Map reparameterised coefficients back to a smooth's own basis

mgcv::smooth2random() returns penalized design blocks (rand), an unpenalized null-space block (Xf), and the transformation back to the smooth's original constrained basis: $$\beta = U (D \cdot c(b_{rand}, b_{fixed})[idx])$$ with idx = c(rind, offset + seq_len(n_fixed)).

Usage

.reconstruct_map(re)

Details

For ordinary smooths rind is the identity, but for bs = "fs" it is a genuine permutation: the random blocks are penalty-major while the coefficients are level-major. Assuming cbind(rand, Xf) therefore gives silently wrong coefficients for factor-smooth interactions, so the map is built once here and reused. Returning it as an explicit matrix means the same object serves the point reconstruction and the delta-method covariance of a smooth.

Verified exact (to 6e-16) for s(), s(bs = "cr"), t2(), by = factors, bs = "fs" and bs = "re".