Nothing
#Predict.matrix <- mgcv::Predict.matrix
#formals(Predict.matrix) <- c(formals(Predict.matrix), alist(... = ))
#### Define penalized splines with truncated lines
#### m is order of the spline, m-1 is the degree
#p-splines with truncated polynomials
`smooth.construct.tl.smooth.spec` <-
function(object,data,knots)
{
m<-object$p.order # p+1
if (is.na(m)) m<-3
if (m==1) {warning("for estimation the order of the spline was set to its default 3"); m <- 3}
m <- c(m-1,m)
nk<-object$bs.dim # number of interior knots
x <- get.var(object$term,data) # find the data
if (!is.null(knots)) k <- get.var(object$term,knots)
else k<-NULL
if (is.null(k))
k <- quantile(unique(x),seq(0,1,length=(nk+2))[-c(1,(nk+2))])
names(k) <- NULL
z=outer(x,k,"-")
z=z*(z>0)
Z=z^(m[1])
X=rep(1,length(x))
for (i in 1:(m[1])) X=cbind(X,x^i)
object$X<-cbind(X,Z) # get model matrix
if (!object$fixed)
{ S<-diag(c(rep(0,m[2]),rep(1,nk)))
object$S<-list(S) # get penalty
}
object$rank<-nk # penalty rank
object$null.space.dim <- m[1] # dimension of unpenalized space
object$knots<-k;object$m<-m # store p-spline specific info.
object$df<-ncol(object$X) # maximum DoF
class(object)<-"tlspline.smooth" # Give object a class
object
}
`Predict.matrix.tlspline.smooth` <-
function(object,data,...)
# prediction method function for the p.spline smooth class
{
x <- get.var(object$term,data)
m=object$m
k=object$knots
z=outer(x,k,"-")
z=z*(z>0)
Z=z^(m[1])
X=rep(1,length(x))
for (i in 1:(m[1])) X=cbind(X,x^i)
X<-cbind(X,Z) # get model matrix
X
}
#### Define penalized splines with cubic B-splines
#### and the penalty as the integrated squared second derivative
#### see Wand and Ormerod (2008) - O'Sullivan splines
`smooth.construct.os.smooth.spec` <- function(object,data,knots)
{
m <- object$p.order
if (length(m)<2) if (is.na(m)) m <- c(3,2)
object$p.order <- m
if (length(m)==1){
if (((object$p.order+1)/2)%%1 != 0) {warning("If only degree of B-spline basis is given, degree must be chosen such that q=(p+1)/2 is an integer. Set to its default p=3, q=2."); m =c(3,2)}
else m <- c(object$p.order, (object$p.order+1)/2)
}
p=m[1]
q=m[2]
if (object$bs.dim < 0) object$bs.dim <- max(10, m[1] + 1)
nk <- object$bs.dim
if (nk <= 0) stop("basis dimension too small for b-spline order")
x <- data[[object$term]]
#if (any(round(diff(knots[[object$term]]),6)!=round(diff(knots[[object$term]])[1],6))) warning("Forcing equidistant knots.")
knots= seq(min(x),max(x),length=nk+2)[-c(1,nk+2)]
names(knots) <- NULL
object$X <-bs(x,knots=knots,degree=m[1],Boundary.knots=c(min(x),max(x)),intercept=T)
object$X=t(apply(object$X,1,function(x) x-colSums(object$X)/length(data[[object$term]]))) # C=(diag(rep(1,n))-1/n)%*%C
d=diag(ncol(object$X))
for(i in 1:q){
d=diff(d)
allKnots_p <- c(rep(min(x),p+1-i),knots,rep(max(x),p+1-i))
weights=matrix(rep(1/(allKnots_p[-(1:(p+1-i))]-allKnots_p[-((nk+2*p-p-i+2):(nk+2*p))]),each=ncol(d)),ncol(d),nrow(d))
d=d*(p+1-i)*t(weights)
}
#calculate the matrix R (integral over product of two B-spline bases)
allKnots <- c(rep(min(x),(p-q)+1),knots,rep(max(x),(p-q)+1))
R_int= matrix(0,nk+p+1-q,nk+p+1-q)
for (i in 1:(nk+p-q+1)){
for (j in i:(min(i+p-q,nk+p-q+1))){
R <- function(x){
Nq <- spline.des(allKnots,x,p-q+1,derivs=0*x,outer.ok=T)$design
Nq[,i]*Nq[,j]
}
x1=allKnots[j]
x2=allKnots[(i+(p-q)+1)]
R_int[i,j] <- integrate(R,x1,x2,subdivisions=1000)$value
}
}
R_int <- R_int+t(R_int)
diag(R_int)<- diag(R_int)/2
Dq=t(d)%*%R_int%*%d
object$S<-list(Dq)
object$rank <- object$bs.dim - m[2]
object$null.space.dim <- m[2]
object$knots <- knots
object$m <- m
class(object) <- "ospline.smooth"
object
}
Predict.matrix.ospline.smooth<-function(object,data,drv=0,...){
# prediction method function for the p.spline smooth class
X <-bs2(data[[object$term]],knots=object$knots,degree=object$m[1],Boundary.knots=c(min(data[[object$term]]),max(data[[object$term]])),intercept=T,drv=drv)
X
}
Predict.matrix.lme <-function(object,data,drv=0,center=T,...)
