Description Usage Arguments Details References Examples

These functions generate uniform samples from lemniscates (figure eights) in 2-dimensional space, optionally with noise.

1 | ```
sample_lemniscate_gerono(n, sd = 0)
``` |

`n` |
Number of observations. |

`sd` |
Standard deviation of (independent multivariate) Gaussian noise. |

These functions use a simple parameterization from the unit circle to the lemniscate of Gerono, as presented on Wikipedia. The uniform sample is generated through a rejection sampling process as described by Diaconis, Holmes, and Shahshahani (2013).

P Diaconis, S Holmes, and M Shahshahani (2013) Sampling from a Manifold.
*Advances in Modern Statistical Theory and Applications: A Festschrift in
honor of Morris L. Eaton*, 102–125. doi: 10.1214/12-IMSCOLL1006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
set.seed(12051L)
# Uniformly sampled figure eight in 2-space
x <- sample_lemniscate_gerono(720)
plot(x, asp = 1, pch = 19, cex = .5)
# Naively sampled figure eight, for comparison
theta <- runif(n = 720, min = 0, max = 2*pi)
x_naive <- cbind(x = cos(theta), y <- cos(theta) * sin(theta))
plot(x_naive, asp = 1, pch = 19, cex = .5)
# Uniformly sampled figure eight in 2-space with Gaussian noise
x <- sample_lemniscate_gerono(720, 0.1)
plot(x, asp = 1, pch = 19, cex = .5)
``` |

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