This notebook contains an excerpt from the Python Data Science Handbook by Jake VanderPlas; the content is available on GitHub.

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Customizing Ticks¶

Matplotlib's default tick locators and formatters are designed to be generally sufficient in many common situations, but are in no way optimal for every plot. This section will give several examples of adjusting the tick locations and formatting for the particular plot type you're interested in.

Before we go into examples, it will be best for us to understand further the object hierarchy of Matplotlib plots. Matplotlib aims to have a Python object representing everything that appears on the plot: for example, recall that the figure is the bounding box within which plot elements appear. Each Matplotlib object can also act as a container of sub-objects: for example, each figure can contain one or more axes objects, each of which in turn contain other objects representing plot contents.

The tick marks are no exception. Each axes has attributes xaxis and yaxis, which in turn have attributes that contain all the properties of the lines, ticks, and labels that make up the axes.

Major and Minor Ticks¶

Within each axis, there is the concept of a major tick mark, and a minor tick mark. As the names would imply, major ticks are usually bigger or more pronounced, while minor ticks are usually smaller. By default, Matplotlib rarely makes use of minor ticks, but one place you can see them is within logarithmic plots:

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import matplotlib.pyplot as plt
plt.style.use('classic')
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt plt.style.use('classic') %matplotlib inline import numpy as np

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ax = plt.axes(xscale='log', yscale='log')
ax.grid();
ax = plt.axes(xscale='log', yscale='log') ax.grid();

We see here that each major tick shows a large tickmark and a label, while each minor tick shows a smaller tickmark with no label.

These tick properties—locations and labels—that is, can be customized by setting the formatter and locator objects of each axis. Let's examine these for the x axis of the just shown plot:

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print(ax.xaxis.get_major_locator())
print(ax.xaxis.get_minor_locator())
print(ax.xaxis.get_major_locator()) print(ax.xaxis.get_minor_locator())

<matplotlib.ticker.LogLocator object at 0x7f649c651060>
<matplotlib.ticker.LogLocator object at 0x7f649c6517b0>

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print(ax.xaxis.get_major_formatter())
print(ax.xaxis.get_minor_formatter())
print(ax.xaxis.get_major_formatter()) print(ax.xaxis.get_minor_formatter())

<matplotlib.ticker.LogFormatterSciNotation object at 0x7f649c651780>
<matplotlib.ticker.LogFormatterSciNotation object at 0x7f64beb86920>

We see that both major and minor tick labels have their locations specified by a LogLocator (which makes sense for a logarithmic plot). Minor ticks, though, have their labels formatted by a NullFormatter: this says that no labels will be shown.

We'll now show a few examples of setting these locators and formatters for various plots.

Hiding Ticks or Labels¶

Perhaps the most common tick/label formatting operation is the act of hiding ticks or labels. This can be done using plt.NullLocator() and plt.NullFormatter(), as shown here:

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ax = plt.axes()
ax.plot(np.random.rand(50))

ax.yaxis.set_major_locator(plt.NullLocator())
ax.xaxis.set_major_formatter(plt.NullFormatter())
ax = plt.axes() ax.plot(np.random.rand(50)) ax.yaxis.set_major_locator(plt.NullLocator()) ax.xaxis.set_major_formatter(plt.NullFormatter())

Notice that we've removed the labels (but kept the ticks/gridlines) from the x axis, and removed the ticks (and thus the labels as well) from the y axis. Having no ticks at all can be useful in many situations—for example, when you want to show a grid of images. For instance, consider the following figure, which includes images of different faces, an example often used in supervised machine learning problems (see, for example, In-Depth: Support Vector Machines):

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fig, ax = plt.subplots(5, 5, figsize=(5, 5))
fig.subplots_adjust(hspace=0, wspace=0)

# Get some face data from scikit-learn
from sklearn.datasets import fetch_olivetti_faces
faces = fetch_olivetti_faces().images

for i in range(5):
    for j in range(5):
        ax[i, j].xaxis.set_major_locator(plt.NullLocator())
        ax[i, j].yaxis.set_major_locator(plt.NullLocator())
        ax[i, j].imshow(faces[10 * i + j], cmap="bone")
fig, ax = plt.subplots(5, 5, figsize=(5, 5)) fig.subplots_adjust(hspace=0, wspace=0) # Get some face data from scikit-learn from sklearn.datasets import fetch_olivetti_faces faces = fetch_olivetti_faces().images for i in range(5): for j in range(5): ax[i, j].xaxis.set_major_locator(plt.NullLocator()) ax[i, j].yaxis.set_major_locator(plt.NullLocator()) ax[i, j].imshow(faces[10 * i + j], cmap="bone")

downloading Olivetti faces from https://ndownloader.figshare.com/files/5976027 to /home/jovyan/scikit_learn_data

