/*---------------------------------------------------------------
 * Programmer(s): Shelby Lockhart @ LLNL
 *---------------------------------------------------------------
 * Based on the serial code ark_heat1D.c developed by
 * Daniel R. Reynolds @ SMU and parallelized with OpenMP
 *---------------------------------------------------------------
 * 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 simple 1D heat equation,
 *    u_t = k*u_xx + f
 * for t in [0, 10], x in [0, 1], with initial conditions
 *    u(0,x) =  0
 * Dirichlet boundary conditions, i.e.
 *    u_t(t,0) = u_t(t,1) = 0,
 * and a point-source heating term,
 *    f = 1 for x=0.5.
 *
 * The spatial derivatives are computed using second-order
 * centered differences, with the data distributed over N points
 * on a uniform spatial grid.
 *
 * This program solves the problem with either an ERK or DIRK
 * method.  For the DIRK method, we use a Newton iteration with
 * the SUNPCG linear solver, and a user-supplied Jacobian-vector
 * product routine.
 *
 * 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_openmp.h> /* OpenMP N_Vector types, fcts., macros */
#include <stdio.h>
#include <stdlib.h>
#include <sundials/sundials_types.h> /* defs. of sunrealtype, sunindextype, etc */
#include <sunlinsol/sunlinsol_pcg.h> /* access to PCG SUNLinearSolver        */

#ifdef _OPENMP
#include <omp.h> /* OpenMP function defs.                */
#endif

#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

/* user data structure */
typedef struct
{
  sunindextype N; /* number of intervals      */
  int nthreads;   /* number of OpenMP threads */
  sunrealtype dx; /* mesh spacing             */
  sunrealtype k;  /* diffusion coefficient    */
}* 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(N_Vector v, N_Vector Jv, sunrealtype t, N_Vector y, N_Vector fy,
               void* user_data, N_Vector tmp);

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

/* Main Program */
int main(int argc, char* argv[])
{
  /* general problem parameters */
  sunrealtype T0   = SUN_RCONST(0.0); /* initial time */
  sunrealtype Tf   = SUN_RCONST(1.0); /* final time */
  int Nt           = 10;              /* total number of output times */
  sunrealtype rtol = 1.e-6;           /* relative tolerance */
  sunrealtype atol = 1.e-10;          /* absolute tolerance */
  UserData udata   = NULL;
  sunrealtype* data;
  sunindextype N = 201; /* spatial mesh size */
  sunrealtype k  = 0.5; /* heat conductivity */
  sunindextype i;

  /* general problem variables */
  int flag;                  /* reusable error-checking flag */
  N_Vector y         = NULL; /* empty vector for storing solution */
  SUNLinearSolver LS = NULL; /* empty linear solver object */
  void* arkode_mem   = NULL; /* empty ARKODE memory structure */
  FILE *FID, *UFID;
  sunrealtype t, dTout, tout;
  int iout, num_threads;
  long int nst, nst_a, nfe, nfi, nsetups, nli, nJv, nlcf, 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; }

  /* set the number of threads to use */
  num_threads = 1; /* default value */
#ifdef _OPENMP
  num_threads =
    omp_get_max_threads(); /* overwrite with OMP_NUM_THREADS environment variable */
#endif
  if (argc > 1)
  { /* overwrite with command line value, if supplied */
    num_threads = (int)strtol(argv[1], NULL, 0);
  }

  /* allocate and fill udata structure */
  udata           = (UserData)malloc(sizeof(*udata));
  udata->N        = N;
  udata->k        = k;
  udata->dx       = SUN_RCONST(1.0) / (N - 1); /* mesh spacing */
  udata->nthreads = num_threads;

  /* Initial problem output */
  printf("\n1D Heat PDE test problem:\n");
  printf("  N = %li\n", (long int)udata->N);
  printf("  diffusion coefficient:  k = %" GSYM "\n", udata->k);

  /* Initialize data structures */
  y = N_VNew_OpenMP(N, num_threads, ctx); /* Create OpenMP vector for solution */
  if (check_flag((void*)y, "N_VNew_OpenMP", 0)) { return 1; }
  N_VConst(0.0, y);                                /* Set initial conditions */
  arkode_mem = ARKStepCreate(NULL, f, T0, y, ctx); /* Create the solver memory */
  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 = ARKodeSetMaxNumSteps(arkode_mem, 10000); /* Increase max num steps  */
  if (check_flag(&flag, "ARKodeSetMaxNumSteps", 1)) { return 1; }
  flag = ARKodeSetPredictorMethod(arkode_mem,
                                  1); /* Specify maximum-order predictor */
  if (check_flag(&flag, "ARKodeSetPredictorMethod", 1)) { return 1; }
  flag = ARKodeSStolerances(arkode_mem, rtol, atol); /* Specify tolerances */
  if (check_flag(&flag, "ARKodeSStolerances", 1)) { return 1; }

  /* Initialize PCG solver -- no preconditioning, with up to N iterations  */
  LS = SUNLinSol_PCG(y, 0, (int)N, ctx);
  if (check_flag((void*)LS, "SUNLinSol_PCG", 0)) { return 1; }

