Produces the derivatives of given order of B-splines.

## Usage

```
dbs(
x,
derivs = 1L,
df = NULL,
knots = NULL,
degree = 3L,
intercept = FALSE,
Boundary.knots = NULL,
...
)
```

## Arguments

- x
The predictor variable. Missing values are allowed and will be returned as they are.

- derivs
A positive integer specifying the order of derivative. The default value is

`1L`

for the first derivative.- df
Degree of freedom that equals to the column number of the returned matrix. One can specify

`df`

rather than`knots`

, then the function chooses`df - degree - as.integer(intercept)`

internal knots at suitable quantiles of`x`

ignoring missing values and those`x`

outside of the boundary. If internal knots are specified via`knots`

, the specified`df`

will be ignored.- knots
The internal breakpoints that define the splines. The default is

`NULL`

, which results in a basis for ordinary polynomial regression. Typical values are the mean or median for one knot, quantiles for more knots.- degree
A nonnegative integer specifying the degree of the piecewise polynomial. The default value is

`3`

for cubic splines. Zero degree is allowed for piecewise constant basis functions.- intercept
If

`TRUE`

, the complete basis matrix will be returned. Otherwise, the first basis will be excluded from the output.- Boundary.knots
Boundary points at which to anchor the splines. By default, they are the range of

`x`

excluding`NA`

. If both`knots`

and`Boundary.knots`

are supplied, the basis parameters do not depend on`x`

. Data can extend beyond`Boundary.knots`

.- ...
Optional arguments that are not used.

## Value

A numeric matrix of `length(x)`

rows and `df`

columns if

`df`

is specified or ```
length(knots) + degree +
as.integer(intercept)
```

columns if `knots`

are specified instead.
Attributes that correspond to the arguments specified are returned
mainly for other functions in this package.

## Details

This function provides a more user-friendly interface and a more consistent
handling for `NA`

's than `splines::splineDesign()`

for derivatives
of B-splines. The implementation is based on the closed-form recursion
formula. At knots, the derivative is defined to be the right derivative
except at the right boundary knot.

## Examples

```
library(splines2)
x <- seq.int(0, 1, 0.01)
knots <- c(0.2, 0.4, 0.7)
## the second derivative of cubic B-splines with three internal knots
dMat <- dbs(x, derivs = 2L, knots = knots, intercept = TRUE)
## compare with the results from splineDesign
ord <- attr(dMat, "degree") + 1L
bKnots <- attr(dMat, "Boundary.knots")
aKnots <- c(rep(bKnots[1L], ord), knots, rep(bKnots[2L], ord))
res <- splines::splineDesign(aKnots, x = x, derivs = 2L)
stopifnot(all.equal(res, dMat, check.attributes = FALSE))
```