NEQ. !! !! Input: For the first call, Y should contain the !! values of y(t) at t = T. (Y is an input !! variable only if ISTATE = 1.) !! !! Output: On return, Y will contain the values at the !! new t-value. !! !! T (intent INOUT) !! !! : Value of the independent variable. On return it !! will be the current value of t (normally TOUT). !! !! TOUT (intent IN) !! !! : Next point where output is desired (.NE. T). !! !! ITOL (intent IN) !! !! : 1 or 2 according as ATOL (below) is a scalar or !! an array. !! !! RTOL (intent IN) !! !! : Relative tolerance parameter (scalar). !! !! ATOL (intent IN) !! !! : Absolute tolerance parameter (scalar or array). !!```text !! If ITOL = 1, ATOL need not be dimensioned. !! If ITOL = 2, ATOL must be dimensioned at least NEQ. !!``` !! !! The estimated local error in Y(i) will be controlled !! so as to be roughly less (in magnitude) than !!```text !! EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or !! EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. !!``` !! !! Thus the local error test passes if, in each !! component, either the absolute error is less than !! ATOL (or ATOL(i)), or the relative error is less !! than RTOL. !! !! Use RTOL = 0.0 for pure absolute error control, and !! use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative !! error control. Caution: Actual (global) errors may !! exceed these local tolerances, so choose them !! conservatively. !! !! ITASK (intent IN) !! !! : Flag indicating the task DLSODE is to perform. !! Use ITASK = 1 for normal computation of output !! values of y at t = TOUT. !! !! ISTATE (intent INOUT) !! !! : Index used for input and output to specify the state !! of the calculation. !! !! Input: !! !! value | description !! ------ | ----------- !! 1 | This is the first call for a problem. !! 2 | This is a subsequent call. !! !! Output: !! !! value | description !! ------ | ----------- !! 1 | Nothing was done, because TOUT was equal to T. !! 2 | DLSODE was successful (otherwise, negative). !! | Note that ISTATE need not be modified after a !! | successful return. !! -1 | Excess work done on this call (perhaps wrong !! | MF). !! -2 | Excess accuracy requested (tolerances too !! | small). !! -3 | Illegal input detected (see printed message). !! -4 | Repeated error test failures (check all !! | inputs). !! -5 | Repeated convergence failures (perhaps bad !! | Jacobian supplied or wrong choice of MF or !! | tolerances). !! -6 | Error weight became zero during problem !! | (solution component i vanished, and ATOL or !! | ATOL(i) = 0.). !! !! IOPT (intent IN) !! !! : Flag indicating whether optional inputs are used: !! !! value | description !! ----- | ----------- !! 0 | No. !! 1 | Yes. (See "Optional inputs" under "Long !! | Description," Part 1.) !! !! RWORK (WORK) !! !! : Real work array of length at least: !!```text !! 20 + 16*NEQ for MF = 10, !! 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, !! 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. !!``` !! !! LRW (intent IN) !! !! : Declared length of RWORK (in user's DIMENSION !! statement). !! !! IWORK (WORK) !! !! : Integer work array of length at least: !!```text !! 20 for MF = 10, !! 20 + NEQ for MF = 21, 22, 24, or 25. !!``` !! !! If MF = 24 or 25, input in IWORK(1),IWORK(2) the !! lower and upper Jacobian half-bandwidths ML,MU. !! !! On return, IWORK contains information that may be !! of interest to the user: !! !! Name | Location | Meaning !! ----- | --------- | ----------------------------------------- !! NST | IWORK(11) | Number of steps taken for the problem so !! | | far. !! NFE | IWORK(12) | Number of f evaluations for the problem !! | | so far. !! NJE | IWORK(13) | Number of Jacobian evaluations (and of !! | | matrix LU decompositions) for the problem !! | | so far. !! NQU | IWORK(14) | Method order last used (successfully). !! LENRW | IWORK(17) | Length of RWORK actually required. This !! | | is defined on normal returns and on an !! | | illegal input return for insufficient !! | | storage. !! LENIW | IWORK(18) | Length of IWORK actually required. This !! | | is defined on normal returns and on an !! | | illegal input return for insufficient !! | | storage. !! !! LIW (intent IN) !! !! : Declared length of IWORK (in user's DIMENSION !! statement). !! !! JAC (external) !! !! : Name of subroutine for Jacobian matrix (MF = !! 21 or 24). If used, this name must be declared !! EXTERNAL in calling program. If not used, pass a !! dummy name. The form of JAC must be: !!```fortran !! SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) !! INTEGER NEQ, ML, MU, NROWPD !! DOUBLE PRECISION T, Y(*), PD(NROWPD,*) !!``` !! !! See item c, under "Description" below for more !! information about JAC. !! !! MF (intent IN) !! !! : Method flag. Standard values are: !! !! value | definition !! ----- | ---------- !! 10 | Nonstiff (Adams) method, no Jacobian used. !! 21 | Stiff (BDF) method, user-supplied full Jacobian. !! 22 | Stiff method, internally generated full !! | Jacobian. !! 24 | Stiff method, user-supplied banded Jacobian. !! 25 | Stiff method, internally generated banded !! | Jacobian. !! !!### Long Description !! DLSODE solves the initial value problem for stiff or nonstiff !! systems of first-order ODE's, !!```text !! dy/dt = f(t,y) , !!``` !! or, in component form, !!```text !! dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) !! (i = 1, ..., NEQ) . !!``` !! DLSODE is a package based on the GEAR and GEARB packages, and on !! the October 23, 1978, version of the tentative ODEPACK user !! interface standard, with minor modifications. !! !! The steps in solving such a problem are as follows. !! !! **(a)** First write a subroutine of the form !!```fortran !! SUBROUTINE F (NEQ, T, Y, YDOT) !! INTEGER NEQ !! DOUBLE PRECISION T, Y(*), YDOT(*) !!``` !! which supplies the vector function f by loading YDOT(i) with !! f(i). !! !! **(b)** Next determine (or guess) whether or not the problem is stiff. !! Stiffness occurs when the Jacobian matrix df/dy has an !! eigenvalue whose real part is negative and large in magnitude !! compared to the reciprocal of the t span of interest. If the !! problem is nonstiff, use method flag MF = 10. If it is stiff, !! there are four standard choices for MF, and DLSODE requires the !! Jacobian matrix in some form. This matrix is regarded either !! as full (MF = 21 or 22), or banded (MF = 24 or 25). In the !! banded case, DLSODE requires two half-bandwidth parameters ML !! and MU. These are, respectively, the widths of the lower and !! upper parts of the band, excluding the main diagonal. Thus the !! band consists of the locations (i,j) with !! !! i - ML <= j <= i + MU , !! !! and the full bandwidth is ML + MU + 1 . !! !! **(c)** If the problem is stiff, you are encouraged to supply the !! Jacobian directly (MF = 21 or 24), but if this is not feasible, !! DLSODE will compute it internally by difference quotients (MF = !! 22 or 25). If you are supplying the Jacobian, write a !! subroutine of the form !!```fortran !! SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) !! INTEGER NEQ, ML, MU, NRWOPD !! DOUBLE PRECISION T, Y(*), PD(NROWPD,*) !!``` !! which provides df/dy by loading PD as follows: !! - For a full Jacobian (MF = 21), load PD(i,j) with df(i)/dy(j), !! the partial derivative of f(i) with respect to y(j). (Ignore !! the ML and MU arguments in this case.) !! - For a banded Jacobian (MF = 24), load PD(i-j+MU+1,j) with !! df(i)/dy(j); i.e., load the diagonal lines of df/dy into the !! rows of PD from the top down. !! - In either case, only nonzero elements need be loaded. !! !! **(d)** Write a main program that calls subroutine DLSODE once for each !! point at which answers are desired. This should also provide !! for possible use of logical unit 6 for output of error messages !! by DLSODE. !! !! Before the first call to DLSODE, set ISTATE = 1, set Y and T to !! the initial values, and set TOUT to the first output point. To !! continue the integration after a successful return, simply !! reset TOUT and call DLSODE again. No other parameters need be !! reset. !! !!### Examples !! The following is a simple example problem, with the coding needed !! for its solution by DLSODE. The problem is from chemical kinetics, !! and consists of the following three rate equations: !!```text !! dy1/dt = -.04*y1 + 1.E4*y2*y3 !! dy2/dt = .04*y1 - 1.E4*y2*y3 - 3.E7*y2**2 !! dy3/dt = 3.E7*y2**2 !!``` !! on the interval from t = 0.0 to t = 4.E10, with initial conditions !! y1 = 1.0, y2 = y3 = 0. The problem is stiff. !! !! The following coding solves this problem with DLSODE, using !! MF = 21 and printing results at t = .4, 4., ..., 4.E10. It uses !! ITOL = 2 and ATOL much smaller for y2 than for y1 or y3 because y2 !! has much smaller values. At the end of the run, statistical !! quantities of interest are printed. !! !!