sid

HydroErr.HydroErr.sid(simulated_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], observed_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], replace_nan: float | None = None, replace_inf: float | None = None, remove_neg: bool = False, remove_zero: bool = False) → floating[Any]

Compute the Spectral Information Divergence (SID).

\[SID = \Biggl\langle \left( \frac{O_i}{\overline{O}} - \frac{S_i}{\overline{S}} \right), \left( log \left( \frac{O_i}{\overline{O}} \right) - log \left( \frac{S_i}{\overline{S}} \right) \right) \Biggr\rangle\]

Range: -π/2 ≤ SID < π/2, closer to 0 is better.

Notes: The spectral information divergence measures the angle between the two vectors in hyperspace. It indicates how well the shape of the two series match - not magnitude.

Parameters:

  • simulated_array – An array of simulated data from the time series.

  • observed_array – An array of observed data from the time series.

  • replace_nan – If given, indicates which value to replace NaN values with in the two arrays. If None, when a NaN value is found at the i-th position in the observed OR simulated array, the i-th value of the observed and simulated array are removed before the computation.

  • replace_inf – If given, indicates which value to replace Inf values with in the two arrays. If None, when an inf value is found at the i-th position in the observed OR simulated array, the i-th value of the observed and simulated array are removed before the computation.

  • remove_neg – If True, when a negative value is found at the i-th position in the observed OR simulated array, the i-th value of the observed AND simulated array are removed before the computation.

  • remove_zero – If true, when a zero value is found at the i-th position in the observed OR simulated array, the i-th value of the observed AND simulated array are removed before the computation.

Return type:

The Spectral information divergence value.

Examples

>>> import HydroErr as he
>>> import numpy as np

>>> sim = np.array([5, 7, 9, 2, 4.5, 6.7])
>>> obs = np.array([4.7, 6, 10, 2.5, 4, 7])
>>> he.sid(sim, obs)
0.03517616895318012

References

  • Robila, S.A., Gershman, A., 2005. Spectral matching accuracy in processing hyperspectral data, Signals, Circuits and Systems, 2005. ISSCS 2005. International Symposium on. IEEE, pp. 163-166.