## Plot weight matrices example

This example demonstrates how to extract the connection strength for all the synapses among two populations of neurons and gather these values in weight matrices for further analysis and visualization.

All connection types between these populations are considered, i.e., four weight matrices are created and plotted.

First, we import all necessary modules to extract, handle and plot the connectivity matrices

import numpy as np
import pylab
import nest
import matplotlib.gridspec as gridspec
from mpl_toolkits.axes_grid1 import make_axes_locatable

We now specify a function which takes as arguments lists of neuron gids corresponding to each population

def plot_weight_matrices(E_neurons, I_neurons):

Function to extract and plot weight matrices for all connections among E_neurons and I_neurons

First, we initialize all the matrices, whose dimensionality is determined by the number of elements in each population Since in this example, we have 2 populations (E/I), 2^2 possible synaptic connections exist (EE, EI, IE, II)

    W_EE = np.zeros([len(E_neurons), len(E_neurons)])
W_EI = np.zeros([len(I_neurons), len(E_neurons)])
W_IE = np.zeros([len(E_neurons), len(I_neurons)])
W_II = np.zeros([len(I_neurons), len(I_neurons)])

Using GetConnections, we extract the information about all the connections involving the populations of interest. GetConnections returns a list of arrays (connection objects), one per connection. Each array has the following elements: [source-gid target-gid target-thread synapse-model-id port]

    a_EE = nest.GetConnections(E_neurons, E_neurons)

Using GetStatus, we can extract the value of the connection weight, for all the connections between these populations

    c_EE = nest.GetStatus(a_EE, keys='weight')

Repeat the two previous steps for all other connection types

    a_EI = nest.GetConnections(I_neurons, E_neurons)
c_EI = nest.GetStatus(a_EI, keys='weight')
a_IE = nest.GetConnections(E_neurons, I_neurons)
c_IE = nest.GetStatus(a_IE, keys='weight')
a_II = nest.GetConnections(I_neurons, I_neurons)
c_II = nest.GetStatus(a_II, keys='weight')

We now iterate through the list of all connections of each type. To populate the corresponding weight matrix, we begin by identifying the source-gid (first element of each connection object, n[0]) and the target-gid (second element of each connection object, n[1]). For each gid, we subtract the minimum gid within the corresponding population, to assure the matrix indices range from 0 to the size of the population.

After determining the matrix indices [i, j], for each connection object, the corresponding weight is added to the entry W[i,j]. The procedure is then repeated for all the different connection types.

    for idx, n in enumerate(a_EE):
W_EE[n[0] - min(E_neurons), n[1] - min(E_neurons)] += c_EE[idx]
for idx, n in enumerate(a_EI):
W_EI[n[0] - min(I_neurons), n[1] - min(E_neurons)] += c_EI[idx]
for idx, n in enumerate(a_IE):
W_IE[n[0] - min(E_neurons), n[1] - min(I_neurons)] += c_IE[idx]
for idx, n in enumerate(a_II):
W_II[n[0] - min(I_neurons), n[1] - min(I_neurons)] += c_II[idx]

We can now specify the figure and axes properties. For this specific example, we wish to display all the weight matrices in a single figure, which requires us to use GridSpec (for example) to specify the spatial arrangement of the axes. A subplot is subsequently created for each connection type.

    fig = pylab.figure()
fig.suptitle('Weight matrices', fontsize=14)
gs = gridspec.GridSpec(4, 4)
ax1 = pylab.subplot(gs[:-1, :-1])
ax2 = pylab.subplot(gs[:-1, -1])
ax3 = pylab.subplot(gs[-1, :-1])
ax4 = pylab.subplot(gs[-1, -1])

Using imshow, we can visualize the weight matrix in the corresponding axis. We can also specify the colormap for this image.

    plt1 = ax1.imshow(W_EE, cmap='jet')

Using the axis_divider module from mpl_toolkits, we can allocate a small extra space on the right of the current axis, which we reserve for a colorbar.

    divider = make_axes_locatable(ax1)
pylab.colorbar(plt1, cax=cax)

We now set the title of each axis and adjust the axis subplot parameters

    ax1.set_title('W_{EE}')
pylab.tight_layout()

Finally, the last three steps are repeated for each synapse type

    plt2 = ax2.imshow(W_IE)
plt2.set_cmap('jet')
divider = make_axes_locatable(ax2)
pylab.colorbar(plt2, cax=cax)
ax2.set_title('W_{EI}')
pylab.tight_layout()

plt3 = ax3.imshow(W_EI)
plt3.set_cmap('jet')
divider = make_axes_locatable(ax3)
pylab.tight_layout()