/*
 * -----------------------------------------------------------------
 * $Revision: 4378 $
 * $Date: 2015-02-19 10:55:14 -0800 (Thu, 19 Feb 2015) $
 * ----------------------------------------------------------------- 
 * Programmer(s): Radu Serban @ LLNL
 * -----------------------------------------------------------------
 * LLNS Copyright Start
 * Copyright (c) 2014, Lawrence Livermore National Security
 * This work was performed under the auspices of the U.S. Department 
 * of Energy by Lawrence Livermore National Laboratory in part under 
 * Contract W-7405-Eng-48 and in part under Contract DE-AC52-07NA27344.
 * Produced at the Lawrence Livermore National Laboratory.
 * All rights reserved.
 * For details, see the LICENSE file.
 * LLNS Copyright End
 * -----------------------------------------------------------------
 * Implementation header file for the main CVODES integrator.
 * -----------------------------------------------------------------
 */

#ifndef _CVODES_IMPL_H
#define _CVODES_IMPL_H

#include <stdarg.h>

#include <cvodes/cvodes.h>
#include <sundials/sundials_nvector.h>
#include <sundials/sundials_types.h>

#ifdef __cplusplus  /* wrapper to enable C++ usage */
extern "C" {
#endif

/* 
 * =================================================================
 *   I N T E R N A L   C V O D E S   C O N S T A N T S
 * =================================================================
 */

/* Basic CVODES constants */

#define ADAMS_Q_MAX 12      /* max value of q for lmm == ADAMS    */
#define BDF_Q_MAX    5      /* max value of q for lmm == BDF      */
#define Q_MAX  ADAMS_Q_MAX  /* max value of q for either lmm      */
#define L_MAX  (Q_MAX+1)    /* max value of L for either lmm      */
#define NUM_TESTS    5      /* number of error test quantities    */

#define HMIN_DEFAULT     RCONST(0.0)    /* hmin default value     */
#define HMAX_INV_DEFAULT RCONST(0.0)    /* hmax_inv default value */
#define MXHNIL_DEFAULT   10             /* mxhnil default value   */
#define MXSTEP_DEFAULT   500            /* mxstep default value   */

/* 
 * =================================================================
 *   F O R W A R D   P O I N T E R   R E F E R E N C E S
 * =================================================================
 */

typedef struct CVadjMemRec  *CVadjMem;
typedef struct CkpntMemRec  *CkpntMem;
typedef struct DtpntMemRec  *DtpntMem;
typedef struct CVodeBMemRec *CVodeBMem;

/* 
 * =================================================================
 *   M A I N    I N T E G R A T O R    M E M O R Y    B L O C K
 * =================================================================
 */


/*
 * -----------------------------------------------------------------
 * Types: struct CVodeMemRec, CVodeMem
 * -----------------------------------------------------------------
 * The type CVodeMem is type pointer to struct CVodeMemRec.
 * This structure contains fields to keep track of problem state.
 * -----------------------------------------------------------------
 */
  
typedef struct CVodeMemRec {
    
  realtype cv_uround;         /* machine unit roundoff                        */   

  /*-------------------------- 
    Problem Specification Data 
    --------------------------*/

  CVRhsFn cv_f;               /* y' = f(t,y(t))                               */
  void *cv_user_data;         /* user pointer passed to f                     */

  int cv_lmm;                 /* lmm = ADAMS or BDF                           */
  int cv_iter;                /* iter = FUNCTIONAL or NEWTON                  */

  int cv_itol;                /* itol = CV_SS, CV_SV, or CV_WF, or CV_NN      */
  realtype cv_reltol;         /* relative tolerance                           */
  realtype cv_Sabstol;        /* scalar absolute tolerance                    */
  N_Vector cv_Vabstol;        /* vector absolute tolerance                    */
  booleantype cv_user_efun;   /* TRUE if user sets efun                       */
  CVEwtFn cv_efun;            /* function to set ewt                          */
  void *cv_e_data;            /* user pointer passed to efun                  */

  /*-----------------------
    Quadrature Related Data 
    -----------------------*/

  booleantype cv_quadr;       /* TRUE if integrating quadratures              */

  CVQuadRhsFn cv_fQ;          /* q' = fQ(t, y(t))                             */

  booleantype cv_errconQ;     /* TRUE if quadrs. are included in error test   */

  int cv_itolQ;               /* itolQ = CV_SS or CV_SV                       */
  realtype cv_reltolQ;        /* relative tolerance for quadratures           */
  realtype cv_SabstolQ;       /* scalar absolute tolerance for quadratures    */
  N_Vector cv_VabstolQ;       /* vector absolute tolerance for quadratures    */

  /*------------------------
    Sensitivity Related Data 
    ------------------------*/

  booleantype cv_sensi;       /* TRUE if computing sensitivities              */

  int cv_Ns;                  /* Number of sensitivities                      */

  int cv_ism;                 /* ism = SIMULTANEOUS or STAGGERED              */

  CVSensRhsFn cv_fS;          /* fS = (df/dy)*yS + (df/dp)                    */
  CVSensRhs1Fn cv_fS1;        /* fS1 = (df/dy)*yS_i + (df/dp)                 */
  void *cv_fS_data;           /* data pointer passed to fS                    */
  booleantype cv_fSDQ;        /* TRUE if using internal DQ functions          */
  int cv_ifS;                 /* ifS = ALLSENS or ONESENS                     */

  realtype *cv_p;             /* parameters in f(t,y,p)                       */
  realtype *cv_pbar;          /* scale factors for parameters                 */
  int *cv_plist;              /* list of sensitivities                        */
  int cv_DQtype;              /* central/forward finite differences           */
  realtype cv_DQrhomax;       /* cut-off value for separate/simultaneous FD   */

  booleantype cv_errconS;     /* TRUE if yS are considered in err. control    */

  int cv_itolS;
  realtype cv_reltolS;        /* relative tolerance for sensitivities         */
  realtype *cv_SabstolS;      /* scalar absolute tolerances for sensi.        */
  N_Vector *cv_VabstolS;      /* vector absolute tolerances for sensi.        */

