/* nag_rand_bb_make_bridge_order (g05xec) Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 *
 * Mark 27.0, 2019.
 */
#include <stdio.h>
#include <math.h>
#include <nag.h>
int get_z(Nag_OrderType order, Integer ntimes, Integer d, Integer a,
          Integer npaths, double *z, Integer pdz);
void display_results(Nag_OrderType order, Integer npaths, Integer ntimes,
                     Integer d, double *b, Integer pdb);

#define CHECK_FAIL(name,fail) if(fail.code != NE_NOERROR) { \
printf("Error calling %s\n%s\n",name,fail.message); exit_status=-1; goto END; }

int main(void)
{
  Integer exit_status = 0;
  NagError fail;
  /*  Scalars */
  double t0, tend;
  Integer a, d, pdb, pdc, pdz, nmove, npaths, ntimes, i;
  Nag_OrderType order;
  /*  Arrays */
  double *b = 0, *c = 0, *intime = 0, *rcomm = 0, *start = 0,
         *term = 0, *times = 0, *z = 0;
  Integer *move = 0;
  INIT_FAIL(fail);

  /* Parameters which determine the bridge */
  ntimes = 10;
  t0 = 0.0;
  npaths = 2;
  a = 0;
  nmove = 3; /* We modify the first 3 points in the construction order */
  d = 3;
#ifdef NAG_COLUMN_MAJOR
  order = Nag_ColMajor;
  pdz = npaths;
  pdb = npaths;
#else
  order = Nag_RowMajor;
  pdz = d * (ntimes + 1 - a);
  pdb = d * (ntimes + 1);
#endif
  pdc = d;
#define C(I,J) c[(J-1)*pdc + I-1]
  /* Allocate memory */
  if (!(intime = NAG_ALLOC((ntimes), double)) ||
      !(times = NAG_ALLOC((ntimes), double)) ||
      !(rcomm = NAG_ALLOC((12 * (ntimes + 1)), double)) ||
      !(start = NAG_ALLOC(d, double)) ||
      !(term = NAG_ALLOC(d, double)) ||
      !(c = NAG_ALLOC(pdc * d, double)) ||
      !(z = NAG_ALLOC(d * (ntimes + 1 - a) * npaths, double)) ||
      !(b = NAG_ALLOC(d * (ntimes + 1) * npaths, double)) ||
      !(move = NAG_ALLOC(nmove, Integer))
         )
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Fix the time points at which the bridge is required */
  for (i = 0; i < ntimes; i++) {
    intime[i] = t0 + 1.71 * (double) (i + 1);
  }
  tend = t0 + 1.71 * (double) (ntimes + 1);
  /* We will use the bridge construction order Nag_RLRoundDown. However
   * we modify this construction order by moving points 3, 5 and 4
   * to the front.  Modifying a construction order would typically only
   * be considered when using quasi-random numbers */
  move[0] = 3;
  move[1] = 5;
  move[2] = 4;

  /* nag_rand_bb_make_bridge_order (g05xec). Creates a Brownian bridge 
   * construction order out of a set of input times */
  nag_rand_bb_make_bridge_order(Nag_RLRoundDown, t0, tend, ntimes, intime,
                                nmove, move, times, &fail);
  CHECK_FAIL("nag_rand_bb_make_bridge_order", fail);

  /* g05xac. Initializes the Brownian bridge generator   */
  nag_rand_bb_init(t0, tend, times, ntimes, rcomm, &fail);
  CHECK_FAIL("nag_rand_bb_init", fail);

  /* We want the following covariance matrix */
  C(1, 1) = 6.0;
  C(2, 1) = 1.0;
  C(3, 1) = -0.2;
  C(1, 2) = 1.0;
  C(2, 2) = 5.0;
  C(3, 2) = 0.3;
  C(1, 3) = -0.2;
  C(2, 3) = 0.3;
  C(3, 3) = 4.0;
  /* g05xbc works with the Cholesky factorization of the covariance matrix C */

  /* f07fdc. Cholesky factorization of real positive definite matrix */
  nag_lapacklin_dpotrf(Nag_ColMajor, Nag_Lower, d, c, pdc, &fail);
  CHECK_FAIL("nag_lapacklin_dpotrf", fail);

  /* Generate the random numbers */
  if (get_z(order, ntimes, d, a, npaths, z, pdz) != 0) {
    printf("Error generating random numbers\n");
    exit_status = -1;
    goto END;
  }

  for (i = 0; i < d; i++)
    start[i] = 0.0;
  /*  g05xbc. Generate paths for a free or non-free Wiener process using the */
  /*  Brownian bridge algorithm   */
  nag_rand_bb(order, npaths, d, start, a, term, z, pdz, c, pdc, b, pdb,
              rcomm, &fail);
  CHECK_FAIL("nag_rand_bb", fail);

  /* Display the results */
  display_results(order, npaths, ntimes, d, b, pdb);
END:
  ;
  NAG_FREE(b);
  NAG_FREE(c);
  NAG_FREE(intime);
  NAG_FREE(rcomm);
  NAG_FREE(start);
  NAG_FREE(term);
  NAG_FREE(times);
  NAG_FREE(z);
  NAG_FREE(move);
  return exit_status;
}

int get_z(Nag_OrderType order, Integer ntimes, Integer d, Integer a,
          Integer npaths, double *z, Integer pdz)
{
  NagError fail;
  Integer lseed, lstate, seed[1], idim, liref, *iref = 0, state[80], i;
  Integer exit_status = 0;
  double *xmean = 0, *stdev = 0;
  lstate = 80;
  lseed = 1;
  INIT_FAIL(fail);
  idim = d * (ntimes + 1 - a);
  liref = 32 * idim + 7;
  if (!(iref = NAG_ALLOC((liref), Integer)) ||
      !(xmean = NAG_ALLOC((idim), double)) ||
      !(stdev = NAG_ALLOC((idim), double)))
  {
    printf("Allocation failure in get_z\n");
    exit_status = -1;
    goto END;
  }

  /* We now need to generate the input pseudorandom numbers */
  seed[0] = 1023401;
  /* g05kfc. Initializes a pseudorandom number generator */
  /* to give a repeatable sequence */
  nag_rand_init_repeat(Nag_MRG32k3a, 0, seed, lseed, state, &lstate,
                           &fail);
  CHECK_FAIL("nag_rand_init_repeat", fail);

  /* g05ync. Initializes a scrambled quasi-random number generator */
  nag_rand_quasi_init_scrambled(Nag_QuasiRandom_Sobol, Nag_FaureTezuka, idim,
                           iref, liref, 0, 32, state, &fail);
  CHECK_FAIL("nag_rand_quasi_init_scrambled", fail);

  for (i = 0; i < idim; i++) {
    xmean[i] = 0.0;
    stdev[i] = 1.0;
  }
  /* g05yjc. Generates a Normal quasi-random number sequence */
  nag_rand_quasi_normal(order, xmean, stdev, npaths, z, pdz, iref, &fail);
  CHECK_FAIL("nag_rand_quasi_normal", fail);

END:
  NAG_FREE(iref);
  NAG_FREE(xmean);
  NAG_FREE(stdev);
  return exit_status;
}

void display_results(Nag_OrderType order, Integer npaths, Integer ntimes,
                     Integer d, double *b, Integer pdb)
{
#define B(I,J) (order==Nag_RowMajor ? b[(I-1)*pdb+J-1]:b[(J-1)*pdb+I-1])

  Integer i, p, k;
  printf("nag_rand_bb_make_bridge_order (g05xec) Example Program Results\n\n");
  for (p = 1; p <= npaths; p++) {
    printf("%s ", "Wiener Path ");
    printf("%1" NAG_IFMT " ", p);
    printf("%s ", ", ");
    printf("%1" NAG_IFMT " ", ntimes + 1);
    printf("%s ", " time steps, ");
    printf("%1" NAG_IFMT " ", d);
    printf("%s ", " dimensions");
    printf("\n");

    for (k = 1; k <= d; k++) {
      printf("%10" NAG_IFMT " ", k);
    }
    printf("\n");

    for (i = 1; i <= ntimes + 1; i++) {
      printf("%2" NAG_IFMT " ", i);
      for (k = 1; k <= d; k++) {
        printf("%10.4f", B(p, k + (i - 1) * d));

      }
      printf("\n");

    }
    printf("\n");
  }
}