EFTTOptions
EFTTOptions(
self,
num_error_samples: int = 1000,
fibre_method: str = 'random',
tol_svd: float = 1e-12,
num_aca: int = 50,
tol_aca: float = 1e-10,
max_fibres: int = 30,
num_snapshots: int = 30,
)Options for configuring the construction of an EFTT object.
Parameters
num_error_samples : int = 1000-
The number of samples to use when estimating the \(L^{2}\) error of the FTT approximation to the target function at each iteration.
fibre_method : str = 'random'-
The method used to compute a set of mode-\(k\) fibres in each dimension \(k \in \{1, \dots, d\}\). This can be
"aca"(apply adaptive cross approximation, as in Strössner, Sun, and Kressner 2024), or"random"(choose a set of fibres at random). tol_svd : float = 1e-12-
The threshold to use when applying truncated SVD to compute an (approximate) orthogonal basis for the mode-\(k\) fibres in each dimension. The minimum number of singular values such that their sum exceeds (\(1-\)
tol_svd) will be retained. num_aca : int = 50-
If
fibre_method="aca", the number of elements of the fibre matrix to sample at each iteration when selecting a new pivot element. tol_aca : float = 1e-10-
If
fibre_method="aca", the stopping tolerance, \(\epsilon\), to use. More concretely, if \(\mathcal{S}\) denotes a set of randomly-sampled indices of the mode-\(k\) fibre matrix \(\boldsymbol{M}\) (and \(\mathcal{I}\) and \(\mathcal{J}\) denote the current sets of row and column indices), the iteration is considered finished when \[ \max_{(i, j) \in \mathcal{S}}\|R_{ij}\| < \epsilon, \] where the residual matrix \(\boldsymbol{R}\) is given by \[ \boldsymbol{R} = \boldsymbol{M} - \boldsymbol{M}[:, \mathcal{J}] \boldsymbol{M}[\mathcal{I}, \mathcal{J}]^{-1} \boldsymbol{M}[\mathcal{I}, :]. \] max_fibres : int = 30-
If
fibre_method="aca", the maximum number of fibres to sample. num_snapshots : int = 30-
If
fibre_method="random", the number of snapshots to sample.