splineDesign Design Matrix for B-splines

Description

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

Usage

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

Arguments

knots	a numeric vector of knot positions (which will be sorted increasingly if needed).
x	a numeric vector of values at which to evaluate the B-spline functions or derivatives. Unless outer.ok is true, the values in x must be between the “inner” knots knots[ord] and knots[ length(knots) - (ord-1)].
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 with values between 0 and ord - 1, conceptually recycled to the length of x. The derivative of the given order is evaluated at the x positions. Defaults to zero (or 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.
sparse	logical indicating if the result should inherit from class "sparseMatrix" (from package Matrix).

Value

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.

Note

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.

Author(s)

Douglas Bates and Bill Venables

Examples

require(graphics)
splineDesign(knots = 1:10, x = 4:7)
splineDesign(knots = 1:10, x = 4:7, derivs = 1)
## visualize band structure
Matrix::drop0(zapsmall(6*splineDesign(knots = 1:40, x = 4:37, sparse = TRUE)))

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.out = 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)