4 ms·

Optimization problems take a vector of parameters. If you want to put units on your quantities & then optimize, you'll end up with this issue. Another instances

• neolog 5y ago
  Isn't a "vector" of parameters is really more of a tuple since they don't follow the vector laws and have fixed types in each field? Why do they use Base.Vector?
  • gradschoolfail 5y ago
    No, it is still base vector but with more structure, and not tuple. I would guess that the parent is talking about the general case, e.g. in (general)relativity where the vector laws you mention are not as simple as you think, i.e. they transform with a “metric” which is not simply the identity (non-Euclidean or non cartesian). It seems to me that this “metric” is a matrix of interunit conversions, though, so it is not that complicated either. In other words, (the Jacobian of) coordinate transforms (in your words, “vector laws”) can be expressed as Base.vector extended with unit conversion. In summary, general coordinates follow a nontrivial vector law where the units for each element of the array are not fixed/the same. E.g. cylindrical coordinates like the parent mentions, the si units are (m, m, rad) which still transform as a vector under the metric mentioned in [1] but which have heterogeneous units [1] https://math.stackexchange.com/questions/1144214/on-the-jacobian-determinant-for-conversion-to-cylindrical-coordinates https://math.stackexchange.com/questions/1144214/on-the-jaco... (The generalization of vector law is described in the first few eqs of the mathSE answer)