In Matplotlib, `Axes`

is
the primary place where we put plot elements, such as lines, texts and
legends. However, for a long time, I failed to grasp the meaning of
aspect ratio in Matplotlib, thus was constantly frustrated by the
behavior of Maplotlib every time I attempted to change the aspect ratio
of a plot. This post is the result of my attempt to understand it and my
findings. Hope it can help you too.

# A first unsuccessful try

Suppose I have the following code:

```
import matplotlib.pyplot as plt
import numpy as np
'ggplot')
plt.style.use(= np.linspace(-5, 5, 100)
x = np.exp(0.5*x)
y1 = np.sin(x)
y2
= plt.figure()
fig = fig.add_subplot(111)
ax
ax.plot(x, y1)
ax.plot(x, y2) plt.show()
```

The code snippet above produces the following image

This image is a bit *thin*. What if I want the width of the
output image to be longer than its height, for example , an image with
aspect ratio 0.6? According to the official documentation of Matplotlib,
we can use set_aspect
method of `Axes`

class to set aspect ratio of an Axes object.
This method has a parameter `aspect`

which can be any
positive number `num`

. The description for `num`

is rather vague:

a circle will be stretched such that the height is num times the width. aspect=1 is the same as aspect=‘equal’.

After I add a statement

`=0.5) ax.set_aspect(aspect`

in the above script, the rendered output image becomes

Apparently, this is not what I want: the new output image is even thinner. But what has gone wrong? It took me a lot of efforts to find out.

# The meaning of aspect ratio in Matplotlib

Before we get into ** aspect ratio**, we should
first know that there are four different coordinate
systems in Matplotlib, which you are dealing with implicitly. Below
is a brief description:

Coordinate system | Description |
---|---|

data | The userland data coordinate system, controlled by the xlim and ylim |

axes | The coordinate system of the Axes; (0,0) is bottom left of the axes, and (1,1) is top right of the axes. |

figure | The coordinate system of the Figure; (0,0) is bottom left of the figure, and (1,1) is top right of the figure. |

display | This is the pixel coordinate system of the display; (0,0) is the bottom left of the display, and (width, height) is the top right of the display in pixels. |

Usually, these coordinate systems will work under the hood and you
can hardly notice their existence. In our case, what we really want to
set is the aspect ratio in the display coordinate system, i.e., the
physical length of axes height divided by its width. But the aspect
ratio in the `set_aspect()`

method refers to the aspect ratio
in **data coordinate system**. For example, if the aspect
ratio equals 1, then in the display coordinate, the same length in data
coordinate have the same displayed length. See the following image for
an example (aspect=1):

You can easily verify that for the same interval in data coordinate system in x and y axis, they have the same length in display coordinate system.

# Transform between data and display coordinate

Now that we know this distinction, the issue boils down to calculating the right aspect ratio to use in data coordinate system given the desired aspect ratio in display coordinate system. Suppose the axes height and width of the output plot are denoted as \(disp_h\) and \(disp_w\), then the desired display aspect ratio is

\[disp_r=\frac{disp_h}{disp_w}\ .\]

If we denote the height and width in the data coordinate system as \(data_h\) and \(data_w\), we have the following equation:

\[\frac{disp_w}{data_w}*aspect=\frac{disp_h}{data_h}\ .\]

Then the aspect we need to use in the `set_aspect()`

method is

\[\begin{equation}\begin{aligned} aspect & = \frac{data_w}{data_h}*\frac{disp_h}{disp_w}\\ & =\frac{data_w}{data_h}*disp_r \\ & = \frac{1}{data_r}*disp_r \end{aligned}\end{equation}\]

\(data_h\) and \(data_w\) in the above equation can be
easily calculated once we get the x and y axis limit using `get_xlim()`

and `get_ylim()`

methods of an
Axes class object. Or we can directly calculate the
`dataRatio`

using the `get_data_ratio()`

method of Axes class.

# The final plot

Now we are ready to set the display aspect ratio to whatever value we want using the following code:

## Click to show the code.

```
import matplotlib.pyplot as plt
import numpy as np
'ggplot')
plt.style.use(= np.linspace(-5, 5, 100)
x = np.exp(0.8*x)
y1 = np.sin(x)
y2
= plt.figure()
fig = fig.add_subplot(111)
ax
ax.plot(x, y1)
ax.plot(x, y2)
= 0.3
ratio = ax.get_xlim()
xleft, xright = ax.get_ylim()
ybottom, ytop # the abs method is used to make sure that all numbers are positive
# because x and y axis of an axes maybe inversed.
abs((xright-xleft)/(ybottom-ytop))*ratio)
ax.set_aspect(
# or we can utilise the get_data_ratio method which is more concise
# ax.set_aspect(1.0/ax.get_data_ratio()*ratio)
plt.show()
```

The following images are plotted using the same data but with different display aspect ratios.

(red numbers in each plot denote their axes aspect ratio)

## When we have shared x axis

Usually, when we plot two subplots in a 1*2 layout, they have the
same x axis but different y axis limit. If we share their x axis, we
must set the parameter `adjustable`

to “box-forced” in order
to set the aspect ratios correctly. Below is a valid example showing how
to do this

## Click to show the code.

```
import matplotlib.pyplot as plt
import numpy as np
= np.random.uniform(0.1, 0.7, size=(167,))
y1 = np.random.uniform(1, 100, size=(167,))
y2 = sorted(y1)
y1 = sorted(y2)
y2
= plt.figure(figsize=(10,3))
fig 'red')
fig.set_edgecolor(= fig.add_subplot(121)
ax1 = fig.add_subplot(122, sharex=ax1)
ax2
ax1.plot(y1)min(y1)*0.9, max(y1)*1.1])
ax1.set_ylim(['y1')
ax1.set_ylabel(
ax2.plot(y2)min(y2)*0.9, max(y2)*1.1])
ax2.set_ylim(['y2')
ax2.set_ylabel(
= 0.4
ratio
for ax in [ax1, ax2]:
= ax.get_xlim()
xmin, xmax = ax.get_ylim()
ymin, ymax print((xmax-xmin)/(ymax-ymin))
abs((xmax-xmin)/(ymax-ymin))*ratio, adjustable='box-forced')
ax.set_aspect(
plt.show()
```

The produced figure is

The two subplots in the above figure have exactly the same display aspect ratio.

OK, this is the end of this post, I hope that now you can finally under this and set the desired image aspect ratio without any difficulty.