/*---------------------------------------------------------------
 * Programmer(s): Daniel R. Reynolds @ SMU
 *---------------------------------------------------------------
 * SUNDIALS Copyright Start
 * Copyright (c) 2002-2024, Lawrence Livermore National Security
 * and Southern Methodist University.
 * All rights reserved.
 *
 * See the top-level LICENSE and NOTICE files for details.
 *
 * SPDX-License-Identifier: BSD-3-Clause
 * SUNDIALS Copyright End
 *---------------------------------------------------------------
 * Example problem:
 *
 * The following test simulates a brusselator problem from chemical
 * kinetics.  This is n PDE system with 3 components, Y = [u,v,w],
 * satisfying the equations,
 *    u_t = du*u_xx + a - (w+1)*u + v*u^2
 *    v_t = dv*v_xx + w*u - v*u^2
 *    w_t = dw*w_xx + (b-w)/ep - w*u
 * for t in [0, 80], x in [0, 1], with initial conditions
 *    u(0,x) =  a  + 0.1*sin(pi*x)
 *    v(0,x) = b/a + 0.1*sin(pi*x)
 *    w(0,x) =  b  + 0.1*sin(pi*x),
 * and with stationary boundary conditions, i.e.
 *    u_t(t,0) = u_t(t,1) = 0,
 *    v_t(t,0) = v_t(t,1) = 0,
 *    w_t(t,0) = w_t(t,1) = 0.
 * Note: these can also be implemented as Dirichlet boundary
 * conditions with values identical to the initial conditions.
 *
 * The spatial derivatives are computed using second-order
 * centered differences, with the data distributed over N points
 * on a uniform spatial grid.
 *
 * The number of spatial points N, the parameters a, b, du, dv,
 * dw and ep, as well as the desired relative and absolute solver
 * tolerances, are provided in the input file
 * input_brusselator1D.txt.
 *
 * This program solves the problem with the DIRK method, using a
 * Newton iteration.  The inner linear systems are solved using
 * the SUNLinSol_KLU linear solver.
 *
 * 100 outputs are printed at equal intervals, and run statistics
 * are printed at the end.
 *---------------------------------------------------------------*/

/* Header files */
#include <arkode/arkode_arkstep.h> /* prototypes for ARKStep fcts., consts */
#include <math.h>
#include <nvector/nvector_serial.h> /* serial N_Vector types, fcts., macros */
#include <stdio.h>
#include <stdlib.h>
#include <sundials/sundials_math.h> /* def. of SUNRsqrt, etc.               */
#include <sundials/sundials_types.h> /* defs. of sunrealtype, sunindextype, etc */
#include <sunlinsol/sunlinsol_klu.h> /* access to KLU SUNLinearSolver        */
#include <sunmatrix/sunmatrix_sparse.h> /* access to sparse SUNMatrix           */

#if defined(SUNDIALS_EXTENDED_PRECISION)
#define GSYM "Lg"
#define ESYM "Le"
#define FSYM "Lf"
#else
#define GSYM "g"
#define ESYM "e"
#define FSYM "f"
#endif

/* accessor macros between (x,v) location and 1D NVector array */
#define IDX(x, v) (3 * (x) + v)

/* constants */
#define ONE (SUN_RCONST(1.0))
#define TWO (SUN_RCONST(2.0))

/* user data structure */
typedef struct
{
  sunindextype N; /* number of intervals     */
  sunrealtype dx; /* mesh spacing            */
  sunrealtype a;  /* constant forcing on u   */
  sunrealtype b;  /* steady-state value of w */
  sunrealtype du; /* diffusion coeff for u   */
  sunrealtype dv; /* diffusion coeff for v   */
  sunrealtype dw; /* diffusion coeff for w   */
  sunrealtype ep; /* stiffness parameter     */
  SUNMatrix R;    /* temporary storage       */
}* UserData;

/* User-supplied Functions Called by the Solver */
static int f(sunrealtype t, N_Vector y, N_Vector ydot, void* user_data);
static int Jac(sunrealtype t, N_Vector y, N_Vector fy, SUNMatrix J,
               void* user_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3);

