Add feature - interpolate on a SingleAmountTaxScale

[RamParameswaran]

New features

• Introduce ability to interpolate between values in a SingleAmountTaxScale

• Currently we can return the nearest value (floor or ceiling) between two thresholds, based on an 'input_value' using SingleAmountTaxScale.calc(input_value)

• This PR allows calculating the linear-interpolated value between two thresholds using SingleAmountTaxScale.calc(input_value, interpolate=True).

  • Behind the scenes it uses the numpy.interp() function
  • I've passed through the right= and left= keyword arguments for user flexibility

Use case example:

# An example: 
thresholds = [0,2,4,6,8,10]    # x-values
values = [0,10,30,60,100,50]   # y-values

# We want to find y values for x=3, x=7, and x=9, using piecewise linear interpolation
y(3) ==> 20
y(7) ==> 80
y(9) ==> 75

[benjello]

@RamParameswaran : it looks like the interpolation procedure you are applying is converting a SingleAmountTaxScale to a LinearAverageRateTaxScale. Could you confirm ? If it is the cas why about using a converter.

[RamParameswaran]

@RamParameswaran : it looks like the interpolation procedure you are applying is converting a SingleAmountTaxScale to a LinearAverageRateTaxScale. Could you confirm ? If it is the cas why about using a converter.

@benjello I think the interpolation in this PR is different from a LinearAverageRateTaxScale because it specifically deals with amounts, not rates.

In my use case, we want to specify the parameters yaml as [threshold, amount] pairs. We probably could use a LinearAverageRateTaxScale, but we'd have to transform the parameter data so much, that it would not be easily traceable back to the legislation. I think this PR is a much cleaner approach.

# An example: 
thresholds = [0,2,4,6,8,10]    # x-values
amounts = [0,10,30,60,100,50]   # y-values

# We want to find y values for x=3, x=7, and x=9, using piecewise linear interpolation
y(3) ==> 20
y(7) ==> 80
y(9) ==> 75

[benjello]

@RamParameswaran : yes you will have to compute the rates but I think that my suggestion is cleaner since in the end what you get is actually a LinearAverageRateTaxScale.

[bonjourmauko]

Thanks @benjello ! And @RamParameswaran thanks for this contribution. One question: why not, instead of adding another responsibility to the SingleAmountTaxScale, create another amount scale responsible for just this use case?

[bonjourmauko]

So for example we would have:

class LinearAverageAmountTaxScale(AmountTaxScaleLike):
   pass

Then we will be able to rely on polymorphism —multiple dispatch— to decide which scale to instantiate depending on the requested simulation parameters.

[benjello]

@maukoquiroga : you will add another object that behaves like an existing one ... But I won't die on this hill and I can live with @RamParameswaran solution but I would definitely like to have a converter to enrich the TaxScale ecosystem.

[RamParameswaran]

you will add another object that behaves like an existing one ...

Agreed - for this reason, I do not think creating another TaxScale is appropriate.

@benjello I see your point about it effectively becoming a LinearAverageRateTaxScale. I'll try my hand at creating a converter tomorrow, and follow up :+1:

[RamParameswaran]

Hi @benjello and @maukoquiroga

I've written a converter function (see branch: 'add-converter-SingAmountTaxScale'). I'm not sure how useful it is, or indeed what it really means to convert a SingleAmountTaxScale to a LinearAverageRateTaxScale. What are the use-cases? :confused: Would you mind doing a sanity-check @benjello?

I think that conceptualising what it means to convert a SingleAmountTaxScale into a LinearAverageRateTaxScale requires quite a lot of mental abstraction. I think it is unreasonable to expect users to do this, just to perform simple arithmetic like linear interpolation between two thresholds. But I appreciate that this comment is rather philosophical :sweat_smile: - keen to hear your thoughts!

For the above reasons, I am still in favour of the approach of this current PR (998).

Thanks! :smile: