# What is the best way to write a function having many arguments?

I'd like to ask you guys what is the best way to write a function having a sequence of arguments?

If a function has $$x$$ and $$y$$ as its arguments then we write, $$f\left(x,y\right)$$ What if we have a function that takes $$x_i$$, $$\forall i=1,\cdots,N$$ ? I can try $$f\left(\mathbf x\right),$$ where $$\mathbf x = [x_1, x_2, \cdots, x_N]^\mathsf T$$.

How about that $$f$$ takes $$\mathbf x_i$$, $$\forall i=1,\cdots,N$$ ? Is it just okay that $$f\left(\mathbf x_i\right), \forall i=1,\cdots,N ?$$

Otherwise, $$f\left(\mathbf X\right),$$ where $$\mathbf X = [\mathbf x_1,\mathbf x_2, \cdots, \mathbf x_N]^\mathsf T$$.

But, I don't like to introduce a new symbol $$\mathbf X$$, and even in the function $$f$$, the $$\mathbf x_i$$s are manipulated individually not all together as a matrix, e.g., $$f\left(\mathbf x_1, \mathbf x_2, \cdots, \mathbf x_N\right) = \sum_{i=1}^N \sigma\left(\mathbf W\mathbf x_i + \mathbf b\right),$$ something like that.

Listing all the arguments as above is too verbose to me. Which way do you prefer to write a function like that? 😎

• Have you considered writing $f:(\mathbb R^N)^N\to \mathbb R^N$? May 14 at 4:28
• @JackozeeHakkiuz Yes, of course. The first introduction of $f$ can be written in that way. But, how about when I define $f$ explicitly, what $f$ takes specifically and which operations are applied to those arguments? I need some simple and neat ways to do it. May 14 at 15:21