matplotlib: colorbars and its text labels

I'd like to create a colorbar legend for a heatmap, such that the labels are in the center of each discrete color. Example borrowed from here:

    import matplotlib.pyplot as plt
    import numpy as np
    from matplotlib.colors import ListedColormap

    #discrete color scheme
    cMap = ListedColormap(['white', 'green', 'blue','red'])

    #data
    np.random.seed(42)
    data = np.random.rand(4, 4)
    fig, ax = plt.subplots()
    heatmap = ax.pcolor(data, cmap=cMap)

    #legend
    cbar = plt.colorbar(heatmap)
    cbar.ax.set_yticklabels(['0','1','2','>3'])
    cbar.set_label('# of contacts', rotation=270)

    # put the major ticks at the middle of each cell
    ax.set_xticks(np.arange(data.shape[1]) + 0.5, minor=False)
    ax.set_yticks(np.arange(data.shape[0]) + 0.5, minor=False)
    ax.invert_yaxis()

    #labels
    column_labels = list('ABCD')
    row_labels = list('WXYZ')
    ax.set_xticklabels(column_labels, minor=False)
    ax.set_yticklabels(row_labels, minor=False)

    plt.show()

This generates the following plot:

pmesh plot

Ideally I'd like to generate a legend bar which has the four colors and for each color, a label in its center: 0,1,2,>3. How can this be achieved?

    import matplotlib.pyplot as plt
    import numpy as np
    from matplotlib.colors import ListedColormap

    #discrete color scheme
    cMap = ListedColormap(['white', 'green', 'blue','red'])

    #data
    np.random.seed(42)
    data = np.random.rand(4, 4)
    fig, ax = plt.subplots()
    heatmap = ax.pcolor(data, cmap=cMap)

    #legend
    cbar = plt.colorbar(heatmap)

    cbar.ax.get_yaxis().set_ticks([])
    for j, lab in enumerate(['$0$','$1$','$2$','$>3$']):
        cbar.ax.text(.5, (2 * j + 1) / 8.0, lab, ha='center', va='center')
    cbar.ax.get_yaxis().labelpad = 15
    cbar.ax.set_ylabel('# of contacts', rotation=270)


    # put the major ticks at the middle of each cell
    ax.set_xticks(np.arange(data.shape[1]) + 0.5, minor=False)
    ax.set_yticks(np.arange(data.shape[0]) + 0.5, minor=False)
    ax.invert_yaxis()

    #labels
    column_labels = list('ABCD')
    row_labels = list('WXYZ')
    ax.set_xticklabels(column_labels, minor=False)
    ax.set_yticklabels(row_labels, minor=False)

    plt.show()

You were very close. Once you have a reference to the color bar axis, you can do what ever you want to it, including putting text labels in the middle. You might want to play with the formatting to make it more visible.

demo

From: stackoverflow.com/q/15908371