# prediction method function for the p.spline smooth class
{
m <- object$m
q=m[2]
p=m[1]
x <- data[[object$term]]
n=length(x)
k=object$knots
nk <- object$bs.dim
if (inherits(object,"ospline.smooth")){
X <- Predict.matrix.ospline.smooth(object, data,drv=drv) # Model matrix
d=diag(ncol(X))
for(i in 1:q){
d=diff(d)
allKnots_p <- c(rep(min(x),p+1-i),k,rep(max(x),p+1-i))
weights=matrix(rep(1/(allKnots_p[-(1:(p+1-i))]-allKnots_p[-((nk+2*p-p-i+2):(nk+2*p))]),each=ncol(d)),ncol(d),nrow(d))
d=d*(p+1-i)*t(weights)
}
#calculate the matrix R (integral over product of two B-spline bases)
allKnots <- c(rep(min(x),(p-q)+1),k,rep(max(x),(p-q)+1))
R_int= matrix(0,nk+p+1-q,nk+p+1-q)
for (i in 1:(nk+p-q+1)){
for (j in i:(min(i+p-q,nk+p-q+1))){
R <- function(x){
Nq <- spline.des(allKnots,x,p-q+1,derivs=0*x,outer.ok=T)$design
Nq[,i]*Nq[,j]
}
x1=allKnots[j]
x2=allKnots[(i+(p-q)+1)]
R_int[i,j] <- integrate(R,x1,x2,subdivisions=1000)$value
}
}
R_int <- R_int+t(R_int)
diag(R_int)<- diag(R_int)/2
# calculate the Durban-decomposition for the mixed models
Re=eigen(R_int)
Re12=Re$vectors%*%diag(sqrt(Re$values))%*%t(Re$vectors)
D=Re12%*%d
DI=tcrossprod(D) #DI=D%*%t(D)
# centering
if (center) X=t(apply(X,1,function(x) x-colSums(X)/n))
Z=X%*%t(D)%*%solve(DI)
Dq=t(d)%*%R_int%*%d
O.e=eigen(Dq)
null.space=(ncol(X)-q+1):(ncol(X)-1)
U0=O.e$vectors[,null.space]
C=X%*%U0
dimnames(C)[[2]]=NULL
newknots=seq(min(x),max(x),length=nk+p+1-q+2)[-c(1,nk+p+1-q+2)]
return(list(C=C,Z=Z, knots=newknots))
}
else if (inherits(object,"tlspline.smooth") | inherits(object, 'trunc.poly')) {
x<- as.vector(data[[object$term]])
Z <- outer(x,k,"-")
Z <- (Z*(Z>0))^m[1]
C=rep(1,length(x))
for (i in 1:(m[1])) C=cbind(C,x^i)
#centering
if(center){
n=nrow(C)
colSC= colSums(C)
colSZ= colSums(Z)
C=t(apply(C,1,function(x) x-colSC/n)) #C=(diag(rep(1,n))-1/n)%*%C
Z=t(apply(Z,1,function(x) x-colSZ/n)) #Z=(diag(rep(1,n))-1/n)%*%Z
}
}
else if (inherits(object,"tps") | inherits(object, 'ts.smooth')){
if (is.null(m)) m=object$p.order
if (is.null(k)) stop("No knots given in smooth.construct.")
