Excitation-contraction coupling/mitochondrial energetics (ECME) model (Cortassa et al. 2006)

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Accession:105383
"An intricate network of reactions is involved in matching energy supply with demand in the heart. This complexity arises because energy production both modulates and is modulated by the electrophysiological and contractile activity of the cardiac myocyte. Here, we present an integrated mathematical model of the cardiac cell that links excitation-contraction coupling with mitochondrial energy generation. The dynamics of the model are described by a system of 50 ordinary differential equations. The formulation explicitly incorporates cytoplasmic ATP-consuming processes associated with force generation and ion transport, as well as the creatine kinase reaction. Changes in the electrical and contractile activity of the myocyte are coupled to mitochondrial energetics through the ATP, Ca21, and Na1 concentrations in the myoplasmic and mitochondrial matrix compartments. ..."
Reference:
1 . Cortassa S, Aon MA, Marbán E, Winslow RL, O'Rourke B (2003) An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics. Biophys J 84:2734-55 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Electrogenic pump;
Brain Region(s)/Organism:
Cell Type(s): Heart cell;
Channel(s): I L high threshold; I Sodium; I Potassium; Na/Ca exchanger; I_SERCA;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: C or C++ program;
Model Concept(s): Activity Patterns; Temporal Pattern Generation; Signaling pathways; Calcium dynamics;
Implementer(s):
Search NeuronDB for information about:  I L high threshold; I Sodium; I Potassium; Na/Ca exchanger; I_SERCA;
/*******************************************************************
 *                                                                 *
 * File          : cvode.h                                         *
 * Programmers   : Scott D. Cohen, Alan C. Hindmarsh, Radu Serban  *
 *                 and Dan Shumaker @ LLNL                         *
 * Version of    : 26 June 2002                                    *
 *-----------------------------------------------------------------*
 * Copyright (c) 2002, The Regents of the University of California * 
 * Produced at the Lawrence Livermore National Laboratory          *
 * All rights reserved                                             *
 * For details, see sundials/cvode/LICENSE                         *
 *-----------------------------------------------------------------*
 * This is the interface file for the main CVODE integrator.       *
 *                                                                 *
 *******************************************************************/


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

#ifndef _cvode_h
#define _cvode_h


#include <stdio.h>
#include "sundialstypes.h"
#include "nvector.h"

/******************************************************************
 *                                                                *
 * CVODE is used to solve numerically the ordinary initial value  *
 * problem :                                                      *
 *                                                                *
 *                 y' = f(t,y),                                   *
 *                 y(t0) = y0,                                    *
 *                                                                *
 *  where t0, y0 in R^N, and f: R x R^N -> R^N are given.         *
 *                                                                *
 ******************************************************************/

 
/******************************************************************
 *                                                                *
 * Enumerations for inputs to CVodeMalloc, CVReInit, and CVode.   *
 *----------------------------------------------------------------*
 * Symbolic constants for the lmm, iter, and itol input           *
 * parameters to CVodeMalloc and CVReInit, as well as the input   *
 * parameter itask to CVode, are given below.                     *
 *                                                                *
 * lmm  : The user of the CVODE package specifies whether to use  *
 *        the ADAMS or BDF (backward differentiation formula)     *
 *        linear multistep method. The BDF method is recommended  *
 *        for stiff problems, and the ADAMS method is recommended *
 *        for nonstiff problems.                                  *
 *                                                                *
 * iter : At each internal time step, a nonlinear equation must   *
 *        be solved. The user can specify either FUNCTIONAL       *
 *        iteration, which does not require linear algebra, or a  *
 *        NEWTON iteration, which requires the solution of linear *
 *        systems. In the NEWTON case, the user also specifies a  *
 *        CVODE linear solver. NEWTON is recommended in case of   *
 *        stiff problems.                                         *
 *                                                                *
 * itol : This parameter specifies the relative and absolute      *
 *        tolerance types to be used. The SS tolerance type means *
 *        a scalar relative and absolute tolerance, while the SV  *
 *        tolerance type means a scalar relative tolerance and a  *
 *        vector absolute tolerance (a potentially different      *
 *        absolute tolerance for each vector component).          *
 *                                                                *
 * itask : The itask input parameter to CVode indicates the job   *
 *         of the solver for the next user step. The NORMAL       *
 *         itask is to have the solver take internal steps until  *
 *         it has reached or just passed the user specified tout  *
 *         parameter. The solver then interpolates in order to    *
 *         return an approximate value of y(tout). The ONE_STEP   *
 *         option tells the solver to just take one internal step *
 *         and return the solution at the point reached by that   *
 *         step.                                                  *
 *                                                                *
 ******************************************************************/

