tf_integrate: Integrals and anti-derivatives of functional data

In tf: S3 Classes and Methods for Tidy Functional Data

Integrals and anti-derivatives of functional data

Description

Integrals of tf-objects are computed by simple quadrature (trapezoid rule). By default the scalar definite integral \int^{upper}_{lower}f(s)ds is returned (option definite = TRUE), alternatively for definite = FALSE the anti-derivative on ⁠[lower, upper]⁠, e.g. a tfd or tfb object representing F(t) \approx \int^{t}_{lower}f(s)ds, for t \in⁠[lower, upper]⁠, is returned.

Usage

tf_integrate(f, arg, lower, upper, ...)

## Default S3 method:
tf_integrate(f, arg, lower, upper, ...)

## S3 method for class 'tfd'
tf_integrate(
  f,
  arg = tf_arg(f),
  lower = tf_domain(f)[1],
  upper = tf_domain(f)[2],
  definite = TRUE,
  ...
)

## S3 method for class 'tfb'
tf_integrate(
  f,
  arg = tf_arg(f),
  lower = tf_domain(f)[1],
  upper = tf_domain(f)[2],
  definite = TRUE,
  ...
)

Arguments

f	a tf-object
arg	(optional) grid to use for the quadrature.
lower	lower limits of the integration range. For definite = TRUE, this can be a vector of the same length as f.
upper	upper limits of the integration range (but see definite arg / description). For definite = TRUE, this can be a vector of the same length as f.
...	not used
definite	should the definite integral be returned (default) or the antiderivative. See description.

Value

For definite = TRUE, the definite integrals of the functions in f. For definite = FALSE and tf-inputs, a tf object containing their anti-derivatives

See Also

Other tidyfun calculus functions: tf_derive()

Examples

arg <- seq(0, 1, length.out = 11)
x <- tfd(rbind(arg, arg^2), arg = arg)
tf_integrate(x)
anti <- tf_integrate(x, definite = FALSE)
tf_arg(anti)

tf documentation built on April 7, 2026, 5:07 p.m.