def test_siso_estimate_parameters_multiple_shoot(self):
mdl = Linear(N=3, M=3)
y = [[0], [4], [13], [24.8], [30.2], [27.96], [11.76], [-16.568],
[-50.384], [-64.7776], [-57.784], [-26.03872], [22.23296],
[76.507136], [98.513024], [86.7539072], [96.2449152],
[154.54439424], [244.89924352], [290.512711168]]
u = [[1], [1], [1], [1], [1], [-2], [-2], [-2], [-2], [-2], [3], [3],
[3], [3], [3], [10], [10], [10], [10], [10]]
true_params = [1, -0.8, 0.2, 4, 5, 6]
initial_guess = [0, 0, 0, 0, 0, 0]
error = SimulationError(mdl, y, u, maxlength=5)
params, info = error.lsq_estimate_parameters(initial_guess)
multiple_shoots = info["multiple_shoots"]
initial_conditions = info["initial_conditions"]
assert_array_almost_equal(params, true_params, decimal=3)
assert_array_almost_equal(multiple_shoots, [(0, 8), (5, 13), (10, 18),
(15, 20)],
decimal=3)
assert_array_almost_equal(
initial_conditions,
[[[0], [4], [13]], [[27.96], [11.76], [-16.568]],
[[-57.784], [-26.03872], [22.23296]],
[[86.7539072], [96.2449152], [154.54439424]]],
decimal=3)
def test_mimo_estimate_parameters_single_shoot(self):
mdl = Linear(N=3, M=3, Ny=2, Nu=2)
y = [[0, 0], [4, 8], [13, 26], [24.8, 49.6], [30.2, 60.4],
[27.96, 63.92], [11.76, 61.52], [-16.568, 55.464],
[-50.384, 34.032], [-64.7776, 8.9648], [-57.784, -10.1680],
[-26.03872, -5.53344], [22.23296, 34.39392],
[76.507136, 112.787072], [98.513024, 180.165248],
[86.7539072, 216.8143744], [96.2449152, 243.2395904],
[154.54439424, 260.82114048], [244.89924352, 271.59234304],
[290.512711168, 231.583348736]]
u = [[1, 1], [1, 1], [1, 1], [1, 1], [1, 3], [-2, 3], [-2, 3], [-2, 3],
[-2, 1], [-2, 1], [3, 1], [3, 1], [3, 5], [3, 5], [3, 5], [10, 5],
[10, -2], [10, -2], [10, -2], [10, -2]]
true_params = [
1, 0, -0.8, 0, 0.2, 0, 0, 1, 0, -0.8, 0, 0.2, 4, 0, 5, 0, 6, 0, 4,
4, 5, 5, 6, 6
]
initial_guess = [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0
]
error = SimulationError(mdl, y, u, maxlength=20)
params, info = error.lsq_estimate_parameters(initial_guess,
use_sparse=False)
multiple_shoots = info["multiple_shoots"]
initial_conditions = info["initial_conditions"]
assert_array_almost_equal(params, true_params)
assert_array_almost_equal(multiple_shoots, [(0, 20)], decimal=3)
assert_array_almost_equal(initial_conditions,
[[[0, 0], [4, 8], [13, 26]]],
decimal=3)
def test_ar_model_simulation_error_multiple_shoot(self):
m1 = Monomial(1, 0, [1], [], [1], [])
m2 = Monomial(1, 0, [1], [], [2], [])
m = [m1, m2]
mdl = Polynomial(m)
y = [[0.500000000000000], [0.925000000000000 - 1.4],
[0.256687500000000 - 1.4], [0.705956401171875 - 1.4],
