ellipse¶
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hyppo.tools.ellipse(n, p, noise=False, low=- 1, high=1)¶ Ellipse simulation.
Ellipse \((X, Y) \in \mathbb{R}^p \times \mathbb{R}^p\): \(U \sim \mathcal{U}(-1, 1)^p\), \(\epsilon \sim \mathcal{N}(0, I_p)\), \(r = 5\),
\[\begin{split}X_{|d|} &= r \left( \sin(\pi U_{|d+1|}) \prod_{j=1}^d \cos(\pi U_{|j|}) + 0.4 \epsilon_{|d|} \right)\ \mathrm{for}\ d = 1, ..., p-1 \\ X_{|p|} &= r \left( \prod_{j=1}^p \cos(\pi U_{|j|}) + 0.4 \epsilon_{|p|} \right) \\ Y_{|d|} &= \sin(\pi U_{|1|})\end{split}\]- Parameters
n (
int) -- The number of samples desired by the simulation (>= 5).p (
int) -- The number of dimensions desired by the simulation (>= 1).noise (
bool, default:False) -- Whether or not to include noise in the simulation.low (
float, default:-1) -- The lower limit of the uniform distribution simulated from.high (
float, default:1) -- The upper limit of the uniform distribution simulated from.
- Returns
x,y (
ndarray) -- Simulated data matrices.x` and ``yhave shapes(n, p)and(n, p)where n is the number of samples and p is the number of dimensions.