Python matplotlib colorbar scientific notation base

Question

I am trying to customise a colorbar on my matpllotlib contourf plots. Whilst I am able to use scientific notation I am trying to change the base of the notation - essentiall

Answer 1

A possible solution can be to subclass the ScalarFormatter and fix the order of magnitude as in this question: Set scientific notation with fixed exponent and significant digits for multiple subplots

You would then call this formatter with the order of magnitude as the argument order, OOMFormatter(-2, mathText=False). mathText is set to false to obtain the notation from the question, i.e. while setting it to True, would give .

You can then set the formatter to the colorbar via the colorbar's format argument.

import numpy as np; np.random.seed(0)
import matplotlib.pyplot as plt
import matplotlib.ticker

class OOMFormatter(matplotlib.ticker.ScalarFormatter):
    def __init__(self, order=0, fformat="%1.1f", offset=True, mathText=True):
        self.oom = order
        self.fformat = fformat
        matplotlib.ticker.ScalarFormatter.__init__(self,useOffset=offset,useMathText=mathText)
    def _set_order_of_magnitude(self):
        self.orderOfMagnitude = self.oom
    def _set_format(self, vmin=None, vmax=None):
        self.format = self.fformat
        if self._useMathText:
             self.format = r'$\mathdefault{%s}$' % self.format


z = (np.random.random((10,10)) - 0.5) * 0.2

fig, ax = plt.subplots()
plot = ax.contourf(z)
cbar = fig.colorbar(plot, format=OOMFormatter(-2, mathText=False))

plt.show()

For matplotlib versions < 3.1 the class needs to look like this:

class OOMFormatter(matplotlib.ticker.ScalarFormatter):
    def __init__(self, order=0, fformat="%1.1f", offset=True, mathText=True):
        self.oom = order
        self.fformat = fformat
        matplotlib.ticker.ScalarFormatter.__init__(self,useOffset=offset,useMathText=mathText)
    def _set_orderOfMagnitude(self, nothing):
        self.orderOfMagnitude = self.oom
    def _set_format(self, vmin, vmax):
        self.format = self.fformat
        if self._useMathText:
            self.format = '$%s$' % matplotlib.ticker._mathdefault(self.format)

Answer 2

Similar to what @ImportanceOfBeingErnes described, you could use a FuncFormatter (docs) to which you just pass a function to determine the tick labels. This removes the auto generation of the 1e-2 header for your colorbar, but I imagine you can manually add that back in (I had trouble doing it, though was able to add it on the side). Using a FuncFormatter, you can just generate string tick values which has the advantage of not having to accept the way python thinks a number should be displayed.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as tk

z = (np.random.random((10,10)) - 0.5) * 0.2

levels = list(np.linspace(-.1,.1,9))

fig, ax = plt.subplots()
plot = ax.contourf(z, levels=levels)

def my_func(x, pos):
    label = levels[pos]
    return str(label*100)

fmt1 = tk.FuncFormatter(my_func)

cbar = fig.colorbar(plot, format=fmt1)
cbar.set_label("1e-2")

plt.show()

This will generate a plot which looks like this.