Manifolds

[kellertuer]

Both MVIRT and Manopt provide a set of manifolds to work with directly, the later a subset from the latter. This Issue keeps track of transferring these manifolds to Manopt.jl. This order follows the one from the Manopt Tutorial. Basic functions refers to all, that are available for any manifold (distance, dot, exp, norm, dot, manifoldDimension, parallelTransport) independent of its type (e.g. embedded or not). Documentation refers to proper documented functions and corresponding Documenter.jl page.

• Circle (phase data, i.e. Sn(1) represented as angles, Circle.jl)
• Euclidean (Euclidean.jl)
• Hyperbolic space (Hyperbolic.jl)
• Power Manifold ℳ ᵐ (Power.jl) extending an arbitrary manifold
• Product Manifold ℳ_1 × ⋯ × ℳ_m (Product.jl) extending an arbitrary manifold
• Symmetric Matrices (Symmetric.jl)
• Sphere (Sphere.jl)
• Symmetric Positive Definite Matrices (SymmetricPositiveDefinite.jl)
• Rotation Group (Rotations.jl)
• Tangent Bundle (´TangentBundle`, for any manifold using the induced metric and parallel transport).
• Skew-symmetric matrices
• Centered Matrices
• Symmetric Sphere
• Complex Sphere
• Oblique Manifold (use Power(Sphere(n-1),m)
• Complex oblique Manifold
• Complex Circle
• Phase of real DFT
• Stiefel Manifold (stacked gets Power)
• Complex Stiefel Manifold
• Generalized Stiefel anifold
• Grassamen manifold
• Complex Grassmann manifold
• Generalized Grassmann manifold
• Special Euclidean Group
• Essential Manifold
• Fixed-rank manifold
• Fixed Rank rensor
• Symmetric positive semidefinite, fixed rank (complex?)
• Symmetric Positive semidefinite, fixed rank with unit diagonal
• Symmetric Positive semidefinite, fixed rank with unit trance
• Multinomial manifold (will become Simplex in Combination with PowerManifold)
• Multinomial doubly stochastic manifold
• Multinomial symmetric and stochastic manifold

[kellertuer]

This issue is paused, since there is the project Manifolds.jl tackling these. Feel free to contribute there