/* Private function to check function return values */
static int LaplaceMatrix(SUNMatrix Jac, UserData udata);
static int ReactionJac(N_Vector y, SUNMatrix Jac, UserData udata);

/* Private function to check function return values */
static int check_flag(void* flagvalue, const char* funcname, int opt);

/* Main Program */
int main(void)
{
  /* general problem parameters */
  sunrealtype T0 = SUN_RCONST(0.0);  /* initial time */
  sunrealtype Tf = SUN_RCONST(10.0); /* final time */
  int Nt         = 10;               /* total number of output times */
  int Nvar       = 3;
  UserData udata = NULL;
  sunrealtype* data;
  sunindextype N     = 201; /* spatial mesh size */
  sunrealtype a      = 0.6; /* problem parameters */
  sunrealtype b      = 2.0;
  sunrealtype du     = 0.025;
  sunrealtype dv     = 0.025;
  sunrealtype dw     = 0.025;
  sunrealtype ep     = 1.0e-5; /* stiffness parameter */
  sunrealtype reltol = 1.0e-6; /* tolerances */
  sunrealtype abstol = 1.0e-10;
  sunindextype NEQ, i, NNZ;

  /* general problem variables */
  int flag; /* reusable error-checking flag */
  N_Vector y         = NULL;
  N_Vector umask     = NULL;
  N_Vector vmask     = NULL;
  N_Vector wmask     = NULL;
  SUNMatrix A        = NULL; /* empty matrix object for solver */
  SUNLinearSolver LS = NULL; /* empty linear solver object */
  void* arkode_mem   = NULL;
  sunrealtype pi;
  FILE *FID, *UFID, *VFID, *WFID;
  sunrealtype t     = T0;
  sunrealtype dTout = (Tf - T0) / Nt;
  sunrealtype tout  = T0 + dTout;
  sunrealtype u, v, w;
  int iout;
  long int nst, nst_a, nfe, nfi, nsetups, nje, nni, ncfn, netf;

  /* Create the SUNDIALS context object for this simulation */
  SUNContext ctx;
  flag = SUNContext_Create(SUN_COMM_NULL, &ctx);
  if (check_flag(&flag, "SUNContext_Create", 1)) { return 1; }

  /* allocate udata structure */
  udata = (UserData)malloc(sizeof(*udata));
  if (check_flag((void*)udata, "malloc", 2)) { return 1; }

  /* store the inputs in the UserData structure */
  udata->N  = N;
  udata->a  = a;
  udata->b  = b;
  udata->du = du;
  udata->dv = dv;
  udata->dw = dw;
  udata->ep = ep;
  udata->R  = NULL;

  /* set total allocated vector length */
  NEQ = Nvar * udata->N;

  /* Initial problem output */
  printf("\n1D Brusselator PDE test problem (KLU solver):\n");
  printf("    N = %li,  NEQ = %li\n", (long int)udata->N, (long int)NEQ);
  printf("    problem parameters:  a = %" GSYM ",  b = %" GSYM ",  ep = %" GSYM
         "\n",
         udata->a, udata->b, udata->ep);
  printf("    diffusion coefficients:  du = %" GSYM ",  dv = %" GSYM
         ",  dw = %" GSYM "\n",
         udata->du, udata->dv, udata->dw);
  printf("    reltol = %.1" ESYM ",  abstol = %.1" ESYM "\n\n", reltol, abstol);

  /* Initialize data structures */
  y = N_VNew_Serial(NEQ, ctx); /* Create serial vector for solution */
  if (check_flag((void*)y, "N_VNew_Serial", 0)) { return 1; }

  umask = N_VClone(y);
  if (check_flag((void*)umask, "N_VClone", 0)) { return 1; }

  vmask = N_VClone(y);
  if (check_flag((void*)vmask, "N_VClone", 0)) { return 1; }

  wmask = N_VClone(y);
  if (check_flag((void*)wmask, "N_VClone", 0)) { return 1; }