  /*-----------------------------------
    Quadrature Sensitivity Related Data 
    -----------------------------------*/

  booleantype cv_quadr_sensi; /* TRUE if computing sensitivties of quadrs.    */

  CVQuadSensRhsFn cv_fQS;     /* fQS = (dfQ/dy)*yS + (dfQ/dp)                 */
  void *cv_fQS_data;          /* data pointer passed to fQS                   */
  booleantype cv_fQSDQ;       /* TRUE if using internal DQ functions          */

  booleantype cv_errconQS;    /* TRUE if yQS are considered in err. con.      */

  int cv_itolQS;
  realtype cv_reltolQS;       /* relative tolerance for yQS                   */
  realtype *cv_SabstolQS;     /* scalar absolute tolerances for yQS           */
  N_Vector *cv_VabstolQS;     /* vector absolute tolerances for yQS           */

  /*-----------------------
    Nordsieck History Array 
    -----------------------*/

  N_Vector cv_zn[L_MAX];      /* Nordsieck array, of size N x (q+1).
                                 zn[j] is a vector of length N (j=0,...,q)
                                 zn[j] = [1/factorial(j)] * h^j * 
                                 (jth derivative of the interpolating poly.)  */

  /*-------------------
    Vectors of length N 
    -------------------*/

  N_Vector cv_ewt;            /* error weight vector                          */
  N_Vector cv_y;              /* y is used as temporary storage by the solver.
                                 The memory is provided by the user to CVode 
                                 where the vector is named yout.              */
  N_Vector cv_acor;           /* In the context of the solution of the
                                 nonlinear equation, acor = y_n(m) - y_n(0).
                                 On return, this vector is scaled to give
                                 the estimated local error in y.              */
  N_Vector cv_tempv;          /* temporary storage vector                     */
  N_Vector cv_ftemp;          /* temporary storage vector                     */
  
  /*--------------------------
    Quadrature Related Vectors 
    --------------------------*/

  N_Vector cv_znQ[L_MAX];     /* Nordsieck arrays for quadratures             */
  N_Vector cv_ewtQ;           /* error weight vector for quadratures          */
  N_Vector cv_yQ;             /* Unlike y, yQ is not allocated by the user    */
  N_Vector cv_acorQ;          /* acorQ = yQ_n(m) - yQ_n(0)                    */
  N_Vector cv_tempvQ;         /* temporary storage vector (~ tempv)           */

  /*---------------------------
    Sensitivity Related Vectors 
    ---------------------------*/

  N_Vector *cv_znS[L_MAX];    /* Nordsieck arrays for sensitivities           */
  N_Vector *cv_ewtS;          /* error weight vectors for sensitivities       */
  N_Vector *cv_yS;            /* yS=yS0 (allocated by the user)               */
  N_Vector *cv_acorS;         /* acorS = yS_n(m) - yS_n(0)                    */
  N_Vector *cv_tempvS;        /* temporary storage vector (~ tempv)           */
  N_Vector *cv_ftempS;        /* temporary storage vector (~ ftemp)           */

  booleantype cv_stgr1alloc;  /* Did we allocate ncfS1, ncfnS1, and nniS1?    */

  /*--------------------------------------
    Quadrature Sensitivity Related Vectors 
    --------------------------------------*/

  N_Vector *cv_znQS[L_MAX];   /* Nordsieck arrays for quadr. sensitivities    */
  N_Vector *cv_ewtQS;         /* error weight vectors for sensitivities       */
  N_Vector *cv_yQS;           /* Unlike yS, yQS is not allocated by the user  */
  N_Vector *cv_acorQS;        /* acorQS = yQS_n(m) - yQS_n(0)                 */
  N_Vector *cv_tempvQS;       /* temporary storage vector (~ tempv)           */
  N_Vector cv_ftempQ;         /* temporary storage vector (~ ftemp)           */
  
  /*-----------------
    Tstop information
    -----------------*/

  booleantype cv_tstopset;
  realtype cv_tstop;

  /*---------
    Step Data 
    ---------*/

  int cv_q;                    /* current order                               */
  int cv_qprime;               /* order to be used on the next step
                                * qprime = q-1, q, or q+1                     */
  int cv_next_q;               /* order to be used on the next step           */
  int cv_qwait;                /* number of internal steps to wait before
                                * considering a change in q                   */
  int cv_L;                    /* L = q + 1                                   */

  realtype cv_hin;
  realtype cv_h;               /* current step size                           */
  realtype cv_hprime;          /* step size to be used on the next step       */ 
  realtype cv_next_h;          /* step size to be used on the next step       */ 
  realtype cv_eta;             /* eta = hprime / h                            */
  realtype cv_hscale;          /* value of h used in zn                       */
  realtype cv_tn;              /* current internal value of t                 */
  realtype cv_tretlast;        /* last value of t returned                    */

  realtype cv_tau[L_MAX+1];    /* array of previous q+1 successful step
                                * sizes indexed from 1 to q+1                 */
  realtype cv_tq[NUM_TESTS+1]; /* array of test quantities indexed from
                                * 1 to NUM_TESTS(=5)                          */
  realtype cv_l[L_MAX];        /* coefficients of l(x) (degree q poly)        */

  realtype cv_rl1;             /* the scalar 1/l[1]                           */
  realtype cv_gamma;           /* gamma = h * rl1                             */
  realtype cv_gammap;          /* gamma at the last setup call                */
  realtype cv_gamrat;          /* gamma / gammap                              */

  realtype cv_crate;           /* est. corrector conv. rate in Nls            */
  realtype cv_crateS;          /* est. corrector conv. rate in NlsStgr        */
  realtype cv_acnrm;           /* | acor |                                    */
  realtype cv_acnrmQ;          /* | acorQ |                                   */
  realtype cv_acnrmS;          /* | acorS |                                   */
  realtype cv_acnrmQS;         /* | acorQS |                                  */
  realtype cv_nlscoef;         /* coeficient in nonlinear convergence test    */
  int  cv_mnewt;               /* Newton iteration counter                    */
  int  *cv_ncfS1;              /* Array of Ns local counters for conv.  
                                * failures (used in CVStep for STAGGERED1)    */

