Evaluate the design matrix for the B-splines defined by knots
at the values in x.
splineDesign(knots, x, ord = 4, derivs, outer.ok = FALSE,
sparse = FALSE)
spline.des (knots, x, ord = 4, derivs, outer.ok = FALSE,
sparse = FALSE)a numeric vector of knot positions (which will be sorted increasingly if needed).
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)].
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.
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).
logical indicating if x should be allowed
outside the inner knots, see the x argument.
logical indicating if the result should inherit from class
"sparseMatrix" (from package Matrix).
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.
# 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)
# }