Mapper for cos/sin functions

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)
#> $offset
#> [1]  7.000000 -7.247183  4.306719 -3.678570
#> 
#> $jacobian
#> 4 x 5 Matrix of class "dgeMatrix"
#>      [,1]       [,2]       [,3]       [,4]       [,5]
#> [1,]    1  1.0000000  0.0000000  1.0000000  0.0000000
#> [2,]    1  0.2205840 -0.9753680 -0.9026854 -0.4303012
#> [3,]    1 -0.9026854 -0.4303012  0.6296817  0.7768532
#> [4,]    1 -0.6188200  0.7855328 -0.2341236 -0.9722068
#>