bm_harmonics: Mapper for cos/sin functions

In inlabru: Bayesian Latent Gaussian Modelling using INLA and Extensions

Mapper for cos/sin functions

Description

Constructs a mapper for cos/sin functions of orders 1 (if intercept is TRUE, otherwise 0) through order. The total number of basis functions is intercept + 2 * order.

Optionally, each order can be given a non-unit scaling, via the scaling vector, of length intercept + order. This can be used to give an effective spectral prior. For example, let

scaling = 1 / (1 + (0:4)^2)
x <- seq(0, 1, length.out = 11)
bmh1 = bm_harmonics(order = 4, interval = c(0, 1))
u1 <- ibm_eval(
  bmh1,
  input = x,
  state = rnorm(9, sd = rep(scaling, c(1, 2, 2, 2, 2)))
)

Then, with

bmh2 = bm_harmonics(order = 4, scaling = scaling)
u2 = ibm_eval(bmh2, input = x, state = rnorm(9))

the stochastic properties of u1 and u2 will be the same, with scaling^2 determining the variance for each frequency contribution.

The period for the first order harmonics is shifted and scaled to match interval.

Usage

bm_harmonics(order = 1, scaling = 1, intercept = TRUE, interval = c(0, 1))

bru_mapper_harmonics(...)

## S3 method for class 'bm_harmonics'
ibm_n(mapper, inla_f = FALSE, ...)

## S3 method for class 'bm_harmonics'
ibm_jacobian(mapper, input, state = NULL, inla_f = FALSE, ...)

Arguments

order	For bm_harmonics, specifies the maximum cos/sin order. (Default 1)
scaling	For bm_harmonics, specifies an optional vector of scaling factors of length intercept + order, or a common single scalar.
intercept	logical; For bm_harmonics, if TRUE, the first basis function is a constant. (Default TRUE)
interval	numeric length-2 vector specifying a domain interval. Default c(0, 1).
...	Arguments passed on to other methods
mapper	A mapper S3 object, inheriting from bru_mapper.
inla_f	logical; when TRUE for ibm_n() and ibm_values(), the result must be compatible with the INLA::f(...) and corresponding INLA::inla.stack(...) constructions. For ⁠ibm_{eval,jacobian,linear}⁠, the input interpretation may be different. Implementations do not normally need to do anything different, except for mappers of the type needed for hidden multicomponent models such as "bym2", which can be handled by bm_collect.
input	Data input for the mapper.
state	A vector of latent state values for the mapping, of length ibm_n(mapper, inla_f = FALSE)

See Also

bru_mapper, bru_mapper_generics

Other mappers: bm_aggregate(), bm_collect(), bm_const(), bm_factor(), bm_fmesher(), bm_index(), bm_linear(), bm_logsumexp(), bm_marginal(), bm_matrix(), bm_mesh_B(), bm_multi(), bm_pipe(), bm_repeat(), bm_scale(), bm_shift(), bm_sum(), bm_taylor(), bru_get_mapper(), bru_mapper(), bru_mapper.fm_mesh_1d(), bru_mapper.fm_mesh_2d(), bru_mapper_generics

Examples

m <- bm_harmonics(2)
ibm_eval2(m, input = c(0, pi / 4, pi / 2, 3 * pi / 4), 1:5)

inlabru documentation built on Aug. 9, 2025, 1:08 a.m.