C      ALGORITHM 658, COLLECTED ALGORITHMS FROM ACM.
C      THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C      VOL. 14, NO. 1, P.61.
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----------------------------------------------------------------------
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 SPRIME. EACH CALL
C                  TO 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 (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 ODESSA, 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 ODESSA..
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 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 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 SVCOM
C                            WITH THE SAME ARGUMENTS.
C
C                            SVCOM AND 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 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 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 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 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        /EH0001/  OF LENGTH  2 (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 SVCOM AND 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) 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 (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 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 EWSET IS PASSED TO THE
C 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 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 /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) 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 (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 VNORM IS CALLED WITH LV = N 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 ODESSA.
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 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  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  STESA   MANAGES THE SOLUTION OF THE SENSITIVITY FUNCTIONS.
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          IT IS ALSO CALLED BY SPRIME (WITH JOPT = 1) TO JUST
C          COMPUTE THE JACOBIAN MATRIX.
C  PREPDF  COMPUTES THE INHOMOGENEITY MATRIX DF/DP.
C  SPRIME  DEFINES THE SYSTEM OF SENSITIVITY EQUATIONS.
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  SVCOM AND RSCOM  ARE USER-CALLABLE ROUTINES TO SAVE AND RESTORE,
C          RESPECTIVELY, THE CONTENTS OF THE INTERNAL COMMON BLOCKS.
C  DGEFA AND DGESL  ARE ROUTINES FROM LINPACK FOR SOLVING FULL
C          SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS.
C  DGBFA AND DGBSL  ARE ROUTINES FROM LINPACK 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  XERR, XSETUN, AND XSETF  HANDLE THE PRINTING OF ALL ERROR
C          MESSAGES AND WARNINGS.
C NOTE..  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 SPRIME TO ESTABLISH INITIAL CONDITIONS
C             FOR THE SENSITIVITY CALCULATIONS.
C
C      STODE  THE ONE STEP INTEGRATOR IS SLIGHTLY MODIFIED AND RETAINS
C             ITS ORIGINAL NAME. IT NOW CONTAINS THE CALL TO STESA,
C             AND ALSO CALLS SPRIME IF KFLAG .LE. -3.
C
C      PREPJ  ALSO NAMED 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 STESA, SPRIME, AND 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 STODE TO 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 STODE TO
C                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      SVCOM,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-----------------------------------------------------------------------
C-----------------------------------------------------------------------
C     S T A R T
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
      SUBROUTINE ODESSA(NEQ, Y, PAR, T, TOUT, ITOL, RTOL, ATOL,
     1    ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF)

      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      LOGICAL IHIT
      EXTERNAL PREPJ, SOLSY, PREPDF
      DIMENSION NEQ(*), Y(*), PAR(*), RTOL(*), ATOL(*), IOPT(*),
     1   RWORK(LRW), IWORK(LIW), MORD(2)


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 STODE, AND FINALLY THOSE USED
C FOR COMMUNICATION.  THE BLOCKS ARE DECLARED IN SUBROUTINES ODESSA
C INTDY, STODE, STESA, PREPJ, PREPDF, AND SOLSY.  GROUPS OF VARIABLES
C ARE REPLACED BY DUMMY ARRAYS IN THE COMMON DECLARATIONS IN ROUTINES
C 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 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) = SQRT(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 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) = SQRT(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 ODE (NEQ(1), NEQ(2), T, Y, RWORK(LF0), PAR)
      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 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 SPRIME TO LOAD FIRST-ORDER SENSITIVITY DERIVATIVES INTO
C REMAINING YH(*,2) POSITIONS.

      CALL SPRIME (NEQ, Y, RWORK(LYH), NYH, N, NSV, RWORK(LWM),
     1     IWORK(LIWM), RWORK(LEWT), RWORK(LF0), RWORK(LACOR),
     2     RWORK(LDFDP), PAR, PREPJ, 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 = ABS(TOUT - T)
      W0 = MAX(ABS(T),ABS(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 = MAX(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 = ABS(Y(I))
        IF (AYI .NE. ZERO) TOL = MAX(TOL,ATOLI/AYI)
 150    CONTINUE
 160   TOL = MAX(TOL,100.0D0*UROUND)
      TOL = MIN(TOL,0.001D0)
      SUM = VNORM (N, RWORK(LF0), RWORK(LEWT))
      SUM = ONE/(TOL*W0*W0) + TOL*SUM**2
      H0 = ONE/SQRT(SUM)
      H0 = MIN(H0,TDIST)
      H0 = SIGN(H0,TOUT-T)
C ADJUST H0 IF NECESSARY TO MEET HMAX BOUND. ---------------------------
 180   RH = ABS(H0)*HMXI
      IF (RH .GT. 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 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 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 = ABS(TN) + ABS(H)
      IHIT = ABS(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 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 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*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 (ADDX(TN,H) .NE. TN) GO TO 290
      NHNIL = NHNIL + 1
      IF (NHNIL .GT. MXHNIL) GO TO 290
      CALL XERR ('ODESSA - WARNING..INTERNAL T (=R1) AND H (=R2) ARE',
     1   101, 1, 0, 0, 0, 0, ZERO, ZERO)
      CALL XERR ('SUCH THAT IN THE MACHINE, T + H = T ON THE NEXT STEP',
     1   101, 1, 0, 0, 0, 0, ZERO, ZERO)
      CALL XERR ('(H = STEP SIZE). SOLVER WILL CONTINUE ANYWAY',
     1   101, 1, 0, 0, 0, 2, TN, H)
      IF (NHNIL .LT. MXHNIL) GO TO 290
      CALL XERR ('ODESSA - ABOVE WARNING HAS BEEN ISSUED I1 TIMES.',
     1   102, 1, 0, 0, 0, 0, ZERO, ZERO)
      CALL XERR ('IT WILL NOT BE ISSUED AGAIN FOR THIS PROBLEM',
     1   102, 1, 1, MXHNIL, 0, 0, ZERO,ZERO)
 290   CONTINUE
C-----------------------------------------------------------------------
C     CALL STODE(NEQ,Y,YH,NYH,YH,WM,IWM,EWT,SAVF,ACOR,PAR,NRS,
C    1   F,JAC,DF,PREPJ,PREPDF,SOLSY)
C-----------------------------------------------------------------------
       CALL STODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LWM),
     1   IWORK(LIWM), RWORK(LEWT), RWORK(LSAVF), RWORK(LACOR),
     2   PAR, IWORK(LNRS), PREPJ, PREPDF, 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 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 INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG)
      T = TOUT
      GO TO 420
 345   HMX = ABS(TN) + ABS(H)
      IHIT = ABS(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 = ABS(TN) + ABS(H)
      IHIT = ABS(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 XERR ('ODESSA -- REPEATED CALLS WITH ISTATE = 1 AND
     1TOUT = T (=R1)', 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 XERR ('ODESSA - AT CURRENT T (=R1), MXSTEP (=I1) STEPS',
     1   201, 1, 0, 0, 0, 0, ZERO,ZERO)
      CALL XERR ('TAKEN ON THIS CALL BEFORE REACHING TOUT',
     1   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 XERR ('ODESSA - AT T (=R1), EWT(I1) HAS BECOME R2 .LE. 0.',
     1   202, 1, 1, I, 0, 2, TN, EWTI)
      ISTATE = -6
      GO TO 580
C TOO MUCH ACCURACY REQUESTED FOR MACHINE PRECISION. -------------------
 520  CALL XERR ('ODESSA - AT T (=R1), TOO MUCH ACCURACY REQUESTED',
     1  203, 1, 0, 0, 0, 0, ZERO,ZERO)
      CALL XERR ('FOR PRECISION OF MACHINE..  SEE TOLSF (=R2)',
     1  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 XERR ('ODESSA - AT T(=R1) AND STEP SIZE H(=R2), THE ERROR',
     1  204, 1, 0, 0, 0, 0, ZERO, ZERO)
      CALL XERR ('TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN',
     1  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 XERR ('ODESSA - AT T (=R1) AND STEP SIZE H (=R2), THE',
     1  205, 1, 0, 0, 0, 0, ZERO,ZERO)
      CALL XERR ('CORRECTOR CONVERGENCE FAILED REPEATEDLY',
     1   205, 1, 0, 0, 0, 0, ZERO,ZERO)
      CALL XERR ('OR WITH ABS(H) = HMIN',
     1   205, 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 = ABS(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 XERR ('ODESSA - ISTATE (=I1) ILLEGAL',
     1  1, 1, 1, ISTATE, 0, 0, ZERO,ZERO)
      GO TO 700
 602   CALL XERR ('ODESSA - ITASK (=I1) ILLEGAL',
     1  2, 1, 1, ITASK, 0, 0, ZERO,ZERO)
      GO TO 700
 603  CALL XERR ('ODESSA - ISTATE .GT. 1 BUT ODESSA NOT INITIALIZED',
     1  3, 1, 0, 0, 0, 0, ZERO,ZERO)
      GO TO 700
 604   CALL XERR ('ODESSA - NEQ (=I1) .LT. 1',
     1  4, 1, 1, NEQ(1), 0, 0, ZERO,ZERO)
      GO TO 700
 605  CALL XERR ('ODESSA - ISTATE = 3 AND NEQ CHANGED.  (I1 TO I2)',
     1  5, 1, 2, N, NEQ(1), 0, ZERO,ZERO)
      GO TO 700
 606   CALL XERR ('ODESSA - ITOL (=I1) ILLEGAL',
     1  6, 1, 1, ITOL, 0, 0, ZERO,ZERO)
      GO TO 700
 607   CALL XERR ('ODESSA - IOPT (=I1) ILLEGAL',
     1   7, 1, 1, IOPT, 0, 0, ZERO,ZERO)
      GO TO 700
 608   CALL XERR('ODESSA - MF (=I1) ILLEGAL',
     1   8, 1, 1, MF, 0, 0, ZERO,ZERO)
      GO TO 700
 609  CALL XERR('ODESSA - ML (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)',
     1   9, 1, 2, ML, NEQ(1), 0, ZERO,ZERO)
      GO TO 700
 610  CALL XERR('ODESSA - MU (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)',
     1   10, 1, 2, MU, NEQ(1), 0, ZERO,ZERO)
      GO TO 700
 611   CALL XERR('ODESSA - MAXORD (=I1) .LT. 0',
     1   11, 1, 1, MAXORD, 0, 0, ZERO,ZERO)
      GO TO 700
 612   CALL XERR('ODESSA - MXSTEP (=I1) .LT. 0',
     1   12, 1, 1, MXSTEP, 0, 0, ZERO,ZERO)
      GO TO 700
 613   CALL XERR('ODESSA - MXHNIL (=I1) .LT. 0',
     1   13, 1, 1, MXHNIL, 0, 0, ZERO,ZERO)
      GO TO 700
 614   CALL XERR('ODESSA - TOUT (=R1) BEHIND T (=R2)',
     1   14, 1, 0, 0, 0, 2, TOUT, T)
      CALL XERR('INTEGRATION DIRECTION IS GIVEN BY H0 (=R1)',
     1   14, 1, 0, 0, 0, 1, H0, ZERO)
      GO TO 700
 615   CALL XERR('ODESSA - HMAX (=R1) .LT. 0.0',
     1   15, 1, 0, 0, 0, 1, HMAX, ZERO)
      GO TO 700
 616   CALL XERR('ODESSA - HMIN (=R1) .LT. 0.0',
     1   16, 1, 0, 0, 0, 1, HMIN, ZERO)
      GO TO 700
 617  CALL XERR('ODESSA - RWORK LENGTH NEEDED, LENRW (=I1), EXCEEDS
     1 LRW (=I2)', 17, 1, 2, LENRW, LRW, 0, ZERO,ZERO)
      GO TO 700
 618  CALL XERR('ODESSA - IWORK LENGTH NEEDED, LENIW (=I1), EXCEEDS
     1 LIW (=I2)', 18, 1, 2, LENIW, LIW, 0, ZERO,ZERO)
      GO TO 700
 619   CALL XERR('ODESSA - RTOL(I1) IS R1 .LT. 0.0',
     1   19, 1, 1, I, 0, 1, RTOLI, ZREO)
      GO TO 700
 620   CALL XERR('ODESSA - ATOL(I1) IS R1 .LT. 0.0',
     1   20, 1, 1, I, 0, 1, ATOLI, ZERO)
      GO TO 700
 621   EWTI = RWORK(LEWT+I-1)
      CALL XERR('ODESSA - EWT(I1) IS R1 .LE. 0.0',
     1   21, 1, 1, I, 0, 1, EWTI, ZERO)
      GO TO 700
 622  CALL XERR('ODESSA - TOUT (=R1) TOO CLOSE TO T(=R2) TO START
     1 INTEGRATION', 22, 1, 0, 0, 0, 2, TOUT, T)
      GO TO 700
 623  CALL XERR('ODESSA - ITASK = I1 AND TOUT (=R1) BEHIND TCUR - HU
     1 (= R2)', 23, 1, 1, ITASK, 0, 2, TOUT, TP)
      GO TO 700
 624  CALL XERR('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TCUR
     1 (=R2)', 24, 1, 0, 0, 0, 2, TCRIT, TN)
      GO TO 700
 625   CALL XERR('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TOUT
     1 (=R2)', 25, 1, 0, 0, 0, 2, TCRIT, TOUT)
      GO TO 700
 626  CALL XERR('ODESSA - AT START OF PROBLEM, TOO MUCH ACCURACY',
     1   26, 1, 0, 0, 0, 0, ZERO,ZERO)
      CALL XERR('REQUESTED FOR PRECISION OF MACHINE. SEE TOLSF (=R1)',
     1   26, 1, 0, 0, 0, 1, TOLSF, ZERO)
      RWORK(14) = TOLSF
      GO TO 700
 627  CALL XERR('ODESSA - TROUBLE FROM INTDY. ITASK = I1, TOUT = R1',
     1   27, 1, 1, ITASK, 0, 1, TOUT, ZERO)
      GO TO 700
C ERROR STATEMENTS ASSOCIATED WITH SENSITIVITY ANALYSIS.
 628  CALL XERR('ODESSA - NPAR (=I1) .LT. 1',
     1   28, 1, 1, NPAR, 0, 0, ZERO,ZERO)
      GO TO 700
 629  CALL XERR('ODESSA - ISTATE = 3 AND NPAR CHANGED (I1 TO I2)',
     1   29, 1, 2, NP, NPAR, 0, ZERO,ZERO)
      GO TO 700
 630  CALL XERR('ODESSA - MITER (=I1) ILLEGAL',
     1   30, 1, 1, MITER, 0, 0, ZERO,ZERO)
      GO TO 700
 631  CALL XERR('ODESSA - TROUBLE IN SPRIME (IERPJ)',
     1   31, 1, 0, 0, 0, 0, ZERO,ZERO)
      GO TO 700
 632  CALL XERR('ODESSA - TROUBLE IN SPRIME (MITER)',
     1   32, 1, 0, 0, 0, 0, ZERO,ZERO)
      GO TO 700
 633  CALL XERR('ODESSA - FATAL ERROR IN STODE (KFLAG = -3)',
     1   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 XERR('ODESSA - REPEATED OCCURRENCES OF ILLEGAL INPUT',
     1   302, 1, 0, 0, 0, 0, ZERO,ZERO)
C
 800  CALL XERR('ODESSA - RUN ABORTED.. APPARENT INFINITE LOOP',
     1   303, 2, 0, 0, 0, 0, ZERO,ZERO)
      RETURN
 801  CALL XERR('ODESSA - RUN ABORTED',
     1   304, 2, 0, 0, 0, 0, ZERO,ZERO)
      RETURN
C-------------------- END OF SUBROUTINE ODESSA -------------------------
      END
      DOUBLE PRECISION FUNCTION ADDX(A,B)
      DOUBLE PRECISION A,B
C
C  THIS FUNCTION IS NECESSARY TO FORCE OPTIMIZING COMPILERS TO
C  EXECUTE AND STORE A SUM, FOR SUCCESSFUL EXECUTION OF THE
C  TEST A + B = B.
C
      ADDX = A + B
      RETURN
C-------------------- END OF FUNCTION SUM ------------------------------
      END

