penalty function

B-Spline penalty

This function calculates the B-Spline basis penalty. It follows the procedure outlined in the paper by Zheyuan Li, Jiguo Cao, 2022 "General P-Splines for Non-Uniform B-Splines" tools:::Rd_expr_doi("10.48550/arXiv.2201.06808") . For equidistant knots it coincides with the usual penalty based on the identitiy. For non-equidistant knots it is a weighted penalty with respect to the knot distances. In addition to the above, we added the possibility to calculate periodic penalties which are based on the periodic differencing matrices.

penalty(knots, order, periodic = FALSE, max_diff = 999L)

Arguments

• knots: Vector of knots.
• order: Order of the Basis (degree + 1).
• periodic: Whether the penalties should be periodic or not.
• max_diff: Maximum difference order to calculate.

Returns

Returns a list of (order - 1) penalty matrices.

Examples

## Not run:

# Equidistant knots with order 2
knots <- 1:10

P <- penalty(knots, order = 2)

print(P[[1]]) # First differences

# Non equidistant knots
knots <- c(0, 0, 0, 0, 1, 3, 4, 4, 4, 4)

P <- penalty(knots, order = 4)

print(P[[1]]) # First differences
print(P[[2]]) # Second differences
print(P[[3]]) # Third differences

# Periodic penalty for equidistant knots
oder <- 4
deg <- order - 1
knots <- 1:15

penalty(knots, order = order, periodic = TRUE)[[1]]
penalty(knots, order = order, periodic = TRUE)[[2]]
penalty(knots, order = order, periodic = TRUE)[[3]]
## End(Not run)