/* -----------------------------------------------------------------
 * Programmer(s): Jimmy Almgren-Bell @ LLNL
 * Based on prior version by: Scott D. Cohen, Alan C. Hindmarsh and
 *                            Radu Serban @ LLNL
 * -----------------------------------------------------------------
 * SUNDIALS Copyright Start
 * Copyright (c) 2002-2019, 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 is a simple example problem, with the coding
 * needed for its solution by CVODE. The problem is from
 * chemical kinetics, and consists of the following three rate
 * equations:         
 *    dy1/dt = -.04*y1 + 1.e4*y2*y3
 *    dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*(y2)^2
 *    dy3/dt = 3.e7*(y2)^2
 * on the interval from t = 0.0 to t = 4.e10, with initial
 * conditions: y1 = 1.0, y2 = y3 = 0. The problem is stiff.
 * While integrating the system, we also use the rootfinding
 * feature to find the points at which y1 = 1e-4 or at which
 * y3 = 0.01. This program solves the problem with the BDF method,
 * Newton iteration with the SUNDENSE dense linear solver, and a
 * user-supplied Jacobian routine. It uses a scalar relative tolerance
 * and a vector absolute tolerance. The constraint y_i >= 0 is
 * posed for all components. Output is printed in decades
 * from t = .4 to t = 4.e10. Run statistics (optional outputs)
 * are printed at the end.
 * -----------------------------------------------------------------*/

#include <stdio.h>

#include <cvode/cvode.h>               /* prototypes for CVODE fcts., consts.  */
#include <nvector/nvector_serial.h>    /* access to serial N_Vector            */
#include <sunmatrix/sunmatrix_dense.h> /* access to dense SUNMatrix            */
#include <sunlinsol/sunlinsol_dense.h> /* access to dense SUNLinearSolver      */
#include <sundials/sundials_types.h>   /* defs. of realtype, sunindextype      */

/* User-defined vector and matrix accessor macros: Ith, IJth */

/* These macros are defined in order to write code which exactly matches
   the mathematical problem description given above.

   Ith(v,i) references the ith component of the vector v, where i is in
   the range [1..NEQ] and NEQ is defined below. The Ith macro is defined
   using the N_VIth macro in nvector.h. N_VIth numbers the components of
   a vector starting from 0.

   IJth(A,i,j) references the (i,j)th element of the dense matrix A, where
   i and j are in the range [1..NEQ]. The IJth macro is defined using the
   SM_ELEMENT_D macro in dense.h. SM_ELEMENT_D numbers rows and columns of 
   a dense matrix starting from 0. */

#define Ith(v,i)    NV_Ith_S(v,i-1)         /* Ith numbers components 1..NEQ */
#define IJth(A,i,j) SM_ELEMENT_D(A,i-1,j-1) /* IJth numbers rows,cols 1..NEQ */


/* Problem Constants */

#define NEQ   3                /* number of equations  */
#define Y1    RCONST(1.0)      /* initial y components */
#define Y2    RCONST(0.0)
#define Y3    RCONST(0.0)
#define RTOL  RCONST(1.0e-4)   /* scalar relative tolerance            */
#define ATOL1 RCONST(1.0e-6)   /* vector absolute tolerance components */
#define ATOL2 RCONST(1.0e-11)
#define ATOL3 RCONST(1.0e-5)
#define T0    RCONST(0.0)      /* initial time           */
#define T1    RCONST(0.4)      /* first output time      */
#define TMULT RCONST(10.0)     /* output time factor     */
#define NOUT  12               /* number of output times */

#define ZERO  RCONST(0.0)
#define ONE   RCONST(1.0)

/* Functions Called by the Solver */

static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data);

static int g(realtype t, N_Vector y, realtype *gout, 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 functions to output results */

static void PrintOutput(realtype t, realtype y1, realtype y2, realtype y3);
static void PrintRootInfo(int root_f1, int root_f2);

