Attach scaling factor (and scaling uncertainty) to dataset

[toqduj]

I know discussions on this have already started, but for mutliple reasons, it would be good to be able to attach a scaling factor (with its own scaling uncertainty) to a dataset/array.

Doing so would allow:

• application of simple scaling operations to the scaling factor first, instead of to the array, followed by a later step "apply scaling", which will reset the scaling factor back to 1, but will still maintain a meaningful scaling uncertainty
• the clear separation of scaling uncertainties from inter-datapoint uncertainties. This helps, as scaling uncertainties can easily be on the order of 10%, whereas inter-datapoint uncertainties can be much, much smaller.

[garryod]

Hi Brian,

I like the idea of being able to separate scaling (and the associated uncertainties) from other pixel-wise operations, though doing this in a clean way may prove difficult:

1. The data array is wrapped in some object like below:

       @dataclass
       class ScalableArray(Generic[T]):
           data: ndarray[Any, T]
           scale_factor: T

   with each method requiring knowledge of the structure of this ScalableArray
2. Have methods produce some scaling metadata which can be applied to an independent variable to track scaling

It is possible we may be able to create something which looks like 1 but which implements the numpy array interface, though this I cannot say for certain at the moment

[toqduj]

Yes, this goes a bit beyond my expertise, but I hope inspiration will strike at some point and you'll come up with something pretty yet robust..

Is it an option to overload the mul and div operations of the scalableArray data class, so that when "other" is an array, it operates on the array, but when it's a scalar, it operates on the scale factor instead? repr can return the array multiplied by its scale factor.