How can I create custom break points in a matplotlib colorbar?

Question

I'm borrowing an example from the matplotlib custom cmap examples page:

https://matplotlib.org/examples/pylab_examples/custom_cmap.html

This produces the same image with different numbers of shading contours, as specified in the number of bins: n_bins :

https://matplotlib.org/_images/custom_cmap_00.png

However, I'm interested not only in the number of bins, but the specific break points between the color values. For example, when nbins=6 in the top right subplot, how can I specify the ranges of the bins to such that the shading is filled in these custom areas:

n_bins_ranges = ([-10,-5],[-5,-2],[-2,-0.5],[-0.5,2.5],[2.5,7.5],[7.5,10])

Is it also possible to specify the inclusivity of the break points? For example, I'd like to specify in the range between -2 and 0.5 whether it's -2 < x <= -0.5 or -2 <= x < -0.5 .

EDIT WITH ANSWER BELOW:

Using the accepted answer below, here is code that plots each step including finally adding custom colorbar ticks at the midpoint. Note I can't post an image since I'm a new user.

Set up data and 6 color bins:

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

# Make some illustrative fake data:
x = np.arange(0, np.pi, 0.1)
y = np.arange(0, 2*np.pi, 0.1)
X, Y = np.meshgrid(x, y)
Z = np.cos(X) * np.sin(Y) * 10

# Create colormap with 6 discrete bins
colors = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]  # R -> G -> B
n_bin = 6
cmap_name = 'my_list'
cm = matplotlib.colors.LinearSegmentedColormap.from_list(
        cmap_name, colors, N=n_bin)

Plot different options:

# Set up 4 subplots
fig, axs = plt.subplots(2, 2, figsize=(6, 9))
fig.subplots_adjust(left=0.02, bottom=0.06, right=0.95, top=0.94, wspace=0.05)

# Plot 6 bin figure
im = axs[0,0].imshow(Z, interpolation='nearest', origin='lower', cmap=cm)
axs[0,0].set_title("Original 6 Bin")
fig.colorbar(im, ax=axs[0,0])

# Change the break points
n_bins_ranges = [-10,-5,-2,-0.5,2.5,7.5,10]
norm = matplotlib.colors.BoundaryNorm(n_bins_ranges, len(n_bins_ranges))
im = axs[0,1].imshow(Z, interpolation='nearest', origin='lower', cmap=cm, norm=norm)
axs[0,1].set_title("Custom Break Points")
fig.colorbar(im, ax=axs[0,1])

# Arrange color labels by data interval (not colors)
im = axs[1,0].imshow(Z, interpolation='nearest', origin='lower', cmap=cm, norm=norm)
axs[1,0].set_title("Linear Color Distribution")
fig.colorbar(im, ax=axs[1,0], spacing="proportional")

# Provide custom labels at color midpoints
# And change inclusive equality by adding arbitrary small value
n_bins_ranges_arr = np.asarray(n_bins_ranges)+1e-9
norm = matplotlib.colors.BoundaryNorm(n_bins_ranges, len(n_bins_ranges))
n_bins_ranges_midpoints = (n_bins_ranges_arr[1:] + n_bins_ranges_arr[:-1])/2.0
im = axs[1,1].imshow(Z, interpolation='nearest', origin='lower', cmap=cm ,norm=norm)
axs[1,1].set_title("Midpoint Labels\n Switched Equal Sign")
cbar=fig.colorbar(im, ax=axs[1,1], spacing="proportional",
        ticks=n_bins_ranges_midpoints.tolist())
cbar.ax.set_yticklabels(['Red', 'Brown', 'Green 1','Green 2','Gray Blue','Blue'])

plt.show()

Answer 1

You can use a BoundaryNorm as follows:

import matplotlib.pyplot as plt
import matplotlib.colors
import numpy as np
x = np.arange(0, np.pi, 0.1)
y = np.arange(0, 2*np.pi, 0.1)
X, Y = np.meshgrid(x, y)
Z = np.cos(X) * np.sin(Y) * 10

colors = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]  # R -> G -> B
n_bin = 6  # Discretizes the interpolation into bins
n_bins_ranges = [-10,-5,-2,-0.5,2.5,7.5,10]
cmap_name = 'my_list'
fig, ax = plt.subplots()

# Create the colormap
cm = matplotlib.colors.LinearSegmentedColormap.from_list(
            cmap_name, colors, N=n_bin)
norm = matplotlib.colors.BoundaryNorm(n_bins_ranges, len(n_bins_ranges))
# Fewer bins will result in "coarser" colomap interpolation
im = ax.imshow(Z, interpolation='nearest', origin='lower', cmap=cm, norm=norm)
ax.set_title("N bins: %s" % n_bin)
fig.colorbar(im, ax=ax)

plt.show()

Or, if you want proportional spacing, ie the distance between colors according to their values,

fig.colorbar(im, ax=ax, spacing="proportional")

As the boundary norm documentation states

If b[i] <= v < b[i+1] then v is mapped to color j; as i varies from 0 to len(boundaries)-2, j goes from 0 to ncolors-1.

So the colors are always chosen as -2 <= x < -0.5 , in order to obtain the equal sign on the other side you would need to supply something like n_bins_ranges = np.array([-10,-5,-2,-0.5,2.5,7.5,10])-1e-9