  /* Set initial conditions into y */
  udata->dx = SUN_RCONST(1.0) / (N - 1); /* set spatial mesh spacing */
  data      = N_VGetArrayPointer(y); /* Access data array for new NVector y */
  if (check_flag((void*)data, "N_VGetArrayPointer", 0)) { return 1; }

  pi = SUN_RCONST(4.0) * atan(ONE);
  for (i = 0; i < N; i++)
  {
    data[IDX(i, 0)] = a + SUN_RCONST(0.1) * sin(pi * i * udata->dx);     /* u */
    data[IDX(i, 1)] = b / a + SUN_RCONST(0.1) * sin(pi * i * udata->dx); /* v */
    data[IDX(i, 2)] = b + SUN_RCONST(0.1) * sin(pi * i * udata->dx);     /* w */
  }

  /* Set mask array values for each solution component */
  N_VConst(0.0, umask);
  data = N_VGetArrayPointer(umask);
  if (check_flag((void*)data, "N_VGetArrayPointer", 0)) { return 1; }
  for (i = 0; i < N; i++) { data[IDX(i, 0)] = ONE; }

  N_VConst(0.0, vmask);
  data = N_VGetArrayPointer(vmask);
  if (check_flag((void*)data, "N_VGetArrayPointer", 0)) { return 1; }
  for (i = 0; i < N; i++) { data[IDX(i, 1)] = ONE; }

  N_VConst(0.0, wmask);
  data = N_VGetArrayPointer(wmask);
  if (check_flag((void*)data, "N_VGetArrayPointer", 0)) { return 1; }
  for (i = 0; i < N; i++) { data[IDX(i, 2)] = ONE; }

  /* Call ARKStepCreate to initialize the ARK timestepper module and
     specify the right-hand side function in y'=f(t,y), the inital time
     T0, and the initial dependent variable vector y.  Note: since this
     problem is fully implicit, we set f_E to NULL and f_I to f. */
  arkode_mem = ARKStepCreate(NULL, f, T0, y, ctx);
  if (check_flag((void*)arkode_mem, "ARKStepCreate", 0)) { return 1; }

  /* Set routines */
  flag = ARKodeSetUserData(arkode_mem,
                           (void*)udata); /* Pass udata to user functions */
  if (check_flag(&flag, "ARKodeSetUserData", 1)) { return 1; }
  flag = ARKodeSStolerances(arkode_mem, reltol, abstol); /* Specify tolerances */
  if (check_flag(&flag, "ARKodeSStolerances", 1)) { return 1; }

  /* Initialize sparse matrix data structure and KLU solver */
  NNZ = 5 * NEQ;
  A   = SUNSparseMatrix(NEQ, NEQ, NNZ, CSC_MAT, ctx);
  if (check_flag((void*)A, "SUNSparseMatrix", 0)) { return 1; }

  LS = SUNLinSol_KLU(y, A, ctx);
  if (check_flag((void*)LS, "SUNLinSol_KLU", 0)) { return 1; }

  /* Attach the matrix, linear solver, and Jacobian construction routine to ARKODE */
  flag = ARKodeSetLinearSolver(arkode_mem, LS, A); /* Attach matrix and LS */
  if (check_flag(&flag, "ARKodeSetLinearSolver", 1)) { return 1; }

  flag = ARKodeSetJacFn(arkode_mem, Jac); /* Supply Jac routine */
  if (check_flag(&flag, "ARKodeSetJacFn", 1)) { return 1; }

  flag = ARKodeSetAutonomous(arkode_mem, SUNTRUE);
  if (check_flag(&flag, "ARKodeSetAutonomous", 1)) { return 1; }

  /* output spatial mesh to disk */
  FID = fopen("bruss_mesh.txt", "w");
  for (i = 0; i < N; i++) { fprintf(FID, "  %.16" ESYM "\n", udata->dx * i); }
  fclose(FID);

  /* Open output stream for results, access data arrays */
  UFID = fopen("bruss_u.txt", "w");
  VFID = fopen("bruss_v.txt", "w");
  WFID = fopen("bruss_w.txt", "w");
  data = N_VGetArrayPointer(y);
  if (check_flag((void*)data, "N_VGetArrayPointer", 0)) { return 1; }