---------------------------------------------------------------------------
OSError                                   Traceback (most recent call last)
File /opt/conda/lib/python3.10/urllib/request.py:1348, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
   1347 try:
-> 1348     h.request(req.get_method(), req.selector, req.data, headers,
   1349               encode_chunked=req.has_header('Transfer-encoding'))
   1350 except OSError as err: # timeout error

File /opt/conda/lib/python3.10/http/client.py:1282, in HTTPConnection.request(self, method, url, body, headers, encode_chunked)
   1281 """Send a complete request to the server."""
-> 1282 self._send_request(method, url, body, headers, encode_chunked)

File /opt/conda/lib/python3.10/http/client.py:1328, in HTTPConnection._send_request(self, method, url, body, headers, encode_chunked)
   1327     body = _encode(body, 'body')
-> 1328 self.endheaders(body, encode_chunked=encode_chunked)

File /opt/conda/lib/python3.10/http/client.py:1277, in HTTPConnection.endheaders(self, message_body, encode_chunked)
   1276     raise CannotSendHeader()
-> 1277 self._send_output(message_body, encode_chunked=encode_chunked)

File /opt/conda/lib/python3.10/http/client.py:1037, in HTTPConnection._send_output(self, message_body, encode_chunked)
   1036 del self._buffer[:]
-> 1037 self.send(msg)
   1039 if message_body is not None:
   1040 
   1041     # create a consistent interface to message_body

File /opt/conda/lib/python3.10/http/client.py:975, in HTTPConnection.send(self, data)
    974 if self.auto_open:
--> 975     self.connect()
    976 else:

File /opt/conda/lib/python3.10/http/client.py:1447, in HTTPSConnection.connect(self)
   1445 "Connect to a host on a given (SSL) port."
-> 1447 super().connect()
   1449 if self._tunnel_host:

File /opt/conda/lib/python3.10/http/client.py:941, in HTTPConnection.connect(self)
    940 sys.audit("http.client.connect", self, self.host, self.port)
--> 941 self.sock = self._create_connection(
    942     (self.host,self.port), self.timeout, self.source_address)
    943 # Might fail in OSs that don't implement TCP_NODELAY

File /opt/conda/lib/python3.10/socket.py:845, in create_connection(address, timeout, source_address)
    844 try:
--> 845     raise err
    846 finally:
    847     # Break explicitly a reference cycle

File /opt/conda/lib/python3.10/socket.py:833, in create_connection(address, timeout, source_address)
    832     sock.bind(source_address)
--> 833 sock.connect(sa)
    834 # Break explicitly a reference cycle

OSError: [Errno 99] Cannot assign requested address

During handling of the above exception, another exception occurred:

URLError                                  Traceback (most recent call last)
Cell In[6], line 6
      4 # Get some face data from scikit-learn
      5 from sklearn.datasets import fetch_olivetti_faces
----> 6 faces = fetch_olivetti_faces().images
      8 for i in range(5):
      9     for j in range(5):

File /opt/conda/lib/python3.10/site-packages/sklearn/datasets/_olivetti_faces.py:117, in fetch_olivetti_faces(data_home, shuffle, random_state, download_if_missing, return_X_y)
    114     raise IOError("Data not found and `download_if_missing` is False")
    116 print("downloading Olivetti faces from %s to %s" % (FACES.url, data_home))
--> 117 mat_path = _fetch_remote(FACES, dirname=data_home)
    118 mfile = loadmat(file_name=mat_path)
    119 # delete raw .mat data

File /opt/conda/lib/python3.10/site-packages/sklearn/datasets/_base.py:1324, in _fetch_remote(remote, dirname)
   1302 """Helper function to download a remote dataset into path
   1303 
   1304 Fetch a dataset pointed by remote's url, save into path using remote's
   (...)
   1320     Full path of the created file.
   1321 """
   1323 file_path = remote.filename if dirname is None else join(dirname, remote.filename)
-> 1324 urlretrieve(remote.url, file_path)
   1325 checksum = _sha256(file_path)
   1326 if remote.checksum != checksum:

File /opt/conda/lib/python3.10/urllib/request.py:241, in urlretrieve(url, filename, reporthook, data)
    224 """
    225 Retrieve a URL into a temporary location on disk.
    226 
   (...)
    237 data file as well as the resulting HTTPMessage object.
    238 """
    239 url_type, path = _splittype(url)
--> 241 with contextlib.closing(urlopen(url, data)) as fp:
    242     headers = fp.info()
    244     # Just return the local path and the "headers" for file://
    245     # URLs. No sense in performing a copy unless requested.

