def test_Diff_order1(self):
f_diff = D(derivative_order=1, axis_name="x") * self.v
assert all(f_diff.data[:, 0] == 0)
assert all(f_diff.data[:, 1] == 0.5)
print(f_diff.name)
s_diff = D(derivative_order=1, axis_name="x") * self.sym_v
assert str(s_diff) == "-1.0*v(x - 1, y) + 1.0*v(x + 1, y)".replace(
' ', '')
def test_Diff_order2(self):
f_diff = D(derivative_order=2, axis_name="x") * self.v
assert all(f_diff.data[:, 0] == 0)
assert all(f_diff.data[:, 1] == 0)
assert all(
f_diff.data[2:-2, 2] ==
0.5) # there is a difference in the borders for using np.gradient
s_diff = D(derivative_order=2, axis_name="x") * self.sym_v
assert str(
s_diff
) == "-2.0*v(x, y) + 1.0*v(x - 2, y) + 1.0*v(x + 2, y)".replace(
' ', '')
def test_evaluator(self):
trainSplit = DataSplit({"x": 0.7})
testSplit = DataSplit({"x": 0.3}, {"x": 0.7})
data_manager = DataManager()
data_manager.add_variables(self.v)
data_manager.add_variables(self.x)
data_manager.set_X_operator(
lambda field: PolyD({"x": 1}) * field) # (PolyD({"x": 1})
data_manager.set_y_operator(lambda field: D(3, "x") * field)
pde_finder = PDEFinder(with_mean=True, with_std=True)
pde_finder.set_fitting_parameters(cv=20, n_alphas=100, alphas=None)
pde_finder.fit(data_manager.get_X_dframe(trainSplit),
data_manager.get_y_dframe(trainSplit))
print(pde_finder.coefs_) # strange th value obtained
real, pred = evaluate_predictions(pde_finder,
data_split_operator=testSplit,
dm=data_manager,
starting_point={"x": -1},
domain_variable2predict="x",
horizon=10,
num_evaluations=1)
assert np.mean(
real.drop(["random_split", "method"], axis=1).values -
pred.drop(["method"], axis=1).values[1:, :]) < 0.001
def test_integrate(self):
trainSplit = DataSplit({"x": 0.7})
testSplit = DataSplit({"x": 0.3}, {"x": 0.7})
data_manager = DataManager()
data_manager.add_variables(self.v)
data_manager.set_X_operator(
lambda field: PolyD({"x": 1}) * field) # (PolyD({"x": 1})
data_manager.set_y_operator(lambda field: D(2, "x") * field)
data_manager.set_domain()
pde_finder = PDEFinder(with_mean=True, with_std=True)
pde_finder.set_fitting_parameters(cv=20, n_alphas=100, alphas=None)
pde_finder.fit(data_manager.get_X_dframe(trainSplit),
data_manager.get_y_dframe(trainSplit))
