splineDesign
Design Matrix for B-splines
Evaluate the design matrix for the B-splines defined by knots
at the values in x.
- Keywords
- models
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.okis true, the values inxmust be between the “inner” knotsknots[ord]andknots[ 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
0andord - 1, conceptually recycled to the length ofx. The derivative of the given order is evaluated at thexpositions. Defaults to zero (or a vector of zeroes of the same length asx).- outer.ok
logical indicating if
xshould be allowed outside the inner knots, see thexargument.- 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.
Examples
library(splines)
# NOT RUN {
require(graphics)
splineDesign(knots = 1:10, x = 4:7)
splineDesign(knots = 1:10, x = 4:7, deriv = 1)
## visualize band structure
# }
# NOT RUN {
Matrix::drop0(zapsmall(6*splineDesign(knots = 1:40, x = 4:37, sparse = TRUE)))
# }
# NOT RUN {
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)
# }