File /opt/conda/lib/python3.10/urllib/request.py:216, in urlopen(url, data, timeout, cafile, capath, cadefault, context)
    214 else:
    215     opener = _opener
--> 216 return opener.open(url, data, timeout)

File /opt/conda/lib/python3.10/urllib/request.py:525, in OpenerDirector.open(self, fullurl, data, timeout)
    523 for processor in self.process_response.get(protocol, []):
    524     meth = getattr(processor, meth_name)
--> 525     response = meth(req, response)
    527 return response

File /opt/conda/lib/python3.10/urllib/request.py:634, in HTTPErrorProcessor.http_response(self, request, response)
    631 # According to RFC 2616, "2xx" code indicates that the client's
    632 # request was successfully received, understood, and accepted.
    633 if not (200 <= code < 300):
--> 634     response = self.parent.error(
    635         'http', request, response, code, msg, hdrs)
    637 return response

File /opt/conda/lib/python3.10/urllib/request.py:557, in OpenerDirector.error(self, proto, *args)
    555     http_err = 0
    556 args = (dict, proto, meth_name) + args
--> 557 result = self._call_chain(*args)
    558 if result:
    559     return result

File /opt/conda/lib/python3.10/urllib/request.py:496, in OpenerDirector._call_chain(self, chain, kind, meth_name, *args)
    494 for handler in handlers:
    495     func = getattr(handler, meth_name)
--> 496     result = func(*args)
    497     if result is not None:
    498         return result

File /opt/conda/lib/python3.10/urllib/request.py:749, in HTTPRedirectHandler.http_error_302(self, req, fp, code, msg, headers)
    746 fp.read()
    747 fp.close()
--> 749 return self.parent.open(new, timeout=req.timeout)

File /opt/conda/lib/python3.10/urllib/request.py:519, in OpenerDirector.open(self, fullurl, data, timeout)
    516     req = meth(req)
    518 sys.audit('urllib.Request', req.full_url, req.data, req.headers, req.get_method())
--> 519 response = self._open(req, data)
    521 # post-process response
    522 meth_name = protocol+"_response"

File /opt/conda/lib/python3.10/urllib/request.py:536, in OpenerDirector._open(self, req, data)
    533     return result
    535 protocol = req.type
--> 536 result = self._call_chain(self.handle_open, protocol, protocol +
    537                           '_open', req)
    538 if result:
    539     return result

File /opt/conda/lib/python3.10/urllib/request.py:496, in OpenerDirector._call_chain(self, chain, kind, meth_name, *args)
    494 for handler in handlers:
    495     func = getattr(handler, meth_name)
--> 496     result = func(*args)
    497     if result is not None:
    498         return result

File /opt/conda/lib/python3.10/urllib/request.py:1391, in HTTPSHandler.https_open(self, req)
   1390 def https_open(self, req):
-> 1391     return self.do_open(http.client.HTTPSConnection, req,
   1392         context=self._context, check_hostname=self._check_hostname)

File /opt/conda/lib/python3.10/urllib/request.py:1351, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
   1348         h.request(req.get_method(), req.selector, req.data, headers,
   1349                   encode_chunked=req.has_header('Transfer-encoding'))
   1350     except OSError as err: # timeout error
-> 1351         raise URLError(err)
   1352     r = h.getresponse()
   1353 except:

URLError: <urlopen error [Errno 99] Cannot assign requested address>

Notice that each image has its own axes, and we've set the locators to null because the tick values (pixel number in this case) do not convey relevant information for this particular visualization.

Reducing or Increasing the Number of Ticks¶

One common problem with the default settings is that smaller subplots can end up with crowded labels. We can see this in the plot grid shown here:

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fig, ax = plt.subplots(4, 4, sharex=True, sharey=True)
fig, ax = plt.subplots(4, 4, sharex=True, sharey=True)

Particularly for the x ticks, the numbers nearly overlap and make them quite difficult to decipher. We can fix this with the plt.MaxNLocator(), which allows us to specify the maximum number of ticks that will be displayed. Given this maximum number, Matplotlib will use internal logic to choose the particular tick locations:

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# For every axis, set the x and y major locator
for axi in ax.flat:
    axi.xaxis.set_major_locator(plt.MaxNLocator(3))
    axi.yaxis.set_major_locator(plt.MaxNLocator(3))
fig
# For every axis, set the x and y major locator for axi in ax.flat: axi.xaxis.set_major_locator(plt.MaxNLocator(3)) axi.yaxis.set_major_locator(plt.MaxNLocator(3)) fig

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This makes things much cleaner. If you want even more control over the locations of regularly-spaced ticks, you might also use plt.MultipleLocator, which we'll discuss in the following section.

