deBoor2 {sglg}

Build the basis matrix and the penalty matrix of cubic B-spline basis.

Description

deBoor builds the basis matrix and penalty matrix to approximate a smooth function using cubic B-spline cubic.

Usage

deBoor2(t, knots)

Arguments

t

a vector of values.

knots

a set of internal knot.

Value

nknot number of knots.

knots set of knots.

N basis matrix.

K penalty matrix.

Author(s)

Carlos Alberto Cardozo Delgado <[e-mail]>

References

Carlos Alberto Cardozo Delgado, Semi-parametric generalized log-gamma regression models. Ph. D. thesis. Sao Paulo University.

Examples

set.seed(1)
t_1 <- runif(120)
range(t_1)
t_2 <- t_1 + 2  #runif(120,2,3)
range(t_2)
knot <- 10
dB1 <- deBoor2(t_1,knot)
dB2 <- deBoor2(t_2,knot)
dB1$knots
dB2$knots
plot(0,0,xlim=c(-0.5,3.5))
points(dB1$knots,rep(0,length(dB1$knots)),pch=20)
delta <- dB2$knots[1] - dB1$knots[1]
points(dB2$knots-delta,rep(0,length(dB2$knots)),pch=2,col= 'blue')
dB1$K
dB2$K
zeros <- vector()
plot(t_1,dB1$N[,1],pch=20)
for(j in 1:knot){
points(t_1,dB1$N[,j],pch=20,col=j)
zeros[j] <- sum(dB1$N[,j]==0)
}
zeros/120
cond_tNN <- vector()
KnotS <- 3:50
for(j in KnotS){
dB1 <- deBoor2(t_1,j)
print(dB1$knots[2]- dB1$knots[1])
min_max <- range(eigen(t(dB1$N)%*%dB1$N)$values)
cond_tNN[j-2] <- min_max[1]/min_max[2]
}
cond_tNN
plot(KnotS,cond_tNN,pch=20,ylim=c(0,0.07))