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sim3001.py
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sim3001.py
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# coding: utf-8
# In[11]:
import matplotlib
matplotlib.use("TkAgg")
from matplotlib import pyplot as plt
from processData import *
from graphics import *
from operator import *
from random import *
import numpy as np
import timeit
# In[12]:
# initialises our agent set with randomly directed speeds
def initialize_agents(speed, N, width, height, radius):
"""
Initializes our agent set with randomly directed speeds, draws the window and the agents
"""
seed()
agents = N * [0]
#agents = [Point(uniform(0, width), uniform(0, height)) for i in range(N)]
speeds = N * [[0,0]]
for i in range(N):
theta = uniform(0, 2 * np.pi)
speeds[i]= speed * np.array([np.cos(theta), np.sin(theta)])
theta = uniform(0, 2 * np.pi)
r = uniform(0, radius)
agents[i] = Point(width / 2 + r * np.cos(theta),
height / 2 + r * np.sin(theta))
return agents, speeds
def initialize_leaders(agents, prop, N_groups, N):
Ns = int(N * prop)
colors = ['red', 'blue', 'yellow']
leader_groups = []
for j in range(N_groups):
leader_groups.append([])
for i in range(Ns):
agent_index = i + j * Ns
leader_groups[j].append(agent_index)
agents[agent_index].setFill(colors[j])
return leader_groups
# draws the window and the agents
def initialize_window(agents, width, height):
#win = GraphWin("Swarm", width, height) # size of box
win = GraphWin("My Swarm", width, height, autoflush=False)
for agent in agents:
agent.draw(win)
win.getMouse()
return win
def couple_speeds(agents, speeds, a, s, N):
"""
Simplest model: for each agent, it will give its nearest neighbour a fraction of its speed and re-normalize it
"""
nearest_neighbours = [nearest_neighbour(agent, agents, N) for agent in agents]
for i in range(N):
weightedSpeed = a * speeds[nearest_neighbours[i]]
speeds[i] = speeds[i] + weightedSpeed
speeds[i] = s * normalized(speeds[i])
def get_distances(agent, agents, N):
"""
Given one angent and the set of all agents,
computes the distances from the first to all of the others
"""
dists = N * [0.0]
for i in range(N):
a, dists[i] = relative_pos(agent, agents[i])
if dists[i] == 0:
dists[i] = 0.1
return dists
def relative_pos(agent1, agent2):
dx = agent2.getX() - agent1.getX()
dy = agent2.getY() - agent1.getY()
return np.array([dx, dy]), np.linalg.norm([dx, dy])
def get_cm(agents, N):
poses = [np.array([a.getX(), a.getY()]) for a in agents]
return np.mean(poses,axis = 0)
def nearest_neighbour(agent, agents, N):
"""
Returns the index for the agent with smallest Eucledian distance to agent in question
"""
distances = get_distances(agent, agents, N)
j = next(i for i in range(N) if agents[i] is agent)
distances[j] = distances[j-1] + 1
return distances.index(min(distances))
def softened_angle(speed, newspeed, s, maxTheta):
proposal = normalized(newspeed + normalized(speed))
theta = angle(speed, proposal)
if maxTheta > theta: # changed to non-square ---> TEST!
