def test_zero_delay_derivative(self):
m1 = Monomial(0, 1, [], [0], [], [2])
m = [m1]
p = Polynomial(m)
y = [[]]
u = [[1]]
params = [2]
dy, du, dparams = p.derivatives(y, u, params)
assert_array_almost_equal(du, [[[4]]])
assert_array_almost_equal(dy, np.reshape([], (1, 0, 1)))
assert_array_almost_equal(dparams, [[1]])
def test_ar_model_predict_derivative(self):
m1 = Monomial(1, 0, [1], [], [1], [])
m2 = Monomial(1, 0, [1], [], [2], [])
m = [m1, m2]
mdl = Polynomial(m)
y = [[0.500000000000000],
[0.925000000000000],
[0.256687500000000],
[0.705956401171875],
[0.768053255020420],
[0.659145574149943],
[0.831288939045395],
[0.518916263804854],
[0.923676047365561],
[0.260844845488171],
[0.713377804660565],
[0.756538676169480],
[0.681495258228080],
[0.803120043590673],
[0.585037484942277],
[0.898243916772361],
[0.338186596189094],
[0.828120762684376],
[0.526646030853067],
[0.922372959447176]]
u = np.reshape([], (20, 0))
params = [3.7, -3.7]
jac = predict_derivatives(mdl, y[:-1], u[:-1], params)
jac_numeric = predict_numeric_derivatives(mdl, y[:-1], u[:-1], params)
assert_array_almost_equal(jac, jac_numeric)
def test_fir_model_predict_derivative(self):
m1 = Monomial(0, 1, [], [1], [], [1])
m2 = Monomial(0, 1, [], [1], [], [2])
m = [m1, m2]
mdl = Polynomial(m)
y = [[0],
[-1],
[-6],
[-15],
[-28],
[-45],
[-66],
[-91],
[-120],
[-153],
[-190],
[-231],
[-276],
[-325],
[-378],
[-435],
[-496],
[-561],
[-630],
[-703]]
u = np.arange(1, 21).reshape((20, 1))
params = [1, -2]
jac = predict_derivatives(mdl, y[:-1], u[:-1], params)
jac_numeric = predict_numeric_derivatives(mdl, y[:-1], u[:-1], params)
assert_array_almost_equal(jac, jac_numeric)
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_fir_derivative(self):
m1 = Monomial(0, 1, [], [1], [], [1])
m2 = Monomial(0, 1, [], [1], [], [2])
m = [m1, m2]
p = Polynomial(m)
y = [[]]
u = [[1]]
params = [1, -2]
dy, du, dparams = p.derivatives(y, u, params)
assert_array_almost_equal(du, [[[-3]]])
assert_array_almost_equal(dy, np.reshape([], (1, 0, 1)))
assert_array_almost_equal(dparams, [[1, 1]])
def test_zero_delay_numeric_derivative(self):
m1 = Monomial(0, 1, [], [0], [], [2])
m = [m1]
p = Polynomial(m)
y = [[]]
u = [[1]]
params = [2]
dy, du, dparams = p.derivatives(y, u, params)
dy_numeric, du_numeric, \
dparams_numeric = p._numeric_derivatives(y, u, params)
assert_array_almost_equal(dy, dy_numeric)
assert_array_almost_equal(du, du_numeric)
assert_array_almost_equal(dparams, dparams_numeric)
def test_noinput_numeric_derivative(self):
m1 = Monomial(1, 0, [1], [], [1], [])
m2 = Monomial(1, 0, [1], [], [2], [])
m = [m1, m2]
p = Polynomial(m)
y = [[1]]
u = [[]]
params = [1, -2]
dy, du, dparams = p.derivatives(y, u, params)
dy_numeric, du_numeric, \
dparams_numeric = p._numeric_derivatives(y, u, params)
assert_array_almost_equal(dy, dy_numeric)
assert_array_almost_equal(du, du_numeric)
assert_array_almost_equal(dparams, dparams_numeric)
def test_siso_derivatives(TestCase):
m1 = Monomial(2, 2, [1, 2], [1, 2],
