R: Differentiating functional data: approximating derivative...

tf_derive {tf}

R Documentation

Differentiating functional data: approximating derivative functions

Description

Derivatives of tf-objects use finite differences of the evaluations for tfd and finite differences of the basis functions for tfb.

Usage

tf_derive(f, arg, order = 1, ...)

## S3 method for class 'matrix'
tf_derive(f, arg, order = 1, ...)

## S3 method for class 'tfd'
tf_derive(f, arg, order = 1, ...)

## S3 method for class 'tfb_spline'
tf_derive(f, arg, order = 1, ...)

## S3 method for class 'tfb_fpc'
tf_derive(f, arg, order = 1, ...)

Arguments

`f`	a `tf`-object
`arg`	grid to use for the finite differences. Not the `arg` of the returned object for `tfd`-inputs, see Details.
`order`	order of differentiation. Maximal value for `tfb_spline` is 2.
`...`	not used

Details

The derivatives of tfd objects use centered finite differences, e.g. for first derivatives f'((t_i + t_{i+1})/2) \approx \frac{f(t_i) + f(t_{i+1})}{t_{i+1} - t_i}, so the domains of differentiated tfd will shrink (slightly) at both ends. Unless the tfd has a rather fine and regular grid, representing the data in a suitable basis representation with tfb() and then computing the derivatives or integrals of those is usually preferable.

Note that, for some spline bases like "cr" or "tp" which always begin/end linearly, computing second derivatives will produce artefacts at the outer limits of the functions' domain due to these boundary constraints. Basis "bs" does not have this problem for sufficiently high orders, but tends to yield slightly less stable fits.

Value

a tf (with slightly different arg or basis for the derivatives, see Details)

Methods (by class)

tf_derive(matrix): row-wise finite differences
tf_derive(tfd): derivatives by finite differencing.
tf_derive(tfb_spline): derivatives by finite differencing.
tf_derive(tfb_fpc): derivatives by finite differencing.