  /* Linear solver interface -- set user-supplied J*v routine (no 'jtsetup' required) */
  flag = ARKodeSetLinearSolver(arkode_mem, LS,
                               NULL); /* Attach linear solver to ARKODE */
  if (check_flag(&flag, "ARKodeSetLinearSolver", 1)) { return 1; }
  flag = ARKodeSetJacTimes(arkode_mem, NULL, Jac); /* Set the Jacobian routine */
  if (check_flag(&flag, "ARKodeSetJacTimes", 1)) { return 1; }

  /* Specify linearly implicit RHS, with non-time-dependent Jacobian */
  flag = ARKodeSetLinear(arkode_mem, 0);
  if (check_flag(&flag, "ARKodeSetLinear", 1)) { return 1; }

  /* output mesh to disk */
  FID = fopen("heat_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 array */
  UFID = fopen("heat1D.txt", "w");
  data = N_VGetArrayPointer(y);

  /* output initial condition to disk */
  for (i = 0; i < N; i++) { fprintf(UFID, " %.16" ESYM "", data[i]); }
  fprintf(UFID, "\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 - T0) / Nt;
  tout  = T0 + dTout;
  printf("        t      ||u||_rms\n");
  printf("   -------------------------\n");
  printf("  %10.6" FSYM "  %10.6f\n", t, sqrt(N_VDotProd(y, y) / N));
  for (iout = 0; iout < Nt; iout++)
  {
    flag = ARKodeEvolve(arkode_mem, tout, y, &t, ARK_NORMAL); /* call integrator */
    if (check_flag(&flag, "ARKodeEvolve", 1)) { break; }
    printf("  %10.6" FSYM "  %10.6f\n", t,
           sqrt(N_VDotProd(y, y) / N)); /* print solution stats */
    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[i]); }
    fprintf(UFID, "\n");
  }
  printf("   -------------------------\n");
  fclose(UFID);

  /* 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 = ARKodeGetNumRhsEvals(arkode_mem, 0, &nfe);
  check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
  flag = ARKodeGetNumRhsEvals(arkode_mem, 1, &nfi);
  check_flag(&flag, "ARKodeGetNumRhsEvals", 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 = ARKodeGetNumLinIters(arkode_mem, &nli);
  check_flag(&flag, "ARKodeGetNumLinIters", 1);
  flag = ARKodeGetNumJtimesEvals(arkode_mem, &nJv);
  check_flag(&flag, "ARKodeGetNumJtimesEvals", 1);
  flag = ARKodeGetNumLinConvFails(arkode_mem, &nlcf);
  check_flag(&flag, "ARKodeGetNumLinConvFails", 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 linear iterations = %li\n", nli);
  printf("   Total number of Jacobian-vector products = %li\n", nJv);
  printf("   Total number of linear solver convergence failures = %li\n", nlcf);
  printf("   Total number of Newton 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 */
  free(udata);             /* Free user data */
  ARKodeFree(&arkode_mem); /* Free integrator memory */
  SUNLinSolFree(LS);       /* Free linear solver */
  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 k  = udata->k;
  sunrealtype dx = udata->dx;
  sunrealtype *Y = NULL, *Ydot = NULL;
  sunrealtype c1, c2;
  sunindextype i = 0;
  sunindextype isource;

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

  /* iterate over domain, computing all equations */
  c1      = k / dx / dx;
  c2      = -SUN_RCONST(2.0) * k / dx / dx;
  isource = N / 2;
  Ydot[0] = 0.0; /* left boundary condition */
#pragma omp parallel for default(shared) private(i) schedule(static) \
  num_threads(udata->nthreads)
  for (i = 1; i < N - 1; i++)
  {
    Ydot[i] = c1 * Y[i - 1] + c2 * Y[i] + c1 * Y[i + 1];
  }
  Ydot[N - 1] = 0.0;          /* right boundary condition */
  Ydot[isource] += 0.01 / dx; /* source term */

  return 0; /* Return with success */
}

/* Jacobian routine to compute J(t,y) = df/dy. */
static int Jac(N_Vector v, N_Vector Jv, sunrealtype t, N_Vector y, N_Vector fy,
               void* user_data, N_Vector tmp)
{
  UserData udata = (UserData)user_data; /* variable shortcuts */
  sunindextype N = udata->N;
  sunrealtype k  = udata->k;
  sunrealtype dx = udata->dx;
  sunrealtype *V = NULL, *JV = NULL;
  sunrealtype c1, c2;
  sunindextype i = 0;

  V = N_VGetArrayPointer(v); /* access data arrays */
  if (check_flag((void*)V, "N_VGetArrayPointer", 0)) { return 1; }
  JV = N_VGetArrayPointer(Jv);
  if (check_flag((void*)JV, "N_VGetArrayPointer", 0)) { return 1; }
  N_VConst(0.0, Jv); /* initialize Jv product to zero */

  /* iterate over domain, computing all Jacobian-vector products */
  c1    = k / dx / dx;
  c2    = -SUN_RCONST(2.0) * k / dx / dx;
  JV[0] = 0.0;
#pragma omp parallel for default(shared) private(i) schedule(static) \
  num_threads(udata->nthreads)
  for (i = 1; i < N - 1; i++)
  {
    JV[i] = c1 * V[i - 1] + c2 * V[i] + c1 * V[i + 1];
  }
  JV[N - 1] = 0.0;

  return 0; /* Return with success */
}

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

/* 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 ----*/
