*DECK SLSODE SUBROUTINE SLSODE (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) EXTERNAL F, JAC INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF REAL Y, T, TOUT, RTOL, ATOL, RWORK DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) C***BEGIN PROLOGUE SLSODE C***PURPOSE Livermore Solver for Ordinary Differential Equations. C SLSODE solves the initial-value problem for stiff or C nonstiff systems of first-order ODE 's,C dy/dt = f(t,y), or, in component form,C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(N)), i=1,...,N.C***CATEGORY I1AC***TYPE SINGLE PRECISION (SLSODE-S, DLSODE-D)C***KEYWORDS ORDINARY DIFFERENTIAL EQUATIONS, INITIAL VALUE PROBLEM,C STIFF, NONSTIFFC***AUTHOR Hindmarsh, Alan C., (LLNL)C Center for Applied Scientific Computing, L-561C Lawrence Livermore National LaboratoryC Livermore, CA 94551.C***DESCRIPTIONCC NOTE: The "Usage" and "Arguments" sections treat only a subset ofC available options, in condensed fashion. The optionsC covered and the information supplied will support mostC standard uses of SLSODE.CC For more sophisticated uses, full details on all options areC given in the concluding section, headed "Long Description."C A synopsis of the SLSODE Long Description is provided at theC beginning of that section; general topics covered are:C - Elements of the call sequence; optional input and outputC - Optional supplemental routines in the SLSODE packageC - internal COMMON blockCC *Usage:C Communication between the user and the SLSODE package, for normalC situations, is summarized here. This summary describes a subsetC of the available options. See "Long Description" for completeC details, including optional communication, nonstandard options,C and instructions for special situations.CC A sample program is given in the "Examples" section.CC Refer to the argument descriptions for the definitions of theC quantities that appear in the following sample declarations.CC For MF = 10,C PARAMETER (LRW = 20 + 16*NEQ, LIW = 20)C For MF = 21 or 22,C PARAMETER (LRW = 22 + 9*NEQ + NEQ**2, LIW = 20 + NEQ)C For MF = 24 or 25,C PARAMETER (LRW = 22 + 10*NEQ + (2*ML+MU)*NEQ,C * LIW = 20 + NEQ)CC EXTERNAL F, JACC INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK(LIW),C * LIW, MFC REAL Y(NEQ), T, TOUT, RTOL, ATOL(ntol), RWORK(LRW)CC CALL SLSODE (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK,C * ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF)CC *Arguments:C F :EXT Name of subroutine for right-hand-side vector f.C This name must be declared EXTERNAL in callingC program. The form of F must be:CC SUBROUTINE F (NEQ, T, Y, YDOT)C INTEGER NEQC REAL T, Y(*), YDOT(*)CC The inputs are NEQ, T, Y. F is to setCC YDOT(i) = f(i,T,Y(1),Y(2),...,Y(NEQ)),C i = 1, ..., NEQ .CC NEQ :IN Number of first-order ODE's. C C Y :INOUT Array of values of the y(t) vector, of length NEQ. C Input: For the first call, Y should contain the C values of y(t) at t = T. (Y is an input C variable only if ISTATE = 1.) C Output: On return, Y will contain the values at the C new t-value. C C T :INOUT Value of the independent variable. On return it C will be the current value of t (normally TOUT). C C TOUT :IN Next point where output is desired (.NE. T). C C ITOL :IN 1 or 2 according as ATOL (below) is a scalar or C an array. C C RTOL :IN Relative tolerance parameter (scalar). C C ATOL :IN Absolute tolerance parameter (scalar or array). C If ITOL = 1, ATOL need not be dimensioned. C If ITOL = 2, ATOL must be dimensioned at least NEQ. C C The estimated local error in Y(i) will be controlled C so as to be roughly less (in magnitude) than C C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. C C Thus the local error test passes if, in each C component, either the absolute error is less than C ATOL (or ATOL(i)), or the relative error is less C than RTOL. C C Use RTOL = 0.0 for pure absolute error control, and C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative C error control. Caution: Actual (global) errors may C exceed these local tolerances, so choose them C conservatively. C C ITASK :IN Flag indicating the task SLSODE is to perform. C Use ITASK = 1 for normal computation of output C values of y at t = TOUT. C C ISTATE:INOUT Index used for input and output to specify the state C of the calculation. C Input: C 1 This is the first call for a problem. C 2 This is a subsequent call. C Output: C 1 Nothing was done, as TOUT was equal to T. C 2 SLSODE was successful (otherwise, negative). C Note that ISTATE need not be modified after a C successful return. C -1 Excess work done on this call (perhaps wrong C MF). C -2 Excess accuracy requested (tolerances too C small). C -3 Illegal input detected (see printed message). C -4 Repeated error test failures (check all C inputs). C -5 Repeated convergence failures (perhaps bad C Jacobian supplied or wrong choice of MF or C tolerances). C -6 Error weight became zero during problem C (solution component i vanished, and ATOL or C ATOL(i) = 0.). C C IOPT :IN Flag indicating whether optional inputs are used: C 0 No. C 1 Yes. (See "Optional inputs" under "LongC Description," Part 1.) C C RWORK :WORK Real work array of length at least: C 20 + 16*NEQ for MF = 10, C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. C C LRW :IN Declared length of RWORK (in user 's DIMENSIONC statement).CC IWORK :WORK Integer work array of length at least:C 20 for MF = 10,C 20 + NEQ for MF = 21, 22, 24, or 25.CC If MF = 24 or 25, input in IWORK(1),IWORK(2) theC lower and upper Jacobian half-bandwidths ML,MU.CC On return, IWORK contains information that may beC of interest to the user:CC Name Location MeaningC ----- --------- -----------------------------------------C NST IWORK(11) Number of steps taken for the problem soC far.C NFE IWORK(12) Number of f evaluations for the problemC so far.C NJE IWORK(13) Number of Jacobian evaluations (and ofC matrix LU decompositions) for the problemC so far.C NQU IWORK(14) Method order last used (successfully).C LENRW IWORK(17) Length of RWORK actually required. ThisC is defined on normal returns and on anC illegal input return for insufficientC storage.C LENIW IWORK(18) Length of IWORK actually required. ThisC is defined on normal returns and on anC illegal input return for insufficientC storage.CC LIW :IN Declared length of IWORK (in user's DIMENSION C statement). C C JAC :EXT Name of subroutine for Jacobian matrix (MF = C 21 or 24). If used, this name must be declared C EXTERNAL in calling program. If not used, pass a C dummy name. The form of JAC must be: C C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) C INTEGER NEQ, ML, MU, NROWPD C REAL T, Y(*), PD(NROWPD,*) C C See item c, under "Description" below for more C information about JAC. C C MF :IN Method flag. Standard values are: C 10 Nonstiff (Adams) method, no Jacobian used. C 21 Stiff (BDF) method, user-supplied full Jacobian. C 22 Stiff method, internally generated full C Jacobian. C 24 Stiff method, user-supplied banded Jacobian. C 25 Stiff method, internally generated banded C Jacobian. C C *Description: C SLSODE solves the initial value problem for stiff or nonstiff C systems of first-order ODE 's,CC dy/dt = f(t,y) ,CC or, in component form,CC dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ))C (i = 1, ..., NEQ) .CC SLSODE is a package based on the GEAR and GEARB packages, and onC the October 23, 1978, version of the tentative ODEPACK userC interface standard, with minor modifications.CC The steps in solving such a problem are as follows.CC a. First write a subroutine of the formCC SUBROUTINE F (NEQ, T, Y, YDOT)C INTEGER NEQC REAL T, Y(*), YDOT(*)CC which supplies the vector function f by loading YDOT(i) withC f(i).CC b. Next determine (or guess) whether or not the problem is stiff.C Stiffness occurs when the Jacobian matrix df/dy has anC eigenvalue whose real part is negative and large in magnitudeC compared to the reciprocal of the t span of interest. If theC problem is nonstiff, use method flag MF = 10. If it is stiff,C there are four standard choices for MF, and SLSODE requires theC Jacobian matrix in some form. This matrix is regarded eitherC as full (MF = 21 or 22), or banded (MF = 24 or 25). In theC banded case, SLSODE requires two half-bandwidth parameters MLC and MU. These are, respectively, the widths of the lower andC upper parts of the band, excluding the main diagonal. Thus theC band consists of