/* -----------------------------------------------------------------
 * Programmer(s): Allan Taylor, Alan Hindmarsh and
 *                Radu Serban @ LLNL
 * -----------------------------------------------------------------
 * 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 (parallel):
 *
 * This example solves a nonlinear system that arises from a system
 * of partial differential equations. The PDE system is a food web
 * population model, with predator-prey interaction and diffusion on
 * the unit square in two dimensions. The dependent variable vector
 * is the following:
 *
 *       1   2         ns
 * c = (c , c ,  ..., c  )     (denoted by the variable cc)
 *
 * and the PDE's are as follows:
 *
 *                    i       i
 *         0 = d(i)*(c     + c    )  +  f  (x,y,c)   (i=1,...,ns)
 *                    xx      yy         i
 *
 *   where
 *
 *                   i             ns         j
 *   f  (x,y,c)  =  c  * (b(i)  + sum a(i,j)*c )
 *    i                           j=1
 *
 * The number of species is ns = 2 * np, with the first np being
 * prey and the last np being predators. The number np is both
 * the number of prey and predator species. The coefficients a(i,j),
 * b(i), d(i) are:
 *
 *   a(i,i) = -AA   (all i)
 *   a(i,j) = -GG   (i <= np , j >  np)
 *   a(i,j) =  EE   (i >  np,  j <= np)
 *   b(i) = BB * (1 + alpha * x * y)   (i <= np)
 *   b(i) =-BB * (1 + alpha * x * y)   (i >  np)
 *   d(i) = DPREY   (i <= np)
 *   d(i) = DPRED   ( i > np)
 *
 * The various scalar parameters are set using define's or in
 * routine InitUserData.
 *
 * The boundary conditions are: normal derivative = 0, and the
 * initial guess is constant in x and y, but the final solution
 * is not.
 *
 * The PDEs are discretized by central differencing on an MX by
 * MY mesh.
 *
 * The nonlinear system is solved by KINSOL using the method
 * specified in the local variable globalstrat.
 *
 * The preconditioner matrix is a block-diagonal matrix based on
 * the partial derivatives of the interaction terms f only.
 * -----------------------------------------------------------------
 * References:
 *
 * 1. Peter N. Brown and Youcef Saad,
 *    Hybrid Krylov Methods for Nonlinear Systems of Equations
 *    LLNL report UCRL-97645, November 1987.
 *
 * 2. Peter N. Brown and Alan C. Hindmarsh,
 *    Reduced Storage Matrix Methods in Stiff ODE systems,
 *    Lawrence Livermore National Laboratory Report  UCRL-95088,
 *    Rev. 1, June 1987, and  Journal of Applied Mathematics and
 *    Computation, Vol. 31 (May 1989), pp. 40-91. (Presents a
 *    description of the time-dependent version of this test
 *    problem.)
 * ----------------------------------------------------------------------
 *  Run command line: mpirun -np N -machinefile machines kinFoodWeb_kry_p
 *  where N = NPEX * NPEY is the number of processors.
 * ----------------------------------------------------------------------
 */

#include <kinsol/kinsol.h> /* access to KINSOL func., consts.      */
#include <math.h>
#include <mpi.h>
#include <nvector/nvector_parallel.h> /* access to MPI parallel N_Vector      */
#include <stdio.h>
#include <stdlib.h>
#include <sundials/sundials_dense.h> /* use generic dense solver in precond. */
#include <sundials/sundials_types.h> /* defs. of sunrealtype, sunindextype      */
#include <sunlinsol/sunlinsol_spgmr.h> /* access to SPGMR SUNLinearSolver      */

/* helpful macros */

#ifndef MAX
#define MAX(A, B) ((A) > (B) ? (A) : (B))
#endif

/* Problem Constants */

#define NUM_SPECIES \
  6 /* must equal 2*(number of prey or predators)
                              number of prey = number of predators       */

#define PI SUN_RCONST(3.1415926535898) /* pi */

#define NPEX     2              /* number of processors in the x-direction  */
#define NPEY     2              /* number of processors in the y-direction  */
#define MXSUB    10             /* number of x mesh points per subgrid      */
#define MYSUB    10             /* number of y mesh points per subgrid      */
#define MX       (NPEX * MXSUB) /* number of mesh points in the x-direction */
#define MY       (NPEY * MYSUB) /* number of mesh points in the y-direction */
#define NSMXSUB  (NUM_SPECIES * MXSUB)
#define NSMXSUB2 (NUM_SPECIES * (MXSUB + 2))
#define NEQ      (NUM_SPECIES * MX * MY) /* number of equations in the system */
#define AA       SUN_RCONST(1.0)    /* value of coefficient AA in above eqns */
#define EE       SUN_RCONST(10000.) /* value of coefficient EE in above eqns */
#define GG       SUN_RCONST(0.5e-6) /* value of coefficient GG in above eqns */
#define BB       SUN_RCONST(1.0)    /* value of coefficient BB in above eqns */
#define DPREY    SUN_RCONST(1.0)    /* value of coefficient dprey above */
#define DPRED    SUN_RCONST(0.5)    /* value of coefficient dpred above */
#define ALPHA    SUN_RCONST(1.0)    /* value of coefficient alpha above */
#define AX       SUN_RCONST(1.0)    /* total range of x variable */
#define AY       SUN_RCONST(1.0)    /* total range of y variable */
#define FTOL     SUN_RCONST(1.e-7)  /* ftol tolerance */
#define STOL     SUN_RCONST(1.e-13) /* stol tolerance */
#define THOUSAND SUN_RCONST(1000.0) /* one thousand */
#define ZERO     SUN_RCONST(0.0)    /* 0. */
#define ONE      SUN_RCONST(1.0)    /* 1. */
#define PREYIN   SUN_RCONST(1.0)    /* initial guess for prey concentrations. */
#define PREDIN   SUN_RCONST(30000.0) /* initial guess for predator concs.      */

