Background
Axis ticks can be converted to scientific format as suggested here.
Numbers can be converted into engineering format, one at a time as shown here
Question
How to format axis ticks in engineering notations i.e. order of magnitude is a multiple of 3.
You may want to explain exactly what you mean by "engineering notation", but there is an EngFormatter, which automatically uses the SI unit prefixes (ie micro, milli, kilo, mega, etc.)
fig, ax = plt.subplots()
ax.set_ylim(0,1e6)
ticker = matplotlib.ticker.EngFormatter(unit='')
ax.yaxis.set_major_formatter(ticker)
Playing around with the decimal module, I came around with the following solution:
from decimal import Decimal
import matplotlib.pyplot as plt
import numpy as np
data1 = np.linspace(-9, 9, 19)
data2 = 2.3 * 10**data1
yticks = 10**(np.linspace(-9, 9, 19))
yticklabels = [Decimal(y).quantize(Decimal('0.0000000001')).normalize().to_eng_string() for y in yticks]
plt.figure(1)
plt.subplot(121)
plt.grid(True)
plt.xlabel('k')
plt.ylabel('10^k')
plt.plot(data1, data2, 'k.')
plt.yscale('log')
plt.xticks(data1)
plt.yticks(yticks)
plt.subplot(122)
plt.grid(True)
plt.xlabel('k')
plt.ylabel('10^k')
plt.plot(data1, data2, 'k.')
plt.yscale('log')
plt.xticks(data1)
plt.yticks(yticks, yticklabels)
plt.show()
Please refer to the accepted answer on your second linked Q&A: Exponents between 0 and -6 are not converted to the desired format by definition/standard. Also, I needed to use the quantize method from decimal, too, because otherwise the outputted numbers would have had to many positions. (Remove the quantize part, and you'll see, what I mean.)
Hope that helps!
If one looks at the source, they realize that the solution proposed by Diziet Asahi can be easily modified to fulfill OP desires, as in the following
import matplotlib.pyplot as plt
from matplotlib.ticker import EngFormatter
fig, ax = plt.subplots()
ax.set_ylim(0,1e6)
ticker = EngFormatter(unit='')
############################################################################
ticker.ENG_PREFIXES = {i:"10**%d"%i if i else "" for i in range(-24, 25,3)}
############################################################################
ax.yaxis.set_major_formatter(ticker)
plt.show()