print(pde_finder.coefs_) # strange th value obtained
# warning!!!
predictions_df = pde_finder.integrate([
DataSplitOnIndex({"x": 5}) * testSplit,
DataSplitOnIndex({"x": 20}) * testSplit
],
data_manager,
starting_point={"x": -1},
domain_variable2predict="x",
horizon=10)
print(predictions_df)
def test_fit_2(self):
data_manager = DataManager()
data_manager.add_variables(self.v)
data_manager.add_variables(self.v**2)
data_manager.set_X_operator(
lambda field: Poly(3) *
(PolyD({"x": 1}) * field)) # (PolyD({"x": 1})
data_manager.set_y_operator(lambda field: D(2, "x") * field)
pde_finder = PDEFinder(with_mean=True, with_std=True)
pde_finder.set_fitting_parameters(cv=10, n_alphas=100, alphas=None)
pde_finder.fit(data_manager.get_X_dframe(),
data_manager.get_y_dframe())
print(pde_finder.coefs_) # strange th value obtained
print((pde_finder.transform(data_manager.get_X_dframe()) -
data_manager.get_y_dframe()).abs().mean().values)
assert np.max((pde_finder.transform(data_manager.get_X_dframe()) -
data_manager.get_y_dframe()).abs().mean().values) < 1e-5
res = pde_finder.get_equation(*data_manager.get_Xy_eq())
print(res)
res = pde_finder.get_equation(data_manager.get_X_sym(),
data_manager.get_y_sym())
print(res)
def test_get_sym(self):
data_manager = DataManager()
data_manager.add_variables([self.v])
data_manager.add_regressors(self.x)
data_manager.set_domain()
data_manager.set_X_operator(
lambda field: (PolyD({"x": 1}) * field)) # (PolyD({"x": 1})
data_manager.set_y_operator(lambda field: D(2, "x") * field)
assert str(data_manager.get_X_sym()
) == "[v(x,y), -0.5*v(x-1,y)+0.5*v(x+1,y), x(x)]"
assert str(data_manager.get_y_sym()
) == "[-0.5*v(x,y)+0.25*v(x-2,y)+0.25*v(x+2,y)]"
data_manager.set_X_operator(
lambda field: (PolyD({"x": 1}) * field)) # (PolyD({"x": 1})
data_manager.set_y_operator(lambda field: D(1, "x") * field)
assert str(data_manager.get_X_sym()) == "[v(x,y), x(x)]"
assert str(data_manager.get_y_sym()) == "[-0.5*v(x-1,y)+0.5*v(x+1,y)]"
def test_get_var(self):
data_manager = DataManager()
data_manager.add_variables([self.v])
data_manager.add_regressors(self.x)
data_manager.set_domain()
data_manager.set_X_operator(
lambda field: PolyD({"x": 1}) * field) # (PolyD({"x": 1})
data_manager.set_y_operator(lambda field: D(1, "x") * field)
assert all(data_manager.get_X_dframe().columns == ['v(x,y)', 'x(x)'])
assert all(data_manager.get_y_dframe().columns ==
['1.0*Derivative(v(x,y),x)'])
def test_getXy_eq(self):
data_manager = DataManager()
data_manager.add_variables([self.v])
data_manager.add_regressors(self.x)
data_manager.set_domain()
data_manager.set_X_operator(
lambda field: (PolyD({"x": 1}) * field)) # (PolyD({"x": 1})
data_manager.set_y_operator(lambda field: D(2, "x") * field)
# print(data_manager.get_Xy_eq()[0].data[1].sym_expression)
assert str(data_manager.get_Xy_eq()
[0]) == "[v(x,y), 1.0*Derivative(v(x,y),x), x(x)]"
assert str(
data_manager.get_Xy_eq()[1]) == "[1.0*Derivative(v(x,y),(x,2))]"
def test_Diff_combining_operations(self):
f_diff = D(derivative_order=1, axis_name="x") * D(
derivative_order=1, axis_name="x") * self.v
assert all(f_diff.data[:, 0] == 0)
assert all(f_diff.data[:, 1] == 0)
assert all(f_diff.data[2:-2, 2] == 0.5)
v_diff = D(derivative_order=1, axis_name="x") * D(
derivative_order=1, axis_name="y") * self.v
w_diff = D(derivative_order=1, axis_name="y") * D(
derivative_order=1, axis_name="x") * self.v
assert v_diff == w_diff
def y_operator(field):
new_field = D(derivative_order_y, "t") * field
return new_field
def y_operator(field):
new_field = D(self.target_derivative_order, "t") * field
return new_field
def y_operator(field):
return D(derivative_order['t'] + 1, "t") * field
def y_operator(field):
return D(derivative_order=2, axis_name='t') * field
def x_operator(field, regressors):
new_field = D(1, 't') * field # M'
new_field.append(((D(1, 't') * field)**2)) # (M')^2
new_field.append((field * (D(1, 't') * field))) # MM'
return new_field
