# p-norms, Vector

peter miller fuchsia.groan at virgin.net
Mon Jun 5 11:09:21 UTC 2017

```Hi,

> In mathematics, the p-norm of a vector is defined as in .
>
> For p = 1, we get the taxicab norm,

`array.reduce( (a,b)=>a+b )` (Although I wouldn't object to `Math.sum()`)

> for p = 2 we get the Euclidean norm,

`Math.hypot(...array)`

> and
> for the limit as p → ±∞ we get the maximum/minimum norm.

`Math.max(...array)`

> Particularly the Euclidean norm is pretty common in graphics-related
> code.
>
> This could be implemented as an addition to`TypedArray.prototype`.
>
> A rough sketch might look like so:
>
> ```js
> TypedArray.prototype.norm = function(p) {
> 	if (Number.isNaN(p)) {
> 		return p;
> 	}
> 	const { abs, min, max, sign } = Math;
> 	if (Number.isFinite(p)) {
> 		return this.map(x => abs(x) ** p).reduce((a, b) => a + b, 0) ** (1 /
> p);
> 	}
> 	return abs((sign(p) === 1 ? max : min)(...this));
> };
> ```
>
> Since norms are a little too specific for `Array` (as they don't
> necessarily
> contain numerical values), it might be worth pondering about a
> native`Vector`
> implementation.
>

Will DOMPoint solve your use cases? (Personal annoyance: you can't index
DOMPoint numerically.)

Peter

--
"There were drawings, and sheets of paper with writing on them, and it
seemed that they were the sustenance of life, that here were the warlocks,
almost the vehicles of destruction of man's life, but at the same time the
very reason for his living." --- Maeve Gilmore/Titus Awakes.
```