Ooura Fourier Integrals

Computing Fourier sine and cosine integrals using Ooura's method.

Usage

ooura_fourier_sin(
  f,
  omega = 1,
  relative_error_tolerance = sqrt(.Machine$double.eps),
  levels = 8
)

ooura_fourier_cos(
  f,
  omega = 1,
  relative_error_tolerance = sqrt(.Machine$double.eps),
  levels = 8
)

Arguments

f

A function to integrate. It should accept a single numeric value and return a single numeric value.

omega

The frequency parameter for the sine integral.

relative_error_tolerance

The relative error tolerance for the approximation.

levels

The number of levels of refinement to apply. Default is 8.

Value

A single numeric value with the computed Fourier sine or cosine integral, with attribute 'relative_error' indicating the relative error of the approximation.

Examples

# Fourier sine integral of sin(x) with omega = 1
ooura_fourier_sin(function(x) { 1 / x }, omega = 1)
#> [1] 1.570796
#> attr(,"relative_error")
#> [1] 1.265522e-11
# Fourier cosine integral of cos(x) with omega = 1
ooura_fourier_cos(function(x) { 1/ (x * x + 1) }, omega = 1)
#> [1] 0.5778637
#> attr(,"relative_error")
#> [1] 6.417739e-09