the locations (i,j) withCC i - ML <= j <= i + MU ,CC and the full bandwidth is ML + MU + 1 .CC c. If the problem is stiff, you are encouraged to supply theC Jacobian directly (MF = 21 or 24), but if this is not feasible,C SLSODE will compute it internally by difference quotients (MF =C 22 or 25). If you are supplying the Jacobian, write aC subroutine of the formCC SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD)C INTEGER NEQ, ML, MU, NRWOPDC REAL T, Y(*), PD(NROWPD,*)CC which provides df/dy by loading PD as follows:C - For a full Jacobian (MF = 21), load PD(i,j) with df(i)/dy(j),C the partial derivative of f(i) with respect to y(j). (IgnoreC the ML and MU arguments in this case.)C - For a banded Jacobian (MF = 24), load PD(i-j+MU+1,j) withC df(i)/dy(j); i.e., load the diagonal lines of df/dy into theC rows of PD from the top down.C - In either case, only nonzero elements need be loaded.CC d. Write a main program that calls subroutine SLSODE once for eachC point at which answers are desired. This should also provideC for possible use of logical unit 6 for output of error messagesC by SLSODE.CC Before the first call to SLSODE, set ISTATE = 1, set Y and T toC the initial values, and set TOUT to the first output point. ToC continue the integration after a successful return, simplyC reset TOUT and call SLSODE again. No other parameters need beC reset.CC *Examples:C The following is a simple example problem, with the coding neededC for its solution by SLSODE. The problem is from chemical kinetics,C and consists of the following three rate equations:CC dy1/dt = -.04*y1 + 1.E4*y2*y3C dy2/dt = .04*y1 - 1.E4*y2*y3 - 3.E7*y2**2C dy3/dt = 3.E7*y2**2CC on the interval from t = 0.0 to t = 4.E10, with initial conditionsC y1 = 1.0, y2 = y3 = 0. The problem is stiff.CC The following coding solves this problem with SLSODE, using C MF = 21 and printing results at t = .4, 4., ..., 4.E10. It uses C ITOL = 2 and ATOL much smaller for y2 than for y1 or y3 because y2 C has much smaller values. At the end of the run, statistical C quantities of interest are printed.CC EXTERNAL FEX, JEXC INTEGER IOPT, IOUT, ISTATE, ITASK, ITOL, IWORK(23), LIW, LRW,C * MF, NEQC REAL ATOL(3), RTOL, RWORK(58), T, TOUT, Y(3)C NEQ = 3C Y(1) = 1.C Y(2) = 0.C Y(3) = 0.C T = 0.C TOUT = .4C ITOL = 2C RTOL = 1.E-4C ATOL(1) = 1.E-6C ATOL(2) = 1.E-10C ATOL(3) = 1.E-6C ITASK = 1C ISTATE = 1C IOPT = 0C LRW = 58C LIW = 23C MF = 21C DO 40 IOUT = 1,12C CALL SLSODE (FEX, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK,C * ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JEX, MF)C WRITE(6,20) T, Y(1), Y(2), Y(3)C 20 FORMAT(' At t =',E12.4,' y = ',3E14.6)C IF (ISTATE .LT. 0) GO TO 80C 40 TOUT = TOUT*10.C WRITE(6,60) IWORK(11), IWORK(12), IWORK(13)C 60 FORMAT(/' No. steps =',i4,', No. f-s =',i4,', No. J-s = ',i4)C STOPC 80 WRITE(6,90) ISTATEC 90 FORMAT(///' Error halt.. ISTATE = ',I3)C STOPC ENDCC SUBROUTINE FEX (NEQ, T, Y, YDOT)C INTEGER NEQC REAL T, Y(3), YDOT(3)C YDOT(1) = -.04*Y(1) + 1.E4*Y(2)*Y(3)C YDOT(3) = 3.E7*Y(2)*Y(2)C YDOT(2) = -YDOT(1) - YDOT(3)C RETURNC ENDCC SUBROUTINE JEX (NEQ, T, Y, ML, MU, PD, NRPD)C INTEGER NEQ, ML, MU, NRPDC REAL T, Y(3), PD(NRPD,3)C PD(1,1) = -.04C PD(1,2) = 1.E4*Y(3)C PD(1,3) = 1.E4*Y(2)C PD(2,1) = .04C PD(2,3) = -PD(1,3)C PD(3,2) = 6.E7*Y(2)C PD(2,2) = -PD(1,2) - PD(3,2)C RETURNC ENDCC The output from this program (on a Cray-1 in single precision)C is as follows.CC At t = 4.0000e-01 y = 9.851726e-01 3.386406e-05 1.479357e-02C At t = 4.0000e+00 y = 9.055142e-01 2.240418e-05 9.446344e-02C At t = 4.0000e+01 y = 7.158050e-01 9.184616e-06 2.841858e-01C At t = 4.0000e+02 y = 4.504846e-01 3.222434e-06 5.495122e-01C At t = 4.0000e+03 y = 1.831701e-01 8.940379e-07 8.168290e-01C At t = 4.0000e+04 y = 3.897016e-02 1.621193e-07 9.610297e-01C At t = 4.0000e+05 y = 4.935213e-03 1.983756e-08 9.950648e-01C At t = 4.0000e+06 y = 5.159269e-04 2.064759e-09 9.994841e-01C At t = 4.0000e+07 y = 5.306413e-05 2.122677e-10 9.999469e-01C At t = 4.0000e+08 y = 5.494530e-06 2.197825e-11 9.999945e-01C At t = 4.0000e+09 y = 5.129458e-07 2.051784e-12 9.999995e-01C At t = 4.0000e+10 y = -7.170603e-08 -2.868241e-13 1.000000e+00CC No. steps = 330, No. f-s = 405, No. J-s = 69CC *Accuracy:C The accuracy of the solution depends on the choice of tolerancesC RTOL and ATOL. Actual (global) errors may exceed these localC tolerances, so choose them conservatively.CC *Cautions:C The work arrays should not be altered between calls to SLSODE forC the same problem, except possibly for the conditional and optionalC inputs.CC *Portability:C Since NEQ is dimensioned inside SLSODE, some compilers may objectC to a call to SLSODE with NEQ a scalar variable. In this event, C use DIMENSION NEQ(1). Similar remarks apply to RTOL and ATOL.CC Note to Cray users:C For maximum efficiency, use the CFT77 compiler. AppropriateC compiler optimization directives have been inserted for CFT77.CC *Reference:C Alan C. Hindmarsh, "ODEPACK, A Systematized Collection of ODEC Solvers," in Scientific Computing, R. S. Stepleman, et al., Eds.C (North-Holland, Amsterdam, 1983), pp. 55-64.CC *Long Description:C The following complete description of the user interface toC SLSODE consists of four parts:CC 1. The call sequence to subroutine SLSODE, which is a driverC routine for the solver. This includes descriptions of bothC the call sequence arguments and user-supplied routines.C Following these descriptions is a description of optionalC inputs available through the call sequence, and then aC description of optional outputs in the work arrays.CC 2. Descriptions of other routines in the SLSODE package that mayC be (optionally) called by the user. These provide the abilityC to alter error message handling, save and restore the internalC COMMON, and obtain specified derivatives of the solution y(t).CC 3. Descriptions of COMMON block to be declared in overlay orC similar environments, or to be saved when doing an interruptC of the problem and continued solution later.CC 4. Description of two routines in the SLSODE package, either ofC which the user may replace with his own version, if desired.C These relate to the measurement of errors.CCC Part 1. Call SequenceC ----------------------CC ArgumentsC ---------C The call sequence parameters used for input only areCC F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF,CC and those used for both input and output areCC Y, T, ISTATE.CC The work arrays RWORK and IWORK are also used for conditional andC optional inputs and optional outputs. (The term output hereC refers to the return from subroutine SLSODE to the user's calling C program.) C C The legality of input parameters will be thoroughly checked on the C initial call for the problem, but not checked thereafter unless a C change in input parameters is flagged by ISTATE = 3 on input. C C The descriptions of the call arguments are as follows. C C F The name of the user-supplied subroutine defining the ODE C system. The system must be put in the first-order form C dy/dt = f(t,y), where f is a vector-valued function of C the scalar t and the vector y. Subroutine F is to compute C the function f. It is to have the form C C SUBROUTINE F (NEQ, T, Y, YDOT) C REAL T, Y(*), YDOT(*) C C where NEQ, T, and Y are input, and the array YDOT = C f(T,Y) is output. Y and YDOT are arrays of length NEQ. C Subroutine F should not alter Y(1),...,Y(NEQ). F must be C declared EXTERNAL in the calling program. C C Subroutine F may access user-defined quantities in C NEQ(2),... and/or in Y(NEQ(1)+1),..., if NEQ is an array C (dimensioned in F) and/or Y has length exceeding NEQ(1). C See the descriptions of NEQ and Y below. C C If quantities computed in the F routine are needed C externally to SLSODE, an extra call to F should be made C for this purpose, for consistent and accurate results. C If only the derivative dy/dt is needed, use SINTDY C instead. C C NEQ The size of the ODE system (number of first-order C ordinary differential equations). Used only for input. C NEQ may be decreased, but not increased, during the C problem. If NEQ is decreased (with ISTATE = 3 on input), C the remaining components of Y should be left undisturbed, C if these are to be accessed in F and/or JAC. C C Normally, NEQ is a scalar, and it is generally referred C to as a scalar in this user interface description. C However, NEQ may be an array, with NEQ(1) set to the C system size. (The