```fortran !!program dlsode_ex !!use m_odepack !!implicit none !!external fex !!external jex !! !!integer,parameter :: dp=kind(0.0d0) !!real(kind=dp),dimension(3) :: atol,y !!integer :: iopt,iout,istate,itask,itol,liw,lrw,mf,neq !!integer,dimension(23) :: iwork !!real(kind=dp) :: rtol,t,tout !!real(kind=dp),dimension(58) :: rwork !! !! neq = 3 !! y(1) = 1.D0 !! y(2) = 0.D0 !! y(3) = 0.D0 !! t = 0.D0 !! tout = .4D0 !! itol = 2 !! rtol = 1.D-4 !! atol(1) = 1.D-6 !! atol(2) = 1.D-10 !! atol(3) = 1.D-6 !! itask = 1 !! istate = 1 !! iopt = 0 !! lrw = 58 !! liw = 23 !! mf = 21 !! do iout = 1,12 !! call dlsode(fex,[neq],y,t,tout,itol,[rtol],atol,itask,istate,iopt, & !! & rwork,lrw,iwork,liw,jex,mf) !! write (6,99010) t,y(1),y(2),y(3) !! 99010 format (' At t =',d12.4,' y =',3D14.6) !! if ( istate<0 ) then !! write (6,99020) istate !! 99020 format (///' Error halt.. ISTATE =',i3) !! stop 1 !! else !! tout = tout*10.D0 !! endif !! enddo !! write (6,99030) iwork(11),iwork(12),iwork(13) !! 99030 format (/' No. steps =',i4,', No. f-s =',i4,', No. J-s =',i4) !! !!end program dlsode_ex !! !!subroutine fex(Neq,T,Y,Ydot) !!implicit none !!integer,parameter :: dp=kind(0.0d0) !! !!integer :: Neq !!real(kind=dp) :: T !!real(kind=dp),intent(in),dimension(3) :: Y !!real(kind=dp),intent(inout),dimension(3) :: Ydot !! !! Ydot(1) = -.04D0*Y(1) + 1.D4*Y(2)*Y(3) !! Ydot(3) = 3.D7*Y(2)*Y(2) !! Ydot(2) = -Ydot(1) - Ydot(3) !!end subroutine fex !! !!subroutine jex(Neq,T,Y,Ml,Mu,Pd,Nrpd) !!implicit none !! !!integer,parameter :: dp=kind(0.0d0) !!integer :: Neq !!real(kind=dp) :: T !!real(kind=dp),intent(in),dimension(3) :: Y !!integer :: Ml !!integer :: Mu !!real(kind=dp),intent(inout),dimension(Nrpd,3) :: Pd !!integer,intent(in) :: Nrpd !! !! Pd(1,1) = -.04D0 !! Pd(1,2) = 1.D4*Y(3) !! Pd(1,3) = 1.D4*Y(2) !! Pd(2,1) = .04D0 !! Pd(2,3) = -Pd(1,3) !! Pd(3,2) = 6.D7*Y(2) !! Pd(2,2) = -Pd(1,2) - Pd(3,2) !!end subroutine jex !!``` !! !! The output from this program (on a Cray-1 in single precision) !! is as follows. !!```text !! At t = 4.0000e-01 y = 9.851726e-01 3.386406e-05 1.479357e-02 !! At t = 4.0000e+00 y = 9.055142e-01 2.240418e-05 9.446344e-02 !! At t = 4.0000e+01 y = 7.158050e-01 9.184616e-06 2.841858e-01 !! At t = 4.0000e+02 y = 4.504846e-01 3.222434e-06 5.495122e-01 !! At t = 4.0000e+03 y = 1.831701e-01 8.940379e-07 8.168290e-01 !! At t = 4.0000e+04 y = 3.897016e-02 1.621193e-07 9.610297e-01 !! At t = 4.0000e+05 y = 4.935213e-03 1.983756e-08 9.950648e-01 !! At t = 4.0000e+06 y = 5.159269e-04 2.064759e-09 9.994841e-01 !! At t = 4.0000e+07 y = 5.306413e-05 2.122677e-10 9.999469e-01 !! At t = 4.0000e+08 y = 5.494530e-06 2.197825e-11 9.999945e-01 !! At t = 4.0000e+09 y = 5.129458e-07 2.051784e-12 9.999995e-01 !! At t = 4.0000e+10 y = -7.170603e-08 -2.868241e-13 1.000000e+00 !! !! No. steps = 330, No. f-s = 405, No. J-s = 69 !!``` !! !!#### Accuracy: !! The accuracy of the solution depends on the choice of tolerances !! RTOL and ATOL. Actual (global) errors may exceed these local !! tolerances, so choose them conservatively. !! !!#### Cautions: !! The work arrays should not be altered between calls to DLSODE for !! the same problem, except possibly for the conditional and optional !! inputs. !! !!#### Portability: !! Since NEQ is dimensioned inside DLSODE, some compilers may object !! to a call to DLSODE with NEQ a scalar variable. In this event, !! use DIMENSION NEQ(1). Similar remarks apply to RTOL and ATOL. !! !! Note to Cray users: !! For maximum efficiency, use the CFT77 compiler. Appropriate !! compiler optimization directives have been inserted for CFT77. !! !!#### Reference: !! Alan C. Hindmarsh, "ODEPACK, A Systematized Collection of ODE !! Solvers," in Scientific Computing, R. S. Stepleman, et al., Eds. !! (North-Holland, Amsterdam, 1983), pp. 55-64. !! !!### Long Description: !! The following complete description of the user interface to !! DLSODE consists of four parts: !! !! 1. The call sequence to subroutine DLSODE, which is a driver !! routine for the solver. This includes descriptions of both !! the call sequence arguments and user-supplied routines. !! Following these descriptions is a description of optional !! inputs available through the call sequence, and then a !! description of optional outputs in the work arrays. !! !! 2. Descriptions of other routines in the DLSODE package that may !! be (optionally) called by the user. These provide the ability !! to alter error message handling, save and restore the internal !! COMMON, and obtain specified derivatives of the solution y(t). !! !! 3. Descriptions of COMMON block to be declared in overlay or !! similar environments, or to be saved when doing an interrupt !! of the problem and continued solution later. !! !! 4. Description of two routines in the DLSODE package, either of !! which the user may replace with his own version, if desired. !! These relate to the measurement of errors. !! !! !!### Part 1. Call Sequence !! !!#### Arguments !! !! The call sequence parameters used for input only are !! !! F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF, !! !! and those used for both input and output are !! !! Y, T, ISTATE. !! !! The work arrays RWORK and IWORK are also used for conditional and !! optional inputs and optional outputs. (The term output here !! refers to the return from subroutine DLSODE to the user's calling !! program.) !! !! The legality of input parameters will be thoroughly checked on the !! initial call for the problem, but not checked thereafter unless a !! change in input parameters is flagged by ISTATE = 3 on input. !! !! The descriptions of the call arguments are as follows. !! !! F !! !! : name of the user-supplied subroutine defining the ODE !! system. The system must be put in the first-order form !! dy/dt = f(t,y), where f is a vector-valued function of !! the scalar t and the vector y. Subroutine F is to compute !! the function f. It is to have the form !!```fortran !! SUBROUTINE F (NEQ, T, Y, YDOT) !! DOUBLE PRECISION T, Y(*), YDOT(*) !!``` !! where NEQ, T, and Y are input, and the array YDOT = !! f(T,Y) is output. Y and YDOT are arrays of length NEQ. !! Subroutine F should not alter Y(1),...,Y(NEQ). F must be !! declared EXTERNAL in the calling program. !! !! Subroutine F may access user-defined quantities in !! NEQ(2),... and/or in Y(NEQ(1)+1),..., if NEQ is an array !! (dimensioned in F) and/or Y has length exceeding NEQ(1). !! See the descriptions of NEQ and Y below. !! !! If quantities computed in the F routine are needed !! externally to DLSODE, an extra call to F should be made !! for this purpose, for consistent and accurate results. !! If only the derivative dy/dt is needed, use DINTDY !! instead. !! !! NEQ !! !! : size of the ODE system (number of first-order !! ordinary differential equations). Used only for input. !! NEQ may be decreased, but not increased, during the !! problem. If NEQ is decreased (with ISTATE = 3 on input), !! the remaining components of Y should be left undisturbed, !! if these are to be accessed in F and/or JAC. !! !! Normally, NEQ is a scalar, and it is generally referred !! to as a scalar in this user interface description. !! However, NEQ may be an array, with NEQ(1) set to the !! system size. (The DLSODE package accesses only NEQ(1).) !! In either case, this parameter is passed as the NEQ !! argument in all calls to F and JAC. Hence, if it is an !! array, locations NEQ(2),... may be used to store other !! integer data and pass it to F and/or JAC. Subroutines !! F and/or JAC must include NEQ in a DIMENSION statement !! in that case. !! !! Y !! !! : real array for the vector of dependent variables, of !! length NEQ or more. Used for both input and output on !! the first call (ISTATE = 1), and only for output on !! other calls. On the first call, Y must contain the !! vector of initial values. On output, Y contains the !! computed solution vector, evaluated at T. If desired, !! the Y array may be used for other purposes between !! calls to the solver. !! !! This array is passed as the Y argument in all calls to F !! and JAC. Hence its length may exceed NEQ, and locations !! Y(NEQ+1),... may be used to store other real data and !! pass it to F and/or JAC. (The DLSODE package accesses !! only Y(1),...,Y(NEQ).) !! !! T !! !! : independent variable. On input, T is used only on !! the first call, as the initial point of the integration. !! On output, after each call, T is the value at which a !! computed solution Y is evaluated (usually the same as !! TOUT). On an