enum { ADAMS, BDF };           /* lmm */

enum { FUNCTIONAL, NEWTON };   /* iter */

enum { SS, SV };               /* itol */

enum { NORMAL, ONE_STEP };     /* itask */
 
 
/******************************************************************
 *                                                                *
 * Type : RhsFn                                                   *
 *----------------------------------------------------------------*        
 * The f function which defines the right hand side of the ODE    *
 * system y' = f(t,y) must have type RhsFn.                       *
 * f takes as input the problem size N, the independent variable  *
 * value t, and the dependent variable vector y.  It stores the   * 
 * result of f(t,y) in the vector ydot.  The y and ydot arguments *
 * are of type N_Vector.                                          *
 * (Allocation of memory for ydot is handled within CVODE.)       *
 * The f_data parameter is the same as the f_data                 *
 * parameter passed by the user to the CVodeMalloc routine. This  *
 * user-supplied pointer is passed to the user's f function       *
 * every time it is called.                                       *
 * A RhsFn f does not have a return value.                        *
 *                                                                *
 ******************************************************************/

typedef void (*RhsFn)(integertype N, realtype t, N_Vector y, 
                      N_Vector ydot, void *f_data);
 
 
/******************************************************************
 *                                                                *
 * Function : CVodeMalloc                                         *
 *----------------------------------------------------------------*
 * CVodeMalloc allocates and initializes memory for a problem to  *
 * to be solved by CVODE.                                         *
 *                                                                *
 * N       is the number of equations in the ODE system.          *
 *                                                                *
 * f       is the right hand side function in y' = f(t,y).        *          
 *                                                                *
 * t0      is the initial value of t.                             *
 *                                                                *
 * y0      is the initial condition vector y(t0).                 *
 *                                                                *
 * lmm     is the type of linear multistep method to be used.     *
 *            The legal values are ADAMS and BDF (see previous    *
 *            description).                                       *
 *                                                                *
 * iter    is the type of iteration used to solve the nonlinear   *
 *            system that arises during each internal time step.  *
 *            The legal values are FUNCTIONAL and NEWTON.         *
 *                                                                *
 * itol    is the type of tolerances to be used.                  *
 *            The legal values are:                               *
 *               SS (scalar relative and absolute  tolerances),   *
 *               SV (scalar relative tolerance and vector         *
 *                   absolute tolerance).                         *
 *                                                                *
 * reltol  is a pointer to the relative tolerance scalar.         *
 *                                                                *
 * abstol  is a pointer to the absolute tolerance scalar or       *
 *            an N_Vector of absolute tolerances.                 *
 *                                                                *
 * The parameters itol, reltol, and abstol define a vector of     *
 * error weights, ewt, with components                            *
 *   ewt[i] = 1/(reltol*abs(y[i]) + abstol)   (if itol = SS), or  *
 *   ewt[i] = 1/(reltol*abs(y[i]) + abstol[i])   (if itol = SV).  *
 * This vector is used in all error and convergence tests, which  *
 * use a weighted RMS norm on all error-like vectors v:           *
 *    WRMSnorm(v) = sqrt( (1/N) sum(i=1..N) (v[i]*ewt[i])^2 ).    *
 *                                                                *
 * f_data  is a pointer to user data that will be passed to the   *
 *             user's f function every time f is called.          *
 *                                                                *
 * errfp   is the file pointer for an error file where all CVODE  *
 *            warning and error messages will be written. This    *
 *            parameter can be stdout (standard output), stderr   *
 *            (standard error), a file pointer (corresponding to  *
 *            a user error file opened for writing) returned by   *
 *            fopen, or NULL. If the user passes NULL, then all   *
 *            messages will be written to standard output.        *
 *                                                                *
 * optIn   is a flag indicating whether there are any optional    *
 *            inputs from the user in the arrays iopt and ropt.   *
 *            Pass FALSE to indicate no optional inputs and TRUE  *
 *            to indicate that optional inputs are present.       *
 *                                                                *
 * iopt    is the user-allocated array (of size OPT_SIZE given    *
 *            later) that will hold optional integer inputs and   *
 *            outputs.  The user can pass NULL if he/she does not *
 *            wish to use optional integer inputs or outputs.     *
 *            If optIn is TRUE, the user should preset to 0 those *
 *            locations for which default values are to be used.  *
 *                                                                *
 * ropt    is the user-allocated array (of size OPT_SIZE given    *
 *            later) that will hold optional real inputs and      *
 *            outputs.  The user can pass NULL if he/she does not *
 *            wish to use optional real inputs or outputs.        *
 *            If optIn is TRUE, the user should preset to 0.0 the *
 *            locations for which default values are to be used.  *
 *                                                                *
 * machEnv is a pointer to machine environment-specific           *
 *            information.                                        *
 *                                                                *
 * Note: The tolerance values may be changed in between calls to  *
 *       CVode for the same problem. These values refer to        *
 *       (*reltol) and either (*abstol), for a scalar absolute    *
 *       tolerance, or the components of abstol, for a vector     *
 *       absolute tolerance.                                      *
 *                                                                * 
 * If successful, CVodeMalloc returns a pointer to initialized    *
 * problem memory. This pointer should be passed to CVode. If     *
 * an initialization error occurs, CVodeMalloc prints an error    *
 * message to the file specified by errfp and returns NULL.       *
 *                                                                *
 ******************************************************************/


