adelie.solver.bvls#

adelie.solver.bvls(X: ndarray | MatrixNaiveBase32 | MatrixNaiveBase64, y: ndarray, lower: ndarray, upper: ndarray, *, weights: ndarray | None = None, kappa: int | None = None, max_iters: int = 100000, tol: float = 1e-07, n_threads: int = 1, warm_start=None)[source]#

Solves bounded variable least squares.

The bounded variable least squares is given by

\[\begin{split}\begin{align*} \mathrm{minimize}_{\beta} &\quad \frac{1}{2} \|y - X \beta\|_{W}^2 \\ \text{subject to} &\quad \ell \leq \beta \leq u \end{align*}\end{split}\]

where \(X \in \mathbb{R}^{n \times p}\) is the feature matrix, \(y \in \mathbb{R}^n\) is the response vector, \(W \in \mathbb{R}_+^{n \times n}\) is the (diagonal) observation weights, and \(\ell \leq u \in \mathbb{R}^p\) are the lower and upper bounds, respectively.

Parameters:

X(n, p) Union[ndarray, MatrixNaiveBase32, MatrixNaiveBase64]: Feature matrix. It is typically one of the matrices defined in adelie.matrix submodule or numpy.ndarray.
y(n,) ndarray: Response vector.
lower(p,) ndarray: Lower bound for each variable.
upper(p,) ndarray: Upper bound for each variable.
weights(n,) ndarray, optional: Observation weights. If None, it is set to np.full(n, 1/n). Default is None.
kappaint, optional: Violation batching size. If None, it is set to min(n, p). Default is None.
max_itersint, optional: Maximum number of coordinate descents. Default is int(1e5).
tolfloat, optional: Convergence tolerance. Default is 1e-7.
n_threadsint, optional: Number of threads. Default is 1.
warm_startoptional: If no warm-start is provided, the initial solution is set to the vertex of the box closest to the origin. Otherwise, the warm-start is used to extract all necessary state variables. Default is None.

Returns:

state: The resulting state after running the solver.