Get definitions for simple manifolds
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)
Dimension for manifold object (see Details)
Dimension for manifold object (see Details)
Multiplicity of this space. For example, use
numofmani = 2 if problem requires 2 points from this manifold
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.
Dimension for manifold object (see Details)
List containing input arguments and name field denoting the type of manifold
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
\(\{X \in R^{n \times n} : X^T X = I\}\)
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.