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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.

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@Peter230655 Peter230655 Jan 20, 2025 •
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I don't think I assumed any specific integration routine in the manually created objective functions.

I have a basic question:
In the current create_objective_function(...) there is a distinction in forming obj, obj_grad depending on the integration method.
But, for example, in the examples-gallery simulation plot_pendulum_swing_up_variable_duration, the gradient is formed as I would naively expect it to be formed.

Can the gradient always be formed as per the method used in plot_pendulum_swing_up_variable_duration, or is this only valid for midpoint euler or is this a (good) approximation, if I understood #30 #31 correctly?
Thanks for any explanations!

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The examples are a little loose, but it probably doesn't matter too much in the objective calc because both methods have about the same minima.

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Thanks!
This would mean one could calculate obj and obj_grad 'naively' without committing a large error?

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The gradient of the objective has to be the valid gradient within some numerical tolerance. But your choice of solving the integral in the objective does not really matter, as there are numerous integration methods.

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Thanks!
The gradient as calculated in the simulation plot_pendulum_swing_up_variable_duration surely is the valid gradient (?)


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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