PiS: Matrix projection onto the nuclear norm unit sphere
Description
Projection (with respect to the inner product defined by the Frobenius norm) of a matrix onto the unit sphere defined by the nuclear norm.
Usage
PiS(M)
Arguments
M
Input matrix
Value
A matrix of the same dimension as the input is returned.
Details
This is an auxiliary function used by the InspectChangepoint package. The projection is achieved by first performing a singular value decomposition, then projecting the vector of singular values onto the standard simplex, and finally using singular value decomposition in reverse to build the projected matrix.