SLSODE package accesses only NEQ(1).) C In either case, this parameter is passed as the NEQ C argument in all calls to F and JAC. Hence, if it is an C array, locations NEQ(2),... may be used to store other C integer data and pass it to F and/or JAC. Subroutines C F and/or JAC must include NEQ in a DIMENSION statement C in that case. C C Y A real array for the vector of dependent variables, of C length NEQ or more. Used for both input and output on C the first call (ISTATE = 1), and only for output on C other calls. On the first call, Y must contain the C vector of initial values. On output, Y contains the C computed solution vector, evaluated at T. If desired, C the Y array may be used for other purposes between C calls to the solver. C C This array is passed as the Y argument in all calls to F C and JAC. Hence its length may exceed NEQ, and locations C Y(NEQ+1),... may be used to store other real data and C pass it to F and/or JAC. (The SLSODE package accesses C only Y(1),...,Y(NEQ).) C C T The independent variable. On input, T is used only on C the first call, as the initial point of the integration. C On output, after each call, T is the value at which a C computed solution Y is evaluated (usually the same as C TOUT). On an error return, T is the farthest point C reached. C C TOUT The next value of T at which a computed solution is C desired. Used only for input. C C When starting the problem (ISTATE = 1), TOUT may be equal C to T for one call, then should not equal T for the next C call. For the initial T, an input value of TOUT .NE. T C is used in order to determine the direction of the C integration (i.e., the algebraic sign of the step sizes) C and the rough scale of the problem. Integration in C either direction (forward or backward in T) is permitted. C C If ITASK = 2 or 5 (one-step modes), TOUT is ignored C after the first call (i.e., the first call with C TOUT .NE. T). Otherwise, TOUT is required on every call. C C If ITASK = 1, 3, or 4, the values of TOUT need not be C monotone, but a value of TOUT which backs up is limited C to the current internal T interval, whose endpoints are C TCUR - HU and TCUR. (See "Optional Outputs" below for C TCUR and HU.) C C C ITOL An indicator for the type of error control. See C description below under ATOL. Used only for input. C C RTOL A relative error tolerance parameter, either a scalar or C an array of length NEQ. See description below under C ATOL. Input only. C C ATOL An absolute error tolerance parameter, either a scalar or C an array of length NEQ. Input only. C C The input parameters ITOL, RTOL, and ATOL determine the C error control performed by the solver. The solver will C control the vector e = (e(i)) of estimated local errors C in Y, according to an inequality of the form C C rms-norm of ( e(i)/EWT(i) ) <= 1, C C where C C EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), C C and the rms-norm (root-mean-square norm) here is C C rms-norm(v) = SQRT(sum v(i)**2 / NEQ). C C Here EWT = (EWT(i)) is a vector of weights which must C always be positive, and the values of RTOL and ATOL C should all be nonnegative. The following table gives the C types (scalar/array) of RTOL and ATOL, and the C corresponding form of EWT(i). C C ITOL RTOL ATOL EWT(i) C ---- ------ ------ ----------------------------- C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) C C When either of these parameters is a scalar, it need not C be dimensioned in the user 's calling program.CC If none of the above choices (with ITOL, RTOL, and ATOLC fixed throughout the problem) is suitable, more generalC error controls can be obtained by substitutingC user-supplied routines for the setting of EWT and/or forC the norm calculation. See Part 4 below.CC If global errors are to be estimated by making a repeatedC run on the same problem with smaller tolerances, then allC components of RTOL and ATOL (i.e., of EWT) should beC scaled down uniformly.CC ITASK An index specifying the task to be performed. InputC only. ITASK has the following values and meanings:C 1 Normal computation of output values of y(t) atC t = TOUT (by overshooting and interpolating).C 2 Take one step only and return.C 3 Stop at the first internal mesh point at or beyondC t = TOUT and return.C 4 Normal computation of output values of y(t) atC t = TOUT but without overshooting t = TCRIT. TCRITC must be input as RWORK(1). TCRIT may be equal to orC beyond TOUT, but not behind it in the direction ofC integration. This option is useful if the problemC has a singularity at or beyond t = TCRIT.C 5 Take one step, without passing TCRIT, and return.C TCRIT must be input as RWORK(1).CC Note: If ITASK = 4 or 5 and the solver reaches TCRITC (within roundoff), it will return T = TCRIT (exactly) toC indicate this (unless ITASK = 4 and TOUT comes beforeC TCRIT, in which case answers at T = TOUT are returnedC first).CC ISTATE An index used for input and output to specify the stateC of the calculation.CC On input, the values of ISTATE are as follows:C 1 This is the first call for the problemC (initializations will be done). See "Note" below.C 2 This is not the first call, and the calculation is toC continue normally, with no change in any inputC parameters except possibly TOUT and ITASK. (If ITOL,C RTOL, and/or ATOL are changed between calls withC ISTATE = 2, the new values will be used but notC tested for legality.)C 3 This is not the first call, and the calculation is toC continue normally, but with a change in inputC parameters other than TOUT and ITASK. Changes areC allowed in NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF,C ML, MU, and any of the optional inputs except H0.C (See IWORK description for ML and MU.)CC Note: A preliminary call with TOUT = T is not counted asC a first call here, as no initialization or checking ofC input is done. (Such a call is sometimes useful for theC purpose of outputting the initial conditions.) Thus theC first call for which TOUT .NE. T requires ISTATE = 1 onC input.CC On output, ISTATE has the following values and meanings:C 1 Nothing was done, as TOUT was equal to T withC ISTATE = 1 on input.C 2 The integration was performed successfully.C -1 An excessive amount of work (more than MXSTEP steps)C was done on this call, before completing theC requested task, but the integration was otherwiseC successful as far as T. (MXSTEP is an optional inputC and is normally 500.) To continue, the user mayC simply reset ISTATE to a value >1 and call again (theC excess work step counter will be reset to 0). InC addition, the user may increase MXSTEP to avoid thisC error return; see "Optional Inputs" below.C -2 Too much accuracy was requested for the precision ofC the machine being used. This was detected beforeC completing the requested task, but the integrationC was successful as far as T. To continue, theC tolerance parameters must be reset, and ISTATE mustC be set to 3. The optional output TOLSF may be usedC for this purpose. (Note: If this condition isC detected before taking any steps, then an illegalC input return (ISTATE = -3) occurs instead.)C -3 Illegal input was detected, before taking anyC integration steps. See written message for details.C (Note: If the solver detects an infinite loop ofC calls to the solver with illegal input, it will causeC the run to stop.)C -4 There were repeated error-test failures on oneC attempted step, before completing the requested task,C but the integration was successful as far as T. TheC problem may have a singularity, or the input may beC inappropriate.C -5 There were repeated convergence-test failures on oneC attempted step, before completing the requested task,C but the integration was successful as far as T. ThisC may be caused by an inaccurate Jacobian matrix, ifC one is being used.C -6 EWT(i) became zero for some i during the integration.C Pure relative error control (ATOL(i)=0.0) wasC requested on a variable which has now vanished. TheC integration was successful as far as T.CC Note: Since the normal output value of ISTATE is 2, itC does not need to be reset for normal continuation. Also,C since a negative input value of ISTATE will be regardedC as illegal, a negative output value requires the user toC change it, and possibly other inputs, before calling theC solver again.CC IOPT An integer flag to specify whether any optional inputsC are being used on this call. Input only. The optionalC inputs