      SUBROUTINE SPRIME (NEQ, Y, YH, NYH, NROW, NCOL, WM, IWM,
     1  EWT, SAVF, FTEM, DFDP, PAR, PJAC, PDF)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION NEQ(*), Y(*), YH(NROW,NCOL,*), WM(*), IWM(*),
     1  EWT(*), SAVF(*), FTEM(*), DFDP(NROW,*), PAR(*)
      EXTERNAL PJAC, PDF
      PARAMETER (ONE=1.0D0,ZERO=0.0D0)
      COMMON /ODE001/ ROWND, ROWNS(173),
     1  RDUM1(37),EL0, H, RDUM2(4), TN, RDUMMY,
     2  IOWND1(14), IOWNS(4),
     3  IDUM1(3), IERPJ, IDUM2(6),
     4  MITER, IDUM3(4), N, IDUM4(5)
      COMMON /ODE002/ RDUM3(3),
     1  IOWND2(3), IDUM5, NSV, IDUM6, NSPE, IDUM7, IERSP, JOPT, IDUM8

C-----------------------------------------------------------------------
C SPRIME IS CALLED BY ODESSA TO INITIALIZE THE YH ARRAY. IT IS ALSO
C CALLED BY STODE TO REEVALUATE FIRST ORDER DERIVATIVES WHEN KFLAG
C .LE. -3. SPRIME COMPUTES THE FIRST DERIVATIVES OF THE SENSITIVITY
C COEFFICIENTS WITH RESPECT TO THE INDEPENDENT VARIABLE T...
C
C        SPRIME = D(DY/DP)/DT = JAC*DY/DP + DF/DP
C                   WHERE JAC = JACOBIAN MATRIX
C                       DY/DP = SENSITIVITY MATRIX
C                       DF/DP = INHOMOGENEITY MATRIX
C THIS ROUTINE USES THE COMMON VARIABLES EL0, H, IERPJ, MITER, N,
C NSV, NSPE, IERSP, JOPT
C-----------------------------------------------------------------------
C CALL PREPJ WITH JOPT = 1.
C IF MITER = 2 OR 5, EL0 IS TEMPORARILY SET TO -1.0 AND H IS
C TEMPORARILY SET TO 1.0D0.
C-----------------------------------------------------------------------

      NSPE = NSPE + 1
      JOPT = 1
      IF (MITER .EQ. 1 .OR. MITER .EQ. 4) GO TO 10
      HTEMP = H
      ETEMP = EL0
      H = ONE
      EL0 = -ONE
 10   CALL PJAC (NEQ, Y, YH, NYH, WM, IWM, EWT, SAVF, FTEM,
     1   PAR, JOPT)
      IF (IERPJ .NE. 0) GO TO 300
      JOPT = 0
      IF (MITER .EQ. 1 .OR. MITER .EQ. 4) GO TO 20
      H = HTEMP
      EL0 = ETEMP
C-----------------------------------------------------------------------
C CALL PREPDF AND LOAD DFDP(*,JPAR).
C-----------------------------------------------------------------------

      
 20   IF (NEQ(4) .EQ. 0) THEN
         CALL AD_ODE ((NSV-1),(NSV-1),N,TN,Y,PAR(NSV-1),PAR(N+NSV-1),
     1        N,PAR,PAR(N+NSV-1+N*(NSV-1)),(NSV-1))
         DO 28 J = 2,NSV
            JPAR = J - 1
            DO 29 I = 1,N
               DFDP(I,JPAR) = PAR(N+NSV-1+(JPAR-1)*N+I-1)
 29         CONTINUE
 28      CONTINUE
      ENDIF

      IF (NEQ(4) .EQ. 1) THEN
         DO 30 J = 2,NSV
            JPAR = J - 1
            CALL PDF (NEQ, Y, WM, SAVF, FTEM, DFDP(1,JPAR),
     1           PAR, JPAR)
 30      CONTINUE
      ENDIF

C-----------------------------------------------------------------------
C COMPUTE JAC*DY/DP AND STORE RESULTS IN YH(*,*,2).
C-----------------------------------------------------------------------
      GO TO (40,40,310,100,100) MITER
C THE JACOBIAN IS FULL.------------------------------------------------
C FOR EACH ROW OF THE JACOBIAN..
 40   DO 70 IROW = 1,N
C AND EACH COLUMN OF THE SENSITIVITY MATRIX..
        DO 60 J = 2,NSV
          SUM = ZERO
C TAKE THE VECTOR DOT PRODUCT..
          DO 50 I = 1,N
            IPD = IROW + N*(I-1) + 2
            SUM = SUM + WM(IPD)*YH(I,J,1)
 50       CONTINUE
          YH(IROW,J,2) = SUM
 60     CONTINUE
 70   CONTINUE
      GO TO 200
C THE JACOBIAN IS BANDED.-----------------------------------------------
 100  ML = IWM(1)
      MU = IWM(2)
      ICOUNT = 1
      MBAND = ML + MU + 1
      MEBAND = MBAND + ML
      NMU = N - MU
      ML1 = ML + 1
C FOR EACH ROW OF THE JACOBIAN..
      DO 160 IROW = 1,N
        IF (IROW .GT. ML1) GO TO 110
        IPD = MBAND + IROW + 1
        IYH = 1
        LBAND = MU + IROW
        GO TO 120
 110    ICOUNT = ICOUNT + 1
        IPD = ICOUNT*MEBAND + 2
        IYH = IYH + 1
        LBAND = LBAND - 1
        IF (IROW .LE. NMU) LBAND = MBAND
C AND EACH COLUMN OF THE SENSITIVITY MATRIX..
 120    DO 150 J = 2,NSV
          SUM = ZERO
          I1 = IPD
          I2 = IYH
C TAKE THE VECTOR DOT PRODUCT.
          DO 140 I = 1,LBAND
            SUM = SUM + WM(I1)*YH(I2,J,1)
            I1 = I1 + MEBAND - 1
            I2 = I2 + 1
 140      CONTINUE
          YH(IROW,J,2) = SUM
 150    CONTINUE
 160  CONTINUE
C-----------------------------------------------------------------------
C ADD THE INHOMOGENEITY TERM, I.E., ADD DFDP(*,JPAR) TO YH(*,JPAR+1,2).
C-----------------------------------------------------------------------
 200  DO 220 J = 2,NSV
        JPAR = J - 1
        DO 210 I = 1,N
          YH(I,J,2) = YH(I,J,2) + DFDP(I,JPAR)
 210    CONTINUE
 220  CONTINUE
      RETURN
C-----------------------------------------------------------------------
C ERROR RETURNS.
C-----------------------------------------------------------------------
 300  IERSP = -1
      RETURN
 310  IERSP = -2
      RETURN
C------------------------END OF SUBROUTINE SPRIME-----------------------
      END
      SUBROUTINE PREPJ (NEQ, Y, YH, NYH, WM, IWM, EWT, SAVF, FTEM,
     1   PAR, JOPT)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION NEQ(*), Y(*), YH(NYH,*), WM(*), IWM(*), EWT(*),
     1   SAVF(*), FTEM(*), PAR(*)
      PARAMETER (ZERO=0.0D0,ONE=1.0D0)
      COMMON /ODE001/ ROWND, ROWNS(173),
     2   RDUM1(37), EL0, H, RDUM2(4), TN, UROUND,
     3   IOWND(14), IOWNS(4),
     4   IDUM1(3), IERPJ, IDUM2, JCUR, IDUM3(4),
     5   MITER, IDUM4(4), N, IDUM5(2), NFE, NJE, IDUM6
C-----------------------------------------------------------------------
C PREPJ IS CALLED BY STODE TO COMPUTE AND PROCESS THE MATRIX
C P = I - H*EL(1)*J , WHERE J IS AN APPROXIMATION TO THE JACOBIAN.
C IF ISOPT = 1, PREPJ IS ALSO CALLED BY SPRIME WITH JOPT = 1.
C HERE J IS COMPUTED BY THE USER-SUPPLIED ROUTINE JAC IF
C MITER = 1 OR 4, OR BY FINITE DIFFERENCING IF MITER = 2, 3, OR 5.
C IF MITER = 3, A DIAGONAL APPROXIMATION TO J IS USED.
C J IS STORED IN WM AND REPLACED BY P.  IF MITER .NE. 3, P IS THEN
C SUBJECTED TO LU DECOMPOSITION (JOPT = 0) IN PREPARATION FOR LATER
C SOLUTION OF LINEAR SYSTEMS WITH P AS COEFFICIENT MATRIX. THIS IS
C DONE BY DGEFA IF MITER = 1 OR 2, AND BY DGBFA IF MITER = 4 OR 5.
C
C IN ADDITION TO VARIABLES DESCRIBED PREVIOUSLY, COMMUNICATION
C WITH PREPJ USES THE FOLLOWING..
C Y     = ARRAY CONTAINING PREDICTED VALUES ON ENTRY.
C FTEM  = WORK ARRAY OF LENGTH N (ACOR IN STODE).
C SAVF  = ARRAY CONTAINING F EVALUATED AT PREDICTED Y.
C WM    = REAL WORK SPACE FOR MATRICES.  ON OUTPUT IT CONTAINS THE
C         INVERSE DIAGONAL MATRIX IF MITER = 3 AND THE LU DECOMPOSITION
C         OF P IF MITER IS 1, 2 , 4, OR 5.
C         STORAGE OF MATRIX ELEMENTS STARTS AT WM(3).
C         WM ALSO CONTAINS THE FOLLOWING MATRIX-RELATED DATA..
C         WM(1) = SQRT(UROUND), USED IN NUMERICAL JACOBIAN INCREMENTS.
C         WM(2) = H*EL0, SAVED FOR LATER USE IF MITER = 3.
C IWM   = INTEGER WORK SPACE CONTAINING PIVOT INFORMATION, STARTING AT
C         IWM(21), IF MITER IS 1, 2, 4, OR 5.  IWM ALSO CONTAINS BAND
C         PARAMETERS ML = IWM(1) AND MU = IWM(2) IF MITER IS 4 OR 5.
C EL0   = EL(1) (INPUT).
C IERPJ = OUTPUT ERROR FLAG,  = 0 IF NO TROUBLE, .GT. 0 IF
C         P MATRIX FOUND TO BE SINGULAR.
C JCUR  = OUTPUT FLAG = 1 TO INDICATE THAT THE JACOBIAN MATRIX
C         (OR APPROXIMATION) IS NOW CURRENT.
C JOPT  = INPUT JACOBIAN OPTION, = 1 IF JAC IS DESIRED ONLY.
C THIS ROUTINE ALSO USES THE COMMON VARIABLES EL0, H, TN, UROUND,
C IERPJ, JCUR, MITER, N, NFE, AND NJE.
C-----------------------------------------------------------------------
      NJE = NJE + 1
      IERPJ = 0
      JCUR = 1
      HL0 = H*EL0
      GO TO (100, 200, 300, 400, 500), MITER
C IF MITER = 1, CALL JAC AND MULTIPLY BY SCALAR. -----------------------
 100   LENP = N*N
      DO 110 I = 1,LENP
 110    WM(I+2) = ZERO

C      CALL JAC (NEQ, TN, Y, PAR, 0, 0, WM(3), N)
      CALL JAC (NEQ, TN, Y, NEQ(1), PAR, NEQ(2), WM(3))

      IF (JOPT .EQ. 1) RETURN
      CON = -HL0
      DO 120 I = 1,LENP
 120    WM(I+2) = WM(I+2)*CON
      GO TO 240
C IF MITER = 2, MAKE N CALLS TO F TO APPROXIMATE J. --------------------
 200   FAC = VNORM (N, SAVF, EWT)
      R0 = 1000.0D0*ABS(H)*UROUND*REAL(N)*FAC
      IF (R0 .EQ. ZERO) R0 = ONE
      SRUR = WM(1)
      J1 = 2
      DO 230 J = 1,N
        YJ = Y(J)
        R = MAX(SRUR*ABS(YJ),R0/EWT(J))
        Y(J) = Y(J) + R
        FAC = -HL0/R
C        CALL F (NEQ, TN, Y, PAR, FTEM)
C        CALL ODE (NEQ, TN, Y, PAR, FTEM)
        CALL ODE (NEQ(1), NEQ(2), TN, Y, FTEM, PAR)
        DO 220 I = 1,N
 220      WM(I+J1) = (FTEM(I) - SAVF(I))*FAC
        Y(J) = YJ
        J1 = J1 + N
 230    CONTINUE
      NFE = NFE + N
      IF (JOPT .EQ. 1) RETURN
C ADD IDENTITY MATRIX. -------------------------------------------------
 240   J = 3
      DO 250 I = 1,N
        WM(J) = WM(J) + ONE
 250    J = J + (N + 1)
C DO LU DECOMPOSITION ON P. --------------------------------------------
      CALL DGEFA (WM(3), N, N, IWM(21), IER)
      IF (IER .NE. 0) IERPJ = 1
      RETURN
C IF MITER = 3, CONSTRUCT A DIAGONAL APPROXIMATION TO J AND P. ---------
 300   WM(2) = HL0
      R = EL0*0.1D0
      DO 310 I = 1,N
 310    Y(I) = Y(I) + R*(H*SAVF(I) - YH(I,2))
C      CALL F (NEQ, TN, Y, PAR, WM(3))
C      CALL ODE (NEQ, TN, Y, PAR, WM(3))
      CALL ODE (NEQ(1), NEQ(2), T, Y, WM(3), PAR)
      NFE = NFE + 1
      DO 320 I = 1,N
        R0 = H*SAVF(I) - YH(I,2)
        DI = 0.1D0*R0 - H*(WM(I+2) - SAVF(I))
        WM(I+2) = 1.0D0
        IF (ABS(R0) .LT. UROUND/EWT(I)) GO TO 320
        IF (ABS(DI) .EQ. ZERO) GO TO 330
        WM(I+2) = 0.1D0*R0/DI
 320    CONTINUE
      RETURN
 330   IERPJ = 1
      RETURN
C IF MITER = 4, CALL JAC AND MULTIPLY BY SCALAR. -----------------------
 400   ML = IWM(1)
      MU = IWM(2)
      ML3 = ML + 3
      MBAND = ML + MU + 1
      MEBAND = MBAND + ML
      LENP = MEBAND*N
      DO 410 I = 1,LENP
 410    WM(I+2) = ZERO
C      CALL JAC (NEQ, TN, Y, PAR, ML, MU, WM(ML3), MEBAND)
      CALL JAC (NEQ, TN, Y, NEQ(1), PAR, NEQ(2), WM(ML3))
      IF (JOPT .EQ. 1) RETURN
      CON = -HL0
      DO 420 I = 1,LENP
 420    WM(I+2) = WM(I+2)*CON
      GO TO 570
C IF MITER = 5, MAKE MBAND CALLS TO F TO APPROXIMATE J. ----------------
 500   ML = IWM(1)
      MU = IWM(2)
      MBAND = ML + MU + 1
      MBA = MIN(MBAND,N)
      MEBAND = MBAND + ML
      MEB1 = MEBAND - 1
      SRUR = WM(1)
      FAC = VNORM (N, SAVF, EWT)
      R0 = 1000.0D0*ABS(H)*UROUND*REAL(N)*FAC
      IF (R0 .EQ. ZERO) R0 = ONE
      DO 560 J = 1,MBA
        DO 530 I = J,N,MBAND
          YI = Y(I)
          R = MAX(SRUR*ABS(YI),R0/EWT(I))
 530      Y(I) = Y(I) + R
C        CALL F (NEQ, TN, Y, PAR, FTEM)
C        CALL ODE (NEQ, TN, Y, PAR, FTEM)
        CALL ODE (NEQ(1), NEQ(2), TN, Y, FTEM, PAR)
        DO 550 JJ = J,N,MBAND
          Y(JJ) = YH(JJ,1)
          YJJ = Y(JJ)
          R = MAX(SRUR*ABS(YJJ),R0/EWT(JJ))
          FAC = -HL0/R
          I1 = MAX(JJ-MU,1)
          I2 = MIN(JJ+ML,N)
          II = JJ*MEB1 - ML + 2
          DO 540 I = I1,I2
 540        WM(II+I) = (FTEM(I) - SAVF(I))*FAC
 550      CONTINUE
 560    CONTINUE
      NFE = NFE + MBA
      IF (JOPT .EQ. 1) RETURN
C ADD IDENTITY MATRIX. -------------------------------------------------
 570   II = MBAND + 2
      DO 580 I = 1,N
        WM(II) = WM(II) + ONE
 580    II = II + MEBAND
C DO LU DECOMPOSITION OF P. --------------------------------------------
      CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER)
      IF (IER .NE. 0) IERPJ = 1
      RETURN
C----------------------- END OF SUBROUTINE PREPJ -----------------------
      END
      SUBROUTINE PREPDF (NEQ, Y, SRUR, SAVF, FTEM, DFDP, PAR,
     1   JPAR)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      INTEGER NUM_DUMMY
      DIMENSION NEQ(*), Y(*), SAVF(*), FTEM(*), DFDP(*), PAR(*)
      COMMON /ODE001/ ROWND, ROWNS(173),
     1   RDUM1(43), TN, RDUM2,
     2   IOWND1(14), IOWNS(4),
     3   IDUM1(10), MITER, IDUM2(4), N, IDUM3(2), NFE, IDUM4(2)
      COMMON /ODE002/ RDUM3(3),
     1   IOWND2(3), IDUM5(2), NDFE, IDUM6, IDF, IDUM7(3)
C-----------------------------------------------------------------------
C PREPDF IS CALLED BY SPRIME AND STESA TO COMPUTE THE INHOMOGENEITY
C VECTORS DF(I)/DP(JPAR). HERE DF/DP IS COMPUTED BY THE USER-SUPPLIED
C ROUTINE DF IF IDF = 1, OR BY FINITE DIFFERENCING IF IDF = 0.
C
C IN ADDITION TO VARIABLES DESCRIBED PREVIOUSLY, COMMUNICATION WITH
C PREPDF USES THE FOLLOWING..
C Y     = REAL ARRAY OF LENGTH NYH CONTAINING DEPENDENT VARIABLES.
C         PREPDF USES ONLY THE FIRST N ENTRIES OF Y(*).
C SRUR  = SQRT(UROUND) (= WM(1)).
C SAVF  = REAL ARRAY OF LENGTH N CONTAINING DERIVATIVES DY/DT.
C FTEM  = REAL ARRAY OF LENGTH N USED TO TEMPORARILY STORE DY/DT FOR
C         NUMERICAL DIFFERENTIATION.
C DFDP  = REAL ARRAY OF LENGTH N USED TO STORE DF(I)/DP(JPAR), I = 1,N.
C PAR   = REAL ARRAY OF LENGTH NPAR CONTAINING EQUATION PARAMETERS
C         OF INTEREST.
C JPAR  = INPUT PARAMETER, 2 .LE. JPAR .LE. NSV, DESIGNATING THE
C         APPROPRIATE SOLUTION VECTOR CORRESPONDING TO PAR(JPAR).
C THIS ROUTINE ALSO USES THE COMMON VARIABLES TN, MITER, N, NFE, NDFE,
C AND IDF.
C-----------------------------------------------------------------------
      NDFE = NDFE + 1
      IDF1 = IDF + 1
      GO TO (100, 200), IDF1
C IDF = 0, CALL F TO APPROXIMATE DFDP. ---------------------------------