[1, 2], [1, 1])
m2 = Monomial(1, 0, [1], [], [1], [])
m3 = Monomial(2, 1, [2, 3], [2], [1, 2], [3])
m = [m1, m2, m3]
p = Polynomial(m)
y = [[1], [2], [3]]
u = [[3], [4]]
params = [1, 2, 3]
dy, du, dparams = p.derivatives(y, u, params)
assert_array_almost_equal(dy, [[[50], [1776], [2304]]])
assert_array_almost_equal(du, [[[16], [2604]]])
assert_array_almost_equal(dparams, [[48, 1, 1152]])
def test_zero_delay_polynomial(self):
m1 = Monomial(0, 1, [], [0], [], [2])
m = [m1]
p = Polynomial(m)
y = [[]]
u = [[2]]
params = [2]
assert_equal(p(y, u, params), [8])
def test_fir_polynomial(self):
m1 = Monomial(0, 1, [], [1], [], [1])
m2 = Monomial(0, 1, [], [1], [], [2])
m = [m1, m2]
p = Polynomial(m)
y = [[]]
u = [[1]]
params = [1, -2]
assert_equal(p(y, u, params), [-1])
def test_noinput_polynomial(self):
m1 = Monomial(1, 0, [1], [], [1], [])
m2 = Monomial(1, 0, [1], [], [2], [])
m = [m1, m2]
p = Polynomial(m)
y = [[1]]
u = [[]]
params = [1, -2]
assert_equal(p(y, u, params), [-1])
def test_zero_delay_atribute_settings(self):
m1 = Monomial(0, 1, [], [0], [], [2])
m = [m1]
p = Polynomial(m)
assert_equal(p.Nparams, 1)
assert_equal(p.N, 0)
assert_equal(p.M, 0)
assert_equal(p.delay, 0)
assert_equal(p.Mu, 1)
assert_equal(p.Ny, 1)
assert_equal(p.Nu, 1)
def test_fir_atribute_settings(self):
m1 = Monomial(0, 1, [], [1], [], [1])
m2 = Monomial(0, 1, [], [1], [], [2])
m = [m1, m2]
p = Polynomial(m)
assert_equal(p.Nparams, 2)
assert_equal(p.N, 0)
assert_equal(p.M, 1)
assert_equal(p.delay, 1)
assert_equal(p.Mu, 1)
assert_equal(p.Ny, 1)
assert_equal(p.Nu, 1)
def test_noinput_atribute_settings(self):
m1 = Monomial(1, 0, [1], [], [1], [])
m2 = Monomial(1, 0, [1], [], [2], [])
m = [m1, m2]
p = Polynomial(m)
assert_equal(p.Nparams, 2)
assert_equal(p.N, 1)
assert_equal(p.M, 0)
assert_equal(p.delay, 0)
assert_equal(p.Mu, 0)
assert_equal(p.Ny, 1)
assert_equal(p.Nu, 0)
def test_siso_numeric_derivatives(TestCase):
m1 = Monomial(2, 2, [1, 2], [1, 2],
[1, 2], [1, 1])
m2 = Monomial(1, 0, [1], [], [1], [])
m3 = Monomial(2, 1, [2, 3], [2], [1, 2], [3])
m4 = Monomial(3, 1, [2, 3, 5], [3], [1, 2, 2], [2])
m5 = Monomial(0, 1, [], [3], [], [2])
m = [m1, m2, m3, m4, m5]
p = Polynomial(m)
y = [[12], [2.23], [4.51], [2.1], [3.24]]
u = [[3.3], [4.45], [3.4]]
params = [1.8, 2.2, 3.232, 32.3, 3.34]
dy, du, dparams = p.derivatives(y, u, params)
dy_numeric, du_numeric, \
dparams_numeric = p._numeric_derivatives(y, u, params)
assert_array_almost_equal(dy, dy_numeric)
assert_array_almost_equal(du, du_numeric)
assert_array_almost_equal(dparams, dparams_numeric)
def test_mimo_polynomial(TestCase):
m1 = Monomial(2, 2, [1, 2], [1, 2],
[1, 2], [1, 1],
[0, 1], [0, 1])
m2 = Monomial(1, 0, [1], [], [1], [], [1])
m3 = Monomial(2, 1, [2, 3], [2], [1, 2], [3], [0, 0], [1])
m = [[m1, m2], [m3]]
p = Polynomial(m)
y = [[1, 2], [2, 3], [3, 4]]
u = [[3, 5], [4, 7]]
params = [1, 2, 3]
dy, du, dparams = p.derivatives(y, u, params)
assert_array_almost_equal(dy, [[[189, 2], [0, 126], [0, 0]],
