B-spline basis by the Cox-de Boor recursion

Equally spaced interior knots with boundary knots repeated degree + 1 times, so the basis spans the interval and sums to one.

Usage

morie_bspline_basis(x, n_basis = 15L, degree = 3L)

Arguments

x

Evaluation points.

n_basis, degree

Basis size and spline degree.

Value

A matrix with one column per basis function.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_bspline_basis(V)
#>      [,1]        [,2]      [,3]       [,4]       [,5]      [,6]         [,7]
#> [1,]    1 0.000000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000000
#> [2,]    0 0.005830904 0.3367347 0.59669582 0.06073858 0.0000000 0.0000000000
#> [3,]    0 0.000000000 0.0000000 0.03109815 0.52235180 0.4334305 0.0131195335
#> [4,]    0 0.000000000 0.0000000 0.00000000 0.00000000 0.1049563 0.6477162293
#> [5,]    0 0.000000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0004859086
#> [6,]    0 0.000000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000000
#> [7,]    0 0.000000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000000
#> [8,]    0 0.000000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000000
#>           [,8]         [,9]     [,10]      [,11]      [,12]     [,13]
#> [1,] 0.0000000 0.0000000000 0.0000000 0.00000000 0.00000000 0.0000000
#> [2,] 0.0000000 0.0000000000 0.0000000 0.00000000 0.00000000 0.0000000
#> [3,] 0.0000000 0.0000000000 0.0000000 0.00000000 0.00000000 0.0000000
#> [4,] 0.2468416 0.0004859086 0.0000000 0.00000000 0.00000000 0.0000000
#> [5,] 0.2468416 0.6477162293 0.1049563 0.00000000 0.00000000 0.0000000
#> [6,] 0.0000000 0.0131195335 0.4334305 0.52235180 0.03109815 0.0000000
#> [7,] 0.0000000 0.0000000000 0.0000000 0.06073858 0.59669582 0.3367347
#> [8,] 0.0000000 0.0000000000 0.0000000 0.00000000 0.00000000 0.0000000
#>            [,14] [,15]
#> [1,] 0.000000000     0
#> [2,] 0.000000000     0
#> [3,] 0.000000000     0
#> [4,] 0.000000000     0
#> [5,] 0.000000000     0
#> [6,] 0.000000000     0
#> [7,] 0.005830904     0
#> [8,] 0.000000000     1