derivkit.forecasting.dali module#

DALI forecasting utilities.

derivkit.forecasting.dali.build_dali(function: Callable[[Sequence[float] | ndarray[tuple[Any, ...], dtype[floating]]], floating | ndarray[tuple[Any, ...], dtype[floating]]], theta0: Sequence[float] | ndarray[tuple[Any, ...], dtype[floating]], cov: Sequence[Sequence[float]] | ndarray[tuple[Any, ...], dtype[floating]], *, method: str | None = None, forecast_order: int = 2, n_workers: int = 1, **dk_kwargs: Any) → dict[int, tuple[ndarray[tuple[Any, ...], dtype[float64]], ...]]#

Builds the DALI expansion for the given model of the supplied order.

Parameters:

  • function – The scalar or vector-valued function to differentiate. It should accept a list or array of parameter values as input and return either a scalar or a np.ndarray of observable values.

  • theta0 – The expansion point (a 1D parameter vector) at which derivatives are evaluated. Accepts a list/array of length p, with p the number of parameters.

  • cov – The covariance matrix of the observables. Should be a square matrix with shape (n_observables, n_observables), where n_observables is the number of observables returned by the function.

  • method – Method name or alias (e.g., "adaptive", "finite"). If None, the derivkit.derivative_kit.DerivativeKit default is used.

  • forecast_order – The requested order of the forecast. Currently supported values and their meaning are given in derivkit.forecasting.forecast_core.SUPPORTED_FORECAST_ORDERS.

  • n_workers – Number of workers for per-parameter parallelization/threads. Default 1 (serial). Inner batch evaluation is kept serial to avoid oversubscription.

  • **dk_kwargs – Additional keyword arguments passed to derivkit.calculus_kit.CalculusKit.

Returns:

A dictionary with the keys equal to the order of the DALI expansion and values equal to the DALI multiplet at that order.

For each forecast order k, the returned multiplet contains the tensors introduced at that order. Concretely:

  • order 1: (F_{(1,1)},) (DALI singlet: Fisher matrix)

  • order 2: (D_{(2,1)}, D_{(2,2)}) (DALI doublet tensors)

  • order 3: (T_{(3,1)}, T_{(3,2)}, T_{(3,3)}) (DALI triplet tensors)

Here D_{(k,l)} and T_{(k,l)} denote contractions of the k-th and l-th order derivatives via the inverse covariance.

Each tensor axis has length p = len(theta0). The additional tensors at order k have parameter-axis ranks from k+1 through 2*k.