R: Derivatives of Spline Bases

deriv {splines2} | R Documentation

## Derivatives of Spline Bases

### Description

Returns derivatives of given order for the spline bases.

### Usage

    ## S3 method for class 'bSpline2'
    deriv(expr, derivs = 1L, ...)

    ## S3 method for class 'dbs'
    deriv(expr, derivs = 1L, ...)

    ## S3 method for class 'ibs'
    deriv(expr, derivs = 1L, ...)

    ## S3 method for class 'mSpline'
    deriv(expr, derivs = 1L, ...)

    ## S3 method for class 'iSpline'
    deriv(expr, derivs = 1L, ...)

    ## S3 method for class 'cSpline'
    deriv(expr, derivs = 1L, ...)

    ## S3 method for class 'bernsteinPoly'
    deriv(expr, derivs = 1L, ...)

### Arguments

`expr` | Objects of class `bSpline2`, `ibs`, `dbs`, `mSpline`, `iSpline`, or `cSpline`, etc.
`derivs` | A positive integer specifying the order of derivatives. By default, it is `1L` for the first derivative.
`...` | Other arguments that are not used.

### Details

At knots, the derivative is defined to be the right derivative. By default, the function returns the first derivatives. For derivatives of order greater than one, the nested call such as `deriv(deriv(expr))` is supported but not recommended. For a better performance, argument `derivs` should be specified instead.

This function is designed for objects produced by this package. It internally extracts necessary specification about the spline/polynomial basis matrix from its attributes. Therefore, the function will not work if the key attributions are not available after some operations.

### Value

A numeric matrix of the same dimension with the input `expr`.

### Examples

    library(splines2)
    x <- c(seq.int(0, 1, 0.1), NA)  # NA's will be kept.
    knots <- c(0.3, 0.5, 0.6)

    ## integal of B-splines and the corresponding B-splines integrated
    ibsMat <- ibs(x, knots = knots)
    bsMat <- bSpline(x, knots = knots)

    ## the first derivative
    d1Mat <- deriv(ibsMat)
    stopifnot(all.equal(bsMat, d1Mat, check.attributes = FALSE))

    ## the second derivative
    d2Mat1 <- deriv(bsMat)
    d2Mat2 <- deriv(ibsMat, derivs = 2L)
    ## nested calls are supported but not recommended
    d2Mat3 <- deriv(deriv(ibsMat))
    stopifnot(all.equal(d2Mat1, d2Mat2, check.attributes = FALSE))
    stopifnot(all.equal(d2Mat2, d2Mat3, check.attributes = FALSE))

    ## C-splines, I-splines, M-splines and the derivatives
    csMat <- cSpline(x, knots = knots, intercept = TRUE, scale = FALSE)
    isMat <- iSpline(x, knots = knots, intercept = TRUE)
    stopifnot(all.equal(isMat, deriv(csMat), check.attributes = FALSE))

    msMat <- mSpline(x, knots = knots, intercept = TRUE)
    stopifnot(all.equal(msMat, deriv(isMat), check.attributes = FALSE))
    stopifnot(all.equal(msMat, deriv(csMat, 2), check.attributes = FALSE))
    stopifnot(all.equal(msMat, deriv(deriv(csMat)), check.attributes = FALSE))

    dmsMat <- mSpline(x, knots = knots, intercept = TRUE, derivs = 1)
    stopifnot(all.equal(dmsMat, deriv(msMat), check.attributes = FALSE))
    stopifnot(all.equal(dmsMat, deriv(isMat, 2), check.attributes = FALSE))
    stopifnot(all.equal(dmsMat, deriv(deriv(isMat)), check.attributes = FALSE))
    stopifnot(all.equal(dmsMat, deriv(csMat, 3), check.attributes = FALSE))
    stopifnot(all.equal(dmsMat, deriv(deriv(deriv(csMat))), check.attributes = FALSE))

[Package splines2 version 0.3.1 Index]