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 = bru_mapper_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 = bru_mapper_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

```
bru_mapper_harmonics(
order = 1,
scaling = 1,
intercept = TRUE,
interval = c(0, 1)
)
# S3 method for bru_mapper_harmonics
ibm_n(mapper, inla_f = FALSE, ...)
# S3 method for bru_mapper_harmonics
ibm_jacobian(mapper, input, state = NULL, inla_f = FALSE, ...)
```

## Arguments

- order
For

`bru_mapper_harmonics`

, specifies the maximum`cos`

/`sin`

order. (Default 1)- scaling
For

`bru_mapper_harmonics`

, specifies an optional vector of scaling factors of length`intercept + order`

, or a common single scalar.- intercept
logical; For

`bru_mapper_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)`

.- 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`bru_mapper_collect`

.- ...
Arguments passed on to other methods

- 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:
`bru_get_mapper()`

,
`bru_mapper()`

,
`bru_mapper.fm_mesh_1d()`

,
`bru_mapper.fm_mesh_2d()`

,
`bru_mapper_aggregate()`

,
`bru_mapper_collect()`

,
`bru_mapper_const()`

,
`bru_mapper_factor()`

,
`bru_mapper_generics`

,
`bru_mapper_index()`

,
`bru_mapper_linear()`

,
`bru_mapper_logsumexp()`

,
`bru_mapper_marginal()`

,
`bru_mapper_matrix()`

,
`bru_mapper_mesh_B()`

,
`bru_mapper_multi()`

,
`bru_mapper_pipe()`

,
`bru_mapper_scale()`

,
`bru_mapper_shift()`

,
`bru_mapper_taylor()`

## Examples

```
m <- bru_mapper_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
#>
```