/* Private function to print final statistics */

static void PrintFinalStats(void *cvode_mem);

/* Private function to check function return values */

static int check_retval(void *returnvalue, const char *funcname, int opt);

/* Private function to check computed solution */

static int check_ans(N_Vector y, realtype t, realtype rtol, N_Vector atol);


/*
 *-------------------------------
 * Main Program
 *-------------------------------
 */

int main()
{
  realtype reltol, t, tout;
  N_Vector y, abstol, constraints;
  SUNMatrix A;
  SUNLinearSolver LS;
  void *cvode_mem;
  int retval, retvalr, iout;
  int rootsfound[2];

  y = abstol = constraints = NULL;
  A = NULL;
  LS = NULL;
  cvode_mem = NULL;

  /* Create serial vector of length NEQ for I.C., abstol, and constraints */
  y = N_VNew_Serial(NEQ);
  if (check_retval((void *)y, "N_VNew_Serial", 0)) return(1);
  abstol = N_VNew_Serial(NEQ); 
  if (check_retval((void *)abstol, "N_VNew_Serial", 0)) return(1);
  constraints = N_VNew_Serial(NEQ);
  if (check_retval((void *)constraints, "N_VNew_Serial", 0)) return(1);

  /* Initialize y */
  Ith(y,1) = Y1;
  Ith(y,2) = Y2;
  Ith(y,3) = Y3;

  /* Set the scalar relative tolerance */
  reltol = RTOL;
  /* Set the vector absolute tolerance */
  Ith(abstol,1) = ATOL1;
  Ith(abstol,2) = ATOL2;
  Ith(abstol,3) = ATOL3;

  /* Set constraints to all 1's for nonnegative solution values. */
  N_VConst(ONE, constraints);

  /* Call CVodeCreate to create the solver memory and specify the 
   * Backward Differentiation Formula */
  cvode_mem = CVodeCreate(CV_BDF);
  if (check_retval((void *)cvode_mem, "CVodeCreate", 0)) return(1);
  
  /* Call CVodeInit to initialize the integrator memory and specify the
   * user's right hand side function in y'=f(t,y), the inital time T0, and
   * the initial dependent variable vector y. */
  retval = CVodeInit(cvode_mem, f, T0, y);
  if (check_retval(&retval, "CVodeInit", 1)) return(1);

  /* Call CVodeSVtolerances to specify the scalar relative tolerance
   * and vector absolute tolerances */
  retval = CVodeSVtolerances(cvode_mem, reltol, abstol);
  if (check_retval(&retval, "CVodeSVtolerances", 1)) return(1);

  /* Call CVodeRootInit to specify the root function g with 2 components */
  retval = CVodeRootInit(cvode_mem, 2, g);
  if (check_retval(&retval, "CVodeRootInit", 1)) return(1);

  /* Create dense SUNMatrix for use in linear solves */
  A = SUNDenseMatrix(NEQ, NEQ);
  if(check_retval((void *)A, "SUNDenseMatrix", 0)) return(1);

  /* Create dense SUNLinearSolver object for use by CVode */
  LS = SUNLinSol_Dense(y, A);
  if(check_retval((void *)LS, "SUNLinSol_Dense", 0)) return(1);

  /* Call CVodeSetLinearSolver to attach the matrix and linear solver to CVode */
  retval = CVodeSetLinearSolver(cvode_mem, LS, A);
  if(check_retval(&retval, "CVodeSetLinearSolver", 1)) return(1);

  /* Set the user-supplied Jacobian routine Jac */
  retval = CVodeSetJacFn(cvode_mem, Jac);
  if(check_retval(&retval, "CVodeSetJacFn", 1)) return(1);

  /* Call CVodeSetConstraints to initialize constraints */
  retval = CVodeSetConstraints(cvode_mem, constraints);
  if(check_retval(&retval, "CVodeSetConstraints", 1)) return(1);

