mass/Lebesgue measure?

[rytis-paskauskas]

It would be useful to allow some measure theoretic operations, such as adding up masses on intervals. I think that mass could be implemented as a value of IntervalDict. What about mass addition?

[AlexandreDecan]

Any link showing me what you mean exactly with "mass" and "mass addition"? If the goal is to associate some value with some intervals, then IntervalDict is the way to go. Operations involving multiple IntervalDict instances can be performed using the combine method (not really efficient, that said).

[AlexandreDecan]

I briefly looked at interval masses and this seems quite specific to real number based intervals. I'm unsure this should fit in portion that aims to stay generic.

[rytis-paskauskas]

Thank you for your consideration.

Here is what I have in mind: if I1, I2 are intervals, and 'mass'[I1]=m1 and 'mass'[I2]=m2, then dict[I1]=m1 and dict[I2]=m2 if I1 and I2 are disjoint, otherwise dict[I1\I2]=m1, dict[I2\I1]=m2, and dict[ I1 & I2]=m1+m2 if they overlap. Masses are summed up in all overlaps, independently of whether intervals are open, closed, integral or real. Not sure I could provide a useful link though.

[rytis-paskauskas]

The current behavior of IntervalDict upon insertion seems to change the existing keys if there are overlaps. My suggestion is to add new behavior or modify the existing one in such a way that separates the overlapping intervals into separate keys, and that handles the values as illustrated in my previous comment. This is in line with existing behavior that does not preserve left-constness (keys), but it would remove arbitrariness of the current behavior. It would be, I think, valuable functionality which is attractive for probability-related calculations.

[AlexandreDecan]

Please have a look at the "combine" method. It handles the example your provided.

[rytis-paskauskas]

Indeed it does. Thanks.

[AlexandreDecan]

Perfect :-)