error return, T is the farthest point !! reached. !! !! TOUT !! !! : next value of T at which a computed solution is !! desired. Used only for input. !! !! When starting the problem (ISTATE = 1), TOUT may be equal !! to T for one call, then should not equal T for the next !! call. For the initial T, an input value of TOUT .NE. T !! is used in order to determine the direction of the !! integration (i.e., the algebraic sign of the step sizes) !! and the rough scale of the problem. Integration in !! either direction (forward or backward in T) is permitted. !! !! If ITASK = 2 or 5 (one-step modes), TOUT is ignored !! after the first call (i.e., the first call with !! TOUT .NE. T). Otherwise, TOUT is required on every call. !! !! If ITASK = 1, 3, or 4, the values of TOUT need not be !! monotone, but a value of TOUT which backs up is limited !! to the current internal T interval, whose endpoints are !! TCUR - HU and TCUR. (See "Optional Outputs" below for !! TCUR and HU.) !! !! !! ITOL !! !! : indicator for the type of error control. See !! description below under ATOL. Used only for input. !! !! RTOL !! !! : relative error tolerance parameter, either a scalar or !! an array of length NEQ. See description below under !! ATOL. Input only. !! !! ATOL !! !! : absolute error tolerance parameter, either a scalar or !! an array of length NEQ. Input only. !! !! The input parameters ITOL, RTOL, and ATOL determine the !! error control performed by the solver. The solver will !! control the vector e = (e(i)) of estimated local errors !! in Y, according to an inequality of the form !! !! rms-norm of ( e(i)/EWT(i) ) <= 1, !! !! where !! !! EWT(i) = RTOL(i)\*ABS(Y(i)) + ATOL(i), !! !! and the rms-norm (root-mean-square norm) here is !! !! rms-norm(v) = SQRT(sum v(i)\*\*2 / NEQ). !! !! Here EWT = (EWT(i)) is a vector of weights which must !! always be positive, and the values of RTOL and ATOL !! should all be nonnegative. The following table gives the !! types (scalar/array) of RTOL and ATOL, and the !! corresponding form of EWT(i). !! !! ITOL | RTOL | ATOL | EWT(i) !! ---- | ------ | ------ | ----------------------------- !! 1 | scalar | scalar | RTOL\*ABS(Y(i)) + ATOL !! 2 | scalar | array | RTOL\*ABS(Y(i)) + ATOL(i) !! 3 | array | scalar | RTOL(i)\*ABS(Y(i)) + ATOL !! 4 | array | array | RTOL(i)\*ABS(Y(i)) + ATOL(i) !! !! When either of these parameters is a scalar, it need not !! be dimensioned in the user's calling program. !! !! If none of the above choices (with ITOL, RTOL, and ATOL !! fixed throughout the problem) is suitable, more general !! error controls can be obtained by substituting !! user-supplied routines for the setting of EWT and/or for !! the norm calculation. See Part 4 below. !! !! If global errors are to be estimated by making a repeated !! run on the same problem with smaller tolerances, then all !! components of RTOL and ATOL (i.e., of EWT) should be !! scaled down uniformly. !! !! ITASK !! !! : index specifying the task to be performed. Input !! only. ITASK has the following values and meanings: !! !! value | description !! ------ | ----------- !! 1 | Normal computation of output values of y(t) at !! | t = TOUT (by overshooting and interpolating). !! 2 | Take one step only and return. !! 3 | Stop at the first internal mesh point at or beyond !! | t = TOUT and return. !! 4 | Normal computation of output values of y(t) at !! | t = TOUT but without overshooting t = TCRIT. TCRIT !! | must be input as RWORK(1). TCRIT may be equal to or !! | beyond TOUT, but not behind it in the direction of !! | integration. This option is useful if the problem !! | has a singularity at or beyond t = TCRIT. !! 5 | Take one step, without passing TCRIT, and return. !! | TCRIT must be input as RWORK(1). !! !! Note: If ITASK = 4 or 5 and the solver reaches TCRIT !! (within roundoff), it will return T = TCRIT (exactly) to !! indicate this (unless ITASK = 4 and TOUT comes before !! TCRIT, in which case answers at T = TOUT are returned !! first). !! !! ISTATE !! !! : index used for input and output to specify the state !! of the calculation. !! !! On input, the values of ISTATE are as follows: !! !! value | description !! ------ | ----------- !! 1 | This is the first call for the problem !! | (initializations will be done). See "Note" below. !! 2 | This is not the first call, and the calculation is to !! | continue normally, with no change in any input !! | parameters except possibly TOUT and ITASK. (If ITOL, !! | RTOL, and/or ATOL are changed between calls with !! | ISTATE = 2, the new values will be used but not !! | tested for legality.) !! 3 | This is not the first call, and the calculation is to !! | continue normally, but with a change in input !! | parameters other than TOUT and ITASK. Changes are !! | allowed in NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, !! | ML, MU, and any of the optional inputs except H0. !! | (See IWORK description for ML and MU.) !! !! Note: A preliminary call with TOUT = T is not counted as !! a first call here, as no initialization or checking of !! input is done. (Such a call is sometimes useful for the !! purpose of outputting the initial conditions.) Thus the !! first call for which TOUT .NE. T requires ISTATE = 1 on !! input. !! !! On output, ISTATE has the following values and meanings: !! !! value | description !! ------ | ----------- !! 1 | Nothing was done, as TOUT was equal to T with !! | ISTATE = 1 on input. !! 2 | The integration was performed successfully. !! -1 | An excessive amount of work (more than MXSTEP steps) !! | was done on this call, before completing the !! | requested task, but the integration was otherwise !! | successful as far as T. (MXSTEP is an optional input !! | and is normally 500.) To continue, the user may !! | simply reset ISTATE to a value >1 and call again (the !! | excess work step counter will be reset to 0). In !! | addition, the user may increase MXSTEP to avoid this !! | error return; see "Optional Inputs" below. !! -2 | Too much accuracy was requested for the precision of !! | the machine being used. This was detected before !! | completing the requested task, but the integration !! | was successful as far as T. To continue, the !! | tolerance parameters must be reset, and ISTATE must !! | be set to 3. The optional output TOLSF may be used !! | for this purpose. (Note: If this condition is !! | detected before taking any steps, then an illegal !! | input return (ISTATE = -3) occurs instead.) !! -3 | Illegal input was detected, before taking any !! | integration steps. See written message for details. !! | (Note: If the solver detects an infinite loop of !! | calls to the solver with illegal input, it will cause !! | the run to stop.) !! -4 | There were repeated error-test failures on one !! | attempted step, before completing the requested task, !! | but the integration was successful as far as T. The !! | problem may have a singularity, or the input may be !! | inappropriate. !! -5 | There were repeated convergence-test failures on one !! | attempted step, before completing the requested task, !! | but the integration was successful as far as T. This !! | may be caused by an inaccurate Jacobian matrix, if !! | one is being used. !! -6 | EWT(i) became zero for some i during the integration. !! | Pure relative error control (ATOL(i)=0.0) was !! | requested on a variable which has now vanished. The !! | integration was successful as far as T. !! !! Note: Since the normal output value of ISTATE is 2, it !! does not need to be reset for normal continuation. Also, !! since a negative input value of ISTATE will be regarded !! as illegal, a negative output value requires the user to !! change it, and possibly other inputs, before calling the !! solver again. !! !! IOPT !! !! : integer flag to specify whether any optional inputs !! are being used on this call. Input only. The optional !! inputs are listed under a separate heading below. !! 0 No optional inputs are being used. Default values !! will be used in all cases. !! 1 One or more optional inputs are being used. !! !! RWORK !! !! : real working array (double precision). The length of !! RWORK must be at least !!```text !! 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM !!``` !! where !!```text !! NYH = the initial value of NEQ, !! MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a !! smaller value is given as an optional input), !! LWM = 0 if MITER = 0, !! LWM = NEQ**2 + 2 if MITER = 1 or 2, !! LWM = NEQ + 2 if MITER = 3, and !! LWM = (2*ML + MU + 1)*NEQ + 2 !! if MITER = 4 or 5. !! (See the MF description below for METH and MITER.) !!``` !! !! Thus if MAXORD has its default value and NEQ is constant, !! this length is: !!