Mercurial > octave-nkf
changeset 4583:70da2b8c91dd
[project @ 2003-10-31 15:18:31 by jwe]
| author | jwe |
|---|---|
| date | Fri, 31 Oct 2003 15:20:51 +0000 |
| parents | db5a24d54915 |
| children | f7697d703481 |
| files | libcruft/ChangeLog libcruft/odepack/dlsode.f libcruft/odepack/lsode.f libcruft/odessa/dodessa.f libcruft/odessa/odessa.f liboctave/ChangeLog liboctave/LSODE.cc liboctave/ODESSA.cc |
| diffstat | 8 files changed, 3466 insertions(+), 3448 deletions(-) [+] |
line wrap: on
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--- a/libcruft/ChangeLog Fri Oct 31 15:11:45 2003 +0000 +++ b/libcruft/ChangeLog Fri Oct 31 15:20:51 2003 +0000 @@ -1,3 +1,15 @@ +2003-10-31 John W. Eaton <jwe@bevo.che.wisc.edu> + + * odepack/dlsode.f: Rename from odepack/lsode.f. + * odepack/dlsode.f (DLSODE): Rename from LSODE to avoid name + conflict with LSODE class constructors on systems that upcase + Fortran names. + + * odessa/dodessa.f: Rename from odessa/odessa.f. + * odessa/dodessa.f (DODESSA): Rename from ODESSA to avoid name + conflict with ODESSA class constructors on systems that upcase + Fortran names. + 2003-10-30 John W. Eaton <jwe@bevo.che.wisc.edu> * Makefile.in (MISC_OBJ): Add misc/cquit.o to the list.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/odepack/dlsode.f Fri Oct 31 15:20:51 2003 +0000 @@ -0,0 +1,1522 @@ + SUBROUTINE DLSODE (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 + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(1), Y(1), RTOL(1), ATOL(1), RWORK(LRW), IWORK(LIW) +C----------------------------------------------------------------------- +C THIS IS THE MARCH 30, 1987 VERSION OF +C LSODE.. LIVERMORE SOLVER FOR ORDINARY DIFFERENTIAL EQUATIONS. +C THIS VERSION IS IN DOUBLE PRECISION. +C +C LSODE SOLVES THE INITIAL VALUE PROBLEM FOR STIFF OR NONSTIFF +C 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(NEQ)) (I = 1,...,NEQ). +C LSODE IS A PACKAGE BASED ON THE GEAR AND GEARB PACKAGES, AND ON THE +C OCTOBER 23, 1978 VERSION OF THE TENTATIVE ODEPACK USER INTERFACE +C STANDARD, WITH MINOR MODIFICATIONS. +C----------------------------------------------------------------------- +C REFERENCE.. +C ALAN C. HINDMARSH, ODEPACK, A SYSTEMATIZED COLLECTION OF ODE +C SOLVERS, IN SCIENTIFIC COMPUTING, R. S. STEPLEMAN ET AL. (EDS.), +C NORTH-HOLLAND, AMSTERDAM, 1983, PP. 55-64. +C----------------------------------------------------------------------- +C AUTHOR AND CONTACT.. ALAN C. HINDMARSH, +C COMPUTING AND MATHEMATICS RESEARCH DIV., L-316 +C LAWRENCE LIVERMORE NATIONAL LABORATORY +C LIVERMORE, CA 94550. +C----------------------------------------------------------------------- +C SUMMARY OF USAGE. +C +C COMMUNICATION BETWEEN THE USER AND THE LSODE PACKAGE, FOR NORMAL +C SITUATIONS, IS SUMMARIZED HERE. THIS SUMMARY DESCRIBES ONLY A SUBSET +C OF THE FULL SET OF OPTIONS AVAILABLE. SEE THE FULL DESCRIPTION FOR +C DETAILS, INCLUDING OPTIONAL COMMUNICATION, NONSTANDARD OPTIONS, +C AND INSTRUCTIONS FOR SPECIAL SITUATIONS. SEE ALSO THE EXAMPLE +C PROBLEM (WITH PROGRAM AND OUTPUT) FOLLOWING THIS SUMMARY. +C +C A. FIRST PROVIDE A SUBROUTINE OF THE FORM.. +C SUBROUTINE F (NEQ, T, Y, YDOT, IERR) +C DIMENSION Y(NEQ), YDOT(NEQ) +C WHICH SUPPLIES THE VECTOR FUNCTION F BY LOADING YDOT(I) WITH F(I). +C +C B. NEXT DETERMINE (OR GUESS) WHETHER OR NOT THE PROBLEM IS STIFF. +C STIFFNESS OCCURS WHEN THE JACOBIAN MATRIX DF/DY HAS AN EIGENVALUE +C WHOSE REAL PART IS NEGATIVE AND LARGE IN MAGNITUDE, COMPARED TO THE +C RECIPROCAL OF THE T SPAN OF INTEREST. IF THE PROBLEM IS NONSTIFF, +C USE A METHOD FLAG MF = 10. IF IT IS STIFF, THERE ARE FOUR STANDARD +C CHOICES FOR MF, AND LSODE REQUIRES THE JACOBIAN MATRIX IN SOME FORM. +C THIS MATRIX IS REGARDED EITHER AS FULL (MF = 21 OR 22), +C OR BANDED (MF = 24 OR 25). IN THE BANDED CASE, LSODE REQUIRES TWO +C HALF-BANDWIDTH PARAMETERS ML AND MU. THESE ARE, RESPECTIVELY, THE +C WIDTHS OF THE LOWER AND UPPER PARTS OF THE BAND, EXCLUDING THE MAIN +C DIAGONAL. THUS THE BAND CONSISTS OF THE LOCATIONS (I,J) WITH +C I-ML .LE. J .LE. I+MU, AND THE FULL BANDWIDTH IS ML+MU+1. +C +C C. IF THE PROBLEM IS STIFF, YOU ARE ENCOURAGED TO SUPPLY THE JACOBIAN +C DIRECTLY (MF = 21 OR 24), BUT IF THIS IS NOT FEASIBLE, LSODE WILL +C COMPUTE IT INTERNALLY BY DIFFERENCE QUOTIENTS (MF = 22 OR 25). +C IF YOU ARE SUPPLYING THE JACOBIAN, PROVIDE A SUBROUTINE OF THE FORM.. +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DIMENSION Y(NEQ), PD(NROWPD,NEQ) +C WHICH SUPPLIES 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). (IGNORE THE +C ML AND MU ARGUMENTS IN THIS CASE.) +C FOR A BANDED JACOBIAN (MF = 24), LOAD PD(I-J+MU+1,J) WITH +C DF(I)/DY(J), I.E. LOAD THE DIAGONAL LINES OF DF/DY INTO THE ROWS OF +C PD FROM THE TOP DOWN. +C IN EITHER CASE, ONLY NONZERO ELEMENTS NEED BE LOADED. +C +C D. WRITE A MAIN PROGRAM WHICH CALLS SUBROUTINE LSODE ONCE FOR +C EACH POINT AT WHICH ANSWERS ARE DESIRED. THIS SHOULD ALSO PROVIDE +C FOR POSSIBLE USE OF LOGICAL UNIT 6 FOR OUTPUT OF ERROR MESSAGES +C BY LSODE. ON THE FIRST CALL TO LSODE, SUPPLY ARGUMENTS AS FOLLOWS.. +C F = NAME OF SUBROUTINE FOR RIGHT-HAND SIDE VECTOR F. +C THIS NAME MUST BE DECLARED EXTERNAL IN CALLING PROGRAM. +C NEQ = NUMBER OF FIRST ORDER ODE-S. +C Y = ARRAY OF INITIAL VALUES, OF LENGTH NEQ. +C T = THE INITIAL VALUE OF THE INDEPENDENT VARIABLE. +C TOUT = FIRST POINT WHERE OUTPUT IS DESIRED (.NE. T). +C ITOL = 1 OR 2 ACCORDING AS ATOL (BELOW) IS A SCALAR OR ARRAY. +C RTOL = RELATIVE TOLERANCE PARAMETER (SCALAR). +C ATOL = ABSOLUTE TOLERANCE PARAMETER (SCALAR OR ARRAY). +C THE ESTIMATED LOCAL ERROR IN Y(I) WILL BE CONTROLLED SO AS +C TO BE ROUGHLY LESS (IN MAGNITUDE) THAN +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 THUS THE LOCAL ERROR TEST PASSES IF, IN EACH COMPONENT, +C EITHER THE ABSOLUTE ERROR IS LESS THAN ATOL (OR ATOL(I)), +C OR THE RELATIVE ERROR IS LESS THAN RTOL. +C USE RTOL = 0.0 FOR PURE ABSOLUTE ERROR CONTROL, AND +C USE ATOL = 0.0 (OR ATOL(I) = 0.0) FOR PURE RELATIVE ERROR +C CONTROL. CAUTION.. ACTUAL (GLOBAL) ERRORS MAY EXCEED THESE +C LOCAL TOLERANCES, SO CHOOSE THEM CONSERVATIVELY. +C ITASK = 1 FOR NORMAL COMPUTATION OF OUTPUT VALUES OF Y AT T = TOUT. +C ISTATE = INTEGER FLAG (INPUT AND OUTPUT). SET ISTATE = 1. +C IOPT = 0 TO INDICATE NO OPTIONAL INPUTS USED. +C RWORK = 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 LRW = DECLARED LENGTH OF RWORK (IN USER-S DIMENSION). +C IWORK = INTEGER WORK ARRAY OF LENGTH AT LEAST.. +C 20 FOR MF = 10, +C 20 + NEQ FOR MF = 21, 22, 24, OR 25. +C IF MF = 24 OR 25, INPUT IN IWORK(1),IWORK(2) THE LOWER +C AND UPPER HALF-BANDWIDTHS ML,MU. +C LIW = DECLARED LENGTH OF IWORK (IN USER-S DIMENSION). +C JAC = NAME OF SUBROUTINE FOR JACOBIAN MATRIX (MF = 21 OR 24). +C IF USED, THIS NAME MUST BE DECLARED EXTERNAL IN CALLING +C PROGRAM. IF NOT USED, PASS A DUMMY NAME. +C MF = METHOD FLAG. STANDARD VALUES ARE.. +C 10 FOR NONSTIFF (ADAMS) METHOD, NO JACOBIAN USED. +C 21 FOR STIFF (BDF) METHOD, USER-SUPPLIED FULL JACOBIAN. +C 22 FOR STIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. +C 24 FOR STIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. +C 25 FOR STIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. +C NOTE THAT THE MAIN PROGRAM MUST DECLARE ARRAYS Y, RWORK, IWORK, +C AND POSSIBLY ATOL. +C +C E. THE OUTPUT FROM THE FIRST CALL (OR ANY CALL) IS.. +C Y = ARRAY OF COMPUTED VALUES OF Y(T) VECTOR. +C T = CORRESPONDING VALUE OF INDEPENDENT VARIABLE (NORMALLY TOUT). +C ISTATE = 2 IF LSODE WAS SUCCESSFUL, NEGATIVE OTHERWISE. +C -1 MEANS EXCESS WORK DONE ON THIS CALL (PERHAPS WRONG MF). +C -2 MEANS EXCESS ACCURACY REQUESTED (TOLERANCES TOO SMALL). +C -3 MEANS ILLEGAL INPUT DETECTED (SEE PRINTED MESSAGE). +C -4 MEANS REPEATED ERROR TEST FAILURES (CHECK ALL INPUTS). +C -5 MEANS REPEATED CONVERGENCE FAILURES (PERHAPS BAD JACOBIAN +C SUPPLIED OR WRONG CHOICE OF MF OR TOLERANCES). +C -6 MEANS ERROR WEIGHT BECAME ZERO DURING PROBLEM. (SOLUTION +C COMPONENT I VANISHED, AND ATOL OR ATOL(I) = 0.) +C -13 MEANS EXIT REQUESTED IN USER-SUPPLIED FUNCTION. +C +C F. TO CONTINUE THE INTEGRATION AFTER A SUCCESSFUL RETURN, SIMPLY +C RESET TOUT AND CALL LSODE AGAIN. NO OTHER PARAMETERS NEED BE RESET. +C +C----------------------------------------------------------------------- +C EXAMPLE PROBLEM. +C +C THE FOLLOWING IS A SIMPLE EXAMPLE PROBLEM, WITH THE CODING +C NEEDED FOR ITS SOLUTION BY LSODE. THE PROBLEM IS FROM CHEMICAL +C KINETICS, AND CONSISTS OF THE FOLLOWING THREE RATE EQUATIONS.. +C DY1/DT = -.04*Y1 + 1.E4*Y2*Y3 +C DY2/DT = .04*Y1 - 1.E4*Y2*Y3 - 3.E7*Y2**2 +C DY3/DT = 3.E7*Y2**2 +C ON THE INTERVAL FROM T = 0.0 TO T = 4.E10, WITH INITIAL CONDITIONS +C Y1 = 1.0, Y2 = Y3 = 0. THE PROBLEM IS STIFF. +C +C THE FOLLOWING CODING SOLVES THIS PROBLEM WITH LSODE, USING MF = 21 +C AND PRINTING RESULTS AT T = .4, 4., ..., 4.E10. IT USES +C ITOL = 2 AND ATOL MUCH SMALLER FOR Y2 THAN Y1 OR Y3 BECAUSE +C Y2 HAS MUCH SMALLER VALUES. +C AT THE END OF THE RUN, STATISTICAL QUANTITIES OF INTEREST ARE +C PRINTED (SEE OPTIONAL OUTPUTS IN THE FULL DESCRIPTION BELOW). +C +C EXTERNAL FEX, JEX +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y +C DIMENSION Y(3), ATOL(3), RWORK(58), IWORK(23) +C NEQ = 3 +C Y(1) = 1.D0 +C Y(2) = 0.D0 +C Y(3) = 0.D0 +C T = 0.D0 +C TOUT = .4D0 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 58 +C LIW = 23 +C MF = 21 +C DO 40 IOUT = 1,12 +C CALL LSODE(FEX,NEQ,Y,T,TOUT,ITOL,RTOL,ATOL,ITASK,ISTATE, +C 1 IOPT,RWORK,LRW,IWORK,LIW,JEX,MF) +C WRITE(6,20)T,Y(1),Y(2),Y(3) +C 20 FORMAT(7H AT T =,E12.4,6H Y =,3E14.6) +C IF (ISTATE .LT. 0) GO TO 80 +C 40 TOUT = TOUT*10.D0 +C WRITE(6,60)IWORK(11),IWORK(12),IWORK(13) +C 60 FORMAT(/12H NO. STEPS =,I4,11H NO. F-S =,I4,11H NO. J-S =,I4) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///22H ERROR HALT.. ISTATE =,I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y, YDOT +C DIMENSION Y(3), YDOT(3) +C YDOT(1) = -.04D0*Y(1) + 1.D4*Y(2)*Y(3) +C YDOT(3) = 3.D7*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C SUBROUTINE JEX (NEQ, T, Y, ML, MU, PD, NRPD) +C DOUBLE PRECISION PD, T, Y +C DIMENSION Y(3), PD(NRPD,3) +C PD(1,1) = -.04D0 +C PD(1,2) = 1.D4*Y(3) +C PD(1,3) = 1.D4*Y(2) +C PD(2,1) = .04D0 +C PD(2,3) = -PD(1,3) +C PD(3,2) = 6.D7*Y(2) +C PD(2,2) = -PD(1,2) - PD(3,2) +C RETURN +C END +C +C THE OUTPUT OF THIS PROGRAM (ON A CDC-7600 IN SINGLE PRECISION) +C IS AS FOLLOWS.. +C +C AT T = 4.0000E-01 Y = 9.851726E-01 3.386406E-05 1.479357E-02 +C AT T = 4.0000E+00 Y = 9.055142E-01 2.240418E-05 9.446344E-02 +C AT T = 4.0000E+01 Y = 7.158050E-01 9.184616E-06 2.841858E-01 +C AT T = 4.0000E+02 Y = 4.504846E-01 3.222434E-06 5.495122E-01 +C AT T = 4.0000E+03 Y = 1.831701E-01 8.940379E-07 8.168290E-01 +C AT T = 4.0000E+04 Y = 3.897016E-02 1.621193E-07 9.610297E-01 +C AT T = 4.0000E+05 Y = 4.935213E-03 1.983756E-08 9.950648E-01 +C AT T = 4.0000E+06 Y = 5.159269E-04 2.064759E-09 9.994841E-01 +C AT T = 4.0000E+07 Y = 5.306413E-05 2.122677E-10 9.999469E-01 +C AT T = 4.0000E+08 Y = 5.494529E-06 2.197824E-11 9.999945E-01 +C AT T = 4.0000E+09 Y = 5.129458E-07 2.051784E-12 9.999995E-01 +C AT T = 4.0000E+10 Y = -7.170586E-08 -2.868234E-13 1.000000E+00 +C +C NO. STEPS = 330 NO. F-S = 405 NO. J-S = 69 +C----------------------------------------------------------------------- +C FULL DESCRIPTION OF USER INTERFACE TO LSODE. +C +C THE USER INTERFACE TO LSODE CONSISTS OF THE FOLLOWING PARTS. +C +C I. THE CALL SEQUENCE TO SUBROUTINE LSODE, WHICH IS A DRIVER +C ROUTINE FOR THE SOLVER. THIS INCLUDES DESCRIPTIONS OF BOTH +C THE CALL SEQUENCE ARGUMENTS AND OF USER-SUPPLIED ROUTINES. +C FOLLOWING THESE DESCRIPTIONS IS A DESCRIPTION OF +C OPTIONAL INPUTS AVAILABLE THROUGH THE CALL SEQUENCE, AND THEN +C A DESCRIPTION OF OPTIONAL OUTPUTS (IN THE WORK ARRAYS). +C +C II. DESCRIPTIONS OF OTHER ROUTINES IN THE LSODE PACKAGE THAT MAY BE +C (OPTIONALLY) CALLED BY THE USER. THESE PROVIDE THE ABILITY TO +C ALTER ERROR MESSAGE HANDLING, SAVE AND RESTORE THE INTERNAL +C COMMON, AND OBTAIN SPECIFIED DERIVATIVES OF THE SOLUTION Y(T). +C +C III. DESCRIPTIONS OF COMMON BLOCKS TO BE DECLARED IN OVERLAY +C OR SIMILAR ENVIRONMENTS, OR TO BE SAVED WHEN DOING AN INTERRUPT +C OF THE PROBLEM AND CONTINUED SOLUTION LATER. +C +C IV. DESCRIPTION OF TWO ROUTINES IN THE LSODE PACKAGE, EITHER OF +C WHICH THE USER MAY REPLACE WITH HIS OWN VERSION, IF DESIRED. +C THESE RELATE TO THE MEASUREMENT OF ERRORS. +C +C----------------------------------------------------------------------- +C PART I. CALL SEQUENCE. +C +C THE CALL SEQUENCE PARAMETERS USED FOR INPUT ONLY ARE +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF, +C AND THOSE USED FOR BOTH INPUT AND OUTPUT ARE +C Y, T, ISTATE. +C THE WORK ARRAYS RWORK AND IWORK ARE ALSO USED FOR CONDITIONAL AND +C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. (THE TERM OUTPUT HERE REFERS +C TO THE RETURN FROM SUBROUTINE LSODE TO THE USER-S CALLING 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 +C ODE SYSTEM. THE SYSTEM MUST BE PUT IN THE FIRST-ORDER +C FORM DY/DT = F(T,Y), WHERE F IS A VECTOR-VALUED FUNCTION +C OF THE SCALAR T AND THE VECTOR Y. SUBROUTINE F IS TO +C COMPUTE THE FUNCTION F. IT IS TO HAVE THE FORM +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DIMENSION Y(1), YDOT(1) +C WHERE NEQ, T, AND Y ARE INPUT, AND THE ARRAY YDOT = F(T,Y) +C IS OUTPUT. Y AND YDOT ARE ARRAYS OF LENGTH NEQ. +C (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY +C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) +C SUBROUTINE F SHOULD NOT ALTER Y(1),...,Y(NEQ). +C F MUST BE 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 LSODE, 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 INTDY 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 PROBLEM. +C IF NEQ IS DECREASED (WITH ISTATE = 3 ON INPUT), THE +C REMAINING COMPONENTS OF Y SHOULD BE LEFT UNDISTURBED, IF +C THESE ARE TO BE ACCESSED IN F AND/OR JAC. +C +C NORMALLY, NEQ IS A SCALAR, AND IT IS GENERALLY REFERRED TO +C AS A SCALAR IN THIS USER INTERFACE DESCRIPTION. HOWEVER, +C NEQ MAY BE AN ARRAY, WITH NEQ(1) SET TO THE SYSTEM SIZE. +C (THE LSODE PACKAGE ACCESSES ONLY NEQ(1).) IN EITHER CASE, +C THIS PARAMETER IS PASSED AS THE NEQ ARGUMENT IN ALL CALLS +C TO F AND JAC. HENCE, IF IT IS AN ARRAY, LOCATIONS +C NEQ(2),... MAY BE USED TO STORE OTHER INTEGER DATA AND PASS +C IT TO F AND/OR JAC. SUBROUTINES F AND/OR JAC MUST INCLUDE +C NEQ IN A DIMENSION STATEMENT 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 THE +C FIRST CALL (ISTATE = 1), AND ONLY FOR OUTPUT ON OTHER CALLS. +C ON THE FIRST CALL, Y MUST CONTAIN THE VECTOR OF INITIAL +C VALUES. ON OUTPUT, Y CONTAINS THE COMPUTED SOLUTION VECTOR, +C EVALUATED AT T. IF DESIRED, THE Y ARRAY MAY BE USED +C FOR OTHER PURPOSES BETWEEN CALLS TO THE SOLVER. +C +C THIS ARRAY IS PASSED AS THE Y ARGUMENT IN ALL CALLS TO +C F 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 LSODE PACKAGE ACCESSES ONLY +C Y(1),...,Y(NEQ).) +C +C T = THE INDEPENDENT VARIABLE. ON INPUT, T IS USED ONLY ON THE +C 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 TOUT). +C ON AN ERROR RETURN, T IS THE FARTHEST POINT REACHED. +C +C TOUT = THE NEXT VALUE OF T AT WHICH A COMPUTED SOLUTION IS DESIRED. +C USED ONLY FOR INPUT. +C +C WHEN STARTING THE PROBLEM (ISTATE = 1), TOUT MAY BE EQUAL +C TO T FOR ONE CALL, THEN SHOULD .NE. T FOR THE NEXT CALL. +C FOR THE INITIAL T, AN INPUT VALUE OF TOUT .NE. T IS USED +C IN ORDER TO DETERMINE THE DIRECTION OF THE INTEGRATION +C (I.E. THE ALGEBRAIC SIGN OF THE STEP SIZES) AND THE ROUGH +C SCALE OF THE PROBLEM. INTEGRATION IN EITHER DIRECTION +C (FORWARD OR BACKWARD IN T) IS PERMITTED. +C +C IF ITASK = 2 OR 5 (ONE-STEP MODES), TOUT IS IGNORED AFTER +C THE FIRST CALL (I.E. THE FIRST CALL WITH TOUT .NE. T). +C 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 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 ATOL. +C 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 +C THE 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 RMS-NORM OF ( E(I)/EWT(I) ) .LE. 1, +C WHERE EWT(I) = RTOL(I)*ABS(Y(I)) + ATOL(I), +C AND THE RMS-NORM (ROOT-MEAN-SQUARE NORM) HERE IS +C RMS-NORM(V) = SQRT(SUM V(I)**2 / NEQ). HERE EWT = (EWT(I)) +C IS A VECTOR OF WEIGHTS WHICH MUST ALWAYS BE POSITIVE, AND +C THE VALUES OF RTOL AND ATOL SHOULD ALL BE NON-NEGATIVE. +C THE FOLLOWING TABLE GIVES THE TYPES (SCALAR/ARRAY) OF +C RTOL AND ATOL, AND THE CORRESPONDING FORM OF EWT(I). +C +C ITOL RTOL ATOL EWT(I) +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. +C +C IF NONE OF THE ABOVE CHOICES (WITH ITOL, RTOL, AND ATOL +C FIXED THROUGHOUT THE PROBLEM) IS SUITABLE, MORE GENERAL +C ERROR CONTROLS CAN BE OBTAINED BY SUBSTITUTING +C USER-SUPPLIED ROUTINES FOR THE SETTING OF EWT AND/OR FOR +C THE NORM CALCULATION. SEE PART IV BELOW. +C +C IF GLOBAL ERRORS ARE TO BE ESTIMATED BY MAKING A REPEATED +C RUN ON THE SAME PROBLEM WITH SMALLER TOLERANCES, THEN ALL +C COMPONENTS OF RTOL AND ATOL (I.E. OF EWT) SHOULD BE SCALED +C DOWN UNIFORMLY. +C +C ITASK = AN INDEX SPECIFYING THE TASK TO BE PERFORMED. +C INPUT ONLY. ITASK HAS THE FOLLOWING VALUES AND MEANINGS. +C 1 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT +C T = TOUT (BY OVERSHOOTING AND INTERPOLATING). +C 2 MEANS TAKE ONE STEP ONLY AND RETURN. +C 3 MEANS STOP AT THE FIRST INTERNAL MESH POINT AT OR +C BEYOND T = TOUT AND RETURN. +C 4 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT +C T = TOUT BUT WITHOUT OVERSHOOTING T = TCRIT. +C TCRIT MUST BE INPUT AS RWORK(1). TCRIT MAY BE EQUAL TO +C OR BEYOND TOUT, BUT NOT BEHIND IT IN THE DIRECTION OF +C INTEGRATION. THIS OPTION IS USEFUL IF THE PROBLEM +C HAS A SINGULARITY AT OR BEYOND T = TCRIT. +C 5 MEANS TAKE ONE STEP, WITHOUT PASSING TCRIT, AND RETURN. +C TCRIT MUST BE INPUT AS RWORK(1). +C +C NOTE.. IF ITASK = 4 OR 5 AND THE SOLVER REACHES TCRIT +C (WITHIN ROUNDOFF), IT WILL RETURN T = TCRIT (EXACTLY) TO +C INDICATE THIS (UNLESS ITASK = 4 AND TOUT COMES BEFORE TCRIT, +C IN WHICH CASE ANSWERS AT T = TOUT ARE RETURNED FIRST). +C +C ISTATE = AN INDEX USED FOR INPUT AND OUTPUT TO SPECIFY THE +C THE STATE OF THE CALCULATION. +C +C ON INPUT, THE VALUES OF ISTATE ARE AS FOLLOWS. +C 1 MEANS THIS IS THE FIRST CALL FOR THE PROBLEM +C (INITIALIZATIONS WILL BE DONE). SEE NOTE BELOW. +C 2 MEANS THIS IS NOT THE FIRST CALL, AND THE CALCULATION +C IS TO CONTINUE NORMALLY, WITH NO CHANGE IN ANY INPUT +C PARAMETERS EXCEPT POSSIBLY TOUT AND ITASK. +C (IF ITOL, RTOL, AND/OR ATOL ARE CHANGED BETWEEN CALLS +C WITH ISTATE = 2, THE NEW VALUES WILL BE USED BUT NOT +C TESTED FOR LEGALITY.) +C 3 MEANS THIS IS NOT THE FIRST CALL, AND THE +C CALCULATION IS TO CONTINUE NORMALLY, BUT WITH +C A CHANGE IN INPUT PARAMETERS OTHER THAN +C TOUT AND ITASK. CHANGES ARE ALLOWED IN +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, ML, MU, +C AND ANY OF THE OPTIONAL INPUTS EXCEPT H0. +C (SEE IWORK DESCRIPTION FOR ML AND MU.) +C NOTE.. A PRELIMINARY CALL WITH TOUT = T IS NOT COUNTED +C AS A FIRST CALL HERE, AS NO INITIALIZATION OR CHECKING OF +C INPUT IS DONE. (SUCH A CALL IS SOMETIMES USEFUL FOR THE +C PURPOSE OF OUTPUTTING THE INITIAL CONDITIONS.) +C THUS THE FIRST CALL FOR WHICH TOUT .NE. T REQUIRES +C ISTATE = 1 ON INPUT. +C +C ON OUTPUT, ISTATE HAS THE FOLLOWING VALUES AND MEANINGS. +C 1 MEANS NOTHING WAS DONE, AS TOUT WAS EQUAL TO T WITH +C ISTATE = 1 ON INPUT. (HOWEVER, AN INTERNAL COUNTER WAS +C SET TO DETECT AND PREVENT REPEATED CALLS OF THIS TYPE.) +C 2 MEANS THE INTEGRATION WAS PERFORMED SUCCESSFULLY. +C -1 MEANS AN EXCESSIVE AMOUNT OF WORK (MORE THAN MXSTEP +C STEPS) WAS DONE ON THIS CALL, BEFORE COMPLETING THE +C REQUESTED TASK, BUT THE INTEGRATION WAS OTHERWISE +C SUCCESSFUL AS FAR AS T. (MXSTEP IS AN OPTIONAL INPUT +C AND IS NORMALLY 500.) TO CONTINUE, THE USER MAY +C SIMPLY RESET ISTATE TO A VALUE .GT. 1 AND CALL AGAIN +C (THE EXCESS WORK STEP COUNTER WILL BE RESET TO 0). +C IN ADDITION, THE USER MAY INCREASE MXSTEP TO AVOID +C THIS ERROR RETURN (SEE BELOW ON OPTIONAL INPUTS). +C -2 MEANS TOO MUCH ACCURACY WAS REQUESTED FOR THE PRECISION +C OF THE MACHINE BEING USED. THIS WAS DETECTED BEFORE +C COMPLETING THE REQUESTED TASK, BUT THE INTEGRATION +C WAS SUCCESSFUL AS FAR AS T. TO CONTINUE, THE TOLERANCE +C PARAMETERS MUST BE RESET, AND ISTATE MUST BE SET +C TO 3. THE OPTIONAL OUTPUT TOLSF MAY BE USED FOR THIS +C PURPOSE. (NOTE.. IF THIS CONDITION IS DETECTED BEFORE +C TAKING ANY STEPS, THEN AN ILLEGAL INPUT RETURN +C (ISTATE = -3) OCCURS INSTEAD.) +C -3 MEANS ILLEGAL INPUT WAS DETECTED, BEFORE TAKING ANY +C INTEGRATION STEPS. SEE WRITTEN MESSAGE FOR DETAILS. +C NOTE.. IF THE SOLVER DETECTS AN INFINITE LOOP OF CALLS +C TO THE SOLVER WITH ILLEGAL INPUT, IT WILL CAUSE +C THE RUN TO STOP. +C -4 MEANS THERE WERE REPEATED ERROR TEST FAILURES ON +C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED +C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. +C THE PROBLEM MAY HAVE A SINGULARITY, OR THE INPUT +C MAY BE INAPPROPRIATE. +C -5 MEANS THERE WERE REPEATED CONVERGENCE TEST FAILURES ON +C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED +C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. +C THIS MAY BE CAUSED BY AN INACCURATE JACOBIAN MATRIX, +C IF ONE IS BEING USED. +C -6 MEANS EWT(I) BECAME ZERO FOR SOME I DURING THE +C INTEGRATION. PURE RELATIVE ERROR CONTROL (ATOL(I)=0.0) +C WAS REQUESTED ON A VARIABLE WHICH HAS NOW VANISHED. +C THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. +C +C NOTE.. SINCE THE NORMAL OUTPUT VALUE OF ISTATE IS 2, +C IT DOES NOT NEED TO BE RESET FOR NORMAL CONTINUATION. +C ALSO, SINCE A NEGATIVE INPUT VALUE OF ISTATE WILL BE +C REGARDED AS ILLEGAL, A NEGATIVE OUTPUT VALUE REQUIRES THE +C USER TO CHANGE IT, AND POSSIBLY OTHER INPUTS, BEFORE +C CALLING THE SOLVER AGAIN. +C +C IOPT = AN INTEGER FLAG TO SPECIFY WHETHER OR NOT ANY OPTIONAL +C INPUTS ARE BEING USED ON THIS CALL. INPUT ONLY. +C THE OPTIONAL INPUTS ARE LISTED SEPARATELY BELOW. +C IOPT = 0 MEANS NO OPTIONAL INPUTS ARE BEING USED. +C DEFAULT VALUES WILL BE USED IN ALL CASES. +C IOPT = 1 MEANS ONE OR MORE OPTIONAL INPUTS ARE BEING USED. +C +C RWORK = A REAL WORKING ARRAY (DOUBLE PRECISION). +C THE LENGTH OF RWORK MUST BE AT LEAST +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM WHERE +C NYH = THE INITIAL VALUE OF NEQ, +C MAXORD = 12 (IF METH = 1) OR 5 (IF METH = 2) (UNLESS A +C SMALLER VALUE IS GIVEN AS AN OPTIONAL INPUT), +C LWM = 0 IF MITER = 0, +C LWM = NEQ**2 + 2 IF MITER IS 1 OR 2, +C LWM = NEQ + 2 IF MITER = 3, AND +C LWM = (2*ML+MU+1)*NEQ + 2 IF MITER IS 4 OR 5. +C (SEE THE MF DESCRIPTION FOR METH AND MITER.) +C 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. +C THE FIRST 20 WORDS OF RWORK ARE RESERVED FOR CONDITIONAL +C AND OPTIONAL INPUTS AND OPTIONAL OUTPUTS. +C +C THE FOLLOWING WORD IN RWORK IS A CONDITIONAL INPUT.. +C RWORK(1) = TCRIT = CRITICAL VALUE OF T WHICH THE SOLVER +C IS NOT TO OVERSHOOT. REQUIRED IF ITASK IS +C 4 OR 5, AND IGNORED OTHERWISE. (SEE ITASK.) +C +C LRW = THE LENGTH OF THE ARRAY RWORK, AS DECLARED BY THE USER. +C (THIS WILL BE CHECKED BY THE SOLVER.) +C +C IWORK = AN INTEGER WORK ARRAY. THE LENGTH OF IWORK MUST BE AT LEAST +C 20 IF MITER = 0 OR 3 (MF = 10, 13, 20, 23), OR +C 20 + NEQ OTHERWISE (MF = 11, 12, 14, 15, 21, 22, 24, 25). +C THE FIRST FEW WORDS OF IWORK ARE USED FOR CONDITIONAL AND +C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. +C +C THE FOLLOWING 2 WORDS IN IWORK ARE CONDITIONAL INPUTS.. +C IWORK(1) = ML THESE ARE THE LOWER AND UPPER +C IWORK(2) = MU HALF-BANDWIDTHS, RESPECTIVELY, OF THE +C BANDED JACOBIAN, EXCLUDING THE MAIN DIAGONAL. +C THE BAND IS DEFINED BY THE MATRIX LOCATIONS +C (I,J) WITH I-ML .LE. J .LE. I+MU. ML AND MU +C MUST SATISFY 0 .LE. ML,MU .LE. NEQ-1. +C THESE ARE REQUIRED IF MITER IS 4 OR 5, AND +C IGNORED OTHERWISE. ML AND MU MAY IN FACT BE +C THE BAND PARAMETERS FOR A MATRIX TO WHICH +C DF/DY IS ONLY APPROXIMATELY EQUAL. +C +C LIW = THE LENGTH OF THE ARRAY IWORK, AS DECLARED BY THE USER. +C (THIS WILL BE CHECKED BY THE SOLVER.) +C +C NOTE.. THE WORK ARRAYS MUST NOT BE ALTERED BETWEEN CALLS TO LSODE +C FOR THE SAME PROBLEM, EXCEPT POSSIBLY FOR THE CONDITIONAL AND +C OPTIONAL INPUTS, AND EXCEPT FOR THE LAST 3*NEQ WORDS OF RWORK. +C THE LATTER SPACE IS USED FOR INTERNAL SCRATCH SPACE, AND SO IS +C AVAILABLE FOR USE BY THE USER OUTSIDE LSODE BETWEEN CALLS, IF +C DESIRED (BUT NOT FOR USE BY F OR JAC). +C +C JAC = THE NAME OF THE USER-SUPPLIED ROUTINE (MITER = 1 OR 4) TO +C COMPUTE THE JACOBIAN MATRIX, DF/DY, AS A FUNCTION OF +C THE SCALAR T AND THE VECTOR Y. IT IS TO HAVE THE FORM +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DIMENSION Y(1), PD(NROWPD,1) +C WHERE NEQ, T, Y, ML, MU, AND NROWPD ARE INPUT AND THE ARRAY +C PD IS TO BE LOADED WITH PARTIAL DERIVATIVES (ELEMENTS OF +C THE JACOBIAN MATRIX) ON OUTPUT. PD MUST BE GIVEN A FIRST +C DIMENSION OF NROWPD. T AND Y HAVE THE SAME MEANING AS IN +C SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A +C DUMMY DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) +C IN THE FULL MATRIX CASE (MITER = 1), ML AND MU ARE +C IGNORED, AND THE JACOBIAN IS TO BE LOADED INTO PD IN +C COLUMNWISE MANNER, WITH DF(I)/DY(J) LOADED INTO PD(I,J). +C IN THE BAND MATRIX CASE (MITER = 4), THE ELEMENTS +C WITHIN THE BAND ARE TO BE LOADED INTO PD IN COLUMNWISE +C MANNER, WITH DIAGONAL LINES OF DF/DY LOADED INTO THE ROWS +C OF PD. THUS DF(I)/DY(J) IS TO BE LOADED INTO PD(I-J+MU+1,J). +C ML AND MU ARE THE HALF-BANDWIDTH PARAMETERS (SEE IWORK). +C THE LOCATIONS IN PD IN THE TWO TRIANGULAR AREAS WHICH +C CORRESPOND TO NONEXISTENT MATRIX ELEMENTS CAN BE IGNORED +C OR LOADED ARBITRARILY, AS THEY ARE OVERWRITTEN BY LSODE. +C JAC NEED NOT PROVIDE DF/DY EXACTLY. A CRUDE +C APPROXIMATION (POSSIBLY WITH A SMALLER BANDWIDTH) WILL DO. +C IN EITHER CASE, PD IS PRESET TO ZERO BY THE SOLVER, +C SO THAT ONLY THE NONZERO ELEMENTS NEED BE LOADED BY JAC. +C EACH CALL TO JAC IS PRECEDED BY A CALL TO F WITH THE SAME +C ARGUMENTS NEQ, T, AND Y. THUS TO GAIN SOME EFFICIENCY, +C INTERMEDIATE QUANTITIES SHARED BY BOTH CALCULATIONS MAY BE +C SAVED IN A USER COMMON BLOCK BY F AND NOT RECOMPUTED BY JAC, +C IF DESIRED. ALSO, JAC MAY ALTER THE Y ARRAY, IF DESIRED. +C JAC MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. +C SUBROUTINE JAC MAY ACCESS USER-DEFINED QUANTITIES IN +C NEQ(2),... AND/OR IN Y(NEQ(1)+1),... IF NEQ IS AN ARRAY +C (DIMENSIONED IN JAC) AND/OR Y HAS LENGTH EXCEEDING NEQ(1). +C SEE THE DESCRIPTIONS OF NEQ AND Y ABOVE. +C +C MF = THE METHOD FLAG. USED ONLY FOR INPUT. THE LEGAL VALUES OF +C MF ARE 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, AND 25. +C MF HAS DECIMAL DIGITS METH AND MITER.. MF = 10*METH + MITER. +C METH INDICATES THE BASIC LINEAR MULTISTEP METHOD.. +C METH = 1 MEANS THE IMPLICIT ADAMS METHOD. +C METH = 2 MEANS THE METHOD BASED ON BACKWARD +C DIFFERENTIATION FORMULAS (BDF-S). +C MITER INDICATES THE CORRECTOR ITERATION METHOD.. +C MITER = 0 MEANS FUNCTIONAL ITERATION (NO JACOBIAN MATRIX +C IS INVOLVED). +C MITER = 1 MEANS CHORD ITERATION WITH A USER-SUPPLIED +C FULL (NEQ BY NEQ) JACOBIAN. +C MITER = 2 MEANS CHORD ITERATION WITH AN INTERNALLY +C GENERATED (DIFFERENCE QUOTIENT) FULL JACOBIAN +C (USING NEQ EXTRA CALLS TO F PER DF/DY VALUE). +C MITER = 3 MEANS CHORD ITERATION WITH AN INTERNALLY +C GENERATED DIAGONAL JACOBIAN APPROXIMATION. +C (USING 1 EXTRA CALL TO F PER DF/DY EVALUATION). +C MITER = 4 MEANS CHORD ITERATION WITH A USER-SUPPLIED +C BANDED JACOBIAN. +C MITER = 5 MEANS CHORD ITERATION WITH AN INTERNALLY +C GENERATED BANDED JACOBIAN (USING ML+MU+1 EXTRA +C CALLS TO F PER DF/DY EVALUATION). +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 II.) 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 +C CASE ALL OF THESE INPUTS ARE EXAMINED. A VALUE OF ZERO FOR ANY +C OF 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, AND +C THEN SET THOSE OF INTEREST TO NONZERO VALUES. +C +C NAME LOCATION MEANING AND DEFAULT VALUE +C +C H0 RWORK(5) THE STEP SIZE TO BE ATTEMPTED ON THE FIRST STEP. +C THE DEFAULT VALUE IS DETERMINED BY THE SOLVER. +C +C HMAX RWORK(6) THE MAXIMUM ABSOLUTE STEP SIZE ALLOWED. +C THE DEFAULT VALUE IS INFINITE. +C +C HMIN RWORK(7) THE MINIMUM ABSOLUTE STEP SIZE ALLOWED. +C THE DEFAULT VALUE IS 0. (THIS LOWER BOUND IS NOT +C ENFORCED ON THE FINAL STEP BEFORE REACHING TCRIT +C WHEN ITASK = 4 OR 5.) +C +C MAXORD IWORK(5) THE MAXIMUM ORDER TO BE ALLOWED. THE DEFAULT +C VALUE IS 12 IF METH = 1, AND 5 IF METH = 2. +C IF MAXORD EXCEEDS THE DEFAULT VALUE, IT WILL +C BE REDUCED TO THE DEFAULT VALUE. +C IF MAXORD IS CHANGED DURING THE PROBLEM, IT MAY +C CAUSE THE CURRENT ORDER TO BE REDUCED. +C +C MXSTEP IWORK(6) MAXIMUM NUMBER OF (INTERNALLY DEFINED) STEPS +C ALLOWED DURING ONE CALL TO THE SOLVER. +C THE DEFAULT VALUE IS 500. +C +C MXHNIL IWORK(7) MAXIMUM NUMBER OF MESSAGES PRINTED (PER PROBLEM) +C WARNING THAT T + H = T ON A STEP (H = STEP SIZE). +C THIS MUST BE POSITIVE TO RESULT IN A NON-DEFAULT +C VALUE. THE DEFAULT VALUE IS 10. +C----------------------------------------------------------------------- +C OPTIONAL OUTPUTS. +C +C AS OPTIONAL ADDITIONAL OUTPUT FROM LSODE, THE VARIABLES LISTED +C BELOW ARE QUANTITIES RELATED TO THE PERFORMANCE OF LSODE +C WHICH ARE AVAILABLE TO THE USER. THESE ARE COMMUNICATED BY WAY OF +C THE WORK ARRAYS, BUT ALSO HAVE INTERNAL MNEMONIC NAMES AS SHOWN. +C EXCEPT WHERE STATED OTHERWISE, ALL OF THESE OUTPUTS ARE DEFINED +C ON ANY SUCCESSFUL RETURN FROM LSODE, AND ON ANY RETURN WITH +C ISTATE = -1, -2, -4, -5, OR -6. ON AN ILLEGAL INPUT RETURN +C (ISTATE = -3), THEY WILL BE UNCHANGED FROM THEIR EXISTING VALUES +C (IF ANY), EXCEPT POSSIBLY FOR TOLSF, LENRW, AND LENIW. +C ON ANY ERROR RETURN, OUTPUTS RELEVANT TO THE ERROR WILL BE DEFINED, +C AS NOTED BELOW. +C +C NAME LOCATION MEANING +C +C HU RWORK(11) THE STEP SIZE IN T LAST USED (SUCCESSFULLY). +C +C HCUR RWORK(12) THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP. +C +C TCUR RWORK(13) THE CURRENT VALUE OF THE INDEPENDENT VARIABLE +C WHICH THE SOLVER HAS ACTUALLY REACHED, I.E. THE +C CURRENT INTERNAL MESH POINT IN T. ON OUTPUT, TCUR +C WILL ALWAYS BE AT LEAST AS FAR AS THE ARGUMENT +C T, BUT MAY BE FARTHER (IF INTERPOLATION WAS DONE). +C +C TOLSF RWORK(14) A TOLERANCE SCALE FACTOR, GREATER THAN 1.0, +C COMPUTED WHEN A REQUEST FOR TOO MUCH ACCURACY WAS +C DETECTED (ISTATE = -3 IF DETECTED AT THE START OF +C THE PROBLEM, ISTATE = -2 OTHERWISE). IF ITOL IS +C LEFT UNALTERED BUT RTOL AND ATOL ARE UNIFORMLY +C SCALED UP BY A FACTOR OF TOLSF FOR THE NEXT CALL, +C THEN THE SOLVER IS DEEMED LIKELY TO SUCCEED. +C (THE USER MAY ALSO IGNORE TOLSF AND ALTER THE +C TOLERANCE PARAMETERS IN ANY OTHER WAY APPROPRIATE.) +C +C NST IWORK(11) THE NUMBER OF STEPS TAKEN FOR THE PROBLEM SO FAR. +C +C NFE IWORK(12) THE NUMBER OF F EVALUATIONS FOR THE PROBLEM SO FAR. +C +C NJE IWORK(13) THE NUMBER OF JACOBIAN EVALUATIONS (AND OF MATRIX +C LU DECOMPOSITIONS) FOR THE PROBLEM SO FAR. +C +C NQU IWORK(14) THE METHOD ORDER LAST USED (SUCCESSFULLY). +C +C NQCUR IWORK(15) THE ORDER TO BE ATTEMPTED ON THE NEXT STEP. +C +C IMXER IWORK(16) THE 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 +C LENRW IWORK(17) THE LENGTH OF RWORK ACTUALLY REQUIRED. +C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL +C INPUT RETURN FOR INSUFFICIENT STORAGE. +C +C LENIW IWORK(18) THE LENGTH OF IWORK ACTUALLY REQUIRED. +C THIS IS 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 +C MAY ALSO BE OF INTEREST TO THE USER AS OPTIONAL OUTPUTS. +C FOR EACH ARRAY, THE TABLE BELOW GIVES ITS INTERNAL NAME, +C ITS BASE ADDRESS 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 +C OF NEQ. FOR J = 0,1,...,NQCUR, COLUMN J+1 +C OF YH CONTAINS HCUR**J/FACTORIAL(J) TIMES +C THE J-TH DERIVATIVE OF THE INTERPOLATING +C POLYNOMIAL CURRENTLY REPRESENTING THE SOLUTION, +C EVALUATED AT T = TCUR. +C +C ACOR LENRW-NEQ+1 ARRAY OF SIZE NEQ USED FOR THE ACCUMULATED +C CORRECTIONS ON EACH STEP, SCALED ON OUTPUT +C TO REPRESENT THE ESTIMATED LOCAL ERROR IN Y +C ON THE LAST STEP. THIS IS THE VECTOR E IN +C THE DESCRIPTION OF THE ERROR CONTROL. IT IS +C DEFINED ONLY ON A SUCCESSFUL RETURN FROM LSODE. +C +C----------------------------------------------------------------------- +C PART II. OTHER ROUTINES CALLABLE. +C +C THE FOLLOWING ARE OPTIONAL CALLS WHICH THE USER MAY MAKE TO +C GAIN ADDITIONAL CAPABILITIES IN CONJUNCTION WITH LSODE. +C (THE ROUTINES XSETUN AND XSETF ARE DESIGNED TO CONFORM TO THE +C SLATEC ERROR HANDLING PACKAGE.) +C +C FORM OF CALL FUNCTION +C CALL XSETUN(LUN) SET THE LOGICAL UNIT NUMBER, LUN, FOR +C OUTPUT OF MESSAGES FROM LSODE, IF +C THE DEFAULT IS NOT DESIRED. +C THE DEFAULT VALUE OF LUN IS 6. +C +C CALL XSETF(MFLAG) SET A FLAG TO CONTROL THE PRINTING OF +C MESSAGES BY LSODE. +C MFLAG = 0 MEANS DO NOT PRINT. (DANGER.. +C THIS RISKS LOSING VALUABLE INFORMATION.) +C MFLAG = 1 MEANS PRINT (THE DEFAULT). +C +C EITHER OF THE ABOVE CALLS MAY BE MADE AT +C ANY TIME AND WILL TAKE EFFECT IMMEDIATELY. +C +C CALL SRCOM(RSAV,ISAV,JOB) SAVES AND RESTORES THE CONTENTS OF +C THE INTERNAL COMMON BLOCKS USED BY +C LSODE (SEE PART III BELOW). +C RSAV MUST BE A REAL ARRAY OF LENGTH 218 +C OR MORE, AND ISAV MUST BE AN INTEGER +C ARRAY OF LENGTH 41 OR MORE. +C JOB=1 MEANS SAVE COMMON INTO RSAV/ISAV. +C JOB=2 MEANS RESTORE COMMON FROM RSAV/ISAV. +C SRCOM IS USEFUL IF ONE IS +C INTERRUPTING A RUN AND RESTARTING +C LATER, OR ALTERNATING BETWEEN TWO OR +C MORE PROBLEMS SOLVED WITH LSODE. +C +C CALL INTDY(,,,,,) PROVIDE DERIVATIVES OF Y, OF VARIOUS +C (SEE BELOW) ORDERS, AT A SPECIFIED POINT T, IF +C DESIRED. IT MAY BE CALLED ONLY AFTER +C A SUCCESSFUL RETURN FROM LSODE. +C +C THE DETAILED INSTRUCTIONS FOR USING INTDY ARE AS FOLLOWS. +C THE FORM OF THE CALL IS.. +C +C CALL INTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C THE INPUT PARAMETERS ARE.. +C +C T = VALUE OF INDEPENDENT VARIABLE WHERE ANSWERS ARE DESIRED +C (NORMALLY THE SAME AS THE T LAST RETURNED BY LSODE). +C FOR VALID RESULTS, T MUST LIE BETWEEN TCUR - HU AND TCUR. +C (SEE OPTIONAL OUTPUTS FOR TCUR AND HU.) +C K = INTEGER ORDER OF THE DERIVATIVE DESIRED. K MUST SATISFY +C 0 .LE. K .LE. NQCUR, WHERE NQCUR IS THE CURRENT ORDER +C (SEE OPTIONAL OUTPUTS). THE CAPABILITY CORRESPONDING +C TO K = 0, I.E. COMPUTING Y(T), IS ALREADY PROVIDED +C BY LSODE DIRECTLY. SINCE NQCUR .GE. 1, THE FIRST +C DERIVATIVE DY/DT IS ALWAYS AVAILABLE WITH INTDY. +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 = A REAL ARRAY OF LENGTH NEQ CONTAINING THE COMPUTED VALUE +C OF THE K-TH 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 PART III. COMMON BLOCKS. +C +C IF LSODE IS TO BE USED IN AN OVERLAY SITUATION, THE USER +C MUST DECLARE, IN THE PRIMARY OVERLAY, THE VARIABLES IN.. +C (1) THE CALL SEQUENCE TO LSODE, +C (2) THE INTERNAL COMMON BLOCK +C /LS0001/ OF LENGTH 257 (218 DOUBLE PRECISION WORDS +C FOLLOWED BY 39 INTEGER WORDS), +C +C IF LSODE 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 TWO COMMON BLOCKS IN HIS MAIN PROGRAM TO INSURE +C THAT THEIR CONTENTS ARE PRESERVED. +C +C IF THE SOLUTION OF A GIVEN PROBLEM BY LSODE IS TO BE INTERRUPTED +C AND THEN LATER CONTINUED, SUCH AS WHEN RESTARTING AN INTERRUPTED RUN +C OR ALTERNATING BETWEEN TWO OR MORE PROBLEMS, THE USER SHOULD SAVE, +C FOLLOWING THE RETURN FROM THE LAST LSODE CALL PRIOR TO THE +C INTERRUPTION, THE CONTENTS OF THE CALL SEQUENCE VARIABLES AND THE +C INTERNAL COMMON BLOCKS, AND LATER RESTORE THESE VALUES BEFORE THE +C NEXT LSODE CALL FOR THAT PROBLEM. TO SAVE AND RESTORE THE COMMON +C BLOCKS, USE SUBROUTINE SRCOM (SEE PART II ABOVE). +C +C----------------------------------------------------------------------- +C PART IV. OPTIONALLY REPLACEABLE SOLVER ROUTINES. +C +C BELOW ARE DESCRIPTIONS OF TWO ROUTINES IN THE LSODE PACKAGE WHICH +C RELATE TO THE MEASUREMENT OF ERRORS. EITHER ROUTINE CAN BE +C REPLACED BY A USER-SUPPLIED VERSION, IF DESIRED. HOWEVER, SINCE SUCH +C A REPLACEMENT MAY HAVE A MAJOR IMPACT ON PERFORMANCE, IT SHOULD BE +C DONE ONLY WHEN ABSOLUTELY NECESSARY, AND ONLY WITH GREAT CAUTION. +C (NOTE.. THE MEANS BY WHICH THE PACKAGE VERSION OF A ROUTINE IS +C SUPERSEDED BY THE USER-S VERSION MAY BE SYSTEM-DEPENDENT.) +C +C (A) EWSET. +C THE FOLLOWING SUBROUTINE IS CALLED JUST BEFORE EACH INTERNAL +C INTEGRATION STEP, AND SETS THE ARRAY OF ERROR WEIGHTS, EWT, AS +C DESCRIBED UNDER ITOL/RTOL/ATOL ABOVE.. +C SUBROUTINE EWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C WHERE NEQ, ITOL, RTOL, AND ATOL ARE AS IN THE LSODE CALL SEQUENCE, +C YCUR CONTAINS THE CURRENT DEPENDENT VARIABLE VECTOR, AND +C EWT IS THE ARRAY OF WEIGHTS SET BY EWSET. +C +C IF THE USER SUPPLIES THIS SUBROUTINE, IT MUST RETURN IN EWT(I) +C (I = 1,...,NEQ) A POSITIVE QUANTITY SUITABLE FOR COMPARING ERRORS +C IN Y(I) TO. THE EWT ARRAY RETURNED BY EWSET IS PASSED TO THE +C VNORM ROUTINE (SEE BELOW), AND ALSO USED BY LSODE IN THE COMPUTATION +C OF THE OPTIONAL OUTPUT IMXER, THE DIAGONAL JACOBIAN APPROXIMATION, +C AND THE INCREMENTS FOR DIFFERENCE QUOTIENT JACOBIANS. +C +C IN THE USER-SUPPLIED VERSION OF EWSET, IT MAY BE DESIRABLE TO USE +C THE CURRENT VALUES OF DERIVATIVES OF Y. DERIVATIVES UP TO ORDER NQ +C ARE AVAILABLE FROM THE HISTORY ARRAY YH, DESCRIBED ABOVE UNDER +C OPTIONAL OUTPUTS. IN EWSET, YH IS IDENTICAL TO THE YCUR ARRAY, +C EXTENDED TO NQ + 1 COLUMNS WITH A COLUMN LENGTH OF NYH AND SCALE +C 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 THE QUANTITIES NQ, NYH, H, AND NST CAN BE OBTAINED BY INCLUDING +C IN EWSET THE STATEMENTS.. +C DOUBLE PRECISION H, RLS +C COMMON /LS0001/ RLS(218),ILS(39) +C NQ = ILS(35) +C NYH = ILS(14) +C NST = ILS(36) +C H = RLS(212) +C THUS, FOR EXAMPLE, THE CURRENT VALUE OF DY/DT CAN BE OBTAINED AS +C YCUR(NYH+I)/H (I=1,...,NEQ) (AND THE DIVISION BY H IS +C UNNECESSARY WHEN NST = 0). +C +C (B) VNORM. +C THE FOLLOWING IS A REAL FUNCTION ROUTINE WHICH COMPUTES THE WEIGHTED +C ROOT-MEAN-SQUARE NORM OF A VECTOR V.. +C D = VNORM (N, V, W) +C 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 ). +C VNORM IS CALLED WITH N = NEQ AND WITH W(I) = 1.0/EWT(I), WHERE +C EWT IS AS SET BY SUBROUTINE EWSET. +C +C IF THE USER SUPPLIES THIS FUNCTION, IT SHOULD RETURN A NON-NEGATIVE +C VALUE OF VNORM SUITABLE FOR USE IN THE ERROR CONTROL IN LSODE. +C NONE OF THE ARGUMENTS SHOULD BE ALTERED BY VNORM. +C FOR EXAMPLE, A USER-SUPPLIED VNORM ROUTINE MIGHT.. +C -SUBSTITUTE A MAX-NORM OF (V(I)*W(I)) FOR THE RMS-NORM, OR +C -IGNORE SOME COMPONENTS OF V IN THE NORM, WITH THE EFFECT OF +C SUPPRESSING THE ERROR CONTROL ON THOSE COMPONENTS OF Y. +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- +C OTHER ROUTINES IN THE LSODE PACKAGE. +C +C IN ADDITION TO SUBROUTINE LSODE, THE LSODE PACKAGE INCLUDES THE +C FOLLOWING SUBROUTINES AND FUNCTION ROUTINES.. +C INTDY COMPUTES AN INTERPOLATED VALUE OF THE Y VECTOR AT T = TOUT. +C STODE IS THE CORE INTEGRATOR, WHICH DOES ONE STEP OF THE +C INTEGRATION AND THE ASSOCIATED ERROR CONTROL. +C CFODE SETS ALL METHOD COEFFICIENTS AND TEST CONSTANTS. +C PREPJ COMPUTES AND PREPROCESSES THE JACOBIAN MATRIX J = DF/DY +C AND THE NEWTON ITERATION MATRIX P = I - H*L0*J. +C SOLSY MANAGES SOLUTION OF LINEAR SYSTEM IN CHORD ITERATION. +C EWSET SETS THE ERROR WEIGHT VECTOR EWT BEFORE EACH STEP. +C VNORM COMPUTES THE WEIGHTED R.M.S. NORM OF A VECTOR. +C SRCOM IS A USER-CALLABLE ROUTINE TO SAVE AND RESTORE +C THE CONTENTS OF THE INTERNAL COMMON BLOCKS. +C DGETRF AND DGETRS ARE ROUTINES FROM LAPACK FOR SOLVING FULL +C SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS. +C DGBTRF AND DGBTRS ARE ROUTINES FROM LAPACK FOR SOLVING BANDED +C LINEAR SYSTEMS. +C DAXPY, DSCAL, IDAMAX, AND DDOT ARE BASIC LINEAR ALGEBRA MODULES +C (BLAS) USED BY THE ABOVE LINPACK ROUTINES. +C D1MACH COMPUTES THE UNIT ROUNDOFF IN A MACHINE-INDEPENDENT MANNER. +C XERRWD, XSETUN, AND XSETF HANDLE THE PRINTING OF ALL ERROR +C MESSAGES AND WARNINGS. XERRWD IS MACHINE-DEPENDENT. +C NOTE.. VNORM, IDAMAX, DDOT, AND D1MACH ARE FUNCTION ROUTINES. +C ALL THE OTHERS ARE SUBROUTINES. +C +C THE INTRINSIC AND EXTERNAL ROUTINES USED BY LSODE ARE.. +C DABS, DMAX1, DMIN1, DBLE, MAX0, MIN0, MOD, DSIGN, DSQRT, AND WRITE. +C +C A BLOCK DATA SUBPROGRAM IS ALSO INCLUDED WITH THE PACKAGE, +C FOR LOADING SOME OF THE VARIABLES IN INTERNAL COMMON. +C +C----------------------------------------------------------------------- +C THE FOLLOWING CARD IS FOR OPTIMIZED COMPILATION ON LLNL COMPILERS. +CLLL. OPTIMIZE +C----------------------------------------------------------------------- + EXTERNAL PREPJ, SOLSY + INTEGER ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM, + 1 MXSTEP, MXHNIL, NHNIL, NTREP, NSLAST, NYH, IOWNS + INTEGER ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER, + 1 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 + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0, + 2 D1MACH, VNORM + DIMENSION MORD(2) + LOGICAL IHIT +C----------------------------------------------------------------------- +C THE FOLLOWING INTERNAL COMMON BLOCK CONTAINS +C (A) VARIABLES WHICH ARE LOCAL TO ANY SUBROUTINE BUT WHOSE VALUES MUST +C BE PRESERVED BETWEEN CALLS TO THE ROUTINE (OWN VARIABLES), AND +C (B) VARIABLES WHICH ARE COMMUNICATED BETWEEN SUBROUTINES. +C THE STRUCTURE OF THE BLOCK IS AS FOLLOWS.. ALL REAL VARIABLES ARE +C LISTED FIRST, FOLLOWED BY ALL INTEGERS. WITHIN EACH TYPE, THE +C VARIABLES ARE GROUPED WITH THOSE LOCAL TO SUBROUTINE LSODE FIRST, +C THEN THOSE LOCAL TO SUBROUTINE STODE, AND FINALLY THOSE USED +C FOR COMMUNICATION. THE BLOCK IS DECLARED IN SUBROUTINES +C LSODE, INTDY, STODE, PREPJ, AND SOLSY. GROUPS OF VARIABLES ARE +C REPLACED BY DUMMY ARRAYS IN THE COMMON DECLARATIONS IN ROUTINES +C WHERE THOSE VARIABLES ARE NOT USED. +C----------------------------------------------------------------------- + COMMON /LS0001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM, + 3 MXSTEP, MXHNIL, NHNIL, NTREP, NSLAST, NYH, IOWNS(6), + 4 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + 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 HAS +C NOT YET BEEN DONE, AN ERROR RETURN OCCURS. +C IF ISTATE = 1 AND TOUT = T, JUMP TO BLOCK G AND RETURN IMMEDIATELY. +C----------------------------------------------------------------------- + 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) GO TO 430 + 20 NTREP = 0 +C----------------------------------------------------------------------- +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. +C +C FIRST CHECK LEGALITY OF THE NON-OPTIONAL INPUTS NEQ, ITOL, IOPT, +C MF, ML, AND MU. +C----------------------------------------------------------------------- + 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 CONTINUE +C 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 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN0(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. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C SET WORK ARRAY POINTERS AND CHECK LENGTHS LRW AND LIW. +C POINTERS TO SEGMENTS OF RWORK AND IWORK ARE NAMED BY PREFIXING L TO +C 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 618 +C 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. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C IF ISTATE = 3, SET FLAG TO SIGNAL PARAMETER CHANGES TO STODE. -------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C 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) = DSQRT(UROUND) + IF (N .EQ. NYH) GO TO 200 +C 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) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +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. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + IF (MITER .GT. 0) RWORK(LWM) = DSQRT(UROUND) + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C INITIAL CALL TO F. (LF0 POINTS TO YH(*,2).) ------------------------- + LF0 = LYH + NYH + IERR = 0 + CALL F (NEQ, T, Y, RWORK(LF0), IERR) + IF (IERR .LT. 0) THEN + ISTATE = -13 + RETURN + ENDIF + NFE = 1 +C 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 = 1.0D0 + CALL EWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C THE CODING BELOW COMPUTES THE STEP SIZE, H0, TO BE ATTEMPTED ON THE +C 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, ADJUSTED +C SO AS TO BE BETWEEN 100*UROUND AND 1.0E-3. +C THEN THE COMPUTED VALUE H0 IS GIVEN BY.. +C NEQ +C H0**2 = TOL / ( W0**-2 + (1/NEQ) * SUM ( F(I)/YWT(I) )**2 ) +C 1 +C 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. 0.0D0) GO TO 180 + TDIST = DABS(TOUT - T) + W0 = DMAX1(DABS(T),DABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = DMAX1(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = DABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = DMAX1(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = DMAX1(TOL,100.0D0*UROUND) + TOL = DMIN1(TOL,0.001D0) + SUM = VNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/DSQRT(SUM) + H0 = DMIN1(H0,TDIST) + H0 = DSIGN(H0,TOUT-T) +C ADJUST H0 IF NECESSARY TO MEET HMAX BOUND. --------------------------- + 180 RH = DABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C 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 270 +C----------------------------------------------------------------------- +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. 0.0D0) GO TO 250 + CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL INTDY (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. 0.0D0) GO TO 624 + 245 HMX = DABS(TN) + DABS(H) + IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C BLOCK E. +C THE NEXT BLOCK IS NORMALLY EXECUTED FOR ALL CALLS AND CONTAINS +C THE CALL TO THE ONE-STEP CORE INTEGRATOR STODE. +C +C THIS IS A LOOPING POINT FOR THE INTEGRATION STEPS. +C +C FIRST CHECK FOR TOO MANY STEPS BEING TAKEN, UPDATE EWT (IF NOT AT +C START OF PROBLEM), CHECK FOR TOO MUCH ACCURACY BEING REQUESTED, AND +C CHECK FOR H BELOW THE ROUNDOFF LEVEL IN T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL EWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*VNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + 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('LSODE-- WARNING..INTERNAL T (=R1) AND H (=R2) ARE', + 1 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + CALL XERRWD( + 1 ' SUCH THAT IN THE MACHINE, T + H = T ON THE NEXT STEP ', + 1 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + 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('LSODE-- ABOVE WARNING HAS BEEN ISSUED I1 TIMES. ', + 1 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + CALL XERRWD(' IT WILL NOT BE ISSUED AGAIN FOR THIS PROBLEM', + 1 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL STODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,PREPJ,SOLSY) +C----------------------------------------------------------------------- + IERR = 0 + CALL STODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), + 2 F, JAC, PREPJ, SOLSY, IERR) + IF (IERR .LT. 0) THEN + ISTATE = -13 + RETURN + ENDIF + KGO = 1 - KFLAG + GO TO (300, 530, 540), KGO +C----------------------------------------------------------------------- +C BLOCK F. +C THE FOLLOWING BLOCK HANDLES THE CASE OF A SUCCESSFUL RETURN FROM THE +C CORE INTEGRATOR (KFLAG = 0). TEST FOR STOP CONDITIONS. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. IF TOUT HAS BEEN REACHED, INTERPOLATE. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. JUMP TO EXIT IF TOUT WAS REACHED. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. SEE IF TOUT OR TCRIT WAS REACHED. ADJUST H IF NECESSARY. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = DABS(TN) + DABS(H) + IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. SEE IF TCRIT WAS REACHED AND JUMP TO EXIT. --------------- + 350 HMX = DABS(TN) + DABS(H) + IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C BLOCK G. +C THE FOLLOWING BLOCK HANDLES ALL SUCCESSFUL RETURNS FROM LSODE. +C IF ITASK .NE. 1, Y IS LOADED FROM YH AND T IS SET ACCORDINGLY. +C ISTATE IS SET TO 2, THE ILLEGAL INPUT COUNTER IS ZEROED, AND THE +C OPTIONAL OUTPUTS ARE LOADED INTO THE WORK ARRAYS BEFORE RETURNING. +C IF ISTATE = 1 AND TOUT = T, THERE IS A RETURN WITH NO ACTION TAKEN, +C EXCEPT THAT IF THIS HAS HAPPENED REPEATEDLY, THE RUN IS TERMINATED. +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 + ILLIN = 0 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C + 430 NTREP = NTREP + 1 + IF (NTREP .LT. 5) RETURN + CALL XERRWD( + 1 'LSODE-- REPEATED CALLS WITH ISTATE = 1 AND TOUT = T (=R1) ', + 1 60, 301, 0, 0, 0, 0, 1, T, 0.0D0) + GO TO 800 +C----------------------------------------------------------------------- +C BLOCK H. +C THE FOLLOWING BLOCK HANDLES ALL UNSUCCESSFUL RETURNS OTHER THAN +C 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, T IS SET TO TN, AND THE ILLEGAL INPUT +C COUNTER ILLIN IS SET TO 0. THE OPTIONAL OUTPUTS ARE LOADED INTO +C THE WORK ARRAYS BEFORE RETURNING. +C----------------------------------------------------------------------- +C THE MAXIMUM NUMBER OF STEPS WAS TAKEN BEFORE REACHING TOUT. ---------- + 500 CALL XERRWD('LSODE-- AT CURRENT T (=R1), MXSTEP (=I1) STEPS ', + 1 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + CALL XERRWD(' TAKEN ON THIS CALL BEFORE REACHING TOUT ', + 1 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(I) .LE. 0.0 FOR SOME I (NOT AT START OF PROBLEM). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + CALL XERRWD('LSODE-- AT T (=R1), EWT(I1) HAS BECOME R2 .LE. 0.', + 1 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C TOO MUCH ACCURACY REQUESTED FOR MACHINE PRECISION. ------------------- + 520 CALL XERRWD('LSODE-- AT T (=R1), TOO MUCH ACCURACY REQUESTED ', + 1 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + 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 580 +C KFLAG = -1. ERROR TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ----- + 530 CALL XERRWD('LSODE-- AT T(=R1) AND STEP SIZE H(=R2), THE ERROR', + 1 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + CALL XERRWD(' TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN', + 1 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. CONVERGENCE FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ---- + 540 CALL XERRWD('LSODE-- AT T (=R1) AND STEP SIZE H (=R2), THE ', + 1 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + CALL XERRWD(' CORRECTOR CONVERGENCE FAILED REPEATEDLY ', + 1 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + CALL XERRWD(' OR WITH ABS(H) = HMIN ', + 1 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 +C COMPUTE IMXER IF RELEVANT. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = DABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C SET Y VECTOR, T, ILLIN, AND OPTIONAL OUTPUTS. ------------------------ + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + ILLIN = 0 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C BLOCK I. +C THE FOLLOWING BLOCK HANDLES ALL ERROR RETURNS DUE TO ILLEGAL INPUT +C (ISTATE = -3), AS DETECTED BEFORE CALLING THE CORE INTEGRATOR. +C FIRST THE ERROR MESSAGE ROUTINE IS CALLED. THEN IF THERE HAVE BEEN +C 5 CONSECUTIVE SUCH RETURNS JUST BEFORE THIS CALL TO THE SOLVER, +C THE RUN IS HALTED. +C----------------------------------------------------------------------- + 601 CALL XERRWD('LSODE-- ISTATE (=I1) ILLEGAL ', + 1 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 602 CALL XERRWD('LSODE-- ITASK (=I1) ILLEGAL ', + 1 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 CALL XERRWD('LSODE-- ISTATE .GT. 1 BUT LSODE NOT INITIALIZED ', + 1 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 CALL XERRWD('LSODE-- NEQ (=I1) .LT. 1 ', + 1 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 CALL XERRWD('LSODE-- ISTATE = 3 AND NEQ INCREASED (I1 TO I2) ', + 1 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 CALL XERRWD('LSODE-- ITOL (=I1) ILLEGAL ', + 1 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 CALL XERRWD('LSODE-- IOPT (=I1) ILLEGAL ', + 1 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 CALL XERRWD('LSODE-- MF (=I1) ILLEGAL ', + 1 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 CALL XERRWD('LSODE-- ML (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', + 1 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 CALL XERRWD('LSODE-- MU (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', + 1 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 CALL XERRWD('LSODE-- MAXORD (=I1) .LT. 0 ', + 1 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 CALL XERRWD('LSODE-- MXSTEP (=I1) .LT. 0 ', + 1 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 CALL XERRWD('LSODE-- MXHNIL (=I1) .LT. 0 ', + 1 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 CALL XERRWD('LSODE-- 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, 0.0D0) + GO TO 700 + 615 CALL XERRWD('LSODE-- HMAX (=R1) .LT. 0.0 ', + 1 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 CALL XERRWD('LSODE-- HMIN (=R1) .LT. 0.0 ', + 1 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 CALL XERRWD( + 1 'LSODE-- RWORK LENGTH NEEDED, LENRW (=I1), EXCEEDS LRW (=I2)', + 1 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 CALL XERRWD( + 1 'LSODE-- IWORK LENGTH NEEDED, LENIW (=I1), EXCEEDS LIW (=I2)', + 1 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 CALL XERRWD('LSODE-- RTOL(I1) IS R1 .LT. 0.0 ', + 1 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 CALL XERRWD('LSODE-- ATOL(I1) IS R1 .LT. 0.0 ', + 1 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + CALL XERRWD('LSODE-- EWT(I1) IS R1 .LE. 0.0 ', + 1 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 CALL XERRWD( + 1 'LSODE-- 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 'LSODE-- 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 'LSODE-- 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 'LSODE-- 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('LSODE-- AT START OF PROBLEM, TOO MUCH ACCURACY ', + 1 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + CALL XERRWD( + 1 ' REQUESTED FOR PRECISION OF MACHINE.. SEE TOLSF (=R1) ', + 1 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 CALL XERRWD('LSODE-- TROUBLE FROM INTDY. ITASK = I1, TOUT = R1', + 1 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 IF (ILLIN .EQ. 5) GO TO 710 + ILLIN = ILLIN + 1 + ISTATE = -3 + RETURN + 710 CALL XERRWD('LSODE-- REPEATED OCCURRENCES OF ILLEGAL INPUT ', + 1 50, 302, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) +C + 800 CALL XERRWD('LSODE-- RUN ABORTED.. APPARENT INFINITE LOOP ', + 1 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- END OF SUBROUTINE LSODE ----------------------- + END
--- a/libcruft/odepack/lsode.f Fri Oct 31 15:11:45 2003 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1522 +0,0 @@ - SUBROUTINE LSODE (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 - DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK - DIMENSION NEQ(1), Y(1), RTOL(1), ATOL(1), RWORK(LRW), IWORK(LIW) -C----------------------------------------------------------------------- -C THIS IS THE MARCH 30, 1987 VERSION OF -C LSODE.. LIVERMORE SOLVER FOR ORDINARY DIFFERENTIAL EQUATIONS. -C THIS VERSION IS IN DOUBLE PRECISION. -C -C LSODE SOLVES THE INITIAL VALUE PROBLEM FOR STIFF OR NONSTIFF -C 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(NEQ)) (I = 1,...,NEQ). -C LSODE IS A PACKAGE BASED ON THE GEAR AND GEARB PACKAGES, AND ON THE -C OCTOBER 23, 1978 VERSION OF THE TENTATIVE ODEPACK USER INTERFACE -C STANDARD, WITH MINOR MODIFICATIONS. -C----------------------------------------------------------------------- -C REFERENCE.. -C ALAN C. HINDMARSH, ODEPACK, A SYSTEMATIZED COLLECTION OF ODE -C SOLVERS, IN SCIENTIFIC COMPUTING, R. S. STEPLEMAN ET AL. (EDS.), -C NORTH-HOLLAND, AMSTERDAM, 1983, PP. 55-64. -C----------------------------------------------------------------------- -C AUTHOR AND CONTACT.. ALAN C. HINDMARSH, -C COMPUTING AND MATHEMATICS RESEARCH DIV., L-316 -C LAWRENCE LIVERMORE NATIONAL LABORATORY -C LIVERMORE, CA 94550. -C----------------------------------------------------------------------- -C SUMMARY OF USAGE. -C -C COMMUNICATION BETWEEN THE USER AND THE LSODE PACKAGE, FOR NORMAL -C SITUATIONS, IS SUMMARIZED HERE. THIS SUMMARY DESCRIBES ONLY A SUBSET -C OF THE FULL SET OF OPTIONS AVAILABLE. SEE THE FULL DESCRIPTION FOR -C DETAILS, INCLUDING OPTIONAL COMMUNICATION, NONSTANDARD OPTIONS, -C AND INSTRUCTIONS FOR SPECIAL SITUATIONS. SEE ALSO THE EXAMPLE -C PROBLEM (WITH PROGRAM AND OUTPUT) FOLLOWING THIS SUMMARY. -C -C A. FIRST PROVIDE A SUBROUTINE OF THE FORM.. -C SUBROUTINE F (NEQ, T, Y, YDOT, IERR) -C DIMENSION Y(NEQ), YDOT(NEQ) -C WHICH SUPPLIES THE VECTOR FUNCTION F BY LOADING YDOT(I) WITH F(I). -C -C B. NEXT DETERMINE (OR GUESS) WHETHER OR NOT THE PROBLEM IS STIFF. -C STIFFNESS OCCURS WHEN THE JACOBIAN MATRIX DF/DY HAS AN EIGENVALUE -C WHOSE REAL PART IS NEGATIVE AND LARGE IN MAGNITUDE, COMPARED TO THE -C RECIPROCAL OF THE T SPAN OF INTEREST. IF THE PROBLEM IS NONSTIFF, -C USE A METHOD FLAG MF = 10. IF IT IS STIFF, THERE ARE FOUR STANDARD -C CHOICES FOR MF, AND LSODE REQUIRES THE JACOBIAN MATRIX IN SOME FORM. -C THIS MATRIX IS REGARDED EITHER AS FULL (MF = 21 OR 22), -C OR BANDED (MF = 24 OR 25). IN THE BANDED CASE, LSODE REQUIRES TWO -C HALF-BANDWIDTH PARAMETERS ML AND MU. THESE ARE, RESPECTIVELY, THE -C WIDTHS OF THE LOWER AND UPPER PARTS OF THE BAND, EXCLUDING THE MAIN -C DIAGONAL. THUS THE BAND CONSISTS OF THE LOCATIONS (I,J) WITH -C I-ML .LE. J .LE. I+MU, AND THE FULL BANDWIDTH IS ML+MU+1. -C -C C. IF THE PROBLEM IS STIFF, YOU ARE ENCOURAGED TO SUPPLY THE JACOBIAN -C DIRECTLY (MF = 21 OR 24), BUT IF THIS IS NOT FEASIBLE, LSODE WILL -C COMPUTE IT INTERNALLY BY DIFFERENCE QUOTIENTS (MF = 22 OR 25). -C IF YOU ARE SUPPLYING THE JACOBIAN, PROVIDE A SUBROUTINE OF THE FORM.. -C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) -C DIMENSION Y(NEQ), PD(NROWPD,NEQ) -C WHICH SUPPLIES 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). (IGNORE THE -C ML AND MU ARGUMENTS IN THIS CASE.) -C FOR A BANDED JACOBIAN (MF = 24), LOAD PD(I-J+MU+1,J) WITH -C DF(I)/DY(J), I.E. LOAD THE DIAGONAL LINES OF DF/DY INTO THE ROWS OF -C PD FROM THE TOP DOWN. -C IN EITHER CASE, ONLY NONZERO ELEMENTS NEED BE LOADED. -C -C D. WRITE A MAIN PROGRAM WHICH CALLS SUBROUTINE LSODE ONCE FOR -C EACH POINT AT WHICH ANSWERS ARE DESIRED. THIS SHOULD ALSO PROVIDE -C FOR POSSIBLE USE OF LOGICAL UNIT 6 FOR OUTPUT OF ERROR MESSAGES -C BY LSODE. ON THE FIRST CALL TO LSODE, SUPPLY ARGUMENTS AS FOLLOWS.. -C F = NAME OF SUBROUTINE FOR RIGHT-HAND SIDE VECTOR F. -C THIS NAME MUST BE DECLARED EXTERNAL IN CALLING PROGRAM. -C NEQ = NUMBER OF FIRST ORDER ODE-S. -C Y = ARRAY OF INITIAL VALUES, OF LENGTH NEQ. -C T = THE INITIAL VALUE OF THE INDEPENDENT VARIABLE. -C TOUT = FIRST POINT WHERE OUTPUT IS DESIRED (.NE. T). -C ITOL = 1 OR 2 ACCORDING AS ATOL (BELOW) IS A SCALAR OR ARRAY. -C RTOL = RELATIVE TOLERANCE PARAMETER (SCALAR). -C ATOL = ABSOLUTE TOLERANCE PARAMETER (SCALAR OR ARRAY). -C THE ESTIMATED LOCAL ERROR IN Y(I) WILL BE CONTROLLED SO AS -C TO BE ROUGHLY LESS (IN MAGNITUDE) THAN -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 THUS THE LOCAL ERROR TEST PASSES IF, IN EACH COMPONENT, -C EITHER THE ABSOLUTE ERROR IS LESS THAN ATOL (OR ATOL(I)), -C OR THE RELATIVE ERROR IS LESS THAN RTOL. -C USE RTOL = 0.0 FOR PURE ABSOLUTE ERROR CONTROL, AND -C USE ATOL = 0.0 (OR ATOL(I) = 0.0) FOR PURE RELATIVE ERROR -C CONTROL. CAUTION.. ACTUAL (GLOBAL) ERRORS MAY EXCEED THESE -C LOCAL TOLERANCES, SO CHOOSE THEM CONSERVATIVELY. -C ITASK = 1 FOR NORMAL COMPUTATION OF OUTPUT VALUES OF Y AT T = TOUT. -C ISTATE = INTEGER FLAG (INPUT AND OUTPUT). SET ISTATE = 1. -C IOPT = 0 TO INDICATE NO OPTIONAL INPUTS USED. -C RWORK = 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 LRW = DECLARED LENGTH OF RWORK (IN USER-S DIMENSION). -C IWORK = INTEGER WORK ARRAY OF LENGTH AT LEAST.. -C 20 FOR MF = 10, -C 20 + NEQ FOR MF = 21, 22, 24, OR 25. -C IF MF = 24 OR 25, INPUT IN IWORK(1),IWORK(2) THE LOWER -C AND UPPER HALF-BANDWIDTHS ML,MU. -C LIW = DECLARED LENGTH OF IWORK (IN USER-S DIMENSION). -C JAC = NAME OF SUBROUTINE FOR JACOBIAN MATRIX (MF = 21 OR 24). -C IF USED, THIS NAME MUST BE DECLARED EXTERNAL IN CALLING -C PROGRAM. IF NOT USED, PASS A DUMMY NAME. -C MF = METHOD FLAG. STANDARD VALUES ARE.. -C 10 FOR NONSTIFF (ADAMS) METHOD, NO JACOBIAN USED. -C 21 FOR STIFF (BDF) METHOD, USER-SUPPLIED FULL JACOBIAN. -C 22 FOR STIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. -C 24 FOR STIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. -C 25 FOR STIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. -C NOTE THAT THE MAIN PROGRAM MUST DECLARE ARRAYS Y, RWORK, IWORK, -C AND POSSIBLY ATOL. -C -C E. THE OUTPUT FROM THE FIRST CALL (OR ANY CALL) IS.. -C Y = ARRAY OF COMPUTED VALUES OF Y(T) VECTOR. -C T = CORRESPONDING VALUE OF INDEPENDENT VARIABLE (NORMALLY TOUT). -C ISTATE = 2 IF LSODE WAS SUCCESSFUL, NEGATIVE OTHERWISE. -C -1 MEANS EXCESS WORK DONE ON THIS CALL (PERHAPS WRONG MF). -C -2 MEANS EXCESS ACCURACY REQUESTED (TOLERANCES TOO SMALL). -C -3 MEANS ILLEGAL INPUT DETECTED (SEE PRINTED MESSAGE). -C -4 MEANS REPEATED ERROR TEST FAILURES (CHECK ALL INPUTS). -C -5 MEANS REPEATED CONVERGENCE FAILURES (PERHAPS BAD JACOBIAN -C SUPPLIED OR WRONG CHOICE OF MF OR TOLERANCES). -C -6 MEANS ERROR WEIGHT BECAME ZERO DURING PROBLEM. (SOLUTION -C COMPONENT I VANISHED, AND ATOL OR ATOL(I) = 0.) -C -13 MEANS EXIT REQUESTED IN USER-SUPPLIED FUNCTION. -C -C F. TO CONTINUE THE INTEGRATION AFTER A SUCCESSFUL RETURN, SIMPLY -C RESET TOUT AND CALL LSODE AGAIN. NO OTHER PARAMETERS NEED BE RESET. -C -C----------------------------------------------------------------------- -C EXAMPLE PROBLEM. -C -C THE FOLLOWING IS A SIMPLE EXAMPLE PROBLEM, WITH THE CODING -C NEEDED FOR ITS SOLUTION BY LSODE. THE PROBLEM IS FROM CHEMICAL -C KINETICS, AND CONSISTS OF THE FOLLOWING THREE RATE EQUATIONS.. -C DY1/DT = -.04*Y1 + 1.E4*Y2*Y3 -C DY2/DT = .04*Y1 - 1.E4*Y2*Y3 - 3.E7*Y2**2 -C DY3/DT = 3.E7*Y2**2 -C ON THE INTERVAL FROM T = 0.0 TO T = 4.E10, WITH INITIAL CONDITIONS -C Y1 = 1.0, Y2 = Y3 = 0. THE PROBLEM IS STIFF. -C -C THE FOLLOWING CODING SOLVES THIS PROBLEM WITH LSODE, USING MF = 21 -C AND PRINTING RESULTS AT T = .4, 4., ..., 4.E10. IT USES -C ITOL = 2 AND ATOL MUCH SMALLER FOR Y2 THAN Y1 OR Y3 BECAUSE -C Y2 HAS MUCH SMALLER VALUES. -C AT THE END OF THE RUN, STATISTICAL QUANTITIES OF INTEREST ARE -C PRINTED (SEE OPTIONAL OUTPUTS IN THE FULL DESCRIPTION BELOW). -C -C EXTERNAL FEX, JEX -C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y -C DIMENSION Y(3), ATOL(3), RWORK(58), IWORK(23) -C NEQ = 3 -C Y(1) = 1.D0 -C Y(2) = 0.D0 -C Y(3) = 0.D0 -C T = 0.D0 -C TOUT = .4D0 -C ITOL = 2 -C RTOL = 1.D-4 -C ATOL(1) = 1.D-6 -C ATOL(2) = 1.D-10 -C ATOL(3) = 1.D-6 -C ITASK = 1 -C ISTATE = 1 -C IOPT = 0 -C LRW = 58 -C LIW = 23 -C MF = 21 -C DO 40 IOUT = 1,12 -C CALL LSODE(FEX,NEQ,Y,T,TOUT,ITOL,RTOL,ATOL,ITASK,ISTATE, -C 1 IOPT,RWORK,LRW,IWORK,LIW,JEX,MF) -C WRITE(6,20)T,Y(1),Y(2),Y(3) -C 20 FORMAT(7H AT T =,E12.4,6H Y =,3E14.6) -C IF (ISTATE .LT. 0) GO TO 80 -C 40 TOUT = TOUT*10.D0 -C WRITE(6,60)IWORK(11),IWORK(12),IWORK(13) -C 60 FORMAT(/12H NO. STEPS =,I4,11H NO. F-S =,I4,11H NO. J-S =,I4) -C STOP -C 80 WRITE(6,90)ISTATE -C 90 FORMAT(///22H ERROR HALT.. ISTATE =,I3) -C STOP -C END -C -C SUBROUTINE FEX (NEQ, T, Y, YDOT) -C DOUBLE PRECISION T, Y, YDOT -C DIMENSION Y(3), YDOT(3) -C YDOT(1) = -.04D0*Y(1) + 1.D4*Y(2)*Y(3) -C YDOT(3) = 3.D7*Y(2)*Y(2) -C YDOT(2) = -YDOT(1) - YDOT(3) -C RETURN -C END -C -C SUBROUTINE JEX (NEQ, T, Y, ML, MU, PD, NRPD) -C DOUBLE PRECISION PD, T, Y -C DIMENSION Y(3), PD(NRPD,3) -C PD(1,1) = -.04D0 -C PD(1,2) = 1.D4*Y(3) -C PD(1,3) = 1.D4*Y(2) -C PD(2,1) = .04D0 -C PD(2,3) = -PD(1,3) -C PD(3,2) = 6.D7*Y(2) -C PD(2,2) = -PD(1,2) - PD(3,2) -C RETURN -C END -C -C THE OUTPUT OF THIS PROGRAM (ON A CDC-7600 IN SINGLE PRECISION) -C IS AS FOLLOWS.. -C -C AT T = 4.0000E-01 Y = 9.851726E-01 3.386406E-05 1.479357E-02 -C AT T = 4.0000E+00 Y = 9.055142E-01 2.240418E-05 9.446344E-02 -C AT T = 4.0000E+01 Y = 7.158050E-01 9.184616E-06 2.841858E-01 -C AT T = 4.0000E+02 Y = 4.504846E-01 3.222434E-06 5.495122E-01 -C AT T = 4.0000E+03 Y = 1.831701E-01 8.940379E-07 8.168290E-01 -C AT T = 4.0000E+04 Y = 3.897016E-02 1.621193E-07 9.610297E-01 -C AT T = 4.0000E+05 Y = 4.935213E-03 1.983756E-08 9.950648E-01 -C AT T = 4.0000E+06 Y = 5.159269E-04 2.064759E-09 9.994841E-01 -C AT T = 4.0000E+07 Y = 5.306413E-05 2.122677E-10 9.999469E-01 -C AT T = 4.0000E+08 Y = 5.494529E-06 2.197824E-11 9.999945E-01 -C AT T = 4.0000E+09 Y = 5.129458E-07 2.051784E-12 9.999995E-01 -C AT T = 4.0000E+10 Y = -7.170586E-08 -2.868234E-13 1.000000E+00 -C -C NO. STEPS = 330 NO. F-S = 405 NO. J-S = 69 -C----------------------------------------------------------------------- -C FULL DESCRIPTION OF USER INTERFACE TO LSODE. -C -C THE USER INTERFACE TO LSODE CONSISTS OF THE FOLLOWING PARTS. -C -C I. THE CALL SEQUENCE TO SUBROUTINE LSODE, WHICH IS A DRIVER -C ROUTINE FOR THE SOLVER. THIS INCLUDES DESCRIPTIONS OF BOTH -C THE CALL SEQUENCE ARGUMENTS AND OF USER-SUPPLIED ROUTINES. -C FOLLOWING THESE DESCRIPTIONS IS A DESCRIPTION OF -C OPTIONAL INPUTS AVAILABLE THROUGH THE CALL SEQUENCE, AND THEN -C A DESCRIPTION OF OPTIONAL OUTPUTS (IN THE WORK ARRAYS). -C -C II. DESCRIPTIONS OF OTHER ROUTINES IN THE LSODE PACKAGE THAT MAY BE -C (OPTIONALLY) CALLED BY THE USER. THESE PROVIDE THE ABILITY TO -C ALTER ERROR MESSAGE HANDLING, SAVE AND RESTORE THE INTERNAL -C COMMON, AND OBTAIN SPECIFIED DERIVATIVES OF THE SOLUTION Y(T). -C -C III. DESCRIPTIONS OF COMMON BLOCKS TO BE DECLARED IN OVERLAY -C OR SIMILAR ENVIRONMENTS, OR TO BE SAVED WHEN DOING AN INTERRUPT -C OF THE PROBLEM AND CONTINUED SOLUTION LATER. -C -C IV. DESCRIPTION OF TWO ROUTINES IN THE LSODE PACKAGE, EITHER OF -C WHICH THE USER MAY REPLACE WITH HIS OWN VERSION, IF DESIRED. -C THESE RELATE TO THE MEASUREMENT OF ERRORS. -C -C----------------------------------------------------------------------- -C PART I. CALL SEQUENCE. -C -C THE CALL SEQUENCE PARAMETERS USED FOR INPUT ONLY ARE -C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF, -C AND THOSE USED FOR BOTH INPUT AND OUTPUT ARE -C Y, T, ISTATE. -C THE WORK ARRAYS RWORK AND IWORK ARE ALSO USED FOR CONDITIONAL AND -C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. (THE TERM OUTPUT HERE REFERS -C TO THE RETURN FROM SUBROUTINE LSODE TO THE USER-S CALLING 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 -C ODE SYSTEM. THE SYSTEM MUST BE PUT IN THE FIRST-ORDER -C FORM DY/DT = F(T,Y), WHERE F IS A VECTOR-VALUED FUNCTION -C OF THE SCALAR T AND THE VECTOR Y. SUBROUTINE F IS TO -C COMPUTE THE FUNCTION F. IT IS TO HAVE THE FORM -C SUBROUTINE F (NEQ, T, Y, YDOT) -C DIMENSION Y(1), YDOT(1) -C WHERE NEQ, T, AND Y ARE INPUT, AND THE ARRAY YDOT = F(T,Y) -C IS OUTPUT. Y AND YDOT ARE ARRAYS OF LENGTH NEQ. -C (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY -C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) -C SUBROUTINE F SHOULD NOT ALTER Y(1),...,Y(NEQ). -C F MUST BE 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 