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make leapfrog integrator as System method

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Thibault Barnouin
2021-11-06 01:23:36 +01:00
parent 6206307f30
commit 0a91802800
14 changed files with 72 additions and 104 deletions
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82
lib/integrator.py
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@@ -1,82 +0,0 @@
#!/usr/bin/python
# -*- coding:utf-8 -*-
"""
Implementation of the various integrators for numerical integration.
Comes from the assumption that the problem is analytically defined in position-momentum (q-p) space for a given hamiltonian H.
"""
from os import system
import numpy as np
from lib.plots import DynamicUpdate
globals()['G'] = 6.67e-11 #Gravitational constant in SI units
globals()['Ms'] = 2e30 #Solar mass in kg
globals()['au'] = 1.5e11 #Astronomical unit in m
def dv_dt(m_array, q_array):
"""
Time derivative of the velocity, given by the position derivative of the Hamiltonian.
dv/dt = -1/m*dH/dq
"""
dv_array = np.zeros(q_array.shape)
for i in range(q_array.shape[0]):
q_j = np.delete(q_array, i, 0)
m_j = np.delete(m_array, i, 0)
dv_array[i] = -G*np.sum((m_j*(q_j-q_array[i])).T/np.sqrt(np.sum((q_j-q_array[i])**2, axis=1))**3, axis=1).T
dv_array[np.isnan(dv_array)] = 0.
return dv_array
def frogleap(duration, step, dyn_syst, recover_param=False, display=False):
"""
Leapfrog integrator for first order partial differential equations.
iteration : half-step drift -> full-step kick -> half-step drift
"""
N = np.ceil(duration/step).astype(int)
q_array = dyn_syst.get_positions()
v_array = dyn_syst.get_velocities()
masses = dyn_syst.get_masses()
m_array = np.ones(q_array.shape)
for i in range(q_array.shape[0]):
m_array[i,:] = masses[i]
E = np.zeros(N)
L = np.zeros((N,3))
if display:
try:
system("mkdir tmp")
except IOError:
system("rm tmp/*")
d = DynamicUpdate()
d.on_launch()
for j in range(N):
# half-step drift
q_array, v_array = q_array + step/2*v_array , v_array
# full-step kick
q_array, v_array = q_array , v_array - step*dv_dt(m_array, q_array)
# half-step drift
q_array, v_array = q_array + step/2*v_array , v_array
for i, body in enumerate(dyn_syst.bodylist):
body.q = q_array[i]
body.v = v_array[i]
body.p = body.v*body.m
dyn_syst.COMShift()
E[j] = dyn_syst.Eval()
L[j] = dyn_syst.Lval()
if display:
# display progression
if len(dyn_syst.bodylist) == 1:
d.on_running(q_array[0], q_array[1], q_array[2], step=j, label="step {0:d}/{1:d}".format(j,N))
else:
d.on_running(q_array[:,0], q_array[:,1], q_array[:,2], step=j, label="step {0:d}/{1:d}".format(j,N))
if display:
system("convert -delay 5 -loop 0 tmp/?????.png tmp/temp.gif && rm tmp/?????.png")
system("convert tmp/temp.gif -fuzz 30% -layers Optimize plots/dynsyst.gif && rm tmp/temp.gif")
if recover_param:
return E, L