  /* output initial condition to disk */
  for (i = 0; i < N; i++) { fprintf(UFID, " %.16" ESYM "", data[IDX(i, 0)]); }
  for (i = 0; i < N; i++) { fprintf(VFID, " %.16" ESYM "", data[IDX(i, 1)]); }
  for (i = 0; i < N; i++) { fprintf(WFID, " %.16" ESYM "", data[IDX(i, 2)]); }
  fprintf(UFID, "\n");
  fprintf(VFID, "\n");
  fprintf(WFID, "\n");

  /* Main time-stepping loop: calls ARKodeEvolve to perform the integration, then
     prints results.  Stops when the final time has been reached */
  t     = T0;
  dTout = Tf / Nt;
  tout  = T0 + dTout;
  printf("        t      ||u||_rms   ||v||_rms   ||w||_rms\n");
  printf("   ----------------------------------------------\n");
  for (iout = 0; iout < Nt; iout++)
  {
    flag = ARKodeEvolve(arkode_mem, tout, y, &t, ARK_NORMAL); /* call integrator */
    u = N_VWL2Norm(y, umask);
    u = SUNRsqrt(u * u / N);
    v = N_VWL2Norm(y, vmask);
    v = SUNRsqrt(v * v / N);
    w = N_VWL2Norm(y, wmask);
    w = SUNRsqrt(w * w / N);
    printf("  %10.6" FSYM "  %10.6" FSYM "  %10.6" FSYM "  %10.6" FSYM "\n", t,
           u, v, w);
    if (flag >= 0)
    { /* successful solve: update output time */
      tout += dTout;
      tout = (tout > Tf) ? Tf : tout;
    }
    else
    { /* unsuccessful solve: break */
      fprintf(stderr, "Solver failure, stopping integration\n");
      break;
    }

    /* output results to disk */
    for (i = 0; i < N; i++) { fprintf(UFID, " %.16" ESYM "", data[IDX(i, 0)]); }
    for (i = 0; i < N; i++) { fprintf(VFID, " %.16" ESYM "", data[IDX(i, 1)]); }
    for (i = 0; i < N; i++) { fprintf(WFID, " %.16" ESYM "", data[IDX(i, 2)]); }
    fprintf(UFID, "\n");
    fprintf(VFID, "\n");
    fprintf(WFID, "\n");
  }
  printf("   ----------------------------------------------\n");
  fclose(UFID);
  fclose(VFID);
  fclose(WFID);

  /* Print some final statistics */
  flag = ARKodeGetNumSteps(arkode_mem, &nst);
  check_flag(&flag, "ARKodeGetNumSteps", 1);
  flag = ARKodeGetNumStepAttempts(arkode_mem, &nst_a);
  check_flag(&flag, "ARKodeGetNumStepAttempts", 1);
  flag = ARKStepGetNumRhsEvals(arkode_mem, &nfe, &nfi);
  check_flag(&flag, "ARKStepGetNumRhsEvals", 1);
  flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
  check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1);
  flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
  check_flag(&flag, "ARKodeGetNumErrTestFails", 1);
  flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
  check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
  flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
  check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1);
  flag = ARKodeGetNumJacEvals(arkode_mem, &nje);
  check_flag(&flag, "ARKodeGetNumJacEvals", 1);

  printf("\nFinal Solver Statistics:\n");
  printf("   Internal solver steps = %li (attempted = %li)\n", nst, nst_a);
  printf("   Total RHS evals:  Fe = %li,  Fi = %li\n", nfe, nfi);
  printf("   Total linear solver setups = %li\n", nsetups);
  printf("   Total number of Jacobian evaluations = %li\n", nje);
  printf("   Total number of nonlinear iterations = %li\n", nni);
  printf("   Total number of nonlinear solver convergence failures = %li\n",
         ncfn);
  printf("   Total number of error test failures = %li\n", netf);

