From 2d82b5649e90107f301810f27ac7358f5e94056c Mon Sep 17 00:00:00 2001 From: Alex_Hubert Date: Fri, 19 Nov 2021 14:32:37 +0100 Subject: [PATCH] file management --- lib/LeapFrog.py | 70 ++++++++++ lib/hermite.py | 115 ++++++++++++++++ lib/objects.py | 147 +++++++------------- lib/objects_hermite.py | 238 --------------------------------- main.py | 6 +- plots/2bodies_leapfrog_dEm.png | Bin 121333 -> 122984 bytes plots/2bodies_leapfrog_dL2.png | Bin 106847 -> 80136 bytes 7 files changed, 239 insertions(+), 337 deletions(-) create mode 100644 lib/LeapFrog.py create mode 100644 lib/hermite.py delete mode 100755 lib/objects_hermite.py diff --git a/lib/LeapFrog.py b/lib/LeapFrog.py new file mode 100644 index 0000000..c786abb --- /dev/null +++ b/lib/LeapFrog.py @@ -0,0 +1,70 @@ +#!/usr/bin/python +# -*- coding:utf-8 -*- +""" +Hermite integrator +""" + + +from os import system +import numpy as np +from lib.plots import DynamicUpdate +from lib.units import * + + +def Drift(dyn_syst, dt): + for body in dyn_syst.bodylist: + body.q = body.q + dt * body.v + + +def Kick(dyn_syst, dt): + for body in dyn_syst.bodylist: + body.a = np.zeros(3) + for otherbody in dyn_syst.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(dyn_syst, dt): + dyn_syst.COMShift() + Drift(dyn_syst, dt / 2) + Kick(dyn_syst, dt) + Drift(dyn_syst, dt / 2) + dyn_syst.time = dyn_syst.time + dt + for body in dyn_syst.bodylist: + body.p = body.v * body.m + + +def leapfrog(dyn_syst, duration, dt, recover_param=False, display=False, savename=None): + if display: + try: + system("mkdir tmp") + except IOError: + system("rm tmp/*") + d = DynamicUpdate(dyn_syst) + d.launch(dyn_syst.blackstyle) + + N = np.ceil(duration / dt).astype(int) + E = np.zeros(N) + L = np.zeros((N, 3)) + for j in range(N): + LP(dyn_syst,dt) + + E[j] = dyn_syst.E + L[j] = dyn_syst.L + + if display and j % 5 == 0: + # display progression + if len(dyn_syst.bodylist) == 1: + d.on_running(dyn_syst, step=j, label="step {0:d}/{1:d}".format(j, N)) + else: + d.on_running(dyn_syst, step=j, label="step {0:d}/{1:d}".format(j, N)) + if display: + d.close() + if not savename is None: + system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png") + system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/{0:s}_dynsyst.gif".format(savename)) + + if recover_param: + return E, L \ No newline at end of file diff --git a/lib/hermite.py b/lib/hermite.py new file mode 100644 index 0000000..8a19900 --- /dev/null +++ b/lib/hermite.py @@ -0,0 +1,115 @@ +#!/usr/bin/python +# -*- coding:utf-8 -*- +""" +Hermite integrator +""" + + +from os import system +import numpy as np +from lib.plots import DynamicUpdate +from lib.units import * + + +def Update_a(dyn_syst): # update acceleration of bodies in system + for body in dyn_syst.bodylist: + body.a = np.zeros(3) + for otherbody in dyn_syst.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) + + +def Update_j(dyn_syst): # update jerk of bodies in system + for body in dyn_syst.bodylist: + body.j = np.zeros(3) + for otherbody in dyn_syst.bodylist: + if body != otherbody: + rij = np.linalg.norm(body.q - otherbody.q) + deltav = (body.v - otherbody.v) + 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 + + +def Predict(dyn_syst, dt): # update predicted position and velocities of bodies in system + for body in dyn_syst.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.) + + +def Update_ap(dyn_syst): # update acceleration of bodies in system + for body in dyn_syst.bodylist: + body.ap = np.zeros(3) + for otherbody in dyn_syst.bodylist: + if body != otherbody: + rij = np.linalg.norm(body.qp - otherbody.qp) + body.ap = body.ap - (body.qp - otherbody.qp) * G * otherbody.m / (rij ** 3) + + +def Update_jp(dyn_syst): # update jerk of bodies in system + for body in dyn_syst.bodylist: + body.jp = np.zeros(3) + for otherbody in dyn_syst.bodylist: + if body != otherbody: + rij = np.linalg.norm(body.qp - otherbody.qp) + deltav = (body.vp - otherbody.vp) + 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 + + +def Correct(dyn_syst, dt): # correct position and velocities of bodies in system + for body in dyn_syst.bodylist: + a2 = (6. * (body.a - body.ap) + dt * (4 * body.j + 2 * body.jp)) / (dt ** 2) + a3 = (12. * (body.a - body.ap) + dt * 6. * (body.j + body.jp)) / (dt ** 3) + + body.q = body.qp + ((dt ** 4) * a2 / 24.) + ((dt ** 5) * a3 / 120.) + body.v = body.vp + ((dt ** 3) * a2 / 6.) + ((dt ** 4) * a3 / 24.) + + +def HPC(dyn_syst, dt): # update position and velocities of bodies in system with hermite predictor corrector + COMShift(dyn_syst) + Update_a(dyn_syst) + Update_j(dyn_syst) + Predict(dyn_syst, dt) + Update_ap(dyn_syst) + Update_jp(dyn_syst) + Correct(dyn_syst, dt) + dyn_syst.time = dyn_syst.time + dt + for body in dyn_syst.bodylist: + body.p = body.v * body.m + + +def hermite(dyn_syst, duration, dt, recover_param=False, display=False, savename=None): + if display: + try: + system("mkdir tmp") + except IOError: + system("rm tmp/*") + d = DynamicUpdate(dyn_syst) + d.launch(dyn_syst.blackstyle) + + N = np.ceil(duration / dt).astype(int) + E = np.zeros(N) + L = np.zeros((N, 3)) + for j in range(N): + HPC(dyn_syst, dt) + + E[j] = dyn_syst.E + L[j] = dyn_syst.L + + if display and j % 100 == 0: + # display progression + if len(dyn_syst.bodylist) == 1: + d.on_running(dyn_syst, step=j, label="step {0:d}/{1:d}".format(j, N)) + else: + d.on_running(dyn_syst, step=j, label="step {0:d}/{1:d}".format(j, N)) + if display: + d.close() + if not savename is None: + system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png") + system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/{0:s}_dynsyst.gif".format(savename)) + + if recover_param: + return E, L \ No newline at end of file diff --git a/lib/objects.py b/lib/objects.py index e09c3e2..492d3c7 100755 --- a/lib/objects.py +++ b/lib/objects.py @@ -8,185 +8,138 @@ import numpy as np from lib.plots import DynamicUpdate from lib.units import * + class Body: def __init__(self, mass, position, velocity): self.m = mass self.q = position self.v = velocity - self.p = velocity*mass + self.p = velocity * mass + self.a = np.zeros(3) + self.ap = np.zeros(3) + self.j = np.zeros(3) + self.jp = np.zeros(3) + self.qp = np.zeros(3) + self.vp = np.zeros(3) - def __repr__(self): # Called upon "print(body)" - return r"Body of mass: {0:.2f} $M_\odot$, position: {1}, velocity: {2}".format(self.m/Ms, self.q, self.v) + def __repr__(self): # Called upon "print(body)" + return r"Body of mass: {0:.2f} $M_\odot$, position: {1}, velocity: {2}".format(self.m / Ms, self.q, self.v) + + def __str__(self): # Called upon "str(body)" + return r"Body of mass: {0:.2f} $M_\odot$".format(self.m / Ms) - def __str__(self): # Called upon "str(body)" - return r"Body of mass: {0:.2f} $M_\odot$".format(self.m/Ms) class System(Body): def __init__(self, bodylist, blackstyle=True): - self.blackstyle = blackstyle #for dark mode in plot + self.blackstyle = blackstyle # for dark mode in plot self.bodylist = np.array(bodylist) - self.time = 0 #lifetime of system + self.time = 0 # lifetime of system self.m = self.M self.q = self.COM self.v = self.COMV - + + 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]) + @property - def get_masses(self): #return the masses of each object + def get_masses(self): # return the masses of each object return np.array([body.m for body in self.bodylist]) - + @property - def get_positions(self): #return the positions of the bodies + def get_positions(self): # return the positions of the bodies xdata = np.array([body.q[0] for body in self.bodylist]) ydata = np.array([body.q[1] for body in self.bodylist]) zdata = np.array([body.q[2] for body in self.bodylist]) return xdata, ydata, zdata - + @property - def get_velocities(self): #return the positions of the bodies + def get_velocities(self): # return the positions of the bodies