C hier müssen nun einige veränderungen durchgeführt werden !
C das problem ist, dass ODESSA davon ausgeht, es gebe genau NEQ(2)
C parameter; es gibt aber zusätzlich parameter, die fest sind und
C nicht variiert werden dürfen ! nur so macht die berechnung der
C finiten differenzen sinn!

C -> stelle also zunächst fest, welche komponente des gesamtparameter-
C vektors verändert werden muss
C ziel: bestimme das neue JPAR ! -> NUM_DUMMY
 100  CALL DOP_KOMPONENTE (NEQ, JPAR, NUM_DUMMY)
      RPAR = PAR(NUM_DUMMY)
      R = MAX(SRUR*ABS(RPAR),SRUR)
      PAR(NUM_DUMMY) = RPAR + R
      FAC = 1.0D0/R
      CALL ODE (NEQ(1), NEQ(2), TN, Y, FTEM, PAR)
      DO 110 I = 1,N
 110    DFDP(I) = (FTEM(I) - SAVF(I))*FAC
      PAR(NUM_DUMMY) = RPAR
      NFE = NFE + 1
      RETURN
C IDF = 1, CALL USER SUPPLIED DF. --------------------------------------
 200  DO 210 I = 1,N
 210    DFDP(I) = 0.0D0

C     BESTIMME DEN ZU JPAR PASSENDEN EINTRAG NUM_DUMMY IN DER INH.MATRIX
      CALL DOP_KOMPONENTE (NEQ, JPAR, NUM_DUMMY)
C     RUFE DIE VON ADIFOR GENERIERTE ROUTINE AUF
      CALL OD_ODE(NEQ, TN, Y, NEQ(1), PAR, NEQ(2), DFDP, NUM_DUMMY)
C      CALL CALL_OD_ODE (NEQ, TN, Y, NEQ(1), PAR, NEQ(2), DFDP, JPAR)
C     CALL CALL_OD_ODESSA (NEQ, TN, Y, NEQ(1), PAR, NEQ(2), DFDP, JPAR)

      RETURN
C -------------------- END OF SUBROUTINE PREPDF ------------------------
      END
C-----------------------------------------------------------------------
      SUBROUTINE DOP_KOMPONENTE (NEQ, J_OPT, J_GES)
      INTEGER NEQ, J_OPT, J_GES, I, K
      DIMENSION NEQ(*)
C-----------------------------------------------------------------------
C     SEI J_OPT DIE X-TE KOMPONENTE DES ZU OPTIMIERENDEN PARAMETERVEKTORS
C     AN WELCHER STELLE BEFINDET SICH DANN SEIN EINTRAG IN DER
C     INHOMOGENITÄTSMATRIX ?
C-----------------------------------------------------------------------
      I = 0
      K = 0
C     Falls dies für einen startwert berechnet werden soll
C     dann überspringe dies und liefere null
      IF ( J_OPT > NEQ(3) ) THEN
C     was again NEQ(5) in 3/02
         J_GES = 0
      ELSE
         DO WHILE(I.LT.J_OPT)
            K = K+1
            IF(NEQ(10+K).EQ.1) THEN
               I = I+1
            ENDIF
         ENDDO
         J_GES = K
      END IF

      RETURN
C -------------------- END OF SUBROUTINE DOP_KOMPONENTE ----------------
      END
C-----------------------------------------------------------------------
      SUBROUTINE INTDY (T, K, YH, NYH, DKY, IFLAG)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION YH(NYH,1), DKY(1)
      COMMON /ODE001/ ROWND, ROWNS(173),
     2   RDUM1(38),H, RDUM2(2), HU, RDUM3, TN, UROUND,
     3   IOWND(14), IOWNS(4),
     4   IDUM1(8), L, IDUM2,
     5   IDUM3(5), N, NQ, IDUM4(4)
C-----------------------------------------------------------------------
C INTDY COMPUTES INTERPOLATED VALUES OF THE K-TH DERIVATIVE OF THE
C DEPENDENT VARIABLE VECTOR Y, AND STORES IT IN DKY.  THIS ROUTINE
C IS CALLED WITHIN THE PACKAGE WITH K = 0 AND T = TOUT, BUT MAY
C ALSO BE CALLED BY THE USER FOR ANY K UP TO THE CURRENT ORDER.
C (SEE DETAILED INSTRUCTIONS IN THE USAGE DOCUMENTATION.)
C-----------------------------------------------------------------------
C THE COMPUTED VALUES IN DKY ARE GOTTEN BY INTERPOLATION USING THE
C NORDSIECK HISTORY ARRAY YH.  THIS ARRAY CORRESPONDS UNIQUELY TO A
C VECTOR-VALUED POLYNOMIAL OF DEGREE NQCUR OR LESS, AND DKY IS SET
C TO THE K-TH DERIVATIVE OF THIS POLYNOMIAL AT T.
C THE FORMULA FOR DKY IS..
C             Q
C  DKY(I)  =  SUM  C(J,K) * (T - TN)**(J-K) * H**(-J) * YH(I,J+1)
C            J=K
C WHERE  C(J,K) = J*(J-1)*...*(J-K+1), Q = NQCUR, TN = TCUR, H = HCUR.
C THE QUANTITIES  NQ = NQCUR, L = NQ+1, N = NEQ, TN, AND H ARE
C COMMUNICATED BY COMMON.  THE ABOVE SUM IS DONE IN REVERSE ORDER.
C IFLAG IS RETURNED NEGATIVE IF EITHER K OR T IS OUT OF BOUNDS.
C-----------------------------------------------------------------------
      IFLAG = 0
      IF (K .LT. 0 .OR. K .GT. NQ) GO TO 80
      TP = TN - HU*(1.0D0 + 100.0D0*UROUND)
      IF ((T-TP)*(T-TN) .GT. 0.0D0) GO TO 90
C
      S = (T - TN)/H
      IC = 1
      IF (K .EQ. 0) GO TO 15
      JJ1 = L - K
      DO 10 JJ = JJ1,NQ
 10     IC = IC*JJ
 15   C = REAL(IC)
      DO 20 I = 1,NYH
 20     DKY(I) = C*YH(I,L)
      IF (K .EQ. NQ) GO TO 55
      JB2 = NQ - K
      DO 50 JB = 1,JB2
        J = NQ - JB
        JP1 = J + 1
        IC = 1
        IF (K .EQ. 0) GO TO 35
        JJ1 = JP1 - K
        DO 30 JJ = JJ1,J
 30       IC = IC*JJ
 35     C = REAL(IC)
        DO 40 I = 1,NYH
 40       DKY(I) = C*YH(I,JP1) + S*DKY(I)
 50     CONTINUE
      IF (K .EQ. 0) RETURN
 55   R = H**(-K)
      DO 60 I = 1,NYH
 60     DKY(I) = R*DKY(I)
      RETURN
C
 80   CALL XERR('INTDY--  K (=I1) ILLEGAL',
     1  51, 1, 1, K, 0, 0, ZERO,ZERO)
      IFLAG = -1
      RETURN
 90   CALL XERR ('INTDY--  T (=R1) ILLEGAL',
     1   52, 1, 0, 0, 0, 1, T, ZERO)
      CALL XERR('T NOT IN INTERVAL TCUR - HU (= R1) TO TCUR (=R2)',
     1   52, 1, 0, 0, 0, 2, TP, TN)
      IFLAG = -2
      RETURN
C----------------------- END OF SUBROUTINE INTDY -----------------------
      END

C-----------------------------------------------------------------------
      SUBROUTINE STESA (NEQ, Y, NROW, NCOL, YH, WM, IWM, EWT, SAVF,
     1   ACOR, PAR, NRS, PJAC, PDF, SOLVE)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      EXTERNAL PJAC, PDF, SOLVE
      DIMENSION NEQ(*), Y(NROW,*), YH(NROW,NCOL,*), WM(*), IWM(*),
     1   EWT(NROW,*), SAVF(*), ACOR(NROW,*), PAR(*), NRS(*)
      PARAMETER (ONE=1.0D0,ZERO=0.0D0)
      COMMON /ODE001/ ROWND, ROWNS(173),
     1   TESCO(3,12), RDUM1, EL0, H, RDUM2(4), TN, RDUM3,
     2   IOWND1(14), IOWNS(4),
     3   IALTH, LMAX, IDUM1, IERPJ, IERSL, JCUR, IDUM2, KFLAG, L, IDUM3,
     4   MITER, IDUM4(4), N, NQ, IDUM5, NFE, IDUM6(2)
      COMMON /ODE002/ DUPS, DSMS, DDNS,
     1   IOWND2(3), IDUM7, NSV, IDUM8(2), IDF, IDUM9, JOPT, KFLAGS
C-----------------------------------------------------------------------
C STESA IS CALLED BY STODE TO PERFORM AN EXPLICIT CALCULATION FOR THE
C FIRST-ORDER SENSITIVITY COEFFICIENTS DY(I)/DP(J), I = 1,N; J = 1,NPAR.
C
C IN ADDITION TO THE VARIABLES DESCRIBED PREVIOUSLY, COMMUNICATION
C WITH STESA USES THE FOLLOWING..
C Y      = AN NROW (=N) BY NCOL (=NSV) REAL ARRAY CONTAINING THE
C          CORRECTED DEPENDENT VARIABLES ON OUTPUT..
C                  Y(I,1) , I = 1,N = STATE VARIABLES (INPUT);
C                  Y(I,J) , I = 1,N , J = 2,NSV ,
C                           = SENSITIVITY COEFFICIENTS, DY(I)/DP(J).
C YH     = AN N BY NSV BY LMAX REAL ARRAY CONTAINING THE PREDICTED
C          DEPENDENT VARIABLES AND THEIR APPROXIMATE SCALED DERIVATIVES.
C SAVF   = A REAL ARRAY OF LENGTH N USED TO STORE FIRST DERIVATIVES
C          OF DEPENDENT VARIABLES IF MITER = 2 OR 5.
C PAR    = A REAL ARRAY OF LENGTH NPAR CONTAINING THE EQUATION
C          PARAMETERS OF INTEREST.
C NRS    = AN INTEGER ARRAY OF LENGTH NPAR + 1 CONTAINING THE NUMBER
C          OF REPEATED STEPS (KFLAGS .LT. 0) DUE TO THE SENSITIVITY
C          CALCULATIONS..
C                  NRS(1) = TOTAL NUMBER OF REPEATED STEPS
C                  NRS(I) , I = 2,NPAR = NUMBER OF REPEATED STEPS DUE
C                                        TO PARAMETER I.
C NSV    = NUMBER OF SOLUTION VECTORS = NPAR + 1.
C KFLAGS = LOCAL ERROR TEST FLAG, = 0 IF TEST PASSES, .LT. 0 IF TEST
C          FAILS, AND STEP NEEDS TO BE REPEATED. ERROR TEST IS APPLIED
C          TO EACH SOLUTION VECTOR INDEPENDENTLY.
C DUPS, DSMS, DDNS = REAL SCALARS USED FOR COMPUTING RHUP, RHSM, RHDN,
C                    ON RETURN TO STODE (IALTH .EQ. 1).
C THIS ROUTINE ALSO USES THE COMMON VARIABLES EL0, H, TN, IALTH, LMAX,
C IERPJ, IERSL, JCUR, KFLAG, L, MITER, N, NQ, NFE, AND JOPT.
C-----------------------------------------------------------------------
      DUPS = ZERO
      DSMS = ZERO
      DDNS = ZERO
      HL0 = H*EL0
      EL0I = ONE/EL0
      TI2 = ONE/TESCO(2,NQ)
      TI3 = ONE/TESCO(3,NQ)
C IF MITER = 2 OR 5 (OR IDF = 0), SUPPLY DERIVATIVES AT CORRECTED
C Y(*,1) VALUES FOR NUMERICAL DIFFERENTIATION IN PJAC AND/OR PDF.
      IF (MITER .EQ. 2  .OR.  MITER .EQ. 5  .OR.  IDF .EQ. 0)  GO TO 10
      GO TO 15
 10   CALL ODE (NEQ(1), NEQ(2), TN, Y, SAVF, PAR)
      NFE = NFE + 1
C IF JCUR = 0, UPDATE THE JACOBIAN MATRIX.
C IF MITER = 5, LOAD CORRECTED Y(*,1) VALUES INTO Y(*,2).
 15   IF (JCUR .EQ. 1) GO TO 30
      IF (MITER .NE. 5) GO TO 25
      DO 20 I = 1,N
 20     Y(I,2) = Y(I,1)
 25   CALL PJAC (NEQ, Y, Y(1,2), N, WM, IWM, EWT, SAVF, ACOR(1,2),
     1   PAR, JOPT)
      IF (IERPJ .NE. 0) RETURN
C-----------------------------------------------------------------------
C THIS IS A LOOPING POINT FOR THE SENSITIVITY CALCULATIONS.
C-----------------------------------------------------------------------
C FOR EACH PARAMETER PAR(*), A SENSITIVITY SOLUTION VECTOR IS COMPUTED
C USING THE SAME STEP SIZE (H) AND ORDER (NQ) AS IN STODE.
C A LOCAL ERROR TEST IS APPLIED INDEPENDENTLY TO EACH SOLUTION VECTOR.
C-----------------------------------------------------------------------


 30   IF (NEQ(4) .EQ. 0) THEN
         CALL AD_ODE ((NSV-1),(NSV-1),N,TN,Y,PAR(NSV-1),PAR(N+NSV-1),
     1        N,PAR,PAR(N+NSV-1+N*(NSV-1)),(NSV-1))
      ENDIF
         
