R: Convert a B-spline function to piece-wise polynomial form

ppBspline {fda} | R Documentation

## Convert a B-spline function to piece-wise polynomial form

### Description

The B-spline basis functions of order `k = length(t) - 1` defined by the knot sequence in argument `t` each consist of polynomial segments with the same order joined end-to-end over the successive gaps in the knot sequence. This function computes the `k` coefficients of these polynomial segments in the rows of the output matrix `coeff`, with each row corresponding to a B-spline basis function that is positive over the interval spanned by the values in `t`. The elements of the output vector `index` indicate where in the sequence `t` we find the knots. Note that we assume `t[1] < t[k+1]`, i.e. `t` is not a sequence of the same knot.

### Usage

      ppBspline(t)

### Arguments

`t` | numeric vector = knot sequence of length norder+1 where norder = the order of the B-spline. The knot sequence must contain at least one gap.

### Value

a list object containing components

`Coeff` | a matrix with rows corresponding to B-spline basis functions positive over the interval spanned by `t` and columns corresponding to the terms `1, x, x^2, ...` in the polynomial representation.
`index` | indices indicating where in the sequence `t` the knots are to be found

### See Also

`bsplineS`

### Examples

      ppBspline(1:5)

[Package fda version 2.4.8 Index]