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empty_corridor.py
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empty_corridor.py
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import numpy as np
import matplotlib.pyplot as plt
import sys
def initial_conditions(n, width, length):
a=np.random.random((3,n))
for i in range(np.ma.size(a, 1)):
a[0,i]= int(np.ceil(2*a[0,i]))
if a[0,i]==1.0:
a[0,i]=1.0
elif a[0,i]==2.0:
a[0,i]=-1.0
a[1,i]=(width-2.0)*a[1, i]+1.0
a[2,i]=np.random.normal(1.3, 0.26)
old=np.zeros((4,n))
for i in range(n):
if a[0,i]==1.0:
old[0,i]=0.0 #Initial x position
elif a[0,i]==-1.0:
old[0,i]=length #Initial x position
old[1, i]=a[1, i] #Initial y position
old[2, i]=a[2, i]*a[0, i] #Initial x velocity vx
old[3, i]=0.0 #Initial y velocity vy
return a, old
def position_evolver(a, old, i, delta_t, tau, width, max_v_coef, sigma, v0, r, u0, c, phi):
n=np.ma.size(a,1)
new=np.zeros(4)
rabx=np.zeros(n)
raby=np.zeros(n)
fy=np.zeros(n)
fx=np.zeros(n)
for j in range(n):
rabx[j]=old[0, i]-old[0, j]
raby[j]=old[1, i]-old[1, j]
#Goal force
new[2]=delta_t*(1.0/tau*(a[2, i]*a[0, i]-old[2, i])) #Term 1
new[3]=delta_t*(1.0/tau*(-old[3, i]))
deltat2=delta_t
#Pedestrian-pedestrian repulsion force
for j in range(n):
if j!=i:
deltax=0.001
rabmod=np.sqrt(rabx[j]**2.0+raby[j]**2.0)
rabmodx=np.sqrt((rabx[j]+deltax)**2.0+raby[j]**2.0)
rabmody=np.sqrt(rabx[j]**2.0+(raby[j]+deltax)**2.0)
theta=np.arctan2(raby[j],rabx[j])
thetax=np.arctan2(raby[j],rabx[j]+deltax)
thetay=np.arctan2(raby[j]+deltax,rabx[j])
vb=np.sqrt(old[2,j]**2.0+old[3, j]**2.0)
root=np.sqrt(rabmod**2.0-2.0*vb*deltat2*rabmod*np.cos(theta)+vb**2.0*deltat2**2.0)
rootx=np.sqrt(rabmodx**2.0-2.0*vb*deltat2*rabmodx*np.cos(thetax)+vb**2.0*deltat2**2.0)
rooty=np.sqrt(rabmody**2.0-2.0*vb*deltat2*rabmody*np.cos(thetay)+vb**2.0*deltat2**2.0)
b=np.sqrt(rabmod**2.0+2.0*rabmod*root+root**2.0-vb**2.0*deltat2**2.0)/2.0
bx=np.sqrt(rabmodx**2.0+2.0*rabmodx*rootx+rootx**2.0-vb**2.0*deltat2**2.0)/2.0
by=np.sqrt(rabmody**2.0+2.0*rabmody*rooty+rooty**2.0-vb**2.0*deltat2**2.0)/2.0
exp=np.e**(-b/sigma)
expx=np.e**(-bx/sigma)
expy=np.e**(-by/sigma)
fx[j]=-v0*(expx-exp)/deltax
fy[j]=-v0*(expy-exp)/deltax
if (-a[0,i]*fx[j]>=np.sqrt(fx[j]**2.0+fy[j]**2.0)*np.cos(phi)):
new[2]+=delta_t*fx[j]
new[3]+=delta_t*fy[j]
else:
new[2]+=delta_t*fx[j]*c
new[3]+=delta_t*fy[j]*c
distInf=np.abs(old[1, i])
distSup=np.abs(width-old[1, i])
wallsInfy=u0/r*np.e**((-distInf)/r)
wallsInfx=0.0
new[2]+=delta_t*wallsInfx
new[3]+=delta_t*(wallsInfy)
#Pedestrian-wall repulsion force
wallsSupy=-u0/r*np.e**((-distSup)/r)
wallsSupx=0.0
new[2]+=delta_t*wallsSupx
new[3]+=delta_t*wallsSupy
new[2]+=old[2, i]
new[3]+=old[3, i]
if np.sqrt(new[2]**2.0+new[3]**2.0)>max_v_coef*a[2, i]:
new[2]=new[2]*max_v_coef*a[2, i]/np.sqrt(new[2]**2.0+new[3]**2.0)
new[3]=new[3]*max_v_coef*a[2, i]/np.sqrt(new[2]**2.0+new[3]**2.0)
new[0]=delta_t*new[2]+old[0,i]
new[1]=delta_t*new[3]+old[1, i]
#El problema de no incluir esto es que si no se pone la restricción sobre el punto inicial es probable
#que se abandone por los lados inferior/superior los bordes
if new[1]<=0.0 or new[1]>=width:
new[0]=old[0,i]
new[1]=old[1, i]
return new
t_delta=0.1 #Have to mantain low deltat. From a physical point of view could be understood as the reaction time of a person
#ie: the time a person needs to analyse a situation and take a decision os their velocity and direction. From a computational
# point of view because the method used to solve is finite differences it cannot be very big, for t=0.1s works fine
t_max=52.0
t_step=int(t_max/t_delta)
n=150
width=10.0
length=50.0
tau=0.5
r=0.2
u0=10.0
max_v_coef=1.3
sigma=0.3
v0=2.1
c=0.5
phi=100.0*2.0*np.pi/360
init, old=initial_conditions(n, width, length)
new=np.zeros((4, n))
for l in range(t_step):
for i in range(n):
new[:,i]=position_evolver(init, old, i, t_delta, tau, width, max_v_coef, sigma, v0, r, u0, c, phi)
if ((l*t_delta)%1.0)==0.0:
azules=[]
rojos=[]
for k in range(n):
if init[0, k]==1.0:
azules.append([new[0,k], new[1, k],10*np.sqrt(new[2, k]**2.0+new[3,k]**2.0)])
elif init[0,k]==-1.0:
rojos.append([new[0,k], new[1, k], 10*np.sqrt(new[2, k]**2.0+new[3,k]**2.0)])
nprojos=np.array(rojos)
npazules=np.array(azules)
try:
plt.scatter(npazules[:,0], npazules[:,1],s=npazules[:,2], c='b')
except:
pass
try:
plt.scatter(nprojos[:,0], nprojos[:,1],s=nprojos[:,2], c='r')
except:
pass
plt.xlim(0,length)
plt.ylim(0,width)
plt.title(str(l*t_delta))
plt.savefig('gif'+str(l*t_delta)+'.png')
plt.show()
print(l*t_delta)
for i in range(4):
for j in range(n):
old[i,j]=new[i,j]