FGfun

M matrix in the envelope objective function. A $p$-by-$p$ positive semi-definite matrix.

U matrix in the envelope objective function. A $p$-by-$p$ positive semi-definite matrix.

The generic objective function listed below for estimating <code>M</code> envelope of <code>span(U)</code>
and its gradient value. For the detailed description, see Cook, R. D., &amp; Zhang, X. (2016).$$F(\Gamma)=\log|\Gamma^T M \Gamma|+\log|\Gamma^T(M+U)^{-1}\Gamma|$$

Provides three estimators for tensor response regression (TRR) and tensor predictor regression (TPR) models with tensor envelope structure. The three types of estimation approaches are generic and can be applied to any envelope estimation problems. The full Grassmannian (FG) optimization is often associated with likelihood-based estimation but requires heavy computation and good initialization; the one-directional optimization approaches (1D and ECD algorithms) are faster, stable and does not require carefully chosen initial values; the SIMPLS-type is motivated by the partial least squares regression and is computationally the least expensive.

Wenjing Wang

FGfun: The Objective function and its gradient

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