      DO 100 J = 2,NSV
         JPAR = J - 1
C     EVALUATE INHOMOGENEITY TERM, TEMPORARILY LOAD INTO Y(*,JPAR+1). ------
         IF (NEQ(4) .EQ. 1) THEN
            CALL PDF(NEQ, Y, WM, SAVF, ACOR(1,J), Y(1,J), PAR,
     1           JPAR)
         ENDIF
         
         IF (NEQ(4) .EQ. 0) THEN
            DO 33 I = 1,N
               NEQ(4) = N+NSV-1+(JPAR-1)*N+I-1
               Y(I,J) = PAR(NEQ(4))
               NEQ(4) = 0
 33         CONTINUE
         ENDIF
            

C-----------------------------------------------------------------------
C LOAD RHS OF SENSITIVITY SOLUTION (CORRECTOR) EQUATION..
C
C       RHS = DY/DP - EL(1)*H*D(DY/DP)/DT + EL(1)*H*DF/DP
C
C-----------------------------------------------------------------------
        DO 40 I = 1,N
 40       Y(I,J) = YH(I,J,1) - EL0*YH(I,J,2) + HL0*Y(I,J)
C-----------------------------------------------------------------------
C SOLVE CORRECTOR EQUATION: THE SOLUTIONS ARE LOCATED IN Y(*,JPAR+1).
C THE EXPLICIT FORMULA IS..
C
C       (I - EL(1)*H*JAC) * DY/DP(CORRECTED) = RHS
C
C-----------------------------------------------------------------------
        CALL SOLVE (WM, IWM, Y(1,J), DUM)
        IF (IERSL .NE. 0) RETURN
C ESTIMATE LOCAL TRUNCATION ERROR. -------------------------------------
        DO 50 I = 1,N
 50       ACOR(I,J) = (Y(I,J) - YH(I,J,1))*EL0I
        ERR = VNORM(N, ACOR(1,J), EWT(1,J))*TI2
        IF (ERR .GT. ONE) GO TO 200
C-----------------------------------------------------------------------
C LOCAL ERROR TEST PASSED. SET KFLAGS TO 0 TO INDICATE THIS.
C IF IALTH = 1, COMPUTE DSMS, DDNS, AND DUPS (IF L .LT. LMAX).
C-----------------------------------------------------------------------
        KFLAGS = 0
        IF (IALTH .GT. 1) GO TO 100
        IF (L .EQ. LMAX) GO TO 70
        DO 60 I= 1,N
 60       Y(I,J) = ACOR(I,J) - YH(I,J,LMAX)
        DUPS = MAX(DUPS,VNORM(N,Y(1,J),EWT(1,J))*TI3)
 70     DSMS = MAX(DSMS,ERR)
 100  CONTINUE
      RETURN
C-----------------------------------------------------------------------
C THIS SECTION IS REACHED IF THE ERROR TOLERANCE FOR SENSITIVITY
C SOLUTION VECTOR JPAR HAS BEEN VIOLATED. KFLAGS IS MADE NEGATIVE TO
C INDICATE THIS. IF KFLAGS = -1, SET KFLAG EQUAL TO ZERO SO THAT KFLAG
C IS SET TO -1 ON RETURN TO STODE BEFORE REPEATING THE STEP.
C INCREMENT NRS(1) (= TOTAL NUMBER OF REPEATED STEPS DUE TO ALL
C SENSITIVITY SOLUTION VECTORS) BY ONE.
C INCREMENT NRS(JPAR+1) (= TOTAL NUMBER OF REPEATED STEPS DUE TO
C SOLUTION VECTOR JPAR+1) BY ONE.
C LOAD DSMS FOR RH CALCULATION IN STODE.
C-----------------------------------------------------------------------
 200  KFLAGS = KFLAGS - 1
      IF (KFLAGS .EQ. -1) KFLAG = 0
      NRS(1) = NRS(1) + 1
      NRS(J) = NRS(J) + 1
      DSMS = ERR
      RETURN
C------------------------ END OF SUBROUTINE STESA ----------------------
      END

C-----------------------------------------------------------------------
      SUBROUTINE STODE (NEQ, Y, YH, NYH, YH1, WM, IWM, EWT, SAVF, ACOR,
     1   PAR, NRS, PJAC, PDF, SLVS)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      EXTERNAL PJAC, PDF, SLVS
      DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), WM(*), IWM(*), EWT(*),
     1   SAVF(*), ACOR(*), PAR(*), NRS(*)
      PARAMETER (ONE=1.0D0,ZERO=0.0D0)
      COMMON /ODE001/ ROWND,
     1   CONIT, CRATE, EL(13), ELCO(13,12), HOLD, RMAX,
     2   TESCO(3,12), CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND,
     3   IOWND1(14), IPUP, MEO, NQNYH, NSLP,
     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   IOWND2(3), ISOPT, NSV, NDFE, NSPE, IDF, IERSP, JOPT, KFLAGS
C-----------------------------------------------------------------------
C STODE PERFORMS ONE STEP OF THE INTEGRATION OF AN INITIAL VALUE
C PROBLEM FOR A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.
C NOTE.. STODE IS INDEPENDENT OF THE VALUE OF THE ITERATION METHOD
C INDICATOR MITER, WHEN THIS IS .NE. 0, AND HENCE IS INDEPENDENT
C OF THE TYPE OF CHORD METHOD USED, OR THE JACOBIAN STRUCTURE.
C FOR ISOPT = 1, STODE CALLS STESA FOR SENSITIVITY CALCULATIONS.
C VARIABLES USED FOR COMMUNICATION WITH STESA ARE DESCRIBED IN STESA.
C COMMUNICATION WITH STODE IS DONE WITH THE FOLLOWING VARIABLES..
C
C NEQ   = INTEGER ARRAY CONTAINING PROBLEM SIZE IN NEQ(1), AND
C         NUMBER OF PARAMETERS TO BE CONSIDERED IN THE SENSITIVITY
C         ANALYSIS NEQ(2) (FOR ISOPT = 1), AND PASSED AS THE
C         NEQ ARGUMENT IN ALL CALLS TO F,  JAC, AND DF.
C Y     = AN ARRAY OF LENGTH .GE. N USED AS THE Y ARGUMENT IN
C         ALL CALLS TO F, JAC, AND DF.
C YH    = AN NYH BY LMAX ARRAY CONTAINING THE DEPENDENT VARIABLES
C         AND THEIR APPROXIMATE SCALED DERIVATIVES, WHERE
C         LMAX = MAXORD + 1.  YH(I,J+1) CONTAINS THE APPROXIMATE
C         J-TH DERIVATIVE OF Y(I), SCALED BY H**J/FACTORIAL(J)
C         (J = 0,1,...,NQ).  ON ENTRY FOR THE FIRST STEP, THE FIRST
C         TWO COLUMNS OF YH MUST BE SET FROM THE INITIAL VALUES.
C NYH   = A CONSTANT INTEGER .GE. N, THE FIRST DIMENSION OF YH.
C         THE TOTAL NUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS..
C         NYH = N, ISOPT = 0,
C         NYH = N * (NPAR + 1), ISOPT = 1
C YH1   = A ONE-DIMENSIONAL ARRAY OCCUPYING THE SAME SPACE AS YH.
C EWT   = AN ARRAY OF LENGTH NYH CONTAINING MULTIPLICATIVE WEIGHTS
C         FOR LOCAL ERROR MEASUREMENTS.  LOCAL ERRORS IN Y(I) ARE
C         COMPARED TO 1.0/EWT(I) IN VARIOUS ERROR TESTS.
C SAVF  = AN ARRAY OF WORKING STORAGE, OF LENGTH N.
C         ALSO USED FOR INPUT OF YH(*,MAXORD+2) WHEN JSTART = -1
C         AND MAXORD .LT. THE CURRENT ORDER NQ.
C ACOR  = A WORK ARRAY OF LENGTH NYH, USED FOR THE ACCUMULATED
C         CORRECTIONS.  ON A SUCCESSFUL RETURN, ACOR(I) CONTAINS
C         THE ESTIMATED ONE-STEP LOCAL ERROR IN Y(I).
C WM,IWM = REAL AND INTEGER WORK ARRAYS ASSOCIATED WITH MATRIX
C         OPERATIONS IN CHORD ITERATION (MITER .NE. 0).
C PJAC  = NAME OF ROUTINE TO EVALUATE AND PREPROCESS JACOBIAN MATRIX
C         AND P = I - H*EL0*JAC, IF A CHORD METHOD IS BEING USED.
C         IF ISOPT = 1, PJAC CAN BE CALLED TO CALCULATE JAC BY
C         SETTING JOPT = 1.
C SLVS  = NAME OF ROUTINE TO SOLVE LINEAR SYSTEM IN CHORD ITERATION.
C CCMAX  = MAXIMUM RELATIVE CHANGE IN H*EL0 BEFORE PJAC IS CALLED.
C H     = THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP.
C         H IS ALTERED BY THE ERROR CONTROL ALGORITHM DURING THE
C         PROBLEM.  H CAN BE EITHER POSITIVE OR NEGATIVE, BUT ITS
C         SIGN MUST REMAIN CONSTANT THROUGHOUT THE PROBLEM.
C HMIN  = THE MINIMUM ABSOLUTE VALUE OF THE STEP SIZE H TO BE USED.
C HMXI  = INVERSE OF THE MAXIMUM ABSOLUTE VALUE OF H TO BE USED.
C         HMXI = 0.0 IS ALLOWED AND CORRESPONDS TO AN INFINITE HMAX.
C         HMIN AND HMXI MAY BE CHANGED AT ANY TIME, BUT WILL NOT
C         TAKE EFFECT UNTIL THE NEXT CHANGE OF H IS CONSIDERED.
C TN    = THE INDEPENDENT VARIABLE. TN IS UPDATED ON EACH STEP TAKEN.
C JSTART = AN INTEGER USED FOR INPUT ONLY, WITH THE FOLLOWING
C         VALUES AND MEANINGS..
C              0  PERFORM THE FIRST STEP.
C          .GT.0  TAKE A NEW STEP CONTINUING FROM THE LAST.
C             -1  TAKE THE NEXT STEP WITH A NEW VALUE OF H, MAXORD,
C                   N, METH, OR MITER.
C             -2  TAKE THE NEXT STEP WITH A NEW VALUE OF H,
C                   BUT WITH OTHER INPUTS UNCHANGED.
C         ON RETURN, JSTART IS SET TO 1 TO FACILITATE CONTINUATION.
C KFLAG  = A COMPLETION CODE WITH THE FOLLOWING MEANINGS..
C              0  THE STEP WAS SUCCESFUL.
C             -1  THE REQUESTED ERROR COULD NOT BE ACHIEVED.
C             -2  CORRECTOR CONVERGENCE COULD NOT BE ACHIEVED.
C             -3  FATAL ERROR IN PJAC, OR SLVS, (OR STESA).
C         A RETURN WITH KFLAG = -1 OR -2 MEANS EITHER
C         ABS(H) = HMIN OR 10 CONSECUTIVE FAILURES OCCURRED.
C         ON A RETURN WITH KFLAG NEGATIVE, THE VALUES OF TN AND
C         THE YH ARRAY ARE AS OF THE BEGINNING OF THE LAST
C         STEP, AND H IS THE LAST STEP SIZE ATTEMPTED.
C MAXORD = THE MAXIMUM ORDER OF INTEGRATION METHOD TO BE ALLOWED.
C MAXCOR = THE MAXIMUM NUMBER OF CORRECTOR ITERATIONS ALLOWED.
C          (= 3, IF ISOPT = 0)
C          (= 4, IF ISOPT = 1)
C MSBP  = MAXIMUM NUMBER OF STEPS BETWEEN PJAC CALLS (MITER .GT. 0).
C         IF ISOPT = 1, PJAC IS CALLED AT LEAST ONCE EVERY STEP.
C MXNCF  = MAXIMUM NUMBER OF CONVERGENCE FAILURES ALLOWED.
C METH/MITER = THE METHOD FLAGS.  SEE DESCRIPTION IN DRIVER.
C N     = THE NUMBER OF FIRST-ORDER MODEL DIFFERENTIAL EQUATIONS.
C-----------------------------------------------------------------------
      KFLAG = 0
      KFLAGS = 0
      TOLD = TN
      NCF = 0
      IERPJ = 0
      IERSL = 0
      JCUR = 0
      ICF = 0
      IF (JSTART .GT. 0) GO TO 200
      IF (JSTART .EQ. -1) GO TO 100
      IF (JSTART .EQ. -2) GO TO 160
C-----------------------------------------------------------------------
C ON THE FIRST CALL, THE ORDER IS SET TO 1, AND OTHER VARIABLES ARE
C INITIALIZED.  RMAX IS THE MAXIMUM RATIO BY WHICH H CAN BE INCREASED
C IN A SINGLE STEP.  IT IS INITIALLY 1.E4 TO COMPENSATE FOR THE SMALL
C INITIAL H, BUT THEN IS NORMALLY EQUAL TO 10.  IF A FAILURE
C OCCURS (IN CORRECTOR CONVERGENCE OR ERROR TEST), RMAX IS SET AT 2
C FOR THE NEXT INCREASE.
C THESE COMPUTATIONS CONSIDER ONLY THE ORIGINAL SOLUTION VECTOR.
C THE SENSITIVITY SOLUTION VECTORS ARE CONSIDERED IN STESA (ISOPT = 1).
C-----------------------------------------------------------------------
      LMAX = MAXORD + 1
      NQ = 1
      L = 2
      IALTH = 2
      RMAX = 10000.0D0
      RC = ZERO
      EL0 = ONE
      CRATE = 0.7D0
      DELP = ZERO
      HOLD = H
      MEO = METH
      NSLP = 0
      IPUP = MITER
      IRET = 3
      GO TO 140
C-----------------------------------------------------------------------
C THE FOLLOWING BLOCK HANDLES PRELIMINARIES NEEDED WHEN JSTART = -1.
C IPUP IS SET TO MITER TO FORCE A MATRIX UPDATE.
C IF AN ORDER INCREASE IS ABOUT TO BE CONSIDERED (IALTH = 1),
C IALTH IS RESET TO 2 TO POSTPONE CONSIDERATION ONE MORE STEP.
C IF THE CALLER HAS CHANGED METH, CFODE IS CALLED TO RESET
C THE COEFFICIENTS OF THE METHOD.
C IF THE CALLER HAS CHANGED MAXORD TO A VALUE LESS THAN THE CURRENT
C ORDER NQ, NQ IS REDUCED TO MAXORD, AND A NEW H CHOSEN ACCORDINGLY.
C IF H IS TO BE CHANGED, YH MUST BE RESCALED.
C IF H OR METH IS BEING CHANGED, IALTH IS RESET TO L = NQ + 1
C TO PREVENT FURTHER CHANGES IN H FOR THAT MANY STEPS.
C-----------------------------------------------------------------------
 100   IPUP = MITER
      LMAX = MAXORD + 1
      IF (IALTH .EQ. 1) IALTH = 2
      IF (METH .EQ. MEO) GO TO 110
      CALL CFODE (METH, ELCO, TESCO)
      MEO = METH
      IF (NQ .GT. MAXORD) GO TO 120
      IALTH = L
      IRET = 1
      GO TO 150
 110   IF (NQ .LE. MAXORD) GO TO 160
 120   NQ = MAXORD
      L = LMAX
      DO 125 I = 1,L
 125    EL(I) = ELCO(I,NQ)
      NQNYH = NQ*NYH
      RC = RC*EL(1)/EL0
      EL0 = EL(1)
      CONIT = 0.5D0/REAL(NQ+2)
      DDN = VNORM (N, SAVF, EWT)/TESCO(1,L)
      EXDN = ONE/REAL(L)
      RHDN = ONE/(1.3D0*DDN**EXDN + 0.0000013D0)
      RH = MIN(RHDN,ONE)
      IREDO = 3
      IF (H .EQ. HOLD) GO TO 170
      RH = MIN(RH,ABS(H/HOLD))
      H = HOLD
      GO TO 175
C-----------------------------------------------------------------------
C CFODE IS CALLED TO GET ALL THE INTEGRATION COEFFICIENTS FOR THE
C CURRENT METH.  THEN THE EL VECTOR AND RELATED CONSTANTS ARE RESET
C WHENEVER THE ORDER NQ IS CHANGED, OR AT THE START OF THE PROBLEM.
C-----------------------------------------------------------------------
 140   CALL CFODE (METH, ELCO, TESCO)
 150   DO 155 I = 1,L
 155    EL(I) = ELCO(I,NQ)
      NQNYH = NQ*NYH
      RC = RC*EL(1)/EL0
      EL0 = EL(1)
      CONIT = 0.5D0/REAL(NQ+2)
      GO TO (160, 170, 200), IRET
C-----------------------------------------------------------------------
C IF H IS BEING CHANGED, THE H RATIO RH IS CHECKED AGAINST
C RMAX, HMIN, AND HMXI, AND THE YH ARRAY RESCALED.  IALTH IS SET TO
C L = NQ + 1 TO PREVENT A CHANGE OF H FOR THAT MANY STEPS, UNLESS
C FORCED BY A CONVERGENCE OR ERROR TEST FAILURE.
C-----------------------------------------------------------------------
 160  IF (H .EQ. HOLD) GO TO 200
      RH = H/HOLD
      H = HOLD
      IREDO = 3
      GO TO 175
 170   RH = MAX(RH,HMIN/ABS(H))
 175   RH = MIN(RH,RMAX)
      RH = RH/MAX(ONE,ABS(H)*HMXI*RH)
      R = ONE
      DO 180 J = 2,L
        R = R*RH
        DO 180 I = 1,NYH
 180      YH(I,J) = YH(I,J)*R
      H = H*RH
      RC = RC*RH
      IALTH = L
      IF (IREDO .EQ. 0) GO TO 690
C-----------------------------------------------------------------------
C THIS SECTION COMPUTES THE PREDICTED VALUES BY EFFECTIVELY
C MULTIPLYING THE YH ARRAY BY THE PASCAL TRIANGLE MATRIX.
C RC IS THE RATIO OF NEW TO OLD VALUES OF THE COEFFICIENT  H*EL(1).
C WHEN RC DIFFERS FROM 1 BY MORE THAN CCMAX, IPUP IS SET TO MITER
C TO FORCE PJAC TO BE CALLED, IF A JACOBIAN IS INVOLVED.
C IN ANY CASE, PJAC IS CALLED AT LEAST EVERY MSBP STEPS FOR ISOPT = 0,
C AND AT LEAST ONCE EVERY STEP FOR ISOPT = 1.
C-----------------------------------------------------------------------
 200  IF (ABS(RC-ONE) .GT. CCMAX) IPUP = MITER
      IF (NST .GE. NSLP+MSBP) IPUP = MITER
      TN = TN + H
      I1 = NQNYH + 1
      DO 215 JB = 1,NQ
        I1 = I1 - NYH
        DO 210 I = I1,NQNYH
 210      YH1(I) = YH1(I) + YH1(I+NYH)
 215    CONTINUE
C-----------------------------------------------------------------------
C UP TO MAXCOR CORRECTOR ITERATIONS ARE TAKEN.  (= 3, FOR ISOPT = 0;
C = 4, FOR ISOPT = 1).  A CONVERGENCE TEST IS MADE ON THE R.M.S. NORM
C OF EACH CORRECTION, WEIGHTED BY THE ERROR WEIGHT VECTOR EWT.  THE SUM
C OF THE CORRECTIONS IS ACCUMULATED IN THE VECTOR ACOR(I), I = 1,N.
C (ACOR(I), I = N+1,NYH IS LOADED IN SUBROUTINE STESA (ISOPT = 1).)
C THE YH ARRAY IS NOT ALTERED IN THE CORRECTOR LOOP.
C-----------------------------------------------------------------------
 220  M = 0
      DO 230 I = 1,N
 230    Y(I) = YH(I,1)
      CALL ODE (NEQ(1), NEQ(2), TN, Y, SAVF, PAR)
      NFE = NFE + 1
      IF (IPUP .LE. 0) GO TO 250
C-----------------------------------------------------------------------
C IF INDICATED, THE MATRIX P = I - H*EL(1)*J IS REEVALUATED AND
C PREPROCESSED BEFORE STARTING THE CORRECTOR ITERATION.  IPUP IS SET
C TO 0 AS AN INDICATOR THAT THIS HAS BEEN DONE.
C-----------------------------------------------------------------------
      IPUP = 0
      RC = ONE
      NSLP = NST
      CRATE = 0.7D0
      CALL PJAC (NEQ, Y, YH, NYH, WM, IWM, EWT, SAVF, ACOR, PAR,
     1   JOPT)
      IF (IERPJ .NE. 0) GO TO 430
 250   DO 260 I = 1,N
 260    ACOR(I) = ZERO
 270   IF (MITER .NE. 0) GO TO 350
C-----------------------------------------------------------------------
C IN THE CASE OF FUNCTIONAL ITERATION, UPDATE Y DIRECTLY FROM
C THE RESULT OF THE LAST FUNCTION EVALUATION.
C (IF ISOPT = 1, FUNCTIONAL ITERATION IS NOT ALLOWED.)
C-----------------------------------------------------------------------
      DO 290 I = 1,N
        SAVF(I) = H*SAVF(I) - YH(I,2)
 290    Y(I) = SAVF(I) - ACOR(I)
      DEL = VNORM (N, Y, EWT)
      DO 300 I = 1,N
        Y(I) = YH(I,1) + EL(1)*SAVF(I)
 300    ACOR(I) = SAVF(I)
      GO TO 400
C-----------------------------------------------------------------------
C IN THE CASE OF THE CHORD METHOD, COMPUTE THE CORRECTOR ERROR,
C AND SOLVE THE LINEAR SYSTEM WITH THAT AS RIGHT-HAND SIDE AND
C P AS COEFFICIENT MATRIX.
C-----------------------------------------------------------------------
 350   DO 360 I = 1,N
 360    Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I))
      CALL SLVS (WM, IWM, Y, SAVF)
      IF (IERSL .LT. 0) GO TO 430
      IF (IERSL .GT. 0) GO TO 410
      DEL = VNORM (N, Y, EWT)
      DO 380 I = 1,N
        ACOR(I) = ACOR(I) + Y(I)
 380    Y(I) = YH(I,1) + EL(1)*ACOR(I)
C-----------------------------------------------------------------------
C TEST FOR CONVERGENCE.  IF M.GT.0, AN ESTIMATE OF THE CONVERGENCE
C RATE CONSTANT IS STORED IN CRATE, AND THIS IS USED IN THE TEST.
C-----------------------------------------------------------------------
 400   IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP)
      DCON = DEL*MIN(ONE,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT)
      IF (DCON .LE. ONE) GO TO 450
      M = M + 1
      IF (M .EQ. MAXCOR) GO TO 410
      IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410
      DELP = DEL
      CALL ODE (NEQ(1), NEQ(2), TN, Y, SAVF, PAR)
      NFE = NFE + 1
      GO TO 270
C-----------------------------------------------------------------------
C THE CORRECTOR ITERATION FAILED TO CONVERGE IN MAXCOR TRIES.
C IF MITER .NE. 0 AND THE JACOBIAN IS OUT OF DATE, PJAC IS CALLED FOR
C THE NEXT TRY.  OTHERWISE THE YH ARRAY IS RETRACTED TO ITS VALUES
C BEFORE PREDICTION, AND H IS REDUCED, IF POSSIBLE.  IF H CANNOT BE
C REDUCED OR MXNCF FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -2.
C-----------------------------------------------------------------------
 410   IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430
      ICF = 1
      IPUP = MITER
      GO TO 220
 430   ICF = 2
      NCF = NCF + 1
      RMAX = 2.0D0
      TN = TOLD
      I1 = NQNYH + 1
      DO 445 JB = 1,NQ
        I1 = I1 - NYH
        DO 440 I = I1,NQNYH
 440      YH1(I) = YH1(I) - YH1(I+NYH)
 445    CONTINUE
      IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680
      IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670
      IF (NCF .EQ. MXNCF) GO TO 670
      RH = 0.25D0
      IPUP = MITER
      IREDO = 1
      GO TO 170
C-----------------------------------------------------------------------
C THE CORRECTOR HAS CONVERGED.
C THE LOCAL ERROR TEST IS MADE AND CONTROL PASSES TO STATEMENT 500
C IF IT FAILS. OTHERWISE, STESA IS CALLED (ISOPT = 1) TO PERFORM
C SENSITIVITY CALCULATIONS AT CURRENT STEP SIZE AND ORDER.
C-----------------------------------------------------------------------
 450   CONTINUE
      IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ)
      IF (M .GT. 0) DSM = VNORM (N, ACOR, EWT)/TESCO(2,NQ)
      IF (DSM .GT. ONE) GO TO 500
C
      IF (ISOPT .EQ. 0) GO TO 460
C-----------------------------------------------------------------------
C CALL STESA TO PERFORM EXPLICIT SENSITIVITY ANALYSIS.
C IF THE LOCAL ERROR TEST FAILS (WITHIN STESA) FOR ANY SOLUTION VECTOR,
C KFLAGS IS SET .LT. 0 AND CONTROL PASSES TO STATEMENT 500 UPON RETURN.
C IN EITHER CASE, JCUR IS SET TO ZERO TO SIGNAL THAT THE JACOBIAN MAY
C NEED UPDATING LATER.
C-----------------------------------------------------------------------