  /*------
    Limits 
    ------*/

  int cv_qmax;             /* q <= qmax                                       */
  long int cv_mxstep;      /* maximum number of internal steps for one 
			      user call                                       */
  int cv_maxcor;           /* maximum number of corrector iterations for 
			      the solution of the nonlinear equation          */
  int cv_maxcorS;
  int cv_mxhnil;           /* max. number of warning messages issued to the
			      user that t + h == t for the next internal step */
  int cv_maxnef;           /* maximum number of error test failures           */
  int cv_maxncf;           /* maximum number of nonlinear conv. failures      */

  realtype cv_hmin;        /* |h| >= hmin                                     */
  realtype cv_hmax_inv;    /* |h| <= 1/hmax_inv                               */
  realtype cv_etamax;      /* eta <= etamax                                   */

  /*----------
    Counters 
    ----------*/

  long int cv_nst;         /* number of internal steps taken                  */

  long int cv_nfe;         /* number of f calls                               */
  long int cv_nfQe;        /* number of fQ calls                              */
  long int cv_nfSe;        /* number of fS calls                              */
  long int cv_nfeS;        /* number of f calls from sensi DQ                 */
  long int cv_nfQSe;       /* number of fQS calls                             */
  long int cv_nfQeS;       /* number of fQ calls from sensi DQ                */


  long int cv_ncfn;        /* number of corrector convergence failures        */
  long int cv_ncfnS;       /* number of total sensi. corr. conv. failures     */
  long int *cv_ncfnS1;     /* number of sensi. corrector conv. failures       */

  long int cv_nni;         /* number of nonlinear iterations performed        */
  long int cv_nniS;        /* number of total sensi. nonlinear iterations     */
  long int *cv_nniS1;      /* number of sensi. nonlinear iterations           */

  long int cv_netf;        /* number of error test failures                   */
  long int cv_netfQ;       /* number of quadr. error test failures            */
  long int cv_netfS;       /* number of sensi. error test failures            */
  long int cv_netfQS;      /* number of quadr. sensi. error test failures     */

  long int cv_nsetups;     /* number of setup calls                           */
  long int cv_nsetupsS;    /* number of setup calls due to sensitivities      */

  int cv_nhnil;            /* number of messages issued to the user that
			      t + h == t for the next iternal step            */

  /*-----------------------------
    Space requirements for CVODES 
    -----------------------------*/

  long int cv_lrw1;        /* no. of realtype words in 1 N_Vector y           */ 
  long int cv_liw1;        /* no. of integer words in 1 N_Vector y            */ 
  long int cv_lrw1Q;       /* no. of realtype words in 1 N_Vector yQ          */ 
  long int cv_liw1Q;       /* no. of integer words in 1 N_Vector yQ           */ 
  long int cv_lrw;         /* no. of realtype words in CVODES work vectors    */
  long int cv_liw;         /* no. of integer words in CVODES work vectors     */

  /*----------------
    Step size ratios
    ----------------*/

  realtype cv_etaqm1;      /* ratio of new to old h for order q-1             */
  realtype cv_etaq;        /* ratio of new to old h for order q               */
  realtype cv_etaqp1;      /* ratio of new to old h for order q+1             */

  /*------------------
    Linear Solver Data 
    ------------------*/

  /* Linear Solver functions to be called */

  int (*cv_linit)(struct CVodeMemRec *cv_mem);

  int (*cv_lsetup)(struct CVodeMemRec *cv_mem, int convfail, 
		   N_Vector ypred, N_Vector fpred, booleantype *jcurPtr, 
		   N_Vector vtemp1, N_Vector vtemp2, N_Vector vtemp3); 

  int (*cv_lsolve)(struct CVodeMemRec *cv_mem, N_Vector b, N_Vector weight,
		   N_Vector ycur, N_Vector fcur);

  void (*cv_lfree)(struct CVodeMemRec *cv_mem);

  /* Linear Solver specific memory */

  void *cv_lmem;           

  /* Flag to request a call to the setup routine */

  booleantype cv_forceSetup;

  /*------------
    Saved Values
    ------------*/

  int cv_qu;                   /* last successful q value used                */
  long int cv_nstlp;           /* step number of last setup call              */
  realtype cv_h0u;             /* actual initial stepsize                     */
  realtype cv_hu;              /* last successful h value used                */
  realtype cv_saved_tq5;       /* saved value of tq[5]                        */
  booleantype cv_jcur;         /* is Jacobian info for linear solver current? */
  realtype cv_tolsf;           /* tolerance scale factor                      */
  int cv_qmax_alloc;           /* qmax used when allocating mem               */
  int cv_qmax_allocQ;          /* qmax used when allocating quad. mem         */
  int cv_qmax_allocS;          /* qmax used when allocating sensi. mem        */
  int cv_qmax_allocQS;         /* qmax used when allocating quad. sensi. mem  */
  int cv_indx_acor;            /* index of zn vector in which acor is saved   */
  booleantype cv_setupNonNull; /* Does setup do something?                    */

  /*--------------------------------------------------------------------
    Flags turned ON by CVodeInit, CVodeSensMalloc, and CVodeQuadMalloc 
    and read by CVodeReInit, CVodeSensReInit, and CVodeQuadReInit
    --------------------------------------------------------------------*/

  booleantype cv_VabstolMallocDone;
  booleantype cv_MallocDone;

  booleantype cv_VabstolQMallocDone;
  booleantype cv_QuadMallocDone;

  booleantype cv_VabstolSMallocDone;
  booleantype cv_SabstolSMallocDone;
  booleantype cv_SensMallocDone;

  booleantype cv_VabstolQSMallocDone;
  booleantype cv_SabstolQSMallocDone;
  booleantype cv_QuadSensMallocDone;

  /*-------------------------------------------
    Error handler function and error ouput file 
    -------------------------------------------*/

  CVErrHandlerFn cv_ehfun;    /* Error messages are handled by ehfun          */
  void *cv_eh_data;           /* dats pointer passed to ehfun                 */
  FILE *cv_errfp;             /* CVODES error messages are sent to errfp      */    