LSODE, 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 INTDY 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 PROBLEM. -C IF NEQ IS DECREASED (WITH ISTATE = 3 ON INPUT), THE -C REMAINING COMPONENTS OF Y SHOULD BE LEFT UNDISTURBED, IF -C THESE ARE TO BE ACCESSED IN F AND/OR JAC. -C -C NORMALLY, NEQ IS A SCALAR, AND IT IS GENERALLY REFERRED TO -C AS A SCALAR IN THIS USER INTERFACE DESCRIPTION. HOWEVER, -C NEQ MAY BE AN ARRAY, WITH NEQ(1) SET TO THE SYSTEM SIZE. -C (THE LSODE PACKAGE ACCESSES ONLY NEQ(1).) IN EITHER CASE, -C THIS PARAMETER IS PASSED AS THE NEQ ARGUMENT IN ALL CALLS -C TO F AND JAC. HENCE, IF IT IS AN ARRAY, LOCATIONS -C NEQ(2),... MAY BE USED TO STORE OTHER INTEGER DATA AND PASS -C IT TO F AND/OR JAC. SUBROUTINES F AND/OR JAC MUST INCLUDE -C NEQ IN A DIMENSION STATEMENT 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 THE -C FIRST CALL (ISTATE = 1), AND ONLY FOR OUTPUT ON OTHER CALLS. -C ON THE FIRST CALL, Y MUST CONTAIN THE VECTOR OF INITIAL -C VALUES. ON OUTPUT, Y CONTAINS THE COMPUTED SOLUTION VECTOR, -C EVALUATED AT T. IF DESIRED, THE Y ARRAY MAY BE USED -C FOR OTHER PURPOSES BETWEEN CALLS TO THE SOLVER. -C -C THIS ARRAY IS PASSED AS THE Y ARGUMENT IN ALL CALLS TO -C F 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 LSODE PACKAGE ACCESSES ONLY -C Y(1),...,Y(NEQ).) -C -C T = THE INDEPENDENT VARIABLE. ON INPUT, T IS USED ONLY ON THE -C 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 TOUT). -C ON AN ERROR RETURN, T IS THE FARTHEST POINT REACHED. -C -C TOUT = THE NEXT VALUE OF T AT WHICH A COMPUTED SOLUTION IS DESIRED. -C USED ONLY FOR INPUT. -C -C WHEN STARTING THE PROBLEM (ISTATE = 1), TOUT MAY BE EQUAL -C TO T FOR ONE CALL, THEN SHOULD .NE. T FOR THE NEXT CALL. -C FOR THE INITIAL T, AN INPUT VALUE OF TOUT .NE. T IS USED -C IN ORDER TO DETERMINE THE DIRECTION OF THE INTEGRATION -C (I.E. THE ALGEBRAIC SIGN OF THE STEP SIZES) AND THE ROUGH -C SCALE OF THE PROBLEM. INTEGRATION IN EITHER DIRECTION -C (FORWARD OR BACKWARD IN T) IS PERMITTED. -C -C IF ITASK = 2 OR 5 (ONE-STEP MODES), TOUT IS IGNORED AFTER -C THE FIRST CALL (I.E. THE FIRST CALL WITH TOUT .NE. T). -C 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 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 ATOL. -C 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 -C THE 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 RMS-NORM OF ( E(I)/EWT(I) ) .LE. 1, -C WHERE EWT(I) = RTOL(I)*ABS(Y(I)) + ATOL(I), -C AND THE RMS-NORM (ROOT-MEAN-SQUARE NORM) HERE IS -C RMS-NORM(V) = SQRT(SUM V(I)**2 / NEQ). HERE EWT = (EWT(I)) -C IS A VECTOR OF WEIGHTS WHICH MUST ALWAYS BE POSITIVE, AND -C THE VALUES OF RTOL AND ATOL SHOULD ALL BE NON-NEGATIVE. -C THE FOLLOWING TABLE GIVES THE TYPES (SCALAR/ARRAY) OF -C RTOL AND ATOL, AND THE CORRESPONDING FORM OF EWT(I). -C -C ITOL RTOL ATOL EWT(I) -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. -C -C IF NONE OF THE ABOVE CHOICES (WITH ITOL, RTOL, AND ATOL -C FIXED THROUGHOUT THE PROBLEM) IS SUITABLE, MORE GENERAL -C ERROR CONTROLS CAN BE OBTAINED BY SUBSTITUTING -C USER-SUPPLIED ROUTINES FOR THE SETTING OF EWT AND/OR FOR -C THE NORM CALCULATION. SEE PART IV BELOW. -C -C IF GLOBAL ERRORS ARE TO BE ESTIMATED BY MAKING A REPEATED -C RUN ON THE SAME PROBLEM WITH SMALLER TOLERANCES, THEN ALL -C COMPONENTS OF RTOL AND ATOL (I.E. OF EWT) SHOULD BE SCALED -C DOWN UNIFORMLY. -C -C ITASK = AN INDEX SPECIFYING THE TASK TO BE PERFORMED. -C INPUT ONLY. ITASK HAS THE FOLLOWING VALUES AND MEANINGS. -C 1 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT -C T = TOUT (BY OVERSHOOTING AND INTERPOLATING). -C 2 MEANS TAKE ONE STEP ONLY AND RETURN. -C 3 MEANS STOP AT THE FIRST INTERNAL MESH POINT AT OR -C BEYOND T = TOUT AND RETURN. -C 4 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT -C T = TOUT BUT WITHOUT OVERSHOOTING T = TCRIT. -C TCRIT MUST BE INPUT AS RWORK(1). TCRIT MAY BE EQUAL TO -C OR BEYOND TOUT, BUT NOT BEHIND IT IN THE DIRECTION OF -C INTEGRATION. THIS OPTION IS USEFUL IF THE PROBLEM -C HAS A SINGULARITY AT OR BEYOND T = TCRIT. -C 5 MEANS TAKE ONE STEP, WITHOUT PASSING TCRIT, AND RETURN. -C TCRIT MUST BE INPUT AS RWORK(1). -C -C NOTE.. IF ITASK = 4 OR 5 AND THE SOLVER REACHES TCRIT -C (WITHIN ROUNDOFF), IT WILL RETURN T = TCRIT (EXACTLY) TO -C INDICATE THIS (UNLESS ITASK = 4 AND TOUT COMES BEFORE TCRIT, -C IN WHICH CASE ANSWERS AT T = TOUT ARE RETURNED FIRST). -C -C ISTATE = AN INDEX USED FOR INPUT AND OUTPUT TO SPECIFY THE -C THE STATE OF THE CALCULATION. -C -C ON INPUT, THE VALUES OF ISTATE ARE AS FOLLOWS. -C 1 MEANS THIS IS THE FIRST CALL FOR THE PROBLEM -C (INITIALIZATIONS WILL BE DONE). SEE NOTE BELOW. -C 2 MEANS THIS IS NOT THE FIRST CALL, AND THE CALCULATION -C IS TO CONTINUE NORMALLY, WITH NO CHANGE IN ANY INPUT -C PARAMETERS EXCEPT POSSIBLY TOUT AND ITASK. -C (IF ITOL, RTOL, AND/OR ATOL ARE CHANGED BETWEEN CALLS -C WITH ISTATE = 2, THE NEW VALUES WILL BE USED BUT NOT -C TESTED FOR LEGALITY.) -C 3 MEANS THIS IS NOT THE FIRST CALL, AND THE -C CALCULATION IS TO CONTINUE NORMALLY, BUT WITH -C A CHANGE IN INPUT PARAMETERS OTHER THAN -C TOUT AND ITASK. CHANGES ARE ALLOWED IN -C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, ML, MU, -C AND ANY OF THE OPTIONAL INPUTS EXCEPT H0. -C (SEE IWORK DESCRIPTION FOR ML AND MU.) -C NOTE.. A PRELIMINARY CALL WITH TOUT = T IS NOT COUNTED -C AS A FIRST CALL HERE, AS NO INITIALIZATION OR CHECKING OF -C INPUT IS DONE. (SUCH A CALL IS SOMETIMES USEFUL FOR THE -C PURPOSE OF OUTPUTTING THE INITIAL CONDITIONS.) -C THUS THE FIRST CALL FOR WHICH TOUT .NE. T REQUIRES -C ISTATE = 1 ON INPUT. -C -C ON OUTPUT, ISTATE HAS THE FOLLOWING VALUES AND MEANINGS. -C 1 MEANS NOTHING WAS DONE, AS TOUT WAS EQUAL TO T WITH -C ISTATE = 1 ON INPUT. (HOWEVER, AN INTERNAL COUNTER WAS -C SET TO DETECT AND PREVENT REPEATED CALLS OF THIS TYPE.) -C 2 MEANS THE INTEGRATION WAS PERFORMED SUCCESSFULLY. -C -1 MEANS AN EXCESSIVE AMOUNT OF WORK (MORE THAN MXSTEP -C STEPS) WAS DONE ON THIS CALL, BEFORE COMPLETING THE -C REQUESTED TASK, BUT THE INTEGRATION WAS OTHERWISE -C SUCCESSFUL AS FAR AS T. (MXSTEP IS AN OPTIONAL INPUT -C AND IS NORMALLY 500.) TO CONTINUE, THE USER MAY -C SIMPLY RESET ISTATE TO A VALUE .GT. 1 AND CALL AGAIN -C (THE EXCESS WORK STEP COUNTER WILL BE RESET TO 0). -C IN ADDITION, THE USER MAY INCREASE MXSTEP TO AVOID -C THIS ERROR RETURN (SEE BELOW ON OPTIONAL INPUTS). -C -2 MEANS TOO MUCH ACCURACY WAS REQUESTED FOR THE PRECISION -C OF THE MACHINE BEING USED. THIS WAS DETECTED BEFORE -C COMPLETING THE REQUESTED TASK, BUT THE INTEGRATION -C WAS SUCCESSFUL AS FAR AS T. TO CONTINUE, THE TOLERANCE -C PARAMETERS MUST BE RESET, AND ISTATE MUST BE SET -C TO 3. THE OPTIONAL OUTPUT TOLSF MAY BE USED FOR THIS -C PURPOSE. (NOTE.. IF THIS CONDITION IS DETECTED BEFORE -C TAKING ANY STEPS, THEN AN ILLEGAL INPUT RETURN -C (ISTATE = -3) OCCURS INSTEAD.) -C -3 MEANS ILLEGAL INPUT WAS DETECTED, BEFORE TAKING ANY -C INTEGRATION STEPS. SEE WRITTEN MESSAGE FOR DETAILS. -C NOTE.. IF THE SOLVER DETECTS AN INFINITE LOOP OF CALLS -C TO THE SOLVER WITH ILLEGAL INPUT, IT WILL CAUSE -C THE RUN TO STOP. -C -4 MEANS THERE WERE REPEATED ERROR TEST FAILURES ON -C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED -C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. -C THE PROBLEM MAY HAVE A SINGULARITY, OR THE INPUT -C MAY BE INAPPROPRIATE. -C -5 MEANS THERE WERE REPEATED CONVERGENCE TEST FAILURES ON -C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED -C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. -C THIS MAY BE CAUSED BY AN INACCURATE JACOBIAN MATRIX, -C IF ONE IS BEING USED. -C -6 MEANS EWT(I) BECAME ZERO FOR SOME I DURING THE -C INTEGRATION. PURE RELATIVE ERROR CONTROL (ATOL(I)=0.0) -C WAS REQUESTED ON A VARIABLE WHICH HAS NOW VANISHED. -C THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. -C -C NOTE.. SINCE THE NORMAL OUTPUT VALUE OF ISTATE IS 2, -C IT DOES NOT NEED TO BE RESET FOR NORMAL CONTINUATION. -C ALSO, SINCE A NEGATIVE INPUT VALUE OF ISTATE WILL BE -C REGARDED AS ILLEGAL, A NEGATIVE OUTPUT VALUE REQUIRES THE -C USER TO CHANGE IT, AND POSSIBLY OTHER INPUTS, BEFORE -C CALLING THE SOLVER AGAIN. -C -C IOPT = AN INTEGER FLAG TO SPECIFY WHETHER OR NOT ANY OPTIONAL -C INPUTS ARE BEING USED ON THIS CALL. INPUT ONLY. -C THE OPTIONAL INPUTS ARE LISTED SEPARATELY BELOW. -C IOPT = 0 MEANS NO OPTIONAL INPUTS ARE BEING USED. -C DEFAULT VALUES WILL BE USED IN ALL CASES. -C IOPT = 1 MEANS ONE OR MORE OPTIONAL INPUTS ARE BEING USED. -C -C RWORK = A REAL WORKING ARRAY (DOUBLE PRECISION). -C THE LENGTH OF RWORK MUST BE AT LEAST -C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM WHERE -C NYH = THE INITIAL VALUE OF NEQ, -C MAXORD = 12 (IF METH = 1) OR 5 (IF METH = 2) (UNLESS A -C SMALLER VALUE IS GIVEN AS AN OPTIONAL INPUT), -C LWM = 0 IF MITER = 0, -C LWM = NEQ**2 + 2 IF MITER IS 1 OR 2, -C LWM = NEQ + 2 IF MITER = 3, AND -C LWM = (2*ML+MU+1)*NEQ + 2 IF MITER IS 4 OR 5. -C (SEE THE MF DESCRIPTION FOR METH AND MITER.) -C 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. -C THE FIRST 20 WORDS OF RWORK ARE RESERVED FOR CONDITIONAL -C AND OPTIONAL INPUTS AND OPTIONAL OUTPUTS. -C -C THE FOLLOWING WORD IN RWORK IS A CONDITIONAL INPUT.. -C RWORK(1) = TCRIT = CRITICAL VALUE OF T WHICH THE SOLVER -C IS NOT TO OVERSHOOT. REQUIRED IF ITASK IS -C 4 OR 5, AND IGNORED OTHERWISE. (SEE ITASK.) -C -C LRW = THE LENGTH OF THE ARRAY RWORK, AS DECLARED BY THE USER. -C (THIS WILL BE CHECKED BY THE SOLVER.) -C -C IWORK = AN INTEGER WORK ARRAY. THE LENGTH OF IWORK MUST BE AT LEAST -C 20 IF MITER = 0 OR 3 (MF = 10, 13, 20, 23), OR -C 20 + NEQ OTHERWISE (MF = 11, 12, 14, 15, 21, 22, 24, 25). -C THE FIRST FEW WORDS OF IWORK ARE USED FOR CONDITIONAL AND -C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. -C -C THE FOLLOWING 2 WORDS IN IWORK ARE CONDITIONAL INPUTS.. -C IWORK(1) = ML THESE ARE THE LOWER AND UPPER -C IWORK(2) = MU HALF-BANDWIDTHS, RESPECTIVELY, OF THE -C BANDED JACOBIAN, EXCLUDING THE MAIN DIAGONAL. -C THE BAND IS DEFINED BY THE MATRIX LOCATIONS -C (I,J) WITH I-ML .LE. J .LE. I+MU. ML AND MU -C MUST SATISFY 0 .LE. ML,MU .LE. NEQ-1. -C THESE ARE REQUIRED IF MITER IS 4 OR 5, AND -C IGNORED OTHERWISE. ML AND MU MAY IN FACT BE -C THE BAND PARAMETERS FOR A MATRIX TO WHICH -C DF/DY IS ONLY APPROXIMATELY EQUAL. -C -C LIW = THE LENGTH OF THE ARRAY IWORK, AS DECLARED BY THE USER. -C (THIS WILL BE CHECKED BY THE SOLVER.) -C -C NOTE.. THE WORK ARRAYS MUST NOT BE ALTERED BETWEEN CALLS TO LSODE -C FOR THE SAME PROBLEM, EXCEPT POSSIBLY FOR THE CONDITIONAL AND -C OPTIONAL INPUTS, AND EXCEPT FOR THE LAST 3*NEQ WORDS OF RWORK. -C THE LATTER SPACE IS USED FOR INTERNAL SCRATCH SPACE, AND SO IS -C AVAILABLE FOR USE BY THE USER OUTSIDE LSODE BETWEEN CALLS, IF -C DESIRED (BUT NOT FOR USE BY F OR JAC). -C -C JAC = THE NAME OF THE USER-SUPPLIED ROUTINE (MITER = 1 OR 4) TO -C COMPUTE THE JACOBIAN MATRIX, DF/DY, AS A FUNCTION OF -C THE SCALAR T AND THE VECTOR Y. IT IS TO HAVE THE FORM -C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) -C DIMENSION Y(1), PD(NROWPD,1) -C WHERE NEQ, T, Y, ML, MU, AND NROWPD ARE INPUT AND THE ARRAY -C PD IS TO BE LOADED WITH PARTIAL DERIVATIVES (ELEMENTS OF -C THE JACOBIAN MATRIX) ON OUTPUT. PD MUST BE GIVEN A FIRST -C DIMENSION OF NROWPD. T AND Y HAVE THE SAME MEANING AS IN -C SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A -C DUMMY DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) -C IN THE FULL MATRIX CASE (MITER = 1), ML AND MU ARE -C IGNORED, AND THE JACOBIAN IS TO BE LOADED INTO PD IN -C COLUMNWISE MANNER, WITH DF(I)/DY(J) LOADED INTO PD(I,J). -C IN THE BAND MATRIX CASE (MITER = 4), THE ELEMENTS -C WITHIN THE BAND ARE TO BE LOADED INTO PD IN COLUMNWISE -C MANNER, WITH DIAGONAL LINES OF DF/DY LOADED INTO THE ROWS -C OF PD. THUS DF(I)/DY(J) IS TO BE LOADED INTO PD(I-J+MU+1,J). -C ML AND MU ARE THE HALF-BANDWIDTH PARAMETERS (SEE IWORK). -C THE LOCATIONS IN PD IN THE TWO TRIANGULAR AREAS WHICH -C CORRESPOND TO NONEXISTENT MATRIX ELEMENTS CAN BE IGNORED -C OR LOADED ARBITRARILY, AS THEY ARE OVERWRITTEN BY LSODE. -C JAC NEED NOT PROVIDE DF/DY EXACTLY. A CRUDE -C APPROXIMATION (POSSIBLY WITH A SMALLER BANDWIDTH) WILL DO. -C IN EITHER CASE, PD IS PRESET TO ZERO BY THE SOLVER, -C SO THAT ONLY THE NONZERO ELEMENTS NEED BE LOADED BY JAC. -C EACH CALL TO JAC IS PRECEDED BY A CALL TO F WITH THE SAME -C ARGUMENTS NEQ, T, AND Y. THUS TO GAIN SOME EFFICIENCY, -C INTERMEDIATE QUANTITIES SHARED BY BOTH CALCULATIONS MAY BE -C SAVED IN A USER COMMON BLOCK BY F AND NOT RECOMPUTED BY JAC, -C IF DESIRED. ALSO, JAC MAY ALTER THE Y ARRAY, IF DESIRED. -C JAC MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. -C SUBROUTINE JAC MAY ACCESS USER-DEFINED QUANTITIES IN -C NEQ(2),... AND/OR IN Y(NEQ(1)+1),... IF NEQ IS AN ARRAY -C (DIMENSIONED IN JAC) AND/OR Y HAS LENGTH EXCEEDING NEQ(1). -C SEE THE DESCRIPTIONS OF NEQ AND Y ABOVE. -C -C MF = THE METHOD FLAG. USED ONLY FOR INPUT. THE LEGAL VALUES OF -C MF ARE 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, AND 25. -C MF HAS DECIMAL DIGITS METH AND MITER.. MF = 10*METH + MITER. -C METH INDICATES THE BASIC LINEAR MULTISTEP METHOD.. -C METH = 1 MEANS THE IMPLICIT ADAMS METHOD. -C METH = 2 MEANS THE METHOD BASED ON BACKWARD -C DIFFERENTIATION FORMULAS (BDF-S). -C MITER INDICATES THE CORRECTOR ITERATION METHOD.. -C MITER = 0 MEANS FUNCTIONAL ITERATION (NO JACOBIAN MATRIX -C IS INVOLVED). -C MITER = 1 MEANS CHORD ITERATION WITH A USER-SUPPLIED -C FULL (NEQ BY NEQ) JACOBIAN. -C MITER = 2 MEANS CHORD ITERATION WITH AN INTERNALLY -C GENERATED (DIFFERENCE QUOTIENT) FULL JACOBIAN -C (USING NEQ EXTRA CALLS TO F PER DF/DY VALUE). -C MITER = 3 MEANS CHORD ITERATION WITH AN INTERNALLY -C GENERATED DIAGONAL JACOBIAN APPROXIMATION. -C (USING 1 EXTRA CALL TO F PER DF/DY EVALUATION). -C MITER = 4 MEANS CHORD ITERATION WITH A USER-SUPPLIED -C BANDED JACOBIAN. -C MITER = 5 MEANS CHORD ITERATION WITH AN INTERNALLY -C GENERATED BANDED JACOBIAN (USING ML+MU+1 EXTRA -C CALLS TO F PER DF/DY EVALUATION). -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 II.) 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 -C CASE ALL OF THESE INPUTS ARE EXAMINED. A VALUE OF ZERO FOR ANY -C OF 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, AND -C THEN SET THOSE OF INTEREST TO NONZERO VALUES. -C -C NAME LOCATION MEANING AND DEFAULT VALUE -C -C H0 RWORK(5) THE STEP SIZE TO BE ATTEMPTED ON THE FIRST STEP. -C THE DEFAULT VALUE IS DETERMINED BY THE SOLVER. -C -C HMAX RWORK(6) THE MAXIMUM ABSOLUTE STEP SIZE ALLOWED. -C THE DEFAULT VALUE IS INFINITE. -C -C HMIN RWORK(7) THE MINIMUM ABSOLUTE STEP SIZE ALLOWED. -C THE DEFAULT VALUE IS 0. (THIS LOWER BOUND IS NOT -C ENFORCED ON THE FINAL STEP BEFORE REACHING TCRIT -C WHEN ITASK = 4 OR 5.) -C -C MAXORD IWORK(5) THE MAXIMUM ORDER TO BE ALLOWED. THE DEFAULT -C VALUE IS 12 IF METH = 1, AND 5 IF METH = 2. -C IF MAXORD EXCEEDS THE DEFAULT VALUE, IT WILL -C BE REDUCED TO THE DEFAULT VALUE. -C IF MAXORD IS CHANGED DURING THE PROBLEM, IT MAY -C CAUSE THE CURRENT ORDER TO BE REDUCED. -C -C MXSTEP IWORK(6) MAXIMUM NUMBER OF (INTERNALLY DEFINED) STEPS -C ALLOWED DURING ONE CALL TO THE SOLVER. -C THE DEFAULT VALUE IS 500. -C -C MXHNIL IWORK(7) MAXIMUM NUMBER OF MESSAGES PRINTED (PER PROBLEM) -C WARNING THAT T + H = T ON A STEP (H = STEP SIZE). -C THIS MUST BE POSITIVE TO RESULT IN A NON-DEFAULT -C VALUE. THE DEFAULT VALUE IS 10. -C----------------------------------------------------------------------- -C OPTIONAL OUTPUTS. -C -C AS OPTIONAL ADDITIONAL OUTPUT FROM LSODE, THE VARIABLES LISTED -C BELOW ARE QUANTITIES RELATED TO THE PERFORMANCE OF LSODE -C WHICH ARE AVAILABLE TO THE USER. THESE ARE COMMUNICATED BY WAY OF -C THE WORK ARRAYS, BUT ALSO HAVE INTERNAL MNEMONIC NAMES AS SHOWN. -C EXCEPT WHERE STATED OTHERWISE, ALL OF THESE OUTPUTS ARE DEFINED -C ON ANY SUCCESSFUL RETURN FROM LSODE, AND ON ANY RETURN WITH -C ISTATE = -1, -2, -4, -5, OR -6. ON AN ILLEGAL INPUT RETURN -C (ISTATE = -3), THEY WILL BE UNCHANGED FROM THEIR EXISTING VALUES -C (IF ANY), EXCEPT POSSIBLY FOR TOLSF, LENRW, AND LENIW. -C ON ANY ERROR RETURN, OUTPUTS RELEVANT TO THE ERROR WILL BE DEFINED, -C AS NOTED BELOW. -C -C NAME LOCATION MEANING -C -C HU RWORK(11) THE STEP SIZE IN T LAST USED (SUCCESSFULLY). -C -C HCUR RWORK(12) THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP. -C -C TCUR RWORK(13) THE CURRENT VALUE OF THE INDEPENDENT VARIABLE -C WHICH THE SOLVER HAS ACTUALLY REACHED, I.E. THE -C CURRENT INTERNAL MESH POINT IN T. ON OUTPUT, TCUR -C WILL ALWAYS BE AT LEAST AS FAR AS THE ARGUMENT -C T, BUT MAY BE FARTHER (IF INTERPOLATION WAS DONE). -C -C TOLSF RWORK(14) A TOLERANCE SCALE FACTOR, GREATER THAN 1.0, -C COMPUTED WHEN A REQUEST FOR TOO MUCH ACCURACY WAS -C DETECTED (ISTATE = -3 IF DETECTED AT THE START OF -C THE PROBLEM, ISTATE = -2 OTHERWISE). IF ITOL IS -C LEFT UNALTERED BUT RTOL AND ATOL ARE UNIFORMLY -C SCALED UP BY A FACTOR OF TOLSF FOR THE NEXT CALL, -C THEN THE SOLVER IS DEEMED LIKELY TO SUCCEED. -C (THE USER MAY ALSO IGNORE TOLSF AND ALTER THE -C TOLERANCE PARAMETERS IN ANY OTHER WAY APPROPRIATE.) -C -C NST IWORK(11) THE NUMBER OF STEPS TAKEN FOR THE PROBLEM SO FAR. -C -C NFE IWORK(12) THE NUMBER OF F EVALUATIONS FOR THE PROBLEM SO FAR. -C -C NJE IWORK(13) THE NUMBER OF JACOBIAN EVALUATIONS (AND OF MATRIX -C LU DECOMPOSITIONS) FOR THE PROBLEM SO FAR. -C -C NQU IWORK(14) THE METHOD ORDER LAST USED (SUCCESSFULLY). -C -C NQCUR IWORK(15) THE ORDER TO BE ATTEMPTED ON THE NEXT STEP. -C -C IMXER IWORK(16) THE 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 -C LENRW IWORK(17) THE LENGTH OF RWORK ACTUALLY REQUIRED. -C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL -C INPUT RETURN FOR INSUFFICIENT STORAGE. -C -C LENIW IWORK(18) THE LENGTH OF IWORK ACTUALLY REQUIRED. -C THIS IS 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 -C MAY ALSO BE OF INTEREST TO THE USER AS OPTIONAL OUTPUTS. -C FOR EACH ARRAY, THE TABLE BELOW GIVES ITS INTERNAL NAME, -C ITS BASE ADDRESS 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 -C OF NEQ. FOR J = 0,1,...,NQCUR, COLUMN J+1 -C OF YH CONTAINS HCUR**J/FACTORIAL(J) TIMES -C THE J-TH DERIVATIVE OF THE INTERPOLATING -C POLYNOMIAL CURRENTLY REPRESENTING THE SOLUTION, -C EVALUATED AT T = TCUR. -C -C ACOR LENRW-NEQ+1 ARRAY OF SIZE NEQ USED FOR THE ACCUMULATED -C CORRECTIONS ON EACH STEP, SCALED ON OUTPUT -C TO REPRESENT THE ESTIMATED LOCAL ERROR IN Y -C ON THE LAST STEP. THIS IS THE VECTOR E IN -C THE DESCRIPTION OF THE ERROR CONTROL. IT IS -C DEFINED ONLY ON A SUCCESSFUL RETURN FROM LSODE. -C -C----------------------------------------------------------------------- -C PART II. OTHER ROUTINES CALLABLE. -C -C THE FOLLOWING ARE OPTIONAL CALLS WHICH THE USER MAY MAKE TO -C GAIN ADDITIONAL CAPABILITIES IN CONJUNCTION WITH LSODE. -C (THE ROUTINES XSETUN AND XSETF ARE DESIGNED TO CONFORM TO THE -C SLATEC ERROR HANDLING PACKAGE.) -C -C FORM OF CALL FUNCTION -C CALL XSETUN(LUN) SET THE LOGICAL UNIT NUMBER, LUN, FOR -C OUTPUT OF MESSAGES FROM LSODE, IF -C THE DEFAULT IS NOT DESIRED. -C THE DEFAULT VALUE OF LUN IS 6. -C -C CALL XSETF(MFLAG) SET A FLAG TO CONTROL THE PRINTING OF -C MESSAGES BY LSODE. -C MFLAG = 0 MEANS DO NOT PRINT. (DANGER.. -C THIS RISKS LOSING VALUABLE INFORMATION.) -C MFLAG = 1 MEANS PRINT (THE DEFAULT). -C -C EITHER OF THE ABOVE CALLS MAY BE MADE AT -C ANY TIME AND WILL TAKE EFFECT IMMEDIATELY. -C -C CALL SRCOM(RSAV,ISAV,JOB) SAVES AND RESTORES THE CONTENTS OF -C THE INTERNAL COMMON BLOCKS USED BY -C LSODE (SEE PART III BELOW). -C RSAV MUST BE A REAL ARRAY OF LENGTH 218 -C OR MORE, AND ISAV MUST BE AN INTEGER -C ARRAY OF LENGTH 41 OR MORE. -C JOB=1 MEANS SAVE COMMON INTO RSAV/ISAV. -C JOB=2 MEANS RESTORE COMMON FROM RSAV/ISAV. -C SRCOM IS USEFUL IF ONE IS -C INTERRUPTING A RUN AND RESTARTING -C LATER, OR ALTERNATING BETWEEN TWO OR -C MORE PROBLEMS SOLVED WITH LSODE. -C -C CALL INTDY(,,,,,) PROVIDE DERIVATIVES OF Y, OF VARIOUS -C (SEE BELOW) ORDERS, AT A SPECIFIED POINT T, IF -C DESIRED. IT MAY BE CALLED ONLY AFTER -C A SUCCESSFUL RETURN FROM LSODE. -C -C THE DETAILED INSTRUCTIONS FOR USING INTDY ARE AS FOLLOWS. -C THE FORM OF THE CALL IS.. -C -C CALL INTDY (T, K, RWORK(21), NYH, DKY, IFLAG) -C -C THE INPUT PARAMETERS ARE.. -C -C T = VALUE OF INDEPENDENT VARIABLE WHERE ANSWERS ARE DESIRED -C (NORMALLY THE SAME AS THE T LAST RETURNED BY LSODE). -C FOR VALID RESULTS, T MUST LIE BETWEEN TCUR - HU AND TCUR. -C (SEE OPTIONAL OUTPUTS FOR TCUR AND HU.) -C K = INTEGER ORDER OF THE DERIVATIVE DESIRED. K MUST SATISFY -C 0 .LE. K .LE. NQCUR, WHERE NQCUR IS THE CURRENT ORDER -C (SEE OPTIONAL OUTPUTS). THE CAPABILITY CORRESPONDING -C TO K = 0, I.E. COMPUTING Y(T), IS ALREADY PROVIDED -C BY LSODE DIRECTLY. SINCE NQCUR .GE. 1, THE FIRST -C DERIVATIVE DY/DT IS ALWAYS AVAILABLE WITH INTDY. -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 = A REAL ARRAY OF LENGTH NEQ CONTAINING THE COMPUTED VALUE -C OF THE K-TH 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 PART III. COMMON BLOCKS. -C -C IF LSODE IS TO BE USED IN AN OVERLAY SITUATION, THE USER -C MUST DECLARE, IN THE PRIMARY OVERLAY, THE VARIABLES IN.. -C (1) THE CALL SEQUENCE TO LSODE, -C (2) THE INTERNAL COMMON BLOCK -C /LS0001/ OF LENGTH 257 (218 DOUBLE PRECISION WORDS -C FOLLOWED BY 39 INTEGER WORDS), -C -C IF LSODE 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 TWO COMMON BLOCKS IN HIS MAIN PROGRAM TO INSURE -C THAT THEIR CONTENTS ARE PRESERVED. -C -C IF THE SOLUTION OF A GIVEN PROBLEM BY LSODE IS TO BE INTERRUPTED -C AND THEN LATER CONTINUED, SUCH AS WHEN RESTARTING AN INTERRUPTED RUN -C OR ALTERNATING BETWEEN TWO OR MORE PROBLEMS, THE USER SHOULD SAVE, -C FOLLOWING THE RETURN FROM THE LAST LSODE CALL PRIOR TO THE -C INTERRUPTION, THE CONTENTS OF THE CALL SEQUENCE VARIABLES AND THE -C INTERNAL COMMON BLOCKS, AND LATER RESTORE THESE VALUES BEFORE THE -C NEXT LSODE CALL FOR THAT PROBLEM. TO SAVE AND RESTORE THE COMMON -C BLOCKS, USE SUBROUTINE SRCOM (SEE PART II ABOVE). -C -C----------------------------------------------------------------------- -C PART IV. OPTIONALLY REPLACEABLE SOLVER ROUTINES. -C -C BELOW ARE DESCRIPTIONS OF TWO ROUTINES IN THE LSODE PACKAGE WHICH -C RELATE TO THE MEASUREMENT OF ERRORS. EITHER ROUTINE CAN BE -C REPLACED BY A USER-SUPPLIED VERSION, IF DESIRED. HOWEVER, SINCE SUCH -C A REPLACEMENT MAY HAVE A MAJOR IMPACT ON PERFORMANCE, IT SHOULD BE -C DONE ONLY WHEN ABSOLUTELY NECESSARY, AND ONLY WITH GREAT CAUTION. -C (NOTE.. THE MEANS BY WHICH THE PACKAGE VERSION OF A ROUTINE IS -C SUPERSEDED BY THE USER-S VERSION MAY BE SYSTEM-DEPENDENT.) -C -C (A) EWSET. -C THE FOLLOWING SUBROUTINE IS CALLED JUST BEFORE EACH INTERNAL -C INTEGRATION STEP, AND SETS THE ARRAY OF ERROR WEIGHTS, EWT, AS -C DESCRIBED UNDER ITOL/RTOL/ATOL ABOVE.. -C SUBROUTINE EWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) -C WHERE NEQ, ITOL, RTOL, AND ATOL ARE AS IN THE LSODE CALL SEQUENCE, -C YCUR CONTAINS THE CURRENT DEPENDENT VARIABLE VECTOR, AND -C EWT IS THE ARRAY OF WEIGHTS SET BY EWSET. -C -C IF THE USER SUPPLIES THIS SUBROUTINE, IT MUST RETURN IN EWT(I) -C (I = 1,...,NEQ) A POSITIVE QUANTITY SUITABLE FOR COMPARING ERRORS -C IN Y(I) TO. THE EWT ARRAY RETURNED BY EWSET IS PASSED TO THE -C VNORM ROUTINE (SEE BELOW), AND ALSO USED BY LSODE IN THE COMPUTATION -C OF THE OPTIONAL OUTPUT IMXER, THE DIAGONAL JACOBIAN APPROXIMATION, -C AND THE INCREMENTS FOR DIFFERENCE QUOTIENT JACOBIANS. -C -C IN THE USER-SUPPLIED VERSION OF EWSET, IT MAY BE DESIRABLE TO USE -C THE CURRENT VALUES OF DERIVATIVES OF Y. DERIVATIVES UP TO ORDER NQ -C ARE AVAILABLE FROM THE HISTORY ARRAY YH, DESCRIBED ABOVE UNDER -C OPTIONAL OUTPUTS. IN EWSET, YH IS IDENTICAL TO THE YCUR ARRAY, -C EXTENDED TO NQ + 1 COLUMNS WITH A COLUMN LENGTH OF NYH AND SCALE -C 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 THE QUANTITIES NQ, NYH, H, AND NST CAN BE OBTAINED BY INCLUDING -C IN EWSET THE STATEMENTS.. -C DOUBLE PRECISION H, RLS -C COMMON /LS0001/ RLS(218),ILS(39) -C NQ = ILS(35) -C NYH = ILS(14) -C NST = ILS(36) -C H = RLS(212) -C THUS, FOR EXAMPLE, THE CURRENT VALUE OF DY/DT CAN BE OBTAINED AS -C YCUR(NYH+I)/H (I=1,...,NEQ) (AND THE DIVISION BY H IS -C UNNECESSARY WHEN NST = 0). -C -C (B) VNORM. -C THE FOLLOWING IS A REAL FUNCTION ROUTINE WHICH COMPUTES THE WEIGHTED -C ROOT-MEAN-SQUARE NORM OF A VECTOR V.. -C D = VNORM (N, V, W) -C 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 ). -C VNORM IS CALLED WITH N = NEQ AND WITH W(I) = 1.0/EWT(I), WHERE -C EWT IS AS SET BY SUBROUTINE EWSET. -C -C IF THE USER SUPPLIES THIS FUNCTION, IT SHOULD RETURN A NON-NEGATIVE -C VALUE OF VNORM SUITABLE FOR USE IN THE ERROR CONTROL IN LSODE. -C NONE OF THE ARGUMENTS SHOULD BE ALTERED BY VNORM. -C FOR EXAMPLE, A USER-SUPPLIED VNORM ROUTINE MIGHT.. -C -SUBSTITUTE A MAX-NORM OF (V(I)*W(I)) FOR THE RMS-NORM, OR -C -IGNORE SOME COMPONENTS OF V IN THE NORM, WITH THE EFFECT OF -C SUPPRESSING THE ERROR CONTROL ON THOSE COMPONENTS OF Y. -C----------------------------------------------------------------------- -C----------------------------------------------------------------------- -C OTHER ROUTINES IN THE LSODE PACKAGE. -C -C IN ADDITION TO SUBROUTINE LSODE, THE LSODE PACKAGE INCLUDES THE -C FOLLOWING SUBROUTINES AND FUNCTION ROUTINES.. -C INTDY COMPUTES AN INTERPOLATED VALUE OF THE Y VECTOR AT T = TOUT. -C STODE IS THE CORE INTEGRATOR, WHICH DOES ONE STEP OF THE -C INTEGRATION AND THE ASSOCIATED ERROR CONTROL. -C CFODE SETS ALL METHOD COEFFICIENTS AND TEST CONSTANTS. -C PREPJ COMPUTES AND PREPROCESSES THE JACOBIAN MATRIX J = DF/DY -C AND THE NEWTON ITERATION MATRIX P = I - H*L0*J. -C SOLSY MANAGES SOLUTION OF LINEAR SYSTEM IN CHORD ITERATION. -C EWSET SETS THE ERROR WEIGHT VECTOR EWT BEFORE EACH STEP. -C VNORM COMPUTES THE WEIGHTED R.M.S. NORM OF A VECTOR. -C SRCOM IS A USER-CALLABLE ROUTINE TO SAVE AND RESTORE -C THE CONTENTS OF THE INTERNAL COMMON BLOCKS. -C DGETRF AND DGETRS ARE ROUTINES FROM LAPACK FOR SOLVING FULL -C SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS. -C DGBTRF AND DGBTRS ARE ROUTINES FROM LAPACK FOR SOLVING BANDED -C LINEAR SYSTEMS. -C DAXPY, DSCAL, IDAMAX, AND DDOT ARE BASIC LINEAR ALGEBRA MODULES -C (BLAS) USED BY THE ABOVE LINPACK ROUTINES. -C D1MACH COMPUTES THE UNIT ROUNDOFF IN A MACHINE-INDEPENDENT MANNER. -C XERRWD, XSETUN, AND XSETF HANDLE THE PRINTING OF ALL ERROR -C MESSAGES AND WARNINGS. XERRWD IS MACHINE-DEPENDENT. -C NOTE.. VNORM, IDAMAX, DDOT, AND D1MACH ARE FUNCTION ROUTINES. -C ALL THE OTHERS ARE SUBROUTINES. -C -C THE INTRINSIC AND EXTERNAL ROUTINES USED BY LSODE ARE.. -C DABS, DMAX1, DMIN1, DBLE, MAX0, MIN0, MOD, DSIGN, DSQRT, AND WRITE. -C -C A BLOCK DATA SUBPROGRAM IS ALSO INCLUDED WITH THE PACKAGE, -C FOR LOADING SOME OF THE VARIABLES IN INTERNAL COMMON. -C -C----------------------------------------------------------------------- -C THE FOLLOWING CARD IS FOR OPTIMIZED COMPILATION ON LLNL COMPILERS. -CLLL. OPTIMIZE -C----------------------------------------------------------------------- - EXTERNAL PREPJ, SOLSY - INTEGER ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM, - 1 MXSTEP, MXHNIL, NHNIL, NTREP, NSLAST, NYH, IOWNS - INTEGER ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER, - 1 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 - DOUBLE PRECISION ROWNS, - 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND - DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, - 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0, - 2 D1MACH, VNORM - DIMENSION MORD(2) - LOGICAL IHIT -C----------------------------------------------------------------------- -C THE FOLLOWING INTERNAL COMMON BLOCK CONTAINS -C (A) VARIABLES WHICH ARE LOCAL TO ANY SUBROUTINE BUT WHOSE VALUES MUST -C BE PRESERVED BETWEEN CALLS TO THE ROUTINE (OWN VARIABLES), AND -C (B) VARIABLES WHICH ARE COMMUNICATED BETWEEN SUBROUTINES. -C THE STRUCTURE OF THE BLOCK IS AS FOLLOWS.. ALL REAL VARIABLES ARE -C LISTED FIRST, FOLLOWED BY ALL INTEGERS. WITHIN EACH TYPE, THE -C VARIABLES ARE GROUPED WITH THOSE LOCAL TO SUBROUTINE LSODE FIRST, -C THEN THOSE LOCAL TO SUBROUTINE STODE, AND FINALLY THOSE USED -C FOR COMMUNICATION. THE BLOCK IS DECLARED IN SUBROUTINES -C LSODE, INTDY, STODE, PREPJ, AND SOLSY. GROUPS OF VARIABLES ARE -C REPLACED BY DUMMY ARRAYS IN THE COMMON DECLARATIONS IN ROUTINES -C WHERE THOSE VARIABLES ARE NOT USED. -C----------------------------------------------------------------------- - COMMON /LS0001/ ROWNS(209), - 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, - 2 ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM, - 3 MXSTEP, MXHNIL, NHNIL, NTREP, NSLAST, NYH, IOWNS(6), - 4 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER, - 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU -C - 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 HAS -C NOT YET BEEN DONE, AN ERROR RETURN OCCURS. -C IF ISTATE = 1 AND TOUT = T, JUMP TO BLOCK G AND RETURN IMMEDIATELY. -C----------------------------------------------------------------------- - 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) GO TO 430 - 20 NTREP = 0 -C----------------------------------------------------------------------- -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. -C -C FIRST CHECK LEGALITY OF THE NON-OPTIONAL INPUTS NEQ, ITOL, IOPT, -C MF, ML, AND MU. -C----------------------------------------------------------------------- - 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 CONTINUE -C 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 = 0.0D0 - HMXI = 0.0D0 - HMIN = 0.0D0 - GO TO 60 - 40 MAXORD = IWORK(5) - IF (MAXORD .LT. 0) GO TO 611 - IF (MAXORD .EQ. 0) MAXORD = 100 - MAXORD = MIN0(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. 0.0D0) GO TO 614 - 50 HMAX = RWORK(6) - IF (HMAX .LT. 0.0D0) GO TO 615 - HMXI = 0.0D0 - IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX - HMIN = RWORK(7) - IF (HMIN .LT. 0.0D0) GO TO 616 -C----------------------------------------------------------------------- -C SET WORK ARRAY POINTERS AND CHECK LENGTHS LRW AND LIW. -C POINTERS TO SEGMENTS OF RWORK AND IWORK ARE NAMED BY PREFIXING L TO -C 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 618 -C 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. 0.0D0) GO TO 619 - IF (ATOLI .LT. 0.0D0) GO TO 620 - 70 CONTINUE - IF (ISTATE .EQ. 1) GO TO 100 -C IF ISTATE = 3, SET FLAG TO SIGNAL PARAMETER CHANGES TO STODE. -------- - JSTART = -1 - IF (NQ .LE. MAXORD) GO TO 90 -C 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) = DSQRT(UROUND) - IF (N .EQ. NYH) GO TO 200 -C 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) = 0.0D0 - GO TO 200 -C----------------------------------------------------------------------- -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. 0.0D0) GO TO 625 - IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) - 1 H0 = TCRIT - T - 110 JSTART = 0 - IF (MITER .GT. 0) RWORK(LWM) = DSQRT(UROUND) - NHNIL = 0 - NST = 0 - NJE = 0 - NSLAST = 0 - HU = 0.0D0 - NQU = 0 - CCMAX = 0.3D0 - MAXCOR = 3 - MSBP = 20 - MXNCF = 10 -C INITIAL CALL TO F. (LF0 POINTS TO YH(*,2).) ------------------------- - LF0 = LYH + NYH - IERR = 0 - CALL F (NEQ, T, Y, RWORK(LF0), IERR) - IF (IERR .LT. 0) THEN - ISTATE = -13 - RETURN - ENDIF - NFE = 1 -C 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 = 1.0D0 - CALL EWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) - DO 120 I = 1,N - IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 - 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) -C----------------------------------------------------------------------- -C THE CODING BELOW COMPUTES THE STEP SIZE, H0, TO BE ATTEMPTED ON THE -C 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, ADJUSTED -C SO AS TO BE BETWEEN 100*UROUND AND 1.0E-3. -C THEN THE COMPUTED VALUE H0 IS GIVEN BY.. -C NEQ -C H0**2 = TOL / ( W0**-2 + (1/NEQ) * SUM ( F(I)/YWT(I) )**2 ) -C 1 -C 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. 0.0D0) GO TO 180 - TDIST = DABS(TOUT - T) - W0 = DMAX1(DABS(T),DABS(TOUT)) - IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 - TOL = RTOL(1) - IF (ITOL .LE. 2) GO TO 140 - DO 130 I = 1,N - 130 TOL = DMAX1(TOL,RTOL(I)) - 140 IF (TOL .GT. 0.0D0) GO TO 160 - ATOLI = ATOL(1) - DO 150 I = 1,N - IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) - AYI = DABS(Y(I)) - IF (AYI .NE. 0.0D0) TOL = DMAX1(TOL,ATOLI/AYI) - 150 CONTINUE - 160 TOL = DMAX1(TOL,100.0D0*UROUND) - TOL = DMIN1(TOL,0.001D0) - SUM = VNORM (N, RWORK(LF0), RWORK(LEWT)) - SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 - H0 = 1.0D0/DSQRT(SUM) - H0 = DMIN1(H0,TDIST) - H0 = DSIGN(H0,TOUT-T) -C ADJUST H0 IF NECESSARY TO MEET HMAX BOUND. --------------------------- - 180 RH = DABS(H0)*HMXI - IF (RH .GT. 1.0D0) H0 = H0/RH -C 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 270 -C----------------------------------------------------------------------- -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. 0.0D0) GO TO 250 - CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) - IF (IFLAG .NE. 0) GO TO 627 - T = TOUT - GO TO 420 - 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) - IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 - IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 - GO TO 400 - 230 TCRIT = RWORK(1) - IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 - IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 - IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 - CALL INTDY (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. 