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[project @ 2004-09-22 03:33:29 by jwe]
| author | jwe |
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| date | Wed, 22 Sep 2004 03:33:29 +0000 |
| parents | 70da2b8c91dd |
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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