x<- as.vector(data[[object$term]])
svd.Omega = svd(abs(outer(k,k,"-"))^m[1])
matrix.sqrt.Omega = t(svd.Omega$v %*% (t(svd.Omega$u) * sqrt(svd.Omega$d)))
Z = t(solve(matrix.sqrt.Omega, t(abs(outer(x, k,"-")^m[1]))))
C = cbind(rep(1,length(x)))
for (i in 1:((m[1]-1)/2)) C=cbind(C,x^i)
#centering
if(center){
n=nrow(C)
colSC= colSums(C)
colSZ= colSums(Z)
C=t(apply(C,1,function(x) x-colSC/n)) #C=(diag(rep(1,n))-1/n)%*%C
Z=t(apply(Z,1,function(x) x-colSZ/n)) #Z=(diag(rep(1,n))-1/n)%*%Z
}
}
else stop ("scbM can be fitted only with os, tl or tps basis functions")
list(C=C,Z=Z)
}
bs2=function (x, df = NULL, knots = NULL, degree = 3, intercept = FALSE, Boundary.knots = range(x),drv=0)
{
nx <- names(x)
x <- as.vector(x)
nax <- is.na(x)
if (nas <- any(nax))
x <- x[!nax]
if (!missing(Boundary.knots)) {
Boundary.knots <- sort(Boundary.knots)
outside <- (ol <- x < Boundary.knots[1L]) | (or <- x >
Boundary.knots[2L])
}
else outside <- FALSE
ord <- 1 + (degree <- as.integer(degree))
if (ord <= 1)
stop("'degree' must be integer >= 1")
if (!missing(df) && missing(knots)) {
nIknots <- df - ord + (1 - intercept)
if (nIknots < 0) {
nIknots <- 0
warning("'df' was too small; have used ", ord -
(1 - intercept))
}
knots <- if (nIknots > 0) {
knots <- seq.int(from = 0, to = 1, length.out = nIknots +
2)[-c(1, nIknots + 2)]
stats::quantile(x[!outside], knots)
}
}
Aknots <- sort(c(rep(Boundary.knots, ord), knots))
if (any(outside)) {
warning("some 'x' values beyond boundary knots may cause ill-conditioned bases")
derivs <- 0:degree
scalef <- gamma(1L:ord)
basis <- array(0, c(length(x), length(Aknots) - degree -
1L))
if (any(ol)) {
k.pivot <- Boundary.knots[1L]
xl <- cbind(1, outer(x[ol] - k.pivot, 1L:degree,
"^"))
tt <- spline.des(Aknots, rep(k.pivot, ord), ord,
derivs)$design
basis[ol, ] <- xl %*% (tt/scalef)
}
if (any(or)) {
k.pivot <- Boundary.knots[2L]
xr <- cbind(1, outer(x[or] - k.pivot, 1L:degree,
"^"))
tt <- spline.des(Aknots, rep(k.pivot, ord), ord,
derivs)$design
basis[or, ] <- xr %*% (tt/scalef)
}
if (any(inside <- !outside))
basis[inside, ] <- spline.des(Aknots, x[inside],
ord)$design
}
else basis <- spline.des(Aknots, x, ord,derivs=rep(drv,length(x)))$design
if (!intercept)
basis <- basis[, -1L, drop = FALSE]
n.col <- ncol(basis)
if (nas) {
nmat <- matrix(NA, length(nax), n.col)
nmat[!nax, ] <- basis
basis <- nmat
}
dimnames(basis) <- list(nx, 1L:n.col)
a <- list(degree = degree, knots = if (is.null(knots)) numeric(0L) else knots,
Boundary.knots = Boundary.knots, intercept = intercept)
attributes(basis) <- c(attributes(basis), a)
class(basis) <- c("bs", "basis")
basis
}
drvbasis<-function(x,degree,knots,drv=0,basis){
if (drv>=degree) stop("WARNING: drv >= degree, derivative order must be lower than degree of the spline.")
X <- NULL
if (basis=="tlspline.smooth") ncol.X <- degree
else if (basis == "tps"|basis=='ts.smooth') ncol.X <- (degree - 1)/2
else stop("Unsupported basis function.")
for (pow in 1:ncol.X) {
pow.drv <- pow - drv
if (pow.drv >= 0) new.col <- prod(pow:(pow.drv + 1)) * (x^pow.drv)
else new.col <- rep(0, length(x))
X <- cbind(X, new.col)
}
X=cbind(0,X)
Z <- outer(as.vector(x), knots, "-")
if (basis=="tlspline.smooth"){
if (degree >= drv) {
mfac <- prod((degree - drv + 1):degree)
Z <- mfac * (Z * (Z > 0))^(degree - drv)
}
}
else if (basis=="tps"|basis=='ts.smooth'){
if (degree >= drv) {
mfac <- prod((degree - drv + 1):degree)
Z <- mfac * (Z^(degree -
drv - 1) * abs(Z))
svd.Omega = svd(abs(outer(knots,knots,"-"))^degree)
sqrt.Omega = t(svd.Omega$v %*% (t(svd.Omega$u) * sqrt(svd.Omega$d)))
Z <- t(solve(sqrt.Omega, t(Z)))
}
}
X <-cbind(X,Z)
X
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.