Fancy Tick Formats¶

Matplotlib's default tick formatting can leave a lot to be desired: it works well as a broad default, but sometimes you'd like do do something more. Consider this plot of a sine and a cosine:

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# Plot a sine and cosine curve
fig, ax = plt.subplots()
x = np.linspace(0, 3 * np.pi, 1000)
ax.plot(x, np.sin(x), lw=3, label='Sine')
ax.plot(x, np.cos(x), lw=3, label='Cosine')

# Set up grid, legend, and limits
ax.grid(True)
ax.legend(frameon=False)
ax.axis('equal')
ax.set_xlim(0, 3 * np.pi);
# Plot a sine and cosine curve fig, ax = plt.subplots() x = np.linspace(0, 3 * np.pi, 1000) ax.plot(x, np.sin(x), lw=3, label='Sine') ax.plot(x, np.cos(x), lw=3, label='Cosine') # Set up grid, legend, and limits ax.grid(True) ax.legend(frameon=False) ax.axis('equal') ax.set_xlim(0, 3 * np.pi);

There are a couple changes we might like to make. First, it's more natural for this data to space the ticks and grid lines in multiples of $\pi$. We can do this by setting a MultipleLocator, which locates ticks at a multiple of the number you provide. For good measure, we'll add both major and minor ticks in multiples of $\pi/4$:

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ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
fig
ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2)) ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4)) fig

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But now these tick labels look a little bit silly: we can see that they are multiples of $\pi$, but the decimal representation does not immediately convey this. To fix this, we can change the tick formatter. There's no built-in formatter for what we want to do, so we'll instead use plt.FuncFormatter, which accepts a user-defined function giving fine-grained control over the tick outputs:

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def format_func(value, tick_number):
    # find number of multiples of pi/2
    N = int(np.round(2 * value / np.pi))
    if N == 0:
        return "0"
    elif N == 1:
        return r"$\pi/2$"
    elif N == 2:
        return r"$\pi$"
    elif N % 2 > 0:
        return r"${0}\pi/2$".format(N)
    else:
        return r"${0}\pi$".format(N // 2)

ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
fig
def format_func(value, tick_number): # find number of multiples of pi/2 N = int(np.round(2 * value / np.pi)) if N == 0: return "0" elif N == 1: return r"$\pi/2$" elif N == 2: return r"$\pi$" elif N % 2 > 0: return r"${0}\pi/2$".format(N) else: return r"${0}\pi$".format(N // 2) ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func)) fig

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This is much better! Notice that we've made use of Matplotlib's LaTeX support, specified by enclosing the string within dollar signs. This is very convenient for display of mathematical symbols and formulae: in this case, "$\pi$" is rendered as the Greek character $\pi$.

The plt.FuncFormatter() offers extremely fine-grained control over the appearance of your plot ticks, and comes in very handy when preparing plots for presentation or publication.

Summary of Formatters and Locators¶

We've mentioned a couple of the available formatters and locators. We'll conclude this section by briefly listing all the built-in locator and formatter options. For more information on any of these, refer to the docstrings or to the Matplotlib online documentaion. Each of the following is available in the plt namespace:

Locator class	Description
`NullLocator`	No ticks
`FixedLocator`	Tick locations are fixed
`IndexLocator`	Locator for index plots (e.g., where x = range(len(y)))
`LinearLocator`	Evenly spaced ticks from min to max
`LogLocator`	Logarithmically ticks from min to max
`MultipleLocator`	Ticks and range are a multiple of base
`MaxNLocator`	Finds up to a max number of ticks at nice locations
`AutoLocator`	(Default.) MaxNLocator with simple defaults.
`AutoMinorLocator`	Locator for minor ticks

Formatter Class	Description
`NullFormatter`	No labels on the ticks
`IndexFormatter`	Set the strings from a list of labels
`FixedFormatter`	Set the strings manually for the labels
`FuncFormatter`	User-defined function sets the labels
`FormatStrFormatter`	Use a format string for each value
`ScalarFormatter`	(Default.) Formatter for scalar values
`LogFormatter`	Default formatter for log axes

We'll see further examples of these through the remainder of the book.

< Text and Annotation | Contents | Customizing Matplotlib: Configurations and Stylesheets >