void *CVodeMalloc(integertype N, RhsFn f, realtype t0, N_Vector y0, 
                  int lmm, int iter, int itol, realtype *reltol, 
                  void *abstol, void *f_data, FILE *errfp, 
                  booleantype optIn, long int iopt[], realtype ropt[],
                  M_Env machEnv);
 
 
/******************************************************************
 *                                                                *
 * Function : CVReInit                                            *
 *----------------------------------------------------------------*
 * CVReInit re-initializes CVode for the solution of a problem,   *
 * where a prior call to CVodeMalloc has been made with the same  *
 * problem size N.  CVReInit performs the same input checking     *
 * and initializations that CVodeMalloc does (except for N).      *
 * But it does no memory allocation, assuming that the existing   *
 * internal memory is sufficient for the new problem.             *
 *                                                                *
 * The use of CVReInit requires that the maximum method order,    *
 * maxord, is no larger for the new problem than for the problem  *
 * specified in the last call to CVodeMalloc.  This condition is  *
 * automatically fulfilled if the multistep method parameter lmm  *
 * is unchanged (or changed from ADAMS to BDF) and the default    *
 * value for maxord is specified.                                 *
 *                                                                *
 * If iter = NEWTON, then following the call to CVReInit, a call  *
 * to the linear solver specification routine is necessary if a   *
 * different linear solver is chosen, but may not be otherwise.   *
 * If the same linear solver is chosen, and there are no changes  *
 * in the input parameters to the specification routine, then no  *
 * call to that routine is needed.                                *
 * If there are changes in parameters, but they do not increase   *
 * the linear solver memory size, then a call to the corresponding*
 * CVReInit<linsol> routine must made to communicate the new      *
 * parameters; in that case the linear solver memory is reused.   *
 * If the parameter changes do increase the linear solver memory  *
 * size, then the main linear solver specification routine must be*
 * called.  See the linear solver documentation for full details. *
 *                                                                *
 * The first argument to CVReInit is:                             *
 *                                                                *
 * cvode_mem = pointer to CVODE memory returned by CVodeMalloc.   *
 *                                                                *
 * All the remaining arguments to CVReInit have names and         *
 * meanings identical to those of CVodeMalloc.  Note that the     *
 * problem size N is not passed as an argument to CVReInit,       *
 * as that is assumed to be unchanged since the CVodeMalloc call. *
 *                                                                *
 * The return value of CVReInit is equal to SUCCESS = 0 if there  *
 * were no errors; otherwise it is a negative int equal to:       *
 *   CVREI_NO_MEM     indicating cvode_mem was NULL, or           *
 *   CVREI_ILL_INPUT  indicating an input argument was illegal    *
 *                    (including an attempt to increase maxord).  *
 * In case of an error return, an error message is also printed.  *
 *                                                                *
 * Note: the reported workspace sizes iopt[LENRW] and iopt[LENIW] *
 * are left unchanged from the values computed by CVodeMalloc, and*
 * so may be larger than would be computed for the new problem.   *
 ******************************************************************/

int CVReInit(void *cvode_mem, RhsFn f, realtype t0, N_Vector y0,
             int lmm, int iter, int itol, realtype *reltol, 
             void *abstol, void *f_data, FILE *errfp, 
             booleantype optIn, long int iopt[],
             realtype ropt[], M_Env machEnv);


/* CVReInit return values: */

/* SUCCESS = 0  (Defined under CVode return values, but listed
                 here also for completeness)                      */
enum {CVREI_NO_MEM = -1, CVREI_ILL_INPUT = -2};
 
 
/******************************************************************
 *                                                                *
 * Function : CVode                                               *
 *----------------------------------------------------------------*
 * CVode integrates the ODE over an interval in t.                *
 * If itask is NORMAL, then the solver integrates from its        *
 * current internal t value to a point at or beyond tout, then    *
 * interpolates to t = tout and returns y(tout) in the user-      *
 * allocated vector yout. If itask is ONE_STEP, then the solver   *
 * takes one internal time step and returns in yout the value of  *
 * y at the new internal time. In this case, tout is used only    *
 * during the first call to CVode to determine the direction of   *
 * integration and the rough scale of the problem. In either      *
 * case, the time reached by the solver is placed in (*t). The    *
 * user is responsible for allocating the memory for this value.  *
 *                                                                *
 * cvode_mem is the pointer to CVODE memory returned by           *
 *              CVodeMalloc.                                      *
 *                                                                *
 * tout  is the next time at which a computed solution is desired *
 *                                                                *
 * yout  is the computed solution vector. In NORMAL mode with no  *
 *          errors, yout=y(tout).                                 *
 *                                                                *
 * t     is a pointer to a real location. CVode sets (*t) to the  *
 *          time reached by the solver and returns yout=y(*t).    *
 *                                                                *
 * itask is either NORMAL or ONE_STEP mode. These two modes have  *
 *          been described above.                                 *
 *                                                                *
 * The return values for CVode are defined later in this file.    *
 * Here is a brief description of each return value:              *
 *                                                                *
 * SUCCESS       : CVode succeeded.                               *
 *                                                                *
 * CVODE_NO_MEM  : The cvode_mem argument was NULL.               *
 *                                                                *
 * ILL_INPUT     : One of the inputs to CVode is illegal. This    *
 *                 includes the situation when a component of the *
 *                 error weight vectors becomes < 0 during        *
 *                 internal time-stepping. The ILL_INPUT flag     *
 *                 will also be returned if the linear solver     *
 *                 routine CV--- (called by the user after        *
 *                 calling CVodeMalloc) failed to set one of the  *
 *                 linear solver-related fields in cvode_mem or   *
 *                 if the linear solver's init routine failed. In *
 *                 any case, the user should see the printed      *
 *                 error message for more details.                *
 *                                                                *
 * TOO_MUCH_WORK : The solver took mxstep internal steps but      *
 *                 could not reach tout. The default value for    *
 *                 mxstep is MXSTEP_DEFAULT = 500.                *
 *                                                                *
 * TOO_MUCH_ACC  : The solver could not satisfy the accuracy      *
 *                 demanded by the user for some internal step.   *
 *                                                                *
 * ERR_FAILURE   : Error test failures occurred too many times    *
 *                 (= MXNEF = 7) during one internal time step or *
 *                 occurred with |h| = hmin.                      *
 *                                                                *
 * CONV_FAILURE  : Convergence test failures occurred too many    *
 *                 times (= MXNCF = 10) during one internal time  *
 *                 step or occurred with |h| = hmin.              *
 *                                                                *
 * SETUP_FAILURE : The linear solver's setup routine failed in an *
 *                 unrecoverable manner.                          *
 *                                                                *
 * SOLVE_FAILURE : The linear solver's solve routine failed in an *
 *                 unrecoverable manner.                          *
 *                                                                *
 ******************************************************************/


int CVode(void *cvode_mem, realtype tout, N_Vector yout, 
          realtype *t, int itask);


/* CVode return values */

enum { SUCCESS=0, CVODE_NO_MEM=-1, ILL_INPUT=-2, TOO_MUCH_WORK=-3,
       TOO_MUCH_ACC=-4, ERR_FAILURE=-5, CONV_FAILURE=-6,
       SETUP_FAILURE=-7, SOLVE_FAILURE=-8 };
 