```text !! 20 + 16*NEQ for MF = 10, !! 22 + 16*NEQ + NEQ**2 for MF = 11 or 12, !! 22 + 17*NEQ for MF = 13, !! 22 + 17*NEQ + (2*ML + MU)*NEQ for MF = 14 or 15, !! 20 + 9*NEQ for MF = 20, !! 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, !! 22 + 10*NEQ for MF = 23, !! 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. !!``` !! !! The first 20 words of RWORK are reserved for conditional !! and optional inputs and optional outputs. !! !! The following word in RWORK is a conditional input: !! !! RWORK(1) = TCRIT, the critical value of t which the !! solver is not to overshoot. Required if ITASK !! is 4 or 5, and ignored otherwise. See ITASK. !! !! LRW !! !! : length of the array RWORK, as declared by the user. !! (This will be checked by the solver.) !! !! IWORK !! !! : integer work array. Its length must be at least !! 20 if MITER = 0 or 3 (MF = 10, 13, 20, 23), or !! 20 + NEQ otherwise (MF = 11, 12, 14, 15, 21, 22, 24, 25). !! (See the MF description below for MITER.) The first few !! words of IWORK are used for conditional and optional !! inputs and optional outputs. !! !! The following two words in IWORK are conditional inputs: !! IWORK(1) = ML These are the lower and upper half- !! IWORK(2) = MU bandwidths, respectively, of the banded !! Jacobian, excluding the main diagonal. !! !! The band is defined by the matrix locations !! (i,j) with i - ML <= j <= i + MU. ML and MU !! must satisfy 0 <= ML,MU <= NEQ - 1. These are !! required if MITER is 4 or 5, and ignored !! otherwise. ML and MU may in fact be the band !! parameters for a matrix to which df/dy is only !! approximately equal. !! !! LIW !! !! : The length of the array IWORK, as declared by the user. !! (This will be checked by the solver.) !! !! Note: The work arrays must not be altered between calls to DLSODE !! for the same problem, except possibly for the conditional and !! optional inputs, and except for the last 3\*NEQ words of RWORK. !! The latter space is used for internal scratch space, and so is !! available for use by the user outside DLSODE between calls, if !! desired (but not for use by F or JAC). !! !! JAC !! !! : The name of the user-supplied routine (MITER = 1 or 4) to !! compute the Jacobian matrix, df/dy, as a function of the !! scalar t and the vector y. (See the MF description below !! for MITER.) It is to have the form !!```fortran !! SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) !! DOUBLE PRECISION T, Y(*), PD(NROWPD,*) !!``` !! where NEQ, T, Y, ML, MU, and NROWPD are input and the !! array PD is to be loaded with partial derivatives !! (elements of the Jacobian matrix) on output. PD must be !! given a first dimension of NROWPD. T and Y have the same !! meaning as in subroutine F. !! !! In the full matrix case (MITER = 1), ML and MU are !! ignored, and the Jacobian is to be loaded into PD in !! columnwise manner, with df(i)/dy(j) loaded into PD(i,j). !! !! In the band matrix case (MITER = 4), the elements within !! the band are to be loaded into PD in columnwise manner, !! with diagonal lines of df/dy loaded into the rows of PD. !! Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). ML !! and MU are the half-bandwidth parameters (see IWORK). !! The locations in PD in the two triangular areas which !! correspond to nonexistent matrix elements can be ignored !! or loaded arbitrarily, as they are overwritten by DLSODE. !! !! JAC need not provide df/dy exactly. A crude approximation !! (possibly with a smaller bandwidth) will do. !! !! In either case, PD is preset to zero by the solver, so !! that only the nonzero elements need be loaded by JAC. !! Each call to JAC is preceded by a call to F with the same !! arguments NEQ, T, and Y. Thus to gain some efficiency, !! intermediate quantities shared by both calculations may !! be saved in a user COMMON block by F and not recomputed !! by JAC, if desired. Also, JAC may alter the Y array, if !! desired. JAC must be declared EXTERNAL in the calling !! program. !! !! Subroutine JAC may access user-defined quantities in !! NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array !! (dimensioned in JAC) and/or Y has length exceeding !! NEQ(1). See the descriptions of NEQ and Y above. !! !! MF !! !! : The method flag. Used only for input. The legal values !! of MF are 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, !! and 25. MF has decimal digits METH and MITER: !!```text !! MF = 10*METH + MITER . !!``` !! METH indicates the basic linear multistep method: !! !! value | description !! ------ | ----------- !! 1 | Implicit Adams method. !! 2 | Method based on backward differentiation formulas !! | (BDF's). !! !! MITER indicates the corrector iteration method: !! !! value | description !! ------ | ----------- !! 0 | Functional iteration (no Jacobian matrix is !! | involved). !! 1 | Chord iteration with a user-supplied full (NEQ by !! | NEQ) Jacobian. !! 2 | Chord iteration with an internally generated !! | (difference quotient) full Jacobian (using NEQ !! | extra calls to F per df/dy value). !! 3 | Chord iteration with an internally generated !! | diagonal Jacobian approximation (using one extra call !! | to F per df/dy evaluation). !! 4 | Chord iteration with a user-supplied banded Jacobian. !! 5 | Chord iteration with an internally generated banded !! | Jacobian (using ML + MU + 1 extra calls to F per !! | df/dy evaluation). !! !! If MITER = 1 or 4, the user must supply a subroutine JAC !! (the name is arbitrary) as described above under JAC. !! For other values of MITER, a dummy argument can be used. !! !!#### Optional Inputs !! !! The following is a list of the optional inputs provided for in the !! call sequence. (See also Part 2.) For each such input variable, !! this table lists its name as used in this documentation, its !! location in the call sequence, its meaning, and the default value. !! The use of any of these inputs requires IOPT = 1, and in that case !! all of these inputs are examined. A value of zero for any of !! these optional inputs will cause the default value to be used. !! Thus to use a subset of the optional inputs, simply preload !! locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, !! and then set those of interest to nonzero values. !! !! Name | Location | Meaning and default value !! ------| ---------| ----------------------------------------------- !! H0 | RWORK(5) | Step size to be attempted on the first step. !! | | The default value is determined by the solver. !! HMAX | RWORK(6) | Maximum absolute step size allowed. The !! | | default value is infinite. !! HMIN | RWORK(7) | Minimum absolute step size allowed. The !! | | default value is 0. (This lower bound is not !! | | enforced on the final step before reaching !! | | TCRIT when ITASK = 4 or 5.) !! MAXORD| IWORK(5) | Maximum order to be allowed. The default value !! | | is 12 if METH = 1, and 5 if METH = 2. (See the !! | | MF description above for METH.) If MAXORD !! | | exceeds the default value, it will be reduced !! | | to the default value. If MAXORD is changed !! | | during the problem, it may cause the current !! | | order to be reduced. !! MXSTEP| IWORK(6) | Maximum number of (internally defined) steps !! | | allowed during one call to the solver. The !! | | default value is 500. !! MXHNIL| IWORK(7) | Maximum number of messages printed (per !! | | problem) warning that T + H = T on a step !! | | (H = step size). This must be positive to !! | | result in a nondefault value. The default !! | | value is 10. !! !!