On Tue, May 17, 2022 at 5:20 AM <saro...@gmail.com> wrote: > ### Proposed new feature or change: > > Description > ======== > > Often you want to randomize a "direction" that doesn't have "size". This > can be useful when: > * You want to randomize the direction of an NPC walk developing in a 2D or > 3D games, where its speed is a predefined constant. > * You're developing particles simulation with all particles moving in > random directions > * etc. > > This random direction should be an `n`th dimensional unit vector which is > randomize **uniformly** from the unit sphere. That means that sections of > the unit sphere with equal areas should have the same chance of getting a > vector from. > > Implementation > =========== > > If one wants to randomize `n`th dimensional direction uniformly, one must > do the following: > 1. Generate `n` components of the vector using the standard normal > distribution > 2. Find the norm the generated vector > 3. Divide the vector by its norm > > In simple Python code: > ```python > import numpy as np > > > def sphere_uniform(n: int): > vec = np.random.normal(size=n) > norm = np.sqrt(np.sum(vec ** 2)) > return vec / norm > ``` > > This implementation suggestion is based on [this blog post]( > https://towardsdatascience.com/the-best-way-to-pick-a-unit-vector-7bd0cc54f9b). > I'm not sure if there's a faster way of implementing it using C++ and > Cython, but I'm confident that someone here will know. >
I would probably use np.linalg.norm() to calculate the norm, but mostly for readability. > Why Implement It in Numpy? > =================== > > I believe that random unit vectors are common enough to be a part of > Numpy. Scientists, gamers and engineers use random directions all the time, > and I believe there is no reason why Numpy won't provide this ability. > As a general policy, we do not plan on adding more methods to Generator (c.f. discussion of a previous suggested addition[1]). This would be a good multivariate distribution to add to scipy.stats, though. [1] https://www.mail-archive.com/numpy-discussion@python.org/msg04724.html -- Robert Kern
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