 
/******************************************************************
 *                                                                *
 * Function : CVodeDky                                            *
 *----------------------------------------------------------------*
 * CVodeDky computes the kth derivative of the y function at      *
 * time t, where tn-hu <= t <= tn, tn denotes the current         *
 * internal time reached, and hu is the last internal step size   *
 * successfully used by the solver. The user may request          *
 * k=0, 1, ..., qu, where qu is the current order. The            *
 * derivative vector is returned in dky. This vector must be      *
 * allocated by the caller. It is only legal to call this         *
 * function after a successful return from CVode.                 *
 *                                                                *
 * cvode_mem is the pointer to CVODE memory returned by           *
 *              CVodeMalloc.                                      *
 *                                                                *
 * t   is the time at which the kth derivative of y is evaluated. *
 *        The legal range for t is [tn-hu,tn] as described above. *
 *                                                                *
 * k   is the order of the derivative of y to be computed. The    *
 *        legal range for k is [0,qu] as described above.         *
 *                                                                *
 * dky is the output derivative vector [(D_k)y](t).               *
 *                                                                *
 * The return values for CVodeDky are defined later in this file. *
 * Here is a brief description of each return value:              *
 *                                                                *
 * OKAY : CVodeDky succeeded.                                     *
 *                                                                *
 * BAD_K : k is not in the range 0, 1, ..., qu.                   *
 *                                                                *
 * BAD_T : t is not in the interval [tn-hu,tn].                   *
 *                                                                *
 * BAD_DKY : The dky argument was NULL.                           *
 *                                                                *
 * DKY_NO_MEM : The cvode_mem argument was NULL.                  *
 *                                                                * 
 ******************************************************************/


int CVodeDky(void *cvode_mem, realtype t, int k, N_Vector dky);


/* CVodeDky return values */

enum { OKAY=0, BAD_K=-1, BAD_T=-2, BAD_DKY=-3, DKY_NO_MEM=-4 };
 
 
/******************************************************************
 *                                                                *
 * Function : CVodeFree                                           *
 *----------------------------------------------------------------*
 * CVodeFree frees the problem memory cvode_mem allocated by      *
 * CVodeMalloc.  Its only argument is the pointer cvode_mem       *
 * returned by CVodeMalloc.                                       *
 *                                                                *
 ******************************************************************/

void CVodeFree(void *cvode_mem);
 
 
/******************************************************************
 *                                                                *
 * Optional Inputs and Outputs                                    *
 *----------------------------------------------------------------*
 * The user should declare two arrays for optional input and      *
 * output, an iopt array for optional integer input and output    *
 * and an ropt array for optional real input and output. The      *
 * size of both these arrays should be OPT_SIZE.                  *
 * So the user's declaration should look like:                    *
 *                                                                *
 * long int iopt[OPT_SIZE];                                       *
 * realtype ropt[OPT_SIZE];                                       *
 *                                                                *
 * The enumerations below the OPT_SIZE definition                 *
 * are indices into the iopt and ropt arrays. Here is a brief     *
 * description of the contents of these positions:                *
 *                                                                *
 * iopt[MAXORD] : maximum lmm order to be used by the solver.     *
 *                Optional input. (Default = 12 for ADAMS, 5 for  *
 *                BDF).                                           *
 *                                                                *
 * iopt[MXSTEP] : maximum number of internal steps to be taken by *
 *                the solver in its attempt to reach tout.        *
 *                Optional input. (Default = 500).                *
 *                                                                *
 * iopt[MXHNIL] : maximum number of warning messages issued by the* 
 *                solver that t + h = t on the next internal step.*
 *                A value of -1 means no such messages are issued.*
 *                Optional input. (Default = 10).                 *
 *                                                                *
 * iopt[NST]    : cumulative number of internal steps taken by    *
 *                the solver (total so far).  Optional output.    *
 *                                                                *
 * iopt[NFE]    : number of calls to the user's f function.       *
 *                Optional output.                                *
 *                                                                *
 * iopt[NSETUPS] : number of calls made to the linear solver's    *
 *                 setup routine. Optional output.                *
 *                                                                *
 * iopt[NNI]     : number of NEWTON iterations performed.         *
 *                 Optional output.                               *
 *                                                                *
 * iopt[NCFN]    : number of nonlinear convergence failures       *
 *                 that have occurred. Optional output.           *
 *                                                                *
 * iopt[NETF]    : number of local error test failures that       *
 *                 have occurred. Optional output.                *
 *                                                                *
 * iopt[QU]      : order used during the last internal step.      *
 *                 Optional output.                               *
 *                                                                *
 * iopt[QCUR]    : order to be used on the next internal step.    *
 *                 Optional output.                               *
 *                                                                *
 * iopt[LENRW]   : size of required CVODE internal real work      *
 *                 space, in realtype words.  Optional output.    *
 *                                                                *
 * iopt[LENIW]   : size of required CVODE internal integer work   *
 *                 space, in integertype words.  Optional output. *
 *                                                                *
 * iopt[SLDET]   : Flag to turn on/off stability limit detection  *
 *                 (1 = on, 0 = off). When BDF is used and order  *
 *                 is 3 or greater, CVsldet is call to detect     *
 *                 stability limit.  If limit is detected, the    *
 *                 order is reduced. Optional input.              *
 *                                                                *
 * iopt[NOR]     : Number of order reductions due to              *
 *                 stability limit detection.                     *
 *                 Optional output.                               *
 *                                                                *
 * ropt[H0]      : initial step size. Optional input.             *
 *                                                                *
 * ropt[HMAX]    : maximum absolute value of step size allowed.   *
 *                 Optional input. (Default is infinity).         *
 *                 Note: If optIn = TRUE, the value of ropt[HMAX] *
 *                 is examined on every call to CVode, and so can *
 *                 be changed between calls.                      *
 *                                                                *
 * ropt[HMIN]    : minimum absolute value of step size allowed.   *
 *                 Optional input. (Default is 0.0).              *
 *                                                                *
 * ropt[HU]      : step size for the last internal step.          *
 *                 Optional output.                               *
 *                                                                *
 * ropt[HCUR]    : step size to be attempted on the next internal *
 *                 step. Optional output.                         *
 *                                                                *
 * ropt[TCUR]    : current internal time reached by the solver.   *
 *                 Optional output.                               *
 *                                                                *
 * ropt[TOLSF]   : a suggested factor by which the user's         *
 *                 tolerances should be scaled when too much      *
 *                 accuracy has been requested for some internal  *
 *                 step. Optional output.                         *
 *                                                                *
 ******************************************************************/

