spbase {JOPS}

Compute a sparse B-spline basis on evenly spaced knots

Description

Constructs a sparse B-spline basis on evenly spaced knots.

Usage

spbase(x, xl = min(x), xr = max(x), nseg = 10, bdeg = 3)

Arguments

x

a vector of argument values, at which the B-spline basis functions are to be evaluated.

xl

the lower limit of the domain of x (default min(x)).

xr

the upper limit of the domain of x (default max(x)) .

nseg

the number of evenly spaced segments between xl and xr (default 10).

bdeg

the degree of the basis, usually 1, 2, or 3 (default).

Value

A sparse matrix (in spam format) with length(x) of rows= and nseg + bdeg columns.

Author(s)

Paul Eilers

References

Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder), Statistical Science, 11: 89-121.

Eilers, P.H.C. and Marx, B.D. (2021). Practical Smoothing, The Joys of P-splines. Cambridge University Press.

Examples

library(JOPS)
# Basis  on grid
x = seq(0, 4, length = 1000)
B = spbase(x, 0, 4, nseg = 50, bdeg = 3)
nb1 = ncol(B)
matplot(x, B, type = 'l', lty = 1, lwd = 1, xlab = 'x', ylab = '')
cat('Dimensions of B:', nrow(B), 'by', ncol(B), 'with', length(B@entries), 'non-zero elements' )