#### Optional Outputs !! !! As optional additional output from DLSODE, the variables listed !! below are quantities related to the performance of DLSODE which !! are available to the user. These are communicated by way of the !! work arrays, but also have internal mnemonic names as shown. !! Except where stated otherwise, all of these outputs are defined on !! any successful return from DLSODE, and on any return with ISTATE = !! -1, -2, -4, -5, or -6. On an illegal input return (ISTATE = -3), !! they will be unchanged from their existing values (if any), except !! possibly for TOLSF, LENRW, and LENIW. On any error return, !! outputs relevant to the error will be defined, as noted below. !! !! Name | Location | Meaning !! ----- | --------- | ------------------------------------------------ !! HU | RWORK(11) | Step size in t last used (successfully). !! HCUR | RWORK(12) | Step size to be attempted on the next step. !! TCUR | RWORK(13) | Current value of the independent variable which !! | | the solver has actually reached, i.e., the !! | | current internal mesh point in t. On output, !! | | TCUR will always be at least as far as the !! | | argument T, but may be farther (if interpolation !! | | was done). !! TOLSF | RWORK(14) | Tolerance scale factor, greater than 1.0, !! | | computed when a request for too much accuracy !! | | was detected (ISTATE = -3 if detected at the !! | | start of the problem, ISTATE = -2 otherwise). !! | | If ITOL is left unaltered but RTOL and ATOL are !! | | uniformly scaled up by a factor of TOLSF for the !! | | next call, then the solver is deemed likely to !! | | succeed. (The user may also ignore TOLSF and !! | | alter the tolerance parameters in any other way !! | | appropriate.) !! NST | IWORK(11) | Number of steps taken for the problem so far. !! NFE | IWORK(12) | Number of F evaluations for the problem so far. !! NJE | IWORK(13) | Number of Jacobian evaluations (and of matrix LU !! | | decompositions) for the problem so far. !! NQU | IWORK(14) | Method order last used (successfully). !! NQCUR | IWORK(15) | Order to be attempted on the next step. !! IMXER | IWORK(16) | Index of the component of largest magnitude in !! | | the weighted local error vector ( e(i)/EWT(i) ), !! | | on an error return with ISTATE = -4 or -5. !! LENRW | IWORK(17) | Length of RWORK actually required. This is !! | | defined on normal returns and on an illegal !! | | input return for insufficient storage. !! LENIW | IWORK(18) | Length of IWORK actually required. This is !! | | defined on normal returns and on an illegal !! | | input return for insufficient storage. !! !! The following two arrays are segments of the RWORK array which may !! also be of interest to the user as optional outputs. For each !! array, the table below gives its internal name, its base address !! in RWORK, and its description. !! !! Name| Base address| Description !! ----| ------------| ---------------------------------------------- !! YH | 21 | The Nordsieck history array, of size NYH by !! | | (NQCUR + 1), where NYH is the initial value of !! | | NEQ. For j = 0,1,...,NQCUR, column j + 1 of !! | | YH contains HCUR\*\*j/factorial(j) times the jth !! | | derivative of the interpolating polynomial !! | | currently representing the solution, evaluated !! | | at t = TCUR. !! ACOR| LENRW-NEQ+1 | Array of size NEQ used for the accumulated !! | | corrections on each step, scaled on output to !! | | represent the estimated local error in Y on !! | | the last step. This is the vector e in the !! | | description of the error control. It is !! | | defined only on successful return from DLSODE. !! !!#### Part 2. Other Callable Routines !! !! The following are optional calls which the user may make to gain !! additional capabilities in conjunction with DLSODE. !! !! Form of call | Function !! ------------------------- | --------------------------------------- !! CALL XSETUN(LUN) | Set the logical unit number, LUN, for !! | output of messages from DLSODE, if the !! | default is not desired. The default !! | value of LUN is 6. This call may be made !! | at any time and will take effect !! | immediately. !! CALL XSETF(MFLAG) | Set a flag to control the printing of !! | messages by DLSODE. MFLAG = 0 means do !! | not print. (Danger: this risks losing !! | valuable information.) MFLAG = 1 means !! | print (the default). This call may be !! | made at any time and will take effect !! | immediately. !! CALL DSRCOM(RSAV,ISAV,JOB)| Saves and restores the contents of the !! | internal COMMON blocks used by DLSODE !! | (see Part 3 below). RSAV must be a !! | real array of length 218 or more, and !! | ISAV must be an integer array of length !! | 37 or more. JOB = 1 means save COMMON !! | into RSAV/ISAV. JOB = 2 means restore !! | COMMON from same. DSRCOM is useful if !! | one is interrupting a run and restarting !! | later, or alternating between two or !! | more problems solved with DLSODE. !! CALL DINTDY(,,,,,) | Provide derivatives of y, of various !! (see below) | orders, at a specified point t, if !! | desired. It may be called only after a !! | successful return from DLSODE. Detailed !! | instructions follow. !! !!#### Detailed instructions for using DINTDY !! !! The form of the CALL is: !! !! CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) !! !! The input parameters are: !! !! value | description !! -------- | -------------------------------------------------------- !! T | Value of independent variable where answers are !! | desired (normally the same as the T last returned by !! | DLSODE). For valid results, T must lie between !! | TCUR - HU and TCUR. (See "Optional Outputs" above !! | for TCUR and HU.) !! K | Integer order of the derivative desired. K must !! | satisfy 0 <= K <= NQCUR, where NQCUR is the current !! | order (see "Optional Outputs"). The capability !! | corresponding to K = 0, i.e., computing y(t), is !! | already provided by DLSODE directly. Since !! | NQCUR >= 1, the first derivative dy/dt is always !! | available with DINTDY. !! RWORK(21)| The base address of the history array YH. !! NYH | Column length of YH, equal to the initial value of NEQ. !! !! The output parameters are: !! !! value | description !! -------- | -------------------------------------------------------- !! DKY | Real array of length NEQ containing the computed value !! | of the Kth derivative of y(t). !! IFLAG | Integer flag, returned as 0 if K and T were legal, !! | -1 if K was illegal, and -2 if T was illegal. !! | On an error return, a message is also written. !! !!#### Part 3. Save and Restore Current State !! !! If the solution of a given problem by DLSODE is to be interrupted !! and then later continued, as when restarting an interrupted run or !! alternating between two or more problems, the user should save, !! following the return from the last DLSODE call prior to the !! interruption, the contents of the call sequence variables and the !! internal state values, and later restore these values before the !! next DLSODE call for that problem. In addition, if XSETUN and/or !! XSETF was called for non-default handling of error messages, then !! these calls must be repeated. To save and restore the current state !! use subroutine DSRCOM (see Part 2 above). !! !! !!#### Part 4. Optionally Replaceable Solver Routines !! !! Below are descriptions of two routines in the DLSODE package which !! relate to the measurement of errors. Either routine can be !! replaced by a user-supplied version, if desired. However, since !! such a replacement may have a major impact on performance, it !! should be done only when absolutely necessary, and only with great !! caution. (Note: The means by which the package version of a !! routine is superseded by the user's version may be system- !! dependent.) !! !!#### DEWSET() !! !! The following subroutine is called just before each internal !! integration step, and sets the array of error weights, EWT, as !! described under ITOL/RTOL/ATOL above: !! !! SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) !! !! where NEQ, ITOL, RTOL, and ATOL are as in the DLSODE call !! sequence, YCUR contains the current dependent variable vector, !! and EWT is the array of weights set by DEWSET. !! !! If the user supplies this subroutine, it must return in EWT(i) !! (i = 1,...,NEQ) a positive quantity suitable for comparing errors !! in Y(i) to. The EWT array returned by DEWSET is passed to the !! DVNORM routine (see below), and also used by DLSODE in the !! computation of the optional output IMXER, the diagonal Jacobian !! approximation, and the increments for difference quotient !! Jacobians. !! !! In the user-supplied version of DEWSET, it may be desirable to use !! the current values of derivatives of y. Derivatives up to order NQ !! are available from the history array YH, described above under !! optional outputs. In DEWSET, YH is identical to the YCUR array, !! extended to NQ + 1 columns with a column length of NYH and scale !! factors of H\*\*j/factorial(j). On the first call for the problem, !! given by NST = 0, NQ is 1 and H is temporarily set to 1.0. !! NYH is the initial value of NEQ. The quantities NQ, H, and NST !! can be obtained by including in SEWSET the statements: !! !! DOUBLE PRECISION RLS !! COMMON /DLS001/ RLS(218),ILS(37) !! NQ = ILS(33) !! NST = ILS(34) !! H = RLS(212) !! Thus, for example, the current value of dy/dt can be obtained as !! YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is unnecessary !! when NST = 0). !! !!#### DVNORM() !! !! DVNORM is a real function routine which computes the weighted !! root-mean-square norm of a vector v: !!```text !! d = DVNORM (n, v, w) !! !! where: !! n = the length of the vector, !! v = real array of length n containing the vector, !! w = real array of length n containing weights, !! d = SQRT( (1/n) * sum(v(i)*w(i))**2 ). !!