Generates basis matrix for integrals of B-splines.

## Arguments

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

- 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.

## Examples

```
library(splines2)
x <- seq.int(0, 1, 0.01)
knots <- c(0.2, 0.4, 0.7, 0.9)
ibsMat <- ibs(x, knots = knots, degree = 1, intercept = TRUE)
## get the corresponding B-splines by bSpline()
bsMat0 <- bSpline(x, knots = knots, degree = 1, intercept = TRUE)
## or by the deriv() method
bsMat <- deriv(ibsMat)
stopifnot(all.equal(bsMat0, bsMat, check.attributes = FALSE))
## plot B-spline basis with their corresponding integrals
op <- par(mfrow = c(1, 2))
matplot(x, bsMat, type = "l", ylab = "B-spline basis")
abline(v = knots, lty = 2, col = "gray")
matplot(x, ibsMat, type = "l", ylab = "Integral of B-spline basis")
abline(v = knots, lty = 2, col = "gray")
## reset to previous plotting settings
par(op)
```