A very helpful graphic used to show the influence of a knot on a (uni-variable) spline function has been a plot of three control polygons:
The original control polygon with ξ and θ
The coarsened control polygon with ξ \ ξj and (WTW)-1WTθ
The control polygon after reinserting ξj, i.e., with ξ and W(WTW)-1WTθ
The function influence_weights already exists for finding the influence weight. This function will need a good name, perhaps influence_of?.
Initial thoughts for the API is:
influence_of(x, j)
where x would be a cpr_cp object and j is the index of attr(x, "xi") to omit.
A warning should be given if j is the index of a boundary knot.
The return should be a graphic and some other information, the index j, the value of the knot (the abscissa), the influence weight and rank.
Perhaps a vector of indices can be passed and a facetted graphic will be returned with a table of information, the index, abscissa, and the influence weight, and rank.
To make this a viable tool you'll need to reconsider how the spline data is used in plot.cpr_cp so that it can be extracted and used in plot.cpr_influence_of.
A very helpful graphic used to show the influence of a knot on a (uni-variable) spline function has been a plot of three control polygons:
The function
influence_weights
already exists for finding the influence weight. This function will need a good name, perhapsinfluence_of
?.Initial thoughts for the API is:
where
x
would be acpr_cp
object andj
is the index ofattr(x, "xi")
to omit.A warning should be given if
j
is the index of a boundary knot.The return should be a graphic and some other information, the index
j
, the value of the knot (the abscissa), the influence weight and rank.Perhaps a vector of indices can be passed and a facetted graphic will be returned with a table of information, the index, abscissa, and the influence weight, and rank.