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/*
COMPILATION: mpicc integral1d_mpi.c -lm
USAGE: mpirun -n processor# ./a.out trial#
This program computes integral of ( 1 / (1 + x*x) ) in x=[0,1] by using importance sampling Monte Carlo
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>
#include <mpi.h>
// f() is the function to be integrated
double f(double x)
{
return (1.0 / (1.0 + x*x) ) ;
}
// random x values are generated according to probability distribution function w()
double w(double x)
{
return ((1.0/3.0) * (4 - 2 * x)) ;
}
// my_rand() function generates random numbers according to p.d.f w()
// this function uses inverse of the p.d.f w()
double my_rand()
{
double y = (double)rand() / (double)RAND_MAX ;
return (2.0 - sqrt(4.0 - 3.0*y) ) ;
}
int main(int argc, char* argv[])
{
int trials, trials_per_p; // trials is total number of random points and trials_per_p number of random points for each processor
int i;
double partial_sum = 0; // each processor uses its variable partial_sum to sum function value
double total_sum; // at the end of the computation all processors' partial_sum gathered in total_sum
double x;
int pnumber, myrank; // pnumber is the number of processor in the computation and myrank is the rank of the processor
MPI_Init(&argc,&argv); // Initialize the MPI execution environment
MPI_Comm_rank(MPI_COMM_WORLD, &myrank); // Each processor learns its rank number
MPI_Comm_size(MPI_COMM_WORLD, &pnumber); // Each processor learns how many processor participate to the calculation
trials = atoi(argv[1]); // command line argument is readed for total random number
trials_per_p = trials / pnumber ; // number of points for each processor is calculated
srand(myrank); // It is desired every processor to generate different random numbers so
// each processor seeded with different number (rank oprocessor)
for(i=0 ; i < trials_per_p ; i++ )
{
x = my_rand() ;
partial_sum += ( f(x) / w(x) ) ;
}
// Assume the processor which has rank=0 is master
int master_p = 0;
//total sum and total random number are gathered to the master processor
MPI_Reduce(&partial_sum, &total_sum, 1, MPI_DOUBLE, MPI_SUM, master_p, MPI_COMM_WORLD);
MPI_Reduce(&trials, &trials_per_p, 1, MPI_INT, MPI_SUM, master_p, MPI_COMM_WORLD);
//Master processor prints the result
if(myrank == master_p)
{
double integral = total_sum / trials ;
printf("computed value of the integral= %f \n", integral);
printf("true value of the integral= %f \n", atan(1.0));
printf("error= %f \n", fabs( integral - atan(1.0)));
}
MPI_Finalize(); //Terminates MPI execution environment
return 0;
}