0.0D0) GO TO 624 - 245 HMX = DABS(TN) + DABS(H) - IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX - IF (IHIT) GO TO 400 - TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) - IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 - H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) - IF (ISTATE .EQ. 2) JSTART = -2 -C----------------------------------------------------------------------- -C BLOCK E. -C THE NEXT BLOCK IS NORMALLY EXECUTED FOR ALL CALLS AND CONTAINS -C THE CALL TO THE ONE-STEP CORE INTEGRATOR STODE. -C -C THIS IS A LOOPING POINT FOR THE INTEGRATION STEPS. -C -C FIRST CHECK FOR TOO MANY STEPS BEING TAKEN, UPDATE EWT (IF NOT AT -C START OF PROBLEM), CHECK FOR TOO MUCH ACCURACY BEING REQUESTED, AND -C CHECK FOR H BELOW THE ROUNDOFF LEVEL IN T. -C----------------------------------------------------------------------- - 250 CONTINUE - IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 - CALL EWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) - DO 260 I = 1,N - IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 - 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) - 270 TOLSF = UROUND*VNORM (N, RWORK(LYH), RWORK(LEWT)) - IF (TOLSF .LE. 1.0D0) GO TO 280 - TOLSF = TOLSF*2.0D0 - 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('LSODE-- WARNING..INTERNAL T (=R1) AND H (=R2) ARE', - 1 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - CALL XERRWD( - 1 ' SUCH THAT IN THE MACHINE, T + H = T ON THE NEXT STEP ', - 1 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - 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('LSODE-- ABOVE WARNING HAS BEEN ISSUED I1 TIMES. ', - 1 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - CALL XERRWD(' IT WILL NOT BE ISSUED AGAIN FOR THIS PROBLEM', - 1 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) - 290 CONTINUE -C----------------------------------------------------------------------- -C CALL STODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,PREPJ,SOLSY) -C----------------------------------------------------------------------- - IERR = 0 - CALL STODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), - 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), - 2 F, JAC, PREPJ, SOLSY, IERR) - IF (IERR .LT. 0) THEN - ISTATE = -13 - RETURN - ENDIF - KGO = 1 - KFLAG - GO TO (300, 530, 540), KGO -C----------------------------------------------------------------------- -C BLOCK F. -C THE FOLLOWING BLOCK HANDLES THE CASE OF A SUCCESSFUL RETURN FROM THE -C CORE INTEGRATOR (KFLAG = 0). TEST FOR STOP CONDITIONS. -C----------------------------------------------------------------------- - 300 INIT = 1 - GO TO (310, 400, 330, 340, 350), ITASK -C ITASK = 1. IF TOUT HAS BEEN REACHED, INTERPOLATE. ------------------- - 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 - CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) - T = TOUT - GO TO 420 -C ITASK = 3. JUMP TO EXIT IF TOUT WAS REACHED. ------------------------ - 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 - GO TO 250 -C ITASK = 4. SEE IF TOUT OR TCRIT WAS REACHED. ADJUST H IF NECESSARY. - 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 - CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) - T = TOUT - GO TO 420 - 345 HMX = DABS(TN) + DABS(H) - IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX - IF (IHIT) GO TO 400 - TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) - IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 - H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) - JSTART = -2 - GO TO 250 -C ITASK = 5. SEE IF TCRIT WAS REACHED AND JUMP TO EXIT. --------------- - 350 HMX = DABS(TN) + DABS(H) - IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX -C----------------------------------------------------------------------- -C BLOCK G. -C THE FOLLOWING BLOCK HANDLES ALL SUCCESSFUL RETURNS FROM LSODE. -C IF ITASK .NE. 1, Y IS LOADED FROM YH AND T IS SET ACCORDINGLY. -C ISTATE IS SET TO 2, THE ILLEGAL INPUT COUNTER IS ZEROED, AND THE -C OPTIONAL OUTPUTS ARE LOADED INTO THE WORK ARRAYS BEFORE RETURNING. -C IF ISTATE = 1 AND TOUT = T, THERE IS A RETURN WITH NO ACTION TAKEN, -C EXCEPT THAT IF THIS HAS HAPPENED REPEATEDLY, THE RUN IS TERMINATED. -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 - ILLIN = 0 - RWORK(11) = HU - RWORK(12) = H - RWORK(13) = TN - IWORK(11) = NST - IWORK(12) = NFE - IWORK(13) = NJE - IWORK(14) = NQU - IWORK(15) = NQ - RETURN -C - 430 NTREP = NTREP + 1 - IF (NTREP .LT. 5) RETURN - CALL XERRWD( - 1 'LSODE-- REPEATED CALLS WITH ISTATE = 1 AND TOUT = T (=R1) ', - 1 60, 301, 0, 0, 0, 0, 1, T, 0.0D0) - GO TO 800 -C----------------------------------------------------------------------- -C BLOCK H. -C THE FOLLOWING BLOCK HANDLES ALL UNSUCCESSFUL RETURNS OTHER THAN -C 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, T IS SET TO TN, AND THE ILLEGAL INPUT -C COUNTER ILLIN IS SET TO 0. THE OPTIONAL OUTPUTS ARE LOADED INTO -C THE WORK ARRAYS BEFORE RETURNING. -C----------------------------------------------------------------------- -C THE MAXIMUM NUMBER OF STEPS WAS TAKEN BEFORE REACHING TOUT. ---------- - 500 CALL XERRWD('LSODE-- AT CURRENT T (=R1), MXSTEP (=I1) STEPS ', - 1 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - CALL XERRWD(' TAKEN ON THIS CALL BEFORE REACHING TOUT ', - 1 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) - ISTATE = -1 - GO TO 580 -C EWT(I) .LE. 0.0 FOR SOME I (NOT AT START OF PROBLEM). ---------------- - 510 EWTI = RWORK(LEWT+I-1) - CALL XERRWD('LSODE-- AT T (=R1), EWT(I1) HAS BECOME R2 .LE. 0.', - 1 50, 202, 0, 1, I, 0, 2, TN, EWTI) - ISTATE = -6 - GO TO 580 -C TOO MUCH ACCURACY REQUESTED FOR MACHINE PRECISION. ------------------- - 520 CALL XERRWD('LSODE-- AT T (=R1), TOO MUCH ACCURACY REQUESTED ', - 1 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - 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 580 -C KFLAG = -1. ERROR TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ----- - 530 CALL XERRWD('LSODE-- AT T(=R1) AND STEP SIZE H(=R2), THE ERROR', - 1 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - CALL XERRWD(' TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN', - 1 50, 204, 0, 0, 0, 0, 2, TN, H) - ISTATE = -4 - GO TO 560 -C KFLAG = -2. CONVERGENCE FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ---- - 540 CALL XERRWD('LSODE-- AT T (=R1) AND STEP SIZE H (=R2), THE ', - 1 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - CALL XERRWD(' CORRECTOR CONVERGENCE FAILED REPEATEDLY ', - 1 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - CALL XERRWD(' OR WITH ABS(H) = HMIN ', - 1 30, 205, 0, 0, 0, 0, 2, TN, H) - ISTATE = -5 -C COMPUTE IMXER IF RELEVANT. ------------------------------------------- - 560 BIG = 0.0D0 - IMXER = 1 - DO 570 I = 1,N - SIZE = DABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) - IF (BIG .GE. SIZE) GO TO 570 - BIG = SIZE - IMXER = I - 570 CONTINUE - IWORK(16) = IMXER -C SET Y VECTOR, T, ILLIN, AND OPTIONAL OUTPUTS. ------------------------ - 580 DO 590 I = 1,N - 590 Y(I) = RWORK(I+LYH-1) - T = TN - ILLIN = 0 - RWORK(11) = HU - RWORK(12) = H - RWORK(13) = TN - IWORK(11) = NST - IWORK(12) = NFE - IWORK(13) = NJE - IWORK(14) = NQU - IWORK(15) = NQ - RETURN -C----------------------------------------------------------------------- -C BLOCK I. -C THE FOLLOWING BLOCK HANDLES ALL ERROR RETURNS DUE TO ILLEGAL INPUT -C (ISTATE = -3), AS DETECTED BEFORE CALLING THE CORE INTEGRATOR. -C FIRST THE ERROR MESSAGE ROUTINE IS CALLED. THEN IF THERE HAVE BEEN -C 5 CONSECUTIVE SUCH RETURNS JUST BEFORE THIS CALL TO THE SOLVER, -C THE RUN IS HALTED. -C----------------------------------------------------------------------- - 601 CALL XERRWD('LSODE-- ISTATE (=I1) ILLEGAL ', - 1 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 602 CALL XERRWD('LSODE-- ITASK (=I1) ILLEGAL ', - 1 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 603 CALL XERRWD('LSODE-- ISTATE .GT. 1 BUT LSODE NOT INITIALIZED ', - 1 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 604 CALL XERRWD('LSODE-- NEQ (=I1) .LT. 1 ', - 1 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 605 CALL XERRWD('LSODE-- ISTATE = 3 AND NEQ INCREASED (I1 TO I2) ', - 1 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) - GO TO 700 - 606 CALL XERRWD('LSODE-- ITOL (=I1) ILLEGAL ', - 1 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 607 CALL XERRWD('LSODE-- IOPT (=I1) ILLEGAL ', - 1 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 608 CALL XERRWD('LSODE-- MF (=I1) ILLEGAL ', - 1 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 609 CALL XERRWD('LSODE-- ML (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', - 1 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) - GO TO 700 - 610 CALL XERRWD('LSODE-- MU (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', - 1 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) - GO TO 700 - 611 CALL XERRWD('LSODE-- MAXORD (=I1) .LT. 0 ', - 1 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 612 CALL XERRWD('LSODE-- MXSTEP (=I1) .LT. 0 ', - 1 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 613 CALL XERRWD('LSODE-- MXHNIL (=I1) .LT. 0 ', - 1 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) - GO TO 700 - 614 CALL XERRWD('LSODE-- 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, 0.0D0) - GO TO 700 - 615 CALL XERRWD('LSODE-- HMAX (=R1) .LT. 0.0 ', - 1 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) - GO TO 700 - 616 CALL XERRWD('LSODE-- HMIN (=R1) .LT. 0.0 ', - 1 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) - GO TO 700 - 617 CALL XERRWD( - 1 'LSODE-- RWORK LENGTH NEEDED, LENRW (=I1), EXCEEDS LRW (=I2)', - 1 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) - GO TO 700 - 618 CALL XERRWD( - 1 'LSODE-- IWORK LENGTH NEEDED, LENIW (=I1), EXCEEDS LIW (=I2)', - 1 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) - GO TO 700 - 619 CALL XERRWD('LSODE-- RTOL(I1) IS R1 .LT. 0.0 ', - 1 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) - GO TO 700 - 620 CALL XERRWD('LSODE-- ATOL(I1) IS R1 .LT. 0.0 ', - 1 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) - GO TO 700 - 621 EWTI = RWORK(LEWT+I-1) - CALL XERRWD('LSODE-- EWT(I1) IS R1 .LE. 0.0 ', - 1 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) - GO TO 700 - 622 CALL XERRWD( - 1 'LSODE-- 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 'LSODE-- 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 'LSODE-- 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 'LSODE-- 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('LSODE-- AT START OF PROBLEM, TOO MUCH ACCURACY ', - 1 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) - CALL XERRWD( - 1 ' REQUESTED FOR PRECISION OF MACHINE.. SEE TOLSF (=R1) ', - 1 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) - RWORK(14) = TOLSF - GO TO 700 - 627 CALL XERRWD('LSODE-- TROUBLE FROM INTDY. ITASK = I1, TOUT = R1', - 1 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) -C - 700 IF (ILLIN .EQ. 5) GO TO 710 - ILLIN = ILLIN + 1 - ISTATE = -3 - RETURN - 710 CALL XERRWD('LSODE-- REPEATED OCCURRENCES OF ILLEGAL INPUT ', - 1 50, 302, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) -C - 800 CALL XERRWD('LSODE-- RUN ABORTED.. APPARENT INFINITE LOOP ', - 1 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) - RETURN -C----------------------- END OF SUBROUTINE LSODE ----------------------- - END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/odessa/dodessa.f Fri Oct 31 15:20:51 2003 +0000 @@ -0,0 +1,1910 @@ +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- +C THIS IS THE SEPTEMBER 1, 1986 VERSION OF ODESSA.. +C AN ORDINARY DIFFERENTIAL EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS +C SENSITIVITY ANALYSIS. +C +C THIS PACKAGE IS A MODIFICATION OF THE AUGUST 13, 1981 VERSION OF +C LSODE.. LIVERMORE SOLVER FOR ORDINARY DIFFERENTIAL EQUATIONS. +C THIS VERSION IS IN DOUBLE PRECISION. +C +C ODESSA SOLVES FOR THE FIRST-ORDER SENSITIVITY COEFFICIENTS.. +C DY(I)/DP, FOR A SINGLE PARAMETER, OR, +C DY(I)/DP(J), FOR MULTIPLE PARAMETERS, +C ASSOCIATED WITH A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.. +C DY/DT = F(Y,T;P). +C----------------------------------------------------------------------- +C REFERENCES... +C +C 1. JORGE R. LEIS AND MARK A. KRAMER, THE SIMULTANEOUS SOLUTION AND +C EXPLICIT SENSITIVITY ANALYSIS OF SYSTEMS DESCRIBED BY ORDINARY +C DIFFERENTIAL EQUATIONS. SUBMITTED TO ACM TRANS. MATH. SOFTWARE, +C (1985). +C +C 2. JORGE R. LEIS AND MARK A. KRAMER, ODESSA - AN ORDINARY DIFFERENTIA +C EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS SENSITIVITY ANALYSIS. +C SUBMITTED TO ACM TRANS. MATH. SOFTWARE, (1985). +C +C 3. ALAN C. HINDMARSH, LSODE AND LSODI, TWO NEW INITIAL VALUE +C ORDINARY DIFFERENTIAL EQUATION SOLVERS, ACM-SIGNUM NEWSLETTER, +C VOL. 15, NO. 4 (1980), PP. 10-11. +C----------------------------------------------------------------------- +C PROBLEM STATEMENT.. +C +C THE ODESSA MODIFICATION OF THE LSODE PACKAGE PROVIDES THE OPTION TO +C CALCULATE FIRST-ORDER SENSITIVITY COEFFICIENTS FOR A SYSTEM OF STIFF +C OR NON-STIFF EXPLICIT ORDINARY DIFFERENTIAL EQUATIONS OF THE GENERAL +C FORM : +C +C DY/DT = F(Y,T;P) (1) +C +C WHERE Y IS AN N-DIMENSIONAL DEPENDENT VARIABLE VECTOR, T IS THE +C INDEPENDENT INTEGRATION VARIABLE, AND P IS AN NPAR-DIMENSIONAL +C CONSTANT VECTOR. THE GOVERNING EQUATIONS FOR THE FIRST-ORDER +C SENSITIVITY COEFFICIENTS ARE GIVEN BY : +C +C S'(T) = J(T)*S(T) + DF/DP (2) +C +C WHERE +C +C S(T) = DY(T)/DP (= SENSITIVITY FUNCTIONS) +C S'(T) = D(DY(T)/DP)/DT +C J(T) = DF(Y,T;P)/DY(T) (= JACOBIAN MATRIX) +C AND DF/DP = DF(Y,T;P)/DP (= INHOMOGENEITY MATRIX) +C +C SOLUTION OF EQUATIONS (1) AND (2) PROCEEDS SIMULTANEOUSLY VIA AN +C EXTENSION OF THE LSODE PACKAGE AS DESCRIBED IN [1]. +C---------------------------------------------------------------------- +C ACKNOWLEDGEMENT : THE FOLLOWING ODESSA PACKAGE DOCUMENTATION IS A +C MODIFICATION OF THE LSODE DOCUMENTATION WHICH +C ACCOMPANIES THE LSODE PACKAGE CODE. +C---------------------------------------------------------------------- +C SUMMARY OF USAGE. +C +C COMMUNICATION BETWEEN THE USER AND THE ODESSA PACKAGE, FOR NORMAL +C SITUATIONS, IS SUMMARIZED HERE. THIS SUMMARY DESCRIBES ONLY A SUBSET +C OF THE FULL SET OF OPTIONS AVAILABLE. SEE THE FULL DESCRIPTION FOR +C DETAILS, INCLUDING OPTIONAL COMMUNICATION, NONSTANDARD OPTIONS, +C AND INSTRUCTIONS FOR SPECIAL SITUATIONS. SEE ALSO THE EXAMPLE +C PROBLEM (WITH PROGRAM AND OUTPUT) FOLLOWING THIS SUMMARY. +C +C A. FIRST PROVIDE A SUBROUTINE OF THE FORM.. +C SUBROUTINE F (N, T, Y, PAR, YDOT) +C DOUBLE PRECISION T, Y, PAR, YDOT +C DIMENSION Y(N), YDOT(N), PAR(NPAR) +C WHICH SUPPLIES THE VECTOR FUNCTION F BY LOADING YDOT(I) WITH F(I). +C N IS THE NUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS IN THE +C ABOVE MODEL. NPAR IS THE NUMBER OF MODEL PARAMETERS FOR WHICH +C VECTOR SENSITIVITY FUNCTIONS ARE DESIRED. YOU ARE ALSO ENCOURAGED +C TO PROVIDE A SUBROUTINE OF THE FORM.. +C SUBROUTINE DF (N, T, Y, PAR, DFDP, JPAR) +C DOUBLE PRECISION T, Y, PAR, DFDP +C DIMENSION Y(N), PAR(NPAR), DFDP(N) +C GO TO (1,...,NPAR) JPAR +C 1 DFDP(1) = DF(1)/DP(1) +C . +C DFDP(I) = DF(I)/DP(1) +C . +C DFDP(N) = DF(N)/DP(1) +C RETURN +C 2 DFDP(1) = DF(1)/DP(2) +C . +C DFDP(I) = DF(I)/DP(2) +C . +C DFDP(N) = DF(N)/DP(2) +C RETURN +C . . +C . . +C RETURN +C NPAR DFDP(1) = DF(1)/DP(NPAR) +C . +C DFDP(I) = DF(I)/DP(NPAR) +C . +C DFDP(N) = DF(N)/DP(NPAR) +C RETURN +C END +C ONLY NONZERO ELEMENTS NEED BE LOADED. IF THIS IS NOT FEASIBLE, +C ODESSA WILL GENERATE THIS MATRIX INTERNALLY BY DIFFERENCE QUOTIENTS. +C +C B. NEXT DETERMINE (OR GUESS) WHETHER OR NOT THE PROBLEM IS STIFF. +C STIFFNESS OCCURS WHEN THE JACOBIAN MATRIX DF/DY HAS AN EIGENVALUE +C WHOSE REAL PART IS NEGATIVE AND LARGE IN MAGNITUDE, COMPARED TO THE +C RECIPROCAL OF THE T SPAN OF INTEREST. IF THE PROBLEM IS NONSTIFF, +C USE METH = 10. IF IT IS STIFF, USE METH = 20. THE USER IS REQUIRED +C TO INPUT THE METHOD FLAG MF = 10*METH + MITER. THERE ARE FOUR +C STANDARD CHOICES FOR MITER WHEN A SENSITIVITY ANALYSIS IS DESIRED, +C AND ODESSA REQUIRES THE JACOBIAN MATRIX IN SOME FORM. +C THIS MATRIX IS REGARDED EITHER AS FULL (MITER = 1 OR 2), +C OR BANDED (MITER = 4 OR 5). IN THE BANDED CASE, ODESSA REQUIRES TWO +C HALF-BANDWIDTH PARAMETERS ML AND MU. THESE ARE, RESPECTIVELY, THE +C WIDTHS OF THE LOWER AND UPPER PARTS OF THE BAND, EXCLUDING THE MAIN +C DIAGONAL. THUS THE BAND CONSISTS OF THE LOCATIONS (I,J) WITH +C I-ML .LE. J .LE. I+MU, AND THE FULL BANDWIDTH IS ML+MU+1. +C +C C. YOU ARE ENCOURAGED TO SUPPLY THE JACOBIAN DIRECTLY (MF = 11, 14, +C 21, OR 24), BUT IF THIS IS NOT FEASIBLE, ODESSA WILL COMPUTE IT +C INTERNALLY BY DIFFERENCE QUOTIENTS (MF = 12, 15, 22, OR 25). IF YOU +C ARE SUPPLYING THE JACOBIAN, PROVIDE A SUBROUTINE OF THE FORM.. +C SUBROUTINE JAC (NEQ, T, Y, PAR, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y, PAR, PD +C DIMENSION Y(N), PD(NROWPD,N), PAR(NPAR) +C WHICH SUPPLIES DF/DY BY LOADING PD AS FOLLOWS.. +C FOR A FULL JACOBIAN (MF = 11, OR 21), LOAD PD(I,J) WITH DF(I)/DY(J), +C THE PARTIAL DERIVATIVE OF F(I) WITH RESPECT TO Y(J). (IGNORE THE +C ML AND MU ARGUMENTS IN THIS CASE.) +C FOR A BANDED JACOBIAN (MF = 14, OR 24), LOAD PD(I-J+MU+1,J) WITH +C DF(I)/DY(J), I.E. LOAD THE DIAGONAL LINES OF DF/DY INTO THE ROWS OF +C PD FROM THE TOP DOWN. +C IN EITHER CASE, ONLY NONZERO ELEMENTS NEED BE LOADED. +C +C D. WRITE A MAIN PROGRAM WHICH CALLS SUBROUTINE ODESSA ONCE FOR +C EACH POINT AT WHICH ANSWERS ARE DESIRED. THIS SHOULD ALSO PROVIDE +C FOR POSSIBLE USE OF LOGICAL UNIT 6 FOR OUTPUT OF ERROR MESSAGES BY +C ODESSA. ON THE FIRST CALL TO ODESSA, SUPPLY ARGUMENTS AS FOLLOWS.. +C F = NAME OF SUBROUTINE FOR RIGHT-HAND SIDE VECTOR F (MODEL). +C THIS NAME MUST BE DECLARED EXTERNAL IN CALLING PROGRAM. +C DF = NAME OF SUBROUTINE FOR INHOMOGENEITY MATRIX DF/DP. +C IF USED (IDF = 1), THIS NAME MUST BE DECLARED EXTERNAL IN +C CALLING PROGRAM. IF NOT USED (IDF = 0), PASS A DUMMY NAME. +C N = NUMBER OF FIRST ORDER ODE-S IN MODEL; LOAD INTO NEQ(1). +C NPAR = NUMBER OF MODEL PARAMETERS OF INTEREST; LOAD INTO NEQ(2). +C Y = AN (N) BY (NPAR+1) REAL ARRAY OF INITIAL VALUES.. +C Y(I,1) , I = 1,N , CONTAIN THE STATE, OR MODEL, DEPENDENT +C VARIABLES, +C Y(I,J) , J = 2,NPAR , CONTAIN THE DEPENDENT SENSITIVITY +C COEFFICIENTS. +C PAR = A REAL ARRAY OF LENGTH NPAR CONTAINING MODEL PARAMETERS +C OF INTEREST. +C T = THE INITIAL VALUE OF THE INDEPENDENT VARIABLE. +C TOUT = FIRST POINT WHERE OUTPUT IS DESIRED (.NE. T). +C ITOL = 1, 2, 3, OR 4 ACCORDING AS RTOL, ATOL (BELOW) ARE SCALARS +C OR ARRAYS. +C RTOL = RELATIVE TOLERANCE PARAMETER (SCALAR OR (N) BY (NPAR+1) +C ARRAY). +C ATOL = ABSOLUTE TOLERANCE PARAMETER (SCALAR OR (N) BY (NPAR+1) +C ARRAY). +C THE ESTIMATED LOCAL ERROR IN Y(I,J) WILL BE CONTROLLED SO AS +C TO BE ROUGHLY LESS (IN MAGNITUDE) THAN +C EWT(I,J) = RTOL*ABS(Y(I,J)) + ATOL IF ITOL = 1, +C EWT(I,J) = RTOL*ABS(Y(I,J)) + ATOL(I,J) IF ITOL = 2, +C EWT(I,J) = RTOL(I,J)*ABS(Y(I,J) + ATOL IF ITOL = 3, OR +C EWT(I,J) = RTOL(I,J)*ABS(Y(I,J) + ATOL(I,J) IF ITOL = 4. +C THUS THE LOCAL ERROR TEST PASSES IF, IN EACH COMPONENT, +C EITHER THE ABSOLUTE ERROR IS LESS THAN ATOL (OR ATOL(I,J)), +C OR THE RELATIVE ERROR IS LESS THAN RTOL (OR RTOL(I,J)). +C USE RTOL = 0.0 FOR PURE ABSOLUTE ERROR CONTROL, AND +C USE ATOL = 0.0 FOR PURE RELATIVE ERROR CONTROL. +C CAUTION.. ACTUAL (GLOBAL) ERRORS MAY EXCEED THESE LOCAL +C TOLERANCES, SO CHOOSE THEM CONSERVATIVELY. +C ITASK = 1 FOR NORMAL COMPUTATION OF OUTPUT VALUES OF Y AT T = TOUT. +C ISTATE = INTEGER FLAG (INPUT AND OUTPUT). SET ISTATE = 1. +C IOPT = 0, TO INDICATE NO OPTIONAL INPUTS FOR INTEGRATION; +C LOAD INTO IOPT(1). +C ISOPT = 1, TO INDICATE SENSITIVITY ANALYSIS, = 0, TO INDICATE +C NO SENSITIVITY ANALYSIS; LOAD INTO IOPT(2). +C IDF = 1, IF SUBROUTINE DF (ABOVE) IS SUPPLIED BY THE USER, +C = 0, OTHERWISE; LOAD INTO IOPT(3). +C RWORK = REAL WORK ARRAY OF LENGTH AT LEAST.. +C 22 + 16*N + N**2 FOR MF = 11 OR 12, +C 22 + 17*N + (2*ML + MU)*N FOR MF = 14 OR 15, +C 22 + 9*N + N**2 FOR MF = 21 OR 22, +C 22 + 10*N + (2*ML + MU)*N FOR MF = 24 OR 25, +C IF ISOPT = 0, OR.. +C 22 + 15*(NPAR+1)*N + N**2 + N FOR MF = 11 OR 12, +C 24 + 15*(NPAR+1)*N + (2*ML+MU+2)*N + N FOR MF = 14 OR 15, +C 22 + 8*(NPAR+1)*N + N**2 + N FOR MF = 21 OR 22, +C 24 + 8*(NPAR+1)*N + (2*ML+MU+2)*N + N FOR MF = 24 OR 25, +C IF ISOPT = 1. +C LRW = DECLARED LENGTH OF RWORK (IN USER-S DIMENSION STATEMENT). +C IWORK = INTEGER WORK ARRAY OF LENGTH AT LEAST.. +C 20 + N IF ISOPT = 0, +C 21 + N + NPAR IF ISOPT = 1. +C IF MITER = 4 OR 5, INPUT IN IWORK(1),IWORK(2) THE LOWER +C AND UPPER HALF-BANDWIDTHS ML,MU (EXCLUDING MAIN DIAGONAL). +C LIW = DECLARED LENGTH OF IWORK (IN USER-S DIMENSION STATEMENT). +C JAC = NAME OF SUBROUTINE FOR JACOBIAN MATRIX. +C IF USED, THIS NAME MUST BE DECLARED EXTERNAL IN CALLING +C PROGRAM. IF NOT USED, PASS A DUMMY NAME. +C MF = METHOD FLAG. STANDARD VALUES FOR ISOPT = 0 ARE.. +C 10 FOR NONSTIFF (ADAMS) METHOD, NO JACOBIAN USED. +C 21 FOR STIFF (BDF) METHOD, USER-SUPPLIED FULL JACOBIAN. +C 22 FOR STIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. +C 24 FOR STIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. +C 25 FOR STIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. +C IF ISOPT = 1, MF = 10 IS ILLEGAL AND CAN BE REPLACED BY.. +C 11 FOR NONSTIFF METHOD, USER-SUPPLIED FULL JACOBIAN. +C 12 FOR NONSTIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. +C 14 FOR NONSTIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. +C 15 FOR NONSTIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. +C NOTE THAT THE MAIN PROGRAM MUST DECLARE ARRAYS Y, RWORK, IWORK, AND +C POSSIBLY ATOL AND RTOL, AS WELL AS NEQ, IOPT, AND PAR IF ISOPT = 1. +C +C E. THE OUTPUT FROM THE FIRST CALL (OR ANY CALL) IS.. +C Y = ARRAY OF COMPUTED VALUES OF Y(T) VECTOR. +C T = CORRESPONDING VALUE OF INDEPENDENT VARIABLE (NORMALLY TOUT). +C ISTATE = 2 IF ODESSA WAS SUCCESSFUL, NEGATIVE OTHERWISE. +C -1 MEANS EXCESS WORK DONE ON THIS CALL (PERHAPS WRONG MF). +C -2 MEANS EXCESS ACCURACY REQUESTED (TOLERANCES TOO SMALL). +C -3 MEANS ILLEGAL INPUT DETECTED (SEE PRINTED MESSAGE). +C -4 MEANS REPEATED ERROR TEST FAILURES (CHECK ALL INPUTS). +C -5 MEANS REPEATED CONVERGENCE FAILURES (PERHAPS BAD JACOBIAN +C SUPPLIED OR WRONG CHOICE OF MF OR TOLERANCES). +C -6 MEANS ERROR WEIGHT BECAME ZERO DURING PROBLEM. (SOLUTION +C COMPONENT I,J VANISHED, AND ATOL OR ATOL(I,J) = 0.0) +C +C F. TO CONTINUE THE INTEGRATION AFTER A SUCCESSFUL RETURN, SIMPLY +C RESET TOUT AND CALL ODESSA AGAIN. NO OTHER PARAMETERS NEED BE RESET. +C---------------------------------------------------------------------- +C EXAMPLE PROBLEM. +C +C THE FOLLOWING IS A SIMPLE EXAMPLE PROBLEM, WITH THE CODING +C NEEDED FOR ITS SOLUTION BY ODESSA. THE PROBLEM IS FROM CHEMICAL +C KINETICS, AND CONSISTS OF THE FOLLOWING THREE RATE EQUATIONS.. +C DY1/DT = -PAR(1)*Y1 + PAR(2)*Y2*Y3 ; PAR(1) = .04, PAR(2) = 1.E4 +C DY2/DT = PAR(1)*Y1 - PAR(2)*Y2*Y3 - PAR(3)*Y2**2 ; PAR(3) = 3.E7 +C DY3/DT = PAR(3)*Y2**2 +C ON THE INTERVAL FROM T = 0.0 TO T = 4.E10, WITH INITIAL CONDITIONS +C Y1 = 1.0, Y2 = Y3 = 0, AND S(I,J) = 0, I = 1,3, J = 1,3. +C THE PROBLEM IS STIFF. +C +C THE FOLLOWING CODING SOLVES THIS PROBLEM WITH ODESSA, USING +C MF = 21 AND PRINTING RESULTS AT T = .4, 4., ..., 4.E10. +C IT USES ITOL = 4 AND ATOL MUCH SMALLER FOR Y2 THAN Y1 OR Y3, +C BECAUSE Y2 HAS MUCH SMALLER VALUES. LESS STRINGENT TOLERANCES +C ARE ASSIGNED FOR THE SENSITIVITIES TO ACHIEVE GREATER EFFICIENCY. +C AT THE END OF THE RUN, STATISTICAL QUANTITIES OF INTEREST ARE +C PRINTED (SEE OPTIONAL OUTPUTS IN THE FULL DESCRIPTION BELOW). +C +C DOUBLE PRECISION ATOL, RWORK, RTOL, T, TOUT, Y, PAR +C EXTERNAL FEX, JEX, DFEX +C DIMENSION Y(3,4), PAR(3), ATOL(3,4), RTOL(3,4), RWORK(130), +C 1 IWORK(27), NEQ(2), IOPT(3) +C N = 3 +C NPAR = 3 +C NEQ(1) = N +C NEQ(2) = NPAR +C NSV = NPAR+1 +C DO 10 I = 1,N +C DO 10 J = 1,NSV +C 10 Y(I,J) = 0.0D0 +C Y(1,1) = 1.0D0 +C PAR(1) = 0.04D0 +C PAR(2) = 1.0D4 +C PAR(3) = 3.0D7 +C T = 0.D0 +C TOUT = .4D0 +C ITOL = 4 +C ATOL(1,1) = 1.D-6 +C ATOL(2,1) = 1.D-10 +C ATOL(3,1) = 1.D-6 +C DO 20 I = 1,N +C RTOL(I,1) = 1.D-4 +C DO 15 J = 2,NSV +C RTOL(I,J) = 1.D-3 +C 15 ATOL(I,J) = 1.D2 * ATOL(I,1) +C 20 CONTINUE +C ITASK = 1 +C ISTATE = 1 +C IOPT(1) = 0 +C IOPT(2) = 1 +C IOPT(3) = 1 +C LRW = 130 +C LIW = 27 +C MF = 21 +C DO 60 IOUT = 1,12 +C CALL ODESSA(FEX,DFEX,NEQ,Y,PAR,T,TOUT,ITOL,RTOL,ATOL, +C 1 ITASK,ISTATE, IOPT,RWORK,LRW,IWORK,LIW,JEX,MF) +C WRITE(6,30)T,Y(1,1),Y(2,1),Y(3,1) +C 30 FORMAT(1X,7H AT T =,E12.4,6H Y =,3E14.6) +C DO 50 J = 2,NSV +C JPAR = J-1 +C WRITE(6,40)JPAR,Y(1,J),Y(2,J),Y(3,J) +C 40 FORMAT(20X,2HS(,I1,3H) =,3E14.6) +C 50 CONTINUE +C IF (ISTATE .LT. 0) GO TO 80 +C 60 TOUT = TOUT*10.D0 +C WRITE(6,70)IWORK(11),IWORK(12),IWORK(13),IWORK(19) +C 70 FORMAT(1X,/,12H NO. STEPS =,I4,11H NO. F-S =,I4,11H NO. J-S =, +C 1 I4,12H NO. DF-S =,I4) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///22H ERROR HALT.. ISTATE =,I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, PAR, YDOT) +C DOUBLE PRECISION T, Y, YDOT, PAR +C DIMENSION Y(3), YDOT(3), PAR(3) +C YDOT(1) = -PAR(1)*Y(1) + PAR(2)*Y(2)*Y(3) +C YDOT(3) = PAR(3)*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C SUBROUTINE JEX (NEQ, T, Y, PAR, ML, MU, PD, NRPD) +C DOUBLE PRECISION PD, T, Y, PAR +C DIMENSION Y(3), PD(NRPD,3), PAR(3) +C PD(1,1) = -PAR(1) +C PD(1,2) = PAR(2)*Y(3) +C PD(1,3) = PAR(2)*Y(2) +C PD(2,1) = PAR(1) +C PD(2,3) = -PD(1,3) +C PD(3,2) = 2.D0*PAR(3)*Y(2) +C PD(2,2) = -PD(1,2) - PD(3,2) +C RETURN +C END +C +C SUBROUTINE DFEX (NEQ, T, Y, PAR, DFDP, JPAR) +C DOUBLE PRECISION T, Y, PAR, DFDP +C DIMENSION Y(3), PAR(3), DFDP(3) +C GO TO (1,2,3), JPAR +C 1 DFDP(1) = -Y(1) +C DFDP(2) = Y(1) +C RETURN +C 2 DFDP(1) = Y(2)*Y(3) +C DFDP(2) = -Y(2)*Y(3) +C RETURN +C 3 DFDP(2) = -Y(2)*Y(2) +C DFDP(3) = Y(2)*Y(2) +C RETURN +C END +C +C THE OUTPUT OF THIS PROGRAM (ON A DATA GENERAL MV-8000 IN +C DOUBLE PRECISION IS AS FOLLOWS: +C +C AT T = .4000E+00 Y = .985173E+00 .338641E-04 .147930E-01 +C S(1) = -.355914E+00 .390261E-03 .355524E+00 +C S(2) = .955150E-07 -.213065E-09 -.953019E-07 +C S(3) = -.158466E-10 -.529012E-12 .163756E-10 +C AT T = .4000E+01 Y = .905516E+00 .224044E-04 .944615E-01 +C S(1) = -.187621E+01 .179197E-03 .187603E+01 +C S(2) = .296093E-05 -.583104E-09 -.296034E-05 +C S(3) = -.493267E-09 -.276246E-12 .493544E-09 +C AT T = .4000E+02 Y = .715848E+00 .918628E-05 .284143E+00 +C S(1) = -.424730E+01 .459360E-04 .424726E+01 +C S(2) = .137294E-04 -.235815E-09 -.137291E-04 +C S(3) = -.228818E-08 -.113803E-12 .228829E-08 +C AT T = .4000E+03 Y = .450526E+00 .322299E-05 .549471E+00 +C S(1) = -.595837E+01 .354310E-05 .595836E+01 +C S(2) = .227380E-04 -.226041E-10 -.227380E-04 +C S(3) = -.378971E-08 -.499501E-13 .378976E-08 +C AT T = .4000E+04 Y = .183185E+00 .894131E-06 .816814E+00 +C S(1) = -.475006E+01 -.599504E-05 .475007E+01 +C S(2) = .188089E-04 .231330E-10 -.188089E-04 +C S(3) = -.313478E-08 -.187575E-13 .313480E-08 +C AT T = .4000E+05 Y = .389733E-01 .162133E-06 .961027E+00 +C S(1) = -.157477E+01 -.276199E-05 .157477E+01 +C S(2) = .628668E-05 .110026E-10 -.628670E-05 +C S(3) = -.104776E-08 -.453588E-14 .104776E-08 +C AT T = .4000E+06 Y = .493609E-02 .198411E-07 .995064E+00 +C S(1) = -.236244E+00 -.458262E-06 .236244E+00 +C S(2) = .944669E-06 .183193E-11 -.944671E-06 +C S(3) = -.157441E-09 -.635990E-15 .157442E-09 +C AT T = .4000E+07 Y = .516087E-03 .206540E-08 .999484E+00 +C S(1) = -.256277E-01 -.509808E-07 .256278E-01 +C S(2) = .102506E-06 .203905E-12 -.102506E-06 +C S(3) = -.170825E-10 -.684002E-16 .170826E-10 +C AT T = .4000E+08 Y = .519314E-04 .207736E-09 .999948E+00 +C S(1) = -.259316E-02 -.518029E-08 .259316E-02 +C S(2) = .103726E-07 .207209E-13 -.103726E-07 +C S(3) = -.172845E-11 -.691450E-17 .172845E-11 +C AT T = .4000E+09 Y = .544710E-05 .217885E-10 .999995E+00 +C S(1) = -.271637E-03 -.541849E-09 .271638E-03 +C S(2) = .108655E-08 .216739E-14 -.108655E-08 +C S(3) = -.180902E-12 -.723615E-18 .180902E-12 +C AT T = .4000E+10 Y = .446748E-06 .178699E-11 .100000E+01 +C S(1) = -.322322E-04 -.842541E-10 .322323E-04 +C S(2) = .128929E-09 .337016E-15 -.128929E-09 +C S(3) = -.209715E-13 -.838859E-19 .209715E-13 +C AT T = .4000E+11 Y = -.363960E-07 -.145584E-12 .100000E+01 +C S(1) = -.164109E-06 -.429604E-11 .164113E-06 +C S(2) = .656436E-12 .171842E-16 -.656451E-12 +C S(3) = -.689361E-15 -.275745E-20 .689363E-15 +C +C NO. STEPS = 340 NO. F-S = 412 NO. J-S = 343 NO. DF-S =1023 +C---------------------------------------------------------------------- +C FULL DESCRIPTION OF USER INTERFACE TO ODESSA. +C +C THE USER INTERFACE TO ODESSA CONSISTS OF THE FOLLOWING PARTS. +C +C I. THE CALL SEQUENCE TO SUBROUTINE ODESSA, WHICH IS A DRIVER +C ROUTINE FOR THE SOLVER. THIS INCLUDES DESCRIPTIONS OF BOTH +C THE CALL SEQUENCE ARGUMENTS AND OF USER-SUPPLIED ROUTINES. +C FOLLOWING THESE DESCRIPTIONS IS A DESCRIPTION OF +C OPTIONAL INPUTS AVAILABLE THROUGH THE CALL SEQUENCE, AND THEN +C A DESCRIPTION OF OPTIONAL OUTPUTS (IN THE WORK ARRAYS). +C +C II. DESCRIPTIONS OF OTHER ROUTINES IN THE ODESSA PACKAGE THAT MAY +C BE (OPTIONALLY) CALLED BY THE USER. THESE PROVIDE THE ABILITY +C TO ALTER ERROR MESSAGE HANDLING, SAVE AND RESTORE THE INTERNAL +C COMMON, AND OBTAIN SPECIFIED DERIVATIVES OF THE SOLUTION Y(T). +C +C III. DESCRIPTIONS OF COMMON BLOCKS TO BE DECLARED IN OVERLAY +C OR SIMILAR ENVIRONMENTS, OR TO BE SAVED WHEN DOING AN INTERRUPT +C OF THE PROBLEM AND CONTINUED SOLUTION LATER. +C +C IV. DESCRIPTION OF TWO SUBROUTINES IN THE ODESSA PACKAGE, EITHER OF +C WHICH THE USER MAY REPLACE WITH HIS OWN VERSION, IF DESIRED. +C THESE RELATE TO THE MEASUREMENT OF ERRORS. +C +C V. GENERAL REMARKS WHICH HIGHLIGHT DIFFERENCES BETWEEN THE LSODE +C PACKAGE AND THE ODESSA PACKAGE. +C---------------------------------------------------------------------- +C PART I. CALL SEQUENCE. +C +C THE CALL SEQUENCE PARAMETERS USED FOR INPUT ONLY ARE.. +C F, DF, NEQ, PAR, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, +C JAC, MF, +C AND THOSE USED FOR BOTH INPUT AND OUTPUT ARE +C Y, T, ISTATE. +C THE WORK ARRAYS RWORK AND IWORK ARE ALSO USED FOR CONDITIONAL AND +C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. (THE TERM OUTPUT HERE REFERS +C TO THE RETURN FROM SUBROUTINE ODESSA TO THE USER-S CALLING 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 +C ODE MODEL. THIS SYSTEM MUST BE PUT IN THE FIRST-ORDER +C FORM DY/DT = F(Y,T;P), WHERE F IS A VECTOR-VALUED FUNCTION +C OF THE SCALAR T AND VECTORS Y, AND PAR. SUBROUTINE F IS TO +C COMPUTE THE FUNCTION F. IT IS TO HAVE THE FORM.. +C SUBROUTINE F (NEQ, T, Y, PAR, YDOT) +C DOUBLE PRECISION T, Y, PAR, YDOT +C DIMENSION Y(1), PAR(1), YDOT(1) +C WHERE NEQ, T, Y, AND PAR ARE INPUT, AND YDOT = F(Y,T;P) +C IS OUTPUT. Y AND YDOT ARE ARRAYS OF LENGTH N (= NEQ(1)). +C (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY +C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) +C F SHOULD NOT ALTER ARRAY Y, OR PAR(1),...,PAR(NPAR). +C F MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. +C +C SUBROUTINE F MAY ACCESS USER-DEFINED QUANTITIES IN +C NEQ(2),... AND PAR(NPAR+1),... IF NEQ IS AN ARRAY +C (DIMENSIONED IN F) AND PAR HAS LENGTH EXCEEDING NPAR. +C SEE THE DESCRIPTIONS OF NEQ AND PAR BELOW. +C +C DF = THE NAME OF THE USER-SUPPLIED ROUTINE (IDF = 1) TO COMPUTE +C THE INHOMOGENEITY MATRIX, DF/DP, AS A FUNCTION OF THE SCALAR +C T, AND THE VECTORS Y, AND PAR. IT IS TO HAVE THE FORM +C SUBROUTINE DF (NEQ, T, Y, PAR, DFDP, JPAR) +C DOUBLE PRECISION T, Y, PAR, DFDP +C DIMENSION Y(1), PAR(1), DFDP(1) +C GO TO (1,2,...,NPAR) JPAR +C 1 DFDP(1) = DF(1)/DP(1) +C . +C DFDP(I) = DF(I)/DP(1) +C . +C DFDP(N) = DF(N)/DP(1) +C RETURN +C 2 DFDP(1) = DF(1)/DP(2) +C . +C DFDP(I) = DF(I)/DP(2) +C . +C DFDP(N) = DF(N)/DP(2) +C . +C RETURN +C . . +C . . +C NPAR DFDP(1) = DF(1)/DP(NPAR) +C . +C DFDP(I) = DF(I)/DP(NPAR) +C . +C DFDP(N) = DF(N)/DP(NPAR) +C RETURN +C END +C WHERE NEQ, T, Y, PAR, AND JPAR ARE INPUT AND THE VECTOR +C DFDP(*,JPAR) IS TO BE LOADED WITH THE PARTIAL DERIVATIVES +C DF(Y,T;PAR)/DP(JPAR) ON OUTPUT. ONLY NONZERO ELEMENTS NEED +C BE LOADED. T, Y, AND PAR HAVE THE SAME MEANING AS IN +C SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY +C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE). +C +C DFDP(*,JPAR) IS PRESET TO ZERO BY THE SOLVER, SO THAT ONLY +C THE NONZERO ELEMENTS NEED BE LOADED BY DF. SUBROUTINE DF +C MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM IF USED. +C IF IDF = 0 (OR ISOPT = 0), A DUMMY ARGUMENT CAN BE USED. +C +C SUBROUTINE DF MAY ACCESS USER-DEFINED QUANTITIES IN +C NEQ(2),... AND PAR(NPAR+1),... IF NEQ IS AN ARRAY +C (DIMENSIONED IN DF) AND PAR HAS A LENGTH EXCEEDING NPAR. +C SEE THE DESCRIPTIONS OF NEQ AND PAR (BELOW). +C +C NEQ = THE SIZE OF THE ODE SYSTEM (NUMBER OF FIRST ORDER ORDINARY +C DIFFERENTIAL EQUATIONS (N) IN THE MODEL). USED ONLY FOR +C INPUT. NEQ MAY NOT BE CHANGED DURING THE PROBLEM. +C +C FOR ISOPT = 0, NEQ IS NORMALLY A SCALAR. HOWEVER, NEQ MAY +C BE AN ARRAY, WITH NEQ(1) SET TO THE SYSTEM SIZE (N), IN WHICH +C CASE THE ODESSA PACKAGE ACCESSES ONLY NEQ(1). HOWEVER, +C THIS PARAMETER IS PASSED AS THE NEQ ARGUMENT IN ALL CALLS +C TO F, DF, AND JAC. HENCE, IF IT IS AN ARRAY, LOCATIONS +C NEQ(2),... MAY BE USED TO STORE OTHER INTEGER DATA AND PASS +C IT TO F, DF, AND/OR JAC. FOR ISOPT = 1, NPAR MUST BE LOADED +C INTO NEQ(2), AND IS NOT ALLOWED TO CHANGE DURING