smape1

HydroErr.HydroErr.smape1(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 the Symmetric Mean Absolute Percentage Error (1) (SMAPE1).

\[sMAPE1=\frac{100\%}{n}\sum_{i=1}^{n}\frac{|S_i-O_i|}{|S_i|+|O_i|}\]

Range: 0 ≤ SMAPE1 < 100%, smaller is better, symmetrical.

Notes: This metric is an adjusted version of the MAPE.

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 symmetric mean absolute percentage error (1).

Examples

Note that if we switch the simulated and observed arrays the result is the same

>>> 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.smape1(sim, obs)
5.871915694397428
>>> he.smape1(obs, sim)
5.871915694397428

References

  • Flores, B.E., 1986. A pragmatic view of accuracy measurement in forecasting. Omega 14(2) 93-98.

  • Goodwin, P., Lawton, R., 1999. On the asymmetry of the symmetric MAPE. International Journal of Forecasting 15(4) 405-408.