/* User-defined vector access macro: IJ_Vptr */

/* IJ_Vptr is defined in order to translate from the underlying 3D structure
   of the dependent variable vector to the 1D storage scheme for an N-vector.
   IJ_Vptr(vv,i,j) returns a pointer to the location in vv corresponding to
   indices is = 0, jx = i, jy = j.    */

#define IJ_Vptr(vv, i, j) (&NV_Ith_P(vv, i * NUM_SPECIES + j * NSMXSUB))

/* Type : UserData
   contains preconditioner blocks, pivot arrays, and problem constants */

typedef struct
{
  sunrealtype** P[MXSUB][MYSUB];
  sunindextype* pivot[MXSUB][MYSUB];
  sunrealtype **acoef, *bcoef;
  N_Vector rates;
  sunrealtype *cox, *coy;
  sunrealtype ax, ay, dx, dy;
  sunrealtype uround, sqruround;
  int mx, my, ns, np;
  sunrealtype cext[NUM_SPECIES * (MXSUB + 2) * (MYSUB + 2)];
  int my_pe, isubx, isuby, nsmxsub, nsmxsub2;
  MPI_Comm comm;
}* UserData;

/* Functions called by the KINSOL Solver */

static int funcprpr(N_Vector cc, N_Vector fval, void* user_data);

static int Precondbd(N_Vector cc, N_Vector cscale, N_Vector fval,
                     N_Vector fscale, void* user_data);

static int PSolvebd(N_Vector cc, N_Vector cscale, N_Vector fval,
                    N_Vector fscale, N_Vector vv, void* user_data);

/* Private Helper Functions */

static UserData AllocUserData(void);
static void InitUserData(int my_pe, MPI_Comm comm, UserData data);
static void FreeUserData(UserData data);
static void SetInitialProfiles(N_Vector cc, N_Vector sc);
static void PrintHeader(int globalstrategy, int maxl, int maxlrst,
                        sunrealtype fnormtol, sunrealtype scsteptol);
static void PrintOutput(int my_pe, MPI_Comm comm, N_Vector cc);
static void PrintFinalStats(void* kmem);
static void WebRate(sunrealtype xx, sunrealtype yy, sunrealtype* cxy,
                    sunrealtype* ratesxy, void* user_data);
static sunrealtype DotProd(int size, sunrealtype* x1, sunrealtype* x2);
static void BSend(MPI_Comm comm, int my_pe, int isubx, int isuby, int dsizex,
                  int dsizey, sunrealtype* cdata);
static void BRecvPost(MPI_Comm comm, MPI_Request request[], int my_pe,
                      int isubx, int isuby, int dsizex, int dsizey,
                      sunrealtype* cext, sunrealtype* buffer);
static void BRecvWait(MPI_Request request[], int isubx, int isuby, int dsizex,
                      sunrealtype* cext, sunrealtype* buffer);
static void ccomm(sunrealtype* cdata, UserData data);
static void fcalcprpr(N_Vector cc, N_Vector fval, void* user_data);
static int check_retval(void* retvalvalue, const char* funcname, int opt, int id);

/*
 *--------------------------------------------------------------------
 * MAIN PROGRAM
 *--------------------------------------------------------------------
 */

int main(int argc, char* argv[])
{
  SUNContext sunctx;
  int globalstrategy;
  sunindextype local_N;
  sunrealtype fnormtol, scsteptol;
  N_Vector cc, sc, constraints;
  UserData data;
  int retval, maxl, maxlrst;
  int my_pe, npes, npelast = NPEX * NPEY - 1;
  void* kmem;
  SUNLinearSolver LS;
  MPI_Comm comm;

  cc = sc = constraints = NULL;
  kmem                  = NULL;
  LS                    = NULL;
  data                  = NULL;

  /* Get processor number and total number of pe's */
  MPI_Init(&argc, &argv);
  comm = MPI_COMM_WORLD;
  MPI_Comm_size(comm, &npes);
  MPI_Comm_rank(comm, &my_pe);

  if (npes != NPEX * NPEY)
  {
    if (my_pe == 0)
    {
      fprintf(stderr,
              "\nMPI_ERROR(0): npes = %d is not equal to NPEX*NPEY = %d\n",
              npes, NPEX * NPEY);
    }
    MPI_Finalize();
    return (1);
  }

  /* Create the SUNDIALS context that all SUNDIALS objects require */
  retval = SUNContext_Create(comm, &sunctx);
  if (check_retval(&retval, "SUNContext_Create", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }

  /* Allocate memory, and set problem data, initial values, tolerances */

  /* Set local vector length */
  local_N = NUM_SPECIES * MXSUB * MYSUB;

  /* Allocate and initialize user data block */
  data = AllocUserData();
  if (check_retval((void*)data, "AllocUserData", 0, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  InitUserData(my_pe, comm, data);

  /* Set global strategy retval */
  globalstrategy = KIN_NONE;