  /* In loop, call CVode, print results, and test for error.
     Break out of loop when NOUT preset output times have been reached.  */
  printf(" \n3-species kinetics problem\n\n");

  iout = 0;  tout = T1;
  while(1) {
    retval = CVode(cvode_mem, tout, y, &t, CV_NORMAL);
    PrintOutput(t, Ith(y,1), Ith(y,2), Ith(y,3));

    if (retval == CV_ROOT_RETURN) {
      retvalr = CVodeGetRootInfo(cvode_mem, rootsfound);
      if (check_retval(&retvalr, "CVodeGetRootInfo", 1)) return(1);
      PrintRootInfo(rootsfound[0],rootsfound[1]);
    }

    if (check_retval(&retval, "CVode", 1)) break;
    if (retval == CV_SUCCESS) {
      iout++;
      tout *= TMULT;
    }

    if (iout == NOUT) break;
  }

  /* Print some final statistics */
  PrintFinalStats(cvode_mem);

  /* check the solution error */
  retval = check_ans(y, t, reltol, abstol);

  /* Free y, abstol, and constraints vectors */
  N_VDestroy(y);
  N_VDestroy(abstol);
  N_VDestroy(constraints);

  /* Free integrator memory */
  CVodeFree(&cvode_mem);

  /* Free the linear solver memory */
  SUNLinSolFree(LS);

  /* Free the matrix memory */
  SUNMatDestroy(A);

  return(retval);
}


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

/*
 * f routine. Compute function f(t,y). 
 */

static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data)
{
  realtype y1, y2, y3, yd1, yd3;

  y1 = Ith(y,1); y2 = Ith(y,2); y3 = Ith(y,3);

  yd1 = Ith(ydot,1) = RCONST(-0.04)*y1 + RCONST(1.0e4)*y2*y3;
  yd3 = Ith(ydot,3) = RCONST(3.0e7)*y2*y2;
        Ith(ydot,2) = -yd1 - yd3;

  return(0);
}

/*
 * g routine. Compute functions g_i(t,y) for i = 0,1. 
 */

static int g(realtype t, N_Vector y, realtype *gout, void *user_data)
{
  realtype y1, y3;

  y1 = Ith(y,1); y3 = Ith(y,3);
  gout[0] = y1 - RCONST(0.0001);
  gout[1] = y3 - RCONST(0.01);

  return(0);
}

/*
 * Jacobian routine. Compute J(t,y) = df/dy. *
 */

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)
{
  realtype y2, y3;

  y2 = Ith(y,2); y3 = Ith(y,3);

  IJth(J,1,1) = RCONST(-0.04);
  IJth(J,1,2) = RCONST(1.0e4)*y3;
  IJth(J,1,3) = RCONST(1.0e4)*y2;

  IJth(J,2,1) = RCONST(0.04); 
  IJth(J,2,2) = RCONST(-1.0e4)*y3-RCONST(6.0e7)*y2;
  IJth(J,2,3) = RCONST(-1.0e4)*y2;

  IJth(J,3,1) = ZERO;
  IJth(J,3,2) = RCONST(6.0e7)*y2;
  IJth(J,3,3) = ZERO;

  return(0);
}

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

static void PrintOutput(realtype t, realtype y1, realtype y2, realtype y3)
{
#if defined(SUNDIALS_EXTENDED_PRECISION)
  printf("At t = %0.4Le      y =%14.6Le  %14.6Le  %14.6Le\n", t, y1, y2, y3);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
  printf("At t = %0.4e      y =%14.6e  %14.6e  %14.6e\n", t, y1, y2, y3);
#else
  printf("At t = %0.4e      y =%14.6e  %14.6e  %14.6e\n", t, y1, y2, y3);
#endif

  return;
}

static void PrintRootInfo(int root_f1, int root_f2)
{
  printf("    rootsfound[] = %3d %3d\n", root_f1, root_f2);

