Why don’t you just add a formatter to the artist? This API May be preferable anyways to using the colorbar formatter though that could be the default.

Because the correct Formatter depends on the Normalization subclass being used, and that logic currently only exists in the colorbar code (nowhere else does it say that LogNorm should use LogFormatter, etc.).

Can’t we refactor that somehow? Seems quite hacky that you have to create a colorbar to make this work.

The relationship between norms, scales, colorbars, locators and formatters has been discussed to death (although in a slightly deconstructed fashion) a few times e.g. in #7294 (#7294 (comment), #7294 (comment), ...); TLDR: I think Norms and Scales should be the same thing.
But I stared too many times at the colorbar code trying to refactor it and in the meantime this is the simplest I can do.

I think the relevant code for matching up the Norm and Formatter is just:

Can't we just make colorbar._get_formatter_(norm) and call here and in colorbar?

No, you also need to have an underlying axes that sets the locs for the formatter (that's list(ax.yaxis.iter_ticks()) in this PR), otherwise the formatter can't format the values (https://github.com/matplotlib/matplotlib/blob/master/lib/matplotlib/ticker.py#L562).

You are right, but that seems quite unfortunate.

I think most places where self.axis.get_view_internal() is called could be changed to min/max(self.locs) if self.axis is None. Then all you'd have to do is manually set the view limits. I understand why we'd generally want to defer to the viewlimits, but its a shame to not allow the formatters to be independent of an axis if possible.

How does this work with lognorms anyways? The log formatter returns empty strings a lot of the time.

Oooh, does Formatter.create_dummy_axis help?

Didn't have time to look at the code, but I agree with @jklymak that this sounds extremely hacky. If it's not simple to refactor: What happens if we do not implement this? Does something crash or do we just not have the output displayed?

import numpy as np
import matplotlib.pyplot as plt

import matplotlib.ticker as mticker

fmt = mticker.ScalarFormatter()
fmt.create_dummy_axis()
fmt.set_locs([0.01, 1000])

print('Scalar:', fmt(20))

fmt = mticker.LogFormatterSciNotation()
fmt.create_dummy_axis()
fmt.set_locs([0.01, 1000])

print('10:', fmt(10))
print('20:', fmt(20))
print('100:', fmt(100))
print('200:', fmt(200))

Gives:

Scalar: 20

10: $\mathdefault{10^{1}}$
20:
100: $\mathdefault{10^{2}}$
200:

As above, not sure you even ever want to LogFormatter, but maybe I'm misunderstanding how this works...

@jklymak Actually, you need to call fmt.axis.set_view_interval (instead of fmt.set_locs).

import numpy as np
import matplotlib.pyplot as plt

import matplotlib.ticker as mticker

fmt = mticker.ScalarFormatter()
fmt.create_dummy_axis()
fmt.axis.set_view_interval(0.01, 1000)

print('Scalar:', fmt(20))

fmt = mticker.LogFormatterSciNotation()
fmt.create_dummy_axis()
fmt.axis.set_view_interval(0.01, 1000)

print('10:', fmt(10))
print('20:', fmt(20))
print('100:', fmt(100))
print('200:', fmt(200))

gives

Scalar: 
False None 1.0
10: $\mathdefault{10^{1}}$
False None 2.0
20: $\mathdefault{2\times10^{1}}$
False None 1.0
100: $\mathdefault{10^{2}}$
False None 2.0
200: $\mathdefault{2\times10^{2}}$

(I guess I should add a \times -> x in strip_math... now added to #12459)

@timhoffm Then we just fallback on the old label string (which is much less useful): #12459 protects everything under a if self.colorbar anyways.

I still think we should create a dummy axis, not colorbar... Formatter.create_dummy_axis should be made to work, but I admit I haven't wrestled with it yet.

Perhaps(??) things will become easier after the followup PRs after format_ticks get handled.

Superseded by #20949.