projections: Projection and Orthogonalisation
In lspls: LS-PLS Models

Description Usage Arguments Details Value Note Author(s) See Also Examples

Functions to project one matrix onto another, or to ortghogonalise it against the other.

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project(M, N)
orth(M, N)
Corth(M, N)

`M`	matrix to be projected or orthogonalised
`N`	matrix to be projected onto or orthogonalised against

project(M, N) calculates the projection of M onto N, i.e., N (N' N)^(-1) N' M.

orth(M, N) orthogonalises M with respect to N, i.e., it calculates the projection of M onto the orthogonal space of N: M - N (N' N)^(-1) N' M.

Corth(M, N) calculates the coefficient matrix needed to orthogonalise future matrices, that is, (N' N)^(-1) N' M. Future matrices m and n can be orthogonalised with m - n %*% Corth(M, N).

A matrix.

The functions need to be opitmised, both for speed and numerical accurracy.

Bjørn-Helge Mevik

lspls, lsplsCv, predict.lspls