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Variable time support in create_objective_function. #205

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Variable time support in create_objective_function. #205

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37 changes: 37 additions & 0 deletions opty/tests/test_utils.py
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Original file line number Diff line number Diff line change
Expand Up @@ -200,6 +200,43 @@ def test_invalid_integration_limits(self):
sym.Integral(self.x ** 2, (self.t, 0, 1)), self.state_symbols,
self.input_symbols, self.unknown_symbols, self.N, 1)

def test_variable_time(self):

def expected_obj(free):
f = free[2*self.N:-1]
return free[-1]*np.sum(f**2)

def expected_obj_grad(free):
f = free[2*self.N:-1]
grad = np.zeros_like(free)
grad[2*self.N:-1] = 2.0*free[-1]*free[2*self.N:-1]
grad[-1] = np.sum(f**2)
return grad
Comment on lines +205 to +214
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@tjstienstra tjstienstra Aug 6, 2024 •
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You should take into account that this is backward Euler, so the first term falls out, see test_backward_single_input.
If free is [x(t), v(t), f1(t), f2(t), c, k, m, h] then the objective should be (f1_vals[1:]**2 + f2_vals[1:]**2).sum() * h_val.
Similarly, the gradient should be a stack of zeros(2*N+1), 2*h_val*f1_vals[1:], [0] 2*h_val*f2_vals[1:], [0, 0, 0, (f1_vals[1:]**2 + f2_vals[1:]**2).sum()]

P.S. quickly wrote out the equations on my phone so would advise checking them.

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I don't think I assumed any specific integration routine in the manually created objective functions.


obj_expr = sym.Integral(self.f1**2 + self.f2**2, self.t)
obj, obj_grad = utils.create_objective_function(
obj_expr, self.state_symbols, self.input_symbols,
self.unknown_symbols, self.N, self.h, time_symbols=self.t)
np.testing.assert_allclose(obj(self.free), expected_obj(self.free))
np.testing.assert_allclose(obj_grad(self.free),
expected_obj_grad(self.free))

def expected_obj(free):
return free[-1]

def expected_obj_grad(free):
grad = np.zeros_like(free)
grad[-1] = 1.0
return grad

obj_expr = sym.Integral(1, self.t)
obj, obj_grad = utils.create_objective_function(
obj_expr, self.state_symbols, self.input_symbols,
self.unknown_symbols, self.N, self.h, time_symbols=self.t)
np.testing.assert_allclose(obj(self.free), expected_obj(self.free))
np.testing.assert_allclose(obj_grad(self.free),
expected_obj_grad(self.free))


def test_parse_free():

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