Metro simulation 2.

Example of a simulation of the evolution of a graph signal over the Santiago Metro network.

Simulation of the distribution of a signal over the metro network. The starting conditions is a graph signal with only one positive integer value bigger.The plots or animation show how this signal distributes over the network using:

\[y = AD^-1x\]

This example adds some constraints to the previous metro simulation example. Some of them are:

1. Eliminates the backward connections on the simulation and substracts 1 to

   every node degree to avoid dilution of the signal by going backwards.

2. If the 2 wagons arrive at the same metro station, there is no other way but

   out. All the people in those wagons will exit the sations.

3. In terminal stations, the people will not travel backwards this will also

   force an exit to everyone that reaches the terminal station.

4. If there are less than the number of people that is set to get out in every

   station then then wagon is emptyed.

The output is a folder with numerated figures. You can use websites such as https://gifmaker.me/ to make an animation with the resulting figures.

The initial condition is a graph signal with only one positive integer value bigger.The plots or animation show how this signal distributes over the network using:

\[y = AD^-1x\]

To run this example, you need to download three files and place them in the same directory as this script.

1. Download the file Tablas de subidas y bajadas nov23.zip from this link:

https://www.dtpm.cl/descargas/modelos_y_matrices/Tablas%20de%20subidas%20y%20bajadas%20nov23.zip

Then, uncompress the zip file and copy 2023.11 Matriz_baj_SS_MH.xlsb to the same location as this script.

2. Download the file santiago_metro_stations_coords.geojson from this link:

https://zenodo.org/records/11637462/files/santiago_metro_stations_coords.geojson

3. Download the file santiago_metro_stations_connections.txt from this link:

https://zenodo.org/records/11637462/files/santiago_metro_stations_connections.txt

import os

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

from pygsp2.utils_examples import fetch_data, make_metro_graph

current_dir = os.getcwd()
os.chdir(current_dir)

try:
    os.mkdir('metro_simulation2/')
except FileExistsError:
    print('Warning: It seems like this folder already exists. Overwritting...')

assets_dir = os.path.join(current_dir, 'data')
fetch_data(assets_dir, 'metro')

G, pos = make_metro_graph(edgesfile=os.path.join(assets_dir, 'santiago_metro_stations_connections.txt'),
                          coordsfile=os.path.join(assets_dir, 'santiago_metro_stations_coords.geojson'))
stations = list(G)

W0 = nx.adjacency_matrix(G).toarray()
D = np.diag(W0 @ np.ones(len(W0)))
# The signal will advance through the graph. In our case
# the backwards direction needs to be subtracted. Otherwise
# the signal will be "diluted" in each step by half since
# there is a backwards connection available.
D[D > 1] = D[D > 1] - 1
D_inv = np.linalg.inv(D)

# Store terminal stations. Anything that arrives here
# will get out of the network.
terminal_stations = np.where(np.sum(W0, axis=1) == 1)

NSTEPS = 27  # Arbitrary units, steps
INIT_VALUE = 5000  # Initial conditions
INIT_STATION = 103  # HOSPITAL DEL PINO
# Set constant value that will exit
# the network in each step
OUT_CONSTANT = 10

signal = np.zeros(len(W0))
signal[INIT_STATION] = INIT_VALUE

normalized_signal = signal / INIT_VALUE
nodelist = [list(G)[INIT_STATION]]

fig, ax = plt.subplots(figsize=(10, 7))
cmap = plt.get_cmap('viridis')
colors = cmap(normalized_signal[signal > 0])

nx.draw_networkx_edges(G, pos, node_size=20, ax=ax)
im = nx.draw_networkx_nodes(G, pos, node_color='gray', node_size=20, ax=ax)
im = nx.draw_networkx_nodes(G, pos, node_color=colors, nodelist=nodelist, node_size=20, ax=ax)
cbar = plt.colorbar(im, ax=ax, label='Number of people', ticks=[0, 0.5, 1])
cbar.set_ticklabels([0, (OUT_CONSTANT * 10) / 2, (OUT_CONSTANT * 10)])
plt.savefig('metro_simulation2/0.png')

visited_stations = [INIT_STATION]
mask = np.ones_like(W0)
W = W0 * mask

# People that leave the
# metro network in each station
left = np.zeros_like(signal)

for it in np.arange(1, NSTEPS):

