How to make "sigma" summation of a function by i variable in GNU Octave? I need to make summation using function of a variable i like this: \begin{equation} \sum_{i=1}^5\left(|x_{i}| - |37-x_i|\right) \end{equation} In Maxima it is done like this (ar - array of $x_1$...$x_i$ values): ar:[1,2,3,4,5]; sum(ar[i]-abs(37-ar[i]), i, 1,5); Besides, Maxima allows even specifying infinite upper limit for summation (just write inf or infinity if I remember correctly). But I cannot find anything similar in GNU Octave - its sum() and symsum() seem to accept and summate only matrix/vector, but not a function.

First, suppose a vector $x$ is given, e.g. by


x = [2 3 5 7 11]


Then the following computes the sum:


sum(arrayfun(@(k) abs(x(k)) - abs(37 - x(k)), 1:5))


**Explanation**

1. `1:5` create a vector from $1$ to $5$
2. `@(k) abs(x(k)) - abs(37 - x(k))` create an anonymous function with one free variable $k$, such that when given $k$, computes $|x_k| - |37 - x_k|$
3. `arrayfun(@(k) abs(x(k)) - abs(37 - x(k)), 1:5)` applies the anonymous function pointwisely to each element in the vector, so it is the same as `map` in most functional programming language
4. `sum` adds up everything in the vector



**Abstraction**

In fact we can define the $\sum$ notation for finite sum by `sigma = @(f, a, b) sum(arrayfun(f, a:b))`. Then we can write the sum more succinctly as `sigma(@(k) abs(x(k)) - abs(37 - x(k)), 1, 5)`.

Feel free to ask if something is not clear.