C-----------------------------------------------------------------------
      CALL STESA (NEQ, Y, N, NSV, YH, WM, IWM, EWT, SAVF, ACOR,
     1   PAR, NRS, PJAC, PDF, SLVS)
      IF (IERPJ .NE. 0 .OR. IERSL .NE. 0) GO TO 680
      IF (KFLAGS .LT. 0) GO TO 500
C-----------------------------------------------------------------------
C AFTER A SUCCESSFUL STEP, UPDATE THE YH ARRAY.
C CONSIDER CHANGING H IF IALTH = 1.  OTHERWISE DECREASE IALTH BY 1.
C IF IALTH IS THEN 1 AND NQ .LT. MAXORD, THEN ACOR IS SAVED FOR
C USE IN A POSSIBLE ORDER INCREASE ON THE NEXT STEP.
C IF A CHANGE IN H IS CONSIDERED, AN INCREASE OR DECREASE IN ORDER
C BY ONE IS CONSIDERED ALSO.  A CHANGE IN H IS MADE ONLY IF IT IS BY A
C FACTOR OF AT LEAST 1.1.  IF NOT, IALTH IS SET TO 3 TO PREVENT
C TESTING FOR THAT MANY STEPS.
C-----------------------------------------------------------------------
 460   JCUR = 0
      KFLAG = 0
      IREDO = 0
      NST = NST + 1
      HU = H
      NQU = NQ
      DO 470 J = 1,L
        DO 470 I = 1,NYH
 470      YH(I,J) = YH(I,J) + EL(J)*ACOR(I)
      IALTH = IALTH - 1
      IF (IALTH .EQ. 0) GO TO 520
      IF (IALTH .GT. 1) GO TO 700
      IF (L .EQ. LMAX) GO TO 700
      DO 490 I = 1,NYH
 490    YH(I,LMAX) = ACOR(I)
      GO TO 700
C-----------------------------------------------------------------------
C THE ERROR TEST FAILED IN EITHER STODE OR STESA.
C KFLAG KEEPS TRACK OF MULTIPLE FAILURES.
C RESTORE TN AND THE YH ARRAY TO THEIR PREVIOUS VALUES, AND PREPARE
C TO TRY THE STEP AGAIN.  COMPUTE THE OPTIMUM STEP SIZE FOR THIS OR
C ONE LOWER ORDER.  AFTER 2 OR MORE FAILURES, H IS FORCED TO DECREASE
C BY A FACTOR OF 0.2 OR LESS.
C-----------------------------------------------------------------------
 500  KFLAG = KFLAG - 1
      JCUR = 0
      TN = TOLD
      I1 = NQNYH + 1
      DO 515 JB = 1,NQ
        I1 = I1 - NYH
        DO 510 I = I1,NQNYH
 510      YH1(I) = YH1(I) - YH1(I+NYH)
 515    CONTINUE
      RMAX = 2.0D0
      IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660
      IF (KFLAG .LE. -3) GO TO 640
      IREDO = 2
      RHUP = ZERO
      GO TO 540
C-----------------------------------------------------------------------
*
C REGARDLESS OF THE SUCCESS OR FAILURE OF THE STEP, FACTORS
C RHDN, RHSM, AND RHUP ARE COMPUTED, BY WHICH H COULD BE MULTIPLIED
C AT ORDER NQ - 1, ORDER NQ, OR ORDER NQ + 1, RESPECTIVELY.
C IN THE CASE OF FAILURE, RHUP = 0.0 TO AVOID AN ORDER INCREASE.
C THE LARGEST OF THESE IS DETERMINED AND THE NEW ORDER CHOSEN
C ACCORDINGLY.  IF THE ORDER IS TO BE INCREASED, WE COMPUTE ONE
C ADDITIONAL SCALED DERIVATIVE.
C FOR ISOPT = 1, DUPS AND DSMS ARE LOADED WITH THE LARGEST RMS-NORMS
C OBTAINED BY CONSIDERING SEPARATELY THE SENSITIVITY SOLUTION VECTORS.
C-----------------------------------------------------------------------
 520   RHUP = ZERO
      IF (L .EQ. LMAX) GO TO 540
      DO 530 I = 1,N
 530    SAVF(I) = ACOR(I) - YH(I,LMAX)
      DUP = VNORM (N, SAVF, EWT)/TESCO(3,NQ)
      DUP = MAX(DUP,DUPS)
      EXUP = ONE/REAL(L+1)
      RHUP = ONE/(1.4D0*DUP**EXUP + 0.0000014D0)
 540   EXSM = ONE/REAL(L)
      DSM = MAX(DSM,DSMS)
      RHSM = ONE/(1.2D0*DSM**EXSM + 0.0000012D0)
      RHDN = ZERO
      IF (NQ .EQ. 1) GO TO 560
      JPOINT = 1
      DO 550 J = 1,NSV
        DDN = VNORM (N, YH(JPOINT,L), EWT(JPOINT))/TESCO(1,NQ)
        DDNS = MAX(DDNS,DDN)
        JPOINT = JPOINT + N
 550  CONTINUE
      DDN = DDNS
      DDNS = ZERO
      EXDN = ONE/REAL(NQ)
      RHDN = ONE/(1.3D0*DDN**EXDN + 0.0000013D0)
 560   IF (RHSM .GE. RHUP) GO TO 570
      IF (RHUP .GT. RHDN) GO TO 590
      GO TO 580
 570   IF (RHSM .LT. RHDN) GO TO 580
      NEWQ = NQ
      RH = RHSM
      GO TO 620
 580   NEWQ = NQ - 1
      RH = RHDN
      IF (KFLAG .LT. 0 .AND. RH .GT. ONE) RH = ONE
      GO TO 620
 590   NEWQ = L
      RH = RHUP
      IF (RH .LT. 1.1D0) GO TO 610
      R = EL(L)/REAL(L)
      DO 600 I = 1,NYH
 600    YH(I,NEWQ+1) = ACOR(I)*R
      GO TO 630
 610   IALTH = 3
      GO TO 700
 620   IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610
      IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0)
C-----------------------------------------------------------------------
C IF THERE IS A CHANGE OF ORDER, RESET NQ, L, AND THE COEFFICIENTS.
C IN ANY CASE H IS RESET ACCORDING TO RH AND THE YH ARRAY IS RESCALED.
C THEN EXIT FROM 690 IF THE STEP WAS OK, OR REDO THE STEP OTHERWISE.
C-----------------------------------------------------------------------
      IF (NEWQ .EQ. NQ) GO TO 170
 630   NQ = NEWQ
      L = NQ + 1
      IRET = 2
      GO TO 150
C-----------------------------------------------------------------------
C CONTROL REACHES THIS SECTION IF 3 OR MORE FAILURES HAVE OCCURED.
C IF 10 FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -1.
C IT IS ASSUMED THAT THE DERIVATIVES THAT HAVE ACCUMULATED IN THE
C YH ARRAY HAVE ERRORS OF THE WRONG ORDER.  HENCE THE FIRST
C DERIVATIVE IS RECOMPUTED, AND THE ORDER IS SET TO 1.  THEN
C H IS REDUCED BY A FACTOR OF 10, AND THE STEP IS RETRIED,
C UNTIL IT SUCCEEDS OR H REACHES HMIN.
C-----------------------------------------------------------------------
 640   IF (KFLAG .EQ. -10) GO TO 660
      RH = 0.1D0
      RH = MAX(HMIN/ABS(H),RH)
      H = H*RH
      DO 645 I = 1,NYH
 645    Y(I) = YH(I,1)
      CALL ODE (NEQ(1), NEQ(2), TN, Y, SAVF, PAR)
      NFE = NFE + 1
      IF (ISOPT .EQ. 0) GO TO 649

