Documentation Index
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The helpers/Metrics.py module provides standalone functions (no class) for evaluating GHI model accuracy. All functions accept numpy arrays or pandas Series. Import the module under an alias for concise notation:
import helpers.Metrics as ms
Point Comparison Functions
These functions operate element-wise on paired arrays of measured (true) and modelled (pred) values of equal length.
mbe(true, pred) → float
Mean Bias Error
ms.mbe(true: array-like, pred: array-like) -> float
| Parameter | Type | Description |
|---|
true | array-like | Measured (reference) values |
pred | array-like | Modelled (estimated) values |
float — mean bias error in the same units as the input.
rmbe(true, pred) → float
Relative Mean Bias Error (%)
ms.rmbe(true: array-like, pred: array-like) -> float
rMBE = mean(pred − true) / mean(true) × 100
float — relative MBE as a percentage.
mae(true, pred) → float
Mean Absolute Error
ms.mae(true: array-like, pred: array-like) -> float
float — mean absolute error in the same units as the input.
rmae(true, pred) → float
Relative Mean Absolute Error (%)
ms.rmae(true: array-like, pred: array-like) -> float
rMAE = MAE / mean(true) × 100
float — relative MAE as a percentage.
rmsd(true, pred) → float
Root Mean Square Deviation
ms.rmsd(true: array-like, pred: array-like) -> float
RMSD = sqrt( Σ(pred − true)² / N )
float — RMSD in the same units as the input.
rrmsd(true, pred) → float
Relative Root Mean Square Deviation (%)
ms.rrmsd(true: array-like, pred: array-like) -> float
rRMSD = RMSD / mean(true) × 100
float — relative RMSD as a percentage.
Distribution Comparison Functions
These functions compare the statistical distributions of two samples rather than paired point differences.
ecdf(x) → tuple
Empirical Cumulative Distribution Function
ms.ecdf(x: array-like) -> tuple[np.ndarray, np.ndarray]
| Parameter | Type | Description |
|---|
x | array-like | Input sample |
(xs, ys) where:
xs — sorted values of x (np.ndarray)ys — cumulative probabilities in [0, 1] (np.ndarray), computed as arange(1, N+1) / N
KSI_OVER(Xval, Xest, CDF=0)
Kolmogorov-Smirnov Integral (KSI) and OVER metric
ms.KSI_OVER(
Xval: array-like,
Xest: array-like,
CDF: int = 0
) -> float | tuple
| Parameter | Type | Default | Description |
|---|
Xval | array-like | — | Measured values |
Xest | array-like | — | Estimated (model) values |
CDF | int | 0 | Output selector: 0 returns KSI only; 1 returns the full tuple |
N = len(Xval).
Internal quantities:
| Symbol | Description |
|---|
Dn | Point-wise absolute difference between the two CDFs on the union grid |
On | Excess above the critical threshold: (Dn − Vc) where Dn > Vc, else 0 |
KSI | ∫ Dn dx (trapezoidal integration over the union x-axis) |
OVER | ∫ On dx |
rKSI | KSI / (Vc × (Xmax − Xmin)) — relative KSI |
rOVER | OVER / (Vc × (Xmax − Xmin)) — relative OVER |
- When
CDF=0 (default): float — KSI value only.
- When
CDF=1: tuple of ten elements:
(KSI, OVER, rKSI, rOVER, xCDF_tot, CDFval_tot, CDFest_tot, Dn, On, Vc)
If len(Xval) ≠ len(Xest), the function prints a warning: “longitudes diferentes, valores relativos no validos” (different lengths, relative values not valid). KSI is still returned but relative metrics (rKSI, rOVER) may be unreliable.
SS4(true, pred) → float
Beyer / Lorenz Skill Score
ms.SS4(true: array-like, pred: array-like) -> float
σ_med = std(true) (population std)
σ_est = std(pred) (population std)
ρ = Pearson correlation(true, pred)
σ_ratio = σ_est / σ_med
SS4 = (1 + ρ)⁴ / (4 × (σ_ratio + 1/σ_ratio)²)
[0, 1]. A perfect model (ρ = 1, σ_ratio = 1) yields SS4 = 1.
Returns float — skill score.
Quick Reference Usage
import helpers.Metrics as ms
import numpy as np
true = df_test['ghi'].values
pred = df_test['GHImod'].values
# --- Point metrics ---
print(f"MBE = {ms.mbe(true, pred):.2f} W/m²")
print(f"rMBE = {ms.rmbe(true, pred):.2f} %")
print(f"MAE = {ms.mae(true, pred):.2f} W/m²")
print(f"rMAE = {ms.rmae(true, pred):.2f} %")
print(f"RMSD = {ms.rmsd(true, pred):.2f} W/m²")
print(f"rRMSD = {ms.rrmsd(true, pred):.2f} %")
# --- Distribution metrics ---
print(f"KSI = {ms.KSI_OVER(true, pred):.4f}")
print(f"SS4 = {ms.SS4(true, pred):.4f}")
# --- Full KSI output for plotting CDFs ---
ksi, over, rksi, rover, x, cdf_val, cdf_est, dn, on, vc = ms.KSI_OVER(
true, pred, CDF=1
)
print(f"KSI={ksi:.4f} OVER={over:.4f} rKSI={rksi:.4f} rOVER={rover:.4f}")
Function Summary Table
| Function | Returns | Formula |
|---|
mbe | float (W/m²) | Σ(pred−true)/N |
rmbe | float (%) | mean(pred−true)/mean(true)×100 |
mae | float (W/m²) | Σ|pred−true|/N |
rmae | float (%) | MAE/mean(true)×100 |
rmsd | float (W/m²) | sqrt(Σ(pred−true)²/N) |
rrmsd | float (%) | RMSD/mean(true)×100 |
ecdf | (xs, ys) | Empirical CDF |
KSI_OVER | float or tuple | KS integral / OVER |
SS4 | float [0–1] | Beyer skill score |