"""
Observability check
Finn Aakre Haugen, TechTeach. finn@techteach.no
2025 06 29
"""

#%% Imports

import numpy as np
import control

#%% Model matrices as 2D arrays

a = 0  # Model param

Ad = np.array([[1, a],
              [0, 1]])
Bd = np.array([[0],
              [1]])
Cd = np.array([[1, 0]])
Dd = np.array([[0]])

#%% Creating and checking the observability matrix

M_obs = control.obsv(Ad, Cd)

#Rank check:
rank_M_obs = np.linalg.matrix_rank(M_obs)
print('rank_M_obs =', rank_M_obs)

# Determinant check:
det_M_obs = np.linalg.det(M_obs)
print('det_M_obs =', det_M_obs)