Library: | fda |
See also: | Fourierevalgd polyevalgd |
Quantlet: | Bsplineevalgd | |
Description: | calculates the basis matrix phi of k-th order B-splines for a given strictly non-decreasing knot sequence. |
Usage: | phi = Bsplineevalgd(tvec,norder{,xvec{,deriv{,boolextend}}}) | |
Input: | ||
tvec | n x 1 vector, strictly non-decreasing knot sequence. The same knot sequence will be applied to all arguments xvec. | |
norder | integer, indicates the B-spline order (e.g. for cubic B-splines norder = 4) | |
xvec | p x q matrix, optional, arguments where the B-splines matrix should be evaluated at. The default value is tvec. | |
deriv | r x 1 vector of integers (>= 0), optional, contains the orders of derivatives to compute. If deriv = 0 the actual B-spline bases will be calculated. The default value is deriv = 0. | |
boolextend | scalar, optional, if boolextend = 1 tvec will be extended sufficiently to get multiple exterior knots. The default value is boolextend = 1. | |
Output: | ||
phi | (n x (n+norder-2) x r x q) array, values of all n+norder-2 B-spline basis functions of the knot sequence |
library("fda") tvec = #(0, 2, 3, 6, 10) Bsplineevalgd(tvec, 4, tvec, #(0, 2))
Contents of phi [,,1,1,1,1,1,1] [1,] 1 0 0 0 0 0 0 [2,] 0 0.11111 0.66667 0.22222 0 0 0 [3,] 0 0 0.375 0.59375 0.03125 0 0 [4,] 0 0 0 0.28571 0.53061 0.18367 0 [5,] 0 0 0 2.5023e-47 3.3808e-31 1.3323e-15 1 [,,2,1,1,1,1,1] [1,] 1.5 -2.5 1 0 0 0 0 [2,] 0 0.66667 -1 0.33333 0 0 0 [3,] 0 0 0.25 -0.4375 0.1875 0 0 [4,] 0 0 0 0.10714 -0.22959 0.12245 0 [5,] 0 0 0 4.7581e-17 0.21429 -0.58929 0.375