/* -----------------------------------------------------------------------------
 * Programmer(s): David J. Gardner @ LLNL
 * -----------------------------------------------------------------------------
 * SUNDIALS Copyright Start
 * Copyright (c) 2002-2020, 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
 * -----------------------------------------------------------------------------
 * Unit test for arkStep_SetInnerForcing
 *
 * arkStep_SetInnerForcing is used to provide a polynomial forcing term in
 * ARKStep when it is used as the inner integrator under MRIStep. To check that
 * the forcing is computed and applied correctly we integrate an ODE in time
 * with ARKStep where to RHS consists of only the polynomial forcing term. The
 * solution should be exact when the method order is greater than or equal to
 * the polynomial order.
 * ---------------------------------------------------------------------------*/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#include "arkode/arkode_arkstep.h"
#include "nvector/nvector_serial.h"
#include "sunmatrix/sunmatrix_dense.h"
#include "sunlinsol/sunlinsol_dense.h"
#include "sundials/sundials_types.h"
#include "sundials/sundials_math.h"

#include "arkode/arkode_arkstep_impl.h"

#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-supplied Functions Called by the Solver */
static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data);

static int Jac(realtype 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 check_flag(void *flagvalue, const char *funcname, int opt);

/* Private function to check computed solution */
static int compute_ans(realtype t, realtype tshift, realtype tscale,
                       N_Vector* forcing, int order, N_Vector ans);
static int compute_error(N_Vector y, N_Vector ans, N_Vector tmp, realtype rtol,
                         realtype atol);

/* Main Program */
int main(int argc, char *argv[])
{
  /* default input values */
  sunindextype NEQ    = 1;           /* number of dependent vars.    */
  int          order  = 3;           /* order of polynomial forcing  */
  realtype     T0     = RCONST(0.0); /* initial time                 */
  realtype     Tf     = RCONST(1.0); /* final time                   */
  realtype     tshift = T0;          /* time shift for normalization */
  realtype     tscale = Tf;          /* time scale for normalization */

  /* tolerances */
  realtype reltol = SUNRsqrt(UNIT_ROUNDOFF);
  realtype abstol = SUNRsqrt(UNIT_ROUNDOFF)/100;

  /* general problem variables */
  int flag;                  /* reusable error-checking flag             */
  N_Vector y   = NULL;       /* vector for storing the computed solution */
  N_Vector ans = NULL;       /* vector for storing the true solution     */
  N_Vector tmp = NULL;       /* temporary workspace vector               */
  N_Vector* forcing = NULL;  /* array of forcing vectors                 */
  SUNMatrix A = NULL;        /* matrix for linear solver                 */
  SUNLinearSolver LS = NULL; /* linear solver object                     */
  void *arkode_mem = NULL;   /* ARKode memory structure                  */
  int i, j;                  /* loop counters                            */
  realtype tret;             /* integrator return time                   */
  realtype* data;            /* array for accessing vector data          */
  long int nst, nst_a;       /* number of integrator steps               */
  long int mxsteps = 100000; /* max steps before output                  */

  /* check inputs */
  if (argc > 1) {
    NEQ = (sunindextype) atol(argv[1]);
    if (NEQ <= 0) {
      printf("ERROR: The problem size must be a positive integer\n");
      return(1);
    }
  }

  if (argc > 2) {
    order = (int) atol(argv[2]);
    if (order < 0) {
      printf("ERROR: The polynomial order must be a non-negative integer\n");
      return(1);
    }
  }

  if (argc > 3) {
    if (argc < 5) {
      printf("ERROR: Both the initial and final time are required\n");
      return(1);
    }
    T0 = (realtype) atof(argv[3]);
    Tf = (realtype) atof(argv[4]);
    if (SUNRabs(T0) >= SUNRabs(Tf)) {
      printf("ERROR: |T0| must be less than |Tf|\n");
      return(1);
    }
  }

  if (argc > 5) {
    if (argc < 7) {
      printf("ERROR: Both tshift and tscale are required\n");
      return(1);
    }
    tshift = (realtype) atof(argv[5]);
    tscale = (realtype) atof(argv[6]);
    if (SUNRabs(tscale) < TINY) {
      printf("ERROR: |tscale| must be greater than %"GSYM"\n", TINY);
      return(1);
    }
  }

