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, deriv = 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)