skfolio.prior.CovarianceSqrt

class skfolio.prior.CovarianceSqrt(components=(), diagonal=None)

Matrix square root decomposition of a covariance matrix.

Encodes \(\Sigma = \sum_i A_i A_i^\top + \operatorname{diag}(d)^2\) in a form suitable for second-order cone (SOC) constraints:

\[\begin{split}\left\lVert \begin{pmatrix} A_1^\top w \\ \vdots \\ A_m^\top w \\ d \odot w \end{pmatrix} \right\rVert_2 \le v \;\Longleftrightarrow\; w^\top \Sigma\, w \le v^2\end{split}\]

This representation avoids forming a full \((n \times n)\) Cholesky factor when the covariance has lower-dimensional components and a diagonal component.

Attributes:

componentstuple of ndarray of shape (n, k_i)

Matrices \(A_i\) of shape \((n, k_i)\) contributing \(\sum_i A_i A_i^\top\) to the covariance.

diagonalndarray of shape (n,) or None

Vector \(d\) contributing \(\operatorname{diag}(d)^2\) to the covariance.