  /* Output test setup */
  printf("\narkStep_SetInnerForcing unit test:\n");
  printf("   NEQ    = %li\n",         (long int) NEQ);
  printf("   order  = %i\n",          order);
  printf("   t0     = %.1"GSYM"\n",   T0);
  printf("   tf     = %.1"GSYM"\n",   Tf);
  printf("   tshift = %.1"GSYM"\n",   tshift);
  printf("   tscale = %.1"GSYM"\n",   tscale);
  printf("   reltol = %.1"ESYM"\n",   reltol);
  printf("   abstol = %.1"ESYM"\n\n", abstol);

  /* Create solution vector and initialize to zero */
  y = N_VNew_Serial(NEQ);
  if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;

  ans = N_VClone(y);
  if (check_flag((void *)ans, "N_VClone", 0)) return 1;

  tmp = N_VClone(y);
  if (check_flag((void *)tmp, "N_VClone", 0)) return 1;

  /* Initialize dense matrix data structure and solver */
  A = SUNDenseMatrix(NEQ, NEQ);
  if (check_flag((void *)A, "SUNDenseMatrix", 0)) return 1;

  LS = SUNLinSol_Dense(y, A);
  if (check_flag((void *)LS, "SUNLinSol_Dense", 0)) return 1;

  /* allocate vector array for polynomial forcing */
  forcing = N_VCloneVectorArray(order + 1, y);
  if (check_flag((void *)forcing, "N_VCloneVectorArray", 0)) return 1;
  for (i = 0; i < order + 1; i++) {
    if (check_flag((void *)forcing[i], "N_VCloneVectorArray", 0)) return 1;
  }

  /* fill forcing vectors with random data */
  for (i = 0; i < order + 1; i++) {
    data = N_VGetArrayPointer(forcing[i]);
    for (j = 0; j < NEQ; j++) {
      data[j] = (realtype) rand() / (realtype) RAND_MAX;
    }
  }

  /* compute the true solution */
  flag = compute_ans(Tf, tshift, tscale, forcing, order, ans);
  if (check_flag(&flag, "compute_ans", 1)) return 1;

  printf("True solution:\n");
  N_VPrint_Serial(ans);

  /* ---------------------------------------------------------------------------
   * explicit test
   * -------------------------------------------------------------------------*/

  /* initialize solution vector */
  flag = compute_ans(T0, tshift, tscale, forcing, order, y);
  if (check_flag(&flag, "compute_ans", 1)) return 1;

  /* Create ARKode mem structure */
  arkode_mem = ARKStepCreate(f, NULL, T0, y);
  if (check_flag((void *)arkode_mem, "ARKStepCreate", 0)) return 1;

  /* Specify tolerances */
  flag = ARKStepSStolerances(arkode_mem, reltol, abstol);
  if (check_flag(&flag, "ARKStepSStolerances", 1)) return 1;

  /* Set stop time */
  flag = ARKStepSetStopTime(arkode_mem, Tf);
  if (check_flag(&flag, "ARKStepSetStopTime", 1)) return 1;

  /* Set max steps before output */
  flag = ARKStepSetMaxNumSteps(arkode_mem, mxsteps);
  if (check_flag(&flag, "ARKStepSetMaxNumSteps", 1)) return 1;

  /* Set forcing */
  flag = arkStep_SetInnerForcing(arkode_mem, tshift, tscale, forcing, order + 1);
  if (check_flag(&flag, "arkStep_SetInnerForcing", 1)) return 1;

  /* Integrate the problem */
  flag = ARKStepEvolve(arkode_mem, Tf, y, &tret, ARK_NORMAL);

  /* check for errors */
  if (flag < 0) {
    fprintf(stderr,"ARKStep failure, flag = %d\n",flag); return 1;
  }

  /* get some integrator stats */
  flag = ARKStepGetNumSteps(arkode_mem, &nst);
  check_flag(&flag, "ARKStepGetNumSteps", 1);

  flag = ARKStepGetNumStepAttempts(arkode_mem, &nst_a);
  check_flag(&flag, "ARKStepGetNumStepAttempts", 1);

  printf("Explicit stats:\n");
  printf("Steps = %li (attempted = %li)\n\n", nst, nst_a);

  /* Free integrator memory */
  ARKStepFree(&arkode_mem);
  arkode_mem = NULL;

