TRES (version 0.1.0)

manifold1D: Estimate the envelope subspace (ManifoldOptim 1D)

Description

The 1D algorithm to estimate the envelope subspace with specified dimension based on R package "ManifoldOptim".

Usage

manifold1D(M, U, u, params=NULL)

Arguments

M

M matrix in the envelope objective function. A \(p\)-by-\(p\) positive semi-definite matrix.

U

U matrix in the envelope objective function. A \(p\)-by-\(p\) positive semi-definite matrix.

u

Dimension of the envelope. An integer between 0 and \(p\).

params

Option structure with fields: "max_iter" -- max number of iterations. "tol" -- Tolerance used to assess convergence. See Huang et al (2018) for details on how this is used. "method" -- Name of optimization method supported by R package ManifoldOptim.

• "LRBFGS": Limited-memory RBFGS

• "LRTRSR1": Limited-memory RTRSR1

• "RBFGS": Riemannian BFGS

• "RBroydenFamily": Riemannian Broyden family

• "RCG": Riemannian conjugate gradients

• "RNewton": Riemannian line-search Newton

• "RSD": Riemannian steepest descent

• "RTRNewton": Riemannian trust-region Newton

• "RTRSD": Riemannian trust-region steepest descent

• "RTRSR1": Riemannian trust-region symmetric rank-one update

• "RWRBFGS": Riemannian BFGS

"check" -- Should internal manifold object check inputs and print summary message before optimization (TRUE or FALSE).

The default values are: "max_iter"=500; "tol"=1e-08; "method"="RCG"; "check"="False".

Value

Ghat

The orthogonal basis of the envelope subspace with each column represent the sequential direction. For example, the 1st column is the most informative direction.

Details

Estimate M-envelope contains span(U) where M > 0 and is symmetric. The dimension of the envelope is u.

References

Huang, W., Absil, P. A., Gallivan, K. A., & Hand, P. (2018). ROPTLIB: an object-oriented C++ library for optimization on Riemannian manifolds. ACM Transactions on Mathematical Software (TOMS), 44(4), 43.

Examples

# NOT RUN {
##simulate two matrices M and U with an envelope structure#
data <- MenvU_sim(n=200, p=20, u=5)
Mhat <- data$Mhat
Uhat <- data$Uhat
G <- data$Gamma

Ghat_1D <- manifold1D(Mhat, Uhat, u=5, params=NULL)
subspace(Ghat_1D, G)
# }