``` !! DVNORM is called with n = NEQ and with w(i) = 1.0/EWT(i), where !! EWT is as set by subroutine DEWSET. !! !! If the user supplies this function, it should return a nonnegative !! value of DVNORM suitable for use in the error control in DLSODE. !! None of the arguments should be altered by DVNORM. For example, a !! user-supplied DVNORM routine might: !! !! - Substitute a max-norm of (v(i)\*w(i)) for the rms-norm, or !! - Ignore some components of v in the norm, with the effect of !! suppressing the error control on those components of Y. !! !! --------------------------------------------------------------------- !!### Pedigree: !! !! DLSODE is derived from the Livermore Solver for Ordinary !! Differential Equations package ODEPACK, !! !!#### AUTHOR !! Hindmarsh, Alan C., (LLNL) !! Center for Applied Scientific Computing, L-561 !! Lawrence Livermore National Laboratory !! Livermore, CA 94551. !! --------------------------------------------------------------------- ! ### BEGIN PROLOGUE DLSODE ! ### CATEGORY I1A ! ### TYPE DOUBLE PRECISION (SLSODE-S, DLSODE-D) ! ### KEYWORDS ORDINARY DIFFERENTIAL EQUATIONS, INITIAL VALUE PROBLEM, ! STIFF, NONSTIFF ! ### ROUTINES CALLED DEWSET, DINTDY, DSTODE, DVNORM, XERRWD ! ### COMMON BLOCKS DLS001 ! ### REVISION HISTORY (YYYYMMDD) ! 19791129 DATE WRITTEN ! 19791213 Minor changes to declarations; DELP init. in STODE. ! 19800118 Treat NEQ as array; integer declarations added throughout; ! minor changes to prologue. ! 19800306 Corrected TESCO(1,NQP1) setting in CFODE. ! 19800519 Corrected access of YH on forced order reduction; ! numerous corrections to prologues and other comments. ! 19800617 In main driver, added loading of SQRT(UROUND) in RWORK; ! minor corrections to main prologue. ! 19800923 Added zero initialization of HU and NQU. ! 19801218 Revised XERRWD routine; minor corrections to main prologue. ! 19810401 Minor changes to comments and an error message. ! 19810814 Numerous revisions: replaced EWT by 1/EWT; used flags ! JCUR, ICF, IERPJ, IERSL between STODE and subordinates; ! added tuning parameters CCMAX, MAXCOR, MSBP, MXNCF; ! reorganized returns from STODE; reorganized type decls.; ! fixed message length in XERRWD; changed default LUNIT to 6; ! changed Common lengths; changed comments throughout. ! 19870330 Major update by ACH: corrected comments throughout; ! removed TRET from Common; rewrote EWSET with 4 loops; ! fixed t test in INTDY; added Cray directives in STODE; ! in STODE, fixed DELP init. and logic around PJAC call; ! combined routines to save/restore Common; ! passed LEVEL = 0 in error message calls (except run abort). ! 19890426 Modified prologue to SLATEC/LDOC format. (FNF) ! 19890501 Many improvements to prologue. (FNF) ! 19890503 A few final corrections to prologue. (FNF) ! 19890504 Minor cosmetic changes. (FNF) ! 19890510 Corrected description of Y in Arguments section. (FNF) ! 19890517 Minor corrections to prologue. (FNF) ! 19920514 Updated with prologue edited 891025 by G. Shaw for manual. ! 19920515 Converted source lines to upper case. (FNF) ! 19920603 Revised XERRWD calls using mixed upper-lower case. (ACH) ! 19920616 Revised prologue comment regarding CFT. (ACH) ! 19921116 Revised prologue comments regarding Common. (ACH). ! 19930326 Added comment about non-reentrancy. (FNF) ! 19930723 Changed D1MACH to DUMACH. (FNF) ! 19930801 Removed ILLIN and NTREP from Common (affects driver logic); ! minor changes to prologue and internal comments; ! changed Hollerith strings to quoted strings; ! changed internal comments to mixed case; ! replaced XERRWD with new version using character type; ! changed dummy dimensions from 1 to *. (ACH) ! 19930809 Changed to generic intrinsic names; changed names of ! subprograms and Common blocks to DLSODE etc. (ACH) ! 19930929 Eliminated use of REAL intrinsic; other minor changes. (ACH) ! 20010412 Removed all 'own' variables from Common block /DLS001/ ! (affects declarations in 6 routines). (ACH) ! 20010509 Minor corrections to prologue. (ACH) ! 20031105 Restored 'own' variables to Common block /DLS001/, to ! enable interrupt/restart feature. (ACH) ! 20031112 Added SAVE statements for data-loaded constants. ! ! ### END PROLOGUE DLSODE ! ! *Internal Notes: ! ! Other Routines in the DLSODE Package. ! ! In addition to Subroutine DLSODE, the DLSODE package includes the ! following subroutines and function routines: ! DINTDY computes an interpolated value of the y vector at t = TOUT. ! DSTODE is the core integrator, which does one step of the ! integration and the associated error control. ! DCFODE sets all method coefficients and test constants. ! DPREPJ computes and preprocesses the Jacobian matrix J = df/dy ! and the Newton iteration matrix P = I - h*l0*J. ! DSOLSY manages solution of linear system in chord iteration. ! DEWSET sets the error weight vector EWT before each step. ! DVNORM computes the weighted R.M.S. norm of a vector. ! DSRCOM is a user-callable routine to save and restore ! the contents of the internal Common block. ! DGEFA and DGESL are routines from LINPACK for solving full ! systems of linear algebraic equations. ! DGBFA and DGBSL are routines from LINPACK for solving banded ! linear systems. ! XERRWD, XSETUN, XSETF, IXSAV handle the printing of all ! error messages and warnings. XERRWD is machine-dependent. ! Note: DVNORM, and IXSAV are function routines. ! All the others are subroutines. ! ! **End ! subroutine dlsode(f,Neq,Y,T,Tout,Itol,Rtol,Atol,Itask,Istate,Iopt,Rwork,Lrw,Iwork,Liw,jac,Mf) ! real(kind=dp), dimension(*) :: Atol, Rtol, Y external f external jac real(kind=dp) :: atoli, ayi, big, ewti, h0, hmax, hmx, rh, rtoli, size, sum, tcrit, tdist, tnext, tol, tolsf, tp, w0 integer :: i, i1, i2, iflag, imxer, kgo, leniw, lenrw, lenwm, lf0, ml, mu logical :: ihit integer :: Iopt, Istate, Itask, Itol, Liw, Lrw, Mf integer, intent(inout), dimension(Liw) :: Iwork integer, dimension(2), save :: mord character(80) :: msg integer, save :: mxhnl0, mxstp0 integer, dimension(*) :: Neq real(kind=dp), intent(inout), dimension(Lrw) :: Rwork real(kind=dp), intent(inout) :: T, Tout ! ! Declare all other variables. ! ----------------------------------------------------------------------- ! The following internal Common block contains ! (a) variables which are local to any subroutine but whose values must ! be preserved between calls to the routine ("own" variables), and ! (b) variables which are communicated between subroutines. ! The block DLS001 is declared in subroutines DLSODE, DINTDY, DSTODE, ! DPREPJ, and DSOLSY. ! Groups of variables are replaced by dummy arrays in the Common ! declarations in routines where those variables are not used. ! ----------------------------------------------------------------------- ! data mord(1), mord(2)/12, 5/, mxstp0/500/, mxhnl0/10/ ihit=.false. ! ----------------------------------------------------------------------- ! Block A. ! This code block is executed on every call. ! It tests ISTATE and ITASK for legality and branches appropriately. ! If ISTATE .GT. 1 but the flag INIT shows that initialization has ! not yet been done, an error return occurs. ! If ISTATE = 1 and TOUT = T, return immediately. ! ----------------------------------------------------------------------- ! ! ### FIRST EXECUTABLE STATEMENT DLSODE if ( Istate<1 .or. Istate>3 ) then ! ----------------------------------------------------------------------- ! Block I. ! The following block handles all error returns due to illegal input ! (ISTATE = -3), as detected before calling the core integrator. ! First the error message routine is called. If the illegal input ! is a negative ISTATE, the run is aborted (apparent infinite loop). ! ----------------------------------------------------------------------- msg = 'DLSODE- ISTATE (=I1) illegal ' call xerrwd(msg,30,1,0,1,Istate,0,0,0.0D0,0.0D0) if ( Istate>=0 ) goto 1100 msg = 'DLSODE- Run aborted.. apparent infinite loop ' call xerrwd(msg,50,303,2,0,0,0,0,0.0D0,0.0D0) goto 99999 else if ( Itask<1 .or. Itask>5 ) then msg = 'DLSODE- ITASK (=I1) illegal ' call xerrwd(msg,30,2,0,1,Itask,0,0,0.0D0,0.0D0) goto 1100 else if ( Istate==1 ) then dls1%init = 0 if ( Tout==T ) return elseif ( dls1%init==0 ) then msg = 'DLSODE- ISTATE .GT. 1 but DLSODE not initialized ' call xerrwd(msg,50,3,0,0,0,0,0,0.0D0,0.0D0) goto 1100 elseif ( Istate==2 ) then goto 50 endif ! ----------------------------------------------------------------------- ! Block B. ! The next code block is executed for the initial call (ISTATE = 1), ! or for a continuation call with parameter changes (ISTATE = 3). ! It contains checking of all inputs and various initializations. ! ! First check legality of the non-optional inputs