  /*-------------------------
    Stability Limit Detection
    -------------------------*/

  booleantype cv_sldeton;     /* Is Stability Limit Detection on?             */
  realtype cv_ssdat[6][4];    /* scaled data array for STALD                  */
  int cv_nscon;               /* counter for STALD method                     */
  long int cv_nor;            /* counter for number of order reductions       */

  /*----------------
    Rootfinding Data
    ----------------*/

  CVRootFn cv_gfun;        /* Function g for roots sought                     */
  int cv_nrtfn;            /* number of components of g                       */
  int *cv_iroots;          /* array for root information                      */
  int *cv_rootdir;         /* array specifying direction of zero-crossing     */
  realtype cv_tlo;         /* nearest endpoint of interval in root search     */
  realtype cv_thi;         /* farthest endpoint of interval in root search    */
  realtype cv_trout;       /* t value returned by rootfinding routine         */
  realtype *cv_glo;        /* saved array of g values at t = tlo              */
  realtype *cv_ghi;        /* saved array of g values at t = thi              */
  realtype *cv_grout;      /* array of g values at t = trout                  */
  realtype cv_toutc;       /* copy of tout (if NORMAL mode)                   */
  realtype cv_ttol;        /* tolerance on root location trout                */
  int cv_taskc;            /* copy of parameter itask                         */
  int cv_irfnd;            /* flag showing whether last step had a root       */
  long int cv_nge;         /* counter for g evaluations                       */
  booleantype *cv_gactive; /* array with active/inactive event functions      */
  int cv_mxgnull;          /* number of warning messages about possible g==0  */

  /*------------------------
    Adjoint sensitivity data
    ------------------------*/

  booleantype cv_adj;             /* TRUE if performing ASA                   */

  struct CVadjMemRec *cv_adj_mem; /* Pointer to adjoint memory structure      */

  booleantype cv_adjMallocDone;

} *CVodeMem;


/* 
 * =================================================================
 *   A D J O I N T   M O D U L E    M E M O R Y    B L O C K
 * =================================================================
 */

/*
 * -----------------------------------------------------------------
 * Types : struct CkpntMemRec, CkpntMem
 * -----------------------------------------------------------------
 * The type CkpntMem is type pointer to struct CkpntMemRec.
 * This structure contains fields to store all information at a
 * check point that is needed to 'hot' start cvodes.
 * -----------------------------------------------------------------
 */

struct CkpntMemRec {

  /* Integration limits */
  realtype ck_t0;
  realtype ck_t1;
    
  /* Nordsieck History Array */
  N_Vector ck_zn[L_MAX];
    
  /* Do we need to carry quadratures? */
  booleantype ck_quadr;
    
  /* Nordsieck History Array for quadratures */
  N_Vector ck_znQ[L_MAX];
    
  /* Do we need to carry sensitivities? */
  booleantype ck_sensi;

  /* number of sensitivities */
  int ck_Ns;

  /* Nordsieck History Array for sensitivities */
  N_Vector *ck_znS[L_MAX];

  /* Do we need to carry quadrature sensitivities? */
  booleantype ck_quadr_sensi;

  /* Nordsieck History Array for quadrature sensitivities */
  N_Vector *ck_znQS[L_MAX];
    
  /* Was ck_zn[qmax] allocated?
     ck_zqm = 0    - no
     ck_zqm = qmax - yes      */
  int ck_zqm;
    
  /* Step data */
  long int ck_nst;
  realtype ck_tretlast;
  int      ck_q;
  int      ck_qprime;
  int      ck_qwait;
  int      ck_L;
  realtype ck_gammap;
  realtype ck_h;
  realtype ck_hprime;
  realtype ck_hscale;
  realtype ck_eta;
  realtype ck_etamax;
  realtype ck_tau[L_MAX+1];
  realtype ck_tq[NUM_TESTS+1];
  realtype ck_l[L_MAX];
    
  /* Saved values */
  realtype ck_saved_tq5;
    
  /* Pointer to next structure in list */
  struct CkpntMemRec *ck_next;
    
};
  
/*
 * -----------------------------------------------------------------
 * Types for functions provided by an interpolation module
 * -----------------------------------------------------------------
 * cvaIMMallocFn: Type for a function that initializes the content
 *                field of the structures in the dt array
 * cvaIMFreeFn:   Type for a function that deallocates the content
 *                field of the structures in the dt array
 * cvaIMGetYFn:   Type for a function that returns the 
 *                interpolated forward solution.
 * cvaIMStorePnt: Type for a function that stores a new
 *                point in the structure d
 * -----------------------------------------------------------------
 */

typedef booleantype (*cvaIMMallocFn)(CVodeMem cv_mem);
typedef void (*cvaIMFreeFn)(CVodeMem cv_mem);
typedef int (*cvaIMGetYFn)(CVodeMem cv_mem, realtype t, N_Vector y, N_Vector *yS);
typedef int (*cvaIMStorePntFn)(CVodeMem cv_mem, DtpntMem d);

/*
 * -----------------------------------------------------------------
 * Type : struct DtpntMemRec
 * -----------------------------------------------------------------
 * This structure contains fields to store all information at a
 * data point that is needed to interpolate solution of forward
 * simulations. Its content field depends on IMtype.
 * -----------------------------------------------------------------
 */
  
struct DtpntMemRec {
  realtype t;    /* time */
  void *content; /* IMtype-dependent content */
};

/* Data for cubic Hermite interpolation */
typedef struct HermiteDataMemRec {
  N_Vector y;
  N_Vector yd;
  N_Vector *yS;
  N_Vector *ySd;
} *HermiteDataMem;

/* Data for polynomial interpolation */
typedef struct PolynomialDataMemRec {
  N_Vector y;
  N_Vector *yS;
  int order;
} *PolynomialDataMem;


/*
 * -----------------------------------------------------------------
 * Type : struct CVodeBMemRec
 * -----------------------------------------------------------------
 * The type CVodeBMem is a pointer to a structure which stores all
 * information for ONE backward problem.
 * The CVadjMem structure contains a linked list of CVodeBMem pointers
 * -----------------------------------------------------------------
 */

struct CVodeBMemRec {

  /* Index of this backward problem */
  int cv_index;

