Generates the B-spline basis matrix representing the family of piecewise
polynomials with the specified interior knots, degree, and boundary knots,
evaluated at the values of `x`

.

## Usage

```
bSpline(
x,
df = NULL,
knots = NULL,
degree = 3L,
intercept = FALSE,
Boundary.knots = NULL,
derivs = 0L,
integral = FALSE,
...
)
```

## 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`

.- derivs
A nonnegative integer specifying the order of derivatives of B-splines. The default value is

`0L`

for B-spline basis functions.- integral
A logical value. If

`TRUE`

, the corresponding integrals of spline basis functions will be returned. The default value is`FALSE`

.- ...
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 extends the `bs()`

function in the `splines`

package
for B-spline basis by allowing piecewise constant (left-closed and
right-open except on the right boundary) spline basis of degree zero.

## Examples

```
library(splines2)
x <- seq.int(0, 1, 0.01)
knots <- c(0.3, 0.5, 0.6)
## cubic B-splines
bsMat <- bSpline(x, knots = knots, degree = 3, intercept = TRUE)
op <- par(mar = c(2.5, 2.5, 0.2, 0.1), mgp = c(1.5, 0.5, 0))
matplot(x, bsMat, type = "l", ylab = "Cubic B-splines")
abline(v = knots, lty = 2, col = "gray")
## reset to previous plotting settings
par(op)
## the first derivaitves
d1Mat <- deriv(bsMat)
## the second derivaitves
d2Mat <- deriv(bsMat, 2)
## evaluate at new values
predict(bsMat, c(0.125, 0.801))
#> 1 2 3 4 5 6 7
#> [1,] 0.1984954 0.5584491 0.2213542 0.02170139 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 0.0000000 0.0000000 0.05628999 0.3604115 0.4564141 0.1268844
```