def testRK4(uCI, dt, n):
t = []
u = []
t.append(0)
u.append(uCI)
for i in range(1, n + 1):
(tf, uf) = rk.rungeKutta4(dt,
t[i - 1],
u[i - 1][0],
u[i - 1][1],
u[i - 1][2],
u[i - 1][3],
key1=dx,
key2=dVx,
key3=dy,
key4=dVy)
t.append(tf)
u.append(uf)
x = [i for i, j, k, l in u]
vx = [j for i, j, k, l in u]
y = [k for i, j, k, l in u]
vy = [l for i, j, k, l in u]
return t, x, vx, y, vy
def tirRK(n,L,y0,z0,yDer,zDer,x0=0,opt=2):
"""
Integrates between x = 0 or x0 and x = L :
opt = 2 : rungeKutta2
opt = 4 : rungeKutta4
"""
h = L/n
x = []; u = []
x.append(x0)
u.append([y0,z0])
for i in range(1,n+1):
if(opt == 2):
(xf,uf)= rungeKutta2(h,x[i-1],u[i-1][0],u[i-1][1],key1=yDer,key2=zDer)
elif(opt == 4):
(xf,uf)= rungeKutta4(h,x[i-1],u[i-1][0],u[i-1][1],key1=yDer,key2=zDer)
elif(opt == 0):
(xf,uf)= explicitEuler(h,x[i-1],u[i-1][0],u[i-1][1],key1=yDer,key2=zDer)
x.append(xf)
u.append(uf)
y = [i for i,j in u]
z = [j for i,j in u]
return x,y,z
def integrationRK4(uCI, dt, n):
t = []
u = []
t.append(0)
u.append(uCI)
for i in range(1, n + 1):
(tf, uf) = rk.rungeKutta4(dt,
t[i - 1],
u[i - 1][0],
u[i - 1][1],
u[i - 1][2],
u[i - 1][3],
u[i - 1][4],
u[i - 1][5],
key1=derx,
key2=derVx,
key3=dery,
key4=derVy,
key5=derz,
key6=derVz)
t.append(tf)
u.append(uf)
x = [i for i, j, k, l, m, n in u]
vx = [j for i, j, k, l, m, n in u]
y = [k for i, j, k, l, m, n in u]
vy = [l for i, j, k, l, m, n in u]
z = [m for i, j, k, l, m, n in u]
vz = [n for i, j, k, l, m, n in u]
return t, x, vx, y, vy, z, vz
def testRK4(uCI, dt, n):
t = []
u = []
t.append(0)
u.append(uCI)
for i in range(1, n + 1):
(tf, uf) = rk.rungeKutta4(dt,
t[i - 1],
u[i - 1][0],
u[i - 1][1],
u[i - 1][2],
u[i - 1][3],
key1=dtheta,
key2=dVtheta,
key3=dphi,
key4=dVphi)
t.append(tf)
u.append(uf)
theta = [i for i, j, k, l in u]
vtheta = [j for i, j, k, l in u]
phi = [k for i, j, k, l in u]
vphi = [l for i, j, k, l in u]
return t, theta, vtheta, phi, vphi
def testRK4(uCI,dt,n):
t = []
u = []
t.append(0)
u.append(uCI)
for i in range(1,n+1):
(tf,uf)=rk.rungeKutta4(dt,t[i-1],u[i-1][0],u[i-1][1],
key1=dertheta,key2=derVtheta)
t.append(tf)
u.append(uf)
theta = [i for i,j in u]
vtheta = [j for i,j in u]
return t,theta,vtheta
def testRK4(uCI, dt, n):
t = []
u = []
t.append(0)
u.append(uCI)
p = 10 # sampling step
tTemp = []
uTemp = []
tTemp.append(0)
uTemp.append(uCI)
print("t0 :", tTemp[0])
for i in range(1, n + 1):
j = (i - 1) % p
#(tf,uf)=rk.rungeKutta4(dt,t[i-1],u[i-1][0],u[i-1][1],u[i-1][2],u[i-1][3],key1=derX1,key2=derY1,key3=derX2,key4=derY2)
(tf, uf) = rk.rungeKutta4(dt,
tTemp[j],
uTemp[j][0],
uTemp[j][1],
uTemp[j][2],
uTemp[j][3],
key1=derX1,
key2=derY1,
key3=derX2,
key4=derY2)
if (i % p == 0):
# Values are added to final lists
t.append(tf)
u.append(uf)
# We empty the temporary tables
tTemp[:] = []
uTemp[:] = []
tTemp.append(tf)
uTemp.append(uf)
x1 = [i for i, j, k, l in u]
y1 = [j for i, j, k, l in u]
x2 = [k for i, j, k, l in u]
y2 = [l for i, j, k, l in u]
return t, x1, y1, x2, y2
def testRK4(uCI,dt,n):
t = []
u = []
t.append(0)
u.append(uCI)
for i in range(1,n+1):
(tf,uf)=rk.rungeKutta4(dt,t[i-1],u[i-1][0],u[i-1][1],u[i-1][2],u[i-1][3],
key1=derR,key2=derVr,key3=dertheta,key4=derVtheta)
t.append(tf)
u.append(uf)
r = [i for i,j,k,l in u]
vr = [j for i,j,k,l in u]
theta = [k for i,j,k,l in u]
vtheta = [l for i,j,k,l in u]
return t,r,vr,theta,vtheta