  /* Time at which the backward problem is initialized */
  realtype cv_t0;
  
  /* CVODES memory for this backward problem */
  CVodeMem cv_mem;

  /* Flags to indicate that this backward problem's RHS or quad RHS
   * require forward sensitivities */
  booleantype cv_f_withSensi;
  booleantype cv_fQ_withSensi;

  /* Right hand side function for backward run */
  CVRhsFnB cv_f;
  CVRhsFnBS cv_fs;

  /* Right hand side quadrature function for backward run */
  CVQuadRhsFnB cv_fQ;
  CVQuadRhsFnBS cv_fQs;

  /* User user_data */
  void *cv_user_data;
    
  /* Memory block for a linear solver's interface to CVODEA */
  void *cv_lmem;

  /* Function to free any memory allocated by the linear solver */
  void (*cv_lfree)(CVodeBMem cvB_mem);

  /* Memory block for a preconditioner's module interface to CVODEA */ 
  void *cv_pmem;

  /* Function to free any memory allocated by the preconditioner module */
  void (*cv_pfree)(CVodeBMem cvB_mem);

  /* Time at which to extract solution / quadratures */
  realtype cv_tout;
  
  /* Workspace Nvector */
  N_Vector cv_y;

  /* Pointer to next structure in list */
  struct CVodeBMemRec *cv_next;

};

/*
 * -----------------------------------------------------------------
 * Type : struct CVadjMemRec
 * -----------------------------------------------------------------
 * The type CVadjMem is type pointer to struct CVadjMemRec.
 * This structure contins fields to store all information
 * necessary for adjoint sensitivity analysis.
 * -----------------------------------------------------------------
 */

struct CVadjMemRec {
    
  /* --------------------
   * Forward problem data
   * -------------------- */

  /* Integration interval */
  realtype ca_tinitial, ca_tfinal;

  /* Flag for first call to CVodeF */
  booleantype ca_firstCVodeFcall;

  /* Flag if CVodeF was called with TSTOP */
  booleantype ca_tstopCVodeFcall;
  realtype ca_tstopCVodeF;
    
  /* ----------------------
   * Backward problems data
   * ---------------------- */

  /* Storage for backward problems */
  struct CVodeBMemRec *cvB_mem;

  /* Number of backward problems */
  int ca_nbckpbs;

  /* Address of current backward problem */
  struct CVodeBMemRec *ca_bckpbCrt;

  /* Flag for first call to CVodeB */
  booleantype ca_firstCVodeBcall;
    
  /* ----------------
   * Check point data
   * ---------------- */

  /* Storage for check point information */
  struct CkpntMemRec *ck_mem;

  /* Number of check points */
  int ca_nckpnts;

  /* address of the check point structure for which data is available */
  struct CkpntMemRec *ca_ckpntData;
    
  /* ------------------
   * Interpolation data
   * ------------------ */

  /* Number of steps between 2 check points */
  long int ca_nsteps;
  
  /* Storage for data from forward runs */
  struct DtpntMemRec **dt_mem;

  /* Actual number of data points in dt_mem (typically np=nsteps+1) */
  long int ca_np;
    
  /* Interpolation type */
  int ca_IMtype;

  /* Functions set by the interpolation module */
  cvaIMMallocFn   ca_IMmalloc; 
  cvaIMFreeFn     ca_IMfree;
  cvaIMStorePntFn ca_IMstore; /* store a new interpolation point */
  cvaIMGetYFn     ca_IMget;   /* interpolate forward solution    */

  /* Flags controlling the interpolation module */
  booleantype ca_IMmallocDone;   /* IM initialized? */
  booleantype ca_IMnewData;      /* new data available in dt_mem?*/
  booleantype ca_IMstoreSensi;   /* store sensitivities? */
  booleantype ca_IMinterpSensi;  /* interpolate sensitivities? */

  /* Workspace for the interpolation module */
  N_Vector ca_Y[L_MAX];     /* pointers to zn[i] */
  N_Vector *ca_YS[L_MAX];   /* pointers to znS[i] */
  realtype ca_T[L_MAX];

  /* -------------------------------
   * Workspace for wrapper functions
   * ------------------------------- */

  N_Vector ca_ytmp;

  N_Vector *ca_yStmp;
    
};
  

/*
 * =================================================================
 *     I N T E R F A C E   T O    L I N E A R   S O L V E R S
 * =================================================================
 */

/*
 * -----------------------------------------------------------------
 * Communication between CVODE and a CVODE Linear Solver
 * -----------------------------------------------------------------
 * convfail (input to cv_lsetup)
 *
 * CV_NO_FAILURES : Either this is the first cv_setup call for this
 *                  step, or the local error test failed on the
 *                  previous attempt at this step (but the Newton
 *                  iteration converged).
 *
 * CV_FAIL_BAD_J  : This value is passed to cv_lsetup if
 *
 *                  (a) The previous Newton corrector iteration
 *                      did not converge and the linear solver's
 *                      setup routine indicated that its Jacobian-
 *                      related data is not current
 *                                   or
 *                  (b) During the previous Newton corrector
 *                      iteration, the linear solver's solve routine
 *                      failed in a recoverable manner and the
 *                      linear solver's setup routine indicated that
 *                      its Jacobian-related data is not current.
 *
 * CV_FAIL_OTHER  : During the current internal step try, the
 *                  previous Newton iteration failed to converge
 *                  even though the linear solver was using current
 *                  Jacobian-related data.
 * -----------------------------------------------------------------
 */

/* Constants for convfail (input to cv_lsetup) */

#define CV_NO_FAILURES 0
#define CV_FAIL_BAD_J  1
#define CV_FAIL_OTHER  2

/*
 * -----------------------------------------------------------------
 * int (*cv_linit)(CVodeMem cv_mem);
 * -----------------------------------------------------------------
 * The purpose of cv_linit is to complete initializations for a
 * specific linear solver, such as counters and statistics.
 * An LInitFn should return 0 if it has successfully initialized the
 * CVODE linear solver and a negative value otherwise.
 * If an error does occur, an appropriate message should be sent to
 * the error handler function.
 * -----------------------------------------------------------------
 */

