Design Matrix for Bsplines
Description
Evaluate the design matrix for the Bsplines 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 Bspline
functions or derivatives. Unless outer.ok is true, the
values in x must be between the “inner” knots
knots[ord] and knots[ length(knots)  (ord1)] .

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 ith row of the matrix contains the coefficients of the
Bsplines (or the indicated derivative of the Bsplines) defined by
the knot
vector and evaluated at the ith value of x
.
Each Bspline is defined by a set of ord
successive knots so
the total number of Bsplines 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)
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)
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 = "Bsplines  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)