| 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. (2002), Smoothing Spline ANOVA Models. 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.