[issue33089] Add multi-dimensional Euclidean distance function to the math module

[Steven D'Aprano]

Steven D'Aprano <steve+python at pearwood.info> added the comment:

The obvious work-around of calling hypot multiple times is not only tedious, but it loses precision. For example, the body diagonal through a 1x1x1 cube should be √3 exactly:

py> from math import hypot, sqrt
py> hypot(hypot(1, 1), 1) == sqrt(3)
False


I know of at least five languages or toolkits which support this feature, or something close to it: Javascript, Julia, Matlab, GNU Scientific Library, and C++.

Javascript and Julia support arbitrary numbers of arguments:

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/hypot

https://github.com/JuliaLang/julia/pull/15649

Using Firefox's javascript console, I get the correct body diagonal for the cube:

>> Math.hypot(1, 1, 1) == Math.sqrt(3)
true


Matlab's hypot() function only takes two arguments, but norm(vector) returns the Euclidean 2-norm of the vector, i.e. equivalent to the hypot of multiple arguments.

https://au.mathworks.com/help/matlab/ref/norm.html

The GNU Scientific Library and C++ support a three-argument form of hypot:

http://git.savannah.gnu.org/cgit/gsl.git/commit/?id=e1711c84f7ba5c2b22d023dcb7e10810233fff27

http://en.cppreference.com/w/cpp/numeric/math/hypot
http://open-std.org/JTC1/SC22/WG21/docs/papers/2015/p0030r1.pdf


So +1 on math.hypot supporting arbitrary number of arguments.

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