/*
 * -----------------------------------------------------------------
 * int (*cv_lsetup)(CVodeMem cv_mem, int convfail, N_Vector ypred,
 *                 N_Vector fpred, booleantype *jcurPtr,
 *                 N_Vector vtemp1, N_Vector vtemp2,
 *                 N_Vector vtemp3);
 * -----------------------------------------------------------------
 * The job of cv_lsetup is to prepare the linear solver for
 * subsequent calls to cv_lsolve. It may recompute Jacobian-
 * related data is it deems necessary. Its parameters are as
 * follows:
 *
 * cv_mem - problem memory pointer of type CVodeMem. See the
 *          typedef earlier in this file.
 *
 * convfail - a flag to indicate any problem that occurred during
 *            the solution of the nonlinear equation on the
 *            current time step for which the linear solver is
 *            being used. This flag can be used to help decide
 *            whether the Jacobian data kept by a CVODE linear
 *            solver needs to be updated or not.
 *            Its possible values have been documented above.
 *
 * ypred - the predicted y vector for the current CVODE internal
 *         step.
 *
 * fpred - f(tn, ypred).
 *
 * jcurPtr - a pointer to a boolean to be filled in by cv_lsetup.
 *           The function should set *jcurPtr=TRUE if its Jacobian
 *           data is current after the call and should set
 *           *jcurPtr=FALSE if its Jacobian data is not current.
 *           Note: If cv_lsetup calls for re-evaluation of
 *           Jacobian data (based on convfail and CVODE state
 *           data), it should return *jcurPtr=TRUE always;
 *           otherwise an infinite loop can result.
 *
 * vtemp1 - temporary N_Vector provided for use by cv_lsetup.
 *
 * vtemp3 - temporary N_Vector provided for use by cv_lsetup.
 *
 * vtemp3 - temporary N_Vector provided for use by cv_lsetup.
 *
 * The cv_lsetup routine should return 0 if successful, a positive
 * value for a recoverable error, and a negative value for an
 * unrecoverable error.
 * -----------------------------------------------------------------
 */

/*
 * -----------------------------------------------------------------
 * int (*cv_lsolve)(CVodeMem cv_mem, N_Vector b, N_Vector weight,
 *                  N_Vector ycur, N_Vector fcur);
 * -----------------------------------------------------------------
 * cv_lsolve must solve the linear equation P x = b, where
 * P is some approximation to (I - gamma J), J = (df/dy)(tn,ycur)
 * and the RHS vector b is input. The N-vector ycur contains
 * the solver's current approximation to y(tn) and the vector
 * fcur contains the N_Vector f(tn,ycur). The solution is to be
 * returned in the vector b. cv_lsolve returns a positive value
 * for a recoverable error and a negative value for an
 * unrecoverable error. Success is indicated by a 0 return value.
 * -----------------------------------------------------------------
 */

/*
 * -----------------------------------------------------------------
 * void (*cv_lfree)(CVodeMem cv_mem);
 * -----------------------------------------------------------------
 * cv_lfree should free up any memory allocated by the linear
 * solver. This routine is called once a problem has been
 * completed and the linear solver is no longer needed.
 * -----------------------------------------------------------------
 */

/*
 * =================================================================
 *   C V O D E S    I N T E R N A L   F U N C T I O N S
 * =================================================================
 */
  
/* Prototype of internal ewtSet function */

int cvEwtSet(N_Vector ycur, N_Vector weight, void *data);

/* High level error handler */

void cvProcessError(CVodeMem cv_mem, 
		    int error_code, const char *module, const char *fname, 
		    const char *msgfmt, ...);

/* Prototype of internal errHandler function */

void cvErrHandler(int error_code, const char *module, const char *function, 
		  char *msg, void *data);

/* Prototypes for internal sensitivity rhs wrappers */

int cvSensRhsWrapper(CVodeMem cv_mem, realtype time, 
                     N_Vector ycur, N_Vector fcur, 
                     N_Vector *yScur, N_Vector *fScur,
                     N_Vector temp1, N_Vector temp2);

int cvSensRhs1Wrapper(CVodeMem cv_mem, realtype time, 
                      N_Vector ycur, N_Vector fcur, 
                      int is, N_Vector yScur, N_Vector fScur,
                      N_Vector temp1, N_Vector temp2);

/* Prototypes for internal sensitivity rhs DQ functions */

int cvSensRhsInternalDQ(int Ns, realtype t, 
                        N_Vector y, N_Vector ydot, 
                        N_Vector *yS, N_Vector *ySdot, 
                        void *fS_data,  
                        N_Vector tempv, N_Vector ftemp);

int cvSensRhs1InternalDQ(int Ns, realtype t, 
                         N_Vector y, N_Vector ydot, 
                         int is, N_Vector yS, N_Vector ySdot, 
                         void *fS_data,
                         N_Vector tempv, N_Vector ftemp);

/* 
 * =================================================================
 *   C V O D E S    E R R O R    M E S S A G E S
 * =================================================================
 */

#if defined(SUNDIALS_EXTENDED_PRECISION)

#define MSG_TIME        "t = %Lg"
#define MSG_TIME_H      "t = %Lg and h = %Lg"
#define MSG_TIME_INT    "t = %Lg is not between tcur - hu = %Lg and tcur = %Lg."
#define MSG_TIME_TOUT   "tout = %Lg"
#define MSG_TIME_TSTOP  "tstop = %Lg"

#elif defined(SUNDIALS_DOUBLE_PRECISION)

#define MSG_TIME        "t = %lg"
#define MSG_TIME_H      "t = %lg and h = %lg"
#define MSG_TIME_INT    "t = %lg is not between tcur - hu = %lg and tcur = %lg."
#define MSG_TIME_TOUT   "tout = %lg"
#define MSG_TIME_TSTOP  "tstop = %lg"

#else

#define MSG_TIME        "t = %g"
#define MSG_TIME_H      "t = %g and h = %g"
#define MSG_TIME_INT    "t = %g is not between tcur - hu = %g and tcur = %g."
#define MSG_TIME_TOUT   "tout = %g"
#define MSG_TIME_TSTOP  "tstop = %g"

