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mipals committed Oct 17, 2023
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A package for efficiently computing with symmetric extended generator representable semiseparable matrices (EGRSS Matrices) and a variant with added diagonal terms. In short this means matrices of the form

$$
K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right), \quad U,V\in\mathbb{R}^{p\times n}
K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right), \quad U,V\in\mathbb{R}^{n\times p}
$$

$$
K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right) + \text{\textbf{diag}}(d), \quad U,V\in\mathbb{R}^{p\times n},\ d\in\mathbb{R}^n
K = \text{\textbf{tril}}(UV^\top) + \text{\textbf{triu}}\left(VU^\top,1\right) + \text{\textbf{diag}}(d), \quad U,V\in\mathbb{R}^{n\times p},\ d\in\mathbb{R}^n
$$

All implemented algorithms (multiplication, Cholesky factorization, forward/backward substitution as well as various traces and determinants) scales with $O(p^kn)$. Since $p \ll n$ this result in very scalable computations.
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