/* iopt, ropt array sizes */

#define OPT_SIZE 40
 

/* iopt and ropt offsets                                          *
 * The constants CVODE_IOPT_SIZE and CVODE_ROPT_SIZE are equal to *
 * the number of integer and real optional inputs and outputs     *
 * actually accessed in cvode.c.  The locations beyond these      *
 * values are used by the linear solvers.                         */

#define CVODE_IOPT_SIZE 15
#define CVODE_ROPT_SIZE  7

/* iopt indices */
enum { MAXORD, MXSTEP, MXHNIL,
       NST, NFE, NSETUPS, NNI, NCFN, NETF, QU, QCUR,
       LENRW, LENIW, SLDET, NOR};

/* ropt indices */

enum { H0, HMAX, HMIN,
       HU, HCUR, TCUR, TOLSF };


/* Basic CVODE 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      */


/******************************************************************
 *                                                                *
 * 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 */

  integertype  cv_N;   /* ODE system size             */
  RhsFn cv_f;          /* y' = f(t,y(t))              */
  void *cv_f_data;     /* user pointer passed to f    */
  int cv_lmm;          /* lmm = ADAMS or BDF          */
  int cv_iter;         /* iter = FUNCTIONAL or NEWTON */
  int cv_itol;         /* itol = SS or SV             */
  realtype *cv_reltol; /* ptr to relative tolerance   */
  void *cv_abstol;     /* ptr to absolute tolerance   */

  /* 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 polynomial  */

  /* 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                     */

  /* Step Data */

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

  realtype cv_h;      /* current step size                     */
  realtype cv_hprime; /* 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_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;     /* 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;   /* estimated corrector convergence rate */
  realtype cv_acnrm;   /* | acor | wrms                        */
  int  cv_mnewt;       /* Newton iteration counter             */

  /* Limits */

  int cv_qmax;   /* q <= qmax                                          */
  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_mxhnil; /* maximum number of warning messages issued to the   */
                 /* user that t + h == t for the next internal step    */

  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_ncfn;        /* number of corrector convergence failures   */
  long int cv_netf;        /* number of error test failures              */
  long int cv_nni;         /* number of Newton iterations performed      */
  long int cv_nsetups;     /* number of setup calls                      */
  int cv_nhnil;            /* number of messages issued to the user that */
                           /* t + h == t for the next iternal step       */
  long int cv_lrw;         /* number of realtype words in CVODE work vectors */
  long int cv_liw;         /* no. of integertype words in CVODE work vectors */
  long int cv_nscon;       /* counter for STALD method                   */