return s * proposal
else:
return np.dot(rot_matrix(maxTheta), speed)
def in_sight_range(rel_pos, speed1, angle_range):
return 360 * angle(speed1, rel_pos) / np.pi < angle_range
def noisy_vector(noise):
return noise * np.array([2 * random() - 1, 2 * random() - 1])
def biaser(agents, leaders, speeds, N, s, prop, bias, dev_bias, weight):
#bias = np.array([0.0,1.0])
#Ns has to be integer
gbias = np.random.normal(bias, dev_bias, )
for i in leaders:
tot_dir = normalized(normalized(speeds[i]) + weight * gbias)
if np.linalg.norm(tot_dir) != 0:
speeds[i] = s * tot_dir
#bias = np.dot(tot_dir,np.array([[np.cos(rot_bias*i), 0],[0, np.sin(rot_bias*i)]]))
return
def rigid_boundary(x_bound, y_bound, agents, speeds, N):
for i in range(N):
[dx, dy] = [0, 0]
[x, y] = [agents[i].getX(), agents[i].getY()]
if x > x_bound:
speeds[i][0] = -speeds[i][0]
dx = x_bound - x
elif x < 0:
speeds[i][0] = -speeds[i][0]
dx = -x
if y > y_bound:
speeds[i][1] = -speeds[i][1]
dy = y_bound - y
elif y < 0:
speeds[i][1] = -speeds[i][1]
dy = -y
agents[i].move(dx, dy)
def periodic_boundary(x_bound, y_bound, agents, speeds, N): #Changed from rigid boundaries to periodic boundary condition
[dx, dy] = [0, 0]
for i in range(N):
[x, y] = [agents[i].getX(), agents[i].getY()]
if x > x_bound:
dx = -x_bound
elif x < 0:
dx = x_bound
if y > y_bound:
dy = -y_bound
elif y < 0:
dy = y_bound
agents[i].move(dx, dy)
def next_step(agents, speeds, dt, N):
dxvec = [dt * speeds[i][0] for i in range(N)]
dyvec = [dt * speeds[i][1] for i in range(N)]
for i in range(N):
agents[i].move(dxvec[i], dyvec[i])
def virtualizer(agents, h, w, N):
vagents = [np.array([agent.getX(),agent.getY()])
for agent in agents]
virtuals = N * [N * [0.0, 0.0]]
virtual_points = N * [N * [0]]
for i in range(N):
d_limit = agents[i].getY() - h / 2
u_limit = agents[i].getY() + h / 2
l_limit = agents[i].getX() - w / 2
r_limit = agents[i].getX() + w / 2
for j in range(N):
virtuals[i][j] = vagents[j]
candidates = [vagents[j],
vagents[j] + [w, 0], vagents[j] + [-w, 0],
vagents[j] + [w, h], vagents[j] + [w, -h],
vagents[j] + [-w, h], vagents[j] + [-w, -h],
vagents[j] + [0, h], vagents[j] + [0, -h]]
#virtuals[j] = next((cand for cand in candidates if lower_limit < cand[1] < upper_limit and left_limit < cand[0] < right_limit),False
for candidate in candidates:
if d_limit < candidate[1] < u_limit and l_limit < candidate[0] < r_limit:
virtuals[i][j] = candidate
virtual_points[i][j] = Point(virtuals[i][j][0],virtuals[i][j][1])
return virtual_points
def get_cm_std(agents, N):
poses = [np.array([a.getX(), a.getY()]) for a in agents]
return np.mean(poses,axis = 0), np.std(poses,axis = 0)
def mill_observables (N, agents, speeds):
cm, std = get_cm_std(agents, N)
mean_R = np.linalg.norm(std)
point_cm = Point(cm[0],cm[1])
norm_R = N*[0.0]
vector_R = N*[0,0]
angles = N*[0.0]
for i in range(N):
vector_R[i],norm_R[i] = relative_pos(point_cm, agents[i])
angles[i] = np.pi() - angle(vector_R[i],speeds[i])
min_R = min(norm_R)
max_R = max(norm_R)
return mean_R, min_R, max_R, angles
# In[13]:
#COUZIN MODEL IMPLEMENTED WITH REPULSION, ATTRACTION AND ORIENTATION ZONE SEPARATED (1ST PAPER)
def couzin(agents, other_agents, speeds, N, width, height, s, noise, dTheta, rr, ro, ra, sight_range, model2, roa, atract, orient):
if not model2:
atract = orient = 1
# watch only particles in repulsion zone
for i in range(N):
r_dir = np.array([0.0, 0.0])
o_dir = np.array([0.0, 0.0])
a_dir = np.array([0.0, 0.0])
repulsion_flag = False
for j in range(N):
if i == j:
#Eliminate the i-i interaction