  /* Clean up and return with successful completion */
  N_VDestroy(y); /* Free vectors */
  N_VDestroy(umask);
  N_VDestroy(vmask);
  N_VDestroy(wmask);
  SUNMatDestroy(udata->R); /* Free user data */
  free(udata);
  ARKodeFree(&arkode_mem); /* Free integrator memory */
  SUNLinSolFree(LS);       /* Free linear solver */
  SUNMatDestroy(A);        /* Free A matrix */
  SUNContext_Free(&ctx);   /* Free context */

  return 0;
}

/*-------------------------------
 * Functions called by the solver
 *-------------------------------*/

/* f routine to compute the ODE RHS function f(t,y). */
static int f(sunrealtype t, N_Vector y, N_Vector ydot, void* user_data)
{
  UserData udata     = (UserData)user_data; /* access problem data */
  sunindextype N     = udata->N;            /* set variable shortcuts */
  sunrealtype a      = udata->a;
  sunrealtype b      = udata->b;
  sunrealtype ep     = udata->ep;
  sunrealtype du     = udata->du;
  sunrealtype dv     = udata->dv;
  sunrealtype dw     = udata->dw;
  sunrealtype dx     = udata->dx;
  sunrealtype *Ydata = NULL, *dYdata = NULL;
  sunrealtype uconst, vconst, wconst, u, ul, ur, v, vl, vr, w, wl, wr;
  sunindextype i;

  Ydata = N_VGetArrayPointer(y); /* access data arrays */
  if (check_flag((void*)Ydata, "N_VGetArrayPointer", 0)) { return 1; }
  dYdata = N_VGetArrayPointer(ydot);
  if (check_flag((void*)dYdata, "N_VGetArrayPointer", 0)) { return 1; }
  N_VConst(0.0, ydot); /* initialize ydot to zero */

  /* iterate over domain, computing all equations */
  uconst = du / dx / dx;
  vconst = dv / dx / dx;
  wconst = dw / dx / dx;
  for (i = 1; i < N - 1; i++)
  {
    /* set shortcuts */
    u  = Ydata[IDX(i, 0)];
    ul = Ydata[IDX(i - 1, 0)];
    ur = Ydata[IDX(i + 1, 0)];
    v  = Ydata[IDX(i, 1)];
    vl = Ydata[IDX(i - 1, 1)];
    vr = Ydata[IDX(i + 1, 1)];
    w  = Ydata[IDX(i, 2)];
    wl = Ydata[IDX(i - 1, 2)];
    wr = Ydata[IDX(i + 1, 2)];

    /* u_t = du*u_xx + a - (w+1)*u + v*u^2 */
    dYdata[IDX(i, 0)] = (ul - TWO * u + ur) * uconst + a - (w + ONE) * u +
                        v * u * u;

    /* v_t = dv*v_xx + w*u - v*u^2 */
    dYdata[IDX(i, 1)] = (vl - TWO * v + vr) * vconst + w * u - v * u * u;

    /* w_t = dw*w_xx + (b-w)/ep - w*u */
    dYdata[IDX(i, 2)] = (wl - TWO * w + wr) * wconst + (b - w) / ep - w * u;
  }

  /* enforce stationary boundaries */
  dYdata[IDX(0, 0)] = dYdata[IDX(0, 1)] = dYdata[IDX(0, 2)] = 0.0;
  dYdata[IDX(N - 1, 0)] = dYdata[IDX(N - 1, 1)] = dYdata[IDX(N - 1, 2)] = 0.0;

  return 0;
}

/* Jacobian routine to compute J(t,y) = df/dy. */
static int Jac(sunrealtype t, N_Vector y, N_Vector fy, SUNMatrix J,
               void* user_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3)
{
  /* problem data */
  UserData udata = (UserData)user_data;
  sunindextype N = udata->N;

  /* ensure that Jac is the correct size */
  if ((SUNSparseMatrix_Rows(J) != N * 3) || (SUNSparseMatrix_Columns(J) != N * 3))
  {
    printf("Jacobian calculation error: matrix is the wrong size!\n");
    return 1;
  }

  /* Fill in the Laplace matrix */
  if (LaplaceMatrix(J, udata))
  {
    printf("Jacobian calculation error in calling LaplaceMatrix!\n");
    return 1;
  }

