Why is sum() slow on a matrix of symbolic expressions?

Question

Anthony 2012-5-10

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https://ww2.mathworks.cn/matlabcentral/answers/38017-why-is-sum-slow-on-a-matrix-of-symbolic-expressions

I have a vector A of symbolic expressions and I need to create a new symbolic expression that is the sum of the elements of A. When I try doing

f=sum(A);

mupkern runs out of memory and gets killed by the OS. However, after some experimentation, I realized that the following finishes quickly:

f=0;
for i=1:n
    f=f+A(i);
end

What is going on here?

I'm running Matlab R2010a on a Linux machine.

Here is some sample code to illustrate:

n=5000;
AA=cell(n,1);
for i=1:n
  AA{i}=sprintf('a%d',i);
end
A=sym(AA);
f=sum(A); % takes about 7 minutes on my machine
g=0;
for i=1:n % takes less than a minute on my machine
  g=g+A(i);
end

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Geoff 2012-5-10

Symbolic expressions are not native to computer hardware, whereas simple arithmetic is.

Anthony 2012-5-14

I'm summing symbolic expressions in both cases. The only difference is that in one I use "sum" and in the other I use "+"

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Answer 1

Walter Roberson 2012-5-10

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sum() applied to symbolic expressions is primarily for symbolic expression of indefinite summation. For example, finding the formula for the sum of 1/n^2 over a span of integers. When one is just wanting a total over a specific number of terms, then addition is the operator to use.

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Walter Roberson 2012-5-11

Good point about symsum()

Anthony 2012-5-14

Alexander, thank you for trying the example. Did the "sum" method and the "+" method take about the same amount of time to finish? It might have been more illustrative if the symbolic expressions in the elements of A were more complicated. This is the case in my application, but I simplified it for the example (since the difference in execution was still significant on my machine).

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