  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        */
  realtype cv_ssdat[6][4]; /* scaled data array for STALD                */

  /* 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 ycur,
                   N_Vector fcur);

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

  /* Linear Solver specific memory */

  void *cv_lmem;           

  /* Saved Values */

  int cv_qu;             /* last successful q value used   */
  long int cv_nstlp;     /* step number of last setup call */
  realtype cv_hu;        /* last successful h value used   */
  realtype cv_saved_tq5; /* saved value of tq[5]           */
  booleantype cv_jcur;   /* Is the Jacobian info used by   */
                         /* linear solver current?         */
  realtype cv_tolsf;     /* tolerance scale factor         */
  booleantype cv_setupNonNull; /* Does setup do something? */

  /* Arrays for Optional Input and Optional Output */

  booleantype cv_optIn; /* boolean input optIn             */
  long int *cv_iopt;    /* long int optional input, output */
  realtype *cv_ropt;    /* real optional input, output     */

  /* Error File */

  FILE *cv_errfp;       /* CVODE error messages are sent to errfp */

  /* Pointer to Machine Environment-Specific Information */

  M_Env cv_machenv;

  /* Stability Limit Detection control flag */

  booleantype cv_sldeton; /* Is Stability Limit Detection on  */

} *CVodeMem;


/******************************************************************
 *                                                                *
 * Communication between user and a CVODE Linear Solver           *
 *----------------------------------------------------------------*
 * Return values of the linear solver specification routine.      *
 * The values of these are given in the enum statement below.     *
 * SUCCESS      : The routine was successful.                     *
 *                                                                *
 * LMEM_FAIL    : A memory allocation failed.                     *
 *                                                                *
 * LIN_ILL_INPUT: Some input was illegal (see message).           *
 *                                                                *
 ******************************************************************/

/* SUCCESS = 0  (Defined under CVode return values, but listed
                 here also for completeness)                      */
enum {LMEM_FAIL = -1, LIN_ILL_INPUT = -2};


/******************************************************************
 *                                                                *
 * Communication between cvode.c and a CVODE Linear Solver        *
 *----------------------------------------------------------------*
 * (1) cv_linit return values                                     *
 *                                                                *
 * LINIT_OK    : The cv_linit routine succeeded.                  *
 *                                                                *
 * LINIT_ERR   : The cv_linit routine failed. Each linear solver  *
 *               init routine should print an appropriate error   *
 *               message to (cv_mem->errfp).                      *
 *                                                                *
 * (2) convfail (input to cv_lsetup)                              *
 *                                                                *
 * 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).                            * 
 *                                                                *
 * FAIL_BAD_J  : This value is passed to cv_lsetup if             *
 *                                                                *
 *               (1) 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                           *
 *               (2) 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.    *
 *                                                                *
 * 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.                           *
 *                                                                *
 * (3) Parameter documentation, as well as a brief description    *
 *     of purpose, for each CVODE linear solver routine to be     *
 *     called in cvode.c is given below the constant declarations *
 *     that follow.                                               *
 *                                                                *
 ******************************************************************/

/* cv_linit return values */

#define LINIT_OK        0
#define LINIT_ERR      -1

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

#define NO_FAILURES 0   
#define FAIL_BAD_J  1  
#define FAIL_OTHER  2  


/*******************************************************************
 *                                                                 *
 * int (*cv_linit)(CVodeMem cv_mem);                               *
 *-----------------------------------------------------------------*
 * The purpose of cv_linit is to complete initializations for      *
 * specific linear solver, such as counters and statistics.        *
 * An LInitFn should return LINIT_OK (= 0) if it has successfully  *
 * initialized the CVODE linear solver and LINIT_ERR (= -1)        *
 * otherwise. These constants are defined above.  If an error does *
 * occur, an appropriate message should be sent to (cv_mem->errfp).*
 *                                                                 *
 *******************************************************************/

/*******************************************************************
 *                                                                 *
 * 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 re-compute Jacobian-      *
 * related data is it deems necessary. Its parameters are as       *
 * follows:                                                        *
 *                                                                 *
 * cv_mem - problem memory pointer of type CVodeMem. See the big   *
 *          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 unconditionally;*
 *           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 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.            *
 *                                                                 *
 *******************************************************************/


#endif

#ifdef __cplusplus
}
#endif

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