are listed under a separate heading below.C 0 No optional inputs are being used. Default valuesC will be used in all cases.C 1 One or more optional inputs are being used.CC RWORK A real working array (single precision). The length ofC RWORK must be at leastCC 20 + NYH*(MAXORD + 1) + 3*NEQ + LWMCC whereC NYH = the initial value of NEQ,C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless aC smaller value is given as an optional input),C LWM = 0 if MITER = 0,C LWM = NEQ**2 + 2 if MITER = 1 or 2,C LWM = NEQ + 2 if MITER = 3, andC LWM = (2*ML + MU + 1)*NEQ + 2C if MITER = 4 or 5.C (See the MF description below for METH and MITER.)CC Thus if MAXORD has its default value and NEQ is constant,C this length is:C 20 + 16*NEQ for MF = 10,C 22 + 16*NEQ + NEQ**2 for MF = 11 or 12,C 22 + 17*NEQ for MF = 13,C 22 + 17*NEQ + (2*ML + MU)*NEQ for MF = 14 or 15,C 20 + 9*NEQ for MF = 20,C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22,C 22 + 10*NEQ for MF = 23,C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25.CC The first 20 words of RWORK are reserved for conditionalC and optional inputs and optional outputs.CC The following word in RWORK is a conditional input:C RWORK(1) = TCRIT, the critical value of t which theC solver is not to overshoot. Required if ITASKC is 4 or 5, and ignored otherwise. See ITASK.CC LRW The length of the array RWORK, as declared by the user.C (This will be checked by the solver.)CC IWORK An integer work array. Its length must be at leastC 20 if MITER = 0 or 3 (MF = 10, 13, 20, 23), orC 20 + NEQ otherwise (MF = 11, 12, 14, 15, 21, 22, 24, 25).C (See the MF description below for MITER.) The first fewC words of IWORK are used for conditional and optionalC inputs and optional outputs.CC The following two words in IWORK are conditional inputs:C IWORK(1) = ML These are the lower and upper half-C IWORK(2) = MU bandwidths, respectively, of the bandedC Jacobian, excluding the main diagonal.C The band is defined by the matrix locationsC (i,j) with i - ML <= j <= i + MU. ML and MUC must satisfy 0 <= ML,MU <= NEQ - 1. These areC required if MITER is 4 or 5, and ignoredC otherwise. ML and MU may in fact be the bandC parameters for a matrix to which df/dy is onlyC approximately equal.CC LIW The length of the array IWORK, as declared by the user.C (This will be checked by the solver.)CC Note: The work arrays must not be altered between calls to SLSODEC for the same problem, except possibly for the conditional andC optional inputs, and except for the last 3*NEQ words of RWORK.C The latter space is used for internal scratch space, and so isC available for use by the user outside SLSODE between calls, ifC desired (but not for use by F or JAC).CC JAC The name of the user-supplied routine (MITER = 1 or 4) toC compute the Jacobian matrix, df/dy, as a function of theC scalar t and the vector y. (See the MF description belowC for MITER.) It is to have the formCC SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD)C REAL T, Y(*), PD(NROWPD,*)CC where NEQ, T, Y, ML, MU, and NROWPD are input and theC array PD is to be loaded with partial derivativesC (elements of the Jacobian matrix) on output. PD must beC given a first dimension of NROWPD. T and Y have the sameC meaning as in subroutine F.CC In the full matrix case (MITER = 1), ML and MU areC ignored, and the Jacobian is to be loaded into PD inC columnwise manner, with df(i)/dy(j) loaded into PD(i,j).CC In the band matrix case (MITER = 4), the elements withinC the band are to be loaded into PD in columnwise manner,C with diagonal lines of df/dy loaded into the rows of PD.C Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). MLC and MU are the half-bandwidth parameters (see IWORK).C The locations in PD in the two triangular areas whichC correspond to nonexistent matrix elements can be ignoredC or loaded arbitrarily, as they are overwritten by SLSODE.CC JAC need not provide df/dy exactly. A crude approximationC (possibly with a smaller bandwidth) will do.CC In either case, PD is preset to zero by the solver, soC that only the nonzero elements need be loaded by JAC.C Each call to JAC is preceded by a call to F with the sameC arguments NEQ, T, and Y. Thus to gain some efficiency,C intermediate quantities shared by both calculations mayC be saved in a user COMMON block by F and not recomputedC by JAC, if desired. Also, JAC may alter the Y array, ifC desired. JAC must be declared EXTERNAL in the callingC program.CC Subroutine JAC may access user-defined quantities inC NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an arrayC (dimensioned in JAC) and/or Y has length exceedingC NEQ(1). See the descriptions of NEQ and Y above.CC MF The method flag. Used only for input. The legal valuesC of MF are 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24,C and 25. MF has decimal digits METH and MITER:C MF = 10*METH + MITER .CC METH indicates the basic linear multistep method:C 1 Implicit Adams method.C 2 Method based on backward differentiation formulasC (BDF's). C C MITER indicates the corrector iteration method: C 0 Functional iteration (no Jacobian matrix is C involved). C 1 Chord iteration with a user-supplied full (NEQ by C NEQ) Jacobian. C 2 Chord iteration with an internally generated C (difference quotient) full Jacobian (using NEQ C extra calls to F per df/dy value). C 3 Chord iteration with an internally generated C diagonal Jacobian approximation (using one extra call C to F per df/dy evaluation). C 4 Chord iteration with a user-supplied banded Jacobian. C 5 Chord iteration with an internally generated banded C Jacobian (using ML + MU + 1 extra calls to F per C df/dy evaluation). C C If MITER = 1 or 4, the user must supply a subroutine JAC C (the name is arbitrary) as described above under JAC. C For other values of MITER, a dummy argument can be used. C C Optional Inputs C --------------- C The following is a list of the optional inputs provided for in the C call sequence. (See also Part 2.) For each such input variable, C this table lists its name as used in this documentation, its C location in the call sequence, its meaning, and the default value. C The use of any of these inputs requires IOPT = 1, and in that case C all of these inputs are examined. A value of zero for any of C these optional inputs will cause the default value to be used. C Thus to use a subset of the optional inputs, simply preload C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, C and then set those of interest to nonzero values. C C Name Location Meaning and default value C ------ --------- ----------------------------------------------- C H0 RWORK(5) Step size to be attempted on the first step. C The default value is determined by the solver. C HMAX RWORK(6) Maximum absolute step size allowed. The C default value is infinite. C HMIN RWORK(7) Minimum absolute step size allowed. The C default value is 0. (This lower bound is not C enforced on the final step before reaching C TCRIT when ITASK = 4 or 5.) C MAXORD IWORK(5) Maximum order to be allowed. The default value C is 12 if METH = 1, and 5 if METH = 2. (See the C MF description above for METH.) If MAXORD C exceeds the default value, it will be reduced C to the default value. If MAXORD is changed C during the problem, it may cause the current C order to be reduced. C MXSTEP IWORK(6) Maximum number of (internally defined) steps C allowed during one call to the solver. The C default value is 500. C MXHNIL IWORK(7) Maximum number of messages printed (per C problem) warning that T + H = T on a step C (H = step size). This must be positive to C result in a nondefault value. The default C value is 10. C C Optional Outputs C ---------------- C As optional additional output from SLSODE, the variables listed C below are quantities related to the performance of SLSODE which C are available to the user. These are communicated by way of the C work arrays, but also have internal mnemonic names as shown. C Except where stated otherwise, all of these outputs are defined on C any successful return from SLSODE, and on any return with ISTATE = C -1, -2, -4, -5, or -6. On an illegal input return (ISTATE = -3), C they will be unchanged from their existing values (if any), except C possibly for TOLSF, LENRW, and LENIW. On any error return, C outputs relevant to the error will be defined, as noted below. C C Name Location Meaning C ----- --------- ------------------------------------------------ C HU RWORK(11) Step size in t last used (successfully). C HCUR RWORK(12) Step size to be attempted on the next step. C TCUR RWORK(13) Current value of the independent variable which C the solver has actually reached, i.e., the C current internal mesh point in t. On output, C TCUR will always be at least as far as the C argument T, but may be farther (if interpolation C was done). C TOLSF RWORK(14) Tolerance scale factor, greater than 1.0, C computed when a request for too much accuracy C was detected (ISTATE = -3 if detected at the C start of the problem, ISTATE = -2 otherwise). C If ITOL is left unaltered but RTOL and ATOL are C uniformly scaled up by a factor of TOLSF for the C next call, then the solver is deemed likely to C succeed. (The user may also ignore TOLSF and C alter the tolerance parameters in any other way C appropriate.) C NST IWORK(11) Number of steps taken for the problem so far. C NFE IWORK(12) Number of F evaluations for the problem so far. C NJE IWORK(13) Number of Jacobian evaluations (and of matrix LU C decompositions) for the problem so far. C NQU IWORK(14) Method order last used (successfully). C NQCUR IWORK(15) Order to be attempted on the next step. C IMXER IWORK(16) Index of the component of largest magnitude in C the weighted local error vector ( e(i)/EWT(i) ), C on an error return with ISTATE = -4 or -5. C LENRW IWORK(17) Length of RWORK actually required. This is C defined on normal returns and on an illegal C input return for insufficient storage. C LENIW IWORK(18) Length of IWORK actually required. This is C defined on normal returns and on an illegal C input return for insufficient storage. C C The following two arrays are segments of the RWORK array which may C also be of interest to the user as optional outputs. For each C array, the table below gives its internal name, its base address C in RWORK, and its description. C C Name Base address Description C ---- ------------ ---------------------------------------------- C YH 21 The Nordsieck history array, of size NYH by C (NQCUR + 1), where NYH is the initial value of C NEQ. For j = 0,1,...,NQCUR, column j + 1 of C YH contains HCUR**j/factorial(j) times the jth C derivative of the interpolating polynomial C currently representing the solution, evaluated C at t = TCUR. C ACOR LENRW-NEQ+1 Array of size NEQ used for the accumulated C corrections on each step, scaled on output to C represent the estimated local error in Y on C the last step. This is the vector e in the C description of the error control. It is C defined only on successful return from SLSODE. C C C Part 2. Other Callable Routines C -------------------------------- C C The following are optional calls which the user may make to gain C additional capabilities in conjunction with SLSODE. C C Form of call Function C ------------------------ ---------------------------------------- C CALL XSETUN(LUN) Set the logical unit number, LUN, for C output of messages from SLSODE, if the C default is not desired. The default C value of LUN is 6. This call may be made C at any time and will take effect C immediately. C CALL XSETF(MFLAG) Set a flag to control the printing of C messages by SLSODE. MFLAG = 0 means do C not print. (Danger: this risks losing C valuable information.) MFLAG = 1 means C print (the default). This call may be C made at any time and will take effect C immediately. C CALL SSRCOM(RSAV,ISAV,JOB) Saves and restores the contents of the C internal COMMON blocks used by SLSODE C (see Part 3 below). RSAV must be a C real array of length 218 or more, and C ISAV must be an integer array of length C 37 or more. JOB = 1 means save COMMON C into RSAV/ISAV. JOB = 2 means restore C COMMON from same. SSRCOM is useful if C one is interrupting a run and restarting C later, or alternating between two or C more problems solved with SLSODE. C CALL SINTDY(,,,,,) Provide derivatives of y, of various C (see below) orders, at a specified point t, if C desired. It may be called only after a C successful return from SLSODE. Detailed C instructions follow. C C Detailed instructions for using SINTDY C -------------------------------------- C The form of the CALL is: C C CALL SINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) C C The input parameters are: C C T Value of independent variable where answers are C desired (normally the same as the T last returned by C SLSODE). For valid results, T must lie between C TCUR - HU and TCUR. (See "Optional Outputs" above C for TCUR and HU.) C K Integer order of the derivative desired. K must C satisfy 0 <= K <= NQCUR, where NQCUR is the current C order (see "Optional Outputs"). The capability C corresponding to K = 0, i.e., computing y(t), is C already provided by SLSODE directly. Since C NQCUR >= 1, the first derivative dy/dt is always C available with SINTDY. C RWORK(21) The base address of the history array YH. C NYH Column length of YH, equal to the initial value of NEQ. C C The output parameters are: C C DKY Real array of length NEQ containing the computed value C of the Kth derivative of y(t). C IFLAG Integer flag, returned as 0 if K and T were legal, C -1 if K was illegal, and -2 if T was illegal. C On an error return, a message is also written. C C C Part 3. Common Blocks C ---------------------- C C If SLSODE is to be used in an overlay situation, the user must C declare, in the primary overlay, the variables in: C (1) the call sequence to SLSODE, C (2) the internal COMMON block /SLS001/, of length 255 C (218 single precision words followed by 37 integer words). C C If SLSODE is used on a system in which the contents of internal C COMMON blocks are not preserved between calls, the user should C declare the above COMMON block in his main program to insure that C its contents are preserved. C C If the solution of a given problem by SLSODE is to be interrupted C and then later continued, as when restarting an interrupted run or C alternating between two or more problems, the user should save, C following the return from the last SLSODE call prior to the C interruption, the contents of the call sequence variables and the C internal COMMON block, and later restore these values before the C next SLSODE call for that problem. In addition, if XSETUN and/or C XSETF was called for non-default handling of error messages, then C these calls must be repeated. To save and restore the COMMON C block, use subroutine SSRCOM (see Part 2 above). C C C Part 4. Optionally Replaceable Solver Routines C ----------------------------------------------- C C Below are descriptions of two routines in the SLSODE package which C relate to the measurement of errors. Either routine can be C replaced by a user-supplied version, if desired. However, since C such a replacement may have a major impact on performance, it C should be done only when absolutely necessary, and only with great C caution. (Note: The means by which the package version of a C routine is superseded by the user 's version may be system-C dependent.)CC SEWSETC ------C The following subroutine is called just before each internalC integration step, and sets the array of error weights, EWT, asC described under ITOL/RTOL/ATOL above:CC SUBROUTINE SEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT)CC where NEQ, ITOL, RTOL, and ATOL are as in the SLSODE callC sequence, YCUR contains the current dependent variable vector,C and EWT is the array of weights set by SEWSET.CC If the user supplies this subroutine, it must return in EWT(i)C (i = 1,...,NEQ) a positive quantity suitable for comparing errorsC in Y(i) to. The EWT array returned by SEWSET is passed to theC SVNORM routine (see below), and also used by SLSODE in theC computation of the optional output IMXER, the diagonal JacobianC approximation, and the increments for difference quotientC Jacobians.CC In the user-supplied version of SEWSET, it may be desirable to useC the current values of derivatives of y. Derivatives up to order NQC are available from the history array YH, described above underC optional outputs. In SEWSET, YH is identical to the YCUR array,C extended to NQ + 1 columns with a column length of NYH and scaleC factors of H**j/factorial(j). On the first call for the problem,C given by NST = 0, NQ is 1 and H is temporarily set to 1.0.C NYH is the initial value of NEQ. The quantities NQ, H, and NSTC can be obtained by including in SEWSET the