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/******************************************************************
* *
* File : cvode.h *
* Programmers : Scott D. Cohen and Alan C. Hindmarsh @ LLNL *
* Last Modified : 1 September 1994 *
*----------------------------------------------------------------*
* This is the interface file for the main CVODE integrator. *
* *
******************************************************************/
#ifndef _cvode_h
#define _cvode_h
#include <stdio.h>
#include "llnltyps.h"
#include "vector.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 input parameters to CVodeMalloc and CVode. *
*----------------------------------------------------------------*
* Symbolic constants for the lmm, iter, and itol input *
* parameters to CVodeMalloc, 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)(integer N, real 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 tolerance. *
* *
* 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(integer N, RhsFn f, real t0, N_Vector y0, int lmm, int iter,
int itol, real *reltol, void *abstol, void *f_data,
FILE *errfp, bool optIn, int iopt[], real ropt[],
void *machEnv);
/******************************************************************
* *
* 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 *
* 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, real tout, N_Vector yout, real *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, real 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: *
* *
* int iopt[OPT_SIZE]; *
* real 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. 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 real words. Optional output. *
* *
* iopt[LENIW] : size of required CVODE internal integer work *
* space, in integer words. Optional output. *
* *
* ropt[H0] : initial step size. Optional input. *
* *
* ropt[HMAX] : maximum absolute value of step size allowed. *
* Optional input. (Default is infinity). *
* *
* 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 13
#define CVODE_ROPT_SIZE 7
/* iopt indices */
enum { MAXORD, MXSTEP, MXHNIL,
NST, NFE, NSETUPS, NNI, NCFN, NETF, QU, QCUR,
LENRW, LENIW };
/* 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 {
real cv_uround; /* machine unit roundoff */
/* Problem Specification Data */
integer 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 */
real *cv_reltol; /* ptr to relative tolerance */
void *cv_abstol; /* ptr to absolute tolerance */
/* Nordsieck History Array */
N_Vector cv_zn[L_MAX]; /* Nordsieck array N x (q+1), */
/* zn[j] is a vector of length N, j=0, ... , q */
/* zn[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 */
real cv_h; /* current step size */
real cv_hprime; /* step size to be used on the next step */
real cv_eta; /* eta = hprime / h */
real cv_hscale; /* value of h used in zn */
real cv_tn; /* current internal value of t */
real cv_tau[L_MAX+1]; /* vector of previous q+1 successful step */
/* sizes indexed from 1 to q+1 */
real cv_tq[NUM_TESTS+1]; /* vector of test quantities indexed from */
/* 1 to NUM_TESTS(=5) */
real cv_l[L_MAX]; /* coefficients of l(x) (degree q poly) */
real cv_rl1; /* 1 / l[1] */
real cv_gamma; /* gamma = h * rl1 */
real cv_gammap; /* gamma at the last setup call */
real cv_gamrat; /* gamma / gammap */
real cv_crate; /* estimated corrector convergence rate */
real 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 */
real cv_hmin; /* |h| >= hmin */
real cv_hmax_inv; /* |h| <= 1/hmax_inv */
real cv_etamax; /* eta <= etamax */
/* Counters */
int cv_nst; /* number of internal steps taken */
int cv_nfe; /* number of f calls */
int cv_ncfn; /* number of corrector convergence failures */
int cv_netf; /* number of error test failures */
int cv_nni; /* number of Newton iterations performed */
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 */
int cv_lrw; /* number of real words in CVODE work vectors */
int cv_liw; /* no. of integer words in CVODE work vectors */
/* Linear Solver Data */
/* Linear Solver functions to be called */
int (*cv_linit)(struct CVodeMemRec *cv_mem, bool *setupNonNull);
int (*cv_lsetup)(struct CVodeMemRec *cv_mem, int convfail, N_Vector ypred,
N_Vector fpred, bool *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;
/* Flag to indicate successful cv_linit call */
bool cv_linitOK;
/* Saved Values */
int cv_qu; /* last successful q value used */
int cv_nstlp; /* step number of last setup call */
real cv_hu; /* last successful h value used */
real cv_saved_tq5; /* saved value of tq[5] */
integer cv_imxer; /* index of max value of */
/* |acor[i]|*ewt[i] */
bool cv_jcur; /* Is the Jacobian info used by */
/* linear solver current? */
real cv_tolsf; /* tolerance scale factor */
bool cv_setupNonNull; /* Does setup do something? */
/* Arrays for Optional Input and Optional Output */
int *cv_iopt; /* int optional input, output */
real *cv_ropt; /* real optional input, output */
/* Error File */
FILE *cv_errfp; /* CVODE error messages are sent to errfp */
/* Pointer to Machine Environment-Specific Information */
void *cv_machenv;
} *CVodeMem;
/******************************************************************
* *
* 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, bool *setupNonNull); *
*-----------------------------------------------------------------*
* The purpose of cv_linit is to allocate memory for the *
* solver-specific fields in the structure *(cv_mem->cv_lmem) and *
* perform any needed initializations of solver-specific memory, *
* such as counters/statistics. The cv_linit routine should set *
* *setupNonNull to be TRUE if the setup operation for the linear *
* solver is non-empty and FALSE if the setup operation does *
* nothing. 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, bool *jcurPtr, N_Vector vtemp, *
* 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 er needed. *
* *
*******************************************************************/
#endif
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