Penalty approximation of unimodality constraints for univariates smooths

Usage

penalty_uni(coef, m, kappa = 1000, concave = TRUE, rho = 20)

Arguments

coef: coefficient vector of matrix on which to apply the unimodality penalty
m: vector of indices for the position of the coefficient mode. If coef is a vector, must be of length 1. Otherwise, must be of length equal to nrow(coef)
kappa: global scaling factor for the penalty
concave: logical; if TRUE (default), the penalty enforces increasing until the mode then decreasing. If the coefficients should decrease until the mode, then increase, set concave = FALSE.
rho: control parameter for smooth approximation to min(x, 0) used internally. For large values, gets closer to true minimum function but less stable.

Value

a numeric value of the penalty for the given coefficients

Examples

## coefficient vector
coef <- c(1, 2, 3, 2, 1)
# mode at position 3
penalty_uni(coef, m = 3) # basically zero
#> [1] 5.152884e-07
#' # mode at position 2
penalty_uni(coef, m = 2) # large positive penalty
#> [1] 1000

## coefficient matrix
coef <- rbind(coef, coef)
m <- c(1, 4)
penalty_uni(coef, m)
#> [1] 3000