polar {epca}

Polar Decomposition

Description

Perform the polar decomposition of an n x p (n > p) matrix x into two parts: u and h, where u is an n x p unitary matrix with orthogonal columns (i.e. crossprod(u) is the identity matrix), and h is a p x p positive-semidefinite Hermitian matrix. The function returns the u matrix. This is a helper function of prs().

Usage

polar(x)

Arguments

x

a matrix or Matrix, which is presumed full-rank.

Value

a matrix of the unitary part of the polar decomposition.

References

Chen, F. and Rohe, K. (2020) "A New Basis for Sparse Principal Component Analysis."

Examples

x <- matrix(1:6, nrow = 3)
polar_x <- polar(x)