  /* Allocate and initialize vectors */
  cc = N_VNew_Parallel(comm, local_N, NEQ, sunctx);
  if (check_retval((void*)cc, "N_VNew_Parallel", 0, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  sc = N_VNew_Parallel(comm, local_N, NEQ, sunctx);
  if (check_retval((void*)sc, "N_VNew_Parallel", 0, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  data->rates = N_VNew_Parallel(comm, local_N, NEQ, sunctx);
  if (check_retval((void*)data->rates, "N_VNew_Parallel", 0, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  constraints = N_VNew_Parallel(comm, local_N, NEQ, sunctx);
  if (check_retval((void*)constraints, "N_VNew_Parallel", 0, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  N_VConst(ZERO, constraints);

  SetInitialProfiles(cc, sc);

  fnormtol  = FTOL;
  scsteptol = STOL;

  /* Call KINCreate/KINInit to initialize KINSOL:
     nvSpec is the nvSpec pointer used in the parallel version
     A pointer to KINSOL problem memory is returned and stored in kmem. */
  kmem = KINCreate(sunctx);
  if (check_retval((void*)kmem, "KINCreate", 0, my_pe)) { MPI_Abort(comm, 1); }

  /* Vector cc passed as template vector. */
  retval = KINInit(kmem, funcprpr, cc);
  if (check_retval(&retval, "KINInit", 1, my_pe)) { MPI_Abort(comm, 1); }
  retval = KINSetNumMaxIters(kmem, 250);
  if (check_retval(&retval, "KINSetNumMaxIters", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  retval = KINSetUserData(kmem, data);
  if (check_retval(&retval, "KINSetUserData", 1, my_pe)) { MPI_Abort(comm, 1); }
  retval = KINSetConstraints(kmem, constraints);
  if (check_retval(&retval, "KINSetConstraints", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  retval = KINSetFuncNormTol(kmem, fnormtol);
  if (check_retval(&retval, "KINSetFuncNormTol", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }
  retval = KINSetScaledStepTol(kmem, scsteptol);
  if (check_retval(&retval, "KINSetScaledStepTol", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }

  /* We no longer need the constraints vector since KINSetConstraints
     creates a private copy for KINSOL to use. */
  N_VDestroy(constraints);

  /* Create SUNLinSol_SPGMR object with right preconditioning and the
     maximum Krylov dimension maxl */
  maxl = 20;
  LS   = SUNLinSol_SPGMR(cc, SUN_PREC_RIGHT, maxl, sunctx);
  if (check_retval((void*)LS, "SUNLinSol_SPGMR", 0, my_pe))
  {
    MPI_Abort(comm, 1);
  }

  /* Attach the linear solver to KINSOL */
  retval = KINSetLinearSolver(kmem, LS, NULL);
  if (check_retval(&retval, "KINSetLinearSolver", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }

  /* Set the maximum number of restarts */
  maxlrst = 2;
  retval  = SUNLinSol_SPGMRSetMaxRestarts(LS, maxlrst);
  if (check_retval(&retval, "SUNLinSol_SPGMRSetMaxRestarts", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }

  /* Specify the preconditioner setup and solve routines */
  retval = KINSetPreconditioner(kmem, Precondbd, PSolvebd);
  if (check_retval(&retval, "KINSetPreconditioner", 1, my_pe))
  {
    MPI_Abort(comm, 1);
  }

  /* Print out the problem size, solution parameters, initial guess. */
  if (my_pe == 0)
  {
    PrintHeader(globalstrategy, maxl, maxlrst, fnormtol, scsteptol);
  }

  /* Call KINSol and print output concentration profile */
  retval = KINSol(kmem,           /* KINSol memory block */
                  cc,             /* initial guess on input; solution vector */
                  globalstrategy, /* global strategy choice */
                  sc,             /* scaling vector for the variable cc */
                  sc);            /* scaling vector for function values fval */
  if (check_retval(&retval, "KINSol", 1, my_pe)) { MPI_Abort(comm, 1); }

  if (my_pe == 0)
  {
    printf("\n\nComputed equilibrium species concentrations:\n");
  }
  if (my_pe == 0 || my_pe == npelast) { PrintOutput(my_pe, comm, cc); }

  /* Print final statistics and free memory */
  if (my_pe == 0) { PrintFinalStats(kmem); }

  N_VDestroy(cc);
  N_VDestroy(sc);
  KINFree(&kmem);
  SUNLinSolFree(LS);
  FreeUserData(data);
  SUNContext_Free(&sunctx);

  MPI_Finalize();

  return (0);
}

/* Readability definitions used in other routines below */

#define acoef (data->acoef)
#define bcoef (data->bcoef)
#define cox   (data->cox)
#define coy   (data->coy)

/*
 *--------------------------------------------------------------------
 * FUNCTIONS CALLED BY KINSOL
 *--------------------------------------------------------------------
 */

/*
 * System function routine.  Evaluate funcprpr(cc).  First call ccomm to do
 *  communication of subgrid boundary data into cext.  Then calculate funcprpr
 *  by a call to fcalcprpr.
 */

static int funcprpr(N_Vector cc, N_Vector fval, void* user_data)
{
  sunrealtype* cdata;
  UserData data;

  cdata = N_VGetArrayPointer(cc);
  data  = (UserData)user_data;

  /* Call ccomm to do inter-processor communicaiton */
  ccomm(cdata, data);