79
lib/objects.py
View File

@@ -91,12 +91,61 @@ class System:
rij = np.linalg.norm(body.q-otherbody.q)
W = W - G*body.m*otherbody.m/rij
return T + W
def __repr__(self): # Called upon "print(system)"
return str([print(body) for body in self.bodylist])
def __str__(self): # Called upon "str(system)"
return str([str(body) for body in self.bodylist])
def Drift(self, dt):
for body in self.bodylist:
body.q = body.q + dt*body.v
def Kick(self, dt):
for body in self.bodylist:
body.a = np.zeros(3)
for otherbody in self.bodylist:
if body != otherbody:
rij = np.linalg.norm(body.q-otherbody.q)
body.a = body.a - (body.q-otherbody.q)*G*otherbody.m/(rij**3)
body.v = body.v + dt*body.a
def LP(self, dt):
self.COMShift()
self.Drift(dt/2)
self.Kick(dt)
self.Drift(dt/2)
self.time = self.time + dt
for body in self.bodylist:
body.p = body.v*body.m
def leapfrog(self, duration, dt, recover_param=False, display=False):
if display:
try:
system("mkdir tmp")
except IOError:
system("rm tmp/*")
d = DynamicUpdate()
d.on_launch()
N = np.ceil(duration/dt).astype(int)
E = np.zeros(N)
L = np.zeros((N,3))
for j in range(N):
self.LP(dt)
E[j] = self.Eval()
L[j] = self.Lval()
if display and j%100==0:
# display progression
q_array = self.get_positions()
if len(self.bodylist) == 1:
d.on_running(q_array[0], q_array[1], q_array[2], step=j, label="step {0:d}/{1:d}".format(j,N))
else:
d.on_running(q_array[:,0], q_array[:,1], q_array[:,2], step=j, label="step {0:d}/{1:d}".format(j,N))
if display:
system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png")
system("convert tmp/temp.gif -fuzz 30% -layers Optimize plots/dynsyst.gif && rm tmp/temp.gif")
if recover_param:
return E, L
def Update_a(self): #update acceleration of bodies in system
for body in self.bodylist:
@@ -105,7 +154,6 @@ class System:
if body != otherbody:
rij = np.linalg.norm(body.q-otherbody.q)
body.a = body.a - (body.q-otherbody.q)*G*otherbody.m/(rij**3)
return 1
def Update_j(self): #update jerk of bodies in system
for body in self.bodylist:
@@ -117,14 +165,11 @@ class System:
deltar = (body.q-otherbody.q)
vr = deltav + 3.*deltar*np.inner(deltav,deltar)/(rij**2)
body.j = body.j - G*otherbody.m/(rij**3)*vr
return 1
def Predict(self,dt): # update predicted position and velocities of bodies in system
for body in self.bodylist:
body.qp = body.q +dt*body.v+((dt**2)*body.a/2.)+((dt**3)*body.j/6.)
body.vp = body.v + dt*body.a + ((dt**2)*body.j/2.)
#print("v=",body.v," vp=" ,body.vp)
return 1
def Update_ap(self): #update acceleration of bodies in system
for body in self.bodylist:
@@ -133,7 +178,6 @@ class System:
if body != otherbody:
rij = np.linalg.norm(body.qp-otherbody.qp)
body.ap = body.ap - (body.qp-otherbody.qp)*G*otherbody.m/(rij**3)
return 1
def Update_jp(self): #update jerk of bodies in system
for body in self.bodylist:
@@ -145,7 +189,6 @@ class System:
deltar = (body.qp-otherbody.qp)
vr = deltav + 3.*deltar*np.inner(deltav,deltar)/(rij**2)
body.jp = body.jp - G*otherbody.m/(rij**3)*vr
return 1
def Correct(self,dt): # correct position and velocities of bodies in system
for body in self.bodylist:
@@ -154,7 +197,6 @@ class System:
body.q = body.qp +((dt**4)*a2/24.) + ((dt**5)*a3/120.)
body.v = body.vp +((dt**3)*a2/6.) + ((dt**4)*a3/24.)
return 1
def HPC(self, dt): # update position and velocities of bodies in system with hermite predictor corrector
self.COMShift()
@@ -186,14 +228,23 @@ class System:
E[j] = self.Eval()
L[j] = self.Lval()
if display:
if display and j%100==0:
# display progression
q_array = self.get_positions()
if len(self.bodylist) == 1:
d.on_running(q_array[0], q_array[1], q_array[2], step=j, label="step {0:d}/{1:d}".format(j,N))
else:
d.on_running(q_array[:,0], q_array[:,1], q_array[:,2], step=j, label="step {0:d}/{1:d}".format(j,N))
if display:
system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png")
system("convert tmp/temp.gif -fuzz 30% -layers Optimize plots/dynsyst.gif && rm tmp/temp.gif")
if recover_param:
return E, L
def __repr__(self): # Called upon "print(system)"
return str([print(body) for body in self.bodylist])
def __str__(self): # Called upon "str(system)"
return str([str(body) for body in self.bodylist])

6
lib/plots.py
View File

@@ -21,7 +21,7 @@ class DynamicUpdate():
def on_launch(self):
#Set up plot
self.fig = plt.figure()
self.fig = plt.figure(figsize=(10,10))
self.ax = self.fig.add_subplot(projection='3d')
self.lines, = self.ax.plot([],[],[],'o')
#Autoscale on unknown axis and known lims on the other
@@ -45,8 +45,8 @@ class DynamicUpdate():
#We need to draw *and* flush
self.fig.canvas.draw()
self.fig.canvas.flush_events()
if not step is None and step%10==0:
self.fig.savefig("tmp/{0:05d}.png".format(step),bbox_inches="tight")
if not step is None and step%1000==0:
self.fig.savefig("tmp/{0:06d}.png".format(step),bbox_inches="tight")
#Example
def __call__(self):