Matplotlib: log scale for values too small for floating point

Question

I want to make a plot with matplotlib with really small values, shown on a log scale. This works fine until the numbers get too small and don't fit in a float.

I am representing values using SymPy arbitrary precision floats, but these are apparently converted to Python or NumPy machine floats internally in matplotlib.

For example

>>> import sympy
>>> import matplotlib.pyplot as plt
>>> plt.plot([0, 1, 2], [sympy.Float('1e-20'), sympy.Float('1e-100'), sympy.Float('1e-700')])
[<matplotlib.lines.Line2D object at 0x11ac0c208>]
>>> plt.yscale('log')

Produces

What it should show is the third value at 10^-700 (not at negative infinity).

Now I have very little hope of getting matplotlib to use SymPy Floats internally (if it's possible, let me know). What I would like to do is provide matplotlib with the log of the value, which I can compute myself just fine, but still display the exponential of that value on the y-axis with a log scale.

HYRY · Accepted Answer · 2017-05-27 06:43:32Z

4

You can do the log calculation and then plot the data, if you want the same tick labels, you can use FuncFormatter:

import sympy
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter

x = [0, 1, 2]
y = [sympy.Float('1e-20'), sympy.Float('1e-100'), sympy.Float('1e-700')]

def log_formatter(x, pos):
    return "$10^{{{:d}}}$".format(int(x))

formatter = FuncFormatter(log_formatter)

fig, ax = plt.subplots()

y2 = list(map(lambda x:sympy.log(x, 10), y))
ax.plot(x, y2)
ax.yaxis.set_major_formatter(formatter)
ax.grid();

EDIT

To add log-scale minor ticks, you can create a Locator:

import sympy
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter, Locator

x = [0, 1, 2]
y = [sympy.Float('1e-20'), sympy.Float('1e-100'), sympy.Float('1e-700')]

def log_formatter(x, pos):
    return "$10^{{{:d}}}$".format(int(x))

class LogMinorLocator(Locator):
    def __call__(self):
        majorlocs = self.axis.get_majorticklocs()
        step = majorlocs[1] - majorlocs[0]
        res = majorlocs[:, None] + np.log10(np.linspace(1, 0.1, 10)) * step
        return res.ravel()

formatter = FuncFormatter(log_formatter)

fig, ax = plt.subplots(figsize=(12, 8))
y2 = list(map(lambda x:sympy.log(x, 10), y))
ax.plot(x, y2)
ax.minorticks_on()
ax.yaxis.set_major_formatter(formatter)
ax.yaxis.set_minor_locator(LogMinorLocator())
ax.grid();

Here is the output:

edited May 27, 2017 at 6:43

answered May 26, 2017 at 23:00

HYRY

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2 Comments

Paul H Over a year ago

fun trick, you can decorate log_formatter with @FuncFormatter and then pass it directly to set_major_formatter

asmeurer Over a year ago

Does this use the logarithmic subticks like the normal log axes does?

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