cubic¶
- hyppo.tools.cubic(n, p, noise=False, low=- 1, high=1, cubs=[- 12, 48, 128], scale=0.3333333333333333)¶
Cubic simulation.
Cubic \((X, Y) \in \mathbb{R}^p \times \mathbb{R}\):
\[\begin{split}X &\sim \mathcal{U}(-1, 1)^p \\ Y &= 128 \left( w^T X - \frac{1}{3} \right)^3 + 48 \left( w^T X - \frac{1}{3} \right)^2 - 12 \left( w^T X - \frac{1}{3} \right) + 80 \kappa \epsilon\end{split}\]- 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:-1) -- The lower limit of the uniform distribution simulated from.high (
float, default:1) -- The upper limit of the uniform distribution simulated from.cubs (
listofints, default:[-12,48,128]) -- Coefficients of the cubic function where each value corresponds to the order of the cubic polynomial.scale (
float, default:1/3) -- Scaling center of the cubic.
- Returns
x,y (
ndarrayoffloat) -- 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.
