Taking the sum of exponentials

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(:)));

[Voss]

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

Answer 1

[Star Strider]

‘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.

Answer 2

[Paul]

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