statements:C REAL RLSC COMMON /SLS001/ RLS(218),ILS(37)C NQ = ILS(33)C NST = ILS(34)C H = RLS(212)C Thus, for example, the current value of dy/dt can be obtained asC YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is unnecessaryC when NST = 0).CC SVNORMC ------C SVNORM is a real function routine which computes the weightedC root-mean-square norm of a vector v:CC d = SVNORM (n, v, w)CC where:C n = the length of the vector,C v = real array of length n containing the vector,C w = real array of length n containing weights,C d = SQRT( (1/n) * sum(v(i)*w(i))**2 ).CC SVNORM is called with n = NEQ and with w(i) = 1.0/EWT(i), whereC EWT is as set by subroutine SEWSET.CC If the user supplies this function, it should return a nonnegativeC value of SVNORM suitable for use in the error control in SLSODE.C None of the arguments should be altered by SVNORM. For example, aC user-supplied SVNORM routine might:C - Substitute a max-norm of (v(i)*w(i)) for the rms-norm, orC - Ignore some components of v in the norm, with the effect ofC suppressing the error control on those components of Y.C ---------------------------------------------------------------------C***ROUTINES CALLED SEWSET, SINTDY, D1MACH, SSTODE, SVNORM, XERRWDC***COMMON BLOCKS SLS001C***REVISION HISTORY (YYYYMMDD)C 19791129 DATE WRITTENC 19791213 Minor changes to declarations; DELP init. in STODE.C 19800118 Treat NEQ as array; integer declarations added throughout;C minor changes to prologue.C 19800306 Corrected TESCO(1,NQP1) setting in CFODE.C 19800519 Corrected access of YH on forced order reduction;C numerous corrections to prologues and other comments.C 19800617 In main driver, added loading of SQRT(UROUND) in RWORK;C minor corrections to main prologue.C 19800923 Added zero initialization of HU and NQU.C 19801218 Revised XERRWV routine; minor corrections to main prologue.C 19810401 Minor changes to comments and an error message.C 19810814 Numerous revisions: replaced EWT by 1/EWT; used flagsC JCUR, ICF, IERPJ, IERSL between STODE and subordinates;C added tuning parameters CCMAX, MAXCOR, MSBP, MXNCF;C reorganized returns from STODE; reorganized type decls.;C fixed message length in XERRWV; changed default LUNIT to 6;C changed Common lengths; changed comments throughout.C 19870330 Major update by ACH: corrected comments throughout;C removed TRET from Common; rewrote EWSET with 4 loops;C fixed t test in INTDY; added Cray directives in STODE;C in STODE, fixed DELP init. and logic around PJAC call;C combined routines to save/restore Common;C passed LEVEL = 0 in error message calls (except run abort).C 19890426 Modified prologue to SLATEC/LDOC format. (FNF)C 19890501 Many improvements to prologue. (FNF)C 19890503 A few final corrections to prologue. (FNF)C 19890504 Minor cosmetic changes. (FNF)C 19890510 Corrected description of Y in Arguments section. (FNF)C 19890517 Minor corrections to prologue. (FNF)C 19920514 Updated with prologue edited 891025 by G. Shaw for manual.C 19920515 Converted source lines to upper case. (FNF)C 19920603 Revised XERRWV calls using mixed upper-lower case. (ACH)C 19920616 Revised prologue comment regarding CFT. (ACH)C 19921116 Revised prologue comments regarding Common. (ACH).C 19930326 Added comment about non-reentrancy. (FNF)C 19930723 Changed R1MACH to RUMACH. (FNF)C 19930801 Removed ILLIN and NTREP from Common (affects driver logic);C minor changes to prologue and internal comments;C changed Hollerith strings to quoted strings; C changed internal comments to mixed case;C replaced XERRWV with new version using character type;C changed dummy dimensions from 1 to *. (ACH)C 19930809 Changed to generic intrinsic names; changed names ofC subprograms and Common blocks to SLSODE etc. (ACH)C 19930929 Eliminated use of REAL intrinsic; other minor changes. (ACH)C 20010412 Removed all 'own ' variables from Common block /SLS001/C (affects declarations in 6 routines). (ACH)C 20010509 Minor corrections to prologue. (ACH)C 20031105 Restored 'own ' variables to Common block /SLS001/, toC enable interrupt/restart feature. (ACH)C 20031112 Added SAVE statements for data-loaded constants.CC*** END PROLOGUE SLSODECC*Internal Notes:CC Other Routines in the SLSODE Package.CC In addition to Subroutine SLSODE, the SLSODE package includes theC following subroutines and function routines:C SINTDY computes an interpolated value of the y vector at t = TOUT.C SSTODE is the core integrator, which does one step of theC integration and the associated error control.C SCFODE sets all method coefficients and test constants.C SPREPJ computes and preprocesses the Jacobian matrix J = df/dyC and the Newton iteration matrix P = I - h*l0*J.C SSOLSY manages solution of linear system in chord iteration.C SEWSET sets the error weight vector EWT before each step.C SVNORM computes the weighted R.M.S. norm of a vector.C SSRCOM is a user-callable routine to save and restoreC the contents of the internal Common block.C DGETRF AND DGETRS ARE ROUTINES FROM LAPACK FOR SOLVING FULLC SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS.C DGBTRF AND DGBTRS ARE ROUTINES FROM LAPACK FOR SOLVING BANDEDC LINEAR SYSTEMS.C D1MACH computes the unit roundoff in a machine-independent manner.C XERRWD, XSETUN, XSETF, IXSAV, IUMACH handle the printing of allC error messages and warnings. XERRWD is machine-dependent.C Note: SVNORM, D1MACH, IXSAV, and IUMACH are function routines.C All the others are subroutines.CC**EndCC Declare externals. EXTERNAL SPREPJ, SSOLSY REAL D1MACH, SVNORMCC Declare all other variables. INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU INTEGER I, I1, I2, IFLAG, IMXER, KGO, LF0, 1 LENIW, LENRW, LENWM, ML, MORD, MU, MXHNL0, MXSTP0 REAL ROWNS, 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND REAL ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 DIMENSION MORD(2) LOGICAL IHIT CHARACTER*80 MSG SAVE MORD, MXSTP0, MXHNL0C-----------------------------------------------------------------------C The following internal Common block containsC (a) variables which are local to any subroutine but whose values mustC be preserved between calls to the routine ("own" variables), andC (b) variables which are communicated between subroutines.C The block SLS001 is declared in subroutines SLSODE, SINTDY, SSTODE,C SPREPJ, and SSOLSY.C Groups of variables are replaced by dummy arrays in the CommonC declarations in routines where those variables are not used.C----------------------------------------------------------------------- COMMON /SLS001/ ROWNS(209), 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQUC DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/C-----------------------------------------------------------------------C Block A.C This code block is executed on every call.C It tests ISTATE and ITASK for legality and branches appropriately.C If ISTATE .GT. 1 but the flag INIT shows that initialization hasC not yet been done, an error return occurs.C If ISTATE = 1 and TOUT = T, return immediately.C-----------------------------------------------------------------------CC***FIRST EXECUTABLE STATEMENT SLSODE IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 IF (ISTATE .EQ. 1) GO TO 10 IF (INIT .EQ. 0) GO TO 603 IF (ISTATE .EQ. 2) GO TO 200 GO TO 20 10 INIT = 0 IF (TOUT .EQ. T) RETURNC-----------------------------------------------------------------------C Block B.C The next code block is executed for the initial call (ISTATE = 1),C or for a continuation call with parameter changes (ISTATE = 3).C It contains checking of all inputs and various initializations.CC First check legality of the non-optional inputs NEQ, ITOL, IOPT,C MF, ML, and MU.C----------------------------------------------------------------------- 20 IF (NEQ(1) .LE. 0) GO TO 604 IF (ISTATE .EQ. 1) GO TO 25 IF (NEQ(1) .GT. N) GO TO 605 25 N = NEQ(1) IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 METH = MF/10 MITER = MF - 10*METH IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 IF (MITER .LT. 0 .OR. MITER .GT. 5) GO TO 608 IF (MITER .LE. 3) GO TO 30 ML = IWORK(1) MU = IWORK(2) IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 30 CONTINUEC Next process and check the optional inputs. -------------------------- IF (IOPT .EQ. 1) GO TO 40 MAXORD = MORD(METH) MXSTEP = MXSTP0 MXHNIL = MXHNL0 IF (ISTATE .EQ. 1) H0 = 0.0E0 HMXI = 0.0E0 HMIN = 0.0E0 GO TO 60 40 MAXORD = IWORK(5) IF (MAXORD .LT. 0) GO TO 611 IF (MAXORD .EQ. 0) MAXORD = 100 MAXORD = MIN(MAXORD,MORD(METH)) MXSTEP = IWORK(6) IF (MXSTEP .LT. 0) GO TO 612 IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 MXHNIL = IWORK(7) IF (MXHNIL .LT. 0) GO TO 613 IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 IF (ISTATE .NE. 1) GO TO 50 H0 = RWORK(5) IF ((TOUT - T)*H0 .LT. 0.0E0) GO TO 614 50 HMAX = RWORK(6) IF (HMAX .LT. 0.0E0) GO TO 615 HMXI = 0.0E0 IF (HMAX .GT. 0.0E0) HMXI = 1.0E0/HMAX HMIN = RWORK(7) IF (HMIN .LT. 0.0E0) GO TO 616C-----------------------------------------------------------------------C Set work array pointers and check lengths LRW and LIW.C Pointers to segments of RWORK and IWORK are named by prefixing L toC the name of the segment. E.g., the segment YH starts at RWORK(LYH).C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVF, ACOR.C----------------------------------------------------------------------- 60 LYH = 21 IF (ISTATE .EQ. 1) NYH = N LWM = LYH + (MAXORD + 1)*NYH IF (MITER .EQ. 0) LENWM = 0 IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LENWM = N*N + 2 IF (MITER .EQ. 3) LENWM = N + 2 IF (MITER .