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I am generating a meshgrid to be able to calculate my result fast:

% x, y, z are some large vectors

[a,b,c] = meshgrid(x,y,z);

% s, t are constants, M some matrix

result = (((c*s - b*t).^2)./(a.^2 + b.^2 + c.^2)).*M;

This is actually working quite nicely. Unfortunately, for very large x,y,z, the meshgrid function is running out of memory.

How do I rewrite the meshgrid function to be memory efficient?

I had thought of three loops like this:

result = zeros(length(x), length(y), length(z));

for i = 1:lenght(x)-1

for j = y = 1:lenght(y)-1

for k = z = 1:lenght(z)-1

b = ??

c = ??

result(i,j,k) = (((c*s - b*t).^2)./(x(i)^2 + y(j)^2 + z(k).^2));

end

end

end

result = result.*M;

What are the values for b and c?

How can I turn the outer for into a parfor?

Fabio Freschi
on 11 Jun 2020

This is how to make the three-loop version analogous to the meshgrid version

% some dummy values

N = 300;

x = linspace(1,10,N);

y = linspace(1,10,N);

z = linspace(1,10,N);

s = 1;

t = 1;

M = rand(N,N,N);

%% meshgrid

tic

% x, y, z are some large vectors

[a,b,c] = meshgrid(x,y,z);

% s, t are constants, M some matrix

result = (((c*s - b*t).^2)./(a.^2 + b.^2 + c.^2)).*M;

toc

%% three-loops

tic

% preallocation

result2 = zeros(length(x), length(y), length(z));

% note the order of the for-loop indices to mimic meshgrid

for iz = 1:length(x)

for jx = 1:length(y)

for ky = 1:length(z)

result2(iz,jx,ky) = M(iz,jx,ky)*(((z(iz)*s - y(ky)*t).^2)./(x(jx)^2 + y(ky)^2 + z(iz).^2));

end

end

end

toc

% check results

norm(result(:)-result2(:))./norm(result(:))

However I don't see how you can avoid running out of memory: meshgrid is creating a N*N*N (with my notation) matrix, if it runs out of memory, also the preallocation of the result matrix will

result2 = zeros(length(x), length(y), length(z));

It is however true that in the second version you only have 2 matrices with dimensions N*N*N (M and result2) whereas in the first case you have 5 (a, b, c, M, result).

Note that according to my tests, the meshgrid version with vectorization is always faster than the version with three loops

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