"Vectorization" of a script with a matrix

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Hayao
Hayao 2018-7-9
编辑： Hayao 2018-7-9
Dear all,
I am trying to make a code that does certain calculations on a (very large) symbolic matrix as fast as possible.
I know that symbolic calculation is a very costly calculation. Therefore, I resolved to initially substituting the variable (with certain intervals), since I will be doing that after the solution is obtained anyway. However that means I have two options: 1) use parfor (I have parallel computing toolbox), or 2) vectorize. I have problem doing the latter, which I suppose many people will recommend over parfor.
For the parfor method, for example, I can make:
M1 = zeros(s,2000);
parfor t = 1:2000
A1 = randi(1000,s);
A2 = diag(diag(A1));
M1(:,t) = (exp(-A2*0.000002*t)-ones(s)+eye(s))*rand(s,1);
end
M1
where "s" defines the size of the diagonal matrix A2.
This code becomes faster than normal for-loop when "s" is larger than somewhere around 65, and significantly faster on the scale that I plan to work in (certainly more than 10000). By the way, I am running the code in 16-workers parallel computing mode.
However, for the latter vectorization method,
M3 = zeros(s,2000);
t = 1:0.000002:0.004;
A1 = randi(1000,s);
A2 = diag(diag(A1));
M3(:,t) = (exp(-A2*t)-ones(s)+eye(s))*rand(s,1);
M3
Obviously, this is not going to work. You can't substitute an array into a calculation like this. Can anyone suggest me a vectorization method for this case? Is it possible? And do you think this will improve in speed (and memory) over parfor?
Thank you.

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