Design Matrix for Bsplines
Description
Evaluate the design matrix for the Bsplines defined by knots
at the values in x
.
Usage
1 2 3 4  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 
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 
outer.ok 
logical indicating if 
sparse 
logical indicating if the result should inherit from class

Value
A matrix with length(x)
rows and length(knots)  ord
columns. The i'th 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 i'th 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  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 => 104 = 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 = "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)