vxdata = np.array([body.v[0] for body in self.bodylist]) vydata = np.array([body.v[1] for body in self.bodylist]) vzdata = np.array([body.v[2] for body in self.bodylist]) return vxdata, vydata, vzdata - + @property - def get_momenta(self): #return the momenta of the bodies + def get_momenta(self): # return the momenta of the bodies pxdata = np.array([body.p[0] for body in self.bodylist]) pydata = np.array([body.p[1] for body in self.bodylist]) pzdata = np.array([body.p[2] for body in self.bodylist]) return pxdata, pydata, pzdata @property - def M(self): #return total system mass + def M(self): # return total system mass mass = 0 for body in self.bodylist: mass = mass + body.m return mass @property - def COM(self): #return center of mass in cartesian np_array + def COM(self): # return center of mass in cartesian np_array coord = np.zeros(3) for body in self.bodylist: - coord = coord + body.m*body.q - coord = coord/self.M + coord = coord + body.m * body.q + coord = coord / self.M return coord @property - def COMV(self): #return center of mass velocity in cartesian np_array + def COMV(self): # return center of mass velocity in cartesian np_array coord = np.zeros(3) for body in self.bodylist: coord = coord + body.p - coord = coord/self.M + coord = coord / self.M return coord - def COMShift(self): #Shift coordinates of bodies in system to COM frame and set COM at rest + def COMShift(self): # Shift coordinates of bodies in system to COM frame and set COM at rest for body in self.bodylist: body.q = body.q - self.COM body.p = body.p - self.COMV @property - def L(self): #return angular momentum of bodies in system + def L(self): # return angular momentum of bodies in system L = np.zeros(3) for body in self.bodylist: - L = L + np.cross(body.q,body.p) + L = L + np.cross(body.q, body.p) return L @property - def E(self): #return total energy of bodies in system + def E(self): # return total energy of bodies in system T = 0 W = 0 for body in self.bodylist: - T = T + 1./2.*body.m*np.linalg.norm(body.v)**2 + T = T + 1. / 2. * body.m * np.linalg.norm(body.v) ** 2 for otherbody in self.bodylist: if body != otherbody: - rij = np.linalg.norm(body.q-otherbody.q) - W = W - G*body.m*otherbody.m/rij + rij = np.linalg.norm(body.q - otherbody.q) + W = W - G * body.m * otherbody.m / rij E = T + W return E - + @property def mu(self): sum = 0 prod = 1 for body in self.bodylist: prod = prod * body.m - mu = prod/self.M + mu = prod / self.M return mu @property - def ex(self): #exentricity of system (if composed of 2 bodies) - if len(self.bodylist) != 2 : + def ex(self): # exentricity of system (if composed of 2 bodies) + if len(self.bodylist) != 2: return np.nan else: - k = (2.*self.E*(np.linalg.norm(self.L)**2))/((G**2)*(self.M**2)*(self.mu**3)) + 1. + k = (2. * self.E * (np.linalg.norm(self.L) ** 2)) / ((G ** 2) * (self.M ** 2) * (self.mu ** 3)) + 1. return k @property - def sma(self): #semi major axis of system (if composed of 2 bodies) - if len(self.bodylist) != 2 : + def sma(self): # semi major axis of system (if composed of 2 bodies) + if len(self.bodylist) != 2: return np.nan else: - sma = -G*self.M*self.mu/(2.*self.E) + sma = -G * self.M * self.mu / (2. * self.E) return sma - - 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, savename=None): - if display: - try: - system("mkdir tmp") - except IOError: - system("rm tmp/*") - d = DynamicUpdate(self) - d.launch(self.blackstyle) - - 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.E - L[j] = self.L - - if display and j%5==0: - # display progression - if len(self.bodylist) == 1: - d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N)) - else: - d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N)) - if display: - d.close() - if not savename is None: - system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png") - system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/{0:s}_dynsyst.gif".format(savename)) - - 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]) diff --git a/lib/objects_hermite.py b/lib/objects_hermite.py deleted file mode 100755 index ca0ca06..0000000 --- a/lib/objects_hermite.py +++ /dev/null @@ -1,238 +0,0 @@ -#!