NEQ, ITOL, IOPT, ! MF, ML, and MU. ! ----------------------------------------------------------------------- if ( Neq(1)<=0 ) then msg = 'DLSODE- NEQ (=I1) .LT. 1 ' call xerrwd(msg,30,4,0,1,Neq(1),0,0,0.0D0,0.0D0) goto 1100 else if ( Istate/=1 ) then if ( Neq(1)>dls1%n ) then msg = 'DLSODE- ISTATE = 3 and NEQ increased (I1 to I2) ' call xerrwd(msg,50,5,0,2,dls1%n,Neq(1),0,0.0D0,0.0D0) goto 1100 endif endif dls1%n = Neq(1) if ( Itol<1 .or. Itol>4 ) then msg = 'DLSODE- ITOL (=I1) illegal ' call xerrwd(msg,30,6,0,1,Itol,0,0,0.0D0,0.0D0) goto 1100 elseif ( Iopt<0 .or. Iopt>1 ) then msg = 'DLSODE- IOPT (=I1) illegal ' call xerrwd(msg,30,7,0,1,Iopt,0,0,0.0D0,0.0D0) goto 1100 else dls1%meth = Mf/10 dls1%miter = Mf - 10*dls1%meth if ( dls1%meth<1 .or. dls1%meth>2 ) goto 700 if ( dls1%miter<0 .or. dls1%miter>5 ) goto 700 if ( dls1%miter>3 ) then ml = Iwork(1) mu = Iwork(2) if ( ml<0 .or. ml>=dls1%n ) then msg = 'DLSODE- ML (=I1) illegal.. .LT.0 or .GE.NEQ (=I2)' call xerrwd(msg,50,9,0,2,ml,Neq(1),0,0.0D0,0.0D0) goto 1100 elseif ( mu<0 .or. mu>=dls1%n ) then msg = 'DLSODE- MU (=I1) illegal.. .LT.0 or .GE.NEQ (=I2)' call xerrwd(msg,50,10,0,2,mu,Neq(1),0,0.0D0,0.0D0) goto 1100 endif endif ! Next process and check the optional inputs. -------------------------- if ( Iopt==1 ) then dls1%maxord = Iwork(5) if ( dls1%maxord<0 ) then msg = 'DLSODE- MAXORD (=I1) .LT. 0 ' call xerrwd(msg,30,11,0,1,dls1%maxord,0,0,0.0D0,0.0D0) goto 1100 else if ( dls1%maxord==0 ) dls1%maxord = 100 dls1%maxord = min(dls1%maxord,mord(dls1%meth)) dls1%mxstep = Iwork(6) if ( dls1%mxstep<0 ) then msg = 'DLSODE- MXSTEP (=I1) .LT. 0 ' call xerrwd(msg,30,12,0,1,dls1%mxstep,0,0,0.0D0,0.0D0) goto 1100 else if ( dls1%mxstep==0 ) dls1%mxstep = mxstp0 dls1%mxhnil = Iwork(7) if ( dls1%mxhnil<0 ) then msg = 'DLSODE- MXHNIL (=I1) .LT. 0 ' call xerrwd(msg,30,13,0,1,dls1%mxhnil,0,0,0.0D0,0.0D0) goto 1100 else if ( dls1%mxhnil==0 ) dls1%mxhnil = mxhnl0 if ( Istate==1 ) then h0 = Rwork(5) if ( (Tout-T)*h0<0.0D0 ) then msg = 'DLSODE- TOUT (=R1) behind T (=R2) ' call xerrwd(msg,40,14,0,0,0,0,2,Tout,T) msg = ' Integration direction is given by H0 (=R1) ' call xerrwd(msg,50,14,0,0,0,0,1,h0,0.0D0) goto 1100 endif endif hmax = Rwork(6) if ( hmax<0.0D0 ) then msg = 'DLSODE- HMAX (=R1) .LT. 0.0 ' call xerrwd(msg,30,15,0,0,0,0,1,hmax,0.0D0) goto 1100 else dls1%hmxi = 0.0D0 if ( hmax>0.0D0 ) dls1%hmxi = 1.0D0/hmax dls1%hmin = Rwork(7) if ( dls1%hmin<0.0D0 ) then msg = 'DLSODE- HMIN (=R1) .LT. 0.0 ' call xerrwd(msg,30,16,0,0,0,0,1,dls1%hmin,0.0D0) goto 1100 endif endif endif endif endif else dls1%maxord = mord(dls1%meth) dls1%mxstep = mxstp0 dls1%mxhnil = mxhnl0 if ( Istate==1 ) h0 = 0.0D0 dls1%hmxi = 0.0D0 dls1%hmin = 0.0D0 endif ! ----------------------------------------------------------------------- ! Set work array pointers and check lengths LRW and LIW. ! Pointers to segments of RWORK and IWORK are named by prefixing L to ! the name of the segment. E.g., the segment YH starts at RWORK(LYH). ! Segments of RWORK (in order) are denoted YH, WM, EWT, SAVF, ACOR. ! ----------------------------------------------------------------------- dls1%lyh = 21 if ( Istate==1 ) dls1%nyh = dls1%n dls1%lwm = dls1%lyh + (dls1%maxord+1)*dls1%nyh if ( dls1%miter==0 ) lenwm = 0 if ( dls1%miter==1 .or. dls1%miter==2 ) lenwm = dls1%n*dls1%n + 2 if ( dls1%miter==3 ) lenwm = dls1%n + 2 if ( dls1%miter>=4 ) lenwm = (2*ml+mu+1)*dls1%n + 2 dls1%lewt = dls1%lwm + lenwm dls1%lsavf = dls1%lewt + dls1%n dls1%lacor = dls1%lsavf + dls1%n lenrw = dls1%lacor + dls1%n - 1 Iwork(17) = lenrw dls1%liwm = 1 leniw = 20 + dls1%n if ( dls1%miter==0 .or. dls1%miter==3 ) leniw = 20 Iwork(18) = leniw if ( lenrw>Lrw ) then msg = 'DLSODE- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' call xerrwd(msg,60,17,0,2,lenrw,Lrw,0,0.0D0,0.0D0) goto 1100 elseif ( leniw>Liw ) then msg = 'DLSODE- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' call xerrwd(msg,60,18,0,2,leniw,Liw,0,0.0D0,0.0D0) goto 1100 else ! Check RTOL and ATOL for legality. ------------------------------------ rtoli = Rtol(1) atoli = Atol(1) do i = 1, dls1%n if ( Itol>=3 ) rtoli = Rtol(i) if ( Itol==2 .or. Itol==4 ) atoli = Atol(i) if ( rtoli<0.0D0 ) then msg = 'DLSODE- RTOL(I1) is R1 .LT. 0.0 ' call xerrwd(msg,40,19,0,1,i,0,1,rtoli,0.0D0) goto 1100 elseif ( atoli<0.0D0 ) then msg = 'DLSODE- ATOL(I1) is R1 .LT. 0.0 ' call xerrwd(msg,40,20,0,1,i,0,1,atoli,0.0D0) goto 1100 endif enddo if ( Istate==1 ) then ! ----------------------------------------------------------------------- ! Block C. ! The next block is for the initial call only (ISTATE = 1). ! It contains all remaining initializations, the initial call to F, ! and the calculation of the initial step size. ! The error weights in EWT are inverted after being loaded. ! ----------------------------------------------------------------------- dls1%uround = epsilon(0.0d0) dls1%tn = T if ( Itask==4 .or. Itask==5 ) then tcrit = Rwork(1) if ( (tcrit-Tout)*(Tout-T)<0.0D0 ) goto 900 if ( h0/=0.0D0 .and. (T+h0-tcrit)*h0>0.0D0 ) h0 = tcrit - T endif dls1%jstart = 0 if ( dls1%miter>0 ) Rwork(dls1%lwm) = sqrt(dls1%uround) dls1%nhnil = 0 dls1%nst = 0 dls1%nje = 0 dls1%nslast = 0 dls1%hu = 0.0D0 dls1%nqu = 0 dls1%ccmax = 0.3D0 dls1%maxcor = 3 dls1%msbp = 20 dls1%mxncf = 10 ! Initial call to F. (LF0 points to YH(*,2).) ------------------------- lf0 = dls1%lyh + dls1%nyh call f(Neq,T,Y,Rwork(lf0)) dls1%nfe = 1 ! Load the initial value vector in YH. --------------------------------- do i = 1, dls1%n Rwork(i+dls1%lyh-1) = Y(i) enddo ! Load and invert the EWT array. (H is temporarily set to 1.0.) ------- dls1%nq = 1 dls1%h = 1.0D0 call dewset(dls1%n,Itol,Rtol,Atol,Rwork(dls1%lyh),Rwork(dls1%lewt)) do i = 1, dls1%n if ( Rwork(i+dls1%lewt-1)<=0.0D0 ) then ewti = Rwork(dls1%lewt+i-1) msg = 'DLSODE- EWT(I1) is R1 .LE. 0.0 ' call xerrwd(msg,40,21,0,1,i,0,1,ewti,0.0D0) goto 1100 else Rwork(i+dls1%lewt-1) = 1.0D0/Rwork(i+dls1%lewt-1) endif enddo ! ----------------------------------------------------------------------- ! The coding below computes the step size, H0, to be attempted on the ! first step, unless the user has supplied a value for this. ! First check that TOUT - T differs significantly from zero. ! A scalar tolerance quantity TOL is computed, as MAX(RTOL(I)) ! if this is positive, or MAX(ATOL(I)/ABS(Y(I))) otherwise, adjusted ! so as to be between 100*UROUND and 1.0E-3. ! Then the computed value H0 is given by.. ! NEQ ! H0**2 = TOL / ( w0**-2 + (1/NEQ) * SUM ( f(i)/ywt(i) )**2 ) ! 1 ! where w0 = MAX ( ABS(T), ABS(TOUT) ), ! f(i) = i-th component of initial value of f, ! ywt(i) = EWT(i)/TOL (a weight for y(i)). ! The sign of H0 is inferred from the initial values of TOUT and T. ! ----------------------------------------------------------------------- if ( h0==0.0D0 ) then tdist = abs(Tout-T) w0 = max(abs(T),abs(Tout)) if ( tdist<2.0D0*dls1%uround*w0 ) then msg = 'DLSODE- TOUT (=R1) too close to T(=R2) to start integration' call xerrwd(msg,60,22,0,0,0,0,2,Tout,T) goto 1100 else tol = Rtol(1) if ( Itol>2 ) then do i = 1, dls1%n tol = max(tol,Rtol(i)) enddo endif if ( tol<=0.0D0 ) then atoli = Atol(1) do i = 1, dls1%n if ( Itol==2 .or. Itol==4 ) atoli = Atol(i) ayi = abs(Y(i)) if ( ayi/=0.0D0 ) tol = max(tol,atoli/ayi) enddo endif tol = max(tol,100.0D0*dls1%uround) tol = min(tol,0.001D0) sum = dvnorm(dls1%n,Rwork(lf0),Rwork(dls1%lewt)) sum = 1.0D0/(tol*w0*w0) + tol*sum**2 h0 = 1.0D0/sqrt(sum) h0 = min(h0,tdist) h0 = sign(h0,Tout-T) endif endif ! Adjust H0 if necessary to meet HMAX bound. --------------------------- rh = abs(h0)*dls1%hmxi if ( rh>1.0D0 ) h0 = h0/rh ! Load H with H0 and scale YH(*,2) by H0. ------------------------------ dls1%h = h0 do i = 1, dls1%n Rwork(i+lf0-1) = h0*Rwork(i+lf0-1) enddo goto 200 else ! If ISTATE = 3, set flag to signal parameter changes to DSTODE. ------- dls1%jstart = -1 if ( dls1%nq>dls1%maxord ) then ! MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- do i = 1, dls1%n Rwork(i+dls1%lsavf-1) = Rwork(i+dls1%lwm-1) enddo endif ! Reload WM(1) = RWORK(LWM), since LWM may have changed. --------------- if ( dls1%miter>0 ) Rwork(dls1%lwm) = sqrt(dls1%uround) if ( dls1%n/=dls1%nyh ) then ! NEQ was reduced. Zero part of YH to avoid undefined references. ----- i1 = dls1%lyh + dls1%l*dls1%nyh i2 = dls1%lyh + (dls1%maxord+1)*dls1%nyh - 1 if ( i1<=i2 ) then do i = i1, i2 Rwork(i) = 0.0D0 enddo endif endif endif endif endif endif endif ! ----------------------------------------------------------------------- ! Block D. ! The next code block is for continuation calls only (ISTATE = 2 or 3) ! and is to check stop conditions before taking a step. ! ----------------------------------------------------------------------- 50 