Simulate a 2D "swiss roll" spiral with a 1D latent parameter

Simulates a 2D spiral (often used as a 1D analogue of a swiss roll) parameterized by \(t \in [t_{\min}, t_{\max}]\). The noiseless curve is \((x(t),y(t)) = (t\cos t, t\sin t)\). Independent Gaussian noise is added to each coordinate.

simulate_swiss_roll_1d_2d(
  n = 800,
  t_range = c(1.5 * base::pi, 6 * base::pi),
  sigma = 0.15,
  seed = 1
)

Arguments

n

Integer \(\ge 1\). Number of samples.

t_range

Numeric vector of length 2 specifying \([t_{\min}, t_{\max}]\).

sigma

Nonnegative numeric. Standard deviation of Gaussian noise. May be a scalar (applied to both coordinates) or a length-2 vector for coordinate-specific noise.

seed

Optional integer. If not NULL, sets the RNG seed via set.seed().

Value

A list with components:

  • t: numeric vector of length n, the latent parameter.

  • truth: data.frame with columns x, y for the noiseless curve.

  • obs: data.frame with columns x, y for the noisy observations.

Examples

sim <- simulate_swiss_roll_1d_2d(n = 300, sigma = 0.1, seed = 1)
head(sim$obs)
#>           x          y
#> 1 -4.818342   7.025793
#> 2 -8.512613  -5.259583
#> 3 12.397960   3.026388
#> 4  4.641363 -17.056883
#> 5  2.016847   7.101558
#> 6  2.224280 -17.250608