[[0, 0], [9261, 0], [12348, 0]]])
assert_array_almost_equal(du, [[[63, 0], [0, 27]],
[[0, 0], [0, 7938]]])
assert_array_almost_equal(dparams, [[189, 2, 0],
[0, 0, 6174]])
def test_siso_atribute_settings(self):
m1 = Monomial(3, 2, [1, 2, 4], [2, 3],
[1, 2, 2], [1, 1])
m2 = Monomial(1, 0, [1], [], [1], [])
m3 = Monomial(2, 1, [2, 3], [2], [1, 2], [3])
m = [m1, m2, m3]
p = Polynomial(m)
assert_equal(p.Nparams, 3)
assert_equal(p.N, 4)
assert_equal(p.M, 3)
assert_equal(p.delay, 2)
assert_equal(p.Ny, 1)
assert_equal(p.Nu, 1)
def test_mimo_numeric_derivatives(TestCase):
m1 = Monomial(2, 2, [1, 2], [1, 2],
[1, 2], [1, 1], [1, 0])
m2 = Monomial(1, 0, [1], [], [1], [], [1])
m3 = Monomial(2, 1, [2, 3], [2], [1, 2], [3], [0, 0], [2])
m4 = Monomial(3, 1, [2, 3, 5], [3], [1, 2, 2], [2], [0, 1, 0], [0])
m5 = Monomial(0, 1, [], [3], [], [2], [], [2])
m = [[m1, m2, m3, m4, m5], [m1, m2]]
p = Polynomial(m)
y = [[12, 1.23], [2.23, 23.3], [4.51, 3.4],
[2.1, 34.54], [3.24, 324.23]]
u = [[3.3, 132, 1.2], [4.45, 32.32, 2.23], [3.4, 1.3214, 2.132]]
params = [1.8, 2.2, 3.232, 32.3, 3.34, 3.3425, 13]
dy, du, dparams = p.derivatives(y, u, params)
dy_numeric, du_numeric, \
dparams_numeric = p._numeric_derivatives(y, u, params)
assert_array_almost_equal(dy, dy_numeric)
assert_array_almost_equal(du, du_numeric)
assert_array_almost_equal(dparams, dparams_numeric)
def test_siso_polynomial(TestCase):
m1 = Monomial(2, 2, [1, 2], [1, 2],
[1, 2], [1, 1])
m2 = Monomial(1, 0, [1], [], [1], [])
m3 = Monomial(2, 1, [2, 3], [2], [1, 2], [3])
m = [m1, m2, m3]
p = Polynomial(m)
y = [[1], [2], [3]]
u = [[3], [4]]
params = [1, 2, 3]
assert_equal(p(y, u, params), [3506])
def test_fir_model_simulate(self):
m1 = Monomial(0, 1, [], [1], [], [1])
m2 = Monomial(0, 1, [], [1], [], [2])
m = [m1, m2]
mdl = Polynomial(m)
y = [[0], [-1], [-6], [-15], [-28], [-45], [-66], [-91], [-120],
[-153], [-190], [-231], [-276], [-325], [-378], [-435], [-496],
[-561], [-630], [-703]]
u = np.arange(1, 21).reshape((20, 1))
params = [1, -2]
ys = simulate(mdl, np.reshape([], [0, 1]), u[:-1], params)
assert_array_almost_equal(ys, y[1:])
def test_mimo_polynomial(TestCase):
m1 = Monomial(2, 2, [1, 2], [1, 2],
[1, 2], [1, 1],
[0, 1], [0, 1])
m2 = Monomial(1, 0, [1], [], [1], [], [1])
m3 = Monomial(2, 1, [2, 3], [2], [1, 2], [3], [0, 0], [1])
m = [[m1, m2], [m3]]
p = Polynomial(m)
y = [[1, 2], [2, 3], [3, 4]]
u = [[3, 5], [4, 7]]
params = [1, 2, 3]
assert_equal(p(y, u, params), [193, 18522])
def test_fir_model_simulate_derivatives(self):
m1 = Monomial(0, 1, [], [1], [], [1])
m2 = Monomial(0, 1, [], [1], [], [2])
m = [m1, m2]
mdl = Polynomial(m)
u = np.arange(1, 21).reshape((20, 1))
params = [1, -2]
y0 = np.reshape([], [0, 1])
jac_params, jac_y0 = simulate_derivatives(mdl, y0, u[:-1], params)
jac_params_numeric \
= simulate_numeric_derivatives(mdl, y0, u[:-1],
params, deriv_y0=False)
assert_array_almost_equal(jac_params, jac_params_numeric, decimal=6)
assert_array_almost_equal(jac_y0, np.reshape([], (19, 1, 0, 1)))