Alternative for matshow()
<p>I have a <code>101x101</code> matrix that I want to visualize graphically. So far I used the function <code>matshow</code> from <code>matplotlib.pyplot</code> as below:</p>

<pre><code>import numpy as np
import random
import matplotlib.pyplot as plt

A = np.zeros((101,101))
# do stuff to randomly change some values of A
plt.ion()
plt.matshow(A,cmap='PuBuGn')
plt.colorbar()
plt.show()
</code></pre>

<p>The output looks like this:
<a href="https://i.stack.imgur.com/IBCLa.png" rel="nofollow"><img src="https://i.stack.imgur.com/IBCLa.png" alt="enter image description here"></a></p>

<p>You should view this as an interaction matrix between species, and as you can see there are only three species strongly interacting. That is why it looks appropriate to consider a visualization like the following graph I found in a <a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004688" rel="nofollow">paper</a>, but I do not know if and how this can be implemented in Python:</p>

<p><a href="https://i.stack.imgur.com/X4xBy.png" rel="nofollow"><img src="https://i.stack.imgur.com/X4xBy.png" alt="enter image description here"></a></p>

<p>This should do the trick:</p>

<pre><code>import numpy as np
import matplotlib.pyplot as plt

def old_graph(A):
    plt.matshow(A,cmap='PuBuGn')
    plt.colorbar()
    plt.title(r"abs$\left(\left[\mathbf{A}_{ij} \right ] \right )$ ; SIS=%d"%(sis,), va='bottom')
    plt.show()

def new_graph(A, sis_list=np.zeros(0,int), symmetric=True, fig=None, pos=111):
    #create and edit figure:
    if fig is None:
        fig = plt.figure()
    ax = fig.add_subplot(pos, projection='polar')
    ax.set_rgrids([1],[' '])
    ax.set_rmax(1)
    ax.set_thetagrids([])
    ax.set_title(r"abs$\left(\left[\mathbf{A}_{ij} \right ] \right )$ ; SIS=%d"%(sis,), va='bottom')
    colormap = plt.get_cmap('PuBuGn')

    # make each species an angle value:
    n_species = A.shape[0]
    angles = np.linspace(0, 2*np.pi, n_species+1)
    # the radius will always be r_max, and each line
    # will always unite two points:
    r = np.ones((2,))
    # prepare list of lines to sort:
    unordered_pairs_and_values = []
    for index_line in xrange(n_species):
        for index_column in xrange(index_line):
            if symmetric:
                value = A[index_line,index_column]
            else: # not symmetric
                value= abs(A[index_line,index_column]- A[index_column,index_line])
            unordered_pairs_and_values.append([[angles[index_line],angles[index_column]], value])
    # sort the lines (otherwise white lines would cover the 'important' ones):
    ordered_pairs_and_values = sorted(unordered_pairs_and_values, key=lambda pair: pair[1])
    # get the maximum value for scaling:
    I_max = ordered_pairs_and_values[-1][1]
    # plot every line in order:
    for pair in ordered_pairs_and_values:
        ax.plot(pair[0], r, color=colormap(pair[1]/I_max), linewidth=2, alpha=0.8)
    # don't know how to add the colorbar:
    #fig.colorbar(orientation='horizontal')
    # mark the angles:
    ax.plot(angles, np.ones(angles.shape), 'ko')
    # mark the important angles (comment if you don't know which ones are these):
    ax.plot(angles[sis_list],  np.ones(sis_list.shape), 'ro')
    fig.show()

if __name__ == '__main__':
    n_species = 51
    sis = 3 # strongly interacting species
    sis_factor = 4.
    A = np.zeros((n_species,n_species))
    # do stuff to randomly change some values of A:
    for index_line in xrange(n_species):
        for index_column in xrange(index_line+1):
            A[index_line,index_column] = np.random.random()
            A[index_column,index_line] = A[index_line,index_column]

    sis_list = np.random.randint(0,n_species,sis)
    for species in sis_list:
        A[species,:] *= sis_factor
        A[:,species] *= sis_factor
        for species2 in sis_list: # correct crossings
            A[species,species2] /= sis_factor
    # stuff to randomly change some values of A done
    old_graph(A=A)
    new_graph(A=A, sis_list=sis_list, symmetric=True)
</code></pre>

<p>Old graph:
<a href="https://i.stack.imgur.com/HqjqG.png" rel="nofollow"><img src="https://i.stack.imgur.com/HqjqG.png" alt="old_graph"></a></p>

<p>New graph:
<a href="https://i.stack.imgur.com/QYcSZ.png" rel="nofollow"><img src="https://i.stack.imgur.com/QYcSZ.png" alt="enter image description here"></a>
I still don't know:</p>

<ul>
<li>how to enter the colorbar, since it requires a plot that was mapped using a colormap.</li>
<li>how to remove the r-ticks without rescaling the graph (you can try uncomment <code>#ax.set_rticks([])</code>)</li>
</ul>

<p>And the plot looks better with less interacting species:
<a href="https://i.stack.imgur.com/mm73A.png" rel="nofollow"><img src="https://i.stack.imgur.com/mm73A.png" alt="enter image description here"></a> </p>

python matrix matplotlib