Integrals and anti-derivatives of functional data

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

Details

When f is irregular and lower / upper are not supplied explicitly, they default to each curve's own observed arg range (i.e., the range of its tf_arg() values) rather than the (shared) domain endpoints; for regular tfd the defaults remain the domain endpoints. Without this per-curve default, curves that do not span the full domain would silently NA-poison the trapezoidal sum, because the default linear evaluator does not extrapolate. Pass explicit lower / upper to integrate over a fixed sub-interval, or switch to an extrapolating evaluator (e.g. tf_approx_fill_extend()) to integrate over the full domain.

See also

Other tidyfun calculus functions: tf_derive()

Examples

arg <- seq(0, 1, length.out = 11)
x <- tfd(rbind(arg, arg^2), arg = arg)
#> New names:
#> • `` -> `...2`
tf_integrate(x)
#>   arg  ...2 
#> 0.500 0.335 
anti <- tf_integrate(x, definite = FALSE)
tf_arg(anti)
#>  [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0