vnew = v + (vk1 + 2 * vk2 + 2 * vk3 + vk4) / 6
return ynew, vnew
def euler(y, v, t, dt): # simple euler integrator
vnew = v + accel(y, v, t) * dt
ynew = y + vnew * dt + 1 / 2 * accel(y, vnew, t) * dt**2
return ynew, vnew
positions_eu, positions_rk = [], []
y_eu, y_rk = np.array(y), np.array(y)
v_eu, v_rk = np.array(v), np.array(v)
t = 0
pb = ProgressBar(0, Nsteps, c="blue", ETA=0)
for i in pb.range():
y_eu, v_eu = euler(y_eu, v_eu, t, dt)
y_rk, v_rk = rk4(y_rk, v_rk, t, dt)
t += dt
positions_eu.append(y_eu) # store result of integration
positions_rk.append(y_rk)
pb.print("Integrate: RK-4 and Euler")
####################################################
# Visualize the result
####################################################
vp = Plotter(interactive=0, axes=2) # choose axes type nr.2
vp.ytitle = "u(x,t)"
vp.ztitle = "" # will not draw z axis
for i in x:
import numpy as np
from Forces.forces import relu_force
from Solvers.solvers import take_euler_step
# Params
N = 200
T = 100
r_max = 1.0
r_eq = 0.8
dt = 0.1
# Initialise cells
ini_x = np.random.uniform(low=-1.0, high=1.0, size=N)
ini_y = np.random.uniform(low=-1.0, high=1.0, size=N)
ini_z = np.random.uniform(low=-1.0, high=1.0, size=N)
X = np.column_stack((ini_x, ini_y, ini_z))
from vedo import ProgressBar, Spheres, interactive
pb = ProgressBar(0, T, c='red')
for t in pb.range():
take_euler_step(X, N, dt, relu_force, r_max, r_eq)
Spheres(X, c='b', r=0.3).show(axes=1, interactive=0)
pb.print()
interactive()