  /* Create matrix for Jacobian of the reaction terms if necessary */
  if (udata->R == NULL)
  {
    udata->R = SUNSparseMatrix(SUNSparseMatrix_Rows(J),
                               SUNSparseMatrix_Columns(J),
                               SUNSparseMatrix_NNZ(J), CSC_MAT, J->sunctx);
    if (udata->R == NULL)
    {
      printf("Jacobian calculation error in allocating R matrix!\n");
      return 1;
    }
  }

  /* Compute the Jacobian of the reaction terms */
  if (ReactionJac(y, udata->R, udata))
  {
    printf("Jacobian calculation error in calling ReactionJac!\n");
    return 1;
  }

  /* Add R to J */
  if (SUNMatScaleAdd(ONE, J, udata->R) != 0)
  {
    printf("Jacobian calculation error in adding sparse matrices!\n");
    return 1;
  }

  return 0;
}

/*-------------------------------
 * Private helper functions
 *-------------------------------*/

/* Routine to compute the stiffness matrix from (L*y) */
static int LaplaceMatrix(SUNMatrix Lap, UserData udata)
{
  sunindextype N = udata->N; /* set shortcuts */
  sunindextype i, nz = 0;
  sunrealtype uconst, uconst2, vconst, vconst2, wconst, wconst2;
  sunindextype* colptrs = SUNSparseMatrix_IndexPointers(Lap);
  sunindextype* rowvals = SUNSparseMatrix_IndexValues(Lap);
  sunrealtype* data     = SUNSparseMatrix_Data(Lap);

  /* clear out matrix */
  SUNMatZero(Lap);

  /* set first column to zero */
  colptrs[IDX(0, 0)] = nz;
  colptrs[IDX(0, 1)] = nz;
  colptrs[IDX(0, 2)] = nz;

  /* iterate over nodes, filling in Laplacian entries depending on these */
  uconst  = (udata->du) / (udata->dx) / (udata->dx);
  uconst2 = -TWO * uconst;
  vconst  = (udata->dv) / (udata->dx) / (udata->dx);
  vconst2 = -TWO * vconst;
  wconst  = (udata->dw) / (udata->dx) / (udata->dx);
  wconst2 = -TWO * wconst;
  for (i = 1; i < N - 1; i++)
  {
    /* dependence on u at this node */
    colptrs[IDX(i, 0)] = nz;
    if (i > 1)
    { /* node to left */
      data[nz]      = uconst;
      rowvals[nz++] = IDX(i - 1, 0);
    }

    data[nz]      = uconst2; /* self */
    rowvals[nz++] = IDX(i, 0);

    if (i < N - 2)
    { /* node to right */
      data[nz]      = uconst;
      rowvals[nz++] = IDX(i + 1, 0);
    }

    /* dependence on v at this node */
    colptrs[IDX(i, 1)] = nz;
    if (i > 1)
    { /* node to left */
      data[nz]      = vconst;
      rowvals[nz++] = IDX(i - 1, 1);
    }

    data[nz]      = vconst2; /* self */
    rowvals[nz++] = IDX(i, 1);

    if (i < N - 2)
    { /* node to right */
      data[nz]      = vconst;
      rowvals[nz++] = IDX(i + 1, 1);
    }

    /* dependence on w at this node */
    colptrs[IDX(i, 2)] = nz;
    if (i > 1)
    { /* node to left */
      data[nz]      = wconst;
      rowvals[nz++] = IDX(i - 1, 2);
    }

    data[nz]      = wconst2; /* self */
    rowvals[nz++] = IDX(i, 2);

    if (i < N - 2)
    { /* node to right */
      data[nz]      = wconst;
      rowvals[nz++] = IDX(i + 1, 2);
    }
  }

  /* set last column to zero */
  colptrs[IDX(N - 1, 0)] = nz;
  colptrs[IDX(N - 1, 1)] = nz;
  colptrs[IDX(N - 1, 2)] = nz;

