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Mapper for cos/sin functions

Source: R/mappers.R
bm_harmonics.Rd

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(...)

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 bm_harmonics()

See also

bru_mapper, bru_mapper_generics

Other mappers: bm_aggregate(), bm_collect(), bm_const(), bm_factor(), bm_fm_mesh_1d, 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()

Other specific bm_harmonics method implementations: ibm_jacobian(), ibm_n()

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
#>