modify the requisite on the function complete_state

[awage]

Following the discussion in issue #209 I propose to loosen the requisites on the function complete_state for the ProjectedDynamicalSystem. The only important aspect is that the function complete_state should return a valid vector on the original state space.

Unfortunately I don't think we can make this check in the code if we don't know the kind of input y.

[Datseris]

I believe we have a classic Y instead of X problem here.

I am not happy with this modification. The projected space is a well defined space. The original space is a well defined space. A projected dynamical system takes states in the projected space and maps them to the projected space. All is well defined. With this PR it isn't any more, because complete_state can take "whatever", and "whatever" is bad practice for designing a clear API that a user can learn simply and intuitively.

Instead of trying to alter this situation, can you tell me what you want to actually achieve? In #209 you only loosely described your situation. Please describe exactly your situation and lets see if this situation can achieve with no changes, or simpler changes that do not change the existing API.

[awage]

I can give you a simple example:

ds = Systems.lorenz96(5)
projection(u) = [sum(u), sqrt(u[1]^2 + u[2]^2)]
complete_state(y) = [y[1]+2*y[2], y[3]+2*y[4]+y[5]] 
prods = ProjectedDynamicalSystem(ds, projection, complete_state)

The definition will throw an error since the input vector should be of dimension 2.

Let suppose I want to match a vector u from the original state space using this projection. I simply cannot directly. I have to use a workaround somehow.

EDIT: My goal is to map attractors using the original state space using the projected state space, such that

mapper = AttractorsViaRecurrences(prods, grid)
l = mapper(rand(5))

works on the original space of ds.

Maybe a keyword to override the usual behavior will do?

[Datseris]

Let suppose I want to match a vector u from the original state space using this projection

Why don't you just call y = projection(u)?

mapper = AttractorsViaRecurrences(prods, grid); l = mapper(rand(5))

why don't you do l = mapper(projection(rand(5)) instead?

I don't see why something so simple to resolve at the user level should instead become a convoluted option at the software level. You will need to provide arguments why using the projection at your end is not an option.

[awage]

I know this solution but it does not solve my problem. Next week I will explain better what is going on in my system. It has to do with the basins with tentacle paper. El El vie, 19 jul 2024 a las 20:50, George Datseris < ***@***.***> escribió:

…

Let suppose I want to match a vector u from the original state space using this projection Why don't you just call y = projection(u)? mapper = AttractorsViaRecurrences(prods, grid); l = mapper(rand(5)) why don't you do l = mapper(projection(rand(5)) instead? I don't see why something so simple to resolve at the user level should instead become a convoluted option at the software level. You will need to provide arguments why using the projection at your end is not an option. — Reply to this email directly, view it on GitHub <#210 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AA2VD4E6F2DPAKXG3B5QYBLZNFNV5AVCNFSM6AAAAABLEMQGV2VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDEMZZHEYTGNJTHE> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[Datseris]

I know this solution but it does not solve my problem.

From what you have described so far, I don't see how this doesn't solve your problem. Let's say you have a sampler() that samples the original dynamical system. Do you want to call basins_fractions with this sampler, but the mapper should be for the projected system? Then call

projected_sampler = () -> projection(sampler())
fs = basins_fractions(projected_mapper, projected_sampler)

so yeah I will keep an eye out for a lengthier explanation next week!

[awage]

I close this PR. It breaks the API. I will describe the specifics in the opened issue.