/usr/bin/python -# -*- coding:utf-8 -*- -""" -Class definition for physical attribute -""" -from os import system -import numpy as np -from lib.plots import DynamicUpdate -from lib.units import * - -class Body: - - def __init__(self, mass, position, velocity): - self.m = mass - self.q = position - self.v = velocity - self.p = velocity*mass - self.a = np.zeros(3) - self.ap = np.zeros(3) - self.j = np.zeros(3) - self.jp = np.zeros(3) - self.qp = np.zeros(3) - self.vp = np.zeros(3) - - def __repr__(self): # Called upon "print(body)" - return r"Body of mass: {0:.2f} $M_\odot$, position: {1}, velocity: {2}".format(self.m/Ms, self.q, self.v) - - def __str__(self): # Called upon "str(body)" - return r"Body of mass: {0:.2f} $M_\odot$".format(self.m/Ms) - -class System(Body): - - def __init__(self, bodylist, blackstyle=True): - self.blackstyle = blackstyle #for dark mode in plot - self.bodylist = np.array(bodylist) - self.time = 0 #lifetime of system - self.m = self.M - self.q = self.COM - self.v = self.COMV - - @property - def get_masses(self): #return the masses of each object - return np.array([body.m for body in self.bodylist]) - - @property - def get_positions(self): #return the positions of the bodies - xdata = np.array([body.q[0] for body in self.bodylist]) - ydata = np.array([body.q[1] for body in self.bodylist]) - zdata = np.array([body.q[2] for body in self.bodylist]) - return xdata, ydata, zdata - - @property - def get_velocities(self): #return the positions of the bodies - vxdata = np.array([body.v[0] for body in self.bodylist]) - vydata = np.array([body.v[1] for body in self.bodylist]) - vzdata = np.array([body.v[2] for body in self.bodylist]) - return vxdata, vydata, vzdata - - @property - def get_momenta(self): #return the momenta of the bodies - pxdata = np.array([body.p[0] for body in self.bodylist]) - pydata = np.array([body.p[1] for body in self.bodylist]) - pzdata = np.array([body.p[2] for body in self.bodylist]) - return pxdata, pydata, pzdata - - @property - def M(self): #return total system mass - mass = 0 - for body in self.bodylist: - mass = mass + body.m - return mass - - @property - def COM(self): #return center of mass in cartesian np_array - coord = np.zeros(3) - for body in self.bodylist: - coord = coord + body.m*body.q - coord = coord/self.M - return coord - - @property - def COMV(self): #return center of mass velocity in cartesian np_array - coord = np.zeros(3) - for body in self.bodylist: - coord = coord + body.p - coord = coord/self.M - return coord - - def COMShift(self): #Shift coordinates of bodies in system to COM frame and set COM at rest - for body in self.bodylist: - body.q = body.q - self.COM - body.p = body.p - self.COMV - - @property - def L(self): #return angular momentum of bodies in system - L = np.zeros(3) - for body in self.bodylist: - L = L + np.cross(body.q,body.p) - return L - - @property - def E(self): #return total energy of bodies in system - T = 0 - W = 0 - for body in self.bodylist: - T = T + 1./2.*body.m*np.linalg.norm(body.v)**2 - for otherbody in self.bodylist: - if body != otherbody: - rij = np.linalg.norm(body.q-otherbody.q) - W = W - G*body.m*otherbody.m/rij - E = T + W - - def Update_a(self): #update acceleration of bodies in system - 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) - - def Update_j(self): #update jerk of bodies in system - for body in self.bodylist: - body.j = np.zeros(3) - for otherbody in self.bodylist: - if body != otherbody: - rij = np.linalg.norm(body.q-otherbody.q) - deltav = (body.v-otherbody.v) - 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 - - 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.) - - def Update_ap(self): #update