IO Slicing of LTIModel

[artpelling]

As a follow up to #1767 and #1916, I added a basic method to slice LTIModels based on numpy arrays. I would like to do this for the CSE tutorial, because it is a bit clunky in the notebook. I was not sure how to do it for arbitrary Operators. Please let me know, if you have an idea. Maybe we can use a RuleTable?

[pmli]

It would be nice to use the special method __getitem__.

[sdrave]

I'd agree, in particular because it allows you to pass proper slices idiomatically. However, we should discuss, whether this operation is common enough and whether the user would expect Models to be sliceable and what the expected behavior is.
As inputs and outputs are well-defined for each Model (at least currently ...), we should also think about a generic implementation which does not assume knowledge of the internal structure.

[pmli]

I can't comment on the commonality of this operation (I never had a use for it myself).
Regarding other Models, for StationaryModels it would make sense to slice by the number of right-hand sides and outputs. For the general, nonlinear InstationaryModel

$$ \begin{align*} M(\mu) \dot{x}(t) & = f(x(t), u(t), \mu) \\ y(t) & = g(x(t), u(t), \mu) \end{align*} $$

the result should be an InstationaryModel

$$ \begin{align*} M(\mu) \dot{x}(t) & = f(x(t), S_1 u(t), \mu) \\ y(t) & = S_2^T g(x(t), u(t), \mu) \end{align*} $$

where $S_1$ and $S_2$ are some columns of the identity matrix. I'm not sure how to represent $S_1$ without defining a new Operator class for $f$ with a restricted input parameter. At least, $S_2$ should be easy when output functionals are separated, or it can be the ComponentProjectionOperator.

[pmli]

I guess, to allow parametric B, C, and D, we would need to use ConcatenationOperators, e.g.,

self.B @ NumpyMatrixOperator(np.eye(self.dim_input)[:, input_indices])

Additionally, pymor.algorithms.simplify.contract could be called to do the multiplication in the case of non-parametric Operators.

[sdrave]

I'd agree with @pmli that this should be the fallback. This not only affects the parametric models but also models coming from an external pde solver. (It would be slightly better to create a VectorArrayOperator instead of a NumpyMatrixOperator as contract will convert it anyway.) One could still have this as a special case when B, C are NumpyMatrixOperators. But maybe it's not worth performance-wise to have extra code.

[pmli]

I would like to do this for the CSE tutorial

Note that we usually don't backport new features to old releases. You could install pyMOR from a git branch, but I feel that it would be good to only use an official release in the tutorial.

[sdrave]

@artpelling, June 22 is hard freeze for the next release. Do you want to finish this by then or should we remove it from the milestone?

[artpelling]

@artpelling, June 22 is hard freeze for the next release. Do you want to finish this by then or should we remove it from the milestone?

I thought about this one. There are too many aspects that still need conceptual decisions to be made. So we should move it.