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K-orthogonal projector onto span(T) in effect space

Source: R/dkge-cpca.R
dkge_projector_K.Rd

Builds both the K-selfadjoint projector operating in effect coordinates and the Euclidean projector in the \(K^{1/2}\) metric. These projectors are useful for CPCA-style splits of the compressed covariance.

Usage

dkge_projector_K(T, K)

Arguments

T

qxq0 matrix whose columns span the subspace of interest.

K

qxq positive semi-definite design kernel.

Value

List with entries `P_K` (effect-space projector) and `P_hat` (projector in the \(K^{1/2}\) metric).

Details

All computations take place in the metric induced by the design kernel `K`. Choosing a non-identity kernel therefore changes the projector: smooth kernels diffuse energy across correlated effects, whereas a diagonal kernel keeps the split tied to the raw effect indices. When the design-aligned subspace is not well represented by coordinate axes, supply `cpca_T` with columns that already capture the kernel geometry so the CPCA basis respects those relationships.

Examples

K <- diag(5)
T <- matrix(rnorm(10), 5, 2)
P <- dkge_projector_K(T, K)
dim(P$P_K)
#> [1] 5 5