  /* Call fcalcprpr to calculate all right-hand sides */
  fcalcprpr(cc, fval, data);

  return (0);
}

/*
 * Preconditioner setup routine. Generate and preprocess P.
 */

static int Precondbd(N_Vector cc, N_Vector cscale, N_Vector fval,
                     N_Vector fscale, void* user_data)
{
  sunrealtype r, r0, uround, sqruround, xx, yy, delx, dely, csave, fac;
  sunrealtype *cxy, *scxy, **Pxy, *ratesxy, *Pxycol, perturb_rates[NUM_SPECIES];
  int i, j, jx, jy;
  sunindextype ret;
  UserData data;

  data = (UserData)user_data;
  delx = data->dx;
  dely = data->dy;

  uround    = data->uround;
  sqruround = data->sqruround;
  fac       = N_VWL2Norm(fval, fscale);
  r0        = THOUSAND * uround * fac * NEQ;
  if (r0 == ZERO) { r0 = ONE; }

  /* Loop over spatial points; get size NUM_SPECIES Jacobian block at each */
  for (jy = 0; jy < MYSUB; jy++)
  {
    yy = dely * (jy + data->isuby * MYSUB);

    for (jx = 0; jx < MXSUB; jx++)
    {
      xx      = delx * (jx + data->isubx * MXSUB);
      Pxy     = (data->P)[jx][jy];
      cxy     = IJ_Vptr(cc, jx, jy);
      scxy    = IJ_Vptr(cscale, jx, jy);
      ratesxy = IJ_Vptr((data->rates), jx, jy);

      /* Compute difference quotients of interaction rate fn. */
      for (j = 0; j < NUM_SPECIES; j++)
      {
        csave = cxy[j]; /* Save the j,jx,jy element of cc */
        r     = MAX(sqruround * fabs(csave), r0 / scxy[j]);
        cxy[j] += r; /* Perturb the j,jx,jy element of cc */
        fac = ONE / r;

        WebRate(xx, yy, cxy, perturb_rates, data);

        /* Restore j,jx,jy element of cc */
        cxy[j] = csave;

        /* Load the j-th column of difference quotients */
        Pxycol = Pxy[j];
        for (i = 0; i < NUM_SPECIES; i++)
        {
          Pxycol[i] = (perturb_rates[i] - ratesxy[i]) * fac;
        }

      } /* end of j loop */

      /* Do LU decomposition of size NUM_SPECIES preconditioner block */
      ret = SUNDlsMat_denseGETRF(Pxy, NUM_SPECIES, NUM_SPECIES,
                                 (data->pivot)[jx][jy]);
      if (ret != 0) { return (1); }

    } /* end of jx loop */

  } /* end of jy loop */

  return (0);
}

/*
 * Preconditioner solve routine
 */

static int PSolvebd(N_Vector cc, N_Vector cscale, N_Vector fval,
                    N_Vector fscale, N_Vector vv, void* user_data)
{
  sunrealtype **Pxy, *vxy;
  sunindextype *piv, jx, jy;
  UserData data;

  data = (UserData)user_data;

  for (jx = 0; jx < MXSUB; jx++)
  {
    for (jy = 0; jy < MYSUB; jy++)
    {
      /* For each (jx,jy), solve a linear system of size NUM_SPECIES.
         vxy is the address of the corresponding portion of the vector vv;
         Pxy is the address of the corresponding block of the matrix P;
         piv is the address of the corresponding block of the array pivot. */
      vxy = IJ_Vptr(vv, jx, jy);
      Pxy = (data->P)[jx][jy];
      piv = (data->pivot)[jx][jy];
      SUNDlsMat_denseGETRS(Pxy, NUM_SPECIES, piv, vxy);

    } /* end of jy loop */

  } /* end of jx loop */

  return (0);
}

/*
 * Interaction rate function routine
 */

static void WebRate(sunrealtype xx, sunrealtype yy, sunrealtype* cxy,
                    sunrealtype* ratesxy, void* user_data)
{
  int i;
  sunrealtype fac;
  UserData data;

  data = (UserData)user_data;

  for (i = 0; i < NUM_SPECIES; i++)
  {
    ratesxy[i] = DotProd(NUM_SPECIES, cxy, acoef[i]);
  }

  fac = ONE + ALPHA * xx * yy;

  for (i = 0; i < NUM_SPECIES; i++)
  {
    ratesxy[i] = cxy[i] * (bcoef[i] * fac + ratesxy[i]);
  }
}

/*
 * Dot product routine for sunrealtype arrays
 */

static sunrealtype DotProd(int size, sunrealtype* x1, sunrealtype* x2)
{
  int i;
  sunrealtype *xx1, *xx2, temp = ZERO;

  xx1 = x1;
  xx2 = x2;
  for (i = 0; i < size; i++) { temp += (*xx1++) * (*xx2++); }

  return (temp);
}

/*
 *--------------------------------------------------------------------
 * PRIVATE FUNCTIONS
 *--------------------------------------------------------------------
 */

/*
 * Allocate memory for data structure of type UserData
 */

static UserData AllocUserData(void)
{
  int jx, jy;
  UserData data;

  data = (UserData)malloc(sizeof *data);

  for (jx = 0; jx < MXSUB; jx++)
  {
    for (jy = 0; jy < MYSUB; jy++)
    {
      (data->P)[jx][jy]     = SUNDlsMat_newDenseMat(NUM_SPECIES, NUM_SPECIES);
      (data->pivot)[jx][jy] = SUNDlsMat_newIndexArray(NUM_SPECIES);
    }
  }

  acoef = SUNDlsMat_newDenseMat(NUM_SPECIES, NUM_SPECIES);
  bcoef = (sunrealtype*)malloc(NUM_SPECIES * sizeof(sunrealtype));
  cox   = (sunrealtype*)malloc(NUM_SPECIES * sizeof(sunrealtype));
  coy   = (sunrealtype*)malloc(NUM_SPECIES * sizeof(sunrealtype));

