Using matlab's spmd to compute simple triple integral is giving me incorrect solution, any thoughts on what I am doing wrong?

Question

Using matlab's spmd to compute simple triple integral is giving me incorrect solution, any thoughts on what I am doing wrong?

close all; clear all; clc;
% Create a parallel pool if none exists
if isempty(gcp())
    parpool();
end
nworkers = gcp().NumWorkers;
% Define the function
f = @(x,y,z) z
% Discretize the interval on the client
x = linspace(0,4,nworkers+1)
y = linspace(0,4,nworkers+1)
z = linspace(0,4,nworkers+1)
% On the workers
spmd
    ainit = x(labindex()) 
    bfin =  x(labindex()+1)
    cinit = y(labindex()) 
    dfin =  y(labindex()+1)
    einit = z(labindex()) 
    ffin =  z(labindex()+1)
%     locint = integral3(f,ainit,bfin,cinit,dfin,einit,ffin) % subinterval integration
    locint = integral3(f,ainit,bfin,ainit,bfin,ainit,bfin) % subinterval integration
    totalint = gplus(locint) % Add all values.
end
% Send the value back the client
totalvalue = totalint{1}

fun = @(x,y,z) z
q = integral3(fun,0,4,0,4,0,4)

q is the correct solution.

Answer 1

The problem here is that your spmd block is dividing the 3-dimensional region to be integrated in each dimension, rather than just a single dimension. You need to pick a dimension in which to divide the integral, and vary the limits in only that dimension. For example, you could correct things by replacing your integral3 call inside spmd with this:

spmd
    ...
    locint = integral3(f,0,4,0,4,einit,ffin)
    ...
end