  /* print solution */
  printf("Explicit solution:\n");
  N_VPrint_Serial(y);

  /* check the solution error */
  flag = compute_error(y, ans, tmp, reltol, abstol);
  if (flag != 0) return(1);

  /* ---------------------------------------------------------------------------
   * implicit test
   * -------------------------------------------------------------------------*/

  /* initialize solution vector */
  flag = compute_ans(T0, tshift, tscale, forcing, order, y);
  if (check_flag(&flag, "compute_ans", 1)) return 1;

  /* Create ARKode mem structure */
  arkode_mem = ARKStepCreate(NULL, f, T0, y);
  if (check_flag((void *)arkode_mem, "ARKStepCreate", 0)) return 1;

  /* Specify tolerances */
  flag = ARKStepSStolerances(arkode_mem, reltol, abstol);
  if (check_flag(&flag, "ARKStepSStolerances", 1)) return 1;

  /* Set stop time */
  flag = ARKStepSetStopTime(arkode_mem, Tf);
  if (check_flag(&flag, "ARKStepSetStopTime", 1)) return 1;

  /* Set max steps before output */
  flag = ARKStepSetMaxNumSteps(arkode_mem, mxsteps);
  if (check_flag(&flag, "ARKStepSetMaxNumSteps", 1)) return 1;

  /* Attach matrix and linear solver */
  flag = ARKStepSetLinearSolver(arkode_mem, LS, A);
  if (check_flag(&flag, "ARKStepSetLinearSolver", 1)) return 1;

  /* Set Jacobian routine */
  flag = ARKStepSetJacFn(arkode_mem, Jac);
  if (check_flag(&flag, "ARKStepSetJacFn", 1)) return 1;

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

  /* Set forcing */
  flag = arkStep_SetInnerForcing(arkode_mem, tshift, tscale, forcing, order + 1);
  if (check_flag(&flag, "arkStep_SetInnerForcing", 1)) return 1;

  /* Integrate the problem */
  flag = ARKStepEvolve(arkode_mem, Tf, y, &tret, ARK_NORMAL);

  /* check for errors */
  if (flag < 0) {
    fprintf(stderr,"ARKStep failure, flag = %d\n",flag); return 1;
  }

  /* get some integrator stats */
  flag = ARKStepGetNumSteps(arkode_mem, &nst);
  check_flag(&flag, "ARKStepGetNumSteps", 1);

  flag = ARKStepGetNumStepAttempts(arkode_mem, &nst_a);
  check_flag(&flag, "ARKStepGetNumStepAttempts", 1);

  printf("Implicit stats:\n");
  printf("Steps = %li (attempted = %li)\n\n", nst, nst_a);

  /* Free integrator memory */
  ARKStepFree(&arkode_mem);
  arkode_mem = NULL;

  /* print solution */
  printf("Implicit solution:\n");
  N_VPrint_Serial(y);

  /* check the solution error */
  flag = compute_error(y, ans, tmp, reltol, abstol);
  if (flag != 0) return(1);

  /* ---------------------------------------------------------------------------
   * imex test
   * -------------------------------------------------------------------------*/

  /* initialize solution vector */
  flag = compute_ans(T0, tshift, tscale, forcing, order, y);
  if (check_flag(&flag, "compute_ans", 1)) return 1;

  /* Create ARKode mem structure */
  arkode_mem = ARKStepCreate(f, f, T0, y);
  if (check_flag((void *)arkode_mem, "ARKStepCreate", 0)) return 1;

  /* Specify tolerances */
  flag = ARKStepSStolerances(arkode_mem, reltol, abstol);
  if (check_flag(&flag, "ARKStepSStolerances", 1)) return 1;

  /* Set stop time */
  flag = ARKStepSetStopTime(arkode_mem, Tf);
  if (check_flag(&flag, "ARKStepSetStopTime", 1)) return 1;

  /* Set max steps before output */
  flag = ARKStepSetMaxNumSteps(arkode_mem, mxsteps);
  if (check_flag(&flag, "ARKStepSetMaxNumSteps", 1)) return 1;

  /* Attach matrix and linear solver */
  flag = ARKStepSetLinearSolver(arkode_mem, LS, A);
  if (check_flag(&flag, "ARKStepSetLinearSolver", 1)) return 1;

