adds rule to select fewer ticks in sqrt scale for bokeh and plotly

[The-Broken-Keyboard]

closes #184

Instead of adding all integer ticks within range [0,max_y_value], new rule adds fewer ticks in same range.
The rule is similar to Matplotlib's autolocator's rule, it calculates the possible no. of ticks first in the given range, then it clips that value between 1 to 5. Then based on the number of ticks it calculates step size to put ticks across the axis.

By default the number of ticks is 5 ( didn't keep it 9, which matplotlib has, because in square root scale higher value ticks are placed more closer so it looks little congested for more number of ticks ).

Bokeh:

Plotly:

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📚 Documentation preview 📚: https://arviz-plots--189.org.readthedocs.build/en/189/

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 9.09091% with 10 lines in your changes missing coverage. Please review.

Project coverage is 72.49%. Comparing base (6265a5e) to head (c4adac4).

Files with missing lines	Patch %	Lines
src/arviz_plots/backend/plotly/__init__.py	14.28%	6 Missing ⚠️
src/arviz_plots/backend/bokeh/__init__.py	0.00%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #189      +/-   ##
==========================================
- Coverage   72.52%   72.49%   -0.03%     
==========================================
  Files          35       35              
  Lines        4026     4029       +3     
==========================================
+ Hits         2920     2921       +1     
- Misses       1106     1108       +2     

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[aloctavodia]

This will still be problematic if frequencies have large values, for instance

dt = azb.from_dict({
'observed_data': {"obs":pz.Poisson(2).rvs(1000)},
'posterior_predictive': {"obs":pz.Poisson(2).rvs((2, 1000, 1000))}
})

[The-Broken-Keyboard]

Yeah, true. I just realised that it will be problematic if maximum y value is high.

To handle this, Can we have a default fix number of ticks which we can determine dynamically between minimum y value and maximum y value? So even for high values, the number of ticks can be fixed.

Or else, we can have a dynamic rule which will determine the good number of ticks for a given range of values. Then determining those ticks won't be a difficult task to do....

What do you suggest @aloctavodia ?

[aloctavodia]

It is probably a good idea to check what matplotlib does by default and implement something similar.

[The-Broken-Keyboard]

Heyy @aloctavodia
I just went through the implementation in Matplotlib ( reference link : https://matplotlib.org/stable/api/ticker_api.html#matplotlib.ticker.AutoLocator ), they have an upper limit for no. of ticks which is 9 and lower limit for no. of ticks which is 1. They compute no. of integral intervals in the given range of y values ( by using function get_tick_space ), if they fall between 1-9 then they place those many ticks. If it goes above or below limits then they clip those values on 1 or 9 ( as you can see in below given screenshot ) . This is similar approach to what I suggested, either to fix no. of ticks or to find optimal no. of ticks based upon the given y value range. Let me know what would you prefer to do.....

[aloctavodia]

Fixing the number of ticks like Matplotlib seems reasonable.

[aloctavodia]

Plotly is missing the highest ytick, and sometimes cropping the highest value . See for example

dt = azb.from_dict({
'observed_data': {"obs":pz.Poisson(2).rvs(100, random_state=1)},
'posterior_predictive': {"obs":pz.Poisson(2).rvs((2, 1000, 100), random_state=1)}
})

[aloctavodia]

Suggested change

	num_ticks = 5
	num_ticks = min(num_ticks, math.ceil(((y_max * y_max) - (y_min * y_min)) / 2))
	step_size = round(((y_max * y_max) - (y_min * y_min)) / num_ticks)
	start_tick = round(y_min * y_min)
	end_tick = step_size * num_ticks
	num_ticks = 5
	num_ticks = min(num_ticks, math.ceil((y_max**2 - y_min**2) / 2))
	step_size = math.ceil((y_max**2 - y_min**2) / num_ticks)
	start_tick = math.ceil(y_min**2)
	end_tick = step_size * num_ticks

[aloctavodia]

Suggested change

	for i in range(start_tick, end_tick, step_size):
	tickvals_transformed = [i**0.5 for i in range(start_tick, end_tick, step_size)]

[aloctavodia]

Suggested change

	num_ticks = 5
	num_ticks = min(num_ticks, math.ceil(max_y / 2))
	step_size = round(math.ceil(max_y) / num_ticks)
	end_tick = num_ticks * step_size
	start_tick = 0
	num_ticks = min(5, math.ceil(max_y / 2))
	step_size = round(math.ceil(max_y) / num_ticks)
	end_tick = num_ticks * step_size
	ticks = [i**0.5 for i in range(0, end_tick + 1, step_size)]

[aloctavodia]

Suggested change

for i in range(start_tick, end_tick + 1, step_size):

[aloctavodia]

One more details. There is a lot of blank space below 0 for plotly. The plot should start at 0 like it does fro bokeh and matplotlib

[The-Broken-Keyboard]

One more details. There is a lot of blank space below 0 for plotly. The plot should start at 0 like it does fro bokeh and matplotlib

Yeah, I kept that knowingly because the circular dots in plotly ( which are little bigger in size than a normal dot ) would get cut if they fall on value 0. I can remove it or I can reduce the gap as well. Whatever you suggest @aloctavodia .

like this would happen without space:

In Bokeh and Matplotlib the dots are not circular with bigger size so it looks good there.

[aloctavodia]

could you please update the images in the PR description?

[The-Broken-Keyboard]

@aloctavodia actually I am currently in a class so couldn't update image when you asked.
I will update it once I get out of this class. Sorry for delay.

[aloctavodia]

Sure, no rush. Thanks