[0.768053255020420 - 1.4], [0.659145574149943 - 1.4],
[0.831288939045395 - 1.4], [0.518916263804854 - 1.4],
[0.923676047365561 - 1.4], [0.260844845488171 - 1.4],
[0.713377804660565 - 1.4], [0.756538676169480 - 1.4],
[0.681495258228080 - 1], [0.803120043590673 - 1],
[0.585037484942277 - 1], [0.898243916772361 - 1],
[0.338186596189094 - 1], [0.828120762684376 - 1],
[0.526646030853067 - 1], [0.922372959447176 - 1]]
u = np.reshape([], (20, 0))
params = [3.7, -3.7]
extended_params = params + [0.5] + \
[0.659145574149943] + \
[0.713377804660565] + \
[0.898243916772361]
error = SimulationError(mdl, y, u, 5)
dparams = error.derivatives(extended_params)
dparams_numeric \
= error_numeric_derivatives(error, extended_params)
assert_array_almost_equal(dparams, dparams_numeric, decimal=3)
def test_mimo_simulation_error_one_shoot_derivatives(self):
mdl = Linear(N=3, M=3, Ny=2, Nu=2)
y = [[0, 0], [4, 8], [13, 26], [24.8, 49.6], [30.2, 60.4],
[27.96, 63.92], [11.76, 61.52], [-16.568, 55.464],
[-50.384, 34.032], [-64.7776, 8.9648], [-57.784, -10.1680],
[-26.03872, -5.53344], [22.23296, 34.39392],
[76.507136, 112.787072], [98.513024, 180.165248],
[86.7539072, 216.8143744], [96.2449152, 243.2395904],
[154.54439424, 260.82114048], [244.89924352, 271.59234304],
[290.512711168, 231.583348736]]
u = [[1 + 0.5, 1 + 0.5], [1 + 0.5, 1 + 0.5], [1 + 0.5, 1 + 0.5],
[1 + 0.5, 1 + 0.5], [1 + 0.5, 3 + 0.5], [-2 + 0.3, 3 + 0.3],
[-2 + 0.3, 3 + 0.3], [-2 + 0.3, 3 + 0.3], [-2 + 0.3, 1 + 0.3],
[-2 + 0.3, 1 + 0.3], [3 + 0.3, 1 + 0.3], [3 + 0.3, 1 + 0.3],
[3 + 0.3, 5 + 0.3], [3 + 0.3, 5 + 0.3], [3 + 0.3, 5 + 0.3],
[10 + 1, 5 + 1], [10 + 1, -2 + 1], [10 + 1, -2 + 1],
[10 + 1, -2 + 1], [10 + 1, -2 + 1]]
params = [
1, 0, -0.8, 0, 0.2, 0, 0, 1, 0, -0.8, 0, 0.2, 4, 0, 5, 0, 6, 0, 4,
4, 5, 5, 6, 6
]
extended_params = params + [0, 0, 4, 8, 13, 26]
error = SimulationError(mdl, y, u)
dparams = error.derivatives(extended_params)
dparams_numeric \
= error_numeric_derivatives(error, extended_params)
assert_array_almost_equal(dparams, dparams_numeric)
def test_mimo_simulation_error_one_shoot(self):
mdl = Linear(N=3, M=3, Ny=2, Nu=2)
y = [[0, 0], [4, 8], [13, 26], [24.8 - 1.23, 49.6 - 2],
[30.2 - 1.23, 60.4 - 2], [27.96 - 1.23, 63.92 - 2],
[11.76 - 1.23, 61.52 - 2], [-16.568 - 1.23, 55.464 - 2],
[-50.384 - 1.23, 34.032 - 2], [-64.7776 - 1.23, 8.9648 - 2],
[-57.784 - 1.23, -10.1680 - 2], [-26.03872 - 1.23, -5.53344 - 2],
[22.23296 - 12, 34.39392 - 2],
[76.507136 - 12, 112.787072 - 2.45],
[98.513024 - 12, 180.165248 - 2.45],
[86.7539072 - 12, 216.8143744 - 2.45],
[96.2449152 - 12, 243.2395904 - 2.45],