  /* Set Jacobian routine */
  flag = ARKStepSetJacFn(arkode_mem, Jac);
  if (check_flag(&flag, "ARKStepSetJacFn", 1)) return 1;

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

  /* Set forcing */
  flag = arkStep_SetInnerForcing(arkode_mem, tshift, tscale, forcing, order + 1);
  if (check_flag(&flag, "arkStep_SetInnerForcing", 1)) return 1;

  /* Integrate the problem */
  flag = ARKStepEvolve(arkode_mem, Tf, y, &tret, ARK_NORMAL);

  /* check for errors */
  if (flag < 0) {
    fprintf(stderr,"ARKStep failure, flag = %d\n",flag); return 1;
  }

  /* get some integrator stats */
  flag = ARKStepGetNumSteps(arkode_mem, &nst);
  check_flag(&flag, "ARKStepGetNumSteps", 1);

  flag = ARKStepGetNumStepAttempts(arkode_mem, &nst_a);
  check_flag(&flag, "ARKStepGetNumStepAttempts", 1);

  printf("IMEX stats:\n");
  printf("Steps = %li (attempted = %li)\n\n", nst, nst_a);

  /* Free integrator memory */
  ARKStepFree(&arkode_mem);
  arkode_mem = NULL;

  /* print solution */
  printf("IMEX solution:\n");
  N_VPrint_Serial(y);

  /* check the solution error */
  flag = compute_error(y, ans, tmp, reltol, abstol);
  if (flag != 0) return(1);

  /* ---------------------------------------------------------------------------
   * Clean up and return
   * -------------------------------------------------------------------------*/

  N_VDestroy(y);            /* Free vectors */
  N_VDestroy(ans);
  N_VDestroy(tmp);
  SUNLinSolFree(LS);        /* Free linear solver */
  SUNMatDestroy(A);         /* Free A matrix */

  N_VDestroyVectorArray(forcing, order + 1);

  return flag;
}

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

/* ODE RHS function */
static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data)
{
  N_VConst(ZERO, ydot);
  return 0;
}

/* ODE RHS Jacobian function */
static int Jac(realtype t, N_Vector y, N_Vector fy, SUNMatrix J,
               void *user_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3)
{
  SUNMatZero(J);
  return 0;
}

/*-------------------------------
 * 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;
}

/* computed the true solution at a given time */
static int compute_ans(realtype t, realtype tshift, realtype tscale,
                       N_Vector* forcing, int order, N_Vector ans)
{
  int       i;
  realtype  tau;
  N_Vector* vecs;
  realtype* vals;

  vals = NULL;
  vals = (realtype*) calloc(order + 1, sizeof(realtype));
  if (vals == NULL) return(1);

  vecs = NULL;
  vecs = (N_Vector*) calloc(order + 1, sizeof(N_Vector));
  if (vecs == NULL) return(1);

  /* compute normalized time */
  tau = (t - tshift) / tscale;

  /* compute true solution */
  for (i = 0; i < order + 1; i++) {
    vals[i] = ((SUNRpowerI(tau, i + 1)) / (i + 1)) * tscale;
    vecs[i] = forcing[i];
  }
  N_VLinearCombination(order + 1, vals, vecs, ans);

  free(vals);
  free(vecs);

  return (0);
}

/* compure the weighted max norm of the difference of two vectors */
static int compute_error(N_Vector y, N_Vector ans, N_Vector tmp, realtype rtol,
                         realtype atol)
{
  int      status; /* success (0) or failure (1) flag */
  realtype error;

  /* compute the error in y */
  N_VLinearSum(ONE, y, -ONE, ans, y);

  /* compute error weights */
  N_VAbs(ans, tmp);
  N_VScale(rtol, tmp, tmp);
  N_VAddConst(tmp, atol, tmp);
  N_VInv(tmp, tmp);

  /* compute weighted max norm */
  N_VProd(tmp, y, y);
  error = N_VMaxNorm(y);

  /* is the solution within the tolerances? */
  status = (error < ONE) ? 0 : 1;

  if (status)
    fprintf(stdout, "ERROR: Test failed with wmax error = %"GSYM"\n\n", error);
  else
    fprintf(stdout, "SUCCESS: Test passed with wmax error = %"GSYM"\n\n", error);

  return (status);
}

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