Design Matrix for B-splines
Evaluate the design matrix for the B-splines defined by
at the values in
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.okis true, the values in
xmust be between the “inner” knots
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
ord - 1, conceptually recycled to the length of
x. The derivative of the given order is evaluated at the
xpositions. Defaults to zero (or a vector of zeroes of the same length as
- logical indicating if
xshould be allowed outside the inner knots, see the
- logical indicating if the result should inherit from class
"sparseMatrix"(from package Matrix">https://CRAN.R-project.org/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
knot vector and evaluated at the i'th value of
Each B-spline is defined by a set of
ord successive knots so
the total number of B-splines is
length(knots) - ord.
spline.des function takes the same arguments but
returns a list with several components including
component is the same as the value of the
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)