How to do a matshow or imshow, but display the axis values as bin boundaries (i.e as you would on a 2d frequency/density plot)

Question

I need to do a 2d density-like plot. However I calculate the "densities" myself. So essentially I have an NxM array of values that I can only plot with plt.matshow (or imshow).

fig, ax = plt.subplots()
im = ax.matshow(value_array)
ax.set_xticklabels(x_edges - 2.5)
ax.set_yticklabels(y_edges - 0.25)

However, in this case, the axis values are the pixels in the plot, whereas I really want it to show some user-defined values. So I manually change the tick labels as above.

This still leaves a problem. matshow still thinks the tick labels are labelling the "pixels" in the image, so the tick labels are printed in the "middle" of each pixel square. However, like I said, what I'm really trying to plot is more like a density plot, so each "pixel square" represents a bin in x,y space. It would make a lot more sense to have the tick labels printed on the square edges, like the way it's done for histogram plots and frequency plots in general.

Should I keep using matshow for this or is there another function that does this? For example, can I use the plt.hist2d but manually set the "heights" without entering data as a bunch of samples? Otherwise, how do I make plt.matshow put the tick labels in the way I want them?

Answer 1

I'm not sure that I understand you correctly. What I understand is that you want to take a 2-d histogram of your data, and want to show the count/density of each bin using a color, while retaining the real coordinates of the bin-edges.

Indeed you can use a combination of numpy.histogram2d and matplotlib.pyplot.imshow.

Let me start by a warning. Withimshow you display pixels. Implicitly you therefore assume that bins are uniformly sized along each axis. They may have a different width and height, but the width/height of each bin has be equal for the representation to be fair.

To achieve what I think you want you'll have to use something like this:

import matplotlib.pyplot as plt
import numpy as np

N = 100000
x = np.random.randn(N)
y = np.random.weibull(2.,N)

P, xedges, yedges = np.histogram2d(x, y, bins=(np.linspace(-4,+5,10), np.linspace(0,4,21)), density=True)

fig, ax = plt.subplots()

cax = ax.imshow(P.T, extent=(xedges[0], xedges[-1], yedges[0], yedges[-1]),
  origin='lower', interpolation='nearest', clim=(0,.4), cmap='afmhot_r')

cbar = fig.colorbar(cax,aspect=10)

ax.set_aspect('auto')

ax.set_xlabel('x')
ax.set_ylabel('y')

plt.savefig('test.png')
plt.show()

Which plots

The tricky part is that to get a natural output:

• You have to overwrite imshow's default of putting the origin of the top of the image. As indicated, this you do with the origin='lower' option.
• You have to plot the transposed output of numpy.histogram, because imshow shows the matrix as-is, while the output of numpy.histogram show has shape (nx, ny): the values along the x-axis correspond to rows.
• You might have to change the aspect ratio, see this answer.

Answer 2

As an addition to @TomdeGeus answer, here is something that could help. Since I needed to plot a figure where the y-axis stretches from 0.5 to 3.5 while the x-axis stretches from 0 to 40, it was very compressed in the image, and I may have had to force the aspect ratio, which wasn't working. There was also something wrong with the ticks it displaying.

However after fixing the aspect ratio, I would definitely recommend you follow Tom de Geus's answer, it's the correct way to do this.

So I still plot the image on "pixel" coordinates, i.e choose the extent so that the x- and y-axes count the pixels, but starting at 0, rather than -0.5 like the default behaviour of plt.imshow()

fig, ax = plt.subplots()

im = ax.matshow(value_grid, origin='lower', extent=(0, len(x_edges)-1, 0, len(y_edges)-1)

Where len(y_edges) - 1 counts the number of pixels I want in the y-axis (and y_edges is a list containing the values of the bin boundaries I want to display on the y-axis as before.

Then I manually replace the tick labels, but I also need to correctly map them to the right ticks.

ax.set_xticks(list(range(len(x_edges))))
ax.set_xticklabels(x_edges)
ax.set_yticks(list(range(len(y_edges))))
ax.set_yticklabels(y_edges)

This preserves the square nature of the pixels produced by imshow, however you have to keep in mind that the underlying axis is still defined in terms of pixels (i.e if I want to place a point on the coordinate (25.0, 2.0), it wouldn't actually look like it ended up at that location below.