C-----------------------------------------------------------------------
      CALL SPRIME (NEQ, Y, YH, NYH, N, NSV, WM, IWM, EWT, SAVF, ACOR,
     1   ACOR(N+1), PAR, PJAC, PDF)
      IF (IERSP .LT. 0) GO TO 680
      DO 646 I = N+1,NYH
 646    YH(I,2) = H*YH(I,2)
 649  DO 650 I = 1,N
 650    YH(I,2) = H*SAVF(I)
      IPUP = MITER
      IALTH = 5
      IF (NQ .EQ. 1) GO TO 200
      NQ = 1
      L = 2
      IRET = 3
      GO TO 150
C-----------------------------------------------------------------------
C ALL RETURNS ARE MADE THROUGH THIS SECTION.  H IS SAVED IN HOLD
C TO ALLOW THE CALLER TO CHANGE H ON THE NEXT STEP.
C-----------------------------------------------------------------------
 660   KFLAG = -1
      GO TO 720
 670   KFLAG = -2
      GO TO 720
 680   KFLAG = -3
      GO TO 720
 690   RMAX = 10.0D0
 700   R = ONE/TESCO(2,NQU)
      DO 710 I = 1,NYH
 710    ACOR(I) = ACOR(I)*R
 720   HOLD = H
      JSTART = 1
      RETURN
C----------------------- END OF SUBROUTINE STODE -----------------------
      END
      SUBROUTINE CFODE (METH, ELCO, TESCO)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION ELCO(13,12), TESCO(3,12)
C-----------------------------------------------------------------------
C CFODE IS CALLED BY THE INTEGRATOR ROUTINE TO SET COEFFICIENTS
C NEEDED THERE.  THE COEFFICIENTS FOR THE CURRENT METHOD, AS
C GIVEN BY THE VALUE OF METH, ARE SET FOR ALL ORDERS AND SAVED.
C THE MAXIMUM ORDER ASSUMED HERE IS 12 IF METH = 1 AND 5 IF METH = 2.
C (A SMALLER VALUE OF THE MAXIMUM ORDER IS ALSO ALLOWED.)
C CFODE IS CALLED ONCE AT THE BEGINNING OF THE PROBLEM,
C AND IS NOT CALLED AGAIN UNLESS AND UNTIL METH IS CHANGED.
C
C THE ELCO ARRAY CONTAINS THE BASIC METHOD COEFFICIENTS.
C THE COEFFICIENTS EL(I), 1 .LE. I .LE. NQ+1, FOR THE METHOD OF
C ORDER NQ ARE STORED IN ELCO(I,NQ).  THEY ARE GIVEN BY A GENETRATING
C POLYNOMIAL, I.E.,
C    L(X) = EL(1) + EL(2)*X + ... + EL(NQ+1)*X**NQ.
C FOR THE IMPLICIT ADAMS METHODS, L(X) IS GIVEN BY
C    DL/DX = (X+1)*(X+2)*...*(X+NQ-1)/FACTORIAL(NQ-1),    L(-1) = 0.
C FOR THE BDF METHODS, L(X) IS GIVEN BY
C    L(X) = (X+1)*(X+2)* ... *(X+NQ)/K,
C WHERE        K = FACTORIAL(NQ)*(1 + 1/2 + ... + 1/NQ).
C
C THE TESCO ARRAY CONTAINS TEST CONSTANTS USED FOR THE
C LOCAL ERROR TEST AND THE SELECTION OF STEP SIZE AND/OR ORDER.
C AT ORDER NQ, TESCO(K,NQ) IS USED FOR THE SELECTION OF STEP
C SIZE AT ORDER NQ - 1 IF K = 1, AT ORDER NQ IF K = 2, AND AT ORDER
C NQ + 1 IF K = 3.
C-----------------------------------------------------------------------
      DIMENSION PC(12)
      PARAMETER (ONE=1.0D0,ZERO=0.0D0)
C
      GO TO (100, 200), METH
C
 100   ELCO(1,1) = ONE
      ELCO(2,1) = ONE
      TESCO(1,1) = ZERO
      TESCO(2,1) = 2.0D0
      TESCO(1,2) = ONE
      TESCO(3,12) = ZERO
      PC(1) = ONE
      RQFAC = ONE
      DO 140 NQ = 2,12
C-----------------------------------------------------------------------
C THE PC ARRAY WILL CONTAIN THE COEFFICIENTS OF THE POLYNOMIAL
C    P(X) = (X+1)*(X+2)*...*(X+NQ-1).
C INITIALLY, P(X) = 1.
C-----------------------------------------------------------------------
        RQ1FAC = RQFAC
        RQFAC = RQFAC/REAL(NQ)
        NQM1 = NQ - 1
        FNQM1 = REAL(NQM1)
        NQP1 = NQ + 1
C FORM COEFFICIENTS OF P(X)*(X+NQ-1). ----------------------------------
        PC(NQ) = ZERO
        DO 110 IB = 1,NQM1
          I = NQP1 - IB
 110      PC(I) = PC(I-1) + FNQM1*PC(I)
        PC(1) = FNQM1*PC(1)
C COMPUTE INTEGRAL, -1 TO 0, OF P(X) AND X*P(X). -----------------------
        PINT = PC(1)
        XPIN = PC(1)/2.0D0
        TSIGN = ONE
        DO 120 I = 2,NQ
          TSIGN = -TSIGN
          PINT = PINT + TSIGN*PC(I)/REAL(I)
 120      XPIN = XPIN + TSIGN*PC(I)/REAL(I+1)
C STORE COEFFICIENTS IN ELCO AND TESCO. --------------------------------
        ELCO(1,NQ) = PINT*RQ1FAC
        ELCO(2,NQ) = ONE
        DO 130 I = 2,NQ
 130      ELCO(I+1,NQ) = RQ1FAC*PC(I)/REAL(I)
        AGAMQ = RQFAC*XPIN
        RAGQ = ONE/AGAMQ
        TESCO(2,NQ) = RAGQ
        IF (NQ .LT. 12) TESCO(1,NQP1) = RAGQ*RQFAC/REAL(NQP1)
        TESCO(3,NQM1) = RAGQ
 140    CONTINUE
      RETURN
C
 200   PC(1) = ONE
      RQ1FAC = ONE
      DO 230 NQ = 1,5
C-----------------------------------------------------------------------
C THE PC ARRAY WILL CONTAIN THE COEFFICIENTS OF THE POLYNOMIAL
C    P(X) = (X+1)*(X+2)*...*(X+NQ).
C INITIALLY, P(X) = 1.
C-----------------------------------------------------------------------
        FNQ = REAL(NQ)
        NQP1 = NQ + 1
C FORM COEFFICIENTS OF P(X)*(X+NQ). ------------------------------------
        PC(NQP1) = ZERO
        DO 210 IB = 1,NQ
          I = NQ + 2 - IB
 210      PC(I) = PC(I-1) + FNQ*PC(I)
        PC(1) = FNQ*PC(1)
C STORE COEFFICIENTS IN ELCO AND TESCO. --------------------------------
        DO 220 I = 1,NQP1
 220      ELCO(I,NQ) = PC(I)/PC(2)
        ELCO(2,NQ) = ONE
        TESCO(1,NQ) = RQ1FAC
        TESCO(2,NQ) = REAL(NQP1)/ELCO(1,NQ)
        TESCO(3,NQ) = REAL(NQ+2)/ELCO(1,NQ)
        RQ1FAC = RQ1FAC/FNQ
 230    CONTINUE
      RETURN
C----------------------- END OF SUBROUTINE CFODE -----------------------
      END
      SUBROUTINE SOLSY (WM, IWM, X, TEM)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION WM(*), IWM(*), X(*), TEM(*)
      PARAMETER (ZERO=0.0D0,ONE=1.0D0)
      COMMON /ODE001/ ROWND, ROWNS(173),
     2   RDUM1(37), EL0, H, RDUM2(6),
     3   IOWND(14), IOWNS(4),
     4   IDUM1(4), IERSL, IDUM2(5),
     5   MITER, IDUM3(4), N, IDUM4(5)
C-----------------------------------------------------------------------
C THIS ROUTINE MANAGES THE SOLUTION OF THE LINEAR SYSTEM ARISING FROM
C A CHORD ITERATION.  IT IS CALLED IF MITER .NE. 0.
C IF MITER IS 1 OR 2, IT CALLS DGESL TO ACCOMPLISH THIS.
C IF MITER = 3 IT UPDATES THE COEFFICIENT H*EL0 IN THE DIAGONAL
C MATRIX, AND THEN COMPUTES THE SOLUTION.
C IF MITER IS 4 OR 5, IT CALLS DGBSL.
C COMMUNICATION WITH SOLSY USES THE FOLLOWING VARIABLES..
C WM   = REAL WORK SPACE CONTAINING THE INVERSE DIAGONAL MATRIX IF
C        MITER = 3 AND THE LU DECOMPOSITION OF THE MATRIX OTHERWISE.
C        STORAGE OF MATRIX ELEMENTS STARTS AT WM(3).
C        WM ALSO CONTAINS THE FOLLOWING MATRIX-RELATED DATA..
C        WM(1) = SQRT(UROUND) (NOT USED HERE),
C        WM(2) = HL0, THE PREVIOUS VALUE OF H*EL0, USED IF MITER = 3.
C IWM  = INTEGER WORK SPACE CONTAINING PIVOT INFORMATION, STARTING AT
C        IWM(21), IF MITER IS 1, 2, 4, OR 5.  IWM ALSO CONTAINS BAND
C        PARAMETERS ML = IWM(1) AND MU = IWM(2) IF MITER IS 4 OR 5.
C X    = THE RIGHT-HAND SIDE VECTOR ON INPUT, AND THE SOLUTION VECTOR
C        ON OUTPUT, OF LENGTH N.
C TEM  = VECTOR OF WORK SPACE OF LENGTH N, NOT USED IN THIS VERSION.
C IERSL = OUTPUT FLAG (IN COMMON).  IERSL = 0 IF NO TROUBLE OCCURRED.
C        IERSL = 1 IF A SINGULAR MATRIX AROSE WITH MITER = 3.
C THIS ROUTINE ALSO USES THE COMMON VARIABLES EL0, H, MITER, AND N.
C-----------------------------------------------------------------------
      IERSL = 0
      GO TO (100, 100, 300, 400, 400), MITER
 100   CALL DGESL (WM(3), N, N, IWM(21), X, 0)
      RETURN
C
 300   PHL0 = WM(2)
      HL0 = H*EL0
      WM(2) = HL0
      IF (HL0 .EQ. PHL0) GO TO 330
      R = HL0/PHL0
      DO 320 I = 1,N
        DI = ONE - R*(ONE - ONE/WM(I+2))
        IF (ABS(DI) .EQ. ZERO) GO TO 390
 320    WM(I+2) = ONE/DI
 330   DO 340 I = 1,N
 340    X(I) = WM(I+2)*X(I)
      RETURN
 390   IERSL = 1
      RETURN
C
 400   ML = IWM(1)
      MU = IWM(2)
      MEBAND = 2*ML + MU + 1
      CALL DGBSL (WM(3), MEBAND, N, ML, MU, IWM(21), X, 0)
      RETURN
C----------------------- END OF SUBROUTINE SOLSY -----------------------
      END
      SUBROUTINE EWSET (N, ITOL, RTOL, ATOL, YCUR, EWT)
C-----------------------------------------------------------------------
C THIS SUBROUTINE SETS THE ERROR WEIGHT VECTOR EWT ACCORDING TO
C    EWT(I) = RTOL(I)*ABS(YCUR(I)) + ATOL(I),  I = 1,...,N,
C WITH THE SUBSCRIPT ON RTOL AND/OR ATOL POSSIBLY REPLACED BY 1 ABOVE,
C DEPENDING ON THE VALUE OF ITOL.
C-----------------------------------------------------------------------
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION RTOL(*), ATOL(*), YCUR(N), EWT(N)
      RTOLI = RTOL(1)
      ATOLI = ATOL(1)
      DO 10 I = 1,N
        IF (ITOL .GE. 3) RTOLI = RTOL(I)
        IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I)
        EWT(I) = RTOLI*ABS(YCUR(I)) + ATOLI
 10     CONTINUE
      RETURN
C----------------------- END OF SUBROUTINE EWSET -----------------------
      END
      DOUBLE PRECISION FUNCTION VNORM (N, V, W)
C-----------------------------------------------------------------------
C THIS FUNCTION ROUTINE COMPUTES THE WEIGHTED ROOT-MEAN-SQUARE NORM
C OF THE VECTOR OF LENGTH N CONTAINED IN THE ARRAY V, WITH WEIGHTS
C CONTAINED IN THE ARRAY W OF LENGTH N..
C  VNORM = SQRT( (1/N) * SUM( V(I)*W(I) )**2 )
C PROTECTION FOR UNDERFLOW/OVERFLOW IS ACCOMPLISHED USING TWO
C CONSTANTS WHICH ARE HOPEFULLY APPLICABLE FOR ALL MACHINES.
C THESE ARE:
C     CUTLO = maximum of SQRT(U/EPS)  over all known machines
C     CUTHI = minimum of SQRT(Z)      over all known machines
C WHERE
C     EPS = smallest number s.t. EPS + 1 .GT. 1
C     U   = smallest positive number (underflow limit)
C     Z   = largest number (overflow limit)
C
C DETAILS OF THE ALGORITHM AND OF VALUES OF CUTLO AND CUTHI ARE
C FOUND IN THE BLAS ROUTINE SNRM2 (SEE ALSO ALGORITHM 539, TRANS.
C MATH. SOFTWARE, VOL. 5 NO. 3, 1979, 308-323.
C FOR SINGLE PRECISION, THE FOLLOWING VALUES SHOULD BE UNIVERSAL:
C     DATA CUTLO,CUTHI /4.441E-16,1.304E19/
C FOR DOUBLE PRECISION, USE
C     DATA CUTLO,CUTHI /8.232D-11,1.304D19/
C
C-----------------------------------------------------------------------
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      INTEGER NEXT,I,J,N
      DIMENSION V(N),W(N)
      DATA CUTLO,CUTHI /8.232D-11,1.304D19/
      DATA ZERO,ONE/0.0D0,1.0D0/
C  BLAS ALGORITHM
      NEXT = 1
      SUM = ZERO
      I = 1
20    SX = V(I)*W(I)
      GO TO (30,40,70,80),NEXT
30    IF (ABS(SX).GT.CUTLO) GO TO 110
      NEXT = 2
      XMAX = ZERO
40    IF (SX.EQ.ZERO) GO TO 130
      IF (ABS(SX).GT.CUTLO) GO TO 110
      NEXT = 3
      GO TO 60
50    I=J
      NEXT = 4
      SUM = (SUM/SX)/SX
60    XMAX = ABS(SX)
      GO TO 90
70    IF(ABS(SX).GT.CUTLO) GO TO 100
80    IF(ABS(SX).LE.XMAX) GO TO 90
      SUM = ONE + SUM * (XMAX/SX)**2
      XMAX = ABS(SX)
      GO TO 130
90    SUM = SUM + (SX/XMAX)**2
      GO TO 130
100   SUM = (SUM*XMAX)*XMAX
110   HITEST = CUTHI/REAL(N)
      DO 120 J = I,N
         SX = V(J)*W(J)
         IF(ABS(SX).GE.HITEST) GO TO 50
         SUM = SUM + SX**2
120   CONTINUE
      VNORM = SQRT(SUM)
      GO TO 140
130   CONTINUE
      I = I + 1
      IF (I.LE.N) GO TO 20
      VNORM = XMAX * SQRT(SUM)
140   CONTINUE
      RETURN
C----------------------- END OF FUNCTION VNORM -------------------------
      END
      SUBROUTINE SVCOM (RSAV, ISAV)
C-----------------------------------------------------------------------
C THIS ROUTINE STORES IN RSAV AND ISAV THE CONTENTS OF COMMON BLOCKS
C ODE001, ODE002 AND EH0001, WHICH ARE USED INTERNALLY IN THE ODESSA
C PACKAGE.
C RSAV = REAL ARRAY OF LENGTH 222 OR MORE.
C ISAV = INTEGER ARRAY OF LENGTH 52 OR MORE.
C-----------------------------------------------------------------------
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION RSAV(*), ISAV(*)
      COMMON /ODE001/ RODE1(219), IODE1(39)
      COMMON /ODE002/ RODE2(3), IODE2(11)
      COMMON /EH0001/ IEH(2)
      DATA LRODE1/219/, LIODE1/39/, LRODE2/3/, LIODE2/11/
C
      DO 10 I = 1,LRODE1
 10     RSAV(I) = RODE1(I)
      DO 20 I = 1,LRODE2
        J = LRODE1 + I
 20     RSAV(J) = RODE2(I)
      DO 30 I = 1,LIODE1
 30     ISAV(I) = IODE1(I)
      DO 40 I = 1,LIODE2
        J = LIODE1 + I
 40     ISAV(J) = IODE2(I)
      ISAV(LIODE1+LIODE2+1) = IEH(1)
      ISAV(LIODE1+LIODE2+2) = IEH(2)
      RETURN
C----------------------- END OF SUBROUTINE SVCOM -----------------------
      END
      SUBROUTINE RSCOM (RSAV, ISAV)
C-----------------------------------------------------------------------
C THIS ROUTINE RESTORES FROM RSAV AND ISAV THE CONTENTS OF COMMON BLOCKS
C ODE001, ODE002 AND EH0001, WHICH ARE USED INTERNALLY IN THE ODESSSA
C PACKAGE.  THIS PRESUMES THAT RSAV AND ISAV WERE LOADED BY MEANS
C OF SUBROUTINE SVCOM OR THE EQUIVALENT.
C-----------------------------------------------------------------------