    # Compute signal in new step
    signal = (W @ D_inv @ signal).astype(int)

    # Eliminate connections of visited stations
    mask[visited_stations, :] = 0
    mask[:, visited_stations] = 0

    W = W0 * mask

    # Check if people reached a terminal station
    stations2empty = np.intersect1d(np.where(signal)[0], terminal_stations)
    # Check if people reached a station that has no connections
    stations2empty2 = np.intersect1d(np.where(signal > 0)[0], np.where(W.sum(1) == 0)[0])

    if stations2empty.size > 0:
        print(f'It {it}: Emptying terminal stations')
        for i in stations2empty:
            print(f'\t{signal[i]} unboarded {stations[i]}')
            left[i] += signal[i]
            signal[i] -= signal[i]
    elif stations2empty2.size > 0:
        print(f'It {it}: Emptying encountered stations')
        for i in stations2empty2:
            print(f'\t{signal[i]} unboarded {stations[i]}')
            left[i] += signal[i]
            signal[i] -= signal[i]

    # Check if there is enough people to get out, otherwise
    # empty the station
    if np.all(signal[np.where(signal)[0]] > OUT_CONSTANT):
        for i in np.where(signal > 0)[0]:
            left[i] += OUT_CONSTANT
            signal[i] -= OUT_CONSTANT
    else:
        print(f'It {it}: Emptying stations')
        for i in np.where(np.logical_and(signal > 0, signal < OUT_CONSTANT))[0]:
            print(f'\t{signal[i]} unboarded {stations[i]}')
            left[i] += signal[i]
            signal[i] -= signal[i]
        for i in np.where(signal > 0)[0]:
            left[i] += OUT_CONSTANT
            signal[i] -= OUT_CONSTANT

    current_station = np.where(signal > 0)[0]
    nodelist = [list(G)[i] for i in current_station]
    nodelist2 = [list(G)[i] for i in np.where(left)[0]]

    normalized_signal = signal / INIT_VALUE
    colors = cmap(normalized_signal[signal > 0])

    normalized_left = left / (OUT_CONSTANT * 10)
    colors2 = cmap(normalized_left[left > 0])

    # Update visited stations list
    for i in np.where(signal)[0]:
        visited_stations.append(i)

    fig, ax = plt.subplots(figsize=(10, 7))

    nx.draw_networkx_edges(G, pos, node_size=20, ax=ax)
    im = nx.draw_networkx_nodes(G, pos, node_color='gray', node_size=20, ax=ax)

    im = nx.draw_networkx_nodes(G, pos, node_color=colors2, nodelist=nodelist2, node_size=20, ax=ax)

    im = nx.draw_networkx_nodes(G, pos, node_color=colors, nodelist=nodelist, node_size=20, ax=ax, node_shape='o',
                                edgecolors='red')

    cbar = plt.colorbar(im, ax=ax, label='Number of people', ticks=[0, 0.5, 1])
    cbar.set_ticklabels([0, (OUT_CONSTANT * 10) / 2, (OUT_CONSTANT * 10)])

    plt.savefig(f'metro_simulation2/{it}.png')
    plt.close()
    # fig.clf()

    if (np.sum(signal) == 0) or (np.sum(left) == INIT_VALUE):
        print(f'It {it}: Finished...')
        break

It 15: Emptying terminal stations
        780 unboarded Cerrillos
It 16: Emptying encountered stations
        802 unboarded Carlos Valdovinos
It 17: Emptying terminal stations
        381 unboarded Fernando Castillo Velasco
It 18: Emptying encountered stations
        371 unboarded Chile España
        70 unboarded Villa Frei
It 19: Emptying terminal stations
        522 unboarded Plaza de Puente Alto
It 20: Emptying encountered stations
        27 unboarded Manuel Montt
        88 unboarded Universidad Católica
        7 unboarded Santa Lucía
        361 unboarded Cristóbal Colón
It 20: Emptying stations
It 21: Emptying stations
        3 unboarded Cementerios
        3 unboarded Conchalí
It 24: Emptying stations
It 25: Emptying encountered stations
        173 unboarded Neptuno
It 25: Finished...

Estimated memory usage: 184 MB