  return (data);
}

/*
 * Load problem constants in data
 */

static void InitUserData(int my_pe, MPI_Comm comm, UserData data)
{
  int i, j, np;
  sunrealtype *a1, *a2, *a3, *a4, dx2, dy2;

  data->mx        = MX;
  data->my        = MY;
  data->ns        = NUM_SPECIES;
  data->np        = NUM_SPECIES / 2;
  data->ax        = AX;
  data->ay        = AY;
  data->dx        = (data->ax) / (MX - 1);
  data->dy        = (data->ay) / (MY - 1);
  data->uround    = SUN_UNIT_ROUNDOFF;
  data->sqruround = sqrt(data->uround);
  data->my_pe     = my_pe;
  data->comm      = comm;
  data->isuby     = my_pe / NPEX;
  data->isubx     = my_pe - data->isuby * NPEX;
  data->nsmxsub   = NUM_SPECIES * MXSUB;
  data->nsmxsub2  = NUM_SPECIES * (MXSUB + 2);

  /* Set up the coefficients a and b plus others found in the equations */
  np = data->np;

  dx2 = (data->dx) * (data->dx);
  dy2 = (data->dy) * (data->dy);

  for (i = 0; i < np; i++)
  {
    a1 = &(acoef[i][np]);
    a2 = &(acoef[i + np][0]);
    a3 = &(acoef[i][0]);
    a4 = &(acoef[i + np][np]);

    /*  Fill in the portion of acoef in the four quadrants, row by row */
    for (j = 0; j < np; j++)
    {
      *a1++ = -GG;
      *a2++ = EE;
      *a3++ = ZERO;
      *a4++ = ZERO;
    }

    /* and then change the diagonal elements of acoef to -AA */
    acoef[i][i]           = -AA;
    acoef[i + np][i + np] = -AA;

    bcoef[i]      = BB;
    bcoef[i + np] = -BB;

    cox[i]      = DPREY / dx2;
    cox[i + np] = DPRED / dx2;

    coy[i]      = DPREY / dy2;
    coy[i + np] = DPRED / dy2;
  }
}

/*
 * Free data memory
 */

static void FreeUserData(UserData data)
{
  int jx, jy;

  for (jx = 0; jx < MXSUB; jx++)
  {
    for (jy = 0; jy < MYSUB; jy++)
    {
      SUNDlsMat_destroyMat((data->P)[jx][jy]);
      SUNDlsMat_destroyArray((data->pivot)[jx][jy]);
    }
  }

  SUNDlsMat_destroyMat(acoef);
  free(bcoef);
  free(cox);
  free(coy);
  N_VDestroy(data->rates);
  free(data);
}

/*
 * Set initial conditions in cc
 */

static void SetInitialProfiles(N_Vector cc, N_Vector sc)
{
  int i, jx, jy;
  sunrealtype *cloc, *sloc;
  sunrealtype ctemp[NUM_SPECIES], stemp[NUM_SPECIES];

  /* Initialize arrays ctemp and stemp used in the loading process */
  for (i = 0; i < NUM_SPECIES / 2; i++)
  {
    ctemp[i] = PREYIN;
    stemp[i] = ONE;
  }
  for (i = NUM_SPECIES / 2; i < NUM_SPECIES; i++)
  {
    ctemp[i] = PREDIN;
    stemp[i] = SUN_RCONST(0.00001);
  }

  /* Load initial profiles into cc and sc vector from ctemp and stemp. */
  for (jy = 0; jy < MYSUB; jy++)
  {
    for (jx = 0; jx < MXSUB; jx++)
    {
      cloc = IJ_Vptr(cc, jx, jy);
      sloc = IJ_Vptr(sc, jx, jy);
      for (i = 0; i < NUM_SPECIES; i++)
      {
        cloc[i] = ctemp[i];
        sloc[i] = stemp[i];
      }
    }
  }
}

/*
 * Print first lines of output (problem description)
 */

static void PrintHeader(int globalstrategy, int maxl, int maxlrst,
                        sunrealtype fnormtol, sunrealtype scsteptol)
{
  printf("\nPredator-prey test problem --  KINSol (parallel version)\n\n");

  printf("Mesh dimensions = %d X %d\n", MX, MY);
  printf("Number of species = %d\n", NUM_SPECIES);
  printf("Total system size = %d\n\n", NEQ);
  printf("Subgrid dimensions = %d X %d\n", MXSUB, MYSUB);
  printf("Processor array is %d X %d\n\n", NPEX, NPEY);
  printf("Flag globalstrategy = %d (0 = None, 1 = Linesearch)\n", globalstrategy);
  printf("Linear solver is SPGMR with maxl = %d, maxlrst = %d\n", maxl, maxlrst);
  printf("Preconditioning uses interaction-only block-diagonal matrix\n");

#if defined(SUNDIALS_EXTENDED_PRECISION)
  printf("Tolerance parameters:  fnormtol = %Lg   scsteptol = %Lg\n", fnormtol,
         scsteptol);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
  printf("Tolerance parameters:  fnormtol = %g   scsteptol = %g\n", fnormtol,
         scsteptol);
#else
  printf("Tolerance parameters:  fnormtol = %g   scsteptol = %g\n", fnormtol,
         scsteptol);
#endif

  printf("\nInitial profile of concentration\n");
#if defined(SUNDIALS_EXTENDED_PRECISION)
  printf("At all mesh points:  %Lg %Lg %Lg   %Lg %Lg %Lg\n", PREYIN, PREYIN,
         PREYIN, PREDIN, PREDIN, PREDIN);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
  printf("At all mesh points:  %g %g %g   %g %g %g\n", PREYIN, PREYIN, PREYIN,
         PREDIN, PREDIN, PREDIN);
#else
  printf("At all mesh points:  %g %g %g   %g %g %g\n", PREYIN, PREYIN, PREYIN,
         PREDIN, PREDIN, PREDIN);
#endif
}

