# bSpline

##### B-Spline Basis for Polynomial Splines

This function generates the B-spline basis matrix for a polynomial spline.

##### Usage

```
bSpline(x, df = NULL, knots = NULL, degree = 3L, intercept = FALSE,
Boundary.knots = range(x, na.rm = TRUE), ...)
```

##### Arguments

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

- df
Degrees of freedom. One can specify

`df`

rather than`knots`

, then the function chooses "df - degree" (minus one if there is an intercept) knots at suitable quantiles of`x`

(which will ignore missing values). The default,`NULL`

, corresponds to no inner knots, i.e., "degree - intercept". If`knots`

was specified,`df`

specified will be ignored.- knots
The internal breakpoints that define the spline. 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. See also`Boundary.knots`

.- degree
Non-negative integer degree of the piecewise polynomial. The default value is 3 for cubic splines. Zero degree is allowed for this function, which is the only difference compared with

`bs`

in package`splines`

.- intercept
If

`TRUE`

, an intercept is included in the basis; Default is`FALSE`

.- Boundary.knots
Boundary points at which to anchor the B-spline basis. By default, they are the range of the non-

`NA`

data. If both`knots`

and`Boundary.knots`

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

. Data can extend beyond`Boundary.knots`

.- ...
Optional arguments for future usage.

##### Details

It is an augmented function of `bs`

in package
`splines`

for B-spline basis that allows piecewise constant (close on
the left, open on the right) spline basis with zero degree. When the
argument `degree`

is greater than zero, it internally calls
`bs`

and generates a basis matrix for representing the
family of piecewise polynomials with the specified interior knots and
degree, evaluated at the values of `x`

. The function has the same
arguments with `bs`

for ease usage.

##### Value

A matrix of dimension `length(x)`

by
`df = degree + length(knots)`

(plus one if intercept is included).
Attributes that correspond to the arguments specified are returned
for usage of other functions in this package.

##### See Also

`predict.bSpline2`

for evaluation at given (new) values;
`dbs`

, `deriv.bSpline2`

for derivatives;
`ibs`

for integral of B-splines;
`mSpline`

for M-splines;
`iSpline`

for I-splines;
`cSpline`

for C-splines.

##### Examples

```
# NOT RUN {
library(splines2)
x <- seq.int(0, 1, 0.01)
knots <- c(0.3, 0.5, 0.6)
bsMat <- bSpline(x, knots = knots, degree = 0, intercept = TRUE)
library(graphics)
matplot(x, bsMat, type = "l", ylab = "Piecewise constant B-spline bases")
abline(v = knots, lty = 2, col = "gray")
# }
```

*Documentation reproduced from package splines2, version 0.2.8, License: GPL (>= 3)*