initial guess with collocation

[thasaarah]

Initial guesses using LINEAR or EACH_FRAME interpolation with COLLOCATION aren't generated correctly.

With the number of iterations of the OCP fixed at 0, the state values of the solution don't correspond to the expected values.

UPDATE 08-2023:
initial guess with:

• InterpolationType.LINEAR works [RTM] collocations for SOCP #744
• InterpolationType.EACH_FRAME works with the same initial guess for each intermediate state in intervals.
• InterpolationType.EACH_FRAME used to be linearly interpolated [RTM] collocation initial guess #504 but this feature has been destroyed in a refactor, #tofind.
• InterpolationType.ALL_POINT works only for collocation, allow to specify the value for every collocation point.
• InterpolationType.CONSTANT and CONSTANT_FIRST_AND_LAST works
• InterpolationType.SPLINE doesn't work.

[Ipuch]

Can you provide the location of the code where it does not do what's expected and a minimum script example ?

[thasaarah]

bioptim/bioptim/optimization/optimization_vector.py

Lines 368 to 375 in f327197

	for k in range(nlp.ns + 1):
	for p in range(repeat if k != nlp.ns else 1):
	span = slice(k * outer_offset + p * nx, k * outer_offset + (p + 1) * nx)
	if nlp.x_init.type == InterpolationType.EACH_FRAME:
	point = k * repeat + p
	else:
	point = k if k != 0 else 0 if p == 0 else 1
	x_init.init[span, 0] = nlp.x_init.init.evaluate_at(shooting_point=point)

When the initial guess is linearly interpolated, 'point' ranges from 0 to 'nlp.ns', where 'nlp.ns' corresponds to the number shooting nodes. With collocation, the value of 'point' corresponds to the shooting node associated to each collocation point, hence 'point' still ranges from 0 to 'nlp.ns', with a repetition of intermediate values for collocation points between shooting nodes.

bioptim/bioptim/limits/path_conditions.py

Line 275 in f327197

return self[:, 0] + (self[:, 1] - self[:, 0]) * shooting_point / self.n_shooting

The interpolation is evaluated at each 'shooting_point' by adding the product of the difference between the initial guess at the start and the end with the ratio of the current 'shooting_point' to 'self.n_shooting' to the initial guess at the first node. However, with collocation, 'self.n_shooting' is defined as the number of collocation points, thus limiting the 'shooting_point' to 'self.n_shooting' ratio to 'nlp.ns' / 'self.n_shooting' by repeatedly evaluating 'x_init' at the same 'shooting_point'.

[Ipuch]

To be resolved for EACHFRAME after #504 is merged.

[EveCharbie]

@Ipuch is this still on?

[Ipuch]

Yes

[Ipuch]

EACH FRAME is no more linearly interpolated in COLLOCATION.
The doc may have to be updated.

[EveCharbie]

The problem is located in bounds_vector and init_vector from optimization_vector.py + evaluate_at from path_conditions.py.
This line should be changed to consider all cases:
point = k if k != 0 else 0 if p == 0 else 1

[mickaelbegon]

I opened draft PR #1077 for the remaining SPLINE/collocation problem. The spline was accepted, but intermediate collocation points within an interval were evaluated at the same time because the sub-node index and repeat count were discarded. The PR preserves those indices and handles non-zero spline time origins.

@pariterre, the focused unit test and the existing collocation/SPLINE OCP test both pass locally; CI is running.