Taking the sum of exponentials

Question

L'O.G. 2022-3-22

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回答： Star Strider 2022-3-22

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To do the calculation,

is the following code correct? Is the (:) necessary? I think that makes a column vector, but I don't think it's necessary. I don't think cumsum would be useful here. Could somebody please advise? If it matters,

. And a is a vector of

.

x = linspace(0.01,100,10000);
f_x = sum(exp(-x./a(:)));

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Voss 2022-3-22

Since a is already a column vector, the (:) is unnecessary, you're right.

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Answer 1

Star Strider 2022-3-22

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‘If it matters,

. And a is a vector of

.’

I don’t see ‘t’ defined anywhere, so it depends on what relationship ‘t’ has to ‘x’ or a.

However, since as @_ noted, since a is already a column vector by definition, the (:) is not necessary. The important aspect is that with respect to MATLAB coding, ‘x./a’ must be a matrix in order that sum produces the row vector necessary for the result.

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Answer 2

Paul 2022-3-22

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Break it up with simple inputs to see what's going on:

x = [1 2]; % row vector
a = [1 2 3]; % row vector
x./a(:) % implicit expansion makes a 3 x 2 matrix
ans = 3×2
    1.0000    2.0000
    0.5000    1.0000
    0.3333    0.6667
exp(x./a(:))  % element wise exp
ans = 3×2
    2.7183    7.3891
    1.6487    2.7183
    1.3956    1.9477
sum(exp(x./a(:))) % sum down the columns
ans = 1×2
    5.7626   12.0551