/*
 * Print sampled values of current cc
 */

static void PrintOutput(int my_pe, MPI_Comm comm, N_Vector cc)
{
  int is, i0, npelast;
  sunrealtype *ct, tempc[NUM_SPECIES];
  MPI_Status status;

  npelast = NPEX * NPEY - 1;

  ct = N_VGetArrayPointer(cc);

  /* Send the cc values (for all species) at the top right mesh point to PE 0 */
  if (my_pe == npelast)
  {
    i0 = NUM_SPECIES * (MXSUB * MYSUB - 1);
    if (npelast != 0)
    {
      MPI_Send(&ct[i0], NUM_SPECIES, MPI_SUNREALTYPE, 0, 0, comm);
    }
    else
    { /* single processor case */
      for (is = 0; is < NUM_SPECIES; is++) { tempc[is] = ct[i0 + is]; }
    }
  }

  /* On PE 0, receive the cc values at top right, then print performance data
     and sampled solution values */
  if (my_pe == 0)
  {
    if (npelast != 0)
    {
      MPI_Recv(&tempc[0], NUM_SPECIES, MPI_SUNREALTYPE, npelast, 0, comm,
               &status);
    }

    printf("\nAt bottom left:");
    for (is = 0; is < NUM_SPECIES; is++)
    {
      if ((is % 6) * 6 == is) { printf("\n"); }
#if defined(SUNDIALS_EXTENDED_PRECISION)
      printf(" %Lg", ct[is]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
      printf(" %g", ct[is]);
#else
      printf(" %g", ct[is]);
#endif
    }

    printf("\n\nAt top right:");
    for (is = 0; is < NUM_SPECIES; is++)
    {
      if ((is % 6) * 6 == is) { printf("\n"); }
#if defined(SUNDIALS_EXTENDED_PRECISION)
      printf(" %Lg", tempc[is]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
      printf(" %g", tempc[is]);
#else
      printf(" %g", tempc[is]);
#endif
    }
    printf("\n\n");
  }
}

/*
 * Print final statistics contained in iopt
 */

static void PrintFinalStats(void* kmem)
{
  long int nni, nfe, nli, npe, nps, ncfl, nfeSG;
  int retval;

  retval = KINGetNumNonlinSolvIters(kmem, &nni);
  check_retval(&retval, "KINGetNumNonlinSolvIters", 1, 0);
  retval = KINGetNumFuncEvals(kmem, &nfe);
  check_retval(&retval, "KINGetNumFuncEvals", 1, 0);
  retval = KINGetNumLinIters(kmem, &nli);
  check_retval(&retval, "KINGetNumLinIters", 1, 0);
  retval = KINGetNumPrecEvals(kmem, &npe);
  check_retval(&retval, "KINGetNumPrecEvals", 1, 0);
  retval = KINGetNumPrecSolves(kmem, &nps);
  check_retval(&retval, "KINGetNumPrecSolves", 1, 0);
  retval = KINGetNumLinConvFails(kmem, &ncfl);
  check_retval(&retval, "KINGetNumLinConvFails", 1, 0);
  retval = KINGetNumLinFuncEvals(kmem, &nfeSG);
  check_retval(&retval, "KINGetNumLinFuncEvals", 1, 0);

  printf("Final Statistics.. \n");
  printf("nni    = %5ld    nli   = %5ld\n", nni, nli);
  printf("nfe    = %5ld    nfeSG = %5ld\n", nfe, nfeSG);
  printf("nps    = %5ld    npe   = %5ld     ncfl  = %5ld\n", nps, npe, ncfl);
}

/*
 * Routine to send boundary data to neighboring PEs
 */

static void BSend(MPI_Comm comm, int my_pe, int isubx, int isuby, int dsizex,
                  int dsizey, sunrealtype* cdata)
{
  int i, ly;
  int offsetc, offsetbuf;
  sunrealtype bufleft[NUM_SPECIES * MYSUB], bufright[NUM_SPECIES * MYSUB];

  /* If isuby > 0, send data from bottom x-line of u */
  if (isuby != 0)
  {
    MPI_Send(&cdata[0], dsizex, MPI_SUNREALTYPE, my_pe - NPEX, 0, comm);
  }

  /* If isuby < NPEY-1, send data from top x-line of u */
  if (isuby != NPEY - 1)
  {
    offsetc = (MYSUB - 1) * dsizex;
    MPI_Send(&cdata[offsetc], dsizex, MPI_SUNREALTYPE, my_pe + NPEX, 0, comm);
  }

  /* If isubx > 0, send data from left y-line of u (via bufleft) */
  if (isubx != 0)
  {
    for (ly = 0; ly < MYSUB; ly++)
    {
      offsetbuf = ly * NUM_SPECIES;
      offsetc   = ly * dsizex;
      for (i = 0; i < NUM_SPECIES; i++)
      {
        bufleft[offsetbuf + i] = cdata[offsetc + i];
      }
    }
    MPI_Send(&bufleft[0], dsizey, MPI_SUNREALTYPE, my_pe - 1, 0, comm);
  }