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 LEWT = LWM + LENWM LSAVF = LEWT + N LACOR = LSAVF + N LENRW = LACOR + N - 1 IWORK(17) = LENRW LIWM = 1 LENIW = 20 + N IF (MITER .EQ. 0 .OR. MITER .EQ. 3) LENIW = 20 IWORK(18) = LENIW IF (LENRW .GT. LRW) GO TO 617 IF (LENIW .GT. LIW) GO TO 618C Check RTOL and ATOL for legality. ------------------------------------ RTOLI = RTOL(1) ATOLI = ATOL(1) DO 70 I = 1,N IF (ITOL .GE. 3) RTOLI = RTOL(I) IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) IF (RTOLI .LT. 0.0E0) GO TO 619 IF (ATOLI .LT. 0.0E0) GO TO 620 70 CONTINUE IF (ISTATE .EQ. 1) GO TO 100C If ISTATE = 3, set flag to signal parameter changes to SSTODE. ------- JSTART = -1 IF (NQ .LE. MAXORD) GO TO 90C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- DO 80 I = 1,N 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1)C Reload WM(1) = RWORK(LWM), since LWM may have changed. --------------- 90 IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) IF (N .EQ. NYH) GO TO 200C NEQ was reduced. Zero part of YH to avoid undefined references. ----- I1 = LYH + L*NYH I2 = LYH + (MAXORD + 1)*NYH - 1 IF (I1 .GT. I2) GO TO 200 DO 95 I = I1,I2 95 RWORK(I) = 0.0E0 GO TO 200C-----------------------------------------------------------------------C Block C.C The next block is for the initial call only (ISTATE = 1).C It contains all remaining initializations, the initial call to F,C and the calculation of the initial step size.C The error weights in EWT are inverted after being loaded.C----------------------------------------------------------------------- 100 UROUND = D1MACH(4) TN = T IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 TCRIT = RWORK(1) IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0E0) GO TO 625 IF (H0 .NE. 0.0E0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0E0) 1 H0 = TCRIT - T 110 JSTART = 0 IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) NHNIL = 0 NST = 0 NJE = 0 NSLAST = 0 HU = 0.0E0 NQU = 0 CCMAX = 0.3E0 MAXCOR = 3 MSBP = 20 MXNCF = 10C Initial call to F. (LF0 points to YH(*,2).) ------------------------- LF0 = LYH + NYH CALL F (NEQ, T, Y, RWORK(LF0)) NFE = 1C Load the initial value vector in YH. --------------------------------- DO 115 I = 1,N 115 RWORK(I+LYH-1) = Y(I)C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- NQ = 1 H = 1.0E0 CALL SEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) DO 120 I = 1,N IF (RWORK(I+LEWT-1) .LE. 0.0E0) GO TO 621 120 RWORK(I+LEWT-1) = 1.0E0/RWORK(I+LEWT-1)C-----------------------------------------------------------------------C The coding below computes the step size, H0, to be attempted on theC first step, unless the user has supplied a value for this.C First check that TOUT - T differs significantly from zero.C A scalar tolerance quantity TOL is computed, as MAX(RTOL(I))C if this is positive, or MAX(ATOL(I)/ABS(Y(I))) otherwise, adjustedC so as to be between 100*UROUND and 1.0E-3.C Then the computed value H0 is given by..C NEQC H0**2 = TOL / ( w0**-2 + (1/NEQ) * SUM ( f(i)/ywt(i) )**2 )C 1C where w0 = MAX ( ABS(T), ABS(TOUT) ),C f(i) = i-th component of initial value of f,C ywt(i) = EWT(i)/TOL (a weight for y(i)).C The sign of H0 is inferred from the initial values of TOUT and T.C----------------------------------------------------------------------- IF (H0 .NE. 0.0E0) GO TO 180 TDIST = ABS(TOUT - T) W0 = MAX(ABS(T),ABS(TOUT)) IF (TDIST .LT. 2.0E0*UROUND*W0) GO TO 622 TOL = RTOL(1) IF (ITOL .LE. 2) GO TO 140 DO 130 I = 1,N 130 TOL = MAX(TOL,RTOL(I)) 140 IF (TOL .GT. 0.0E0) GO TO 160 ATOLI = ATOL(1) DO 150 I = 1,N IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) AYI = ABS(Y(I)) IF (AYI .NE. 0.0E0) TOL = MAX(TOL,ATOLI/AYI) 150 CONTINUE 160 TOL = MAX(TOL,100.0E0*UROUND) TOL = MIN(TOL,0.001E0) SUM = SVNORM (N, RWORK(LF0), RWORK(LEWT)) SUM = 1.0E0/(TOL*W0*W0) + TOL*SUM**2 H0 = 1.0E0/SQRT(SUM) H0 = MIN(H0,TDIST) H0 = SIGN(H0,TOUT-T)C Adjust H0 if necessary to meet HMAX bound. --------------------------- 180 RH = ABS(H0)*HMXI IF (RH .GT. 1.0E0) H0 = H0/RHC Load H with H0 and scale YH(*,2) by H0. ------------------------------ H = H0 DO 190 I = 1,N 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) GO TO 270C-----------------------------------------------------------------------C Block D.C The next code block is for continuation calls only (ISTATE = 2 or 3)C and is to check stop conditions before taking a step.C----------------------------------------------------------------------- 200 NSLAST = NST GO TO (210, 250, 220, 230, 240), ITASK 210 IF ((TN - TOUT)*H .LT. 0.0E0) GO TO 250 CALL SINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) IF (IFLAG .NE. 0) GO TO 627 T = TOUT GO TO 420 220 TP = TN - HU*(1.0E0 + 100.0E0*UROUND) IF ((TP - TOUT)*H .GT. 0.0E0) GO TO 623 IF ((TN - TOUT)*H .LT. 0.0E0) GO TO 250 GO TO 400 230 TCRIT = RWORK(1) IF ((TN - TCRIT)*H .GT. 0.0E0) GO TO 624 IF ((TCRIT - TOUT)*H .LT. 0.0E0) GO TO 625 IF ((TN - TOUT)*H .LT. 0.0E0) GO TO 245 CALL SINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) IF (IFLAG .NE. 0) GO TO 627 T = TOUT GO TO 420 240 TCRIT = RWORK(1) IF ((TN - TCRIT)*H .GT. 0.0E0) GO TO 624 245 HMX = ABS(TN) + ABS(H) IHIT = ABS(TN - TCRIT) .LE. 100.0E0*UROUND*HMX IF (IHIT) GO TO 400 TNEXT = TN + H*(1.0E0 + 4.0E0*UROUND) IF ((TNEXT - TCRIT)*H .LE. 0.0E0) GO TO 250 H = (TCRIT - TN)*(1.0E0 - 4.0E0*UROUND) IF (ISTATE .EQ. 2) JSTART = -2C-----------------------------------------------------------------------C Block E.C The next block is normally executed for all calls and containsC the call to the one-step core integrator SSTODE.CC This is a looping point for the integration steps.CC First check for too many steps being taken, update EWT (if not atC start of problem), check for too much accuracy being requested, andC check for H below the roundoff level in T.C----------------------------------------------------------------------- 250 CONTINUE IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 CALL SEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) DO 260 I = 1,N IF (RWORK(I+LEWT-1) .LE. 0.0E0) GO TO 510 260 RWORK(I+LEWT-1) = 1.0E0/RWORK(I+LEWT-1) 270 TOLSF = UROUND*SVNORM (N, RWORK(LYH), RWORK(LEWT)) IF (TOLSF .LE. 1.0E0) GO TO 280 TOLSF = TOLSF*2.0E0 IF (NST .EQ. 0) GO TO 626 GO TO 520 280 IF ((TN + H) .NE. TN) GO TO 290 NHNIL = NHNIL + 1 IF (NHNIL .GT. MXHNIL) GO TO 290 CALL XERRWD('SLSODE- Warning..internal T (=R1) and H (=R2) are ', 1 50, 101, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD( 1 ' such that in the machine, T + H = T on the next step ', 1 60, 101, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD(' (H = step size). Solver will continue anyway ', 1 50, 101, 0, 0, 0, 0, 2, TN, H) IF (NHNIL .LT. MXHNIL) GO TO 290 CALL XERRWD('SLSODE- Above warning has been issued I1 times. ', 1 50, 102, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD(' It will not be issued again for this problem ', 1 50, 102, 0, 1, MXHNIL, 0, 0, 0.0E0, 0.0E0) 290 CONTINUEC-----------------------------------------------------------------------C CALL SSTODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,SPREPJ,SSOLSY)C----------------------------------------------------------------------- CALL SSTODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), 2 F, JAC, SPREPJ, SSOLSY) KGO = 1 - KFLAG GO TO (300, 530, 540), KGOC-----------------------------------------------------------------------C Block F.C The following block handles the case of a successful return from theC core integrator (KFLAG = 0). Test for stop conditions.C----------------------------------------------------------------------- 300 INIT = 1 GO TO (310, 400, 330, 340, 350), ITASKC ITASK = 1. If TOUT has been reached, interpolate. ------------------- 310 IF ((TN - TOUT)*H .LT. 0.0E0) GO TO 250 CALL SINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) T = TOUT GO TO 420C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ 330 IF ((TN - TOUT)*H .GE. 0.0E0) GO TO 400 GO TO 250C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. 