def pr1d(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts3, xs3 = rungekutta.rk4(
pfunc2,
0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.02,
250000
)
xs3[0,:] = numpy.array(
[pendulum.mod2pi(x) for x in xs3[0,:]],
dtype=numpy.float64
)
points3 = xs3.transpose()
ps4 = poincare.section(ts3, points3, interval=2*numpy.pi/drive_freq)
plot.mod2pi(
ps4[:,0],
ps4[:,1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare section, increased step size',
file_prefix=_suffixed(file_prefix, '_1d')
)
def pr2x(file_prefix, step, nsteps, title, suffix):
drive_freq = 7.4246
pfunc = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1.0, freq=drive_freq)
ts, xs = rungekutta.rk4(
pfunc,
0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
step,
nsteps
)
xs[0,:] = numpy.array(
[pendulum.mod2pi(x) for x in xs[0,:]],
dtype=numpy.float64
)
points = xs.transpose()
ps = poincare.linear(ts, points, interval=2*numpy.pi/drive_freq)
plot.mod2pi(
ps[:,0],
ps[:,1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title=title,
file_prefix=_suffixed(file_prefix, suffix)
)
def pr1c(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts2, xs2 = rungekutta.rk4(
pfunc2,
0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.005,
1000000
)
xs2[0,:] = numpy.array(
[pendulum.mod2pi(x) for x in xs2[0,:]],
dtype=numpy.float64
)
points2 = xs2.transpose()
ps3 = poincare.section(ts2, points2, interval=2*numpy.pi/drive_freq)
plot.mod2pi(
ps3[:,0],
ps3[:,1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Chaotic Trajectory)',
file_prefix=_suffixed(file_prefix, '_1c')
)
def pr1(file_prefix=None):
data = numpy.loadtxt('data/ps8/data1', dtype=numpy.float64)
points = construct_angular_velocity(data[::30, 1], data[::30, 0])
thetas = numpy.array([pendulum.mod2pi(theta) for theta in points[:, 1]],
dtype=numpy.float64)
plot.render(thetas,
points[:, 2],
'b',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
title='State-space Trajectory, Data Set 1',
file_prefix=suffixed(file_prefix, '_1'))
def pr1(file_prefix=None):
data = numpy.loadtxt('data/ps8/data1', dtype=numpy.float64)
points = construct_angular_velocity(data[::30,1], data[::30,0])
thetas = numpy.array([
pendulum.mod2pi(theta) for theta in points[:,1]
], dtype=numpy.float64)
plot.render(
thetas,
points[:,2],
'b',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
title='State-space Trajectory, Data Set 1',
file_prefix=suffixed(file_prefix, '_1')
)
def pr1d(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts3, xs3 = rungekutta.rk4(pfunc2, 0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.02, 250000)
xs3[0, :] = numpy.array([pendulum.mod2pi(x) for x in xs3[0, :]],
dtype=numpy.float64)
points3 = xs3.transpose()
ps4 = poincare.section(ts3, points3, interval=2 * numpy.pi / drive_freq)
plot.mod2pi(ps4[:, 0],
ps4[:, 1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare section, increased step size',
file_prefix=_suffixed(file_prefix, '_1d'))
def pr1c(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts2, xs2 = rungekutta.rk4(pfunc2, 0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.005, 1000000)
xs2[0, :] = numpy.array([pendulum.mod2pi(x) for x in xs2[0, :]],
dtype=numpy.float64)
points2 = xs2.transpose()
ps3 = poincare.section(ts2, points2, interval=2 * numpy.pi / drive_freq)
plot.mod2pi(ps3[:, 0],
ps3[:, 1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Chaotic Trajectory)',
file_prefix=_suffixed(file_prefix, '_1c'))
def pr2x(file_prefix, step, nsteps, title, suffix):
drive_freq = 7.4246
pfunc = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1.0, freq=drive_freq)
ts, xs = rungekutta.rk4(pfunc, 0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64), step,
nsteps)
xs[0, :] = numpy.array([pendulum.mod2pi(x) for x in xs[0, :]],
dtype=numpy.float64)
points = xs.transpose()
ps = poincare.linear(ts, points, interval=2 * numpy.pi / drive_freq)
plot.mod2pi(ps[:, 0],
ps[:, 1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title=title,
file_prefix=_suffixed(file_prefix, suffix))