Further updates to manifolds docs #840
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I've read the page once again and changed to notation to something more similar to JuliaManifolds. Tangent vectors are denoted by capital letters X, Y, Z, Lie algebras are written using `\mathfrak` and manifolds using `\mathcal` fonts. I have a few notes to clarify some parts: 1. What do you mean by "Multiple `X = log(M,p,q)` types" in Q2? The fact that on some manifolds logarithmic map may have multiple values? That there are multiple ways to compute or approximate `log` (not really on (most of) the manifolds you use, but it's important for Stiefel for example)? 2. Regarding "Projections are somewhat ambiguous, since on the one hand it might mean that a point from the manifold is projected up onto a nearby tangent space.", this is not something we do in Manifolds.jl. Projections either project a point in the embedding to a point on the manifold, or a vector from the embedding onto a tangent space at a certain point. The operation in Manifolds.jl that does more or less "a point from the manifold is projected up onto a nearby tangent space" is what we call an inverse retraction.
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Ah great thanks!
We should probably clarify that properly here. I'm referring to the micro Lie theory discussion: I'll send a small PR review over with the change to fix this.
Can I just copy this in? I'll send a second small PR... |
OK, I see. I will try to find a good wording for that -- on one hand we have different parametrizations, on another one we have different metrics.
Sure, of course! |
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@mateuszbaran , I was not able to request a review through the Github interface on the two small PRs, |
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both are there, thanks very much for taking a look! |
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No problem! |
I've read the page once again and changed to notation to something more similar to JuliaManifolds. Tangent vectors are denoted by capital letters X, Y, Z, Lie algebras are written using
\mathfrakand manifolds using\mathcalfonts.I have a few notes to clarify some parts:
X = log(M,p,q)types" in Q2? The fact that on some manifolds logarithmic map may have multiple values? That there are multiple ways to compute or approximatelog(not really on (most of) the manifolds you use, but it's important for Stiefel for example)?