spiral¶
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hyppo.tools.spiral(n, p, noise=False, low=0, high=5)¶ Spiral simulation.
Spiral \((X, Y) \in \mathbb{R}^p \times \mathbb{R}\): \(U \sim \mathcal{U}(0, 5)\), \(\epsilon \sim \mathcal{N}(0, 1)\)
\[\begin{split}X_{|d|} &= U \sin(\pi U) \cos^d(\pi U)\ \mathrm{for}\ d = 1,...,p-1 \\ X_{|p|} &= U \cos^p(\pi U) \\ Y &= U \sin(\pi U) + 0.4 p \epsilon\end{split}\]- 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:0) -- The lower limit of the uniform distribution simulated from.high (
float, default:5) -- The upper limit of the uniform distribution simulated from.
- Returns
x,y (
ndarray) -- Simulated data matrices.x` and ``yhave shapes(n, p)and(n, 1)where n is the number of samples and p is the number of dimensions.
