xref: /petsc/src/sys/classes/random/tutorials/ex2.c (revision d0609ced746bc51b019815ca91d747429db24893)

static char help[] = "Tests PetscRandom functions.\n\n";

#include <petscsys.h>

#define PETSC_MAXBSIZE     40
#define DATAFILENAME "ex2_stock.txt"

struct himaInfoTag {
  PetscInt    n;
  PetscReal   r;
  PetscReal   dt;
  PetscInt    totalNumSim;
  PetscReal   *St0;
  PetscReal   *vol;
};
typedef struct himaInfoTag himaInfo;

PetscErrorCode readData(MPI_Comm,himaInfo *);
PetscReal mcVal(PetscReal, PetscReal, PetscReal, PetscReal, PetscReal);
void exchangeVal(PetscReal*, PetscReal*);
PetscReal basketPayoff(PetscReal[], PetscReal[], PetscInt, PetscReal,PetscReal, PetscReal[]);
PetscErrorCode stdNormalArray(PetscReal*, PetscInt,PetscRandom);
PetscInt divWork(PetscMPIInt, PetscInt, PetscMPIInt);

/*
   Contributed by Xiaoyan Zeng <zengxia@iit.edu> and Liu, Kwong Ip" <kiliu@math.hkbu.edu.hk>

   Example of usage:
     mpiexec -n 4 ./ex2 -num_of_stocks 30 -interest_rate 0.4 -time_interval 0.01 -num_of_simulations 10000
*/

int main(int argc, char *argv[])
{
  PetscReal      r,dt;
  PetscInt       n;
  unsigned long  i,myNumSim,totalNumSim,numdim;
  PetscReal      *vol, *St0, x, totalx;
  PetscMPIInt    size,rank;
  PetscReal      *eps;
  himaInfo       hinfo;
  PetscRandom    ran;

  PetscCall(PetscInitialize(&argc,&argv,(char*)0,help));
  PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,&ran));
  PetscCall(PetscRandomSetFromOptions(ran));

  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));

  hinfo.n           = 31;
  hinfo.r           = 0.04;
  hinfo.dt          = 1.0/12;   /* a month as a period */
  hinfo.totalNumSim = 1000;

  PetscCall(PetscOptionsGetInt(NULL,NULL,"-num_of_stocks",&(hinfo.n),NULL));
  PetscCheckFalse(hinfo.n <1 || hinfo.n > 31,PETSC_COMM_SELF,PETSC_ERR_SUP,"Only 31 stocks listed in stock.txt. num_of_stocks %" PetscInt_FMT " must between 1 and 31",hinfo.n);
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-interest_rate",&(hinfo.r),NULL));
  PetscCall(PetscOptionsGetReal(NULL,NULL,"-time_interval",&(hinfo.dt),NULL));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-num_of_simulations",&(hinfo.totalNumSim),NULL));

  n           = hinfo.n;
  r           = hinfo.r;
  dt          = hinfo.dt;
  totalNumSim = hinfo.totalNumSim;
  PetscCall(PetscMalloc1(2*n+1,&hinfo.vol));
  vol         = hinfo.vol;
  St0         = hinfo.St0 = hinfo.vol + n;
  PetscCall(readData(PETSC_COMM_WORLD,&hinfo));

  numdim = n*(n+1)/2;
  if (numdim%2 == 1) numdim++;
  PetscCall(PetscMalloc1(numdim,&eps));

  myNumSim = divWork(rank,totalNumSim,size);

  x = 0;
  for (i=0; i<myNumSim; i++) {
    PetscCall(stdNormalArray(eps,numdim,ran));
    x += basketPayoff(vol,St0,n,r,dt,eps);
  }

  PetscCallMPI(MPI_Reduce(&x, &totalx, 1, MPIU_REAL, MPIU_SUM,0,PETSC_COMM_WORLD));
  /* payoff = exp(-r*dt*n)*(totalx/totalNumSim);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Option price = $%.3f using %ds of %s computation with %d %s for %d stocks, %d trading period per year, %.2f%% interest rate\n",
   payoff,(int)(stop - start),"parallel",size,"processors",n,(int)(1/dt),r); */