  /* end of data */
  colptrs[IDX(N - 1, 2) + 1] = nz;

  return 0;
}

/* Routine to compute the Jacobian matrix from R(y) */
static int ReactionJac(N_Vector y, SUNMatrix Jac, UserData udata)
{
  sunindextype N = udata->N; /* set shortcuts */
  sunindextype i, nz = 0;
  sunrealtype u, v, w;
  sunrealtype ep        = udata->ep;
  sunindextype* colptrs = SUNSparseMatrix_IndexPointers(Jac);
  sunindextype* rowvals = SUNSparseMatrix_IndexValues(Jac);
  sunrealtype* data     = SUNSparseMatrix_Data(Jac);
  sunrealtype* Ydata    = N_VGetArrayPointer(y); /* access solution array */
  if (check_flag((void*)Ydata, "N_VGetArrayPointer", 0)) { return 1; }

  /* clear out matrix */
  SUNMatZero(Jac);

  /* set first matrix column to zero */
  colptrs[IDX(0, 0)] = 0;
  colptrs[IDX(0, 1)] = 0;
  colptrs[IDX(0, 2)] = 0;

  /* iterate over interior nodes, filling in Jacobian entries */
  for (i = 1; i < N - 1; i++)
  {
    /* set nodal value shortcuts */
    u = Ydata[IDX(i, 0)];
    v = Ydata[IDX(i, 1)];
    w = Ydata[IDX(i, 2)];

    /* dependence on u at this node */
    colptrs[IDX(i, 0)] = nz;

    rowvals[nz] = IDX(i, 0); /* fu wrt u */
    data[nz++]  = TWO * u * v - w - ONE;

    rowvals[nz] = IDX(i, 1); /* fv wrt u */
    data[nz++]  = w - TWO * u * v;

    rowvals[nz] = IDX(i, 2); /* fw wrt u */
    data[nz++]  = -w;

    /* dependence on v at this node */
    colptrs[IDX(i, 1)] = nz;

    rowvals[nz] = IDX(i, 0); /* fu wrt v */
    data[nz++]  = u * u;

    rowvals[nz] = IDX(i, 1); /* fv wrt v */
    data[nz++]  = -u * u;

    /* dependence on w at this node */
    colptrs[IDX(i, 2)] = nz;

    rowvals[nz] = IDX(i, 0); /* fu wrt w */
    data[nz++]  = -u;

    rowvals[nz] = IDX(i, 1); /* fv wrt w */
    data[nz++]  = u;

    rowvals[nz] = IDX(i, 2); /* fw wrt w */
    data[nz++]  = -ONE / ep - u;
  }

  /* set last matrix column to zero */
  colptrs[IDX(N - 1, 0)] = nz;
  colptrs[IDX(N - 1, 1)] = nz;
  colptrs[IDX(N - 1, 2)] = nz;

  /* end of data */
  colptrs[IDX(N - 1, 2) + 1] = nz;

  return 0;
}

/* Check function return value...
    opt == 0 means SUNDIALS function allocates memory so check if
             returned NULL pointer
    opt == 1 means SUNDIALS function returns a flag so check if
             flag >= 0
    opt == 2 means function allocates memory so check if returned
             NULL pointer
*/
static int check_flag(void* flagvalue, const char* funcname, int opt)
{
  int* errflag;

  /* Check if SUNDIALS function returned NULL pointer - no memory allocated */
  if (opt == 0 && flagvalue == NULL)
  {
    fprintf(stderr, "\nSUNDIALS_ERROR: %s() failed - returned NULL pointer\n\n",
            funcname);
    return 1;
  }

  /* Check if flag < 0 */
  else if (opt == 1)
  {
    errflag = (int*)flagvalue;
    if (*errflag < 0)
    {
      fprintf(stderr, "\nSUNDIALS_ERROR: %s() failed with flag = %d\n\n",
              funcname, *errflag);
      return 1;
    }
  }

  /* Check if function returned NULL pointer - no memory allocated */
  else if (opt == 2 && flagvalue == NULL)
  {
    fprintf(stderr, "\nMEMORY_ERROR: %s() failed - returned NULL pointer\n\n",
            funcname);
    return 1;
  }

  return 0;
}

/*---- end of file ----*/