  /* If isubx < NPEX-1, send data from right y-line of u (via bufright) */
  if (isubx != NPEX - 1)
  {
    for (ly = 0; ly < MYSUB; ly++)
    {
      offsetbuf = ly * NUM_SPECIES;
      offsetc   = offsetbuf * MXSUB + (MXSUB - 1) * NUM_SPECIES;
      for (i = 0; i < NUM_SPECIES; i++)
      {
        bufright[offsetbuf + i] = cdata[offsetc + i];
      }
    }
    MPI_Send(&bufright[0], dsizey, MPI_SUNREALTYPE, my_pe + 1, 0, comm);
  }
}

/*
 * Routine to start receiving boundary data from neighboring PEs.
 *  Notes:
 *  1) buffer should be able to hold 2*NUM_SPECIES*MYSUB sunrealtype entries,
 *     should be passed to both the BRecvPost and BRecvWait functions, and
 *     should not be manipulated between the two calls.
 *  2) request should have 4 entries, and should be passed in both calls also.
 */

static void BRecvPost(MPI_Comm comm, MPI_Request request[], int my_pe,
                      int isubx, int isuby, int dsizex, int dsizey,
                      sunrealtype* cext, sunrealtype* buffer)
{
  int offsetce;

  /* Have bufleft and bufright use the same buffer */
  sunrealtype *bufleft = buffer, *bufright = buffer + NUM_SPECIES * MYSUB;

  /* If isuby > 0, receive data for bottom x-line of cext */
  if (isuby != 0)
  {
    MPI_Irecv(&cext[NUM_SPECIES], dsizex, MPI_SUNREALTYPE, my_pe - NPEX, 0,
              comm, &request[0]);
  }

  /* If isuby < NPEY-1, receive data for top x-line of cext */
  if (isuby != NPEY - 1)
  {
    offsetce = NUM_SPECIES * (1 + (MYSUB + 1) * (MXSUB + 2));
    MPI_Irecv(&cext[offsetce], dsizex, MPI_SUNREALTYPE, my_pe + NPEX, 0, comm,
              &request[1]);
  }

  /* If isubx > 0, receive data for left y-line of cext (via bufleft) */
  if (isubx != 0)
  {
    MPI_Irecv(&bufleft[0], dsizey, MPI_SUNREALTYPE, my_pe - 1, 0, comm,
              &request[2]);
  }

  /* If isubx < NPEX-1, receive data for right y-line of cext (via bufright) */
  if (isubx != NPEX - 1)
  {
    MPI_Irecv(&bufright[0], dsizey, MPI_SUNREALTYPE, my_pe + 1, 0, comm,
              &request[3]);
  }
}

/*
 * Routine to finish receiving boundary data from neighboring PEs.
 *  Notes:
 *  1) buffer should be able to hold 2*NUM_SPECIES*MYSUB sunrealtype entries,
 *     should be passed to both the BRecvPost and BRecvWait functions, and
 *  should not be manipulated between the two calls.
 *  2) request should have 4 entries, and should be passed in both calls also.
 */

static void BRecvWait(MPI_Request request[], int isubx, int isuby, int dsizex,
                      sunrealtype* cext, sunrealtype* buffer)
{
  int i, ly;
  int dsizex2, offsetce, offsetbuf;
  sunrealtype *bufleft = buffer, *bufright = buffer + NUM_SPECIES * MYSUB;
  MPI_Status status;

  dsizex2 = dsizex + 2 * NUM_SPECIES;

  /* If isuby > 0, receive data for bottom x-line of cext */
  if (isuby != 0) { MPI_Wait(&request[0], &status); }

  /* If isuby < NPEY-1, receive data for top x-line of cext */
  if (isuby != NPEY - 1) { MPI_Wait(&request[1], &status); }

  /* If isubx > 0, receive data for left y-line of cext (via bufleft) */
  if (isubx != 0)
  {
    MPI_Wait(&request[2], &status);

    /* Copy the buffer to cext */
    for (ly = 0; ly < MYSUB; ly++)
    {
      offsetbuf = ly * NUM_SPECIES;
      offsetce  = (ly + 1) * dsizex2;
      for (i = 0; i < NUM_SPECIES; i++)
      {
        cext[offsetce + i] = bufleft[offsetbuf + i];
      }
    }
  }

  /* If isubx < NPEX-1, receive data for right y-line of cext (via bufright) */
  if (isubx != NPEX - 1)
  {
    MPI_Wait(&request[3], &status);

    /* Copy the buffer to cext */
    for (ly = 0; ly < MYSUB; ly++)
    {
      offsetbuf = ly * NUM_SPECIES;
      offsetce  = (ly + 2) * dsizex2 - NUM_SPECIES;
      for (i = 0; i < NUM_SPECIES; i++)
      {
        cext[offsetce + i] = bufright[offsetbuf + i];
      }
    }
  }
}

/*
 * ccomm routine.  This routine performs all communication
 * between processors of data needed to calculate f.
 */

static void ccomm(sunrealtype* cdata, UserData data)
{
  sunrealtype *cext, buffer[2 * NUM_SPECIES * MYSUB];
  MPI_Comm comm;
  int my_pe, isubx, isuby, nsmxsub, nsmysub;
  MPI_Request request[4];

  /* Get comm, my_pe, subgrid indices, data sizes, extended array cext */
  comm    = data->comm;
  my_pe   = data->my_pe;
  isubx   = data->isubx;
  isuby   = data->isuby;
  nsmxsub = data->nsmxsub;
  nsmysub = NUM_SPECIES * MYSUB;
  cext    = data->cext;

  /* Start receiving boundary data from neighboring PEs */
  BRecvPost(comm, request, my_pe, isubx, isuby, nsmxsub, nsmysub, cext, buffer);