340 IF ((TN - TOUT)*H .LT. 0.0E0) GO TO 345 CALL SINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) T = TOUT GO TO 420 345 HMX = ABS(TN) + ABS(H) IHIT = ABS(TN - TCRIT) .LE. 100.0E0*UROUND*HMX IF (IHIT) GO TO 400 TNEXT = TN + H*(1.0E0 + 4.0E0*UROUND) IF ((TNEXT - TCRIT)*H .LE. 0.0E0) GO TO 250 H = (TCRIT - TN)*(1.0E0 - 4.0E0*UROUND) JSTART = -2 GO TO 250C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- 350 HMX = ABS(TN) + ABS(H) IHIT = ABS(TN - TCRIT) .LE. 100.0E0*UROUND*HMXC-----------------------------------------------------------------------C Block G.C The following block handles all successful returns from SLSODE.C If ITASK .NE. 1, Y is loaded from YH and T is set accordingly.C ISTATE is set to 2, and the optional outputs are loaded into theC work arrays before returning.C----------------------------------------------------------------------- 400 DO 410 I = 1,N 410 Y(I) = RWORK(I+LYH-1) T = TN IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 IF (IHIT) T = TCRIT 420 ISTATE = 2 RWORK(11) = HU RWORK(12) = H RWORK(13) = TN IWORK(11) = NST IWORK(12) = NFE IWORK(13) = NJE IWORK(14) = NQU IWORK(15) = NQ RETURNC-----------------------------------------------------------------------C Block H.C The following block handles all unsuccessful returns other thanC those for illegal input. First the error message routine is called.C If there was an error test or convergence test failure, IMXER is set.C Then Y is loaded from YH and T is set to TN. The optional outputsC are loaded into the work arrays before returning.C-----------------------------------------------------------------------C The maximum number of steps was taken before reaching TOUT. ---------- 500 CALL XERRWD('SLSODE- At current T (=R1), MXSTEP (=I1) steps ', 1 50, 201, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD(' taken on this call before reaching TOUT ', 1 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0E0) ISTATE = -1 GO TO 580C EWT(I) .LE. 0.0 for some I (not at start of problem). ---------------- 510 EWTI = RWORK(LEWT+I-1) CALL XERRWD('SLSODE- At T (=R1), EWT(I1) has become R2 .LE. 0. ', 1 50, 202, 0, 1, I, 0, 2, TN, EWTI) ISTATE = -6 GO TO 580C Too much accuracy requested for machine precision. ------------------- 520 CALL XERRWD('SLSODE- At T (=R1), too much accuracy requested ', 1 50, 203, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD(' for precision of machine.. see TOLSF (=R2) ', 1 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) RWORK(14) = TOLSF ISTATE = -2 GO TO 580C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- 530 CALL XERRWD('SLSODE- At T(=R1) and step size H(=R2), the error ', 1 50, 204, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD(' test failed repeatedly or with ABS(H) = HMIN ', 1 50, 204, 0, 0, 0, 0, 2, TN, H) ISTATE = -4 GO TO 560C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- 540 CALL XERRWD('SLSODE- At T (=R1) and step size H (=R2), the ', 1 50, 205, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD(' corrector convergence failed repeatedly ', 1 50, 205, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD(' or with ABS(H) = HMIN ', 1 30, 205, 0, 0, 0, 0, 2, TN, H) ISTATE = -5C Compute IMXER if relevant. ------------------------------------------- 560 BIG = 0.0E0 IMXER = 1 DO 570 I = 1,N SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) IF (BIG .GE. SIZE) GO TO 570 BIG = SIZE IMXER = I 570 CONTINUE IWORK(16) = IMXERC Set Y vector, T, and optional outputs. ------------------------------- 580 DO 590 I = 1,N 590 Y(I) = RWORK(I+LYH-1) T = TN RWORK(11) = HU RWORK(12) = H RWORK(13) = TN IWORK(11) = NST IWORK(12) = NFE IWORK(13) = NJE IWORK(14) = NQU IWORK(15) = NQ RETURNC-----------------------------------------------------------------------C Block I.C The following block handles all error returns due to illegal inputC (ISTATE = -3), as detected before calling the core integrator.C First the error message routine is called. If the illegal input C is a negative ISTATE, the run is aborted (apparent infinite loop).C----------------------------------------------------------------------- 601 CALL XERRWD('SLSODE- ISTATE (=I1) illegal ', 1 30, 1, 0, 1, ISTATE, 0, 0, 0.0E0, 0.0E0) IF (ISTATE .LT. 0) GO TO 800 GO TO 700 602 CALL XERRWD('SLSODE- ITASK (=I1) illegal ', 1 30, 2, 0, 1, ITASK, 0, 0, 0.0E0, 0.0E0) GO TO 700 603 CALL XERRWD('SLSODE- ISTATE .GT. 1 but SLSODE not initialized ', 1 50, 3, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) GO TO 700 604 CALL XERRWD('SLSODE- NEQ (=I1) .LT. 1 ', 1 30, 4, 0, 1, NEQ(1), 0, 0, 0.0E0, 0.0E0) GO TO 700 605 CALL XERRWD('SLSODE- ISTATE = 3 and NEQ increased (I1 to I2) ', 1 50, 5, 0, 2, N, NEQ(1), 0, 0.0E0, 0.0E0) GO TO 700 606 CALL XERRWD('SLSODE- ITOL (=I1) illegal ', 1 30, 6, 0, 1, ITOL, 0, 0, 0.0E0, 0.0E0) GO TO 700 607 CALL XERRWD('SLSODE- IOPT (=I1) illegal ', 1 30, 7, 0, 1, IOPT, 0, 0, 0.0E0, 0.0E0) GO TO 700 608 CALL XERRWD('SLSODE- MF (=I1) illegal ', 1 30, 8, 0, 1, MF, 0, 0, 0.0E0, 0.0E0) GO TO 700 609 CALL XERRWD('SLSODE- ML (=I1) illegal.. .LT.0 or .GE.NEQ (=I2) ', 1 50, 9, 0, 2, ML, NEQ(1), 0, 0.0E0, 0.0E0) GO TO 700 610 CALL XERRWD('SLSODE- MU (=I1) illegal.. .LT.0 or .GE.NEQ (=I2) ', 1 50, 10, 0, 2, MU, NEQ(1), 0, 0.0E0, 0.0E0) GO TO 700 611 CALL XERRWD('SLSODE- MAXORD (=I1) .LT. 0 ', 1 30, 11, 0, 1, MAXORD, 0, 0, 0.0E0, 0.0E0) GO TO 700 612 CALL XERRWD('SLSODE- MXSTEP (=I1) .LT. 0 ', 1 30, 12, 0, 1, MXSTEP, 0, 0, 0.0E0, 0.0E0) GO TO 700 613 CALL XERRWD('SLSODE- MXHNIL (=I1) .LT. 0 ', 1 30, 13, 0, 1, MXHNIL, 0, 0, 0.0E0, 0.0E0) GO TO 700 614 CALL XERRWD('SLSODE- TOUT (=R1) behind T (=R2) ', 1 40, 14, 0, 0, 0, 0, 2, TOUT, T) CALL XERRWD(' Integration direction is given by H0 (=R1) ', 1 50, 14, 0, 0, 0, 0, 1, H0, 0.0E0) GO TO 700 615 CALL XERRWD('SLSODE- HMAX (=R1) .LT. 0.0 ', 1 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0E0) GO TO 700 616 CALL XERRWD('SLSODE- HMIN (=R1) .LT. 0.0 ', 1 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0E0) GO TO 700 617 CALL XERRWD( 1 'SLSODE- RWORK length needed, LENRW (=I1), exceeds LRW (=I2) ', 1 60, 17, 0, 2, LENRW, LRW, 0, 0.0E0, 0.0E0) GO TO 700 618 CALL XERRWD( 1 'SLSODE- IWORK length needed, LENIW (=I1), exceeds LIW (=I2) ', 1 60, 18, 0, 2, LENIW, LIW, 0, 0.0E0, 0.0E0) GO TO 700 619 CALL XERRWD('SLSODE- RTOL(I1) is R1 .LT. 0.0 ', 1 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0E0) GO TO 700 620 CALL XERRWD('SLSODE- ATOL(I1) is R1 .LT. 0.0 ', 1 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0E0) GO TO 700 621 EWTI = RWORK(LEWT+I-1) CALL XERRWD('SLSODE- EWT(I1) is R1 .LE. 0.0 ', 1 40, 21, 0, 1, I, 0, 1, EWTI, 0.0E0) GO TO 700 622 CALL XERRWD( 1 'SLSODE- TOUT (=R1) too close to T(=R2) to start integration ', 1 60, 22, 0, 0, 0, 0, 2, TOUT, T) GO TO 700 623 CALL XERRWD( 1 'SLSODE- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ', 1 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) GO TO 700 624 CALL XERRWD( 1 'SLSODE- ITASK = 4 OR 5 and TCRIT (=R1) behind TCUR (=R2) ', 1 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) GO TO 700 625 CALL XERRWD( 1 'SLSODE- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ', 1 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) GO TO 700 626 CALL XERRWD('SLSODE- At start of problem, too much accuracy ', 1 50, 26, 0, 0, 0, 0, 0, 0.0E0, 0.0E0) CALL XERRWD( 1 ' requested for precision of machine.. See TOLSF (=R1) ', 1 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0E0) RWORK(14) = TOLSF GO TO 700 627 CALL XERRWD('SLSODE- Trouble in SINTDY. ITASK = I1, TOUT = R1 ', 1 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0E0)C 700 ISTATE = -3 RETURNC 800 CALL XERRWD('SLSODE- Run aborted.. apparent infinite loop

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