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_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_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_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_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)