acceleration of bodies in system - for body in self.bodylist: - body.ap = np.zeros(3) - for otherbody in self.bodylist: - if body != otherbody: - rij = np.linalg.norm(body.qp-otherbody.qp) - body.ap = body.ap - (body.qp-otherbody.qp)*G*otherbody.m/(rij**3) - - def Update_jp(self): #update jerk of bodies in system - for body in self.bodylist: - body.jp = np.zeros(3) - for otherbody in self.bodylist: - if body != otherbody: - rij = np.linalg.norm(body.qp-otherbody.qp) - deltav = (body.vp-otherbody.vp) - 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 - - def Correct(self,dt): # correct position and velocities of bodies in system - for body in self.bodylist: - a2 = (6.*(body.a-body.ap)+dt*(4*body.j+2*body.jp))/(dt**2) - a3 = (12. * (body.a - body.ap) + dt * 6. * (body.j + body.jp)) / (dt ** 3) - - body.q = body.qp +((dt**4)*a2/24.) + ((dt**5)*a3/120.) - body.v = body.vp +((dt**3)*a2/6.) + ((dt**4)*a3/24.) - - def HPC(self, dt): # update position and velocities of bodies in system with hermite predictor corrector - self.COMShift() - self.Update_a() - self.Update_j() - self.Predict(dt) - self.Update_ap() - self.Update_jp() - self.Correct(dt) - self.time = self.time + dt - for body in self.bodylist: - body.p = body.v*body.m - - def hermite(self, duration, dt, recover_param=False, display=False, savename=None): - if display: - try: - system("mkdir tmp") - except IOError: - system("rm tmp/*") - d = DynamicUpdate(self) - d.launch(self.blackstyle) - - N = np.ceil(duration/dt).astype(int) - E = np.zeros(N) - L = np.zeros((N,3)) - for j in range(N): - self.HPC(dt) - - E[j] = self.E - L[j] = self.L - - if display and j%100==0: - # display progression - if len(self.bodylist) == 1: - d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N)) - else: - d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N)) - if display: - d.close() - if not savename is None: - system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png") - system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/{0:s}_dynsyst.gif".format(savename)) - - if recover_param: - return E, L - - @property - def mu(self): - sum = 0 - prod = 1 - for body in self.bodylist: - prod = prod * body.m - mu = prod/self.M - return mu - - @property - def ex(self): #exentricity of system (if composed of 2 bodies) - if len(self.bodylist) != 2 : - return np.nan - else: - k = (2.*self.E*(np.linalg.norm(self.L)**2))/((G**2)*(self.M**2)*(self.mu**3)) + 1. - return k - - @property - def sma(self): #semi major axis of system (if composed of 2 bodies) - if len(self.bodylist) != 2 : - return np.nan - else: - sma = -G*self.M*self.mu/(2.*self.E) - return sma - - 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]) diff --git a/main.py b/main.py index b7352aa..8e70fba 100755 --- a/main.py +++ b/main.py @@ -4,6 +4,8 @@ from sys import exit as sysexit import numpy as np import matplotlib.pyplot as plt from lib.objects import Body, System +from lib.LeapFrog import leapfrog +from lib.hermite import hermite from lib.plots import display_parameters from lib.units import * @@ -41,9 +43,9 @@ def main(): E, L = [], [] for step0 in step: if integrator.lower() in ['leapfrog', 'frogleap', 'frog']: - E0, L0 = dyn_syst.leapfrog(duration, step0, recover_param=True, display=display, savename=savename) + E0, L0 = leapfrog(dyn_syst,duration, step0, recover_param=True, display=display, savename=savename) elif integrator.lower() in ['hermite','herm']: - E0, L0 = dyn_syst.hermite(duration, step0, recover_param=True, display=display, savename=savename) + E0, L0 = hermite(dyn_syst, duration, step0, recover_param=True, display=display, savename=savename) E.append(E0) L.append(L0) diff --git a/plots/2bodies_leapfrog_dEm.png b/plots/2bodies_leapfrog_dEm.png index 64c45949c73a70574bd81adaab74259809da5d69..48ebfd69ec25ef752fef3cfe93851275f23a01a9 100644 GIT binary patch literal 122984 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