continue
rel_pos, distance = relative_pos(agents[i], other_agents[i][j])
if in_sight_range(rel_pos, speeds[i], sight_range):
if distance < rr:
rel_pos = normalized(rel_pos)
r_dir = r_dir + rel_pos
repulsion_flag = True
elif not repulsion_flag:
# Couzin 2
if model2:
if distance < roa:
o_dir = o_dir + speeds[j]
rel_pos = normalized(rel_pos)
a_dir = a_dir + rel_pos
# Couzin 1
else:
if distance < ro:
o_dir = o_dir + speeds[j]
elif distance < ra:
rel_pos = normalized(rel_pos)
a_dir = a_dir + rel_pos
#Out of for (j), we treat now the resulting direction vector
if repulsion_flag:
tot_dir = normalized(- r_dir)
else:
tot_dir = orient * normalized(o_dir) + atract * normalized(a_dir)
tot_dir = normalized(tot_dir)
tot_dir = normalized(normalized(tot_dir) + noisy_vector(noise))
#avoid pts stoping when not interacting
if np.linalg.norm(tot_dir) != 0:
speeds[i] = softened_angle(speeds[i], tot_dir, s, dTheta)
return
def vicsek(agents, other_agents, speeds, N, s, noise, r): # s=speed, noise= letter csi temperature factor, r=radius of interaction
# consider only particles within 'r' from pt_i, align pt_i with v_avg
for i in range(N):
tot_dir = np.array([0.0, 0.0])
for j in range(N):
rel_pos, distance = relative_pos(agents[i], agents[j])
if distance < r:
tot_dir = tot_dir + speeds[j]
tot_dir = s * normalized(normalized(tot_dir) + noise * np.array([(-1)+2*random(),(-1)+2*random()]))
if np.linalg.norm(tot_dir) != 0:
speeds[i] = tot_dir
return
##MILL MODEL
def mill(agents, other_agents, speeds, dt, N, width, height, cr, ca, lr, la, alpha, beta, mass):
clr = cr / lr
cla = ca / la
for i in range(N):
u_dir = np.array([0.0, 0.0])
propulsion = np.array([0.0, 0.0])
friction = np.array([0.0, 0.0])
grad_U = np.array([0.0, 0.0])
#virtuals = virtualizer(agents[i], agents, height, width, N)
for j in range(N): #Duality interactions, by the Morse potential
if i == j:
#Eliminate the i-i interaction
continue
rel_pos, distance = relative_pos(agents[i], other_agents[i][j])
u_dir = normalized(rel_pos)
grad_U = grad_U + u_dir * (clr*np.exp(- distance / lr) - cla * np.exp(- distance / la))
propulsion = alpha * speeds[i] # self-propulsion propto alpha
norm = (np.linalg.norm(speeds[i]))
friction = beta * (norm ** 2) * speeds[i] #friction force prop to beta
d_speed = (propulsion - friction - grad_U) / mass
speeds[i]= speeds[i] + dt * d_speed
return
#mill (dt, agents, speeds, N, width, height, cr=100, ca=150, lr=80, la=200.0, alpha=1.0, beta=0.01, mass=1) # we're there! N=30, s=5, dt=0.1, Radius=height/4
#mill (dt, agents, speeds, N, width, height, cr=100, ca=150, lr=80, la=200.0, alpha=1.2, beta=0.01, mass=3) # we're there! N=30, s=5, dt=0.1, Radius=height/4
#mill (dt, agents, speeds, N, width, height, cr=100, ca=150, lr=80, la=200.0, alpha=1.0, beta=0.01, mass=1) # we're there aswell! N=20, s=5, dt=0.1, Radius=height/4
#mill (dt, agents, speeds, N, width, height, cr=50, ca=100, lr=50, la=100.0, alpha=1.0, beta=0.01, mass=1) # The winner at 12:28 (1/8/2017)! N=60, s=5, dt=0.1, Radius=height/2
#mill (dt, agents, speeds, N, width, height, cr=50, ca=100, lr=50, la=100.0, alpha=1.0, beta=0.5, mass=1)
##OBSERVABLES FOR MILL MODEL
#mean_R, min_R, max_R, angles = mill_observables(N, agents, speeds)
#if (i > 500):
# print mean_R, min_R, max_R
# print angles[0],angles[N/2], angles[N-1]
# WE WANT TO PLOT:
#Rmin, Rmax, Rmean OVER THE TIME OF THE SIMULATION, SEE IT CONVERGES
#angles[i] AT ONE STABLE MOMENT OF THE SIMULATION (END) AS A DISTRIBUTION OF ANGLES, SEE TWO PEAKS AROUND 90º
# In[ ]: