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;
% I want to do this triple integral using SPMD
fun = @(x,y,z) z
totalval_s = integral3(fun,0,4,0,4,0,4)
% So I know the answer is 128, and integral3 works well
%
% Now I want to do the same triple integral but using SPMD
% 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()) %left point of subinterval
    bfin =  x(labindex()+1) %right point of subinterval
    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
    totalint = gplus(locint) % Add all values.
end
% Send the value back the client
totalvalue_spmd = totalint{1}
% However, the answer, totalvalue_spmd = 32, is incorrect. 
% I am novice at using SPMD, need help troubleshooting what I did wrong

I want to break the three intervals into two subintervals each, and use integral3 in spmd to integrate in each dimension.

[Raymond Norris]

Hi Austin,

Can you be a bit more specific about what solution you're getting and what you're expecting?

Raymond

[Austin Taylor]

Hi Raymond, thank you for the reply.

I want to do this triple integral:

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

in MATLAB's spmd, using two cores, one doing subinterval [0,2] and the other doing [2,4] for each integrand of the triple integral.

The last two lines of my script shows the expected answer, 128.

I appreciate your time,

Austin

Answer 1

[Walter Roberson]

You integrate the first section of x with the first section of y and the first section of z, and the second section of x with the second section of y and the second section of z, and so on.

You never integrate the first section of x with the third section of y and the second section of z.

[Austin Taylor]

Hi Robert, thank you for your reply.

May you please exand on your reply? I am new to using MATLAB's spmd, so the last to lines of my script give me the expected answer of 128. How do I make sure to integrate in correct orders?

I initially was going to write this line that I commented out:

%     locint = integral3(f,ainit,bfin,cinit,dfin,einit,ffin) % subinterval integration

However, I was getting the wrong solution, 32.

This following script works, but I want to be able to use MATLAB's spmd, using two cores, one doing subinterval [0,2] and the other doing [2,4] for each of the three integrands that make up the triple integral, not just one like I am using here (but this script gives correct 128 solution):

close all; clear all; clc;
syms f
% 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
z = linspace(0,4,nworkers+1)
% double(max([x,y]))

% 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,0,4,0,4,einit,ffin)
%     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)

I appreciate your time,

Austin

[Walter Roberson]

I want to be able to use MATLAB's spmd, using two cores, one doing subinterval [0,2] and the other doing [2,4] for each of the three integrands that make up the triple integral, not just one like I am using here

Then you would need 8 cores. Each core should decode (labindex minus one) to binary, add one to each digit result (getting 1 or 2), and use the first value to select the half-interval for x, the second value to select the half-interval for y, and the third value to select the half-interval for z.

More generally, for N sub-intervals, you need N^3 cores and each lab should decode (labindex-1) to a base N number, add one to each digit, and use that as an index to determine the N'th portion of the interval for x, y, z.

selectors = dec2base(labindex-1, N, 3) - '0' + 1;
ainit = x(selectors(1));
bfin = x(selectors(1)+1);
cinit = y(selectors(2));
dfin = y(selectors(2)+1);
einit = z(selectors(3));
ffin = z(selectors(3)+1);