#endif


/* Initialization and I/O error messages */

#define MSGCV_NO_MEM "cvode_mem = NULL illegal."
#define MSGCV_CVMEM_FAIL "Allocation of cvode_mem failed."
#define MSGCV_MEM_FAIL "A memory request failed."
#define MSGCV_BAD_LMM  "Illegal value for lmm. The legal values are CV_ADAMS and CV_BDF."
#define MSGCV_BAD_ITER  "Illegal value for iter. The legal values are CV_FUNCTIONAL and CV_NEWTON."
#define MSGCV_NO_MALLOC "Attempt to call before CVodeInit."
#define MSGCV_NEG_MAXORD "maxord <= 0 illegal."
#define MSGCV_BAD_MAXORD  "Illegal attempt to increase maximum method order."
#define MSGCV_SET_SLDET  "Attempt to use stability limit detection with the CV_ADAMS method illegal."
#define MSGCV_NEG_HMIN "hmin < 0 illegal."
#define MSGCV_NEG_HMAX "hmax < 0 illegal."
#define MSGCV_BAD_HMIN_HMAX "Inconsistent step size limits: hmin > hmax."
#define MSGCV_BAD_RELTOL "reltol < 0 illegal."
#define MSGCV_BAD_ABSTOL "abstol has negative component(s) (illegal)."
#define MSGCV_NULL_ABSTOL "abstol = NULL illegal."
#define MSGCV_NULL_Y0 "y0 = NULL illegal."
#define MSGCV_NULL_F "f = NULL illegal."
#define MSGCV_NULL_G "g = NULL illegal."
#define MSGCV_BAD_NVECTOR "A required vector operation is not implemented."
#define MSGCV_BAD_K "Illegal value for k."
#define MSGCV_NULL_DKY "dky = NULL illegal."
#define MSGCV_BAD_T "Illegal value for t." MSG_TIME_INT
#define MSGCV_NO_ROOT "Rootfinding was not initialized."

#define MSGCV_NO_QUAD  "Quadrature integration not activated."
#define MSGCV_BAD_ITOLQ "Illegal value for itolQ. The legal values are CV_SS and CV_SV."
#define MSGCV_NULL_ABSTOLQ "abstolQ = NULL illegal."
#define MSGCV_BAD_RELTOLQ "reltolQ < 0 illegal."
#define MSGCV_BAD_ABSTOLQ "abstolQ has negative component(s) (illegal)."  

#define MSGCV_SENSINIT_2 "Sensitivity analysis already initialized."
#define MSGCV_NO_SENSI  "Forward sensitivity analysis not activated."
#define MSGCV_BAD_ITOLS "Illegal value for itolS. The legal values are CV_SS, CV_SV, and CV_EE."
#define MSGCV_NULL_ABSTOLS "abstolS = NULL illegal."
#define MSGCV_BAD_RELTOLS "reltolS < 0 illegal."
#define MSGCV_BAD_ABSTOLS "abstolS has negative component(s) (illegal)."  
#define MSGCV_BAD_PBAR "pbar has zero component(s) (illegal)."
#define MSGCV_BAD_PLIST "plist has negative component(s) (illegal)."
#define MSGCV_BAD_NS "NS <= 0 illegal."
#define MSGCV_NULL_YS0 "yS0 = NULL illegal."
#define MSGCV_BAD_ISM "Illegal value for ism. Legal values are: CV_SIMULTANEOUS, CV_STAGGERED and CV_STAGGERED1."
#define MSGCV_BAD_IFS "Illegal value for ifS. Legal values are: CV_ALLSENS and CV_ONESENS."
#define MSGCV_BAD_ISM_IFS "Illegal ism = CV_STAGGERED1 for CVodeSensInit."
#define MSGCV_BAD_IS "Illegal value for is."
#define MSGCV_NULL_DKYA "dkyA = NULL illegal."
#define MSGCV_BAD_DQTYPE "Illegal value for DQtype. Legal values are: CV_CENTERED and CV_FORWARD."
#define MSGCV_BAD_DQRHO "DQrhomax < 0 illegal."

#define MSGCV_BAD_ITOLQS "Illegal value for itolQS. The legal values are CV_SS, CV_SV, and CV_EE."
#define MSGCV_NULL_ABSTOLQS "abstolQS = NULL illegal."
#define MSGCV_BAD_RELTOLQS "reltolQS < 0 illegal."
#define MSGCV_BAD_ABSTOLQS "abstolQS has negative component(s) (illegal)."  
#define MSGCV_NO_QUADSENSI  "Forward sensitivity analysis for quadrature variables not activated."
#define MSGCV_NULL_YQS0 "yQS0 = NULL illegal."