  /* Send data from boundary of local grid to neighboring PEs */
  BSend(comm, my_pe, isubx, isuby, nsmxsub, nsmysub, cdata);

  /* Finish receiving boundary data from neighboring PEs */
  BRecvWait(request, isubx, isuby, nsmxsub, cext, buffer);
}

/*
 * System function for predator-prey system - calculation part
 */

static void fcalcprpr(N_Vector cc, N_Vector fval, void* user_data)
{
  sunrealtype xx, yy, *cxy, *rxy, *fxy, dcydi, dcyui, dcxli, dcxri;
  sunrealtype *cext, dely, delx, *cdata;
  int i, jx, jy, is, ly;
  int isubx, isuby, nsmxsub, nsmxsub2;
  int shifty, offsetc, offsetce, offsetcl, offsetcr, offsetcd, offsetcu;
  UserData data;

  data  = (UserData)user_data;
  cdata = N_VGetArrayPointer(cc);

  /* Get subgrid indices, data sizes, extended work array cext */
  isubx    = data->isubx;
  isuby    = data->isuby;
  nsmxsub  = data->nsmxsub;
  nsmxsub2 = data->nsmxsub2;
  cext     = data->cext;

  /* Copy local segment of cc vector into the working extended array cext */
  offsetc  = 0;
  offsetce = nsmxsub2 + NUM_SPECIES;
  for (ly = 0; ly < MYSUB; ly++)
  {
    for (i = 0; i < nsmxsub; i++) { cext[offsetce + i] = cdata[offsetc + i]; }
    offsetc  = offsetc + nsmxsub;
    offsetce = offsetce + nsmxsub2;
  }

  /* To facilitate homogeneous Neumann boundary conditions, when this is a
  boundary PE, copy data from the first interior mesh line of cc to cext   */

  /* If isuby = 0, copy x-line 2 of cc to cext */
  if (isuby == 0)
  {
    for (i = 0; i < nsmxsub; i++)
    {
      cext[NUM_SPECIES + i] = cdata[nsmxsub + i];
    }
  }

  /* If isuby = NPEY-1, copy x-line MYSUB-1 of cc to cext */
  if (isuby == NPEY - 1)
  {
    offsetc  = (MYSUB - 2) * nsmxsub;
    offsetce = (MYSUB + 1) * nsmxsub2 + NUM_SPECIES;
    for (i = 0; i < nsmxsub; i++) { cext[offsetce + i] = cdata[offsetc + i]; }
  }

  /* If isubx = 0, copy y-line 2 of cc to cext */
  if (isubx == 0)
  {
    for (ly = 0; ly < MYSUB; ly++)
    {
      offsetc  = ly * nsmxsub + NUM_SPECIES;
      offsetce = (ly + 1) * nsmxsub2;
      for (i = 0; i < NUM_SPECIES; i++)
      {
        cext[offsetce + i] = cdata[offsetc + i];
      }
    }
  }

  /* If isubx = NPEX-1, copy y-line MXSUB-1 of cc to cext */
  if (isubx == NPEX - 1)
  {
    for (ly = 0; ly < MYSUB; ly++)
    {
      offsetc  = (ly + 1) * nsmxsub - 2 * NUM_SPECIES;
      offsetce = (ly + 2) * nsmxsub2 - NUM_SPECIES;
      for (i = 0; i < NUM_SPECIES; i++)
      {
        cext[offsetce + i] = cdata[offsetc + i];
      }
    }
  }

  /* Loop over all mesh points, evaluating rate arra at each point */
  delx   = data->dx;
  dely   = data->dy;
  shifty = (MXSUB + 2) * NUM_SPECIES;

  for (jy = 0; jy < MYSUB; jy++)
  {
    yy = dely * (jy + isuby * MYSUB);

    for (jx = 0; jx < MXSUB; jx++)
    {
      xx  = delx * (jx + isubx * MXSUB);
      cxy = IJ_Vptr(cc, jx, jy);
      rxy = IJ_Vptr(data->rates, jx, jy);
      fxy = IJ_Vptr(fval, jx, jy);

      WebRate(xx, yy, cxy, rxy, user_data);

      offsetc  = (jx + 1) * NUM_SPECIES + (jy + 1) * NSMXSUB2;
      offsetcd = offsetc - shifty;
      offsetcu = offsetc + shifty;
      offsetcl = offsetc - NUM_SPECIES;
      offsetcr = offsetc + NUM_SPECIES;

      for (is = 0; is < NUM_SPECIES; is++)
      {
        /* differencing in x */
        dcydi = cext[offsetc + is] - cext[offsetcd + is];
        dcyui = cext[offsetcu + is] - cext[offsetc + is];

        /* differencing in y */
        dcxli = cext[offsetc + is] - cext[offsetcl + is];
        dcxri = cext[offsetcr + is] - cext[offsetc + is];

        /* compute the value at xx , yy */
        fxy[is] = (coy)[is] * (dcyui - dcydi) + (cox)[is] * (dcxri - dcxli) +
                  rxy[is];

      } /* end of is loop */

    } /* end of jx loop */

  } /* end of jy loop */
}

/*
 * Check function return value...
 *    opt == 0 means SUNDIALS function allocates memory so check if
 *             returned NULL pointer
 *    opt == 1 means SUNDIALS function returns a retval so check if
 *             retval >= 0
 *    opt == 2 means function allocates memory so check if returned
 *             NULL pointer
 */

static int check_retval(void* retvalvalue, const char* funcname, int opt, int id)
{
  int* errretval;

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

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

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

  return (0);
}