THE PROBLEM. +C IN THESE CASES, SUBROUTINES F, DF, AND/OR JAC MUST INCLUDE +C NEQ IN A DIMENSION STATEMENT. +C +C Y = A REAL ARRAY FOR THE VECTOR OF DEPENDENT VARIABLES, OF +C DIMENSION (N) BY (NPAR+1). USED FOR BOTH INPUT AND +C OUTPUT ON THE FIRST CALL (ISTATE = 1), AND ONLY FOR +C OUTPUT ON OTHER CALLS. ON THE FIRST CALL, Y MUST CONTAIN +C THE VECTORS OF INITIAL VALUES. ON OUTPUT, Y CONTAINS THE +C COMPUTED SOLUTION VECTORS, EVALUATED AT T. +C +C PAR = A REAL ARRAY FOR THE VECTOR OF CONSTANT MODEL PARAMETERS +C OF INTEREST IN THE SENSITIVITY ANALYSIS, OF LENGTH NPAR +C OR MORE. PAR IS PASSED AS AN ARGUMENT IN ALL CALLS TO F, +C DF, AND JAC. HENCE LOCATIONS PAR(NPAR+1),... MAY BE USED +C TO STORE OTHER REAL DATA AND PASS IT TO F, DF, AND/OR JAC. +C LOCATIONS PAR(1),...,PAR(NPAR) ARE USED AS INPUT ONLY, +C AND MUST NOT BE CHANGED DURING THE PROBLEM. +C +C T = THE INDEPENDENT VARIABLE. ON INPUT, T IS USED ONLY ON THE +C 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 TOUT). +C ON AN ERROR RETURN, T IS THE FARTHEST POINT REACHED. +C +C TOUT = THE NEXT VALUE OF T AT WHICH A COMPUTED SOLUTION IS DESIRED. +C USED ONLY FOR INPUT. +C +C WHEN STARTING THE PROBLEM (ISTATE = 1), TOUT MAY BE EQUAL +C TO T FOR ONE CALL, THEN SHOULD .NE. T FOR THE NEXT CALL. +C FOR THE INITIAL T, AN INPUT VALUE OF TOUT .NE. T IS USED +C IN ORDER TO DETERMINE THE DIRECTION OF THE INTEGRATION +C (I.E. THE ALGEBRAIC SIGN OF THE STEP SIZES) AND THE ROUGH +C SCALE OF THE PROBLEM. INTEGRATION IN EITHER DIRECTION +C (FORWARD OR BACKWARD IN T) IS PERMITTED. +C +C IF ITASK = 2 OR 5 (ONE-STEP MODES), TOUT IS IGNORED AFTER +C THE FIRST CALL (I.E. THE FIRST CALL WITH TOUT .NE. T). +C 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 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 SPACE (N) BY (NPAR+1). SEE DESCRIPTION BELOW +C UNDER ATOL. INPUT ONLY. +C +C ATOL = AN ABSOLUTE ERROR TOLERANCE PARAMETER, EITHER A SCALAR OR +C AN ARRAY OF SPACE (N) BY (NPAR+1). INPUT ONLY. +C +C THE INPUT PARAMETERS ITOL, RTOL, AND ATOL DETERMINE +C THE ERROR CONTROL PERFORMED BY THE SOLVER. THE SOLVER WILL +C CONTROL THE VECTOR E = (E(I,J)) OF ESTIMATED LOCAL ERRORS +C IN Y, ACCORDING TO AN INEQUALITY OF THE FORM +C RMS-NORM OF ( E(I,J)/EWT(I,J) ) .LE. 1, +C WHERE EWT(I,J) = RTOL(I,J)*ABS(Y(I,J)) + ATOL(I,J), +C AND THE RMS-NORM (ROOT-MEAN-SQUARE NORM) HERE IS +C RMS-NORM(V) = SQRT ( (1/N) * SUM (V(I,J)**2) ); I =1,...,N. +C HERE EWT = (EWT(I,J)) IS A VECTOR OF WEIGHTS WHICH MUST +C ALWAYS BE POSITIVE, AND THE VALUES OF RTOL AND ATOL SHOULD +C ALL BE NON-NEGATIVE. THE FOLLOWING TABLE GIVES THE TYPES +C (SCALAR/ARRAY) OF RTOL AND ATOL, AND THE CORRESPONDING FORM +C OF EWT(I,J). +C +C ITOL RTOL ATOL EWT(I,J) +C 1 SCALAR SCALAR RTOL*ABS(Y(I,J)) + ATOL +C 2 SCALAR ARRAY RTOL*ABS(Y(I,J)) + ATOL(I,J) +C 3 ARRAY SCALAR RTOL(I,J)*ABS(Y(I,J)) + ATOL +C 4 ARRAY ARRAY RTOL(I,J)*ABS(Y(I,J)) + ATOL(I,J) +C +C WHEN EITHER OF THESE PARAMETERS IS A SCALAR, IT NEED NOT +C BE DIMENSIONED IN THE USER-S CALLING PROGRAM. +C +C THE TOTAL NUMBER OF ERROR TEST FAILURES DUE TO THE SENSITIVITY +C ANALYSIS, AND WHICH REQUIRE AN INTEGRATION STEP TO BE +C REPEATED, ARE ACCUMULATED IN THE LAST NPAR+1 LOCATIONS OF THE +C INTEGER WORK ARRAY IWORK (SEE OPTIONAL OUTPUTS BELOW). +C THIS INFORMATION MAY BE OF VALUE IN DETERMINING APPROPRIATE +C ERROR TOLERANCES TO BE APPLIED TO THE SENSITIVITY FUNCTIONS. +C +C IF NONE OF THE ABOVE CHOICES (WITH ITOL, RTOL, AND ATOL +C FIXED THROUGHOUT THE PROBLEM) IS SUITABLE, MORE GENERAL +C ERROR CONTROLS CAN BE OBTAINED BY SUBSTITUTING +C USER-SUPPLIED ROUTINES FOR THE SETTING OF EWT AND/OR FOR +C THE NORM CALCULATION. SEE PART IV BELOW. +C +C IF GLOBAL ERRORS ARE TO BE ESTIMATED BY MAKING A REPEATED +C RUN ON THE SAME PROBLEM WITH SMALLER TOLERANCES, THEN ALL +C COMPONENTS OF RTOL AND ATOL (I.E. OF EWT) SHOULD BE SCALED +C DOWN UNIFORMLY. +C +C ITASK = AN INDEX SPECIFYING THE TASK TO BE PERFORMED. +C INPUT ONLY. ITASK HAS THE FOLLOWING VALUES AND MEANINGS. +C 1 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT +C T = TOUT (BY OVERSHOOTING AND INTERPOLATING). +C 2 MEANS TAKE ONE STEP ONLY AND RETURN. +C 3 MEANS STOP AT THE FIRST INTERNAL MESH POINT AT OR +C BEYOND T = TOUT AND RETURN. +C 4 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT +C T = TOUT BUT WITHOUT OVERSHOOTING T = TCRIT. +C TCRIT MUST BE INPUT AS RWORK(1). TCRIT MAY BE EQUAL TO +C OR BEYOND TOUT, BUT NOT BEHIND IT IN THE DIRECTION OF +C INTEGRATION. THIS OPTION IS USEFUL IF THE PROBLEM +C HAS A SINGULARITY AT OR BEYOND T = TCRIT. +C 5 MEANS TAKE ONE STEP, WITHOUT PASSING TCRIT, AND RETURN. +C TCRIT MUST BE INPUT AS RWORK(1). +C +C NOTE.. IF ITASK = 4 OR 5 AND THE SOLVER REACHES TCRIT +C (WITHIN ROUNDOFF), IT WILL RETURN T = TCRIT (EXACTLY) TO +C INDICATE THIS (UNLESS ITASK = 4 AND TOUT COMES BEFORE TCRIT, +C IN WHICH CASE ANSWERS AT T = TOUT ARE RETURNED FIRST). +C +C ISTATE = AN INDEX USED FOR INPUT AND OUTPUT TO SPECIFY THE +C THE STATE OF THE CALCULATION. +C +C ON INPUT, THE VALUES OF ISTATE ARE AS FOLLOWS. +C 1 MEANS THIS IS THE FIRST CALL FOR THE PROBLEM +C (INITIALIZATIONS WILL BE DONE). SEE NOTE BELOW. +C 2 MEANS THIS IS NOT THE FIRST CALL, AND THE CALCULATION +C IS TO CONTINUE NORMALLY, WITH NO CHANGE IN ANY INPUT +C PARAMETERS EXCEPT POSSIBLY TOUT AND ITASK. +C (IF ITOL, RTOL, AND/OR ATOL ARE CHANGED BETWEEN CALLS +C WITH ISTATE = 2, THE NEW VALUES WILL BE USED BUT NOT +C TESTED FOR LEGALITY.) +C 3 MEANS THIS IS NOT THE FIRST CALL, AND THE +C CALCULATION IS TO CONTINUE NORMALLY, BUT WITH +C A CHANGE IN INPUT PARAMETERS OTHER THAN +C TOUT AND ITASK. CHANGES ARE ALLOWED IN +C ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, ML, MU, +C AND ANY OF THE OPTIONAL INPUTS EXCEPT H0. +C (SEE IWORK DESCRIPTION FOR ML AND MU.) +C NOTE.. A PRELIMINARY CALL WITH TOUT = T IS NOT COUNTED +C AS A FIRST CALL HERE, AS NO INITIALIZATION OR CHECKING OF +C INPUT IS DONE. (SUCH A CALL IS SOMETIMES USEFUL FOR THE +C PURPOSE OF OUTPUTTING THE INITIAL CONDITIONS.) +C THUS THE FIRST CALL FOR WHICH TOUT .NE. T REQUIRES +C ISTATE = 1 ON INPUT. +C +C ON OUTPUT, ISTATE HAS THE FOLLOWING VALUES AND MEANINGS. +C 1 MEANS NOTHING WAS DONE, AS TOUT WAS EQUAL TO T WITH +C ISTATE = 1 ON INPUT. (HOWEVER, AN INTERNAL COUNTER WAS +C SET TO DETECT AND PREVENT REPEATED CALLS OF THIS TYPE.) +C 2 MEANS THE INTEGRATION WAS PERFORMED SUCCESSFULLY. +C -1 MEANS AN EXCESSIVE AMOUNT OF WORK (MORE THAN MXSTEP +C STEPS) WAS DONE ON THIS CALL, BEFORE COMPLETING THE +C REQUESTED TASK, BUT THE INTEGRATION WAS OTHERWISE +C SUCCESSFUL AS FAR AS T. (MXSTEP IS AN OPTIONAL INPUT +C AND IS NORMALLY 500.) TO CONTINUE, THE USER MAY +C SIMPLY RESET ISTATE TO A VALUE .GT. 1 AND CALL AGAIN +C (THE EXCESS WORK STEP COUNTER WILL BE RESET TO 0). +C IN ADDITION, THE USER MAY INCREASE MXSTEP TO AVOID +C THIS ERROR RETURN (SEE BELOW ON OPTIONAL INPUTS). +C -2 MEANS TOO MUCH ACCURACY WAS REQUESTED FOR THE PRECISION +C OF THE MACHINE BEING USED. THIS WAS DETECTED BEFORE +C COMPLETING THE REQUESTED TASK, BUT THE INTEGRATION +C WAS SUCCESSFUL AS FAR AS T. TO CONTINUE, THE TOLERANCE +C PARAMETERS MUST BE RESET, AND ISTATE MUST BE SET +C TO 3. THE OPTIONAL OUTPUT TOLSF MAY BE USED FOR THIS +C PURPOSE. (NOTE.. IF THIS CONDITION IS DETECTED BEFORE +C TAKING ANY STEPS, THEN AN ILLEGAL INPUT RETURN +C (ISTATE = -3) OCCURS INSTEAD.) +C -3 MEANS ILLEGAL INPUT WAS DETECTED, BEFORE TAKING ANY +C INTEGRATION STEPS. SEE WRITTEN MESSAGE FOR DETAILS. +C NOTE.. IF THE SOLVER DETECTS AN INFINITE LOOP OF CALLS +C TO THE SOLVER WITH ILLEGAL INPUT, IT WILL CAUSE +C THE RUN TO STOP. +C -4 MEANS THERE WERE REPEATED ERROR TEST FAILURES ON +C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED +C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. +C THE PROBLEM MAY HAVE A SINGULARITY, OR THE INPUT +C MAY BE INAPPROPRIATE. +C -5 MEANS THERE WERE REPEATED CONVERGENCE TEST FAILURES ON +C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED +C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. +C THIS MAY BE CAUSED BY AN INACCURATE JACOBIAN MATRIX, +C IF ONE IS BEING USED. +C -6 MEANS EWT(I,J) BECAME ZERO FOR SOME I,J DURING THE +C INTEGRATION. PURE RELATIVE ERROR CONTROL (ATOL(I,J)=0.0) +C WAS REQUESTED ON A VARIABLE WHICH HAS NOW VANISHED. +C THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. +C +C NOTE.. SINCE THE NORMAL OUTPUT VALUE OF ISTATE IS 2, +C IT DOES NOT NEED TO BE RESET FOR NORMAL CONTINUATION. +C ALSO, SINCE A NEGATIVE INPUT VALUE OF ISTATE WILL BE +C REGARDED AS ILLEGAL, A NEGATIVE OUTPUT VALUE REQUIRES THE +C USER TO CHANGE IT, AND POSSIBLY OTHER INPUTS, BEFORE +C CALLING THE SOLVER AGAIN. +C +C IOPT = AN INTEGER ARRAY FLAG TO SPECIFY WHETHER OR NOT ANY OPTIONAL +C INPUTS ARE BEING USED ON THIS CALL. INPUT ONLY. +C THE OPTIONAL INPUTS ARE LISTED SEPARATELY BELOW. +C IOPT(1) = 0 MEANS NO OPTIONAL INPUTS FOR THE SOLVER WILL BE +C USED. DEFAULT VALUES WILL BE USED IN ALL CASES. +C = 1 MEANS ONE OR MORE OPTIONAL INPUTS FOR THE +C SOLVER ARE BEING USED. +C NOTE : IOPT(1) IS INDEPENDENT OF ISOPT AND IDF. +C IOPT(2) = 0 MEANS NO SENSITIVITY ANALYSIS WILL BE PERFORMED. +C = 1 MEANS A SENSITIVITY ANALYSIS WILL BE PERFORMED. +C NOTE : IOPT(2) IS RENAMED TO ISOPT IN ODESSA. +C = 0 MEANS DF/DP WILL BE CALCULATED BY FINITE +C DIFFERENCE WITHIN ODESSA. +C IOPT(3) = 1 MEANS DF/DP WILL BE CALCULATED BY A USER-SUPPLIED +C ROUTINE. +C NOTE : IOPT(3) IS RENAMED TO IDF IN ODESSA. +C IF IDF = 1, THE USER MUST SUPPLY A +C SUBROUTINE DF (THE NAME IS ARBITRARY) AS +C DESCRIBED BELOW UNDER DF. FOR IDF = 0, +C A DUMMY ARGUMENT CAN BE USED. +C +C RWORK = A REAL WORKING ARRAY (DOUBLE PRECISION). +C FOR ISOPT = 0, THE LENGTH OF RWORK MUST BE AT LEAST.. +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM +C FOR ISOPT = 1, THE LENGTH OF RWORK MUST BE AT LEAST.. +C 20 + NYH*(MAXORD + 1) + 2*NYH + LWM + N +C WHERE.. +C NYH = THE TOTAL NUMBER OF DEPENDENT VARIABLES; +C (= N IF ISOPT = 0, AND N*(NPAR+1) IF ISOPT = 1). +C MAXORD = 12 (IF METH = 1) OR 5 (IF METH = 2) (UNLESS A +C SMALLER VALUE IS GIVEN AS AN OPTIONAL INPUT), +C LWM = 0 IF MITER = 0, +C LWM = N**2 + 2 IF MITER IS 1 OR 2, +C LWM = N + 2 IF MITER = 3, AND +C LWM = (2*ML+MU+1)*N + 2 IF MITER IS 4 OR 5. +C (SEE THE MF DESCRIPTION FOR METH AND MITER.) +C +C THE FIRST 20 WORDS OF RWORK ARE RESERVED FOR CONDITIONAL +C AND OPTIONAL INPUTS AND OPTIONAL OUTPUTS. +C +C THE FOLLOWING WORD IN RWORK IS A CONDITIONAL INPUT.. +C RWORK(1) = TCRIT = CRITICAL VALUE OF T WHICH THE SOLVER +C IS NOT TO OVERSHOOT. REQUIRED IF ITASK IS +C 4 OR 5, AND IGNORED OTHERWISE. (SEE ITASK.) +C +C LRW = THE LENGTH OF THE ARRAY RWORK, AS DECLARED BY THE USER. +C (THIS WILL BE CHECKED BY THE SOLVER.) +C +C IWORK = AN INTEGER WORK ARRAY. THE LENGTH MUST BE AT LEAST.. +C 20 IF MITER = 0 OR 3 (MF = 10, 13, 20, 23), OR +C 20 + N OTHERWISE (MF = 11, 12, 14, 15, 21, 22, 24, 25). +C FOR ISOPT = 0, OR.. +C 21 + N + NPAR +C FOR ISOPT = 1. +C THE FIRST FEW WORDS OF IWORK ARE USED FOR CONDITIONAL AND +C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. +C +C THE FOLLOWING 2 WORDS IN IWORK ARE CONDITIONAL INPUTS.. +C IWORK(1) = ML THESE ARE THE LOWER AND UPPER +C IWORK(2) = MU HALF-BANDWIDTHS, RESPECTIVELY, OF THE +C BANDED JACOBIAN, EXCLUDING THE MAIN DIAGONAL. +C THE BAND IS DEFINED BY THE MATRIX LOCATIONS +C (I,J) WITH I-ML .LE. J .LE. I+MU. ML AND MU +C MUST SATISFY 0 .LE. ML,MU .LE. NEQ-1. +C THESE ARE REQUIRED IF MITER IS 4 OR 5, AND +C IGNORED OTHERWISE. ML AND MU MAY IN FACT BE +C THE BAND PARAMETERS FOR A MATRIX TO WHICH +C DF/DY IS ONLY APPROXIMATELY EQUAL. +* +C +C LIW = THE LENGTH OF THE ARRAY IWORK, AS DECLARED BY THE USER. +C (THIS WILL BE CHECKED BY THE SOLVER.) +C +C NOTE.. THE WORK ARRAYS MUST NOT BE ALTERED BETWEEN CALLS TO ODESSA +C FOR THE SAME PROBLEM, EXCEPT POSSIBLY FOR THE CONDITIONAL AND +C OPTIONAL INPUTS, AND EXCEPT FOR THE LAST 2*NYH + N WORDS OF RWORK. +C THE LATTER SPACE IS USED FOR INTERNAL SCRATCH SPACE, AND SO IS +C AVAILABLE FOR USE BY THE USER OUTSIDE ODESSA BETWEEN CALLS, IF +C DESIRED (BUT NOT FOR USE BY F, DF, OR JAC). +C +C JAC = THE NAME OF THE USER-SUPPLIED ROUTINE (MITER = 1 OR 4) TO +C COMPUTE THE JACOBIAN MATRIX, DF/DY, AS A FUNCTION OF THE +C SCALAR T AND THE VECTORS Y, AND PAR. IT IS TO HAVE THE FORM +C SUBROUTINE JAC (NEQ, T, Y, PAR, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y, PAR, PD +C DIMENSION Y(1), PAR(1), PD(NROWPD,1) +C WHERE NEQ, T, Y, PAR, ML, MU, AND NROWPD ARE INPUT AND THE +C ARRAY PD IS TO BE LOADED WITH PARTIAL DERIVATIVES (ELEMENTS +C OF THE JACOBIAN MATRIX) ON OUTPUT. PD MUST BE GIVEN A FIRST +C DIMENSION OF NROWPD. T, Y, AND PAR HAVE THE SAME MEANING AS +C IN SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A +C DUMMY DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) +C IN THE FULL MATRIX CASE (MITER = 1), ML AND MU ARE +C IGNORED, AND THE JACOBIAN IS TO BE LOADED INTO PD IN +C COLUMNWISE MANNER, WITH DF(I)/DY(J) LOADED INTO PD(I,J). +C IN THE BAND MATRIX CASE (MITER = 4), THE ELEMENTS +C WITHIN THE BAND ARE TO BE LOADED INTO PD IN COLUMNWISE +C MANNER, WITH DIAGONAL LINES OF DF/DY LOADED INTO THE ROWS +C OF PD. THUS DF(I)/DY(J) IS TO BE LOADED INTO PD(I-J+MU+1,J). +C ML AND MU ARE THE HALF-BANDWIDTH PARAMETERS (SEE IWORK). +C THE LOCATIONS IN PD IN THE TWO TRIANGULAR AREAS WHICH +C CORRESPOND TO NONEXISTENT MATRIX ELEMENTS CAN BE IGNORED +C OR LOADED ARBITRARILY, AS THEY ARE OVERWRITTEN BY ODESSA. +C PD IS PRESET TO ZERO BY THE SOLVER, SO THAT ONLY THE +C NONZERO ELEMENTS NEED BE LOADED BY JAC. EACH CALL TO JAC IS +C PRECEDED BY A CALL TO F WITH THE SAME ARGUMENTS NEQ, T, Y, +C AND PAR. THUS TO GAIN SOME EFFICIENCY, INTERMEDIATE +C QUANTITIES SHARED BY BOTH CALCULATIONS MAY BE SAVED IN A +C USER COMMON BLOCK BY F AND NOT RECOMPUTED BY JAC, IF +C DESIRED. ALSO, JAC MAY ALTER THE Y ARRAY, IF DESIRED. +C JAC MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. +C SUBROUTINE JAC MAY ACCESS USER-DEFINED QUANTITIES IN +C NEQ(2),... AND PAR(NPAR+1),.... SEE THE DESCRIPTIONS OF +C NEQ (ABOVE) AND PAR (BELOW). +C +C MF = THE METHOD FLAG. USED ONLY FOR INPUT. THE LEGAL VALUES OF +C MF ARE 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, AND 25. +C MF HAS DECIMAL DIGITS METH AND MITER.. MF = 10*METH + MITER. +C METH INDICATES THE BASIC LINEAR MULTISTEP METHOD.. +C METH = 1 MEANS THE IMPLICIT ADAMS METHOD. +* +C METH = 2 MEANS THE METHOD BASED ON BACKWARD +C DIFFERENTIATION FORMULAS (BDF-S). +C MITER INDICATES THE CORRECTOR ITERATION METHOD.. +C MITER = 0 MEANS FUNCTIONAL ITERATION (NO JACOBIAN MATRIX +C IS INVOLVED). +C MITER = 1 MEANS CHORD ITERATION WITH A USER-SUPPLIED +C FULL (NEQ BY NEQ) JACOBIAN. +C MITER = 2 MEANS CHORD ITERATION WITH AN INTERNALLY +C GENERATED (DIFFERENCE QUOTIENT) FULL JACOBIAN +C (USING NEQ EXTRA CALLS TO F PER DF/DY VALUE). +C MITER = 3 MEANS CHORD ITERATION WITH AN INTERNALLY +C GENERATED DIAGONAL JACOBIAN APPROXIMATION. +C (USING 1 EXTRA CALL TO F PER DF/DY EVALUATION). +C MITER = 4 MEANS CHORD ITERATION WITH A USER-SUPPLIED +C BANDED JACOBIAN. +C MITER = 5 MEANS CHORD ITERATION WITH AN INTERNALLY +C GENERATED BANDED JACOBIAN (USING ML+MU+1 EXTRA +C CALLS TO F PER DF/DY EVALUATION). +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 IF A SENSITIVITY ANLYSIS IS DESIRED (ISOPT = 1), MITER = 0 +C AND 3 ARE DISALLOWED. IN THESE CASES, THE USER IS RECOMMENDED +C TO SUPPLY AN ANALYTICAL JACOBIAN (MITER = 1 OR 4) AND AN +C ANALYTICAL INHOMOGENEITY MATRIX (IDF = 1). +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 II.) 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) = 1, AND IN THAT +C CASE ALL OF THESE INPUTS ARE EXAMINED. A VALUE OF ZERO FOR ANY +C OF 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, AND +C THEN SET THOSE OF INTEREST TO NONZERO VALUES. +C +C NAME LOCATION MEANING AND DEFAULT VALUE +C +C H0 RWORK(5) THE STEP SIZE TO BE ATTEMPTED ON THE FIRST STEP. +C THE DEFAULT VALUE IS DETERMINED BY THE SOLVER. +C +C HMAX RWORK(6) THE MAXIMUM ABSOLUTE STEP SIZE ALLOWED. +C THE DEFAULT VALUE IS INFINITE. +C +C HMIN RWORK(7) THE MINIMUM ABSOLUTE STEP SIZE ALLOWED. +C THE DEFAULT VALUE IS 0. (THIS LOWER BOUND IS NOT +C ENFORCED ON THE FINAL STEP BEFORE REACHING TCRIT +C WHEN ITASK = 4 OR 5.) +C +C MAXORD IWORK(5) THE MAXIMUM ORDER TO BE ALLOWED. THE DEFAULT +C VALUE IS 12 IF METH = 1, AND 5 IF METH = 2. +C IF MAXORD EXCEEDS THE DEFAULT VALUE, IT WILL +C BE REDUCED TO THE DEFAULT VALUE. +C IF MAXORD IS CHANGED DURING THE PROBLEM, IT MAY +C CAUSE THE CURRENT ORDER TO BE REDUCED. +C +C MXSTEP IWORK(6) MAXIMUM NUMBER OF (INTERNALLY DEFINED) STEPS +C ALLOWED DURING ONE CALL TO THE SOLVER. +C THE DEFAULT VALUE IS 500. +C +C MXHNIL IWORK(7) MAXIMUM NUMBER OF MESSAGES PRINTED (PER PROBLEM) +C WARNING THAT T + H = T ON A STEP (H = STEP SIZE). +C THIS MUST BE POSITIVE TO RESULT IN A NON-DEFAULT +C VALUE. THE DEFAULT VALUE IS 10. +C---------------------------------------------------------------------- +C OPTIONAL OUTPUTS. +C +C AS OPTIONAL ADDITIONAL OUTPUT FROM ODESSA, THE VARIABLES LISTED +C BELOW ARE QUANTITIES RELATED TO THE PERFORMANCE OF ODESSA +C WHICH ARE AVAILABLE TO THE USER. THESE ARE COMMUNICATED BY WAY OF +C THE WORK ARRAYS, BUT ALSO HAVE INTERNAL MNEMONIC NAMES AS SHOWN. +C EXCEPT WHERE STATED OTHERWISE, ALL OF THESE OUTPUTS ARE DEFINED +C ON ANY SUCCESSFUL RETURN FROM ODESSA, AND ON ANY RETURN WITH +C ISTATE = -1, -2, -4, -5, OR -6. ON AN ILLEGAL INPUT RETURN +C (ISTATE = -3), THEY WILL BE UNCHANGED FROM THEIR EXISTING VALUES +C (IF ANY), EXCEPT POSSIBLY FOR TOLSF, LENRW, AND LENIW. +C ON ANY ERROR RETURN, OUTPUTS RELEVANT TO THE ERROR WILL BE DEFINED, +C AS NOTED BELOW. +C +C NAME LOCATION MEANING +C +C HU RWORK(11) THE STEP SIZE IN T LAST USED (SUCCESSFULLY). +C +C HCUR RWORK(12) THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP. +C +C TCUR RWORK(13) THE CURRENT VALUE OF THE INDEPENDENT VARIABLE +C WHICH THE SOLVER HAS ACTUALLY REACHED, I.E. THE +C CURRENT INTERNAL MESH POINT IN T. ON OUTPUT, TCUR +C WILL ALWAYS BE AT LEAST AS FAR AS THE ARGUMENT +C T, BUT MAY BE FARTHER (IF INTERPOLATION WAS DONE). +C +C TOLSF RWORK(14) A TOLERANCE SCALE FACTOR, GREATER THAN 1.0, +C COMPUTED WHEN A REQUEST FOR TOO MUCH ACCURACY WAS +C DETECTED (ISTATE = -3 IF DETECTED AT THE START OF +C THE PROBLEM, ISTATE = -2 OTHERWISE). IF ITOL IS +C LEFT UNALTERED BUT RTOL AND ATOL ARE UNIFORMLY +C SCALED UP BY A FACTOR OF TOLSF FOR THE NEXT CALL, +C THEN THE SOLVER IS DEEMED LIKELY TO SUCCEED. +C (THE USER MAY ALSO IGNORE TOLSF AND ALTER THE +C TOLERANCE PARAMETERS IN ANY OTHER WAY APPROPRIATE.) +C +C NST IWORK(11) THE NUMBER OF STEPS TAKEN FOR THE PROBLEM SO FAR. +C +C NFE IWORK(12) THE NUMBER OF F EVALUATIONS FOR THE PROBLEM SO FAR. +C +C NJE IWORK(13) THE NUMBER OF JACOBIAN EVALUATIONS (AND OF MATRIX +C LU DECOMPOSITIONS IF ISOPT = 0) FOR THE PROBLEM SO +C FAR. IF ISOPT = 1, THE NUMBER OF LU DECOMPOSITIONS +C IS EQUAL TO NJE - NSPE (SEE BELOW). +C +C NQU IWORK(14) THE METHOD ORDER LAST USED (SUCCESSFULLY). +C +C NQCUR IWORK(15) THE ORDER TO BE ATTEMPTED ON THE NEXT STEP. +C +C IMXER IWORK(16) THE INDEX OF THE COMPONENT OF LARGEST MAGNITUDE IN +C THE WEIGHTED LOCAL ERROR VECTOR (E(I,J)/EWT(I,J)), +C ON AN ERROR RETURN WITH ISTATE = -4 OR -5. +C +C LENRW IWORK(17) THE LENGTH OF RWORK ACTUALLY REQUIRED. +C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL +C INPUT RETURN FOR INSUFFICIENT STORAGE. +C +C LENIW IWORK(18) THE LENGTH OF IWORK ACTUALLY REQUIRED. +C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL +C INPUT RETURN FOR INSUFFICIENT STORAGE. +C +C NDFE IWORK(19) THE NUMBER OF DF/DP (VECTOR) EVALUATIONS. +C +C NSPE IWORK(20) THE NUMBER OF CALLS TO SUBROUTINE ODESSA_SPRIME. EACH CALL +C TO ODESSA_SPRIME REQUIRES A JACOBIAN EVALUATION, BUT NOT +C AN LU DECOMPOSITION. +C +C THE FOLLOWING ARRAYS ARE SEGMENTS OF THE RWORK AND IWORK ARRAYS +C WHICH MAY ALSO BE OF INTEREST TO THE USER AS OPTIONAL OUTPUTS. +C FOR EACH ARRAY, THE TABLE BELOW GIVES ITS INTERNAL NAME, ITS BASE +C ADDRESS IN RWORK OR IWORK, AND ITS DESCRIPTION. +C +C NAME BASE ADDRESS DESCRIPTION +C +C YH 21 IN RWORK THE NORDSIECK HISTORY ARRAY, OF SIZE NYH BY +C (NQCUR + 1). FOR J = 0,1,...,NQCUR, COLUMN J+1 +C OF YH CONTAINS HCUR**J/FACTORIAL(J) TIMES +C THE J-TH DERIVATIVE OF THE INTERPOLATING +C POLYNOMIAL CURRENTLY REPRESENTING THE SOLUTION, +C EVALUATED AT T = TCUR. +C +C ACOR LENRW-NYH+1 ARRAY OF SIZE NYH USED FOR THE ACCUMULATED +C IN RWORK CORRECTIONS ON EACH STEP, SCALED ON OUTPUT +C TO REPRESENT THE ESTIMATED LOCAL ERROR IN Y +C ON THE LAST STEP. THIS IS THE VECTOR E IN +C THE DESCRIPTION OF THE ERROR CONTROL. +C IT IS DEFINED ONLY ON A SUCCESSFUL RETURN +C FROM ODESSA. +C NRS LENIW-NPAR ARRAY OF SIZE NPAR+1, USED TO STORE THE +C IN IWORK ACCUMULATED NUMBER OF REPEATED STEPS DUE TO +C THE SENSITIVITY ANALYSIS.. +C NRS(1) = TOTAL NUMBER OF REPEATED STEPS, +C NRS(2),... = NUMBER OF REPEATED STEPS DUE TO +C MODEL PARAMETER 1,... +C +C---------------------------------------------------------------------- +C PART II. OTHER ROUTINES CALLABLE. +C +C THE FOLLOWING ARE OPTIONAL CALLS WHICH THE USER MAY MAKE TO +C GAIN ADDITIONAL CAPABILITIES IN CONJUNCTION WITH ODESSA. +C +C CALL ODESSA_SVCOM (RSAV, ISAV) STORE IN RSAV AND ISAV THE CONTENTS +C OF THE INTERNAL COMMON BLOCKS USED BY +C ODESSA (SEE PART III BELOW). +C RSAV MUST BE A REAL ARRAY OF LENGTH 222 +C OR MORE, AND ISAV MUST BE AN INTEGER +C ARRAY OF LENGTH 54 OR MORE. +C +C CALL ODESSA_RSCOM (RSAV, ISAV) RESTORE, FROM RSAV AND ISAV, THE CONTENTS +C OF THE INTERNAL COMMON BLOCKS USED BY +C ODESSA. PRESUMES A PRIOR CALL TO ODESSA_SVCOM +C WITH THE SAME ARGUMENTS. +C +C ODESSA_SVCOM AND ODESSA_RSCOM ARE USEFUL IF +C INTERRUPTING A RUN AND RESTARTING +C LATER, OR ALTERNATING BETWEEN TWO OR +C MORE PROBLEMS SOLVED WITH ODESSA. +C +C CALL ODESSA_INTDY(,,,,,) PROVIDE DERIVATIVES OF Y, OF VARIOUS +C (SEE BELOW) ORDERS, AT A SPECIFIED POINT T, IF +C DESIRED. IT MAY BE CALLED ONLY AFTER +C A SUCCESSFUL RETURN FROM ODESSA. +C +C THE DETAILED INSTRUCTIONS FOR USING ODESSA_INTDY ARE AS FOLLOWS. +C THE FORM OF THE CALL IS.. +C +C CALL ODESSA_INTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C THE INPUT PARAMETERS ARE.. +C +C T = VALUE OF INDEPENDENT VARIABLE WHERE ANSWERS ARE DESIRED +C (NORMALLY THE SAME AS THE T LAST RETURNED BY ODESSA). +C FOR VALID RESULTS, T MUST LIE BETWEEN TCUR - HU AND TCUR. +C (SEE OPTIONAL OUTPUTS FOR TCUR AND HU.) +C K = INTEGER ORDER OF THE DERIVATIVE DESIRED. K MUST SATISFY +C 0 .LE. K .LE. NQCUR, WHERE NQCUR IS THE CURRENT ORDER +C (SEE OPTIONAL OUTPUTS). THE CAPABILITY CORRESPONDING +C TO K = 0, I.E. COMPUTING Y(T), IS ALREADY PROVIDED +C BY ODESSA DIRECTLY. SINCE NQCUR .GE. 1, THE FIRST +C DERIVATIVE DY/DT IS ALWAYS AVAILABLE WITH ODESSA_INTDY. +C RWORK(21) = THE BASE ADDRESS OF THE HISTORY ARRAY YH. +C NYH = COLUMN LENGTH OF YH, EQUAL TO THE TOTAL NUMBER OF +C DEPENDENT VARIABLES. IF ISOPT = 0, NYH = N. IF ISOPT = 1, +C NYH = N * (NPAR + 1). +C +C THE OUTPUT PARAMETERS ARE.. +C +C DKY = A REAL ARRAY OF LENGTH NYH CONTAINING THE COMPUTED VALUE +C OF THE K-TH 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 PART III. COMMON BLOCKS. +C +C IF ODESSA IS TO BE USED IN AN OVERLAY SITUATION, THE USER +C MUST DECLARE, IN THE PRIMARY OVERLAY, THE VARIABLES IN.. +C (1) THE CALL SEQUENCE TO ODESSA, +C (2) THE THREE INTERNAL COMMON BLOCKS +C /ODE001/ OF LENGTH 258 (219 DOUBLE PRECISION WORDS +C FOLLOWED BY 39 INTEGER WORDS), +C /ODE002/ OF LENGTH 14 (3 DOUBLE PRECISION WORDS FOLLOWED +C BY 11 INTEGER WORDS), +C +C IF ODESSA 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 THREE COMMON BLOCKS IN HIS MAIN PROGRAM TO INSURE +C THAT THEIR CONTENTS ARE PRESERVED. +C +C IF THE SOLUTION OF A GIVEN PROBLEM BY ODESSA IS TO BE INTERRUPTED +C AND THEN LATER CONTINUED, SUCH AS WHEN RESTARTING AN INTERRUPTED RUN +C OR ALTERNATING BETWEEN TWO OR MORE PROBLEMS, THE USER SHOULD SAVE, +C FOLLOWING THE RETURN FROM THE LAST ODESSA CALL PRIOR TO THE +C INTERRUPTION, THE CONTENTS OF THE CALL SEQUENCE VARIABLES AND THE +C INTERNAL COMMON BLOCKS, AND LATER RESTORE THESE VALUES BEFORE THE +C NEXT ODESSA CALL FOR THAT PROBLEM. TO SAVE AND RESTORE THE COMMON +C BLOCKS, USE SUBROUTINES ODESSA_SVCOM AND ODESSA_RSCOM (SEE PART II ABOVE). +C +C---------------------------------------------------------------------- +C PART IV. OPTIONALLY REPLACEABLE SOLVER ROUTINES. +C +C BELOW ARE DESCRIPTIONS OF TWO ROUTINES IN THE ODESSA PACKAGE WHICH +C RELATE TO THE MEASUREMENT OF ERRORS. EITHER ROUTINE CAN BE +C REPLACED BY A USER-SUPPLIED VERSION, IF DESIRED. HOWEVER, SINCE SUCH +C A REPLACEMENT MAY HAVE A MAJOR IMPACT ON PERFORMANCE, IT SHOULD BE +C DONE ONLY WHEN ABSOLUTELY NECESSARY, AND ONLY WITH GREAT CAUTION. +C (NOTE.. THE MEANS BY WHICH THE PACKAGE VERSION OF A ROUTINE IS +C SUPERSEDED BY THE USER-S VERSION MAY BE SYSTEM-DEPENDENT.) +C +C (A) ODESSA_EWSET. +C THE FOLLOWING SUBROUTINE IS CALLED JUST BEFORE EACH INTERNAL +C INTEGRATION STEP, AND SETS THE ARRAY OF ERROR WEIGHTS, EWT, AS +C DESCRIBED UNDER ITOL/RTOL/ATOL ABOVE.. +C SUBROUTINE ODESSA_EWSET (NYH, ITOL, RTOL, ATOL, YCUR, EWT) +C WHERE NEQ, ITOL, RTOL, AND ATOL ARE AS IN THE ODESSA CALL SEQUENCE, +C YCUR CONTAINS THE CURRENT DEPENDENT VARIABLE VECTOR, AND +C EWT IS THE ARRAY OF WEIGHTS SET BY ODESSA_EWSET. +C +C IF THE USER SUPPLIES THIS SUBROUTINE, IT MUST RETURN IN EWT(I) +C (I = 1,...,NYH) A POSITIVE QUANTITY SUITABLE FOR COMPARING ERRORS +C IN Y(I) TO. THE EWT ARRAY RETURNED BY ODESSA_EWSET IS PASSED TO THE +C ODESSA_VNORM ROUTINE (SEE BELOW), AND ALSO USED BY ODESSA IN THE COMPUTATION +C OF THE OPTIONAL OUTPUT IMXER, THE DIAGONAL JACOBIAN APPROXIMATION, +C AND THE INCREMENTS FOR DIFFERENCE QUOTIENT JACOBIANS. +C +C IN THE USER-SUPPLIED VERSION OF ODESSA_EWSET, IT MAY BE DESIRABLE TO USE +C THE CURRENT VALUES OF DERIVATIVES OF Y. DERIVATIVES UP TO ORDER NQ +C ARE AVAILABLE FROM THE HISTORY ARRAY YH, DESCRIBED ABOVE UNDER +C OPTIONAL OUTPUTS. IN ODESSA_EWSET, YH IS IDENTICAL TO THE YCUR ARRAY, +C EXTENDED TO NQ + 1 COLUMNS WITH A COLUMN LENGTH OF NYH AND SCALE +C 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 THE QUANTITIES NQ, NYH, H, AND NST CAN BE OBTAINED BY INCLUDING +C IN ODESSA_EWSET THE STATEMENTS.. +C DOUBLE PRECISION H, RLS +C COMMON /ODE001/ RLS(219),ILS(39) +C NQ = ILS(35) +C NYH = ILS(14) +C NST = ILS(36) +C H = RLS(213) +C THUS, FOR EXAMPLE, THE CURRENT VALUE OF DY/DT CAN BE OBTAINED AS +C YCUR(NYH+I)/H (I=1,...,N) (AND THE DIVISION BY H IS +C UNNECESSARY WHEN NST = 0). +C +C (B) ODESSA_VNORM. +C THE FOLLOWING IS A REAL FUNCTION ROUTINE WHICH COMPUTES THE WEIGHTED +C ROOT-MEAN-SQUARE NORM OF A VECTOR V.. +C D = ODESSA_VNORM (LV, V, W) +C WHERE.. +C LV = 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 ). +C ODESSA_VNORM IS CALLED WITH LV = N AND WITH W(I) = 1.0/EWT(I), WHERE +C EWT IS AS SET BY SUBROUTINE ODESSA_EWSET. +C +C IF THE USER SUPPLIES THIS FUNCTION, IT SHOULD RETURN A NON-NEGATIVE +C VALUE OF ODESSA_VNORM SUITABLE FOR USE IN THE ERROR CONTROL IN ODESSA. +C NONE OF THE ARGUMENTS SHOULD BE ALTERED BY ODESSA_VNORM. +C FOR EXAMPLE, A USER-SUPPLIED ODESSA_VNORM ROUTINE MIGHT.. +C -SUBSTITUTE A MAX-NORM OF (V(I)*W(I)) FOR THE RMS-NORM, OR +C -IGNORE SOME COMPONENTS OF V IN THE NORM, WITH THE EFFECT OF +C SUPPRESSING THE ERROR CONTROL ON THOSE COMPONENTS OF Y. +C---------------------------------------------------------------------- +C OTHER ROUTINES IN THE ODESSA PACKAGE. +C +C IN ADDITION TO SUBROUTINE ODESSA, THE ODESSA PACKAGE INCLUDES THE +C FOLLOWING SUBROUTINES AND FUNCTION ROUTINES.. +C ODESSA_INTDY COMPUTES AN INTERPOLATED VALUE OF THE Y VECTOR AT T = TOUT. +C ODESSA_STODE IS THE CORE INTEGRATOR, WHICH DOES ONE STEP OF THE +C INTEGRATION AND THE ASSOCIATED ERROR CONTROL. +C ODESSA_STESA MANAGES THE SOLUTION OF THE SENSITIVITY FUNCTIONS. +C ODESSA_CFODE SETS ALL METHOD COEFFICIENTS AND TEST CONSTANTS. +C ODESSA_PREPJ COMPUTES AND PREPROCESSES THE JACOBIAN MATRIX J = DF/DY +C AND THE NEWTON ITERATION MATRIX P = I - H*L0*J. +C IT IS ALSO CALLED BY ODESSA_SPRIME (WITH JOPT = 1) TO JUST +C COMPUTE THE JACOBIAN MATRIX. +C ODESSA_PREPDF COMPUTES THE INHOMOGENEITY MATRIX DF/DP. +C ODESSA_SPRIME DEFINES THE SYSTEM OF SENSITIVITY EQUATIONS. +C ODESSA_SOLSY MANAGES SOLUTION OF LINEAR SYSTEM IN CHORD ITERATION. +C ODESSA_EWSET SETS THE ERROR WEIGHT VECTOR EWT BEFORE EACH STEP. +C ODESSA_VNORM COMPUTES THE WEIGHTED R.M.S. NORM OF A VECTOR. +C ODESSA_SVCOM AND ODESSA_RSCOM ARE USER-CALLABLE ROUTINES TO SAVE AND RESTORE, +C RESPECTIVELY, THE CONTENTS OF THE INTERNAL COMMON BLOCKS. +C DGETRF AND DGETRS ARE ROUTINES FROM LAPACK FOR SOLVING FULL +C SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS. +C DGBTRF AND DGBTRS ARE ROUTINES FROM LAPACK FOR SOLVING BANDED +C LINEAR SYSTEMS. +C DAXPY, DSCAL, IDAMAX, AND DDOT ARE BASIC LINEAR ALGEBRA MODULES +C (BLAS) USED BY THE ABOVE LINPACK ROUTINES. +C D1MACH COMPUTES THE UNIT ROUNDOFF IN A MACHINE-INDEPENDENT MANNER. +C XERRWD, XSETUN, AND ODESSA_XSETF HANDLE THE PRINTING OF ALL ERROR +C MESSAGES AND WARNINGS. +C NOTE.. ODESSA_VNORM, IDAMAX, DDOT, AND D1MACH ARE FUNCTION ROUTINES. +C ALL THE OTHERS ARE SUBROUTINES. +C +C THE FORTRAN GENERIC INTRINSIC FUNCTIONS USED BY ODESSA ARE.. +C ABS, MAX, MIN, REAL, MOD, SIGN, SQRT, AND WRITE +C +C A BLOCK DATA SUBPROGRAM IS ALSO INCLUDED WITH THE PACKAGE, +C FOR LOADING SOME OF THE VARIABLES IN INTERNAL COMMON. +C +C---------------------------------------------------------------------- +C PART V. GENERAL REMARKS +C +C THIS SECTION HIGHLIGHTS THE BASIC DIFFERENCES BETWEEN THE ORIGINAL +C LSODE PACKAGE AND THE ODESSA MODIFICATION. THIS IS PROVIDED AS A +C SERVICE TO EXPERIENCED LSODE USERS TO EXPEDITE FAMILIARIZATION WITH +C ODESSA. +C +C (A). ORIGINAL SUBROUTINES AND FUNCTIONS. +C +C OF THE ORIGINAL 22 SUBROUTINES AND FUNCTIONS USED IN THE LSODE +C PACKAGE, ALL ARE USED BY ODESSA, WITH THE FOLLOWING HAVING BEEN +C MODIFIED.. +C +C LSODE THE ORIGINAL DRIVER SUBROUTINE FOR THE LSODE PACKAGE IS +C EXTENSIVELY MODIFIED AND RENAMED ODESSA, WHICH NOW +C CONTAINS A CALL TO ODESSA_SPRIME TO ESTABLISH INITIAL CONDITIONS +C FOR THE SENSITIVITY CALCULATIONS. +C +C ODESSA_STODE THE ONE STEP INTEGRATOR IS SLIGHTLY MODIFIED AND RETAINS +C ITS ORIGINAL NAME. IT NOW CONTAINS THE CALL TO ODESSA_STESA, +C AND ALSO CALLS ODESSA_SPRIME IF KFLAG .LE. -3. +C +C ODESSA_PREPJ ALSO NAMED ODESSA_PREPJ IN ODESSA IS SLIGHTLY MODIFIED TO ALLOW +C FOR THE CALCULATION OF JACOBIAN WITH NO PREPROCESSING +C (JOPT = 1). +C +C (B). NEW SUBROUTINES. +C +C IN ADDITION TO THE CHANGES NOTED ABOVE, THREE NEW SUBROUTINES +C HAVE BEEN INTRODUCED (SEE ODESSA_STESA, ODESSA_SPRIME, AND ODESSA_PREPDF AS DESCRIBED +C IN PART IV. ABOVE). +C +C (C). COMMON BLOCKS. +C +C /LS0001/ RETAINS THE SAME LENGTH AND IS RENAMED /ODE001/; +C HOWEVER THE REAL ARRAY ROWNS(209) IS SHORTENED TO A +C LENGTH OF (173) REAL WORDS, ALLOWING THE REMOVAL OF +C TESCO(3,12) WHICH IS NOW PASSED FROM ODESSA_STODE TO ODESSA_STESA. +C IN ADDITION, THE INTEGER ARRAY IOWNS(6) IS SHORTENED +C TO A LENGTH OF (4) INTEGER WORDS, ALLOWING THE REMOVAL +C OF IALTH AND LMAX WHICH ARE NOW PASSED FROM ODESSA_STODE TO +C ODESSA_STESA. +C +C /ODE002/ ADDED COMMON BLOCK FOR VARIABLES IMPORTANT TO +C SENSITIVITY ANALYSIS (SEE PART III. ABOVE). A BLOCK +C DATA PROGRAM IS NOT REQUIRED FOR THIS COMMON BLOCK. +C +C ODESSA_SVCOM,ODESSA_RSCOM THESE TWO SUBROUTINES ARE MODIFIED TO HANDLE +C COMMON BLOCK /ODE002/ AS WELL. +C +C (D). OPTIONAL INPUTS. +C +C THE FULL SET OF OPTIONAL INPUTS AVAILABLE IN LSODE IS ALSO +C AVAILABLE IN ODESSA, WITH THE EXCEPTION THAT THE NUMBER OF ODE'S +C IN THE MODEL (NEQ(1)), MAY NOT BE CHANGED DURING THE PROBLEM. +C IN ODESSA, NYH NOW REFERS TO THE TOTAL NUMBER OF FIRST-ORDER +C ODE'S (MODEL AND SENSITIVITY EQUATIONS) WHICH IS EQUAL TO +C NEQ(1) IF ISOPT = 0, OR NEQ(1)*(NEQ(2)+1) IF ISOPT = 1. +C NEQ(1), NEQ(2), AND NYH ARE NOT ALLOWED TO CHANGE DURING +C THE COURSE OF AN INTEGRATION. +C +C (E). OPTIONAL OUTPUTS. +C +C THE FULL SET OF OPTIONAL OUTPUTS AVAILABLE IN LSODE IS ALSO +C AVAILABLE IN ODESSA. IN ADDITION, IWORK(19) AND IWORK(20) ARE +C LOADED WITH NDFE AND NSPE, RESPECTIVELY, UPON OUTPUT. THE TOTAL +C NUMBER OF LU DECOMPOSITIONS OF THE PROCESSED JACOBIAN IS EQUAL +C TO NJE - NSPE. +C----------------------------------------------------------------------- + SUBROUTINE DODESSA (F, DF, NEQ, Y, PAR, T, TOUT, ITOL, RTOL, ATOL, + 1 ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) + IMPLICIT DOUBLE PRECISION (A-H,O-Z) + LOGICAL IHIT + EXTERNAL F, DF, JAC, ODESSA_PREPJ, ODESSA_SOLSY, ODESSA_PREPDF + DIMENSION NEQ(*), Y(*), PAR(*), RTOL(*), ATOL(*), IOPT(*), + 1 RWORK(LRW), IWORK(LIW), MORD(2) +C----------------------------------------------------------------------- +C THIS IS THE SEPTEMBER 1, 1986 VERSION OF ODESSA.. +C AN ORDINARY DIFFERENTIAL EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS +C SENSITIVITY ANALYSIS. +C +C THIS PACKAGE IS A MODIFICATION OF THE AUGUST 13, 1981 VERSION OF +C LSODE.. LIVERMORE SOLVER FOR ORDINARY DIFFERENTIAL EQUATIONS. +C THIS VERSION IS IN DOUBLE PRECISION. +C +C ODESSA SOLVES FOR THE FIRST-ORDER SENSITIVITY COEFFICIENTS.. +C DY(I)/DP, FOR A SINGLE PARAMETER, OR, +C DY(I)/DP(J), FOR MULTIPLE PARAMETERS, +C ASSOCIATED WITH A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.. +C DY(T)/DT = F(Y,T;P). +C----------------------------------------------------------------------- +C REFERENCES... +C +C 1. JORGE R. LEIS AND MARK A. KRAMER, THE SIMULTANEOUS SOLUTION AND +C EXPLICIT SENSITIVITY ANALYSIS OF SYSTEMS DESCRIBED BY ORDINARY +C DIFFERENTIAL EQUATIONS, SUBMITTED TO ACM TRANS. MATH. SOFTWARE, +C (1985). +C +C 2. JORGE R. LEIS AND MARK A. KRAMER, ODESSA - AN ORDINARY +C DIFFERENTIAL EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS +C SENSITIVITY ANALYSIS, SUBMITTED TO ACM TRANS. MATH. SOFTWARE. +C (1985). +C +C 3. ALAN C. HINDMARSH, LSODE AND LSODI, TWO NEW INITIAL VALUE +C ORDINARY DIFFERENTIAL EQUATION SOLVERS, ACM-SIGNUM NEWSLETTER, +C VOL. 15, NO. 4 (1980), PP. 10-11. +C----------------------------------------------------------------------- +C THE FOLLOWING INTERNAL COMMON BLOCKS CONTAIN +C (A) VARIABLES WHICH ARE LOCAL TO ANY SUBROUTINE BUT WHOSE VALUES MUST +C BE PRESERVED BETWEEN CALLS TO THE ROUTINE (OWN VARIABLES), AND +C (B) VARIABLES WHICH ARE COMMUNICATED BETWEEN SUBROUTINES. +C THE STRUCTURE OF THE BLOCKS ARE AS FOLLOWS.. ALL REAL VARIABLES ARE +C LISTED FIRST, FOLLOWED BY ALL INTEGERS. WITHIN EACH TYPE, THE +C VARIABLES ARE GROUPED WITH THOSE LOCAL TO SUBROUTINE ODESSA FIRST, +C THEN THOSE LOCAL TO SUBROUTINE ODESSA_STODE, AND FINALLY THOSE USED +C FOR COMMUNICATION. THE BLOCKS ARE DECLARED IN SUBROUTINES ODESSA +C ODESSA_INTDY, ODESSA_STODE, ODESSA_STESA, ODESSA_PREPJ, ODESSA_PREPDF, +C AND ODESSA_SOLSY. GROUPS OF VARIABLES ARE REPLACED BY DUMMY ARRAYS IN +C THE COMMON DECLARATIONS IN ROUTINES WHERE THOSE VARIABLES ARE NOT USED. +C----------------------------------------------------------------------- + COMMON /ODE001/ TRET, ROWNS(173), + 1 TESCO(3,12), CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM, + 3 MXSTEP, MXHNIL, NHNIL, NTREP, NSLAST, NYH, IOWNS(4), + 4 IALTH, LMAX, ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, + 5 MITER, MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /ODE002/ DUPS, DSMS, DDNS, + 1 NPAR, LDFDP, LNRS, + 2 ISOPT, NSV, NDFE, NSPE, IDF, IERSP, JOPT, KFLAGS + PARAMETER (ZERO=0.0D0,ONE=1.0D0,TWO=2.0D0,FOUR=4.0D0) + 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 APPROPIATELY. +C IF ISTATE .GT. 1 BUT THE FLAG INIT SHOWS THAT INITIALIZATION HAS +C NOT YET BEEN DONE, AN ERROR RETURN OCCURS. +C IF ISTATE = 1 AND TOUT = T, JUMP TO BLOCK G AND RETURN IMMEDIATELY. +C----------------------------------------------------------------------- + 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) GO TO 430 + 20 NTREP = 0 +C----------------------------------------------------------------------- +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. +C +C FIRST CHECK LEGALITY OF THE NON-OPTIONAL INPUTS NEQ, ITOL, IOPT, +C MF, ML, AND MU. +C----------------------------------------------------------------------- + IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .NE. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + DO 26 I = 1,3 + 26 IF (IOPT(I) .LT. 0 .OR. IOPT(I) .GT. 1) GO TO 607 + ISOPT = IOPT(2) + IDF = IOPT(3) + NYH = N + NSV = 1 + 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 IF (ISOPT .EQ. 0) GO TO 32 +C CHECK LEGALITY OF THE NON-OPTIONAL INPUTS ISOPT, NPAR. +C COMPUTE NUMBER OF SOLUTION VECTORS AND TOTAL NUMBER OF EQUATIONS. + IF (NEQ(2) .LE. 0) GO TO 628 + IF (ISTATE .EQ. 1) GO TO 31 + IF (NEQ(2) .NE. NPAR) GO TO 629 + 31 NPAR = NEQ(2) + NSV = NPAR + 1 + NYH = NSV * N + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) GO TO 630 +C NEXT PROCESS AND CHECK THE OPTIONAL INPUTS. -------------------------- + 32 IF (IOPT(1) .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = ZERO + HMXI = ZERO + HMIN = ZERO + 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. ZERO) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. ZERO) GO TO 615 + HMXI = ZERO + IF (HMAX .GT. ZERO) HMXI = ONE/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. ZERO) GO TO 616 +C----------------------------------------------------------------------- +C SET WORK ARRAY POINTERS AND CHECK LENGTHS LRW AND LIW. +C POINTERS TO SEGMENTS OF RWORK AND IWORK ARE NAMED BY PREFIXING L TO +C 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 WORK SPACE FOR DFDP IS CONTAINED IN ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + 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 + NYH + LACOR = LSAVF + N + LDFDP = LACOR + N + LENRW = LACOR + NYH - 1 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) LENIW = 20 + LNRS = LENIW + LIWM + IF (ISOPT .EQ. 1) LENIW = LNRS + NPAR + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C CHECK RTOL AND ATOL FOR LEGALITY. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,NYH + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. ZERO) GO TO 619 + IF (ATOLI .LT. ZERO) GO TO 620 + 70 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C IF ISTATE = 3, SET FLAG TO SIGNAL PARAMETER CHANGES TO ODESSA_STODE. - + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C 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) = DSQRT(UROUND) + GO TO 200 +C----------------------------------------------------------------------- +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 THE INITIAL CALL TO ODESSA_SPRIME IF ISOPT = 1, +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 105 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. ZERO) GO TO 625 + IF (H0 .NE. ZERO .AND. (T + H0 - TCRIT)*H0 .GT. ZERO) + 1 H0 = TCRIT - T + 105 JSTART = 0 + IF (MITER .GT. 0) RWORK(LWM) = DSQRT(UROUND) + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = ZERO + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + IF (ISOPT .EQ. 1) MAXCOR = 4 + MSBP = 20 + MXNCF = 10 +C INITIAL CALL TO F. (LF0 POINTS TO YH(1,2) AND LOADS IN VALUES). + LF0 = LYH + NYH + CALL F (NEQ, T, Y, PAR, RWORK(LF0)) + NFE = 1 + DUPS = ZERO + DSMS = ZERO + DDNS = ZERO + NDFE = 0 + NSPE = 0 + IF (ISOPT .EQ. 0) GO TO 114 +C INITIALIZE COUNTS FOR REPEATED STEPS DUE TO SENSITIVITY ANALYSIS. + DO 110 J = 1,NSV + 110 IWORK(J + LNRS - 1) = 0 +C LOAD THE INITIAL VALUE VECTOR IN YH. --------------------------------- + 114 DO 115 I = 1,NYH + 115 RWORK(I+LYH-1) = Y(I) +C LOAD AND INVERT THE EWT ARRAY. (H IS TEMPORARILY SET TO ONE.) ------- + NQ = 1 + H = ONE + CALL ODESSA_EWSET (NYH, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,NYH + IF (RWORK(I+LEWT-1) .LE. ZERO) GO TO 621 + 120 RWORK(I+LEWT-1) = ONE/RWORK(I+LEWT-1) + IF (ISOPT .EQ. 0) GO TO 125 +C CALL ODESSA_SPRIME TO LOAD FIRST-ORDER SENSITIVITY DERIVATIVES INTO +C REMAINING YH(*,2) POSITIONS. + CALL ODESSA_SPRIME (NEQ, Y, RWORK(LYH), NYH, N, NSV, RWORK(LWM), + 1 IWORK(LIWM), RWORK(LEWT), RWORK(LF0), RWORK(LACOR), + 2 RWORK(LDFDP), PAR, F, JAC, DF, ODESSA_PREPJ, ODESSA_PREPDF) + IF (IERSP .EQ. -1) GO TO 631 + IF (IERSP .EQ. -2) GO TO 632 +C----------------------------------------------------------------------- +C THE CODING BELOW COMPUTES THE STEP SIZE, H0, TO BE ATTEMPTED ON THE +C 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, ADJUSTED +C SO AS TO BE BETWEEN 100*UROUND AND 1.0E-3. ONLY THE ORIGINAL +C SOLUTION VECTOR IS CONSIDERED IN THIS CALCULATION (ISOPT = 0 OR 1). +C THEN THE COMPUTED VALUE H0 IS GIVEN BY.. +C NEQ +C H0**2 = TOL / ( W0**-2 + (1/NEQ) * SUM ( F(I)/YWT(I) )**2 ) +C 1 +C 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----------------------------------------------------------------------- + 125 IF (H0 .NE. ZERO) GO TO 180 + TDIST = DABS(TOUT - T) + W0 = DMAX1(DABS(T),DABS(TOUT)) + IF (TDIST .LT. TWO*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = DMAX1(TOL,RTOL(I)) + 140 IF (TOL .GT. ZERO) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = DABS(Y(I)) + IF (AYI .NE. ZERO) TOL = DMAX1(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = DMAX1(TOL,100.0D0*UROUND) + TOL = DMIN1(TOL,0.001D0) + SUM = ODESSA_VNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = ONE/(TOL*W0*W0) + TOL*SUM**2 + H0 = ONE/DSQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = DSIGN(H0,TOUT-T) +C ADJUST H0 IF NECESSARY TO MEET HMAX BOUND. --------------------------- + 180 RH = DABS(H0)*HMXI + IF (RH .GT. ONE) H0 = H0/RH +C LOAD H WITH H0 AND SCALE YH(*,2) BY H0. ------------------------------ + H = H0 + DO 190 I = 1,NYH + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +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. ZERO) GO TO 250 + CALL ODESSA_INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(ONE + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. ZERO) GO TO 623 + IF ((TN - TOUT)*H .LT. ZERO) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. ZERO) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. ZERO) GO TO 625 + IF ((TN - TOUT)*H .LT. ZERO) GO TO 245 + CALL ODESSA_INTDY (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. ZERO) GO TO 624 + 245 HMX = DABS(TN) + DABS(H) + IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(ONE + FOUR*UROUND) + IF ((TNEXT - TCRIT)*H .LE. ZERO) GO TO 250 + H = (TCRIT - TN)*(ONE - FOUR*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C BLOCK E. +C THE NEXT BLOCK IS NORMALLY EXECUTED FOR ALL CALLS AND CONTAINS +C THE CALL TO THE ONE-STEP CORE INTEGRATOR ODESSA_STODE. +C +C THIS IS A LOOPING POINT FOR THE INTEGRATION STEPS. +C +C FIRST CHECK FOR TOO MANY STEPS BEING TAKEN, UPDATE EWT (IF NOT AT +C START OF PROBLEM), CHECK FOR TOO MUCH ACCURACY BEING REQUESTED, AND +C CHECK FOR H BELOW THE ROUNDOFF LEVEL IN T. +C TOLSF IS CALCULATED CONSIDERING ALL SOLUTION VECTORS. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL ODESSA_EWSET (NYH, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,NYH + IF (RWORK(I+LEWT-1) .LE. ZERO) GO TO 510 + 260 RWORK(I+LEWT-1) = ONE/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*ODESSA_VNORM (NYH, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. ONE) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF (ODESSA_ADDX(TN,H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + CALL XERRWD ('ODESSA - WARNING..INTERNAL T (=R1) AND H (=R2) ARE', + 1 50, 101, 1, 0, 0, 0, 0, ZERO, ZERO) + CALL XERRWD + 1 ('SUCH THAT IN THE MACHINE, T + H = T ON THE NEXT STEP', + 1 52, 101, 1, 0, 0, 0, 0, ZERO, ZERO) + CALL XERRWD ('(H = STEP SIZE). SOLVER WILL CONTINUE ANYWAY', + 1 44, 101, 1, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + CALL XERRWD ('ODESSA - ABOVE WARNING HAS BEEN ISSUED I1 TIMES.', + 1 48, 102, 1, 0, 0, 0, 0, ZERO, ZERO) + CALL XERRWD ('IT WILL NOT BE ISSUED AGAIN FOR THIS PROBLEM', + 1 44, 102, 1, 1, MXHNIL, 0, 0, ZERO,ZERO) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL ODESSA_STODE(NEQ,Y,YH,NYH,YH,WM,IWM,EWT,SAVF,ACOR,PAR,NRS, +C 1 F,JAC,DF,ODESSA_PREPJ,ODESSA_PREPDF,ODESSA_SOLSY) +C----------------------------------------------------------------------- + CALL ODESSA_STODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), + 1 RWORK(LWM), IWORK(LIWM), RWORK(LEWT), RWORK(LSAVF), + 2 RWORK(LACOR), PAR, IWORK(LNRS), F, JAC, DF, ODESSA_PREPJ, + 3 ODESSA_PREPDF, ODESSA_SOLSY) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 633), KGO +C----------------------------------------------------------------------- +C BLOCK F. +C THE FOLLOWING BLOCK HANDLES THE CASE OF A SUCCESSFUL RETURN FROM THE +C CORE INTEGRATOR (KFLAG = 0). TEST FOR STOP CONDITIONS. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. IF TOUT HAS BEEN REACHED, INTERPOLATE. ------------------- + 310 IF ((TN - TOUT)*H .LT. ZERO) GO TO 250 + CALL ODESSA_INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. JUMP TO EXIT IF TOUT WAS REACHED. ------------------------ + 330 IF ((TN - TOUT)*H .GE. ZERO) GO TO 400 + GO TO 250 +C ITASK = 4. SEE IF TOUT OR TCRIT WAS REACHED. ADJUST H IF NECESSARY. + 340 IF ((TN - TOUT)*H .LT. ZERO) GO TO 345 + CALL ODESSA_INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = DABS(TN) + DABS(H) + IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(ONE + FOUR*UROUND) + IF ((TNEXT - TCRIT)*H .LE. ZERO) GO TO 250 + H = (TCRIT - TN)*(ONE - FOUR*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. SEE IF TCRIT WAS REACHED AND JUMP TO EXIT. --------------- + 350 HMX = DABS(TN) + DABS(H) + IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C BLOCK G. +C THE FOLLOWING BLOCK HANDLES ALL SUCCESSFUL RETURNS FROM ODESSA. +C IF ITASK .NE. 1, Y IS LOADED FROM YH AND T IS SET ACCORDINGLY. +C ISTATE IS SET TO 2, THE ILLEGAL INPUT COUNTER IS ZEROED, AND THE +C OPTIONAL OUTPUTS ARE LOADED INTO THE WORK ARRAYS BEFORE RETURNING. +C IF ISTATE = 1 AND TOUT = T, THERE IS A RETURN WITH NO ACTION TAKEN, +C EXCEPT THAT IF THIS HAS HAPPENED REPEATEDLY, THE RUN IS TERMINATED. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,NYH + 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 + ILLIN = 0 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IF (ISOPT .EQ. 0) RETURN + IWORK(19) = NDFE + IWORK(20) = NSPE + RETURN + 430 NTREP = NTREP + 1 + IF (NTREP .LT. 5) RETURN + CALL XERRWD ('ODESSA -- REPEATED CALLS WITH ISTATE = 1 AND + 1 TOUT = T (=R1)', 59, 301, 1, 0, 0, 0, 1, T, ZERO) + GO TO 800 +C----------------------------------------------------------------------- +C BLOCK H. +C THE FOLLOWING BLOCK HANDLES ALL UNSUCCESSFUL RETURNS OTHER THAN +C 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, T IS SET TO TN, AND THE ILLEGAL INPUT +C COUNTER ILLIN IS SET TO 0. THE OPTIONAL OUTPUTS ARE LOADED INTO +C THE WORK ARRAYS BEFORE RETURNING. +C----------------------------------------------------------------------- +C THE MAXIMUM NUMBER OF STEPS WAS TAKEN BEFORE REACHING TOUT. ---------- + 500 CALL XERRWD ('ODESSA - AT CURRENT T (=R1), MXSTEP (=I1) STEPS', + 1 47, 201, 1, 0, 0, 0, 0, ZERO,ZERO) + CALL XERRWD ('TAKEN ON THIS CALL BEFORE REACHING TOUT', + 1 39, 201, 1, 1, MXSTEP, 0, 1, TN, ZERO) + ISTATE = -1 + GO TO 580 +C EWT(I) .LE. 0.0 FOR SOME I (NOT AT START OF PROBLEM). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + CALL XERRWD ('ODESSA - AT T (=R1), EWT(I1) HAS BECOME R2 .LE. 0.', + 1 50, 202, 1, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C TOO MUCH ACCURACY REQUESTED FOR MACHINE PRECISION. ------------------- + 520 CALL XERRWD ('ODESSA - AT T (=R1), TOO MUCH ACCURACY REQUESTED', + 1 48, 203, 1, 0, 0, 0, 0, ZERO,ZERO) + CALL XERRWD ('FOR PRECISION OF MACHINE.. SEE TOLSF (=R2)', + 1 43, 203, 1, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. ERROR TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ----- + 530 CALL XERRWD ('ODESSA - AT T(=R1) AND STEP SIZE H(=R2), THE ERROR', + 1 50, 204, 1, 0, 0, 0, 0, ZERO, ZERO) + CALL XERRWD ('TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN', + 1 44, 204, 1, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. CONVERGENCE FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ---- + 540 CALL XERRWD ('ODESSA - AT T (=R1) AND STEP SIZE H (=R2), THE', + 1 46, 205, 1, 0, 0, 0, 0, ZERO,ZERO) + CALL XERRWD ('CORRECTOR CONVERGENCE FAILED REPEATEDLY', + 1 39, 205, 1, 0, 0, 0, 0, ZERO,ZERO) + CALL XERRWD ('OR WITH ABS(H) = HMIN', + 1 21, 0, 1, 0, 0, 0, 2, TN, H) + ISTATE = -5 +C COMPUTE IMXER IF RELEVANT. ------------------------------------------- + 560 BIG = ZERO + IMXER = 1 + DO 570 I = 1,NYH + SIZE = DABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C SET Y VECTOR, T, ILLIN, AND OPTIONAL OUTPUTS. ------------------------ + 580 DO 590 I = 1,NYH + 590 Y(I) = RWORK(I+LYH-1) + T = TN + ILLIN = 0 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IF (ISOPT .EQ. 0) RETURN + IWORK(19) = NDFE + IWORK(20) = NSPE + RETURN +C----------------------------------------------------------------------- +C BLOCK I. +C THE FOLLOWING BLOCK HANDLES ALL ERROR RETURNS DUE TO ILLEGAL INPUT +C (ISTATE = -3), AS DETECTED BEFORE CALLING THE CORE INTEGRATOR. +C FIRST THE ERROR MESSAGE ROUTINE IS CALLED. THEN IF THERE HAVE BEEN +C 5 CONSECUTIVE SUCH RETURNS JUST BEFORE THIS CALL TO THE SOLVER, +C THE RUN IS HALTED. +C----------------------------------------------------------------------- + 601 CALL XERRWD ('ODESSA - ISTATE (=I1) ILLEGAL', + 1 29, 1, 1, 1, ISTATE, 0, 0, ZERO,ZERO) + GO TO 700 + 602 CALL XERRWD ('ODESSA - ITASK (=I1) ILLEGAL', + 1 28, 2, 1, 1, ITASK, 0, 0, ZERO,ZERO) + GO TO 700 + 603 CALL XERRWD ('ODESSA - ISTATE .GT. 1 BUT ODESSA NOT INITIALIZED', + 1 49, 3, 1, 0, 0, 0, 0, ZERO,ZERO) + GO TO 700 + 604 CALL XERRWD ('ODESSA - NEQ (=I1) .LT. 1', + 1 25, 4, 1, 1, NEQ(1), 0, 0, ZERO,ZERO) + GO TO 700 + 605 CALL XERRWD ('ODESSA - ISTATE = 3 AND NEQ CHANGED. (I1 TO I2)', + 1 48, 5, 1, 2, N, NEQ(1), 0, ZERO,ZERO) + GO TO 700 + 606 CALL XERRWD ('ODESSA - ITOL (=I1) ILLEGAL', + 1 27, 6, 1, 1, ITOL, 0, 0, ZERO,ZERO) + GO TO 700 + 607 CALL XERRWD ('ODESSA - IOPT (=I1) ILLEGAL', + 1 27, 7, 1, 1, IOPT, 0, 0, ZERO,ZERO) + GO TO 700 + 608 CALL XERRWD('ODESSA - MF (=I1) ILLEGAL', + 1 25, 8, 1, 1, MF, 0, 0, ZERO,ZERO) + GO TO 700 + 609 CALL XERRWD('ODESSA - ML (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', + 1 50, 9, 1, 2, ML, NEQ(1), 0, ZERO,ZERO) + GO TO 700 + 610 CALL XERRWD('ODESSA - MU (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', + 1 50, 10, 1, 2, MU, NEQ(1), 0, ZERO,ZERO) + GO TO 700 + 611 CALL XERRWD('ODESSA - MAXORD (=I1) .LT. 0', + 1 28, 11, 1, 1, MAXORD, 0, 0, ZERO,ZERO) + GO TO 700 + 612 CALL XERRWD('ODESSA - MXSTEP (=I1) .LT. 0', + 1 28, 12, 1, 1, MXSTEP, 0, 0, ZERO,ZERO) + GO TO 700 + 613 CALL XERRWD('ODESSA - MXHNIL (=I1) .LT. 0', + 1 28, 13, 1, 1, MXHNIL, 0, 0, ZERO,ZERO) + GO TO 700 + 614 CALL XERRWD('ODESSA - TOUT (=R1) BEHIND T (=R2)', + 1 34, 14, 1, 0, 0, 0, 2, TOUT, T) + CALL XERRWD('INTEGRATION DIRECTION IS GIVEN BY H0 (=R1)', + 1 42, 14, 1, 0, 0, 0, 1, H0, ZERO) + GO TO 700 + 615 CALL XERRWD('ODESSA - HMAX (=R1) .LT. 0.0', + 1 28, 15, 1, 0, 0, 0, 1, HMAX, ZERO) + GO TO 700 + 616 CALL XERRWD('ODESSA - HMIN (=R1) .LT. 0.0', + 1 28, 16, 1, 0, 0, 0, 1, HMIN, ZERO) + GO TO 700 + 617 CALL XERRWD('ODESSA - RWORK LENGTH NEEDED, LENRW (=I1), EXCEEDS + 1 LRW (=I2)', 60, 17, 1, 2, LENRW, LRW, 0, ZERO,ZERO) + GO TO 700 + 618 CALL XERRWD('ODESSA - IWORK LENGTH NEEDED, LENIW (=I1), EXCEEDS + 1 LIW (=I2)', 60, 18, 1, 2, LENIW, LIW, 0, ZERO,ZERO) + GO TO 700 + 619 CALL XERRWD('ODESSA - RTOL(I1) IS R1 .LT. 0.0', + 1 32, 19, 1, 1, I, 0, 1, RTOLI, ZREO) + GO TO 700 + 620 CALL XERRWD('ODESSA - ATOL(I1) IS R1 .LT. 0.0', + 1 32, 20, 1, 1, I, 0, 1, ATOLI, ZERO) + GO TO 700 +* + 621 EWTI = RWORK(LEWT+I-1) + CALL XERRWD('ODESSA - EWT(I1) IS R1 .LE. 0.0', + 1 31, 21, 1, 1, I, 0, 1, EWTI, ZERO) + GO TO 700 + 622 CALL XERRWD('ODESSA - TOUT (=R1) TOO CLOSE TO T(=R2) TO START + 1 INTEGRATION', 60, 22, 1, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 CALL XERRWD('ODESSA - ITASK = I1 AND TOUT (=R1) BEHIND TCUR - HU + 1 (= R2)', 58, 23, 1, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 CALL XERRWD('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TCUR + 1 (=R2)', 57, 24, 1, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 CALL XERRWD('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TOUT + 1 (=R2)', 57, 25, 1, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 CALL XERRWD('ODESSA - AT START OF PROBLEM, TOO MUCH ACCURACY', + 1 47, 26, 1, 0, 0, 0, 0, ZERO,ZERO) + CALL XERRWD('REQUESTED FOR PRECISION OF MACHINE. SEE TOLSF (=R1)', + 1 51, 26, 1, 0, 0, 0, 1, TOLSF, ZERO) + RWORK(14) = TOLSF + GO TO 700 + 627 CALL XERRWD + 1 ('ODESSA - TROUBLE FROM ODESSA_INTDY. ITASK = I1, TOUT = R1', + 1 57, 27, 1, 1, ITASK, 0, 1, TOUT, ZERO) + GO TO 700 +C ERROR STATEMENTS ASSOCIATED WITH SENSITIVITY ANALYSIS. + 628 CALL XERRWD('ODESSA - NPAR (=I1) .LT. 1', + 1 26, 28, 1, 1, NPAR, 0, 0, ZERO,ZERO) + GO TO 700 + 629 CALL XERRWD('ODESSA - ISTATE = 3 AND NPAR CHANGED (I1 TO I2)', + 1 47, 29, 1, 2, NP, NPAR, 0, ZERO,ZERO) + GO TO 700 + 630 CALL XERRWD('ODESSA - MITER (=I1) ILLEGAL', + 1 28, 30, 1, 1, MITER, 0, 0, ZERO,ZERO) + GO TO 700 + 631 CALL XERRWD('ODESSA - TROUBLE IN ODESSA_SPRIME (IERPJ)', + 1 41, 31, 1, 0, 0, 0, 0, ZERO,ZERO) + GO TO 700 + 632 CALL XERRWD('ODESSA - TROUBLE IN ODESSA_SPRIME (MITER)', + 1 41, 32, 1, 0, 0, 0, 0, ZERO,ZERO) + GO TO 700 + 633 CALL XERRWD('ODESSA - FATAL ERROR IN ODESSA_STODE (KFLAG = -3)', + 1 49, 33, 2, 0, 0, 0, 0, ZERO,ZERO) + GO TO 801 +C + 700 IF (ILLIN .EQ. 5) GO TO 710 + ILLIN = ILLIN + 1 + ISTATE = -3 + RETURN + 710 CALL XERRWD('ODESSA - REPEATED OCCURRENCES OF ILLEGAL INPUT', + 1 46, 302, 1, 0, 0, 0, 0, ZERO,ZERO) +C + 800 CALL XERRWD('ODESSA - RUN ABORTED.. APPARENT INFINITE LOOP', + 1 45, 303, 2, 0, 0, 0, 0, ZERO,ZERO) + RETURN + 801 CALL XERRWD('ODESSA - RUN ABORTED', + 1 20, 304, 2, 0, 0, 0, 0, ZERO,ZERO) + RETURN +C-------------------- END OF SUBROUTINE ODESSA ------------------------- + END
--- a/libcruft/odessa/odessa.f Fri Oct 31 15:11:45 2003 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1910 +0,0 @@ -C----------------------------------------------------------------------- -C----------------------------------------------------------------------- -C THIS IS THE SEPTEMBER 1, 1986 VERSION OF ODESSA.. -C AN ORDINARY DIFFERENTIAL EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS -C SENSITIVITY ANALYSIS. -C -C THIS PACKAGE IS A MODIFICATION OF THE AUGUST 13, 1981 VERSION OF -C LSODE.. LIVERMORE SOLVER FOR ORDINARY DIFFERENTIAL EQUATIONS. -C THIS VERSION IS IN DOUBLE PRECISION. -C -C ODESSA SOLVES FOR THE FIRST-ORDER SENSITIVITY COEFFICIENTS.. -C DY(I)/DP, FOR A SINGLE PARAMETER, OR, -C DY(I)/DP(J), FOR MULTIPLE PARAMETERS, -C ASSOCIATED WITH A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.. -C DY/DT = F(Y,T;P). -C----------------------------------------------------------------------- -C REFERENCES... -C -C 1. JORGE R. LEIS AND MARK A. KRAMER, THE SIMULTANEOUS SOLUTION AND -C EXPLICIT SENSITIVITY ANALYSIS OF SYSTEMS DESCRIBED BY ORDINARY -C DIFFERENTIAL EQUATIONS. SUBMITTED TO ACM TRANS. MATH. SOFTWARE, -C (1985). -C -C 2. JORGE R. LEIS AND MARK A. KRAMER, ODESSA - AN ORDINARY DIFFERENTIA -C EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS SENSITIVITY ANALYSIS. -C SUBMITTED TO ACM TRANS. MATH. SOFTWARE, (1985). -C -C 3. ALAN C. HINDMARSH, LSODE AND LSODI, TWO NEW INITIAL VALUE -C ORDINARY DIFFERENTIAL EQUATION SOLVERS, ACM-SIGNUM NEWSLETTER, -C VOL. 15, NO. 4 (1980), PP. 10-11. -C----------------------------------------------------------------------- -C PROBLEM STATEMENT.. -C -C THE ODESSA MODIFICATION OF THE LSODE PACKAGE PROVIDES THE OPTION TO -C CALCULATE FIRST-ORDER SENSITIVITY COEFFICIENTS FOR A SYSTEM OF STIFF -C OR NON-STIFF EXPLICIT ORDINARY DIFFERENTIAL EQUATIONS OF THE GENERAL -C FORM : -C -C DY/DT = F(Y,T;P) (1) -C -C WHERE Y IS AN N-DIMENSIONAL DEPENDENT VARIABLE VECTOR, T IS THE -C INDEPENDENT INTEGRATION VARIABLE, AND P IS AN NPAR-DIMENSIONAL -C CONSTANT VECTOR. THE GOVERNING EQUATIONS FOR THE FIRST-ORDER -C SENSITIVITY COEFFICIENTS ARE GIVEN BY : -C -C S'(T) = J(T)*S(T) + DF/DP (2) -C -C WHERE -C -C S(T) = DY(T)/DP (= SENSITIVITY FUNCTIONS) -C S'(T) = D(DY(T)/DP)/DT -C J(T) = DF(Y,T;P)/DY(T) (= JACOBIAN MATRIX) -C AND DF/DP = DF(Y,T;P)/DP (= INHOMOGENEITY MATRIX) -C -C SOLUTION OF EQUATIONS (1) AND (2) PROCEEDS SIMULTANEOUSLY VIA AN -C EXTENSION OF THE LSODE PACKAGE AS DESCRIBED IN [1]. -C---------------------------------------------------------------------- -C ACKNOWLEDGEMENT : THE FOLLOWING ODESSA PACKAGE DOCUMENTATION IS A -C MODIFICATION OF THE LSODE DOCUMENTATION WHICH -C ACCOMPANIES THE LSODE PACKAGE CODE. -C---------------------------------------------------------------------- -C SUMMARY OF USAGE. -C -C COMMUNICATION BETWEEN THE USER AND THE ODESSA PACKAGE, FOR NORMAL -C SITUATIONS, IS SUMMARIZED HERE. THIS SUMMARY DESCRIBES ONLY A SUBSET -C OF THE FULL SET OF OPTIONS AVAILABLE. SEE THE FULL DESCRIPTION FOR -C DETAILS, INCLUDING OPTIONAL COMMUNICATION, NONSTANDARD OPTIONS, -C AND INSTRUCTIONS FOR SPECIAL SITUATIONS. SEE ALSO THE EXAMPLE -C PROBLEM (WITH PROGRAM AND OUTPUT) FOLLOWING THIS SUMMARY. -C -C A. FIRST PROVIDE A SUBROUTINE OF THE FORM.. -C SUBROUTINE F (N, T, Y, PAR, YDOT) -C DOUBLE PRECISION T, Y, PAR, YDOT -C DIMENSION Y(N), YDOT(N), PAR(NPAR) -C WHICH SUPPLIES THE VECTOR FUNCTION F BY LOADING YDOT(I) WITH F(I). -C N IS THE NUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS IN THE -C ABOVE MODEL. NPAR IS THE NUMBER OF MODEL PARAMETERS FOR WHICH -C VECTOR SENSITIVITY FUNCTIONS ARE DESIRED. YOU ARE ALSO ENCOURAGED -C TO PROVIDE A SUBROUTINE OF THE FORM.. -C SUBROUTINE DF (N, T, Y, PAR, DFDP, JPAR) -C DOUBLE PRECISION T, Y, PAR, DFDP -C DIMENSION Y(N), PAR(NPAR), DFDP(N) -C GO TO (1,...,NPAR) JPAR -C 1 DFDP(1) = DF(1)/DP(1) -C . -C DFDP(I) = DF(I)/DP(1) -C . -C DFDP(N) = DF(N)/DP(1) -C RETURN -C 2 DFDP(1) = DF(1)/DP(2) -C . -C DFDP(I) = DF(I)/DP(2) -C . -C DFDP(N) = DF(N)/DP(2) -C RETURN -C . . -C . . -C RETURN -C NPAR DFDP(1) = DF(1)/DP(NPAR) -C . -C DFDP(I) = DF(I)/DP(NPAR) -C . -C DFDP(N) = DF(N)/DP(NPAR) -C RETURN -C END -C ONLY NONZERO ELEMENTS NEED BE LOADED. IF THIS IS NOT FEASIBLE, -C ODESSA WILL GENERATE THIS MATRIX INTERNALLY BY DIFFERENCE QUOTIENTS. -C -C B. NEXT DETERMINE (OR GUESS) WHETHER OR NOT THE PROBLEM IS STIFF. -C STIFFNESS OCCURS WHEN THE JACOBIAN MATRIX DF/DY HAS AN EIGENVALUE -C WHOSE REAL PART IS NEGATIVE AND LARGE IN MAGNITUDE, COMPARED TO THE -C RECIPROCAL OF THE T SPAN OF INTEREST. IF THE PROBLEM IS NONSTIFF, -C USE METH = 10. IF IT IS STIFF, USE METH = 20. THE USER IS REQUIRED -C TO INPUT THE METHOD FLAG MF = 10*METH + MITER. THERE ARE FOUR -C STANDARD CHOICES FOR MITER WHEN A SENSITIVITY ANALYSIS IS DESIRED, -C AND ODESSA REQUIRES THE JACOBIAN MATRIX IN SOME FORM. -C THIS MATRIX IS REGARDED EITHER AS FULL (MITER = 1 OR 2), -C OR BANDED (MITER = 4 OR 5). IN THE BANDED CASE, ODESSA REQUIRES TWO -C HALF-BANDWIDTH PARAMETERS ML AND MU. THESE ARE, RESPECTIVELY, THE -C WIDTHS OF THE LOWER AND UPPER PARTS OF THE BAND, EXCLUDING THE MAIN -C DIAGONAL. THUS THE BAND CONSISTS OF THE LOCATIONS (I,J) WITH -C I-ML .LE. J .LE. I+MU, AND THE FULL BANDWIDTH IS ML+MU+1. -C -C C. YOU ARE ENCOURAGED TO SUPPLY THE JACOBIAN DIRECTLY (MF = 11, 14, -C 21, OR 24), BUT IF THIS IS NOT FEASIBLE, ODESSA WILL COMPUTE IT -C INTERNALLY BY DIFFERENCE QUOTIENTS (MF = 12, 15, 22, OR 25). IF YOU -C ARE SUPPLYING THE JACOBIAN, PROVIDE A SUBROUTINE OF THE FORM.. -C SUBROUTINE JAC (NEQ, T, Y, PAR, ML, MU, PD, NROWPD) -C DOUBLE PRECISION T, Y, PAR, PD -C DIMENSION Y(N), PD(NROWPD,N), PAR(NPAR) -C WHICH SUPPLIES DF/DY BY LOADING PD AS FOLLOWS.. -C FOR A FULL JACOBIAN (MF = 11, OR 21), LOAD PD(I,J) WITH DF(I)/DY(J), -C THE PARTIAL DERIVATIVE OF F(I) WITH RESPECT TO Y(J). (IGNORE THE -C ML AND MU ARGUMENTS IN THIS CASE.) -C FOR A BANDED JACOBIAN (MF = 14, OR 24), LOAD PD(I-J+MU+1,J) WITH -C DF(I)/DY(J), I.E. LOAD THE DIAGONAL LINES OF DF/DY INTO THE ROWS OF -C PD FROM THE TOP DOWN. -C IN EITHER CASE, ONLY NONZERO ELEMENTS NEED BE LOADED. -C -C D. WRITE A MAIN PROGRAM WHICH CALLS SUBROUTINE ODESSA ONCE FOR -C EACH POINT AT WHICH ANSWERS ARE DESIRED. THIS SHOULD ALSO PROVIDE -C FOR POSSIBLE USE OF LOGICAL UNIT 6 FOR OUTPUT OF ERROR MESSAGES BY -C ODESSA. ON THE FIRST CALL TO ODESSA, SUPPLY ARGUMENTS AS FOLLOWS.. -C F = NAME OF SUBROUTINE FOR RIGHT-HAND SIDE VECTOR F (MODEL). -C THIS NAME MUST BE DECLARED EXTERNAL IN CALLING PROGRAM. -C DF = NAME OF SUBROUTINE FOR INHOMOGENEITY MATRIX DF/DP. -C IF USED (IDF = 1), THIS NAME MUST BE DECLARED EXTERNAL IN -C CALLING PROGRAM. IF NOT USED (IDF = 0), PASS A DUMMY NAME. -C N = NUMBER OF FIRST ORDER ODE-S IN MODEL; LOAD INTO NEQ(1). -C NPAR = NUMBER OF MODEL PARAMETERS OF INTEREST; LOAD INTO NEQ(2). -C Y = AN (N) BY (NPAR+1) REAL ARRAY OF INITIAL VALUES.. -C Y(I,1) , I = 1,N , CONTAIN THE STATE, OR MODEL, DEPENDENT -C VARIABLES, -C Y(I,J) , J = 2,NPAR , CONTAIN THE DEPENDENT SENSITIVITY -C COEFFICIENTS. -C PAR = A REAL ARRAY OF LENGTH NPAR CONTAINING MODEL PARAMETERS -C OF INTEREST. -C T = THE INITIAL VALUE OF THE INDEPENDENT VARIABLE. -C TOUT = FIRST POINT WHERE OUTPUT IS DESIRED (.NE. T). -C ITOL = 1, 2, 3, OR 4 ACCORDING AS RTOL, ATOL (BELOW) ARE SCALARS -C OR ARRAYS. -C RTOL = RELATIVE TOLERANCE PARAMETER (SCALAR OR (N) BY (NPAR+1) -C ARRAY). -C ATOL = ABSOLUTE TOLERANCE PARAMETER (SCALAR OR (N) BY (NPAR+1) -C ARRAY). -C THE ESTIMATED LOCAL ERROR IN Y(I,J) WILL BE CONTROLLED SO AS -C TO BE ROUGHLY LESS (IN MAGNITUDE) THAN -C EWT(I,J) = RTOL*ABS(Y(I,J)) + ATOL IF ITOL = 1, -C EWT(I,J) = RTOL*ABS(Y(I,J)) + ATOL(I,J) IF ITOL = 2, -C EWT(I,J) = RTOL(I,J)*ABS(Y(I,J) + ATOL IF ITOL = 3, OR -C EWT(I,J) = RTOL(I,J)*ABS(Y(I,J) + ATOL(I,J) IF ITOL = 4. -C THUS THE LOCAL ERROR TEST PASSES IF, IN EACH COMPONENT, -C EITHER THE ABSOLUTE ERROR IS LESS THAN ATOL (OR ATOL(I,J)), -C OR THE RELATIVE ERROR IS LESS THAN RTOL (OR RTOL(I,J)). -C USE RTOL = 0.0 FOR PURE ABSOLUTE ERROR CONTROL, AND -C USE ATOL = 0.0 FOR PURE RELATIVE ERROR CONTROL. -C CAUTION.. ACTUAL (GLOBAL) ERRORS MAY EXCEED THESE LOCAL -C TOLERANCES, SO CHOOSE THEM CONSERVATIVELY. -C ITASK = 1 FOR NORMAL COMPUTATION OF OUTPUT VALUES OF Y AT T = TOUT. -C ISTATE = INTEGER FLAG (INPUT AND OUTPUT). SET ISTATE = 1. -C IOPT = 0, TO INDICATE NO OPTIONAL INPUTS FOR INTEGRATION; -C LOAD INTO IOPT(1). -C ISOPT = 1, TO INDICATE SENSITIVITY ANALYSIS, = 0, TO INDICATE -C NO SENSITIVITY ANALYSIS; LOAD INTO IOPT(2). -C IDF = 1, IF SUBROUTINE DF (ABOVE) IS SUPPLIED BY THE USER, -C = 0, OTHERWISE; LOAD INTO IOPT(3). -C RWORK = REAL WORK ARRAY OF LENGTH AT LEAST.. -C 22 + 16*N + N**2 FOR MF = 11 OR 12, -C 22 + 17*N + (2*ML + MU)*N FOR MF = 14 OR 15, -C 22 + 9*N + N**2 FOR MF = 21 OR 22, -C 22 + 10*N + (2*ML + MU)*N FOR MF = 24 OR 25, -C IF ISOPT = 0, OR.. -C 22 + 15*(NPAR+1)*N + N**2 + N FOR MF = 11 OR 12, -C 24 + 15*(NPAR+1)*N + (2*ML+MU+2)*N + N FOR MF = 14 OR 15, -C 22 + 8*(NPAR+1)*N + N**2 + N FOR MF = 21 OR 22, -C 24 + 8*(NPAR+1)*N + (2*ML+MU+2)*N + N FOR MF = 24 OR 25, -C IF ISOPT = 1. -C LRW = DECLARED LENGTH OF RWORK (IN USER-S DIMENSION STATEMENT). -C IWORK = INTEGER WORK ARRAY OF LENGTH AT LEAST.. -C 20 + N IF ISOPT = 0, -C 21 + N + NPAR IF ISOPT = 1. -C IF MITER = 4 OR 5, INPUT IN IWORK(1),IWORK(2) THE LOWER -C AND UPPER HALF-BANDWIDTHS ML,MU (EXCLUDING MAIN DIAGONAL). -C LIW = DECLARED LENGTH OF IWORK (IN USER-S DIMENSION STATEMENT). -C JAC = NAME OF SUBROUTINE FOR JACOBIAN MATRIX. -C IF USED, THIS NAME MUST BE DECLARED EXTERNAL IN CALLING -C PROGRAM. IF NOT USED, PASS A DUMMY NAME. -C MF = METHOD FLAG. STANDARD VALUES FOR ISOPT = 0 ARE.. -C 10 FOR NONSTIFF (ADAMS) METHOD, NO JACOBIAN USED. -C 21 FOR STIFF (BDF) METHOD, USER-SUPPLIED FULL JACOBIAN. -C 22 FOR STIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. -C 24 FOR STIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. -C 25 FOR STIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. -C IF ISOPT = 1, MF = 10 IS ILLEGAL AND CAN BE REPLACED BY.. -C 11 FOR NONSTIFF METHOD, USER-SUPPLIED FULL JACOBIAN. -C 12 FOR NONSTIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. -C 14 FOR NONSTIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. -C 15 FOR NONSTIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. -C NOTE THAT THE MAIN PROGRAM MUST DECLARE ARRAYS Y, RWORK, IWORK, AND -C POSSIBLY ATOL AND RTOL, AS WELL AS NEQ, IOPT, AND PAR IF ISOPT = 1. -C -C E. THE OUTPUT FROM THE FIRST CALL (OR ANY CALL) IS.. -C Y = ARRAY OF COMPUTED VALUES OF Y(T) VECTOR. -C T = CORRESPONDING VALUE OF INDEPENDENT VARIABLE (NORMALLY TOUT). -C ISTATE = 2 IF ODESSA WAS SUCCESSFUL, NEGATIVE OTHERWISE. -C -1 MEANS EXCESS WORK DONE ON THIS CALL (PERHAPS WRONG MF). -C -2 MEANS EXCESS ACCURACY REQUESTED (TOLERANCES TOO SMALL). -C -3 MEANS ILLEGAL INPUT DETECTED (SEE PRINTED MESSAGE). -C -4 MEANS REPEATED ERROR TEST FAILURES (CHECK ALL INPUTS). -C -5 MEANS REPEATED CONVERGENCE FAILURES (PERHAPS BAD JACOBIAN -C SUPPLIED OR WRONG CHOICE OF MF OR TOLERANCES). -C -6 MEANS ERROR WEIGHT BECAME ZERO DURING PROBLEM. (SOLUTION -C COMPONENT I,J VANISHED, AND ATOL OR ATOL(I,J) = 0.0) -C -C F. TO CONTINUE THE INTEGRATION AFTER A SUCCESSFUL RETURN, SIMPLY -C RESET TOUT AND CALL ODESSA AGAIN. NO OTHER PARAMETERS NEED BE RESET. -C---------------------------------------------------------------------- -C EXAMPLE PROBLEM. -C -C THE FOLLOWING IS A SIMPLE EXAMPLE PROBLEM, WITH THE CODING -C NEEDED FOR ITS SOLUTION BY ODESSA. THE PROBLEM IS FROM CHEMICAL -C KINETICS, AND CONSISTS OF THE FOLLOWING THREE RATE EQUATIONS.. -C DY1/DT = -PAR(1)*Y1 + PAR(2)*Y2*Y3 ; PAR(1) = .04, PAR(2) = 1.E4 -C DY2/DT = PAR(1)*Y1 - PAR(2)*Y2*Y3 - PAR(3)*Y2**2 ; PAR(3) = 3.E7 -C DY3/DT = PAR(3)*Y2**2 -C ON THE INTERVAL FROM T = 0.0 TO T = 4.E10, WITH INITIAL CONDITIONS -C Y1 = 1.0, Y2 = Y3 = 0, AND S(I,J) = 0, I = 1,3, J = 1,3. -C THE PROBLEM IS STIFF. -C -C THE FOLLOWING CODING SOLVES THIS PROBLEM WITH ODESSA, USING -C MF = 21 AND PRINTING RESULTS AT T = .4, 4., ..., 4.E10. -C IT USES ITOL = 4 AND ATOL MUCH SMALLER FOR Y2 THAN Y1 OR Y3, -C BECAUSE Y2 HAS MUCH SMALLER VALUES. LESS STRINGENT TOLERANCES -C ARE ASSIGNED FOR THE SENSITIVITIES TO ACHIEVE GREATER EFFICIENCY. -C AT THE END OF THE RUN, STATISTICAL QUANTITIES OF INTEREST ARE -C PRINTED (SEE OPTIONAL OUTPUTS IN THE FULL DESCRIPTION BELOW). -C -C DOUBLE PRECISION ATOL, RWORK, RTOL, T, TOUT, Y, PAR -C EXTERNAL FEX, JEX, DFEX -C DIMENSION Y(3,4), PAR(3), ATOL(3,4), RTOL(3,4), RWORK(130), -C 1 IWORK(27), NEQ(2), IOPT(3) -C N = 3 -C NPAR = 3 -C NEQ(1) = N -C NEQ(2) = NPAR -C NSV = NPAR+1 -C DO 10 I = 1,N -C DO 10 J = 1,NSV -C 10 Y(I,J) = 0.0D0 -C Y(1,1) = 1.0D0 -C PAR(1) = 0.04D0 -C PAR(2) = 1.0D4 -C PAR(3) = 3.0D7 -C T = 0.D0 -C TOUT = .4D0 -C ITOL = 4 -C ATOL(1,1) = 1.D-6 -C ATOL(2,1) = 1.D-10 -C ATOL(3,1) = 1.D-6 -C DO 20 I = 1,N -C RTOL(I,1) = 1.D-4 -C DO 15 J = 2,NSV -C RTOL(I,J) = 1.D-3 -C 15 ATOL(I,J) = 1.D2 * ATOL(I,1) -C 20 CONTINUE -C ITASK = 1 -C ISTATE = 1 -C IOPT(1) = 0 -C IOPT(2) = 1 -C IOPT(3) = 