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JuliaManifolds / ManifoldDiff.jl

Differentiation on manifolds
https://juliamanifolds.github.io/ManifoldDiff.jl/
MIT License
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Add diagonalizing bases for Grassmann and Stiefel #7

Open mateuszbaran opened 2 years ago

mateuszbaran commented 2 years ago

The formula for Grassmann is in Q. Rentmeesters, “A gradient method for geodesic data fitting on some symmetric Riemannian manifolds,” in 2011 50th IEEE Conference on Decision and Control and European Control Conference, Dec. 2011, pp. 7141–7146. doi: 10.1109/CDC.2011.6161280.

kellertuer commented 2 years ago

In IV. D I See Grassmann, where can I find Stiefel? And it seems a PDF can be obtained at https://folk.ntnu.no/skoge/prost/proceedings/cdc-ecc-2011/data/papers/1913.pdf

mateuszbaran commented 2 years ago

I don't currently know where to find Stiefel, I tried looking for it yesterday but didn't find it. Anyway, it would be nice to have it :slightly_smiling_face: .

mateuszbaran commented 2 years ago

For reference, for Grassmann manifold the better approach is diagonalizing projectors (which will be put in https://github.com/JuliaManifolds/ManifoldDiff.jl ). For Stiefel it seems unlikely that a closed-form formula exists.