mkfun.tp {gss} | R Documentation |
Craft numerical functions to be used by mkterm
to
assemble model terms.
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)
dm |
Dimension of the variable d. |
order |
Order of the differential operator m. |
mesh |
Normalizing mesh. |
weight |
Normalizing weights. |
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.
A list of two components.
fun |
Function definition. |
env |
Portable local constants derived from the arguments. |
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.
Chong Gu, chong@stat.purdue.edu
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.
mkterm
, mkfun.poly
, and
mkrk.nominal
.