# splineDesign

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##### 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.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 \href{https://CRAN.R-project.org/package=#1}{\pkg{#1}}MatrixMatrix).
##### 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.

• splineDesign
• spline.des
##### Examples
library(splines) 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) 
Documentation reproduced from package splines, version 3.2.3, License: Part of R 3.2.3

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