# splineBasis1D: Calculate a spline basis decomposition for functional data on... In MFPCA: Multivariate Functional Principal Component Analysis for Data Observed on Different Dimensional Domains

## Description

These functions calculate a penalized or unpenalized spline basis decomposition for functional data on one-dimensional domains based on the gam function in the mgcv package.

## Usage

 ```1 2 3``` ```splineBasis1D(funDataObject, bs = "ps", m = NA, k = -1) splineBasis1Dpen(funDataObject, bs = "ps", m = NA, k = -1, parallel = FALSE) ```

## Arguments

 `funDataObject` An object of class `funData` containing the observed functional data samples and for which the basis decomposition is calculated. `bs` A character string, specifying the type of basis functions to be used. Defaults to `"ps"` (B-spline functions). Please refer to `smooth.terms` for a list of possible basis functions. `m` A numeric, the order of the spline basis. Defaults to `NA`, i.e. the order is chosen automatically. See `s` for details. `k` A numeric, the number of basis functions used. Defaults to `-1`, i.e. the number of basis functions is chosen automatically. See `s` for details. `parallel` Logical (only for `splineBasis1Dpen`. If `TRUE`, the coefficients for the basis functions are calculated in parallel. The implementation is based on the `foreach` function and requires a parallel backend that must be registered before. See `foreach` for details.

## Value

 `scores` A matrix of scores (coefficients) with dimension `N x K`, reflecting the weights for each of the `K` basis functions and for each of the `N` observations. `B` A matrix containing the scalar product of all pairs of basis functions. `ortho` Logical, set to `FALSE`, as basis functions are not orthonormal. `functions` `NULL`, as basis functions are known `settings` A list with entries `bs`, `m` and `k`, giving the actual parameters used for generating the spline basis functions.

`univDecomp`, `gam`, `foreach`