mkfun.tp {gss} | R Documentation |
Crafting Building Blocks for Thin-Plate and Spherical Splines
Description
Craft numerical functions to be used by mkterm
to
assemble model terms.
Usage
mkrk.tp(dm, order, mesh, weight)
mkphi.tp(dm, order, mesh, weight)
mkrk.tp.p(dm, order)
mkphi.tp.p(dm, order)
mkrk.sphere(order)
Arguments
dm |
Dimension of the variable |
order |
Order of the differential operator |
mesh |
Normalizing mesh. |
weight |
Normalizing weights. |
Details
mkrk.tp
, mkphi.tp
, mkrk.tp.p
, and
mkphi.tp.p
implement the construction in Gu (2002,
Sec. 4.4). Thin-plate splines are defined for 2m>d
.
mkrk.tp.p
generates the pseudo kernel, and mkphi.tp.p
generates the (m+d-1)!/d!/(m-1)!
lower order polynomials with
total order less than m
.
mkphi.tp
generates normalized lower order polynomials
orthonormal w.r.t. a norm specified by mesh
and
weight
, and mkrk.tp
conditions the pseudo kernel to
generate the reproducing kernel orthogonal to the lower order
polynomials w.r.t. the norm.
mkrk.sphere
implements the reproducing kernel construction of
Wahba (1981) for m=2,3,4
.
Value
A list of two elements.
fun |
Function definition. |
env |
Portable local constants derived from the arguments. |
Note
mkrk.tp
and mkrk.sphere
create a bivariate function
fun(x,y,env,outer=FALSE)
, where x
, y
are real
arguments and local constants can be passed in through env
.
mkphi.tp
creates a collection of univariate functions
fun(x,nu,env)
, where x
is the argument and nu
is the index.
References
Gu, C. (2013), Smoothing Spline ANOVA Models (2nd Ed). New York: Springer-Verlag.
Wahba, G. (1981), Spline interpolation and smoothing on the sphere. SIAM Journal on Scientific and Statistical Computing, 2, 5–16.
See Also
mkterm
, mkfun.poly
, and
mkrk.nominal
.