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION RSAV(*), ISAV(*)
      COMMON /ODE001/ RODE1(219), IODE1(39)
      COMMON /ODE002/ RODE2(3), IODE2(11)
      COMMON /EH0001/ IEH(2)
      DATA LRODE1/219/, LIODE1/39/, LRODE2/3/, LIODE2/11/
C
      DO 10 I = 1,LRODE1
 10     RODE1(I) = RSAV(I)
      DO 20 I = 1,LRODE2
        J = LRODE1 + I
 20     RODE2(I) = RSAV(J)
      DO 30 I = 1,LIODE1
 30     IODE1(I) = ISAV(I)
      DO 40 I = 1,LODE2
        J = LIODE1 + I
 40     IODE2(I) = ISAV(J)
      IEH(1) = ISAV(LIODE1+LIODE2+1)
      IEH(2) = ISAV(LIODE1+LIODE2+2)
      RETURN
C----------------------- END OF SUBROUTINE RSCOM -----------------------
      END
      SUBROUTINE DGEFA(A,LDA,N,IPVT,INFO)
      INTEGER LDA,N,IPVT(*),INFO
      DOUBLE PRECISION A(LDA,*)
C
C    DGEFA FACTORS A DOUBLE PRECISION MATRIX BY GAUSSIAN ELIMINATION.
C
C    DGEFA IS USUALLY CALLED BY DGECO, BUT IT CAN BE CALLED
C    DIRECTLY WITH A SAVING IN TIME IF  RCOND  IS NOT NEEDED.
C    (TIME FOR DGECO) = (1 + 9/N)*(TIME FOR DGEFA) .
C
C    ON ENTRY
C
C       A       DOUBLE PRECISION(LDA, N)
C               THE MATRIX TO BE FACTORED.
C
C       LDA     INTEGER
C               THE LEADING DIMENSION OF THE ARRAY  A .
C
C       N       INTEGER
C               THE ORDER OF THE MATRIX  A .
C
C    ON RETURN
C
C       A       AN UPPER TRIANGULAR MATRIX AND THE MULTIPLIERS
C               WHICH WERE USED TO OBTAIN IT.
C               THE FACTORIZATION CAN BE WRITTEN  A = L*U  WHERE
C               L  IS A PRODUCT OF PERMUTATION AND UNIT LOWER
C               TRIANGULAR MATRICES AND  U  IS UPPER TRIANGULAR.
C
C       IPVT    INTEGER(N)
C               AN INTEGER VECTOR OF PIVOT INDICES.
C
C       INFO    INTEGER
C               = 0  NORMAL VALUE.
C               = K  IF  U(K,K) .EQ. 0.0 .  THIS IS NOT AN ERROR
C                    CONDITION FOR THIS SUBROUTINE, BUT IT DOES
C                    INDICATE THAT DGESL OR DGEDI WILL DIVIDE BY ZERO
C                    IF CALLED.  USE  RCOND  IN DGECO FOR A RELIABLE
C                    INDICATION OF SINGULARITY.
C
C    LINPACK. THIS VERSION DATED 08/14/78 .
C    CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C    SUBROUTINES AND FUNCTIONS
C
C    BLAS DAXPY,DSCAL,IDAMAX
C
C    INTERNAL VARIABLES
C
      DOUBLE PRECISION T
      INTEGER IDAMAX,J,K,KP1,L,NM1
C
C
C     GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
C
      INFO = 0
      NM1 = N - 1
      IF (NM1 .LT. 1) GO TO 70
      DO 60 K = 1, NM1
         KP1 = K + 1
C
C        FIND L = PIVOT INDEX
C
         L = IDAMAX(N-K+1,A(K,K),1) + K - 1
         IPVT(K) = L
C
C        ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
C
         IF (A(L,K) .EQ. 0.0D0) GO TO 40
C
C           INTERCHANGE IF NECESSARY
C
            IF (L .EQ. K) GO TO 10
               T = A(L,K)
               A(L,K) = A(K,K)
               A(K,K) = T
  10        CONTINUE
C
C           COMPUTE MULTIPLIERS
C
            T  = -1.0D0/A(K,K)
            CALL DSCAL(N-K,T,A(K+1,K),1)
C
C           ROW ELIMINATION WITH COLUMN INDEXING
C
            DO 30 J = KP1, N
               T = A(L,J)
               IF (L .EQ. K) GO TO 20
                  A(L,J) = A(K,J)
                  A(K,J) = T
  20           CONTINUE
               CALL DAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1)
  30        CONTINUE
         GO TO 50
  40     CONTINUE
            INFO = K
  50     CONTINUE
  60  CONTINUE
  70  CONTINUE
      IPVT(N) = N
      IF (A(N,N) .EQ. 0.0D0) INFO = N
      RETURN
      END
      SUBROUTINE DGESL(A,LDA,N,IPVT,B,JOB)
      INTEGER LDA,N,IPVT(*),JOB
      DOUBLE PRECISION A(LDA,*),B(*)
C
C     DGESL SOLVES THE DOUBLE PRECISION SYSTEM
C     A * X = B  OR  TRANS(A) * X = B
C    USING THE FACTORS COMPUTED BY DGECO OR DGEFA.
C
C    ON ENTRY
C
C       A       DOUBLE PRECISION(LDA, N)
C               THE OUTPUT FROM DGECO OR DGEFA.
C
C       LDA     INTEGER
C               THE LEADING DIMENSION OF THE ARRAY  A .
C
C       N       INTEGER
C               THE ORDER OF THE MATRIX  A .
C
C       IPVT    INTEGER(N)
C               THE PIVOT VECTOR FROM DGECO OR DGEFA.
C
C       B       DOUBLE PRECISION(N)
C               THE RIGHT HAND SIDE VECTOR.
C
C       JOB     INTEGER
C               = 0         TO SOLVE  A*X = B ,
C               = NONZERO   TO SOLVE  TRANS(A)*X = B  WHERE
C                           TRANS(A)  IS THE TRANSPOSE.
C
C    ON RETURN
C
C       B       THE SOLUTION VECTOR  X .
C
C    ERROR CONDITION
C
C       A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS A
C       ZERO ON THE DIAGONAL.  TECHNICALLY THIS INDICATES SINGULARITY
C       BUT IT IS OFTEN CAUSED BY IMPROPER ARGUMENTS OR IMPROPER
C       SETTING OF LDA .  IT WILL NOT OCCUR IF THE SUBROUTINES ARE
C       CALLED CORRECTLY AND IF DGECO HAS SET RCOND .GT. 0.0
C       OR DGEFA HAS SET INFO .EQ. 0 .
C
C    TO COMPUTE  INVERSE(A) * C  WHERE  C  IS A MATRIX
C    WITH  P  COLUMNS
C          CALL DGECO(A,LDA,N,IPVT,RCOND,Z)
C          IF (RCOND IS TOO SMALL) GO TO ...
C          DO 10 J = 1, P
C             CALL DGESL(A,LDA,N,IPVT,C(1,J),0)
C       10 CONTINUE
C
C    LINPACK. THIS VERSION DATED 08/14/78 .
C    CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C    SUBROUTINES AND FUNCTIONS
C
C    BLAS DAXPY,DDOT
C
C    INTERNAL VARIABLES
C
      DOUBLE PRECISION DDOT,T
      INTEGER K,KB,L,NM1
C
      NM1 = N - 1
      IF (JOB .NE. 0) GO TO 50
C
C        JOB = 0 , SOLVE  A * X = B
C        FIRST SOLVE  L*Y = B
C
         IF (NM1 .LT. 1) GO TO 30
         DO 20 K = 1, NM1
            L = IPVT(K)
            T = B(L)
            IF (L .EQ. K) GO TO 10
               B(L) = B(K)
               B(K) = T
  10        CONTINUE
            CALL DAXPY(N-K,T,A(K+1,K),1,B(K+1),1)
  20     CONTINUE
  30     CONTINUE
C
C        NOW SOLVE  U*X = Y
C
         DO 40 KB = 1, N
            K = N + 1 - KB
            B(K) = B(K)/A(K,K)
            T = -B(K)
            CALL DAXPY(K-1,T,A(1,K),1,B(1),1)
  40     CONTINUE
      GO TO 100
  50  CONTINUE
C
C        JOB = NONZERO, SOLVE  TRANS(A) * X = B
C        FIRST SOLVE  TRANS(U)*Y = B
C
         DO 60 K = 1, N
            T = DDOT(K-1,A(1,K),1,B(1),1)
            B(K) = (B(K) - T)/A(K,K)
  60     CONTINUE
C
C        NOW SOLVE TRANS(L)*X = Y
C
         IF (NM1 .LT. 1) GO TO 90
         DO 80 KB = 1, NM1
            K = N - KB
            B(K) = B(K) + DDOT(N-K,A(K+1,K),1,B(K+1),1)
            L = IPVT(K)
            IF (L .EQ. K) GO TO 70
               T = B(L)
               B(L) = B(K)
               B(K) = T
  70        CONTINUE
  80     CONTINUE
  90     CONTINUE
  100  CONTINUE
      RETURN
      END
      SUBROUTINE DGBFA(ABD,LDA,N,ML,MU,IPVT,INFO)
      INTEGER LDA,N,ML,MU,IPVT(*),INFO
      DOUBLE PRECISION ABD(LDA,*)
C
C    DGBFA FACTORS A DOUBLE PRECISION BAND MATRIX BY ELIMINATION.
C
C    DGBFA IS USUALLY CALLED BY DGBCO, BUT IT CAN BE CALLED
C    DIRECTLY WITH A SAVING IN TIME IF  RCOND  IS NOT NEEDED.
C
C    ON ENTRY
C
C       ABD     DOUBLE PRECISION(LDA, N)
C               CONTAINS THE MATRIX IN BAND STORAGE.  THE COLUMNS
C               OF THE MATRIX ARE STORED IN THE COLUMNS OF  ABD  AND
C               THE DIAGONALS OF THE MATRIX ARE STORED IN ROWS
C               ML+1 THROUGH 2*ML+MU+1 OF  ABD .
C               SEE THE COMMENTS BELOW FOR DETAILS.
C
C       LDA     INTEGER
C               THE LEADING DIMENSION OF THE ARRAY  ABD .
C               LDA MUST BE .GE. 2*ML + MU + 1 .
C
C       N       INTEGER
C               THE ORDER OF THE ORIGINAL MATRIX.
C
C       ML      INTEGER
C               NUMBER OF DIAGONALS BELOW THE MAIN DIAGONAL.
C               0 .LE. ML .LT. N .
C
C       MU      INTEGER
C               NUMBER OF DIAGONALS ABOVE THE MAIN DIAGONAL.
C               0 .LE. MU .LT. N .
C               MORE EFFICIENT IF  ML .LE. MU .
C    ON RETURN
C
C       ABD     AN UPPER TRIANGULAR MATRIX IN BAND STORAGE AND
C               THE MULTIPLIERS WHICH WERE USED TO OBTAIN IT.
C               THE FACTORIZATION CAN BE WRITTEN  A = L*U  WHERE
C               L  IS A PRODUCT OF PERMUTATION AND UNIT LOWER
C               TRIANGULAR MATRICES AND  U  IS UPPER TRIANGULAR.
C
C       IPVT    INTEGER(N)
C               AN INTEGER VECTOR OF PIVOT INDICES.
C
C       INFO    INTEGER
C               = 0  NORMAL VALUE.
C               = K  IF  U(K,K) .EQ. 0.0 .  THIS IS NOT AN ERROR
C                    CONDITION FOR THIS SUBROUTINE, BUT IT DOES
C                    INDICATE THAT DGBSL WILL DIVIDE BY ZERO IF
C                    CALLED.  USE  RCOND  IN DGBCO FOR A RELIABLE
C                    INDICATION OF SINGULARITY.
C
C    BAND STORAGE
C
C          IF  A  IS A BAND MATRIX, THE FOLLOWING PROGRAM SEGMENT
C          WILL SET UP THE INPUT.
C
C                  ML = (BAND WIDTH BELOW THE DIAGONAL)
C                  MU = (BAND WIDTH ABOVE THE DIAGONAL)
C                  M = ML + MU + 1
C                  DO 20 J = 1, N
C                     I1 = MAX0(1, J-MU)
C                     I2 = MIN0(N, J+ML)
C                     DO 10 I = I1, I2
C                        K = I - J + M
C                        ABD(K,J) = A(I,J)
C               10    CONTINUE
C               20 CONTINUE
C
C          THIS USES ROWS  ML+1  THROUGH  2*ML+MU+1  OF  ABD .
C          IN ADDITION, THE FIRST  ML  ROWS IN  ABD  ARE USED FOR
C          ELEMENTS GENERATED DURING THE TRIANGULARIZATION.
C          THE TOTAL NUMBER OF ROWS NEEDED IN  ABD  IS  2*ML+MU+1 .
C          THE  ML+MU BY ML+MU  UPPER LEFT TRIANGLE AND THE
C          ML BY ML  LOWER RIGHT TRIANGLE ARE NOT REFERENCED.
C
C    LINPACK. THIS VERSION DATED 08/14/78 .
C    CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C    SUBROUTINES AND FUNCTIONS
C
C    BLAS DAXPY,DSCAL,IDAMAX
C    FORTRAN MAX0,MIN0
C
C    INTERNAL VARIABLES
C
      DOUBLE PRECISION T
      INTEGER I,IDAMAX,I0,J,JU,JZ,J0,J1,K,KP1,L,LM,M,MM,NM1
C
C
      M = ML + MU + 1
      INFO = 0
C
C     ZERO INITIAL FILL-IN COLUMNS
C
      J0 = MU + 2
      J1 = MIN0(N,M) - 1
      IF (J1 .LT. J0) GO TO 30
      DO 20 JZ = J0, J1
         I0 = M + 1 - JZ
         DO 10 I = I0, ML
            ABD(I,JZ) = 0.0D0
  10     CONTINUE
  20  CONTINUE
  30  CONTINUE
      JZ = J1
      JU = 0
C
C     GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
C
      NM1 = N - 1
      IF (NM1 .LT. 1) GO TO 130
      DO 120 K = 1, NM1
         KP1 = K + 1
C
C        ZERO NEXT FILL-IN COLUMN
C
         JZ = JZ + 1
         IF (JZ .GT. N) GO TO 50
         IF (ML .LT. 1) GO TO 50
            DO 40 I = 1, ML
               ABD(I,JZ) = 0.0D0
  40        CONTINUE
  50     CONTINUE
C
C        FIND L = PIVOT INDEX
C
         LM = MIN0(ML,N-K)
         L = IDAMAX(LM+1,ABD(M,K),1) + M - 1
         IPVT(K) = L + K - M
C
C        ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
C
         IF (ABD(L,K) .EQ. 0.0D0) GO TO 100
C
C           INTERCHANGE IF NECESSARY
C
            IF (L .EQ. M) GO TO 60
               T = ABD(L,K)
               ABD(L,K) = ABD(M,K)
               ABD(M,K) = T
  60        CONTINUE
C
C           COMPUTE MULTIPLIERS
C
            T = -1.0D0/ABD(M,K)
            CALL DSCAL(LM,T,ABD(M+1,K),1)
C
C           ROW ELIMINATION WITH COLUMN INDEXING
C
            JU = MIN0(MAX0(JU,MU+IPVT(K)),N)
            MM = M
            IF (JU .LT. KP1) GO TO 90
            DO 80 J = KP1, JU
               L = L - 1
               MM = MM - 1
               T = ABD(L,J)
               IF (L .EQ. MM) GO TO 70
                  ABD(L,J) = ABD(MM,J)
                  ABD(MM,J) = T
  70           CONTINUE
               CALL DAXPY(LM,T,ABD(M+1,K),1,ABD(MM+1,J),1)
  80        CONTINUE
  90        CONTINUE
         GO TO 110
  100    CONTINUE
            INFO = K
  110    CONTINUE
  120  CONTINUE
  130  CONTINUE
      IPVT(N) = N
      IF (ABD(M,N) .EQ. 0.0D0) INFO = N
      RETURN
      END
      SUBROUTINE DGBSL(ABD,LDA,N,ML,MU,IPVT,B,JOB)
      INTEGER LDA,N,ML,MU,IPVT(*),JOB
      DOUBLE PRECISION ABD(LDA,*),B(*)
C
C    DGBSL SOLVES THE DOUBLE PRECISION BAND SYSTEM
C    A * X = B  OR  TRANS(A) * X = B
C    USING THE FACTORS COMPUTED BY DGBCO OR DGBFA.
C
C    ON ENTRY
C
C       ABD     DOUBLE PRECISION(LDA, N)
C               THE OUTPUT FROM DGBCO OR DGBFA.
C
C       LDA     INTEGER
C               THE LEADING DIMENSION OF THE ARRAY  ABD .
C
C       N       INTEGER
C               THE ORDER OF THE ORIGINAL MATRIX.
C
C       ML      INTEGER
C               NUMBER OF DIAGONALS BELOW THE MAIN DIAGONAL.
C
