"""
import numpy as np
import Steppers.scovel as scv
import Plotting.TwoDimensions as plt
# inital values and preallocted arrays
Dt = np.float64(0.1)
T = np.float64(100.0)
N = np.int(T/Dt)
p = np.zeros((N, 3), dtype = np.float64)
q = np.zeros((N, 3), dtype = np.float64)
q[0, :] = np.ones(3)
b = np.zeros(3)
b[2] = 1.0
V = lambda x, y, z: -1/np.sqrt(x**2 + y**2 + z**2)
dVdq = lambda q: q/(q[0]**2 + q[1]**2 + q[2]**2)**3/2
M = np.float64(1.0)
# integrate Hamiltonian
stepper = scv._ScovelsMethod(dVdq, M, b, Dt)
for nn in range(N - 1):
# 2nd Order Scovel method calculations
q[nn + 1, :], p[nn + 1, :] = stepper.m_integrate(q[nn, :], p[nn, :])
#%% Plot
# plot in 2D
plt.plotTrajectory(1, q, [-2.0, 2.0, -2.0, 2.0])#[0.98, 0.995, -0.01, 0.01])
plt.plotPhaseSpace(2, q, p)#,
#[-1.5, 1.5, -1.5, 1.5], [-1.5, 1.5, -1.5, 1.5])
plt.plot(3, q, p)#,
#[-1.5, 1.5, -1.5, 1.5], [-1.5, 1.5, -1.5, 1.5])
def V(x, y, z):
return -(x**2 + y**2)/2 - mu1/r1(x, y) - mu2/r2(x, y)
def dVdq(q):
return - q - \
mu1/r1(q[0], q[1])**3*np.array([mu2 - q[0],
-q[1],
0.0]) + \
mu2/r2(q[0], q[1])**3*np.array([mu1 + q[0],
q[1],
0.0])
# integrate Hamiltonian
stepper = {}
for Dt in Dts:
key = 'Scovel, Dt = {}'.format(Dt)
stepper[key] = stp._ScovelsMethod(dVdq, 1.0, b, Dt)
key = '4th order, s = 5, Dt = {}'.format(Dt)
w = np.array([0.28, 0.62546642846767004501])
stepper[key] = stp.Composition(dVdq, 1.0, b, w, Dt)
key = '6th order, s = 7, Dt = {}'.format(Dt)
w = np.array([0.78451361047755726382, 0.23557321335935813368, \
-1.17767998417887100695])
stepper[key] = stp.Composition(dVdq, 1.0, b, w, Dt)
key = '6th order, s = 9, Dt = {}'.format(Dt)
w = np.array([0.39216144400731413928, 0.33259913678935943860, \
-0.70624617255763935981, 0.08221359629355080023])
stepper[key] = stp.Composition(dVdq, 1.0, b, w, Dt)
key = '8th order, s = 15, Dt = {}'.format(Dt)
w = np.array([0.74167036435061295345, -0.40910082580003159400,
0.19075471029623837995, -0.57386247111608226666,
0.29906418130365592384, 0.33462491824529818378,