  PetscCall(PetscFree(vol));
  PetscCall(PetscFree(eps));
  PetscCall(PetscRandomDestroy(&ran));
  PetscCall(PetscFinalize());
  return 0;
}

PetscErrorCode stdNormalArray(PetscReal *eps, PetscInt numdim, PetscRandom ran)
{
  PetscInt       i;
  PetscScalar    u1,u2;
  PetscReal      t;

  PetscFunctionBegin;
  for (i=0; i<numdim; i+=2) {
    PetscCall(PetscRandomGetValue(ran,&u1));
    PetscCall(PetscRandomGetValue(ran,&u2));

    t        = PetscSqrtReal(-2*PetscLogReal(PetscRealPart(u1)));
    eps[i]   = t * PetscCosReal(2*PETSC_PI*PetscRealPart(u2));
    eps[i+1] = t * PetscSinReal(2*PETSC_PI*PetscRealPart(u2));
  }
  PetscFunctionReturn(0);
}

PetscReal basketPayoff(PetscReal vol[], PetscReal St0[], PetscInt n, PetscReal r,PetscReal dt, PetscReal eps[])
{
  PetscReal Stk[PETSC_MAXBSIZE], temp;
  PetscReal payoff;
  PetscInt  maxk,i,j;
  PetscInt  pointcount=0;

  for (i=0;i<n;i++) Stk[i] = St0[i];

  for (i=0;i<n;i++) {
    maxk = 0;
    for (j=0;j<(n-i);j++) {
      Stk[j] = mcVal(Stk[j],r,vol[j],dt,eps[pointcount++]);
      if ((Stk[j]/St0[j]) > (Stk[maxk]/St0[maxk])) maxk = j;
    }
    exchangeVal(Stk+j-1,Stk+maxk);
    exchangeVal(St0+j-1,St0+maxk);
    exchangeVal(vol+j-1,vol+maxk);
  }

  payoff = 0;
  for (i=0; i<n; i++) {
    temp = (Stk[i]/St0[i]) - 1;
    if (temp > 0) payoff += temp;
  }
  return payoff;
}

PetscErrorCode readData(MPI_Comm comm,himaInfo *hinfo)
{
  PetscInt       i;
  FILE           *fd;
  char           temp[50];
  PetscMPIInt    rank;
  PetscReal      *v = hinfo->vol, *t = hinfo->St0;
  PetscInt       num=hinfo->n;

  PetscFunctionBeginUser;
  PetscCallMPI(MPI_Comm_rank(comm,&rank));
  if (rank == 0) {
    PetscCall(PetscFOpen(PETSC_COMM_SELF,DATAFILENAME,"r",&fd));
    for (i=0;i<num;i++) {
      double vv,tt;
      PetscCheck(fscanf(fd,"%s%lf%lf",temp,&vv,&tt) == 3,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Badly formatted input file");
      v[i] = vv;
      t[i] = tt;
    }
    fclose(fd);
  }
  PetscCallMPI(MPI_Bcast(v,2*num,MPIU_REAL,0,PETSC_COMM_WORLD));
  /* ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] vol %g, ... %g; St0 %g, ... %g\n",rank,hinfo->vol[0],hinfo->vol[num-1],hinfo->St0 [0],hinfo->St0[num-1]); */
  PetscFunctionReturn(0);
}

void exchangeVal(PetscReal *a, PetscReal *b)
{
  PetscReal t;

  t  = *a;
  *a = *b;
  *b = t;
}

PetscReal mcVal(PetscReal St, PetscReal r, PetscReal vol, PetscReal dt, PetscReal eps)
{
  return (St * PetscExpReal((r-0.5*vol*vol)*dt + vol*PetscSqrtReal(dt)*eps));
}

PetscInt divWork(PetscMPIInt id, PetscInt num, PetscMPIInt size)
{
  PetscInt numit;

  numit = (PetscInt)(((PetscReal)num)/size);
  numit++;
  return numit;
}

/*TEST

   test:
      nsize: 2
      output_file: output/ex1_1.out
      localrunfiles: ex2_stock.txt

TEST*/