C       MU      INTEGER
C               NUMBER OF DIAGONALS ABOVE THE MAIN DIAGONAL.
C
C       IPVT    INTEGER(N)
C               THE PIVOT VECTOR FROM DGBCO OR DGBFA.
C
C       B       DOUBLE PRECISION(N)
C               THE RIGHT HAND SIDE VECTOR.
C
C       JOB     INTEGER
C               = 0         TO SOLVE  A*X = B ,
C               = NONZERO   TO SOLVE  TRANS(A)*X = B , WHERE
C                           TRANS(A)  IS THE TRANSPOSE.
C
C    ON RETURN
C
C       B       THE SOLUTION VECTOR  X .
C
C    ERROR CONDITION
C
C       A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS A
C       ZERO ON THE DIAGONAL.  TECHNICALLY THIS INDICATES SINGULARITY
C       BUT IT IS OFTEN CAUSED BY IMPROPER ARGUMENTS OR IMPROPER
C       SETTING OF LDA .  IT WILL NOT OCCUR IF THE SUBROUTINES ARE
C       CALLED CORRECTLY AND IF DGBCO HAS SET RCOND .GT. 0.0
C       OR DGBFA HAS SET INFO .EQ. 0 .
C
C    TO COMPUTE  INVERSE(A) * C  WHERE  C  IS A MATRIX
C    WITH  P  COLUMNS
C          CALL DGBCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z)
C          IF (RCOND IS TOO SMALL) GO TO ...
C          DO 10 J = 1, P
C             CALL DGBSL(ABD,LDA,N,ML,MU,IPVT,C(1,J),0)
C       10 CONTINUE
C
C    LINPACK. THIS VERSION DATED 08/14/78 .
C    CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C    SUBROUTINES AND FUNCTIONS
C
C    BLAS DAXPY,DDOT
C    FORTRAN MIN0
C
C    INTERNAL VARIABLES
C
      DOUBLE PRECISION DDOT,T
      INTEGER K,KB,L,LA,LB,LM,M,NM1
C
      M = MU + ML + 1
      NM1 = N - 1
      IF (JOB .NE. 0) GO TO 50
C
C        JOB = 0 , SOLVE  A * X = B
C        FIRST SOLVE L*Y = B
C
         IF (ML .EQ. 0) GO TO 30
         IF (NM1 .LT. 1) GO TO 30
            DO 20 K = 1, NM1
               LM = MIN0(ML,N-K)
               L = IPVT(K)
               T = B(L)
               IF (L .EQ. K) GO TO 10
                  B(L) = B(K)
                  B(K) = T
  10           CONTINUE
               CALL DAXPY(LM,T,ABD(M+1,K),1,B(K+1),1)
  20        CONTINUE
  30     CONTINUE
C
C        NOW SOLVE  U*X = Y
C
         DO 40 KB = 1, N
            K = N + 1 - KB
            B(K) = B(K)/ABD(M,K)
            LM = MIN0(K,M) - 1
            LA = M - LM
            LB = K - LM
            T = -B(K)
            CALL DAXPY(LM,T,ABD(LA,K),1,B(LB),1)
  40     CONTINUE
      GO TO 100
  50  CONTINUE
C
C        JOB = NONZERO, SOLVE  TRANS(A) * X = B
C        FIRST SOLVE  TRANS(U)*Y = B
C
         DO 60 K = 1, N
            LM = MIN0(K,M) - 1
            LA = M - LM
            LB = K - LM
            T = DDOT(LM,ABD(LA,K),1,B(LB),1)
            B(K) = (B(K) - T)/ABD(M,K)
  60     CONTINUE
C
C        NOW SOLVE TRANS(L)*X = Y
C
         IF (ML .EQ. 0) GO TO 90
         IF (NM1 .LT. 1) GO TO 90
            DO 80 KB = 1, NM1
               K = N - KB
               LM = MIN0(ML,N-K)
               B(K) = B(K) + DDOT(LM,ABD(M+1,K),1,B(K+1),1)
               L = IPVT(K)
               IF (L .EQ. K) GO TO 70
                  T = B(L)
                  B(L) = B(K)
                  B(K) = T
  70           CONTINUE
  80        CONTINUE
  90     CONTINUE
  100  CONTINUE
      RETURN
      END
      DOUBLE PRECISION FUNCTION D1MACH (IDUM)
      INTEGER IDUM
C-----------------------------------------------------------------------
C THIS ROUTINE COMPUTES THE UNIT ROUNDOFF OF THE MACHINE IN DOUBLE
C PRECISION.  THIS IS DEFINED AS THE SMALLEST POSITIVE MACHINE NUMBER
C U SUCH THAT  1.0D0 + U .NE. 1.0D0 (IN DOUBLE PRECISION).
C-----------------------------------------------------------------------
      DOUBLE PRECISION U, COMP
      U = 1.0D0
 10   U = U*0.5D0
      COMP = 1.0D0 + U
      IF (COMP .NE. 1.0D0) GO TO 10
      D1MACH = U*2.0D0
      RETURN
C----------------------- END OF FUNCTION D1MACH ------------------------
      END
      SUBROUTINE XSETF (MFLAG)
C
C THIS ROUTINE RESETS THE PRINT CONTROL FLAG MFLAG.
C
      INTEGER MFLAG, MESFLG, LUNIT
      COMMON /EH0001/ MESFLG, LUNIT
C
      IF (MFLAG .EQ. 0 .OR. MFLAG .EQ. 1) MESFLG = MFLAG
      RETURN
C----------------------- END OF SUBROUTINE XSETF -----------------------
      END
      SUBROUTINE XSETUN (LUN)
C
C THIS ROUTINE RESETS THE LOGICAL UNIT NUMBER FOR MESSAGES.
C
      INTEGER LUN, MESFLG, LUNIT
      COMMON /EH0001/ MESFLG, LUNIT
C
      IF (LUN .GT. 0) LUNIT = LUN
      RETURN
C----------------------- END OF SUBROUTINE XSETUN ----------------------
      END
      BLOCK DATA
C-----------------------------------------------------------------------
C THIS DATA SUBPROGRAM LOADS VARIABLES INTO THE INTERNAL COMMON
C BLOCKS USED BY ODESSA AND ITS VARIANTS.  THE VARIABLES ARE
C DEFINED AS FOLLOWS..
C  ILLIN  = COUNTER FOR THE NUMBER OF CONSECUTIVE TIMES THE PACKAGE
C           WAS CALLED WITH ILLEGAL INPUT.  THE RUN IS STOPPED WHEN
C           ILLIN REACHES 5.
C  NTREP  = COUNTER FOR THE NUMBER OF CONSECUTIVE TIMES THE PACKAGE
C           WAS CALLED WITH ISTATE = 1 AND TOUT = T.  THE RUN IS
C           STOPPED WHEN NTREP REACHES 5.
C  MESFLG = FLAG TO CONTROL PRINTING OF ERROR MESSAGES.  1 MEANS PRINT,
C           0 MEANS NO PRINTING.
C  LUNIT  = DEFAULT VALUE OF LOGICAL UNIT NUMBER FOR PRINTING OF ERROR
C           MESSAGES.
C-----------------------------------------------------------------------
      INTEGER ILLIN, IDUMA, NTREP, IDUMB, IOWNS, ICOMM, MESFLG, LUNIT
      DOUBLE PRECISION ROWND, ROWNS, RCOMM
      COMMON /ODE001/ ROWND, ROWNS(173), RCOMM(45),
     1   ILLIN, IDUMA(10), NTREP, IDUMB(2), IOWNS(4), ICOMM(21)
      COMMON /EH0001/ MESFLG, LUNIT
      DATA ILLIN/0/, NTREP/0/
      DATA MESFLG/1/, LUNIT/6/
C
C------------------------ END OF BLOCK DATA ----------------------------
      END
*
C-----------------------------------------------------------------------
C INSTRUCTIONS FOR INSTALLING THE ODESSA PACKAGE. (see @ below.)
C
C ODESSA is an enhanced version of the widely disseminated ODE solver
C LSODE, and as such retains the same properties regarding portability.
C The notes below, adapted from the installation instructions for LSODE,
C are intended to facilitate the installation of the ODESSA package in
C the user's software library.
C
C 1. Both a single and a double precision version of ODESSA are
C provided in this release.  It is expected that most users will
C utilize the double precision version, except in the case of
C extended word-length computers. Most routines used by ODESSA
C are named the same regardless of whether they are single or
C double precision.  The exceptions are the LINPAK and BLAS
C routines that follow the LINPAK/BLAS naming conventions, i.e.
C D--- for a double precision routine, and S--- for a single
C precision routine.  Thus, care should be taken if both single
C and double precision versions are stored in the same library.
C
C 2. Several routines in ODESSA have the same names as the LSODE
C routines from which they were derived, although they contain
C different code.  These are: INTDY, STODE, PREPJ, SVCOM, and
C RSCOM.  If ODESSA is added to a subroutine library of which
C LSODE is already a member, these routine names must be changed
C in one of the two programs.  Also see the note regarding BLOCK
C DATA subroutines below.
C
C 3.  In many cases, ODESSA uses unaltered LSODE routines and
C common library routines that may already reside on your system.
C The installation of ODESSA should be done so that identical routines
C are shared rather than kept as duplicate copies.
C a.  Normally, the user calls only subroutine ODESSA, but for optional
C     capabilities the user may also call XSETUN, XSETF, SVCOM, RSCOM,
C     or INTDY, as described in Part II of the Full Description in the
C     User Documentation (ODESSA.DOC, see below).  Except for INTDY,
C     none of these are called from within the package.
C b.  Two routines, EWSET and VNORM, are optionally replaceable by the
C     user if the package version is unsuitable.  Hence, the install-
C     ation of the package should be done so that the user's version
C     for either routine overrides the package version.
C c.  The function routine D1MACH is provided to compute the unit
C     roundoff of the machine and precision in use, in a manner com-
C     patible with machine parameter routines developed at Bell Lab-
C     oratories.  If such a routine has already been installed on
C     your system, the version supplied here may be discarded.
C d.  Linear algebraic systems are solved with routines from the
C     LINPACK collection, in conjunction with routines from the Basic
C     Linear Algebra module collection (BLAS).  In double precision,
C     the names are DGEFA, DGESL, DGBFA, and DGBSL (from LINPACK), and
C     DAXPY, DSCAL, IDAMAX, and DDOT (from BLAS). If these routines
C     have already been installed on your system, copies supplied with
C     ODESSA may be discarded.  The single precision versions of these
C     routines are used in the single precision version.
C
C 4. There are four integer variables, in the two labeled COMMON
C blocks /ODE001/ and /EH0001/, which need to be loaded with DATA
C statements.  They can vary during execution, and are in common to
C assure their retention between calls.  This is legal in ANSI Fortran
C only if done in a BLOCK DATA subprogram, and this package has a
C BLOCK DATA for this purpose.  However, BLOCK DATA subprograms can be
C difficult to install in libraries, and many compilers allow such DATA
C statements in subroutines.  If your system allows this, the location
C of the DATA statements are just after the initial type and common
C declarations in subroutines ODESSA and XERR.  In ODESSA, ILLIN and
C NTREP are DATA-loaded as 0.  In XERR, MESFLG is loaded as 1 and
C LUNIT is loaded as the appropriate default logical unit number.
C
C 5. The ODESSA package contains subscript expressions which may not
C be accepted by some compilers.  Subscripts of the form I + J, I - J,
C etc., occur in various routines.  If any of these forms are
C unacceptable to your compiler, an extra line of code setting the
C subscript to a dummy integer value should be added for each subscipt.
C
C 6. User documentation is provided in a two-level structure
C to accommmodate both the casual and serious user.  The novice or
C casual user should need to read only the Summary of Usage and the
C Example Problem located at the beginning of the documentation.  More
C experienced users, requiring the full set of available options,
C should read the Full Description which follows the Example Problem.
C
C 7. The user documentation may need corrections in the following ways:
C a.  If subroutine names have been changed to avoid conflicts between
C     the LSODE and ODESSA packages, the corresponding name changes
C     should be made in the documentation.
C b.  In the Summary of Usage, and in the description of XSETUN under
C     Part II of the Full Description, the default logical unit number
C     should be corrected if it is not 6.
C c.  In the Summary of Usage, users should be instructed to execute
C     CALL XSETF(1) before the first call to ODESSA, if this is neces-
C     sary for proper error message handling.  (see note 2(e) above.)
C d.  In the description of the subroutines DF and JAC in the Summary
C     of Usage and in Part I of the Full Description, it is stated
C     that dummy names may be passed if these two routines are not user
C     supplied.  Your system may require the user to supply a dummy
C     subroutine instead.
C e.  The ODESSA package treats the arguments NEQ, RTOL, and ATOL as
C     arrays (possibly of length 1), while the usage documentation
C     states that these arguments may be either arrays or scalars.
C     If your system does not allow such a mismatch, then the
C     documentation should be changed to reflect this.
C 8.  A demonstration program is provided with the package for
C     verification.
C
C
C     Jorge R. Leis and Mark A. Kramer
C     Department of Chemical Engineering
C     Massachusetts Institute of Technology
C     Cambridge, Massachusetts  02139
C     U.S.A.
C
C     Current address of J.R. Leis (Jan. 1988):
C
C     Shell Development Company
C     Westhollow Research Center
C     Houston, TX
C
C  @ Adapted from 'Instructions for Installing LSODE', written by
C    Alan C. Hindmarsh, Mathematics & Statistics Division, L-316,
C    Lawrence Livermore National Laboratory, Livermore, CA. 94550
C-----------------------------------------------------------------------
C
