# 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.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 Matrix">https://CRAN.R-project.org/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)`

```
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 3.4.0, License: Part of R 3.4.0*

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