splineDesign {splines}R Documentation

Design Matrix for B-splines


Evaluate the design matrix for the B-splines defined by knots at the values in x.


splineDesign(knots, x, ord = 4, derivs, outer.ok = FALSE)
spline.des(knots, x, ord = 4, derivs, outer.ok = FALSE)


knots a numeric vector of knot positions with non-decreasing values.
x a numeric vector of values at which to evaluate the B-spline functions or derivatives. Unless outer.ok is truee, the values in x must be between knots[ord] and knots[ length(knots) + 1 - ord ].
ord a positive integer giving the order of the spline function. This is the number of coefficients in each piecewise polynomial segment, thus a cubic spline has order 4. Defaults to 4.
derivs an integer vector of the same length as x and with values between 0 and ord - 1. The derivative of the given order is evaluated at the x positions. Defaults to a vector of zeroes of the same length as x.
outer.ok logical indicating if x should be allowed outside the inner knots, see the x argument.


A matrix with length( x ) rows and length( knots ) - ord columns. The i'th row of the matrix contains the coefficients of the B-splines (or the indicated derivative of the B-splines) defined by the knot vector and evaluated at the i'th value of x. Each B-spline is defined by a set of ord successive knots so the total number of B-splines is length(knots)-ord.


The older spline.des function takes the same arguments but returns a list with several components including knots, ord, derivs, and design. The design component is the same as the value of the splineDesign function.


Douglas Bates and Bill Venables


splineDesign(knots = 1:10, x = 4:7)

knots <- c(1,1.8,3:5,6.5,7,8.1,9.2,10)# 10 => 10-4 = 6 Basis splines
x <- seq(min(knots)-1, max(knots)+1, length=501)
bb <- splineDesign(knots, x=x, outer.ok = TRUE)

plot(range(x), c(0,1), type="n", xlab="x", ylab="",
     main= "B-splines - sum to 1 inside inner knots")
mtext(expression(B[j](x) *"  and "* sum(B[j](x), j==1, 6)), adj=0)
abline(v=knots, lty=3, col="light gray")
abline(v=knots[c(4,length(knots)-3)], lty=3, col="gray10")
lines(x, rowSums(bb), col="gray", lwd=2)
matlines(x, bb, ylim = c(0,1), lty=1)

[Package splines version 2.5.0 Index]