[154.54439424 - 12, 260.82114048 - 2.45],
[244.89924352 - 12, 271.59234304 - 2.45],
[290.512711168 - 12, 231.583348736 - 2.45]]
u = [[1, 1], [1, 1], [1, 1], [1, 1], [1, 3], [-2, 3], [-2, 3], [-2, 3],
[-2, 1], [-2, 1], [3, 1], [3, 1], [3, 5], [3, 5], [3, 5], [10, 5],
[10, -2], [10, -2], [10, -2], [10, -2]]
params = [
1, 0, -0.8, 0, 0.2, 0, 0, 1, 0, -0.8, 0, 0.2, 4, 0, 5, 0, 6, 0, 4,
4, 5, 5, 6, 6
]
expected_error = [
1.23, 2, 1.23, 2, 1.23, 2, 1.23, 2, 1.23, 2, 1.23, 2, 1.23, 2,
1.23, 2, 1.23, 2, 12, 2, 12, 2.45, 12, 2.45, 12, 2.45, 12, 2.45,
12, 2.45, 12, 2.45, 12, 2.45
]
error = SimulationError(mdl, y, u)(params + [0, 0, 4, 8, 13, 26])
assert_array_almost_equal(error, expected_error)
def test_siso_simulation_error_one_shoot_derivatives(self):
mdl = Linear(N=3, M=3)
y = [[0], [4], [13], [24.8], [30.2], [27.96], [11.76], [-16.568],
[-50.384], [-64.7776], [-57.784], [-26.03872], [22.23296],
[76.507136], [98.513024], [86.7539072], [96.2449152],
[154.54439424], [244.89924352], [290.512711168]]
u = [[1 + 0.5], [1 + 0.5], [1 + 0.5], [1 + 0.5], [1 + 0.5], [-2 + 0.3],
[-2 + 0.3], [-2 + 0.3], [-2 + 0.3], [-2 + 0.3], [3 + 0.3],
[3 + 0.3], [3 + 0.3], [3 + 0.3], [3 + 0.3], [10 + 1], [10 + 1],
[10 + 1], [10 + 1], [10 + 1]]
params = [1, -0.8, 0.2, 4, 5, 6]
extended_params = params + [0, 4, 13]
error = SimulationError(mdl, y, u)
dparams = error.derivatives(extended_params)
dparams_numeric \
= error_numeric_derivatives(error, extended_params)
assert_array_almost_equal(dparams, dparams_numeric)
def test_siso_simulation_error_multiple_shoot(self):
mdl = Linear(N=3, M=3)
y = [[0], [4], [13], [24.8 - 1.34], [30.2 - 1.34], [27.96 - 1.34],
[11.76 - 1.34], [-16.568 - 1.34], [-50.384 - 1.34],
[-64.7776 - 1.34], [-57.784 - 1.34], [-26.03872 - 5.34],
[22.23296 - 5.34], [76.507136 - 5.34], [98.513024 - 5.34],
[86.7539072 - 5.34], [96.2449152 - 5.34], [154.54439424 - 5.34],
[244.89924352 - 5.34], [290.512711168 - 5.34]]
u = [[1], [1], [1], [1], [1], [-2], [-2], [-2], [-2], [-2], [3], [3],
[3], [3], [3], [10], [10], [10], [10], [10]]
params = [1, -0.8, 0.2, 4, 5, 6]
expected_error = [
1.34,
1.34,
1.34,
1.34,
1.34,
0, # overlap error
0, # overlap error
0, # overlap error
1.34,
1.34,
1.34,
5.34,
5.34,
0, # overlap error
0, # overlap error
0, # overlap error
5.34,
5.34,
5.34,
5.34,
5.34,
0, # overlap error
0, # overlap error
0, # overlap error
5.34,
5.34
]
e = SimulationError(mdl, y, u, 5)
error = e(params + [0, 4, 13] + [27.96, 11.76, -16.568] +
[-57.784, -26.03872, 22.23296] +
[86.7539072, 96.2449152, 154.54439424])
assert_array_almost_equal(error, expected_error)