Description Usage Arguments Details Value References
Get definitions for simple manifolds
1 2 3 4 5 6 7 8 9 10 11 12 13 | get.stiefel.defn(n, p, numofmani = 1L, ParamSet = 1L)
get.grassmann.defn(n, p, numofmani = 1L, ParamSet = 1L)
get.spd.defn(n, numofmani = 1L, ParamSet = 1L)
get.sphere.defn(n, numofmani = 1L, ParamSet = 1L)
get.euclidean.defn(n, m, numofmani = 1L, ParamSet = 1L)
get.lowrank.defn(n, m, p, numofmani = 1L, ParamSet = 1L)
get.orthgroup.defn(n, numofmani = 1L, ParamSet = 1L)
|
n |
Dimension for manifold object (see Details) |
p |
Dimension for manifold object (see Details) |
numofmani |
Multiplicity of this space. For example, use
|
ParamSet |
A positive integer indicating a set of properties for the manifold which can be used by the solver. See Huang et al (2016b) for details. |
m |
Dimension for manifold object (see Details) |
The functions define manifolds as follows:
get.stiefel.defn
: Stiefel manifold
\{X \in R^{n \times p} : X^T X = I\}
get.grassmann.defn
: Grassmann manifold of p-dimensional
subspaces in R^n
get.spd.defn
: Manifold of n \times n symmetric positive
definite matrices
get.sphere.defn
: Manifold of n-dimensional vectors on
the unit sphere
get.euclidean.defn
: Euclidean R^{n \times m} space
get.lowrank.defn
: Low-rank manifold
\{ X \in R^{n \times m} : \textrm{rank}(X) = p \}
get.orthgroup.defn
: Orthonormal group
\{X \in R^{n \times n} : X^T X = I\}
List containing input arguments and name field denoting the type of manifold
Wen Huang, P.A. Absil, K.A. Gallivan, Paul Hand (2016a). "ROPTLIB: an object-oriented C++ library for optimization on Riemannian manifolds." Technical Report FSU16-14, Florida State University.
Wen Huang, Kyle A. Gallivan, and P.A. Absil (2016b). Riemannian Manifold Optimization Library. URL https://www.math.fsu.edu/~whuang2/pdf/USER_MANUAL_for_2016-04-29.pdf
S. Martin, A. Raim, W. Huang, and K. Adragni (2020). "ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization." Journal of Statistical Software, 93(1):1-32.
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