[equalizing_difference] Update numpy code in to remove vectorization

[HumphreyYang]

This PR completes the first stage of #385.

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[mmcky]

Wow -- nice work. this reduces a LOT of code.

[HumphreyYang]

Many thanks @mmcky,

Please let me know if you approve this PR. Once this is merged, I will work on improving the sympy code and migrating the entrepreneur model into exercise.

[jstac]

After π=None put # Extra parameter (modified version) and then replace Tweaked model with Modification for reinterpreted model

[HumphreyYang]

Hi @jstac,

Since $\pi$ is only used for the entrepreneur model, would it be a good idea to remove it here and create a new namedtuple for the entrepreneur model when moving it into the exercise?

[jstac]

Hi @HumphreyYang , yes, good call. Let's do exactly that.

[jstac]

Wow, this actually works?? That's amazing. So create_edm(R=R_arr) returns a numpy array of namedtuples??

This definitely needs some comments.

[HumphreyYang]

I think this is passing the model with parameter R as a numpy array into compute_gap but not creating a numpy array of namedtuple.

The R_arr is then unpacked in the compute_gap function, and the operation on the array is broadcasted within the function.

This definitely needs some comments.

I agree! Would you think a comment like # Create a model and compute the gap suffice?

[jstac]

Please see my response below.

[jstac]

"as we did with our graphical analysis earlier" -> "in line with our earlier graphical analysis"

[jstac]

Thanks @HumphreyYang , please see my comments.

@longye-tian , do you have any suggestions or are you happy with these changes?

[longye-tian]

@jstac Thank you for asking me. I learn a lot from how @HumphreyYang improve the code.

It's really amazing how he creates the array of namedtuples.

Maybe we can create some variables to store this array of namedtuples and the gap values using list comprehension.
This may be useful if we need to examine some changes in the gap values.

models = [create_edm(R=r) for r in R_arr]
gaps = [compute_gap(model) for model in models]
plt.plot(R_arr, gaps)

Best,
Longye
:)

[jstac]

Thanks @longye-tian for the nice suggestion.

@HumphreyYang , your code is elegant, fast and concise but @longye-tian 's version is more explicit and I think it's better for this intro lecture series. Can you please switch to his version?

[HumphreyYang]

Thanks @longye-tian for the nice suggestion.

@HumphreyYang , your code is elegant, fast and concise but @longye-tian 's version is more explicit and I think it's better for this intro lecture series. Can you please switch to his version?

Many thanks @jstac and @longye-tian for the suggestions. I will switch to the more explicit version.

[jstac]

Very nice work @HumphreyYang and many thanks @longye-tian for helpful suggestions. This is a big improvement. Merging.