Example 1.4 Numerical Integration with MPI_Gather Collective Communication
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This example demonstrates parallel integration (see Example 1 for detail) via the following MPI library routines:
Example 1.4 Fortran Code
Program Example1_4
c#######################################################################
c# #
c# This is an MPI example on parallel integration to demonstrate the #
c# use of: #
c# #
c# * MPI_Init, MPI_Comm_rank, MPI_Comm_size, MPI_Finalize #
c# * MPI_Gather #
c# #
c# Dr. Kadin Tseng #
c# Scientific Computing and Visualization #
c# Boston University #
c# 1998 #
c# #
c#######################################################################
implicit none
integer n, p, i, j, proc, ierr, master, myid, tag, comm
real h, a, b, integral, pi, ai, my_int, integral_sum, buf(50)
include "mpif.h" ! brings in pre-defined MPI constants, ...
data master/0/ ! processor 0 collects integral sums from other processors
comm = MPI_COMM_WORLD 
call MPI_Init(ierr) ! starts MPI
call MPI_Comm_rank(comm, myid, ierr) ! get current proc ID
call MPI_Comm_size(comm, p, ierr) ! get number of procs
pi = acos(-1.0) ! = 3.14159...
a = 0.0 ! lower limit of integration
b = pi*1./2. ! upper limit of integration
n = 500 ! number of intervals in (b-a)/p
h = (b-a)/n/p ! length of increment
ai = a + myid*n*h ! lower limit of integration for partition myid
my_int = integral(ai, h, n)
write(*,"('Process ',i2,' has the partial sum of',f10.6)")
& myid,my_int
call MPI_Gather(
& my_int, 1, MPI_REAL, ! Send buffer, size, data type
& buf, 1, MPI_REAL, ! Receive buffer, size, data type
& master, ! destination process
& comm, ierr)
if(myid .eq. master) then
integral_sum = 0.0
do i=1,p
integral_sum = integral_sum + buf(i)
enddo
print *,'The Integral =',integral_sum
endif
call MPI_Finalize(ierr) ! let MPI finish up ...
end
real function integral(ai, h, n)
implicit none
integer n, j
real h, ai, aij
integral = 0.0 ! initialize integral
do j=0,n-1 ! sum integrals
aij = ai +(j+0.5)*h ! abscissa mid-point
integral = integral + cos(aij)*h
enddo
return
endExample 1.4 C code
#include <mpi.h>
#include <math.h>
#include <stdio.h>
/* Prototype */
float integral(float ai, float h, int n);
int main(int argc, char* argv[])
/*######################################################################
# #
# This is an MPI example on parallel integration to demonstrate the #
# use of: #
# #
# * MPI_Init, MPI_Comm_rank, MPI_Comm_size, MPI_Finalize #
# * MPI_Gather #
# #
# Dr. Kadin Tseng #
# Scientific Computing and Visualization #
# Boston University #
# 1998 #
# #
#####################################################################*/
{
int n, p, myid, tag, proc, ierr, i;
float h, integral_sum, a, b, ai, pi, my_int, buf[50];
int master = 0; /* processor performing total sum */
MPI_Comm comm;
comm = MPI_COMM_WORLD;
ierr = MPI_Init(&argc,&argv); /* starts MPI */
MPI_Comm_rank(comm, &myid); /* get current process id */
MPI_Comm_size(comm, &p); /* get number of processes */
pi = acos(-1.0); /* = 3.14159... */
a = 0.; /* lower limit of integration */
b = pi*1./2.; /* upper limit of integration */
n = 500; /* number of increment within each process */
tag = 123; /* set the tag to identify this particular job */
h = (b-a)/n/p; /* length of increment */
ai = a + myid*n*h; /* lower limit of integration for partition myid */
my_int = integral(ai, h, n); /* 0<=myid<=p-1 */
printf("Process %d has the partial sum of %fn", myid,my_int);
MPI_Gather( /* collects my_int from all processes to master */
&my_int, 1, MPI_FLOAT, /* send buffer, size, data type */
buf, 1, MPI_FLOAT, 
/* receive buffer, size, data type */
master, comm);
if(myid == master) {
integral_sum = 0.0;
for (i=0; i< i++) {
integral_sum += buf[i];
}
printf("The Integral =%fn",integral_sum);
}
MPI_Finalize(); /* let MPI finish up ... */
}
float integral(float ai, float h, int n)
{
int j;
float aij, integ;
integ = 0.0; /* initialize */
for (j=0;j<j++) { /* sum integrals */
aij = ai + (j+0.5)*h; /* mid-point */
integ += cos(aij)*h;
}
return integ;
}Example 1 | Example 1.1 | Example 1.2 | Example 1.3 | Example 1.4 | Example 1.5