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Derivatives of Spline Basis Functions

Source: R/deriv.R
deriv.Rd

Returns derivatives of given order for the given spline basis functions.

Usage

# S3 method for class 'BSpline'
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, ...)

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

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

Arguments

expr

Objects of class bSpline2, ibs, mSpline, iSpline, cSpline, bernsteinPoly or naturalSpline with attributes describing knots, degree, etc.

derivs

A positive integer specifying the order of derivatives. By default, it is 1L for the first derivatives.

...

Optional arguments that are not used.

Value

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

Details

At knots, the derivative is defined to be the right derivative except at the right boundary knot. By default, the function returns the first derivatives. For derivatives of order greater than one, nested function calls such as deriv(deriv(expr)) are 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 attributes are not available after some operations.

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)

## helper function
stopifnot_equivalent <- function(...) {
    stopifnot(all.equal(..., check.attributes = FALSE))
}

## 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_equivalent(bsMat, d1Mat)

## the second derivative
d2Mat1 <- deriv(bsMat)
d2Mat2 <- deriv(ibsMat, derivs = 2L)
stopifnot_equivalent(d2Mat1, d2Mat2)

## nested calls are supported
d2Mat3 <- deriv(deriv(ibsMat))
stopifnot_equivalent(d2Mat2, d2Mat3)

## 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_equivalent(isMat, deriv(csMat))

msMat <- mSpline(x, knots = knots, intercept = TRUE)
stopifnot_equivalent(msMat, deriv(isMat))
stopifnot_equivalent(msMat, deriv(csMat, 2))
stopifnot_equivalent(msMat, deriv(deriv(csMat)))

dmsMat <- mSpline(x, knots = knots, intercept = TRUE, derivs = 1)
stopifnot_equivalent(dmsMat, deriv(msMat))
stopifnot_equivalent(dmsMat, deriv(isMat, 2))
stopifnot_equivalent(dmsMat, deriv(deriv(isMat)))
stopifnot_equivalent(dmsMat, deriv(csMat, 3))
stopifnot_equivalent(dmsMat, deriv(deriv(deriv(csMat))))