bspline_basis-class {MECfda} | R Documentation |
b-spline basis
Description
A s4 class that represents a b-spline basis \{B_{i,p}(x)\}_{i=-p}^{k}
on the interval [t_0,t_{k+1}]
,
where B_{i,p}(x)
is defined as
B_{i,0}(x) = \left\{
\begin{aligned}
&I_{(t_i,t_{i+1}]}(x), & i = 0,1,\dots,k\\
&0, &i<0\ or\ i>k
\end{aligned}
\right.
B_{i,r}(x) = \frac{x - t_{i}}{t_{i+r}-t_{i}} B_{i,r-1}(x) + \frac{t_{i+r+1} - x}
{t_{i+r+1} - t_{i+1}}B_{i+1,r-1}(x)
For all the discontinuity points of B_{i,r}
(r>0
) in the interval (t_0,t_k)
,
let the value equals its limit, which means
B_{i,r}(x) = \lim_{t\to x} B_{i,r}(t)
Slots
Boundary.knots
boundary of the domain of the splines (start and end), which is
t_0
andt_{k+1}
. Default is[0,1]
. SeeBoundary.knots
inbs
.knots
knots of the splines, which is
(t_1,\dots,t_k)
, equally spaced sequence is chosen by the function automatically with equal space (t_j = t_0 + j\cdot\frac{t_{k+1}-t_0}{k+1}
) when not assigned. Seeknots
inbs
.intercept
Whether an intercept is included in the basis, default value is
TRUE
, and must beTRUE
. Seeintercept
bs
.df
degree of freedom of the basis, which is the number of the splines, equal to
p+k+1
. By defaultk = 0
, anddf
= p+1
. Seedf
bs
.degree
degree of the splines, which is the degree of piecewise polynomials
p
, default value is 3. Seedegree
inbs
.
Author(s)
Heyang Ji
Examples
bsb = bspline_basis(
Boundary.knots = c(0,24),
intercept = TRUE,
df = NULL,
degree = 3
)