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Allow squeeze to search over non-monotonic polynomials #256
Description
I think we should just allow squeeze to be non-monotonic. Like my previous suggestion, sort the grid (and in parallel the function values). Since we have discrete data, overlap is unlikely. In the case of overlap, take the average value of the overlaps. We would no longer have this error. I suggest warning the user if the final (only the final) squeeze parameters results in non-monotonicity and allowing them to disable it with another setting:
Warning: The squeeze morph has interpolated your morphed function from a non-monotonically increasing grid. This can result in strange behavior in the regions {list_of_regions}. To disable this setting, please enable --check-increasing.
If the final result is still on a monotonic increasing grid, good! That means only the intermediates were non-monotonic. This change only benefits us since if we do not implement this, the user will see an error on all cases where the grid is non-monotonic, and they recover the same behavior using check-increasing (or perhaps a better name for this option).
Use something like this to find non-unique values efficiently.
Use np.diff and check for negatives to quickly find the region where the interpolation has resulted in non-monotonicity. Specifically, for each set of continuous negative values in np.diff(a) for some array a, your non-monotonic region is a[idx2+1] to a[idx1] where idx1 is the index of where the negative region in np.diff(a) starts and and idx2 is the index where it ends. For example, if np.diff(a) is negative on the range 10-20, your non-monotonic region is a[21] to a[10]. You will not have index out of bounds errors from this since np.diff returns an array one smaller than the original.
Note that the grid size can change, but we implemented ways to handle that in morphrgrid.py.
Activity
sbillinge commentedon Sep 13, 2025
I am ok with this. It is a bit odd, but if there is a unique mapping from domain to the function value, I guess it is ok, right?
ycexiao commentedon Sep 15, 2025
@Sparks29032, I have one small question. Assume the resulting
x_sqeezeis composed of sequential intervalsc_1,c_2,...x_squeezeis monotonic in each interval. Two neighboring intervals have opposite monotonicity. If the continuous interval ofc_iandc_joverlaps, but not the discrete grid. When we runsort, we will find that adjacent regions in the resulting y values will change abruptly from one interval to another, and the derivative's relation is not preserved. Are they expected?Sparks29032 commentedon Sep 16, 2025
@ycexiao It is possible the derivative can become unbounded, but if our target is a sufficiently smooth function, I expect there to be some Lipschitz condition bounding our derivative as well since we are still performing a regression to minimize over this function. Furthermore, the changes in derivative are bounded by the lengths of these interval, so if your squeeze is small, the derivative is not going to become super jumpy. It may be interesting to formalize this claim and give some bounds relative to the maximum derivative in a region, though I digress.
In the scenario we do get extremely unexpected behavior, since we report the region of non-monotonicity, the user should know that this is a convergence artifact.
We should definitely run some numerical experiments to see the general behavior. Here is a suggested test:
Here is another:
Some motivation for the second test. Take
y = sin(x)sampled on the grid with spacing0.1. Sincesineis2piperiodic, each sampledypoint must necessarily be distinct. Thus, we can sort all they. One can show (I will not do so here) that as the interval of our grid goes to infinity, the maximum of the discrete derivative ofxwith respect toy(this is the converse of your concern) also goes to infinity. This is sort of a worst case scenario.ycexiao commentedon Sep 16, 2025
@Sparks29032, sorry, I didn't get some parts about the tests. Can you explain more?
Which input's initial value?
What is the objective function here? The morph y?
Sparks29032 commentedon Sep 16, 2025
Initial values for the squeeze parameters.
Objective function for both is squeeze. I just motivated the example using a function of y.
Sparks29032 commentedon Sep 30, 2025
Need more discussion. Can move this to 0.4.0 release.
Sparks29032 commentedon Dec 18, 2025
Closed by #272