/* CVode Error Messages */

#define MSGCV_NO_TOL "No integration tolerances have been specified."
#define MSGCV_LSOLVE_NULL "The linear solver's solve routine is NULL."
#define MSGCV_YOUT_NULL "yout = NULL illegal."
#define MSGCV_TRET_NULL "tret = NULL illegal."
#define MSGCV_BAD_EWT "Initial ewt has component(s) equal to zero (illegal)."
#define MSGCV_EWT_NOW_BAD "At " MSG_TIME ", a component of ewt has become <= 0."
#define MSGCV_BAD_ITASK "Illegal value for itask."
#define MSGCV_BAD_H0 "h0 and tout - t0 inconsistent."
#define MSGCV_BAD_TOUT "Trouble interpolating at " MSG_TIME_TOUT ". tout too far back in direction of integration"
#define MSGCV_EWT_FAIL "The user-provide EwtSet function failed."
#define MSGCV_EWT_NOW_FAIL "At " MSG_TIME ", the user-provide EwtSet function failed."
#define MSGCV_LINIT_FAIL "The linear solver's init routine failed."
#define MSGCV_HNIL_DONE "The above warning has been issued mxhnil times and will not be issued again for this problem."
#define MSGCV_TOO_CLOSE "tout too close to t0 to start integration."
#define MSGCV_MAX_STEPS "At " MSG_TIME ", mxstep steps taken before reaching tout."
#define MSGCV_TOO_MUCH_ACC "At " MSG_TIME ", too much accuracy requested."
#define MSGCV_HNIL "Internal " MSG_TIME_H " are such that t + h = t on the next step. The solver will continue anyway."
#define MSGCV_ERR_FAILS "At " MSG_TIME_H ", the error test failed repeatedly or with |h| = hmin."
#define MSGCV_CONV_FAILS "At " MSG_TIME_H ", the corrector convergence test failed repeatedly or with |h| = hmin."
#define MSGCV_SETUP_FAILED "At " MSG_TIME ", the setup routine failed in an unrecoverable manner."
#define MSGCV_SOLVE_FAILED "At " MSG_TIME ", the solve routine failed in an unrecoverable manner."
#define MSGCV_RHSFUNC_FAILED "At " MSG_TIME ", the right-hand side routine failed in an unrecoverable manner."
#define MSGCV_RHSFUNC_UNREC "At " MSG_TIME ", the right-hand side failed in a recoverable manner, but no recovery is possible."
#define MSGCV_RHSFUNC_REPTD "At " MSG_TIME " repeated recoverable right-hand side function errors."
#define MSGCV_RHSFUNC_FIRST "The right-hand side routine failed at the first call."
#define MSGCV_RTFUNC_FAILED "At " MSG_TIME ", the rootfinding routine failed in an unrecoverable manner."
#define MSGCV_CLOSE_ROOTS "Root found at and very near " MSG_TIME "."
#define MSGCV_BAD_TSTOP "The value " MSG_TIME_TSTOP " is behind current " MSG_TIME " in the direction of integration."
#define MSGCV_INACTIVE_ROOTS "At the end of the first step, there are still some root functions identically 0. This warning will not be issued again."

#define MSGCV_NO_TOLQ "No integration tolerances for quadrature variables have been specified."
#define MSGCV_BAD_EWTQ "Initial ewtQ has component(s) equal to zero (illegal)."
#define MSGCV_EWTQ_NOW_BAD "At " MSG_TIME ", a component of ewtQ has become <= 0."
#define MSGCV_QRHSFUNC_FAILED "At " MSG_TIME ", the quadrature right-hand side routine failed in an unrecoverable manner."
#define MSGCV_QRHSFUNC_UNREC "At " MSG_TIME ", the quadrature right-hand side failed in a recoverable manner, but no recovery is possible."
#define MSGCV_QRHSFUNC_REPTD "At " MSG_TIME " repeated recoverable quadrature right-hand side function errors."
#define MSGCV_QRHSFUNC_FIRST "The quadrature right-hand side routine failed at the first call."

#define MSGCV_NO_TOLS "No integration tolerances for sensitivity variables have been specified."
#define MSGCV_NULL_P "p = NULL when using internal DQ for sensitivity RHS illegal."
#define MSGCV_BAD_EWTS "Initial ewtS has component(s) equal to zero (illegal)."
#define MSGCV_EWTS_NOW_BAD "At " MSG_TIME ", a component of ewtS has become <= 0."
#define MSGCV_SRHSFUNC_FAILED "At " MSG_TIME ", the sensitivity right-hand side routine failed in an unrecoverable manner."
#define MSGCV_SRHSFUNC_UNREC "At " MSG_TIME ", the sensitivity right-hand side failed in a recoverable manner, but no recovery is possible."
#define MSGCV_SRHSFUNC_REPTD "At " MSG_TIME " repeated recoverable sensitivity right-hand side function errors."
#define MSGCV_SRHSFUNC_FIRST "The sensitivity right-hand side routine failed at the first call."

#define MSGCV_NULL_FQ "CVODES is expected to use DQ to evaluate the RHS of quad. sensi., but quadratures were not initialized."
#define MSGCV_NO_TOLQS "No integration tolerances for quadrature sensitivity variables have been specified."
#define MSGCV_BAD_EWTQS "Initial ewtQS has component(s) equal to zero (illegal)."
#define MSGCV_EWTQS_NOW_BAD "At " MSG_TIME ", a component of ewtQS has become <= 0."
#define MSGCV_QSRHSFUNC_FAILED "At " MSG_TIME ", the quadrature sensitivity right-hand side routine failed in an unrecoverable manner."
#define MSGCV_QSRHSFUNC_UNREC "At " MSG_TIME ", the quadrature sensitivity right-hand side failed in a recoverable manner, but no recovery is possible."
#define MSGCV_QSRHSFUNC_REPTD "At " MSG_TIME " repeated recoverable quadrature sensitivity right-hand side function errors."
#define MSGCV_QSRHSFUNC_FIRST "The quadrature sensitivity right-hand side routine failed at the first call."

/* 
 * =================================================================
 *   C V O D E A    E R R O R    M E S S A G E S
 * =================================================================
 */

#define MSGCV_NO_ADJ      "Illegal attempt to call before calling CVodeAdjMalloc."
#define MSGCV_BAD_STEPS   "Steps nonpositive illegal."
#define MSGCV_BAD_INTERP  "Illegal value for interp."
#define MSGCV_BAD_WHICH   "Illegal value for which."
#define MSGCV_NO_BCK      "No backward problems have been defined yet."
#define MSGCV_NO_FWD      "Illegal attempt to call before calling CVodeF."
#define MSGCV_BAD_TB0     "The initial time tB0 for problem %d is outside the interval over which the forward problem was solved."
#define MSGCV_BAD_SENSI   "At least one backward problem requires sensitivities, but they were not stored for interpolation."
#define MSGCV_BAD_ITASKB  "Illegal value for itaskB. Legal values are CV_NORMAL and CV_ONE_STEP."
#define MSGCV_BAD_TBOUT   "The final time tBout is outside the interval over which the forward problem was solved."
#define MSGCV_BACK_ERROR  "Error occured while integrating backward problem # %d" 
#define MSGCV_BAD_TINTERP "Bad t = %g for interpolation."
#define MSGCV_WRONG_INTERP "This function cannot be called for the specified interp type."

#ifdef __cplusplus
}
#endif

#endif