1 -C LRW = 130 -C LIW = 27 -C MF = 21 -C DO 60 IOUT = 1,12 -C CALL ODESSA(FEX,DFEX,NEQ,Y,PAR,T,TOUT,ITOL,RTOL,ATOL, -C 1 ITASK,ISTATE, IOPT,RWORK,LRW,IWORK,LIW,JEX,MF) -C WRITE(6,30)T,Y(1,1),Y(2,1),Y(3,1) -C 30 FORMAT(1X,7H AT T =,E12.4,6H Y =,3E14.6) -C DO 50 J = 2,NSV -C JPAR = J-1 -C WRITE(6,40)JPAR,Y(1,J),Y(2,J),Y(3,J) -C 40 FORMAT(20X,2HS(,I1,3H) =,3E14.6) -C 50 CONTINUE -C IF (ISTATE .LT. 0) GO TO 80 -C 60 TOUT = TOUT*10.D0 -C WRITE(6,70)IWORK(11),IWORK(12),IWORK(13),IWORK(19) -C 70 FORMAT(1X,/,12H NO. STEPS =,I4,11H NO. F-S =,I4,11H NO. J-S =, -C 1 I4,12H NO. DF-S =,I4) -C STOP -C 80 WRITE(6,90)ISTATE -C 90 FORMAT(///22H ERROR HALT.. ISTATE =,I3) -C STOP -C END -C -C SUBROUTINE FEX (NEQ, T, Y, PAR, YDOT) -C DOUBLE PRECISION T, Y, YDOT, PAR -C DIMENSION Y(3), YDOT(3), PAR(3) -C YDOT(1) = -PAR(1)*Y(1) + PAR(2)*Y(2)*Y(3) -C YDOT(3) = PAR(3)*Y(2)*Y(2) -C YDOT(2) = -YDOT(1) - YDOT(3) -C RETURN -C END -C -C SUBROUTINE JEX (NEQ, T, Y, PAR, ML, MU, PD, NRPD) -C DOUBLE PRECISION PD, T, Y, PAR -C DIMENSION Y(3), PD(NRPD,3), PAR(3) -C PD(1,1) = -PAR(1) -C PD(1,2) = PAR(2)*Y(3) -C PD(1,3) = PAR(2)*Y(2) -C PD(2,1) = PAR(1) -C PD(2,3) = -PD(1,3) -C PD(3,2) = 2.D0*PAR(3)*Y(2) -C PD(2,2) = -PD(1,2) - PD(3,2) -C RETURN -C END -C -C SUBROUTINE DFEX (NEQ, T, Y, PAR, DFDP, JPAR) -C DOUBLE PRECISION T, Y, PAR, DFDP -C DIMENSION Y(3), PAR(3), DFDP(3) -C GO TO (1,2,3), JPAR -C 1 DFDP(1) = -Y(1) -C DFDP(2) = Y(1) -C RETURN -C 2 DFDP(1) = Y(2)*Y(3) -C DFDP(2) = -Y(2)*Y(3) -C RETURN -C 3 DFDP(2) = -Y(2)*Y(2) -C DFDP(3) = Y(2)*Y(2) -C RETURN -C END -C -C THE OUTPUT OF THIS PROGRAM (ON A DATA GENERAL MV-8000 IN -C DOUBLE PRECISION IS AS FOLLOWS: -C -C AT T = .4000E+00 Y = .985173E+00 .338641E-04 .147930E-01 -C S(1) = -.355914E+00 .390261E-03 .355524E+00 -C S(2) = .955150E-07 -.213065E-09 -.953019E-07 -C S(3) = -.158466E-10 -.529012E-12 .163756E-10 -C AT T = .4000E+01 Y = .905516E+00 .224044E-04 .944615E-01 -C S(1) = -.187621E+01 .179197E-03 .187603E+01 -C S(2) = .296093E-05 -.583104E-09 -.296034E-05 -C S(3) = -.493267E-09 -.276246E-12 .493544E-09 -C AT T = .4000E+02 Y = .715848E+00 .918628E-05 .284143E+00 -C S(1) = -.424730E+01 .459360E-04 .424726E+01 -C S(2) = .137294E-04 -.235815E-09 -.137291E-04 -C S(3) = -.228818E-08 -.113803E-12 .228829E-08 -C AT T = .4000E+03 Y = .450526E+00 .322299E-05 .549471E+00 -C S(1) = -.595837E+01 .354310E-05 .595836E+01 -C S(2) = .227380E-04 -.226041E-10 -.227380E-04 -C S(3) = -.378971E-08 -.499501E-13 .378976E-08 -C AT T = .4000E+04 Y = .183185E+00 .894131E-06 .816814E+00 -C S(1) = -.475006E+01 -.599504E-05 .475007E+01 -C S(2) = .188089E-04 .231330E-10 -.188089E-04 -C S(3) = -.313478E-08 -.187575E-13 .313480E-08 -C AT T = .4000E+05 Y = .389733E-01 .162133E-06 .961027E+00 -C S(1) = -.157477E+01 -.276199E-05 .157477E+01 -C S(2) = .628668E-05 .110026E-10 -.628670E-05 -C S(3) = -.104776E-08 -.453588E-14 .104776E-08 -C AT T = .4000E+06 Y = .493609E-02 .198411E-07 .995064E+00 -C S(1) = -.236244E+00 -.458262E-06 .236244E+00 -C S(2) = .944669E-06 .183193E-11 -.944671E-06 -C S(3) = -.157441E-09 -.635990E-15 .157442E-09 -C AT T = .4000E+07 Y = .516087E-03 .206540E-08 .999484E+00 -C S(1) = -.256277E-01 -.509808E-07 .256278E-01 -C S(2) = .102506E-06 .203905E-12 -.102506E-06 -C S(3) = -.170825E-10 -.684002E-16 .170826E-10 -C AT T = .4000E+08 Y = .519314E-04 .207736E-09 .999948E+00 -C S(1) = -.259316E-02 -.518029E-08 .259316E-02 -C S(2) = .103726E-07 .207209E-13 -.103726E-07 -C S(3) = -.172845E-11 -.691450E-17 .172845E-11 -C AT T = .4000E+09 Y = .544710E-05 .217885E-10 .999995E+00 -C S(1) = -.271637E-03 -.541849E-09 .271638E-03 -C S(2) = .108655E-08 .216739E-14 -.108655E-08 -C S(3) = -.180902E-12 -.723615E-18 .180902E-12 -C AT T = .4000E+10 Y = .446748E-06 .178699E-11 .100000E+01 -C S(1) = -.322322E-04 -.842541E-10 .322323E-04 -C S(2) = .128929E-09 .337016E-15 -.128929E-09 -C S(3) = -.209715E-13 -.838859E-19 .209715E-13 -C AT T = .4000E+11 Y = -.363960E-07 -.145584E-12 .100000E+01 -C S(1) = -.164109E-06 -.429604E-11 .164113E-06 -C S(2) = .656436E-12 .171842E-16 -.656451E-12 -C S(3) = -.689361E-15 -.275745E-20 .689363E-15 -C -C NO. STEPS = 340 NO. F-S = 412 NO. J-S = 343 NO. DF-S =1023 -C---------------------------------------------------------------------- -C FULL DESCRIPTION OF USER INTERFACE TO ODESSA. -C -C THE USER INTERFACE TO ODESSA CONSISTS OF THE FOLLOWING PARTS. -C -C I. THE CALL SEQUENCE TO SUBROUTINE ODESSA, WHICH IS A DRIVER -C ROUTINE FOR THE SOLVER. THIS INCLUDES DESCRIPTIONS OF BOTH -C THE CALL SEQUENCE ARGUMENTS AND OF USER-SUPPLIED ROUTINES. -C FOLLOWING THESE DESCRIPTIONS IS A DESCRIPTION OF -C OPTIONAL INPUTS AVAILABLE THROUGH THE CALL SEQUENCE, AND THEN -C A DESCRIPTION OF OPTIONAL OUTPUTS (IN THE WORK ARRAYS). -C -C II. DESCRIPTIONS OF OTHER ROUTINES IN THE ODESSA PACKAGE THAT MAY -C BE (OPTIONALLY) CALLED BY THE USER. THESE PROVIDE THE ABILITY -C TO ALTER ERROR MESSAGE HANDLING, SAVE AND RESTORE THE INTERNAL -C COMMON, AND OBTAIN SPECIFIED DERIVATIVES OF THE SOLUTION Y(T). -C -C III. DESCRIPTIONS OF COMMON BLOCKS TO BE DECLARED IN OVERLAY -C OR SIMILAR ENVIRONMENTS, OR TO BE SAVED WHEN DOING AN INTERRUPT -C OF THE PROBLEM AND CONTINUED SOLUTION LATER. -C -C IV. DESCRIPTION OF TWO SUBROUTINES IN THE ODESSA PACKAGE, EITHER OF -C WHICH THE USER MAY REPLACE WITH HIS OWN VERSION, IF DESIRED. -C THESE RELATE TO THE MEASUREMENT OF ERRORS. -C -C V. GENERAL REMARKS WHICH HIGHLIGHT DIFFERENCES BETWEEN THE LSODE -C PACKAGE AND THE ODESSA PACKAGE. -C---------------------------------------------------------------------- -C PART I. CALL SEQUENCE. -C -C THE CALL SEQUENCE PARAMETERS USED FOR INPUT ONLY ARE.. -C F, DF, NEQ, PAR, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, -C JAC, MF, -C AND THOSE USED FOR BOTH INPUT AND OUTPUT ARE -C Y, T, ISTATE. -C THE WORK ARRAYS RWORK AND IWORK ARE ALSO USED FOR CONDITIONAL AND -C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. (THE TERM OUTPUT HERE REFERS -C TO THE RETURN FROM SUBROUTINE ODESSA TO THE USER-S CALLING 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 -C ODE MODEL. THIS SYSTEM MUST BE PUT IN THE FIRST-ORDER -C FORM DY/DT = F(Y,T;P), WHERE F IS A VECTOR-VALUED FUNCTION -C OF THE SCALAR T AND VECTORS Y, AND PAR. SUBROUTINE F IS TO -C COMPUTE THE FUNCTION F. IT IS TO HAVE THE FORM.. -C SUBROUTINE F (NEQ, T, Y, PAR, YDOT) -C DOUBLE PRECISION T, Y, PAR, YDOT -C DIMENSION Y(1), PAR(1), YDOT(1) -C WHERE NEQ, T, Y, AND PAR ARE INPUT, AND YDOT = F(Y,T;P) -C IS OUTPUT. Y AND YDOT ARE ARRAYS OF LENGTH N (= NEQ(1)). -C (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY -C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) -C F SHOULD NOT ALTER ARRAY Y, OR PAR(1),...,PAR(NPAR). -C F MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. -C -C SUBROUTINE F MAY ACCESS USER-DEFINED QUANTITIES IN -C NEQ(2),... AND PAR(NPAR+1),... IF NEQ IS AN ARRAY -C (DIMENSIONED IN F) AND PAR HAS LENGTH EXCEEDING NPAR. -C SEE THE DESCRIPTIONS OF NEQ AND PAR BELOW. -C -C DF = THE NAME OF THE USER-SUPPLIED ROUTINE (IDF = 1) TO COMPUTE -C THE INHOMOGENEITY MATRIX, DF/DP, AS A FUNCTION OF THE SCALAR -C T, AND THE VECTORS Y, AND PAR. IT IS TO HAVE THE FORM -C SUBROUTINE DF (NEQ, T, Y, PAR, DFDP, JPAR) -C DOUBLE PRECISION T, Y, PAR, DFDP -C DIMENSION Y(1), PAR(1), DFDP(1) -C GO TO (1,2,...,NPAR) JPAR -C 1 DFDP(1) = DF(1)/DP(1) -C . -C DFDP(I) = DF(I)/DP(1) -C . -C DFDP(N) = DF(N)/DP(1) -C RETURN -C 2 DFDP(1) = DF(1)/DP(2) -C . -C DFDP(I) = DF(I)/DP(2) -C . -C DFDP(N) = DF(N)/DP(2) -C . -C RETURN -C . . -C . . -C NPAR DFDP(1) = DF(1)/DP(NPAR) -C . -C DFDP(I) = DF(I)/DP(NPAR) -C . -C DFDP(N) = DF(N)/DP(NPAR) -C RETURN -C END -C WHERE NEQ, T, Y, PAR, AND JPAR ARE INPUT AND THE VECTOR -C DFDP(*,JPAR) IS TO BE LOADED WITH THE PARTIAL DERIVATIVES -C DF(Y,T;PAR)/DP(JPAR) ON OUTPUT. ONLY NONZERO ELEMENTS NEED -C BE LOADED. T, Y, AND PAR HAVE THE SAME MEANING AS IN -C SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY -C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE). -C -C DFDP(*,JPAR) IS PRESET TO ZERO BY THE SOLVER, SO THAT ONLY -C THE NONZERO ELEMENTS NEED BE LOADED BY DF. SUBROUTINE DF -C MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM IF USED. -C IF IDF = 0 (OR ISOPT = 0), A DUMMY ARGUMENT CAN BE USED. -C -C SUBROUTINE DF MAY ACCESS USER-DEFINED QUANTITIES IN -C NEQ(2),... AND PAR(NPAR+1),... IF NEQ IS AN ARRAY -C (DIMENSIONED IN DF) AND PAR HAS A LENGTH EXCEEDING NPAR. -C SEE THE DESCRIPTIONS OF NEQ AND PAR (BELOW). -C -C NEQ = THE SIZE OF THE ODE SYSTEM (NUMBER OF FIRST ORDER ORDINARY -C DIFFERENTIAL EQUATIONS (N) IN THE MODEL). USED ONLY FOR -C INPUT. NEQ MAY NOT BE CHANGED DURING THE PROBLEM. -C -C FOR ISOPT = 0, NEQ IS NORMALLY A SCALAR. HOWEVER, NEQ MAY -C BE AN ARRAY, WITH NEQ(1) SET TO THE SYSTEM SIZE (N), IN WHICH -C CASE THE ODESSA PACKAGE ACCESSES ONLY NEQ(1). HOWEVER, -C THIS PARAMETER IS PASSED AS THE NEQ ARGUMENT IN ALL CALLS -C TO F, DF, AND JAC. HENCE, IF IT IS AN ARRAY, LOCATIONS -C NEQ(2),... MAY BE USED TO STORE OTHER INTEGER DATA AND PASS -C IT TO F, DF, AND/OR JAC. FOR ISOPT = 1, NPAR MUST BE LOADED -C INTO NEQ(2), AND IS NOT ALLOWED TO CHANGE DURING THE PROBLEM. -C IN THESE CASES, SUBROUTINES F, DF, AND/OR JAC MUST INCLUDE -C NEQ IN A DIMENSION STATEMENT. -C -C Y = A REAL ARRAY FOR THE VECTOR OF DEPENDENT VARIABLES, OF -C DIMENSION (N) BY (NPAR+1). USED FOR BOTH INPUT AND -C OUTPUT ON THE FIRST CALL (ISTATE = 1), AND ONLY FOR -C OUTPUT ON OTHER CALLS. ON THE FIRST CALL, Y MUST CONTAIN -C THE VECTORS OF INITIAL VALUES. ON OUTPUT, Y CONTAINS THE -C COMPUTED SOLUTION VECTORS, EVALUATED AT T. -C -C PAR = A REAL ARRAY FOR THE VECTOR OF CONSTANT MODEL PARAMETERS -C OF INTEREST IN THE SENSITIVITY ANALYSIS, OF LENGTH NPAR -C OR MORE. PAR IS PASSED AS AN ARGUMENT IN ALL CALLS TO F, -C DF, AND JAC. HENCE LOCATIONS PAR(NPAR+1),... MAY BE USED -C TO STORE OTHER REAL DATA AND PASS IT TO F, DF, AND/OR JAC. -C LOCATIONS PAR(1),...,PAR(NPAR) ARE USED AS INPUT ONLY, -C AND MUST NOT BE CHANGED DURING THE PROBLEM. -C -C T = THE INDEPENDENT VARIABLE. ON INPUT, T IS USED ONLY ON THE -C 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 TOUT). -C ON AN ERROR RETURN, T IS THE FARTHEST POINT REACHED. -C -C TOUT = THE NEXT VALUE OF T AT WHICH A COMPUTED SOLUTION IS DESIRED. -C USED ONLY FOR INPUT. -C -C WHEN STARTING THE PROBLEM (ISTATE = 1), TOUT MAY BE EQUAL -C TO T FOR ONE CALL, THEN SHOULD .NE. T FOR THE NEXT CALL. -C FOR THE INITIAL T, AN INPUT VALUE OF TOUT .NE. T IS USED -C IN ORDER TO DETERMINE THE DIRECTION OF THE INTEGRATION -C (I.E. THE ALGEBRAIC SIGN OF THE STEP SIZES) AND THE ROUGH -C SCALE OF THE PROBLEM. INTEGRATION IN EITHER DIRECTION -C (FORWARD OR BACKWARD IN T) IS PERMITTED. -C -C IF ITASK = 2 OR 5 (ONE-STEP MODES), TOUT IS IGNORED AFTER -C THE FIRST CALL (I.E. THE FIRST CALL WITH TOUT .NE. T). -C 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 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 SPACE (N) BY (NPAR+1). SEE DESCRIPTION BELOW -C UNDER ATOL. INPUT ONLY. -C -C ATOL = AN ABSOLUTE ERROR TOLERANCE PARAMETER, EITHER A SCALAR OR -C AN ARRAY OF SPACE (N) BY (NPAR+1). INPUT ONLY. -C -C THE INPUT PARAMETERS ITOL, RTOL, AND ATOL DETERMINE -C THE ERROR CONTROL PERFORMED BY THE SOLVER. THE SOLVER WILL -C CONTROL THE VECTOR E = (E(I,J)) OF ESTIMATED LOCAL ERRORS -C IN Y, ACCORDING TO AN INEQUALITY OF THE FORM -C RMS-NORM OF ( E(I,J)/EWT(I,J) ) .LE. 1, -C WHERE EWT(I,J) = RTOL(I,J)*ABS(Y(I,J)) + ATOL(I,J), -C AND THE RMS-NORM (ROOT-MEAN-SQUARE NORM) HERE IS -C RMS-NORM(V) = SQRT ( (1/N) * SUM (V(I,J)**2) ); I =1,...,N. -C HERE EWT = (EWT(I,J)) IS A VECTOR OF WEIGHTS WHICH MUST -C ALWAYS BE POSITIVE, AND THE VALUES OF RTOL AND ATOL SHOULD -C ALL BE NON-NEGATIVE. THE FOLLOWING TABLE GIVES THE TYPES -C (SCALAR/ARRAY) OF RTOL AND ATOL, AND THE CORRESPONDING FORM -C OF EWT(I,J). -C -C ITOL RTOL ATOL EWT(I,J) -C 1 SCALAR SCALAR RTOL*ABS(Y(I,J)) + ATOL -C 2 SCALAR ARRAY RTOL*ABS(Y(I,J)) + ATOL(I,J) -C 3 ARRAY SCALAR RTOL(I,J)*ABS(Y(I,J)) + ATOL -C 4 ARRAY ARRAY RTOL(I,J)*ABS(Y(I,J)) + ATOL(I,J) -C -C WHEN EITHER OF THESE PARAMETERS IS A SCALAR, IT NEED NOT -C BE DIMENSIONED IN THE USER-S CALLING PROGRAM. -C -C THE TOTAL NUMBER OF ERROR TEST FAILURES DUE TO THE SENSITIVITY -C ANALYSIS, AND WHICH REQUIRE AN INTEGRATION STEP TO BE -C REPEATED, ARE ACCUMULATED IN THE LAST NPAR+1 LOCATIONS OF THE -C INTEGER WORK ARRAY IWORK (SEE OPTIONAL OUTPUTS BELOW). -C THIS INFORMATION MAY BE OF VALUE IN DETERMINING APPROPRIATE -C ERROR TOLERANCES TO BE APPLIED TO THE SENSITIVITY FUNCTIONS. -C -C IF NONE OF THE ABOVE CHOICES (WITH ITOL, RTOL, AND ATOL -C FIXED THROUGHOUT THE PROBLEM) IS SUITABLE, MORE GENERAL -C ERROR CONTROLS CAN BE OBTAINED BY SUBSTITUTING -C USER-SUPPLIED ROUTINES FOR THE SETTING OF EWT AND/OR FOR -C THE NORM CALCULATION. SEE PART IV BELOW. -C -C IF GLOBAL ERRORS ARE TO BE ESTIMATED BY MAKING A REPEATED -C RUN ON THE SAME PROBLEM WITH SMALLER TOLERANCES, THEN ALL -C COMPONENTS OF RTOL AND ATOL (I.E. OF EWT) SHOULD BE SCALED -C DOWN UNIFORMLY. -C -C ITASK = AN INDEX SPECIFYING THE TASK TO BE PERFORMED. -C INPUT ONLY. ITASK HAS THE FOLLOWING VALUES AND MEANINGS. -C 1 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT -C T = TOUT (BY OVERSHOOTING AND INTERPOLATING). -C 2 MEANS TAKE ONE STEP ONLY AND RETURN. -C 3 MEANS STOP AT THE FIRST INTERNAL MESH POINT AT OR -C BEYOND T = TOUT AND RETURN. -C 4 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT -C T = TOUT BUT WITHOUT OVERSHOOTING T = TCRIT. -C TCRIT MUST BE INPUT AS RWORK(1). TCRIT MAY BE EQUAL TO -C OR BEYOND TOUT, BUT NOT BEHIND IT IN THE DIRECTION OF -C INTEGRATION. THIS OPTION IS USEFUL IF THE PROBLEM -C HAS A SINGULARITY AT OR BEYOND T = TCRIT. -C 5 MEANS TAKE ONE STEP, WITHOUT PASSING TCRIT, AND RETURN. -C TCRIT MUST BE INPUT AS RWORK(1). -C -C NOTE.. IF ITASK = 4 OR 5 AND THE SOLVER REACHES TCRIT -C (WITHIN ROUNDOFF), IT WILL RETURN T = TCRIT (EXACTLY) TO -C INDICATE THIS (UNLESS ITASK = 4 AND TOUT COMES BEFORE TCRIT, -C IN WHICH CASE ANSWERS AT T = TOUT ARE RETURNED FIRST). -C -C ISTATE = AN INDEX USED FOR INPUT AND OUTPUT TO SPECIFY THE -C THE STATE OF THE CALCULATION. -C -C ON INPUT, THE VALUES OF ISTATE ARE AS FOLLOWS. -C 1 MEANS THIS IS THE FIRST CALL FOR THE PROBLEM -C (INITIALIZATIONS WILL BE DONE). SEE NOTE BELOW. -C 2 MEANS THIS IS NOT THE FIRST CALL, AND THE CALCULATION -C IS TO CONTINUE NORMALLY, WITH NO CHANGE IN ANY INPUT -C PARAMETERS EXCEPT POSSIBLY TOUT AND ITASK. -C (IF ITOL, RTOL, AND/OR ATOL ARE CHANGED BETWEEN CALLS -C WITH ISTATE = 2, THE NEW VALUES WILL BE USED BUT NOT -C TESTED FOR LEGALITY.) -C 3 MEANS THIS IS NOT THE FIRST CALL, AND THE -C CALCULATION IS TO CONTINUE NORMALLY, BUT WITH -C A CHANGE IN INPUT PARAMETERS OTHER THAN -C TOUT AND ITASK. CHANGES ARE ALLOWED IN -C ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, ML, MU, -C AND ANY OF THE OPTIONAL INPUTS EXCEPT H0. -C (SEE IWORK DESCRIPTION FOR ML AND MU.) -C NOTE.. A PRELIMINARY CALL WITH TOUT = T IS NOT COUNTED -C AS A FIRST CALL HERE, AS NO INITIALIZATION OR CHECKING OF -C INPUT IS DONE. (SUCH A CALL IS SOMETIMES USEFUL FOR THE -C PURPOSE OF OUTPUTTING THE INITIAL CONDITIONS.) -C THUS THE FIRST CALL FOR WHICH TOUT .NE. T REQUIRES -C ISTATE = 1 ON INPUT. -C -C ON OUTPUT, ISTATE HAS THE FOLLOWING VALUES AND MEANINGS. -C 1 MEANS NOTHING WAS DONE, AS TOUT WAS EQUAL TO T WITH -C ISTATE = 1 ON INPUT. (HOWEVER, AN INTERNAL COUNTER WAS -C SET TO DETECT AND PREVENT REPEATED CALLS OF THIS TYPE.) -C 2 MEANS THE INTEGRATION WAS PERFORMED SUCCESSFULLY. -C -1 MEANS AN EXCESSIVE AMOUNT OF WORK (MORE THAN MXSTEP -C STEPS) WAS DONE ON THIS CALL, BEFORE COMPLETING THE -C REQUESTED TASK, BUT THE INTEGRATION WAS OTHERWISE -C SUCCESSFUL AS FAR AS T. (MXSTEP IS AN OPTIONAL INPUT -C AND IS NORMALLY 500.) TO CONTINUE, THE USER MAY -C SIMPLY RESET ISTATE TO A VALUE .GT. 1 AND CALL AGAIN -C (THE EXCESS WORK STEP COUNTER WILL BE RESET TO 0). -C IN ADDITION, THE USER MAY INCREASE MXSTEP TO AVOID -C THIS ERROR RETURN (SEE BELOW ON OPTIONAL INPUTS). -C -2 MEANS TOO MUCH ACCURACY WAS REQUESTED FOR THE PRECISION -C OF THE MACHINE BEING USED. THIS WAS DETECTED BEFORE -C COMPLETING THE REQUESTED TASK, BUT THE INTEGRATION -C WAS SUCCESSFUL AS FAR AS T. TO CONTINUE, THE TOLERANCE -C PARAMETERS MUST BE RESET, AND ISTATE MUST BE SET -C TO 3. THE OPTIONAL OUTPUT TOLSF MAY BE USED FOR THIS -C PURPOSE. (NOTE.. IF THIS CONDITION IS DETECTED BEFORE -C TAKING ANY STEPS, THEN AN ILLEGAL INPUT RETURN -C (ISTATE = -3) OCCURS INSTEAD.) -C -3 MEANS ILLEGAL INPUT WAS DETECTED, BEFORE TAKING ANY -C INTEGRATION STEPS. SEE WRITTEN MESSAGE FOR DETAILS. -C NOTE.. IF THE SOLVER DETECTS AN INFINITE LOOP OF CALLS -C TO THE SOLVER WITH ILLEGAL INPUT, IT WILL CAUSE -C THE RUN TO STOP. -C -4 MEANS THERE WERE REPEATED ERROR TEST FAILURES ON -C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED -C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. -C THE PROBLEM MAY HAVE A SINGULARITY, OR THE INPUT -C MAY BE INAPPROPRIATE. -C -5 MEANS THERE WERE REPEATED CONVERGENCE TEST FAILURES ON -C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED -C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. -C THIS MAY BE CAUSED BY AN INACCURATE JACOBIAN MATRIX, -C IF ONE IS BEING USED. -C -6 MEANS EWT(I,J) BECAME ZERO FOR SOME I,J DURING THE -C INTEGRATION. PURE RELATIVE ERROR CONTROL (ATOL(I,J)=0.0) -C WAS REQUESTED ON A VARIABLE WHICH HAS NOW VANISHED. -C THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. -C -C NOTE.. SINCE THE NORMAL OUTPUT VALUE OF ISTATE IS 2, -C IT DOES NOT NEED TO BE RESET FOR NORMAL CONTINUATION. -C ALSO, SINCE A NEGATIVE INPUT VALUE OF ISTATE WILL BE -C REGARDED AS ILLEGAL, A NEGATIVE OUTPUT VALUE REQUIRES THE -C USER TO CHANGE IT, AND POSSIBLY OTHER INPUTS, BEFORE -C CALLING THE SOLVER AGAIN. -C -C IOPT = AN INTEGER ARRAY FLAG TO SPECIFY WHETHER OR NOT ANY OPTIONAL -C INPUTS ARE BEING USED ON THIS CALL. INPUT ONLY. -C THE OPTIONAL INPUTS ARE LISTED SEPARATELY BELOW. -C IOPT(1) = 0 MEANS NO OPTIONAL INPUTS FOR THE SOLVER WILL BE -C USED. DEFAULT VALUES WILL BE USED IN ALL CASES. -C = 1 MEANS ONE OR MORE OPTIONAL INPUTS FOR THE -C SOLVER ARE BEING USED. -C NOTE : IOPT(1) IS INDEPENDENT OF ISOPT AND IDF. -C IOPT(2) = 0 MEANS NO SENSITIVITY ANALYSIS WILL BE PERFORMED. -C = 1 MEANS A SENSITIVITY ANALYSIS WILL BE PERFORMED. -C NOTE : IOPT(2) IS RENAMED TO ISOPT IN ODESSA. -C = 0 MEANS DF/DP WILL BE CALCULATED BY FINITE -C DIFFERENCE WITHIN ODESSA. -C IOPT(3) = 1 MEANS DF/DP WILL BE CALCULATED BY A USER-SUPPLIED -C ROUTINE. -C NOTE : IOPT(3) IS RENAMED TO IDF IN ODESSA. -C IF IDF = 1, THE USER MUST SUPPLY A -C SUBROUTINE DF (THE NAME IS ARBITRARY) AS -C DESCRIBED BELOW UNDER DF. FOR IDF = 0, -C A DUMMY ARGUMENT CAN BE USED. -C -C RWORK = A REAL WORKING ARRAY (DOUBLE PRECISION). -C FOR ISOPT = 0, THE LENGTH OF RWORK MUST BE AT LEAST.. -C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM -C FOR ISOPT = 1, THE LENGTH OF RWORK MUST BE AT LEAST.. -C 20 + NYH*(MAXORD + 1) + 2*NYH + LWM + N -C WHERE.. -C NYH = THE TOTAL NUMBER OF DEPENDENT VARIABLES; -C (= N IF ISOPT = 0, AND N*(NPAR+1) IF ISOPT = 1). -C MAXORD = 12 (IF METH = 1) OR 5 (IF METH = 2) (UNLESS A -C SMALLER VALUE IS GIVEN AS AN OPTIONAL INPUT), -C LWM = 0 IF MITER = 0, -C LWM = N**2 + 2 IF MITER IS 1 OR 2, -C LWM = N + 2 IF MITER = 3, AND -C LWM = (2*ML+MU+1)*N + 2 IF MITER IS 4 OR 5. -C (SEE THE MF DESCRIPTION FOR METH AND MITER.) -C -C THE FIRST 20 WORDS OF RWORK ARE RESERVED FOR CONDITIONAL -C AND OPTIONAL INPUTS AND OPTIONAL OUTPUTS. -C -C THE FOLLOWING WORD IN RWORK IS A CONDITIONAL INPUT.. -C RWORK(1) = TCRIT = CRITICAL VALUE OF T WHICH THE SOLVER -C IS NOT TO OVERSHOOT. REQUIRED IF ITASK IS -C 4 OR 5, AND IGNORED OTHERWISE. (SEE ITASK.) -C -C LRW = THE LENGTH OF THE ARRAY RWORK, AS DECLARED BY THE USER. -C (THIS WILL BE CHECKED BY THE SOLVER.) -C -C IWORK = AN INTEGER WORK ARRAY. THE LENGTH MUST BE AT LEAST.. -C 20 IF MITER = 0 OR 3 (MF = 10, 13, 20, 23), OR -C 20 + N OTHERWISE (MF = 11, 12, 14, 15, 21, 22, 24, 25). -C FOR ISOPT = 0, OR.. -C 21 + N + NPAR -C FOR ISOPT = 1. -C THE FIRST FEW WORDS OF IWORK ARE USED FOR CONDITIONAL AND -C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. -C -C THE FOLLOWING 2 WORDS IN IWORK ARE CONDITIONAL INPUTS.. -C IWORK(1) = ML THESE ARE THE LOWER AND UPPER -C IWORK(2) = MU HALF-BANDWIDTHS, RESPECTIVELY, OF THE -C BANDED JACOBIAN, EXCLUDING THE MAIN DIAGONAL. -C THE BAND IS DEFINED BY THE MATRIX LOCATIONS -C (I,J) WITH I-ML .LE. J .LE. I+MU. ML AND MU -C MUST SATISFY 0 .LE. ML,MU .LE. NEQ-1. -C THESE ARE REQUIRED IF MITER IS 4 OR 5, AND -C IGNORED OTHERWISE. ML AND MU MAY IN FACT BE -C THE BAND PARAMETERS FOR A MATRIX TO WHICH -C DF/DY IS ONLY APPROXIMATELY EQUAL. -* -C -C LIW = THE LENGTH OF THE ARRAY IWORK, AS DECLARED BY THE USER. -C (THIS WILL BE CHECKED BY THE SOLVER.) -C -C NOTE.. THE WORK ARRAYS MUST NOT BE ALTERED BETWEEN CALLS TO ODESSA -C FOR THE SAME PROBLEM, EXCEPT POSSIBLY FOR THE CONDITIONAL AND -C OPTIONAL INPUTS, AND EXCEPT FOR THE LAST 2*NYH + N WORDS OF RWORK. -C THE LATTER SPACE IS USED FOR INTERNAL SCRATCH SPACE, AND SO IS -C AVAILABLE FOR USE BY THE USER OUTSIDE ODESSA BETWEEN CALLS, IF -C DESIRED (BUT NOT FOR USE BY F, DF, OR JAC). -C -C JAC = THE NAME OF THE USER-SUPPLIED ROUTINE (MITER = 1 OR 4) TO -C COMPUTE THE JACOBIAN MATRIX, DF/DY, AS A FUNCTION OF THE -C SCALAR T AND THE VECTORS Y, AND PAR. IT IS TO HAVE THE FORM -C SUBROUTINE JAC (NEQ, T, Y, PAR, ML, MU, PD, NROWPD) -C DOUBLE PRECISION T, Y, PAR, PD -C DIMENSION Y(1), PAR(1), PD(NROWPD,1) -C WHERE NEQ, T, Y, PAR, ML, MU, AND NROWPD ARE INPUT AND THE -C ARRAY PD IS TO BE LOADED WITH PARTIAL DERIVATIVES (ELEMENTS -C OF THE JACOBIAN MATRIX) ON OUTPUT. PD MUST BE GIVEN A FIRST -C DIMENSION OF NROWPD. T, Y, AND PAR HAVE THE SAME MEANING AS -C IN SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A -C DUMMY DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) -C IN THE FULL MATRIX CASE (MITER = 1), ML AND MU ARE -C IGNORED, AND THE JACOBIAN IS TO BE LOADED INTO PD IN -C COLUMNWISE MANNER, WITH DF(I)/DY(J) LOADED INTO PD(I,J). -C IN THE BAND MATRIX CASE (MITER = 4), THE ELEMENTS -C WITHIN THE BAND ARE TO BE LOADED INTO PD IN COLUMNWISE -C MANNER, WITH DIAGONAL LINES OF DF/DY LOADED INTO THE ROWS -C OF PD. THUS DF(I)/DY(J) IS TO BE LOADED INTO PD(I-J+MU+1,J). -C ML AND MU ARE THE HALF-BANDWIDTH PARAMETERS (SEE IWORK). -C THE LOCATIONS IN PD IN THE TWO TRIANGULAR AREAS WHICH -C CORRESPOND TO NONEXISTENT MATRIX ELEMENTS CAN BE IGNORED -C OR LOADED ARBITRARILY, AS THEY ARE OVERWRITTEN BY ODESSA. -C PD IS PRESET TO ZERO BY THE SOLVER, SO THAT ONLY THE -C NONZERO ELEMENTS NEED BE LOADED BY JAC. EACH CALL TO JAC IS -C PRECEDED BY A CALL TO F WITH THE SAME ARGUMENTS NEQ, T, Y, -C AND PAR. THUS TO GAIN SOME EFFICIENCY, INTERMEDIATE -C QUANTITIES SHARED BY BOTH CALCULATIONS MAY BE SAVED IN A -C USER COMMON BLOCK BY F AND NOT RECOMPUTED BY JAC, IF -C DESIRED. ALSO, JAC MAY ALTER THE Y ARRAY, IF DESIRED. -C JAC MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. -C SUBROUTINE JAC MAY ACCESS USER-DEFINED QUANTITIES IN -C NEQ(2),... AND PAR(NPAR+1),.... SEE THE DESCRIPTIONS OF -C NEQ (ABOVE) AND PAR (BELOW). -C -C MF = THE METHOD FLAG. USED ONLY FOR INPUT. THE LEGAL VALUES OF -C MF ARE 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, AND 25. -C MF HAS DECIMAL DIGITS METH AND MITER.. MF = 10*METH + MITER. -C METH INDICATES THE BASIC LINEAR MULTISTEP METHOD.. -C METH = 1 MEANS THE IMPLICIT ADAMS METHOD. -* -C METH = 2 MEANS THE METHOD BASED ON BACKWARD -C DIFFERENTIATION FORMULAS (BDF-S). -C MITER INDICATES THE CORRECTOR ITERATION METHOD.. -C MITER = 0 MEANS FUNCTIONAL ITERATION (NO JACOBIAN MATRIX -C IS INVOLVED). -C MITER = 1 MEANS CHORD ITERATION WITH A USER-SUPPLIED -C FULL (NEQ BY NEQ) JACOBIAN. -C MITER = 2 MEANS CHORD ITERATION WITH AN INTERNALLY -C GENERATED (DIFFERENCE QUOTIENT) FULL JACOBIAN -C (USING NEQ EXTRA CALLS TO F PER DF/DY VALUE). -C MITER = 3 MEANS CHORD ITERATION WITH AN INTERNALLY -C GENERATED DIAGONAL JACOBIAN APPROXIMATION. -C (USING 1 EXTRA CALL TO F PER DF/DY EVALUATION). -C MITER = 4 MEANS CHORD ITERATION WITH A USER-SUPPLIED -C BANDED JACOBIAN. -C MITER = 5 MEANS CHORD ITERATION WITH AN INTERNALLY -C GENERATED BANDED JACOBIAN (USING ML+MU+1 EXTRA -C CALLS TO F PER DF/DY EVALUATION). -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 IF A SENSITIVITY ANLYSIS IS DESIRED (ISOPT = 1), MITER = 0 -C AND 3 ARE DISALLOWED. IN THESE CASES, THE USER IS RECOMMENDED -C TO SUPPLY AN ANALYTICAL JACOBIAN (MITER = 1 OR 4) AND AN -C ANALYTICAL INHOMOGENEITY MATRIX (IDF = 1). -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 II.) 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) = 1, AND IN THAT -C CASE ALL OF THESE INPUTS ARE EXAMINED. A VALUE OF ZERO FOR ANY -C OF 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, AND -C THEN SET THOSE OF INTEREST TO NONZERO VALUES. -C -C NAME LOCATION MEANING AND DEFAULT VALUE -C -C H0 RWORK(5) THE STEP SIZE TO BE ATTEMPTED ON THE FIRST STEP. -C THE DEFAULT VALUE IS DETERMINED BY THE SOLVER. -C -C HMAX RWORK(6) THE MAXIMUM ABSOLUTE STEP SIZE ALLOWED. -C THE DEFAULT VALUE IS INFINITE. -C -C HMIN RWORK(7) THE MINIMUM ABSOLUTE STEP SIZE ALLOWED. -C THE DEFAULT VALUE IS 0. (THIS LOWER BOUND IS NOT -C ENFORCED ON THE FINAL STEP BEFORE REACHING TCRIT -C WHEN ITASK = 4 OR 5.) -C -C MAXORD IWORK(5) THE MAXIMUM ORDER TO BE ALLOWED. THE DEFAULT -C VALUE IS 12 IF METH = 1, AND 5 IF METH = 2. -C IF MAXORD EXCEEDS THE DEFAULT VALUE, IT WILL -C BE REDUCED TO THE DEFAULT VALUE. -C IF MAXORD IS CHANGED DURING THE PROBLEM, IT MAY -C CAUSE THE CURRENT ORDER TO BE REDUCED. -C -C MXSTEP IWORK(6) MAXIMUM NUMBER OF (INTERNALLY DEFINED) STEPS -C ALLOWED DURING ONE CALL TO THE SOLVER. -C THE DEFAULT VALUE IS 500. -C -C MXHNIL IWORK(7) MAXIMUM NUMBER OF MESSAGES PRINTED (PER PROBLEM) -C WARNING THAT T + H = T ON A STEP (H = STEP SIZE). -C THIS MUST BE POSITIVE TO RESULT IN A NON-DEFAULT -C VALUE. THE DEFAULT VALUE IS 10. -C---------------------------------------------------------------------- -C OPTIONAL OUTPUTS. -C -C AS OPTIONAL ADDITIONAL OUTPUT FROM ODESSA, THE VARIABLES LISTED -C BELOW ARE QUANTITIES RELATED TO THE PERFORMANCE OF ODESSA -C WHICH ARE AVAILABLE TO THE USER. THESE ARE COMMUNICATED BY WAY OF -C THE WORK ARRAYS, BUT ALSO HAVE INTERNAL MNEMONIC NAMES AS SHOWN. -C EXCEPT WHERE STATED OTHERWISE, ALL OF THESE OUTPUTS ARE DEFINED -C ON ANY SUCCESSFUL RETURN FROM ODESSA, AND ON ANY RETURN WITH -C ISTATE = -1, -2, -4, -5, OR -6. ON AN ILLEGAL INPUT RETURN -C (ISTATE = -3), THEY WILL BE UNCHANGED FROM THEIR EXISTING VALUES -C (IF ANY), EXCEPT POSSIBLY FOR TOLSF, LENRW, AND LENIW. -C ON ANY ERROR RETURN, OUTPUTS RELEVANT TO THE ERROR WILL BE DEFINED, -C AS NOTED BELOW. -C -C NAME LOCATION MEANING -C -C HU RWORK(11) THE STEP SIZE IN T LAST USED (SUCCESSFULLY). -C -C HCUR RWORK(12) THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP. -C -C TCUR RWORK(13) THE CURRENT VALUE OF THE INDEPENDENT VARIABLE -C WHICH THE SOLVER HAS ACTUALLY REACHED, I.E. THE -C CURRENT INTERNAL MESH POINT IN T. ON OUTPUT, TCUR -C WILL ALWAYS BE AT LEAST AS FAR AS THE ARGUMENT -C T, BUT MAY BE FARTHER (IF INTERPOLATION WAS DONE). -C -C TOLSF RWORK(14) A TOLERANCE SCALE FACTOR, GREATER THAN 1.0, -C COMPUTED WHEN A REQUEST FOR TOO MUCH ACCURACY WAS -C DETECTED (ISTATE = -3 IF DETECTED AT THE START OF -C THE PROBLEM, ISTATE = -2 OTHERWISE). IF ITOL IS -C LEFT UNALTERED BUT RTOL AND ATOL ARE UNIFORMLY -C SCALED UP BY A FACTOR OF TOLSF FOR THE NEXT CALL, -C THEN THE SOLVER IS DEEMED LIKELY TO SUCCEED. -C (THE USER MAY ALSO IGNORE TOLSF AND ALTER THE -C TOLERANCE PARAMETERS IN ANY OTHER WAY APPROPRIATE.) -C -C NST IWORK(11) THE NUMBER OF STEPS TAKEN FOR THE PROBLEM SO FAR. -C -C NFE IWORK(12) THE NUMBER OF F EVALUATIONS FOR THE PROBLEM SO FAR. -C -C NJE IWORK(13) THE NUMBER OF JACOBIAN EVALUATIONS (AND OF MATRIX -C LU DECOMPOSITIONS IF ISOPT = 0) FOR THE PROBLEM SO -C FAR. IF ISOPT = 1, THE NUMBER OF LU DECOMPOSITIONS -C IS EQUAL TO NJE - NSPE (SEE BELOW). -C -C NQU IWORK(14) THE METHOD ORDER LAST USED (SUCCESSFULLY). -C -C NQCUR IWORK(15) THE ORDER TO BE ATTEMPTED ON THE NEXT STEP. -C -C IMXER IWORK(16) THE INDEX OF THE COMPONENT OF LARGEST MAGNITUDE IN -C THE WEIGHTED LOCAL ERROR VECTOR (E(I,J)/EWT(I,J)), -C ON AN ERROR RETURN WITH ISTATE = -4 OR -5. -C -C LENRW IWORK(17) THE LENGTH OF RWORK ACTUALLY REQUIRED. -C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL -C INPUT RETURN FOR INSUFFICIENT STORAGE. -C -C LENIW IWORK(18) THE LENGTH OF IWORK ACTUALLY REQUIRED. -C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL -C INPUT RETURN FOR INSUFFICIENT STORAGE. -C -C NDFE IWORK(19) THE NUMBER OF DF/DP (VECTOR) EVALUATIONS. -C -C NSPE IWORK(20) THE NUMBER OF CALLS TO SUBROUTINE ODESSA_SPRIME. EACH CALL -C TO ODESSA_SPRIME REQUIRES A JACOBIAN EVALUATION, BUT NOT -C AN LU DECOMPOSITION. -C -C THE FOLLOWING ARRAYS ARE SEGMENTS OF THE RWORK AND IWORK ARRAYS -C WHICH MAY ALSO BE OF INTEREST TO THE USER AS OPTIONAL OUTPUTS. -C FOR EACH ARRAY, THE TABLE BELOW GIVES ITS INTERNAL NAME, ITS BASE -C ADDRESS IN RWORK OR IWORK, AND ITS DESCRIPTION. -C -C NAME BASE ADDRESS DESCRIPTION -C -C YH 21 IN RWORK THE NORDSIECK HISTORY ARRAY, OF SIZE NYH BY -C (NQCUR + 1). FOR J = 0,1,...,NQCUR, COLUMN J+1 -C OF YH CONTAINS HCUR**J/FACTORIAL(J) TIMES -C THE J-TH DERIVATIVE OF THE INTERPOLATING -C POLYNOMIAL CURRENTLY REPRESENTING THE SOLUTION, -C EVALUATED AT T = TCUR. -C -C ACOR LENRW-NYH+1 ARRAY OF SIZE NYH USED FOR THE ACCUMULATED -C IN RWORK CORRECTIONS ON EACH STEP, SCALED ON OUTPUT -C TO REPRESENT THE ESTIMATED LOCAL ERROR IN Y -C ON THE LAST STEP. THIS IS THE VECTOR E IN -C THE DESCRIPTION OF THE ERROR CONTROL. -C IT IS DEFINED ONLY ON A SUCCESSFUL RETURN -C FROM ODESSA. -C NRS LENIW-NPAR ARRAY OF SIZE NPAR+1, USED TO STORE THE -C IN IWORK ACCUMULATED NUMBER OF REPEATED STEPS DUE TO -C THE SENSITIVITY ANALYSIS.. -C NRS(1) = TOTAL NUMBER OF REPEATED STEPS, -C NRS(2),... = NUMBER OF REPEATED STEPS DUE TO -C MODEL PARAMETER 1,... -C -C---------------------------------------------------------------------- -C PART II. OTHER ROUTINES CALLABLE. -C -C THE FOLLOWING ARE OPTIONAL CALLS WHICH THE USER MAY MAKE TO -C GAIN ADDITIONAL CAPABILITIES IN CONJUNCTION WITH ODESSA. -C -C CALL ODESSA_SVCOM (RSAV, ISAV) STORE IN RSAV AND ISAV THE CONTENTS -C OF THE INTERNAL COMMON BLOCKS USED BY -C ODESSA (SEE PART III BELOW). -C RSAV MUST BE A REAL ARRAY OF LENGTH 222 -C OR MORE, AND ISAV MUST BE AN INTEGER -C ARRAY OF LENGTH 54 OR MORE. -C -C CALL ODESSA_RSCOM (RSAV, ISAV) RESTORE, FROM RSAV AND ISAV, THE CONTENTS -C OF THE INTERNAL COMMON BLOCKS USED BY -C ODESSA. PRESUMES A PRIOR CALL TO ODESSA_SVCOM -C WITH THE SAME ARGUMENTS. -C -C ODESSA_SVCOM AND ODESSA_RSCOM ARE USEFUL IF -C INTERRUPTING A RUN AND RESTARTING -C LATER, OR ALTERNATING BETWEEN TWO OR -C MORE PROBLEMS SOLVED WITH ODESSA. -C -C CALL ODESSA_INTDY(,,,,,) PROVIDE DERIVATIVES OF Y, OF VARIOUS -C (SEE BELOW) ORDERS, AT A SPECIFIED POINT T, IF -C DESIRED. IT MAY BE CALLED ONLY AFTER -C A SUCCESSFUL RETURN FROM ODESSA. -C -C THE DETAILED INSTRUCTIONS FOR USING ODESSA_INTDY ARE AS FOLLOWS. -C THE FORM OF THE CALL IS.. -C -C CALL ODESSA_INTDY (T, K, RWORK(21), NYH, DKY, IFLAG) -C -C THE INPUT PARAMETERS ARE.. -C -C T = VALUE OF INDEPENDENT VARIABLE WHERE ANSWERS ARE DESIRED -C (NORMALLY THE SAME AS THE T LAST RETURNED BY ODESSA). -C FOR VALID RESULTS, T MUST LIE BETWEEN TCUR - HU AND TCUR. -C (SEE OPTIONAL OUTPUTS FOR TCUR AND HU.) -C K = INTEGER ORDER OF THE DERIVATIVE DESIRED. K MUST SATISFY -C 0 .LE. K .LE. NQCUR, WHERE NQCUR IS THE CURRENT ORDER -C (SEE OPTIONAL OUTPUTS). THE CAPABILITY CORRESPONDING -C TO K = 0, I.E. COMPUTING Y(T), IS ALREADY PROVIDED -C BY ODESSA DIRECTLY. SINCE NQCUR .GE. 1, THE FIRST -C DERIVATIVE DY/DT IS ALWAYS AVAILABLE WITH ODESSA_INTDY. -C RWORK(21) = THE BASE ADDRESS OF THE HISTORY ARRAY YH. -C NYH = COLUMN LENGTH OF YH, EQUAL TO THE TOTAL NUMBER OF -C DEPENDENT VARIABLES. IF ISOPT = 0, NYH = N. IF ISOPT = 1, -C NYH = N * (NPAR + 1). -C -C THE OUTPUT PARAMETERS ARE.. -C -C DKY = A REAL ARRAY OF LENGTH NYH CONTAINING THE COMPUTED VALUE -C OF THE K-TH 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 PART III. COMMON BLOCKS. -C -C IF ODESSA IS TO BE USED IN AN OVERLAY SITUATION, THE USER -C MUST DECLARE, IN THE PRIMARY OVERLAY, THE VARIABLES IN.. -C (1) THE CALL SEQUENCE TO ODESSA, -C (2) THE THREE INTERNAL COMMON BLOCKS -C /ODE001/ OF LENGTH 258 (219 DOUBLE PRECISION WORDS -C FOLLOWED BY 39 INTEGER WORDS), -C /ODE002/ OF LENGTH 14 (3 DOUBLE PRECISION WORDS FOLLOWED -C BY 11 INTEGER WORDS), -C -C IF ODESSA 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 THREE COMMON BLOCKS IN HIS MAIN PROGRAM TO INSURE -C THAT THEIR CONTENTS ARE PRESERVED. -C -C IF THE SOLUTION OF A GIVEN PROBLEM BY ODESSA IS TO BE INTERRUPTED -C AND THEN LATER CONTINUED, SUCH AS WHEN RESTARTING AN INTERRUPTED RUN -C OR ALTERNATING BETWEEN TWO OR MORE PROBLEMS, THE USER SHOULD SAVE, -C FOLLOWING THE RETURN FROM THE LAST ODESSA CALL PRIOR TO THE -C INTERRUPTION, THE CONTENTS OF THE CALL SEQUENCE VARIABLES AND THE -C INTERNAL COMMON BLOCKS, AND LATER RESTORE THESE VALUES BEFORE THE -C NEXT ODESSA CALL FOR THAT PROBLEM. TO SAVE AND RESTORE THE COMMON -C BLOCKS, USE SUBROUTINES ODESSA_SVCOM AND ODESSA_RSCOM (SEE PART II ABOVE). -C -C---------------------------------------------------------------------- -C PART IV. OPTIONALLY REPLACEABLE SOLVER ROUTINES. -C -C BELOW ARE DESCRIPTIONS OF TWO ROUTINES IN THE ODESSA PACKAGE WHICH -C RELATE TO THE MEASUREMENT OF ERRORS. EITHER ROUTINE CAN BE -C REPLACED BY A USER-SUPPLIED VERSION, IF DESIRED. HOWEVER, SINCE SUCH -C A REPLACEMENT MAY HAVE A MAJOR IMPACT ON PERFORMANCE, IT SHOULD BE -C DONE ONLY WHEN ABSOLUTELY NECESSARY, AND ONLY WITH GREAT CAUTION. -C (NOTE.. THE MEANS BY WHICH THE PACKAGE VERSION OF A ROUTINE IS -C SUPERSEDED BY THE USER-S VERSION MAY BE SYSTEM-DEPENDENT.) -C -C (A) ODESSA_EWSET. -C THE FOLLOWING SUBROUTINE IS CALLED JUST BEFORE EACH INTERNAL -C INTEGRATION STEP, AND SETS THE ARRAY OF ERROR WEIGHTS, EWT, AS -C DESCRIBED UNDER ITOL/RTOL/ATOL ABOVE.. -C SUBROUTINE ODESSA_EWSET (NYH, ITOL, RTOL, ATOL, YCUR, EWT) -C WHERE NEQ, ITOL, RTOL, AND ATOL ARE AS IN THE ODESSA CALL SEQUENCE, -C YCUR CONTAINS THE CURRENT DEPENDENT VARIABLE VECTOR, AND -C EWT IS THE ARRAY OF WEIGHTS SET BY ODESSA_EWSET. -C -C IF THE USER SUPPLIES THIS SUBROUTINE, IT MUST RETURN IN EWT(I) -C (I = 1,...,NYH) A POSITIVE QUANTITY SUITABLE FOR COMPARING ERRORS -C IN Y(I) TO. THE EWT ARRAY RETURNED BY ODESSA_EWSET IS PASSED TO THE -C ODESSA_VNORM ROUTINE (SEE BELOW), AND ALSO USED BY ODESSA IN THE COMPUTATION -C OF THE OPTIONAL OUTPUT IMXER, THE DIAGONAL JACOBIAN APPROXIMATION, -C AND THE INCREMENTS FOR DIFFERENCE QUOTIENT JACOBIANS. -C -C IN THE USER-SUPPLIED VERSION OF ODESSA_EWSET, IT MAY BE DESIRABLE TO USE -C THE CURRENT VALUES OF DERIVATIVES OF Y. DERIVATIVES UP TO ORDER NQ -C ARE AVAILABLE FROM THE HISTORY ARRAY YH, DESCRIBED ABOVE UNDER -C OPTIONAL OUTPUTS. IN ODESSA_EWSET, YH IS IDENTICAL TO THE YCUR ARRAY, -C EXTENDED TO NQ + 1 COLUMNS WITH A COLUMN LENGTH OF NYH AND SCALE -C 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 THE QUANTITIES NQ, NYH, H, AND NST CAN BE OBTAINED BY INCLUDING -C IN ODESSA_EWSET THE STATEMENTS.. -C DOUBLE PRECISION H, RLS -C COMMON /ODE001/ RLS(219),ILS(39) -C NQ = ILS(35) -C NYH = ILS(14) -C NST = ILS(36) -C H = RLS(213) -C THUS, FOR EXAMPLE, THE CURRENT VALUE OF DY/DT CAN BE OBTAINED AS -C YCUR(NYH+I)/H (I=1,...,N) (AND THE DIVISION BY H IS -C UNNECESSARY WHEN NST = 0). -C -C (B) ODESSA_VNORM. -C THE FOLLOWING IS A REAL FUNCTION ROUTINE WHICH COMPUTES THE WEIGHTED -C ROOT-MEAN-SQUARE NORM OF A VECTOR V.. -C D = ODESSA_VNORM (LV, V, W) -C WHERE.. -C LV = 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 ). -C ODESSA_VNORM IS CALLED WITH LV = N AND WITH W(I) = 1.0/EWT(I), WHERE -C EWT IS AS SET BY SUBROUTINE ODESSA_EWSET. -C -C IF THE USER SUPPLIES THIS FUNCTION, IT SHOULD RETURN A NON-NEGATIVE -C VALUE OF ODESSA_VNORM SUITABLE FOR USE IN THE ERROR CONTROL IN ODESSA. -C NONE OF THE ARGUMENTS SHOULD BE ALTERED BY ODESSA_VNORM. -C FOR EXAMPLE, A USER-SUPPLIED ODESSA_VNORM ROUTINE MIGHT.. -C -SUBSTITUTE A MAX-NORM OF (V(I)*W(I)) FOR THE RMS-NORM, OR -C -IGNORE SOME COMPONENTS OF V IN THE NORM, WITH THE EFFECT OF -C SUPPRESSING THE ERROR CONTROL ON THOSE COMPONENTS OF Y. -C---------------------------------------------------------------------- -C OTHER ROUTINES IN THE ODESSA PACKAGE. -C -C IN ADDITION TO SUBROUTINE ODESSA, THE ODESSA PACKAGE INCLUDES THE -C FOLLOWING SUBROUTINES AND FUNCTION ROUTINES.. -C ODESSA_INTDY COMPUTES AN INTERPOLATED VALUE OF THE Y VECTOR AT T = TOUT. -C ODESSA_STODE IS THE CORE INTEGRATOR, WHICH DOES ONE STEP OF THE -C INTEGRATION AND THE ASSOCIATED ERROR CONTROL. -C ODESSA_STESA MANAGES THE SOLUTION OF THE SENSITIVITY FUNCTIONS. -C ODESSA_CFODE SETS ALL METHOD COEFFICIENTS AND TEST CONSTANTS. -C ODESSA_PREPJ COMPUTES AND PREPROCESSES THE JACOBIAN MATRIX J = DF/DY -C AND THE NEWTON ITERATION MATRIX P = I - H*L0*J. -C IT IS ALSO CALLED BY ODESSA_SPRIME (WITH JOPT = 1) TO JUST -C COMPUTE THE JACOBIAN MATRIX. -C ODESSA_PREPDF COMPUTES THE INHOMOGENEITY MATRIX DF/DP. -C ODESSA_SPRIME DEFINES THE SYSTEM OF SENSITIVITY EQUATIONS. -C ODESSA_SOLSY MANAGES SOLUTION OF LINEAR SYSTEM IN CHORD ITERATION. -C ODESSA_EWSET SETS THE ERROR WEIGHT VECTOR EWT BEFORE EACH STEP. -C ODESSA_VNORM COMPUTES THE WEIGHTED R.M.S. NORM OF A VECTOR. -C ODESSA_SVCOM AND ODESSA_RSCOM ARE USER-CALLABLE ROUTINES TO SAVE AND RESTORE, -C RESPECTIVELY, THE CONTENTS OF THE INTERNAL COMMON BLOCKS. -C DGETRF AND DGETRS ARE ROUTINES FROM LAPACK FOR SOLVING FULL -C SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS. -C DGBTRF AND DGBTRS ARE ROUTINES FROM LAPACK FOR SOLVING BANDED -C LINEAR SYSTEMS. -C DAXPY, DSCAL, IDAMAX, AND DDOT ARE BASIC LINEAR ALGEBRA MODULES -C (BLAS) USED BY THE ABOVE LINPACK ROUTINES. -C D1MACH COMPUTES THE UNIT ROUNDOFF IN A MACHINE-INDEPENDENT MANNER. -C XERRWD, XSETUN, AND ODESSA_XSETF HANDLE THE PRINTING OF ALL ERROR -C MESSAGES AND WARNINGS. -C NOTE.. ODESSA_VNORM, IDAMAX, DDOT, AND D1MACH ARE FUNCTION ROUTINES. -C ALL THE OTHERS ARE SUBROUTINES. -C -C THE FORTRAN GENERIC INTRINSIC FUNCTIONS USED BY ODESSA ARE.. -C ABS, MAX, MIN, REAL, MOD, SIGN, SQRT, AND WRITE -C -C A BLOCK DATA SUBPROGRAM IS ALSO INCLUDED WITH THE PACKAGE, -C FOR LOADING SOME OF THE VARIABLES IN INTERNAL COMMON. -C -C---------------------------------------------------------------------- -C PART V. GENERAL REMARKS -C -C THIS SECTION HIGHLIGHTS THE BASIC DIFFERENCES BETWEEN THE ORIGINAL -C LSODE PACKAGE AND THE ODESSA MODIFICATION. THIS IS PROVIDED AS A -C SERVICE TO EXPERIENCED LSODE USERS TO EXPEDITE FAMILIARIZATION WITH -C ODESSA. -C -C (A). ORIGINAL SUBROUTINES AND FUNCTIONS. -C -C OF THE ORIGINAL 22 SUBROUTINES AND FUNCTIONS USED IN THE LSODE -C PACKAGE, ALL ARE USED BY ODESSA, WITH THE FOLLOWING HAVING BEEN -C MODIFIED.. -C -C LSODE THE ORIGINAL DRIVER SUBROUTINE FOR THE LSODE PACKAGE IS -C EXTENSIVELY MODIFIED AND RENAMED ODESSA, WHICH NOW -C CONTAINS A CALL TO ODESSA_SPRIME TO ESTABLISH INITIAL CONDITIONS -C FOR THE SENSITIVITY CALCULATIONS. -C -C ODESSA_STODE THE ONE STEP INTEGRATOR IS SLIGHTLY MODIFIED AND RETAINS -C ITS ORIGINAL NAME. IT NOW CONTAINS THE CALL TO ODESSA_STESA, -C AND ALSO CALLS ODESSA_SPRIME IF KFLAG .LE. -3. -C -C ODESSA_PREPJ ALSO NAMED ODESSA_PREPJ IN ODESSA IS SLIGHTLY MODIFIED TO ALLOW -C FOR THE CALCULATION OF JACOBIAN WITH NO PREPROCESSING -C (JOPT = 1). -C -C (B). NEW SUBROUTINES. -C -C IN ADDITION TO THE CHANGES NOTED ABOVE, THREE NEW SUBROUTINES -C HAVE BEEN INTRODUCED (SEE ODESSA_STESA, ODESSA_SPRIME, AND ODESSA_PREPDF AS DESCRIBED -C IN PART IV. ABOVE). -C -C (C). COMMON BLOCKS. -C -C /LS0001/ RETAINS THE SAME LENGTH AND IS RENAMED /ODE001/; -C HOWEVER THE REAL ARRAY ROWNS(209) IS SHORTENED TO A -C LENGTH OF (173) REAL WORDS, ALLOWING THE REMOVAL OF -C TESCO(3,12) WHICH IS NOW PASSED FROM ODESSA_STODE TO ODESSA_STESA. -C IN ADDITION, THE INTEGER ARRAY IOWNS(6) IS SHORTENED -C TO A LENGTH OF (4) INTEGER WORDS, ALLOWING THE REMOVAL -C OF IALTH AND LMAX WHICH ARE NOW PASSED FROM ODESSA_STODE TO -C ODESSA_STESA. -C -C /ODE002/ ADDED COMMON BLOCK FOR VARIABLES IMPORTANT TO -C SENSITIVITY ANALYSIS (SEE PART III. ABOVE). A BLOCK -C DATA PROGRAM IS NOT REQUIRED FOR THIS COMMON BLOCK. -C -C ODESSA_SVCOM,ODESSA_RSCOM THESE TWO SUBROUTINES ARE MODIFIED TO HANDLE -C COMMON BLOCK /ODE002/ AS WELL. -C -C (D). OPTIONAL INPUTS. -C -C THE FULL SET OF OPTIONAL INPUTS AVAILABLE IN LSODE IS ALSO -C AVAILABLE IN ODESSA, WITH THE EXCEPTION THAT THE NUMBER OF ODE'S -C IN THE MODEL (NEQ(1)), MAY NOT BE CHANGED DURING THE PROBLEM. -C IN ODESSA, NYH NOW REFERS TO THE TOTAL NUMBER OF FIRST-ORDER -C ODE'S (MODEL AND SENSITIVITY EQUATIONS) WHICH IS EQUAL TO -C NEQ(1) IF ISOPT = 0, OR NEQ(1)*(NEQ(2)+1) IF ISOPT = 1. -C NEQ(1), NEQ(2), AND NYH ARE NOT ALLOWED TO CHANGE DURING -C THE COURSE OF AN INTEGRATION. -C -C (E). OPTIONAL OUTPUTS. -C -C THE FULL SET OF OPTIONAL OUTPUTS AVAILABLE IN LSODE IS ALSO -C AVAILABLE IN ODESSA. IN ADDITION, IWORK(19) AND IWORK(20) ARE -C LOADED WITH NDFE AND NSPE, RESPECTIVELY, UPON OUTPUT. THE TOTAL -C NUMBER OF LU DECOMPOSITIONS OF THE PROCESSED JACOBIAN IS EQUAL -C TO NJE - NSPE. -C----------------------------------------------------------------------- - SUBROUTINE ODESSA (F, DF, NEQ, Y, PAR, T, TOUT, ITOL, RTOL, ATOL, - 1 ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) - IMPLICIT DOUBLE PRECISION (A-H,O-Z) - LOGICAL IHIT - EXTERNAL F, DF, JAC, ODESSA_PREPJ, ODESSA_SOLSY, ODESSA_PREPDF - DIMENSION NEQ(*), Y(*), PAR(*), RTOL(*), ATOL(*), IOPT(*), - 1 RWORK(LRW), IWORK(LIW), MORD(2) -C----------------------------------------------------------------------- -C THIS IS THE SEPTEMBER 1, 1986 VERSION OF ODESSA.. -C AN ORDINARY DIFFERENTIAL EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS -C SENSITIVITY ANALYSIS. -C -C THIS PACKAGE IS A MODIFICATION OF THE AUGUST 13, 1981 VERSION OF -C LSODE.. LIVERMORE SOLVER FOR ORDINARY DIFFERENTIAL EQUATIONS. -C THIS VERSION IS IN DOUBLE PRECISION. -C -C ODESSA SOLVES FOR THE FIRST-ORDER SENSITIVITY COEFFICIENTS.. -C DY(I)/DP, FOR A SINGLE PARAMETER, OR, -C DY(I)/DP(J), FOR MULTIPLE PARAMETERS, -C ASSOCIATED WITH A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.. -C DY(T)/DT = F(Y,T;P). -C----------------------------------------------------------------------- -C REFERENCES... -C -C 1. JORGE R. LEIS AND MARK A. KRAMER, THE SIMULTANEOUS SOLUTION AND -C EXPLICIT SENSITIVITY ANALYSIS OF SYSTEMS DESCRIBED BY ORDINARY -C DIFFERENTIAL EQUATIONS, SUBMITTED TO ACM TRANS. MATH. SOFTWARE, -C (1985). -C -C 2. JORGE R. LEIS AND MARK A. KRAMER, ODESSA - AN ORDINARY -C DIFFERENTIAL EQUATION SOLVER WITH EXPLICIT SIMULTANEOUS -C SENSITIVITY ANALYSIS, SUBMITTED TO ACM TRANS. MATH. SOFTWARE. -C (1985). -C -C 3. ALAN C. HINDMARSH, LSODE AND LSODI, TWO NEW INITIAL VALUE -C ORDINARY DIFFERENTIAL EQUATION SOLVERS, ACM-SIGNUM NEWSLETTER, -C VOL. 15, NO. 4 (1980), PP. 10-11. -C----------------------------------------------------------------------- -C THE FOLLOWING INTERNAL COMMON BLOCKS CONTAIN -C (A) VARIABLES WHICH ARE LOCAL TO ANY SUBROUTINE BUT WHOSE VALUES MUST -C BE PRESERVED BETWEEN CALLS TO THE ROUTINE (OWN VARIABLES), AND -C (B) VARIABLES WHICH ARE COMMUNICATED BETWEEN SUBROUTINES. -C THE STRUCTURE OF THE BLOCKS ARE AS FOLLOWS.. ALL REAL VARIABLES ARE -C LISTED FIRST, FOLLOWED BY ALL INTEGERS. WITHIN EACH TYPE, THE -C VARIABLES ARE GROUPED WITH THOSE LOCAL TO SUBROUTINE ODESSA FIRST, -C THEN THOSE LOCAL TO SUBROUTINE ODESSA_STODE, AND FINALLY THOSE USED -C FOR COMMUNICATION. THE BLOCKS ARE DECLARED IN SUBROUTINES ODESSA -C ODESSA_INTDY, ODESSA_STODE, ODESSA_STESA, ODESSA_PREPJ, ODESSA_PREPDF, -C AND ODESSA_SOLSY. GROUPS OF VARIABLES ARE REPLACED BY DUMMY ARRAYS IN -C THE COMMON DECLARATIONS IN ROUTINES WHERE THOSE VARIABLES ARE NOT USED. -C----------------------------------------------------------------------- - COMMON /ODE001/ TRET, ROWNS(173), - 1 TESCO(3,12), CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, - 2 ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM, - 3 MXSTEP, MXHNIL, NHNIL, NTREP, NSLAST, NYH, IOWNS(4), - 4 IALTH, LMAX, ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, - 5 MITER, MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU - COMMON /ODE002/ DUPS, DSMS, DDNS, - 1 NPAR, LDFDP, LNRS, - 2 ISOPT, NSV, NDFE, NSPE, IDF, IERSP, JOPT, KFLAGS - PARAMETER (ZERO=0.0D0,ONE=1.0D0,TWO=2.0D0,FOUR=4.0D0) - 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 APPROPIATELY. -C IF ISTATE .GT. 1 BUT THE FLAG INIT SHOWS THAT INITIALIZATION HAS -C NOT YET BEEN DONE, AN ERROR RETURN OCCURS. -C IF ISTATE = 1 AND TOUT = T, JUMP TO BLOCK G AND RETURN IMMEDIATELY. -C----------------------------------------------------------------------- - 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) GO TO 430 - 20 NTREP = 0 -C----------------------------------------------------------------------- -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. -C -C FIRST CHECK LEGALITY OF THE NON-OPTIONAL INPUTS NEQ, ITOL, IOPT, -C MF, ML, AND MU. -C----------------------------------------------------------------------- - IF (NEQ(1) .LE. 0) GO TO 604 - IF (ISTATE .EQ. 1) GO TO 25 - IF (NEQ(1) .NE. N) GO TO 605 - 25 N = NEQ(1) - IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 - DO 26 I = 1,3 - 26 IF (IOPT(I) .LT. 0 .OR. IOPT(I) .GT. 1) GO TO 607 - ISOPT = IOPT(2) - IDF = IOPT(3) - NYH = N - NSV = 1 - 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 IF (ISOPT .EQ. 0) GO TO 32 -C CHECK LEGALITY OF THE NON-OPTIONAL INPUTS ISOPT, NPAR. -C COMPUTE NUMBER OF SOLUTION VECTORS AND TOTAL NUMBER OF EQUATIONS. - IF (NEQ(2) .LE. 0) GO TO 628 - IF (ISTATE .EQ. 1) GO TO 31 - IF (NEQ(2) .NE. NPAR) GO TO 629 - 31 NPAR = NEQ(2) - NSV = NPAR + 1 - NYH = NSV * N - IF (MITER .EQ. 0 .OR. MITER .EQ. 3) GO TO 630 -C NEXT PROCESS AND CHECK THE OPTIONAL INPUTS. -------------------------- - 32 IF (IOPT(1) .EQ. 1) GO TO 40 - MAXORD = MORD(METH) - MXSTEP = MXSTP0 - MXHNIL = MXHNL0 - IF (ISTATE .EQ. 1) H0 = ZERO - HMXI = ZERO - HMIN = ZERO - 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. ZERO) GO TO 614 - 50 HMAX = RWORK(6) - IF (HMAX .LT. ZERO) GO TO 615 - HMXI = ZERO - IF (HMAX .GT. ZERO) HMXI = ONE/HMAX - HMIN = RWORK(7) - IF (HMIN .LT. ZERO) GO TO 616 -C----------------------------------------------------------------------- -C SET WORK ARRAY POINTERS AND CHECK LENGTHS LRW AND LIW. -C POINTERS TO SEGMENTS OF RWORK AND IWORK ARE NAMED BY PREFIXING L TO -C 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 WORK SPACE FOR DFDP IS CONTAINED IN ACOR. -C----------------------------------------------------------------------- - 60 LYH = 21 - 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 + NYH - LACOR = LSAVF + N - LDFDP = LACOR + N - LENRW = LACOR + NYH - 1 - IWORK(17) = LENRW - LIWM = 1 - LENIW = 20 + N - IF (MITER .EQ. 0 .OR. MITER .EQ. 3) LENIW = 20 - LNRS = LENIW + LIWM - IF (ISOPT .EQ. 1) LENIW = LNRS + NPAR - IWORK(18) = LENIW - IF (LENRW .GT. LRW) GO TO 617 - IF (LENIW .GT. LIW) GO TO 618 -C CHECK RTOL AND ATOL FOR LEGALITY. ------------------------------------ - RTOLI = RTOL(1) - ATOLI = ATOL(1) - DO 70 I = 1,NYH - IF (ITOL .GE. 3) RTOLI = RTOL(I) - IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) - IF (RTOLI .LT. ZERO) GO TO 619 - IF (ATOLI .LT. ZERO) GO TO 620 - 70 CONTINUE - IF (ISTATE .EQ. 1) GO TO 100 -C IF ISTATE = 3, SET FLAG TO SIGNAL PARAMETER CHANGES TO ODESSA_STODE. - - JSTART = -1 - IF (NQ .LE. MAXORD) GO TO 90 -C 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) = DSQRT(UROUND) - GO TO 200 -C----------------------------------------------------------------------- -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 THE INITIAL CALL TO ODESSA_SPRIME IF ISOPT = 1, -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 105 - TCRIT = RWORK(1) - IF ((TCRIT - TOUT)*(TOUT - T) .LT. ZERO) GO TO 625 - IF (H0 .NE. ZERO .AND. (T + H0 - TCRIT)*H0 .GT. ZERO) - 1 H0 = TCRIT - T - 105 JSTART = 0 - IF (MITER .GT. 0) RWORK(LWM) = DSQRT(UROUND) - NHNIL = 0 - NST = 0 - NJE = 0 - NSLAST = 0 - HU = ZERO - NQU = 0 - CCMAX = 0.3D0 - MAXCOR = 3 - IF (ISOPT .EQ. 1) MAXCOR = 4 - MSBP = 20 - MXNCF = 10 -C INITIAL CALL TO F. (LF0 POINTS TO YH(1,2) AND LOADS IN VALUES). - LF0 = LYH + NYH - CALL F (NEQ, T, Y, PAR, RWORK(LF0)) - NFE = 1 - DUPS = ZERO - DSMS = ZERO - DDNS = ZERO - NDFE = 0 - NSPE = 0 - IF (ISOPT .EQ. 0) GO TO 114 -C INITIALIZE COUNTS FOR REPEATED STEPS DUE TO SENSITIVITY ANALYSIS. - DO 110 J = 1,NSV - 110 IWORK(J + LNRS - 1) = 0 -C LOAD THE INITIAL VALUE VECTOR IN YH. --------------------------------- - 114 DO 115 I = 1,NYH - 115 RWORK(I+LYH-1) = Y(I) -C LOAD AND INVERT THE EWT ARRAY. (H IS TEMPORARILY SET TO ONE.) ------- - NQ = 1 - H = ONE - CALL ODESSA_EWSET (NYH, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) - DO 120 I = 1,NYH - IF (RWORK(I+LEWT-1) .LE. ZERO) GO TO 621 - 120 RWORK(I+LEWT-1) = ONE/RWORK(I+LEWT-1) - IF (ISOPT .EQ. 0) GO TO 125 -C CALL ODESSA_SPRIME TO LOAD FIRST-ORDER SENSITIVITY DERIVATIVES INTO -C REMAINING YH(*,2) POSITIONS. - CALL ODESSA_SPRIME (NEQ, Y, RWORK(LYH), NYH, N, NSV, RWORK(LWM), - 1 IWORK(LIWM), RWORK(LEWT), RWORK(LF0), RWORK(LACOR), - 2 RWORK(LDFDP), PAR, F, JAC, DF, ODESSA_PREPJ, ODESSA_PREPDF) - IF (IERSP .EQ. -1) GO TO 631 - IF (IERSP .EQ. -2) GO TO 632 -C----------------------------------------------------------------------- -C THE CODING BELOW COMPUTES THE STEP SIZE, H0, TO BE ATTEMPTED ON THE -C 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, ADJUSTED -C SO AS TO BE BETWEEN 100*UROUND AND 1.0E-3. ONLY THE ORIGINAL -C SOLUTION VECTOR IS CONSIDERED IN THIS CALCULATION (ISOPT = 0 OR 1). -C THEN THE COMPUTED VALUE H0 IS GIVEN BY.. -C NEQ -C H0**2 = TOL / ( W0**-2 + (1/NEQ) * SUM ( F(I)/YWT(I) )**2 ) -C 1 -C 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----------------------------------------------------------------------- - 125 IF (H0 .NE. ZERO) GO TO 180 - TDIST = DABS(TOUT - T) - W0 = DMAX1(DABS(T),DABS(TOUT)) - IF (TDIST .LT. TWO*UROUND*W0) GO TO 622 - TOL = RTOL(1) - IF (ITOL .LE. 2) GO TO 140 - DO 130 I = 1,N - 130 TOL = DMAX1(TOL,RTOL(I)) - 140 IF (TOL .GT. ZERO) GO TO 160 - ATOLI = ATOL(1) - DO 150 I = 1,N - IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) - AYI = DABS(Y(I)) - IF (AYI .NE. ZERO) TOL = DMAX1(TOL,ATOLI/AYI) - 150 CONTINUE - 160 TOL = DMAX1(TOL,100.0D0*UROUND) - TOL = DMIN1(TOL,0.001D0) - SUM = ODESSA_VNORM (N, RWORK(LF0), RWORK(LEWT)) - SUM = ONE/(TOL*W0*W0) + TOL*SUM**2 - H0 = ONE/DSQRT(SUM) - H0 = MIN(H0,TDIST) - H0 = DSIGN(H0,TOUT-T) -C ADJUST H0 IF NECESSARY TO MEET HMAX BOUND. --------------------------- - 180 RH = DABS(H0)*HMXI - IF (RH .GT. ONE) H0 = H0/RH -C LOAD H WITH H0 AND SCALE YH(*,2) BY H0. ------------------------------ - H = H0 - DO 190 I = 1,NYH - 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) - GO TO 270 -C----------------------------------------------------------------------- -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. ZERO) GO TO 250 - CALL ODESSA_INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) - IF (IFLAG .NE. 0) GO TO 627 - T = TOUT - GO TO 420 - 220 TP = TN - HU*(ONE + 100.0D0*UROUND) - IF ((TP - TOUT)*H .GT. ZERO) GO TO 623 - IF ((TN - TOUT)*H .LT. ZERO) GO TO 250 - GO TO 400 - 230 TCRIT = RWORK(1) - IF ((TN - TCRIT)*H .GT. ZERO) GO TO 624 - IF ((TCRIT - TOUT)*H .LT. ZERO) GO TO 625 - IF ((TN - TOUT)*H .LT. ZERO) GO TO 245 - CALL ODESSA_INTDY (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. ZERO) GO TO 624 - 245 HMX = DABS(TN) + DABS(H) - IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX - IF (IHIT) GO TO 400 - TNEXT = TN + H*(ONE + FOUR*UROUND) - IF ((TNEXT - TCRIT)*H .LE. ZERO) GO TO 250 - H = (TCRIT - TN)*(ONE - FOUR*UROUND) - IF (ISTATE .EQ. 2) JSTART = -2 -C----------------------------------------------------------------------- -C BLOCK E. -C THE NEXT BLOCK IS NORMALLY EXECUTED FOR ALL CALLS AND CONTAINS -C THE CALL TO THE ONE-STEP CORE INTEGRATOR ODESSA_STODE. -C -C THIS IS A LOOPING POINT FOR THE INTEGRATION STEPS. -C -C FIRST CHECK FOR TOO MANY STEPS BEING TAKEN, UPDATE EWT (IF NOT AT -C START OF PROBLEM), CHECK FOR TOO MUCH ACCURACY BEING REQUESTED, AND -C CHECK FOR H BELOW THE ROUNDOFF LEVEL IN T. -C TOLSF IS CALCULATED CONSIDERING ALL SOLUTION VECTORS. -C----------------------------------------------------------------------- - 250 CONTINUE - IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 - CALL ODESSA_EWSET (NYH, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) - DO 260 I = 1,NYH - IF (RWORK(I+LEWT-1) .LE. ZERO) GO TO 510 - 260 RWORK(I+LEWT-1) = ONE/RWORK(I+LEWT-1) - 270 TOLSF = UROUND*ODESSA_VNORM (NYH, RWORK(LYH), RWORK(LEWT)) - IF (TOLSF .LE. ONE) GO TO 280 - TOLSF = TOLSF*2.0D0 - IF (NST .EQ. 0) GO TO 626 - GO TO 520 - 280 IF (ODESSA_ADDX(TN,H) .NE. TN) GO TO 290 - NHNIL = NHNIL + 1 - IF (NHNIL .GT. MXHNIL) GO TO 290 - CALL XERRWD ('ODESSA - WARNING..INTERNAL T (=R1) AND H (=R2) ARE', - 1 50, 101, 1, 0, 0, 0, 0, ZERO, ZERO) - CALL XERRWD - 1 ('SUCH THAT IN THE MACHINE, T + H = T ON THE NEXT STEP', - 1 52, 101, 1, 0, 0, 0, 0, ZERO, ZERO) - CALL XERRWD ('(H = STEP SIZE). SOLVER WILL CONTINUE ANYWAY', - 1 44, 101, 1, 0, 0, 0, 2, TN, H) - IF (NHNIL .LT. MXHNIL) GO TO 290 - CALL XERRWD ('ODESSA - ABOVE WARNING HAS BEEN ISSUED I1 TIMES.', - 1 48, 102, 1, 0, 0, 0, 0, ZERO, ZERO) - CALL XERRWD ('IT WILL NOT BE ISSUED AGAIN FOR THIS PROBLEM', - 1 44, 102, 1, 1, MXHNIL, 0, 0, ZERO,ZERO) - 290 CONTINUE -C----------------------------------------------------------------------- -C CALL ODESSA_STODE(NEQ,Y,YH,NYH,YH,WM,IWM,EWT,SAVF,ACOR,PAR,NRS, -C 1 F,JAC,DF,ODESSA_PREPJ,ODESSA_PREPDF,ODESSA_SOLSY) -C----------------------------------------------------------------------- - CALL ODESSA_STODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), - 1 RWORK(LWM), IWORK(LIWM), RWORK(LEWT), RWORK(LSAVF), - 2 RWORK(LACOR), PAR, IWORK(LNRS), F, JAC, DF, ODESSA_PREPJ, - 3 ODESSA_PREPDF, ODESSA_SOLSY) - KGO = 1 - KFLAG - GO TO (300, 530, 540, 633), KGO -C----------------------------------------------------------------------- -C BLOCK F. -C THE FOLLOWING BLOCK HANDLES THE CASE OF A SUCCESSFUL RETURN FROM THE -C CORE INTEGRATOR (KFLAG = 0). TEST FOR STOP CONDITIONS. -C----------------------------------------------------------------------- - 300 INIT = 1 - GO TO (310, 400, 330, 340, 350), ITASK -C ITASK = 1. IF TOUT HAS BEEN REACHED, INTERPOLATE. ------------------- - 310 IF ((TN - TOUT)*H .LT. ZERO) GO TO 250 - CALL ODESSA_INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) - T = TOUT - GO TO 420 -C ITASK = 3. JUMP TO EXIT IF TOUT WAS REACHED. ------------------------ - 330 IF ((TN - TOUT)*H .GE. ZERO) GO TO 400 - GO TO 250 -C ITASK = 4. SEE IF TOUT OR TCRIT WAS REACHED. ADJUST H IF NECESSARY. - 340 IF ((TN - TOUT)*H .LT. ZERO) GO TO 345 - CALL ODESSA_INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) - T = TOUT - GO TO 420 - 345 HMX = DABS(TN) + DABS(H) - IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX - IF (IHIT) GO TO 400 - TNEXT = TN + H*(ONE + FOUR*UROUND) - IF ((TNEXT - TCRIT)*H .LE. ZERO) GO TO 250 - H = (TCRIT - TN)*(ONE - FOUR*UROUND) - JSTART = -2 - GO TO 250 -C ITASK = 5. SEE IF TCRIT WAS REACHED AND JUMP TO EXIT. --------------- - 350 HMX = DABS(TN) + DABS(H) - IHIT = DABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX -C----------------------------------------------------------------------- -C BLOCK G. -C THE FOLLOWING BLOCK HANDLES ALL SUCCESSFUL RETURNS FROM ODESSA. -C IF ITASK .NE. 1, Y IS LOADED FROM YH AND T IS SET ACCORDINGLY. -C ISTATE IS SET TO 2, THE ILLEGAL INPUT COUNTER IS ZEROED, AND THE -C OPTIONAL OUTPUTS ARE LOADED INTO THE WORK ARRAYS BEFORE RETURNING. -C IF ISTATE = 1 AND TOUT = T, THERE IS A RETURN WITH NO ACTION TAKEN, -C EXCEPT THAT IF THIS HAS HAPPENED REPEATEDLY, THE RUN IS TERMINATED. -C----------------------------------------------------------------------- - 400 DO 410 I = 1,NYH - 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 - ILLIN = 0 - RWORK(11) = HU - RWORK(12) = H - RWORK(13) = TN - IWORK(11) = NST - IWORK(12) = NFE - IWORK(13) = NJE - IWORK(14) = NQU - IWORK(15) = NQ - IF (ISOPT .EQ. 0) RETURN - IWORK(19) = NDFE - IWORK(20) = NSPE - RETURN - 430 NTREP = NTREP + 1 - IF (NTREP .LT. 5) RETURN - CALL XERRWD ('ODESSA -- REPEATED CALLS WITH ISTATE = 1 AND - 1 TOUT = T (=R1)', 59, 301, 1, 0, 0, 0, 1, T, ZERO) - GO TO 800 -C----------------------------------------------------------------------- -C BLOCK H. -C THE FOLLOWING BLOCK HANDLES ALL UNSUCCESSFUL RETURNS OTHER THAN -C 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, T IS SET TO TN, AND THE ILLEGAL INPUT -C COUNTER ILLIN IS SET TO 0. THE OPTIONAL OUTPUTS ARE LOADED INTO -C THE WORK ARRAYS BEFORE RETURNING. -C----------------------------------------------------------------------- -C THE MAXIMUM NUMBER OF STEPS WAS TAKEN BEFORE REACHING TOUT. ---------- - 500 CALL XERRWD ('ODESSA - AT CURRENT T (=R1), MXSTEP (=I1) STEPS', - 1 47, 201, 1, 0, 0, 0, 0, ZERO,ZERO) - CALL XERRWD ('TAKEN ON THIS CALL BEFORE REACHING TOUT', - 1 39, 201, 1, 1, MXSTEP, 0, 1, TN, ZERO) - ISTATE = -1 - GO TO 580 -C EWT(I) .LE. 0.0 FOR SOME I (NOT AT START OF PROBLEM). ---------------- - 510 EWTI = RWORK(LEWT+I-1) - CALL XERRWD ('ODESSA - AT T (=R1), EWT(I1) HAS BECOME R2 .LE. 0.', - 1 50, 202, 1, 1, I, 0, 2, TN, EWTI) - ISTATE = -6 - GO TO 580 -C TOO MUCH ACCURACY REQUESTED FOR MACHINE PRECISION. ------------------- - 520 CALL XERRWD ('ODESSA - AT T (=R1), TOO MUCH ACCURACY REQUESTED', - 1 48, 203, 1, 0, 0, 0, 0, ZERO,ZERO) - CALL XERRWD ('FOR PRECISION OF MACHINE.. SEE TOLSF (=R2)', - 1 43, 203, 1, 0, 0, 0, 2, TN, TOLSF) - RWORK(14) = TOLSF - ISTATE = -2 - GO TO 580 -C KFLAG = -1. ERROR TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ----- - 530 CALL XERRWD ('ODESSA - AT T(=R1) AND STEP SIZE H(=R2), THE ERROR', - 1 50, 204, 1, 0, 0, 0, 0, ZERO, ZERO) - CALL XERRWD ('TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN', - 1 44, 204, 1, 0, 0, 0, 2, TN, H) - ISTATE = -4 - GO TO 560 -C KFLAG = -2. CONVERGENCE FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ---- - 540 CALL XERRWD ('ODESSA - AT T (=R1) AND STEP SIZE H (=R2), THE', - 1 46, 205, 1, 0, 0, 0, 0, ZERO,ZERO) - CALL XERRWD ('CORRECTOR CONVERGENCE FAILED REPEATEDLY', - 1 39, 205, 1, 0, 0, 0, 0, ZERO,ZERO) - CALL XERRWD ('OR WITH ABS(H) = HMIN', - 1 21, 0, 1, 0, 0, 0, 2, TN, H) - ISTATE = -5 -C COMPUTE IMXER IF RELEVANT. ------------------------------------------- - 560 BIG = ZERO - IMXER = 1 - DO 570 I = 1,NYH - SIZE = DABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) - IF (BIG .GE. SIZE) GO TO 570 - BIG = SIZE - IMXER = I - 570 CONTINUE - IWORK(16) = IMXER -C SET Y VECTOR, T, ILLIN, AND OPTIONAL OUTPUTS. ------------------------ - 580 DO 590 I = 1,NYH - 590 Y(I) = RWORK(I+LYH-1) - T = TN - ILLIN = 0 - RWORK(11) = HU - RWORK(12) = H - RWORK(13) = TN - IWORK(11) = NST - IWORK(12) = NFE - IWORK(13) = NJE - IWORK(14) = NQU - IWORK(15) = NQ - IF (ISOPT .EQ. 0) RETURN - IWORK(19) = NDFE - IWORK(20) = NSPE - RETURN -C----------------------------------------------------------------------- -C BLOCK I. -C THE FOLLOWING BLOCK HANDLES ALL ERROR RETURNS DUE TO ILLEGAL INPUT -C (ISTATE = -3), AS DETECTED BEFORE CALLING THE CORE INTEGRATOR. -C FIRST THE ERROR MESSAGE ROUTINE IS CALLED. THEN IF THERE HAVE BEEN -C 5 CONSECUTIVE SUCH RETURNS JUST BEFORE THIS CALL TO THE SOLVER, -C THE RUN IS HALTED. -C----------------------------------------------------------------------- - 601 CALL XERRWD ('ODESSA - ISTATE (=I1) ILLEGAL', - 1 29, 1, 1, 1, ISTATE, 0, 0, ZERO,ZERO) - GO TO 700 - 602 CALL XERRWD ('ODESSA - ITASK (=I1) ILLEGAL', - 1 28, 2, 1, 1, ITASK, 0, 0, ZERO,ZERO) - GO TO 700 - 603 CALL XERRWD ('ODESSA - ISTATE .GT. 1 BUT ODESSA NOT INITIALIZED', - 1 49, 3, 1, 0, 0, 0, 0, ZERO,ZERO) - GO TO 700 - 604 CALL XERRWD ('ODESSA - NEQ (=I1) .LT. 1', - 1 25, 4, 1, 1, NEQ(1), 0, 0, ZERO,ZERO) - GO TO 700 - 605 CALL XERRWD ('ODESSA - ISTATE = 3 AND NEQ CHANGED. (I1 TO I2)', - 1 48, 5, 1, 2, N, NEQ(1), 0, ZERO,ZERO) - GO TO 700 - 606 CALL XERRWD ('ODESSA - ITOL (=I1) ILLEGAL', - 1 27, 6, 1, 1, ITOL, 0, 0, ZERO,ZERO) - GO TO 700 - 607 CALL XERRWD ('ODESSA - IOPT (=I1) ILLEGAL', - 1 27, 7, 1, 1, IOPT, 0, 0, ZERO,ZERO) - GO TO 700 - 608 CALL XERRWD('ODESSA - MF (=I1) ILLEGAL', - 1 25, 8, 1, 1, MF, 0, 0, ZERO,ZERO) - GO TO 700 - 609 CALL XERRWD('ODESSA - ML (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', - 1 50, 9, 1, 2, ML, NEQ(1), 0, ZERO,ZERO) - GO TO 700 - 610 CALL XERRWD('ODESSA - MU (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', - 1 50, 10, 1, 2, MU, NEQ(1), 0, ZERO,ZERO) - GO TO 700 - 611 CALL XERRWD('ODESSA - MAXORD (=I1) .LT. 0', - 1 28, 11, 1, 1, MAXORD, 0, 0, ZERO,ZERO) - GO TO 700 - 612 CALL XERRWD('ODESSA - MXSTEP (=I1) .LT. 0', - 1 28, 12, 1, 1, MXSTEP, 0, 0, ZERO,ZERO) - GO TO 700 - 613 CALL XERRWD('ODESSA - MXHNIL (=I1) .LT. 0', - 1 28, 13, 1, 1, MXHNIL, 0, 0, ZERO,ZERO) - GO TO 700 - 614 CALL XERRWD('ODESSA - TOUT (=R1) BEHIND T (=R2)', - 1 34, 14, 1, 0, 0, 0, 2, TOUT, T) - CALL XERRWD('INTEGRATION DIRECTION IS GIVEN BY H0 (=R1)', - 1 42, 14, 1, 0, 0, 0, 1, H0, ZERO) - GO TO 700 - 615 CALL XERRWD('ODESSA - HMAX (=R1) .LT. 0.0', - 1 28, 15, 1, 0, 0, 0, 1, HMAX, ZERO) - GO TO 700 - 616 CALL XERRWD('ODESSA - HMIN (=R1) .LT. 0.0', - 1 28, 16, 1, 0, 0, 0, 1, HMIN, ZERO) - GO TO 700 - 617 CALL XERRWD('ODESSA - RWORK LENGTH NEEDED, LENRW (=I1), EXCEEDS - 1 LRW (=I2)', 60, 17, 1, 2, LENRW, LRW, 0, ZERO,ZERO) - GO TO 700 - 618 CALL XERRWD('ODESSA - IWORK LENGTH NEEDED, LENIW (=I1), EXCEEDS - 1 LIW (=I2)', 60, 18, 1, 2, LENIW, LIW, 0, ZERO,ZERO) - GO TO 700 - 619 CALL XERRWD('ODESSA - RTOL(I1) IS R1 .LT. 0.0', - 1 32, 19, 1, 1, I, 0, 1, RTOLI, ZREO) - GO TO 700 - 620 CALL XERRWD('ODESSA - ATOL(I1) IS R1 .LT. 0.0', - 1 32, 20, 1, 1, I, 0, 1, ATOLI, ZERO) - GO TO 700 -* - 621 EWTI = RWORK(LEWT+I-1) - CALL XERRWD('ODESSA - EWT(I1) IS R1 .LE. 0.0', - 1 31, 21, 1, 1, I, 0, 1, EWTI, ZERO) - GO TO 700 - 622 CALL XERRWD('ODESSA - TOUT (=R1) TOO CLOSE TO T(=R2) TO START - 1 INTEGRATION', 60, 22, 1, 0, 0, 0, 2, TOUT, T) - GO TO 700 - 623 CALL XERRWD('ODESSA - ITASK = I1 AND TOUT (=R1) BEHIND TCUR - HU - 1 (= R2)', 58, 23, 1, 1, ITASK, 0, 2, TOUT, TP) - GO TO 700 - 624 CALL XERRWD('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TCUR - 1 (=R2)', 57, 24, 1, 0, 0, 0, 2, TCRIT, TN) - GO TO 700 - 625 CALL XERRWD('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TOUT - 1 (=R2)', 57, 25, 1, 0, 0, 0, 2, TCRIT, TOUT) - GO TO 700 - 626 CALL XERRWD('ODESSA - AT START OF PROBLEM, TOO MUCH ACCURACY', - 1 47, 26, 1, 0, 0, 0, 0, ZERO,ZERO) - CALL XERRWD('REQUESTED FOR PRECISION OF MACHINE. SEE TOLSF (=R1)', - 1 51, 26, 1, 0, 0, 0, 1, TOLSF, ZERO) - RWORK(14) = TOLSF - GO TO 700 - 627 CALL XERRWD - 1 ('ODESSA - TROUBLE FROM ODESSA_INTDY. ITASK = I1, TOUT = R1', - 1 57, 27, 1, 1, ITASK, 0, 1, TOUT, ZERO) - GO TO 700 -C ERROR STATEMENTS ASSOCIATED WITH SENSITIVITY ANALYSIS. - 628 CALL XERRWD('ODESSA - NPAR (=I1) .LT. 1', - 1 26, 28, 1, 1, NPAR, 0, 0, ZERO,ZERO) - GO TO 700 - 629 CALL XERRWD('ODESSA - ISTATE = 3 AND NPAR CHANGED (I1 TO I2)', - 1 47, 29, 1, 2, NP, NPAR, 0, ZERO,ZERO) - GO TO 700 - 630 CALL XERRWD('ODESSA - MITER (=I1) ILLEGAL', - 1 28, 30, 1, 1, MITER, 0, 0, ZERO,ZERO) - GO TO 700 - 631 CALL XERRWD('ODESSA - TROUBLE IN ODESSA_SPRIME (IERPJ)', - 1 41, 31, 1, 0, 0, 0, 0, ZERO,ZERO) - GO TO 700 - 632 CALL XERRWD('ODESSA - TROUBLE IN ODESSA_SPRIME (MITER)', - 1 41, 32, 1, 0, 0, 0, 0, ZERO,ZERO) - GO TO 700 - 633 CALL XERRWD('ODESSA - FATAL ERROR IN ODESSA_STODE (KFLAG = -3)', - 1 49, 33, 2, 0, 0, 0, 0, ZERO,ZERO) - GO TO 801 -C - 700 IF (ILLIN .EQ. 5) GO TO 710 - ILLIN = ILLIN + 1 - ISTATE = -3 - RETURN - 710 CALL XERRWD('ODESSA - REPEATED OCCURRENCES OF ILLEGAL INPUT', - 1 46, 302, 1, 0, 0, 0, 0, ZERO,ZERO) -C - 800 CALL XERRWD('ODESSA - RUN ABORTED.. APPARENT INFINITE LOOP', - 1 45, 303, 2, 0, 0, 0, 0, ZERO,ZERO) - RETURN - 801 CALL XERRWD('ODESSA - RUN ABORTED', - 1 20, 304, 2, 0, 0, 0, 0, ZERO,ZERO) - RETURN -C-------------------- END OF SUBROUTINE ODESSA ------------------------- - END
--- a/liboctave/ChangeLog Fri Oct 31 15:11:45 2003 +0000 +++ b/liboctave/ChangeLog Fri Oct 31 15:20:51 2003 +0000 @@ -1,5 +1,11 @@ 2003-10-31 John W. Eaton <jwe@bevo.che.wisc.edu> + * LSODE.cc (LSODE::do_integrate): Avoid name conflict on systems + that upcase Fortran names by calling dlsode instead of lsode. + + * ODESSA.cc (ODESSA::do_integrate): Avoid name conflict on systems + that upcase Fortran names by calling dodessa instead of odessa. + * file-ops.cc (file_ops::symlink): Cope with systems that expect non-const args for symlink system call. (file_ops::readlink): Likewise, for readlink.
--- a/liboctave/LSODE.cc Fri Oct 31 15:11:45 2003 +0000 +++ b/liboctave/LSODE.cc Fri Oct 31 15:20:51 2003 +0000 @@ -47,10 +47,10 @@ extern "C" { F77_RET_T - F77_FUNC (lsode, LSODE) (lsode_fcn_ptr, int&, double*, double&, - double&, int&, double&, const double*, int&, - int&, int&, double*, int&, int*, int&, - lsode_jac_ptr, int&); + F77_FUNC (dlsode, DLSODE) (lsode_fcn_ptr, int&, double*, double&, + double&, int&, double&, const double*, int&, + int&, int&, double*, int&, int*, int&, + lsode_jac_ptr, int&); } static ODEFunc::ODERHSFunc user_fun; @@ -273,9 +273,9 @@ LSODE_options::reset = false; } - F77_XFCN (lsode, LSODE, (lsode_f, nn, px, t, tout, itol, rel_tol, - pabs_tol, itask, istate, iopt, prwork, lrw, - piwork, liw, lsode_j, method_flag)); + F77_XFCN (dlsode, DLSODE, (lsode_f, nn, px, t, tout, itol, rel_tol, + pabs_tol, itask, istate, iopt, prwork, lrw, + piwork, liw, lsode_j, method_flag)); if (f77_exception_encountered) {
--- a/liboctave/ODESSA.cc Fri Oct 31 15:11:45 2003 +0000 +++ b/liboctave/ODESSA.cc Fri Oct 31 15:20:51 2003 +0000 @@ -55,11 +55,11 @@ extern "C" { F77_RET_T - F77_FUNC (odessa, ODESSA) (odessa_fcn_ptr, odessa_dfdp_ptr, int*, - double*, double*, double&, double&, - int&, double&, const double*, int&, - int&, int*, double*, int&, int*, int&, - odessa_jac_ptr, int&); + F77_FUNC (dodessa, DODESSA) (odessa_fcn_ptr, odessa_dfdp_ptr, int*, + double*, double*, double&, double&, + int&, double&, const double*, int&, + int&, int*, double*, int&, int*, int&, + odessa_jac_ptr, int&); } template class Array<Matrix>; @@ -457,10 +457,10 @@ const double *pabs_tol = abs_tol.fortran_vec (); - F77_XFCN (odessa, ODESSA, (odessa_f, odessa_b, pneq, py, ppar, t, - tout, itol, rel_tol, pabs_tol, itask, - istate, piopt, prwork, lrw, piwork, liw, - odessa_j, method_flag)); + F77_XFCN (dodessa, DODESSA, (odessa_f, odessa_b, pneq, py, ppar, t, + tout, itol, rel_tol, pabs_tol, itask, + istate, piopt, prwork, lrw, piwork, liw, + odessa_j, method_flag)); if (f77_exception_encountered) {