continue dls1%nslast = dls1%nst select case (Itask) case (2) goto 100 case (3) tp = dls1%tn - dls1%hu*(1.0D0+100.0D0*dls1%uround) if ( (tp-Tout)*dls1%h>0.0D0 ) then msg = 'DLSODE- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' call xerrwd(msg,60,23,0,1,Itask,0,2,Tout,tp) goto 1100 else if ( (dls1%tn-Tout)*dls1%h>=0.0D0 ) goto 300 goto 100 endif case (4) tcrit = Rwork(1) if ( (dls1%tn-tcrit)*dls1%h>0.0D0 ) goto 800 if ( (tcrit-Tout)*dls1%h<0.0D0 ) goto 900 if ( (dls1%tn-Tout)*dls1%h>=0.0D0 ) then call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) if ( iflag/=0 ) goto 1000 T = Tout goto 400 endif case (5) tcrit = Rwork(1) if ( (dls1%tn-tcrit)*dls1%h>0.0D0 ) goto 800 case default if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) goto 100 call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) if ( iflag/=0 ) goto 1000 T = Tout goto 400 endselect hmx = abs(dls1%tn) + abs(dls1%h) ihit = abs(dls1%tn-tcrit)<=100.0D0*dls1%uround*hmx if ( ihit ) goto 300 tnext = dls1%tn + dls1%h*(1.0D0+4.0D0*dls1%uround) if ( (tnext-tcrit)*dls1%h>0.0D0 ) then dls1%h = (tcrit-dls1%tn)*(1.0D0-4.0D0*dls1%uround) if ( Istate==2 ) dls1%jstart = -2 endif endif ! ----------------------------------------------------------------------- ! Block E. ! The next block is normally executed for all calls and contains ! the call to the one-step core integrator DSTODE. ! ! This is a looping point for the integration steps. ! ! First check for too many steps being taken, update EWT (if not at ! start of problem), check for too much accuracy being requested, and ! check for H below the roundoff level in T. ! ----------------------------------------------------------------------- 100 continue if ( (dls1%nst-dls1%nslast)>=dls1%mxstep ) then ! ----------------------------------------------------------------------- ! Block H. ! The following block handles all unsuccessful returns other than ! those for illegal input. First the error message routine is called. ! If there was an error test or convergence test failure, IMXER is set. ! Then Y is loaded from YH and T is set to TN. The optional outputs ! are loaded into the work arrays before returning. ! ----------------------------------------------------------------------- ! The maximum number of steps was taken before reaching TOUT. ---------- msg = 'DLSODE- At current T (=R1), MXSTEP (=I1) steps ' call xerrwd(msg,50,201,0,0,0,0,0,0.0D0,0.0D0) msg = ' taken on this call before reaching TOUT ' call xerrwd(msg,50,201,0,1,dls1%mxstep,0,1,dls1%tn,0.0D0) Istate = -1 goto 600 else call dewset(dls1%n,Itol,Rtol,Atol,Rwork(dls1%lyh),Rwork(dls1%lewt)) do i = 1, dls1%n if ( Rwork(i+dls1%lewt-1)<=0.0D0 ) then ! EWT(I) .LE. 0.0 for some I (not at start of problem). ---------------- ewti = Rwork(dls1%lewt+i-1) msg = 'DLSODE- At T (=R1), EWT(I1) has become R2 .LE. 0.' call xerrwd(msg,50,202,0,1,i,0,2,dls1%tn,ewti) Istate = -6 goto 600 else Rwork(i+dls1%lewt-1) = 1.0D0/Rwork(i+dls1%lewt-1) endif enddo endif 200 continue tolsf = dls1%uround*dvnorm(dls1%n,Rwork(dls1%lyh),Rwork(dls1%lewt)) if ( tolsf<=1.0D0 ) then if ( (dls1%tn+dls1%h)==dls1%tn ) then dls1%nhnil = dls1%nhnil + 1 if ( dls1%nhnil<=dls1%mxhnil ) then msg = 'DLSODE- Warning..internal T (=R1) and H (=R2) are' call xerrwd(msg,50,101,0,0,0,0,0,0.0D0,0.0D0) msg = ' such that in the machine, T + H = T on the next step ' call xerrwd(msg,60,101,0,0,0,0,0,0.0D0,0.0D0) msg = ' (H = step size). Solver will continue anyway' call xerrwd(msg,50,101,0,0,0,0,2,dls1%tn,dls1%h) if ( dls1%nhnil>=dls1%mxhnil ) then msg = 'DLSODE- Above warning has been issued I1 times. ' call xerrwd(msg,50,102,0,0,0,0,0,0.0D0,0.0D0) msg = ' It will not be issued again for this problem' call xerrwd(msg,50,102,0,1,dls1%mxhnil,0,0,0.0D0,0.0D0) endif endif endif ! ----------------------------------------------------------------------- ! CALL DSTODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,f,JAC,DPREPJ,DSOLSY) ! ----------------------------------------------------------------------- call dstode(Neq,Y,Rwork(dls1%lyh),dls1%nyh,Rwork(dls1%lyh),Rwork(dls1%lewt), & & Rwork(dls1%lsavf),Rwork(dls1%lacor),Rwork(dls1%lwm), & & Iwork(dls1%liwm),f,jac,dprepj,dsolsy) kgo = 1 - dls1%kflag select case (kgo) case (2) ! KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- msg = 'DLSODE- At T(=R1) and step size H(=R2), the error' call xerrwd(msg,50,204,0,0,0,0,0,0.0D0,0.0D0) msg = ' test failed repeatedly or with ABS(H) = HMIN' call xerrwd(msg,50,204,0,0,0,0,2,dls1%tn,dls1%h) Istate = -4 goto 500 case (3) ! KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- msg = 'DLSODE- At T (=R1) and step size H (=R2), the ' call xerrwd(msg,50,205,0,0,0,0,0,0.0D0,0.0D0) msg = ' corrector convergence failed repeatedly ' call xerrwd(msg,50,205,0,0,0,0,0,0.0D0,0.0D0) msg = ' or with ABS(H) = HMIN ' call xerrwd(msg,30,205,0,0,0,0,2,dls1%tn,dls1%h) Istate = -5 goto 500 case default ! ----------------------------------------------------------------------- ! Block F. ! The following block handles the case of a successful return from the ! core integrator (KFLAG = 0). Test for stop conditions. ! ----------------------------------------------------------------------- dls1%init = 1 select case (Itask) case (2) case (3) ! ITASK = 3. Jump to exit if TOUT was reached. ------------------------ if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) goto 100 case (4) ! ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) then hmx = abs(dls1%tn) + abs(dls1%h) ihit = abs(dls1%tn-tcrit)<=100.0D0*dls1%uround*hmx if ( .not.(ihit) ) then tnext = dls1%tn + dls1%h*(1.0D0+4.0D0*dls1%uround) if ( (tnext-tcrit)*dls1%h>0.0D0 ) then dls1%h = (tcrit-dls1%tn)*(1.0D0-4.0D0*dls1%uround) dls1%jstart = -2 endif goto 100 endif else call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) T = Tout goto 400 endif case (5) ! ITASK = 5. See if TCRIT was reached and jump to exit. --------------- hmx = abs(dls1%tn) + abs(dls1%h) ihit = abs(dls1%tn-tcrit)<=100.0D0*dls1%uround*hmx case default ! ITASK = 1. If TOUT has been reached, interpolate. ------------------- if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) goto 100 call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) T = Tout goto 400 endselect endselect else tolsf = tolsf*2.0D0 if ( dls1%nst==0 ) then msg = 'DLSODE- At start of problem, too much accuracy ' call xerrwd(msg,50,26,0,0,0,0,0,0.0D0,0.0D0) msg = ' requested for precision of machine.. See TOLSF (=R1) ' call xerrwd(msg,60,26,0,0,0,0,1,tolsf,0.0D0) Rwork(14) = tolsf goto 1100 else ! Too much accuracy requested for machine precision. ------------------- msg = 'DLSODE- At T (=R1), too much accuracy requested ' call xerrwd(msg,50,203,0,0,0,0,0,0.0D0,0.0D0) msg = ' for precision of machine.. see TOLSF (=R2) ' call xerrwd(msg,50,203,0,0,0,0,2,dls1%tn,tolsf) Rwork(14) = tolsf Istate = -2 goto 600 endif endif ! ----------------------------------------------------------------------- ! Block G. ! The following block handles all successful returns from DLSODE. ! If ITASK .NE. 1, Y is loaded from YH and T is set accordingly. ! ISTATE is set to 2, and the optional outputs are loaded into the ! work arrays before returning. ! ----------------------------------------------------------------------- 300 continue do i = 1, dls1%n Y(i) = Rwork(i+dls1%lyh-1) enddo T = dls1%tn if ( Itask==4 .or. Itask==5 ) then if ( ihit ) T = tcrit endif 400 continue Istate = 2 Rwork(11) = dls1%hu Rwork(12) = dls1%h Rwork(13) = dls1%tn Iwork(11) = dls1%nst Iwork(12) = dls1%nfe Iwork(13) = dls1%nje Iwork(14) = dls1%nqu Iwork(15) = dls1%nq return ! Compute IMXER if relevant. ------------------------------------------- 500 continue big = 0.0D0 imxer = 1 do i = 1, dls1%n size = abs(Rwork(i+dls1%lacor-1)*Rwork(i+dls1%lewt-1)) if ( big<size ) then big = size imxer = i endif enddo Iwork(16) = imxer ! Set Y vector, T, and optional outputs. ------------------------------- 600 continue do i = 1, dls1%n Y(i) = Rwork(i+dls1%lyh-1) enddo T = dls1%tn Rwork(11) = dls1%hu Rwork(12) = dls1%h Rwork(13) = dls1%tn Iwork(11) = dls1%nst Iwork(12) = dls1%nfe Iwork(13) = dls1%nje Iwork(14) = dls1%nqu Iwork(15) = dls1%nq return 700 continue msg = 'DLSODE- MF (=I1) illegal ' call xerrwd(msg,30,8,0,1,Mf,0,0,0.0D0,0.0D0) goto 1100 800 continue msg = 'DLSODE- ITASK = 4 OR 5 and TCRIT (=R1) behind TCUR (=R2) ' call xerrwd(msg,60,24,0,0,0,0,2,tcrit,dls1%tn) goto 1100 900 continue msg = 'DLSODE- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' call xerrwd(msg,60,25,0,0,0,0,2,tcrit,Tout) goto 1100 1000 continue msg = 'DLSODE- Trouble in DINTDY. ITASK = I1, TOUT = R1' call xerrwd(msg,50,27,0,1,Itask,0,1,Tout,0.0D0) ! 1100 continue Istate = -3 return 99999 continue end subroutine dlsode