  return;
}

/* 
 * Get and print some final statistics
 */

static void PrintFinalStats(void *cvode_mem)
{
  long int nst, nfe, nsetups, nje, nfeLS, nni, ncfn, netf, nge;
  int retval;

  retval = CVodeGetNumSteps(cvode_mem, &nst);
  check_retval(&retval, "CVodeGetNumSteps", 1);
  retval = CVodeGetNumRhsEvals(cvode_mem, &nfe);
  check_retval(&retval, "CVodeGetNumRhsEvals", 1);
  retval = CVodeGetNumLinSolvSetups(cvode_mem, &nsetups);
  check_retval(&retval, "CVodeGetNumLinSolvSetups", 1);
  retval = CVodeGetNumErrTestFails(cvode_mem, &netf);
  check_retval(&retval, "CVodeGetNumErrTestFails", 1);
  retval = CVodeGetNumNonlinSolvIters(cvode_mem, &nni);
  check_retval(&retval, "CVodeGetNumNonlinSolvIters", 1);
  retval = CVodeGetNumNonlinSolvConvFails(cvode_mem, &ncfn);
  check_retval(&retval, "CVodeGetNumNonlinSolvConvFails", 1);

  retval = CVodeGetNumJacEvals(cvode_mem, &nje);
  check_retval(&retval, "CVodeGetNumJacEvals", 1);
  retval = CVodeGetNumLinRhsEvals(cvode_mem, &nfeLS);
  check_retval(&retval, "CVodeGetNumLinRhsEvals", 1);

  retval = CVodeGetNumGEvals(cvode_mem, &nge);
  check_retval(&retval, "CVodeGetNumGEvals", 1);

  printf("\nFinal Statistics:\n");
  printf("nst = %-6ld nfe  = %-6ld nsetups = %-6ld nfeLS = %-6ld nje = %ld\n",
	 nst, nfe, nsetups, nfeLS, nje);
  printf("nni = %-6ld ncfn = %-6ld netf = %-6ld nge = %ld\n \n",
	 nni, ncfn, netf, nge);
}

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

static int check_retval(void *returnvalue, const char *funcname, int opt)
{
  int *retval;

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

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

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

  return(0);
}

/* compare the solution at the final time 4e10s to a reference solution computed
   using a relative tolerance of 1e-8 and absoltue tolerance of 1e-14 */
static int check_ans(N_Vector y, realtype t, realtype rtol, N_Vector atol)
{
  int      passfail=0;        /* answer pass (0) or fail (1) flag */  
  N_Vector ref;               /* reference solution vector        */
  N_Vector ewt;               /* error weight vector              */
  realtype err;               /* wrms error                       */

  /* create reference solution and error weight vectors */
  ref = N_VClone(y);
  ewt = N_VClone(y);

  /* set the reference solution data */
  NV_Ith_S(ref,0) = RCONST(5.2083495894337328e-08);
  NV_Ith_S(ref,1) = RCONST(2.0833399429795671e-13);
  NV_Ith_S(ref,2) = RCONST(9.9999994791629776e-01);

  /* compute the error weight vector, loosen atol */
  N_VAbs(ref, ewt);
  N_VLinearSum(rtol, ewt, RCONST(10.0), atol, ewt);
  if (N_VMin(ewt) <= ZERO) {
    fprintf(stderr, "\nSUNDIALS_ERROR: check_ans failed - ewt <= 0\n\n");
    return(-1);
  }
  N_VInv(ewt, ewt);   

  /* compute the solution error */
  N_VLinearSum(ONE, y, -ONE, ref, ref);
  err = N_VWrmsNorm(ref, ewt);

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

  if (passfail) {
    fprintf(stdout, "\nSUNDIALS_WARNING: check_ans error=%g \n\n", err);
  }

  /* Free vectors */
  N_VDestroy(ref);
  N_VDestroy(ewt);

  return(passfail);
}
