def pr2b(file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, xxs = rungekutta.rk4(lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64), 0.0001, 1000000)
xs = xxs.transpose()
x0 = numpy.array([-30, -40, 4], dtype=numpy.float64)
d_cap = find_loglog_slope(xs[100000:400000, :], x0, file_prefix=suffixed(file_prefix, "_2b"))
print "Lorenz\tshort\td_cap = {0:.6f}".format(d_cap)
return xs
def runit():
lfunc = lorenz.lorenz(16, 45, 4)
ts, xxs = rungekutta.rk4(
lfunc,
0.0,
numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64),
0.0001,
100000
)
def pr2b(file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, xxs = rungekutta.rk4(
lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64),
0.0001, 1000000)
xs = xxs.transpose()
x0 = numpy.array([-30, -40, 4], dtype=numpy.float64)
d_cap = find_loglog_slope(xs[100000:400000, :],
x0,
file_prefix=suffixed(file_prefix, '_2b'))
print 'Lorenz\tshort\td_cap = {0:.6f}'.format(d_cap)
return xs
def pr2a(file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, xxs = rungekutta.rk4(lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64), 0.0001, 300000)
xs = xxs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.mutual("-D", 16000, input=data)
tau = first_min(ms)
ws = tispy.delay("-d", int(tau), "-m", 7, input=data)
x0 = numpy.array([-35, -35], dtype=numpy.float64)
zs = numpy.array(zip(ws[100000:, 0], ws[100000:, 5]), dtype=numpy.float64)
d_cap = find_loglog_slope(zs, x0, file_prefix=suffixed(file_prefix, "_2a"))
print "Lorenz\tembed\td_cap = {0:.6f}".format(d_cap)
def __init__(self):
super().__init__()
self.steps_min = 10
self.steps_max = 10000
self.steps = 1000
# self.dt = 0.001
self.dt = 0.01
self.dt_min = 0.0001
self.dt_max = 0.1
# self.dt_max = 1
# self.dt = 1
self.color = 1
self.p = np.zeros((self.steps, 3), dtype=np.float64)
self.p[0] = np.array([1, 0, 0]) # initial conditions
self.s = 10
self.r = 28
self.b = 8 / 3
self.s_min = 0.5
self.s_max = 60
self.r_min = 0.5
self.r_max = 60
self.b_min = 0.1
self.b_max = 10
# self.b_max = 1
# self.lastPosition = np.array([0,0,-10])
self.init_ui()
self.qt_connections()
lorenz.lorenz(self.p, self.s, self.r, self.b, self.steps, self.dt)
lorenz.lorenz(self.p, self.s_slider.value(), self.r_slider.value(),
self.b_slider.value(), self.steps, self.dt)
def pr2a(file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, xxs = rungekutta.rk4(
lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64),
0.0001, 300000)
xs = xxs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.mutual('-D', 16000, input=data)
tau = first_min(ms)
ws = tispy.delay('-d', int(tau), '-m', 7, input=data)
x0 = numpy.array([-35, -35], dtype=numpy.float64)
zs = numpy.array(zip(ws[100000:, 0], ws[100000:, 5]), dtype=numpy.float64)
d_cap = find_loglog_slope(zs, x0, file_prefix=suffixed(file_prefix, '_2a'))
print 'Lorenz\tembed\td_cap = {0:.6f}'.format(d_cap)
def params_changed(self):
# print(self.p.min(), self.p.max())
self.s = util.fit(self.s_slider.value(), 0, self.sliders_positions,
self.s_min, self.s_max)
self.r = util.fit(self.r_slider.value(), 0, self.sliders_positions,
self.r_min, self.r_max)
self.b = util.fit(self.b_slider.value(), 0, self.sliders_positions,
self.b_min, self.b_max)
print(self.dt_slider.value(), '$$$$$$')
self.dt = util.fit(self.dt_slider.value(), 0, self.sliders_positions,
self.dt_min, self.dt_max)
lorenz.lorenz(self.p, self.s, self.r, self.b, self.steps, self.dt)
# self.main_scatter_plot.setData(pos=self.p, size=np.ones(self.p.shape[0])*0.3, color=self.color, pxMode=False)
self.main_scatter_plot.setData(pos=self.p,
size=0.3,
color=self.color,
pxMode=False)
self.xcurve.setData(self.p[:, 0], connect='finite')
self.ycurve.setData(self.p[:, 1], connect='finite')
self.zcurve.setData(self.p[:, 2], connect='finite')
# print(self.steps, self.dt, f'min = {np.min(self.p)} max = {np.max(self.p)}')
# self.xplot.setYRange(np.min(self.p[:, 0]), np.max(self.p[:, 0]))
# self.yplot.setYRange(np.min(self.p[:, 1]), np.max(self.p[:, 0]))
# self.zplot.setYRange(np.min(self.p[:, 2]), np.max(self.p[:, 1]))
print(self.dt, '<<<<')
# print(self.steps)
self.steps_label.setText(f'steps {self.steps}')
self.dt_label.setText(f'dt {self.dt}')
self.s_label.setText(f'σ {self.s}')
self.r_label.setText(f'ρ {self.r}')
self.b_label.setText(f'β {self.b}')
def extrema():
lfunc = lorenz.lorenz(16, 45, 4)
ts, xxs = rungekutta.rk4(lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64), 0.0001, 300000)
xs = xxs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.mutual("-D", 16000, input=data)
tau = first_min(ms)
print "Tau: {0:.6f}".format(tau)
ws = tispy.delay("-d", int(tau), "-m", 7, input=data)
zs = ws[100000:, :]
mins = numpy.empty(7, dtype=numpy.float64)
maxs = numpy.empty(7, dtype=numpy.float64)
for i in xrange(7):
mins[i] = min(zs[:, i])
maxs[i] = max(zs[:, i])
print "Mins: {0}".format(mins)
print "Maxs: {0}".format(maxs)
def __init__(self):
super().__init__()
surface_format = QtGui.QSurfaceFormat()
surface_format.setMajorVersion(3)
surface_format.setMajorVersion(2)
surface_format.setProfile(QtGui.QSurfaceFormat.CoreProfile)
surface_format.setOption(QtGui.QSurfaceFormat.DebugContext)
self.setFormat(surface_format)
self.update_timer = QtCore.QTimer()
self.update_timer.timeout.connect(self.update_tick)
self.update_timer.start(1000//60)
self.tick = 0
self.t1 = self.t2 = 0
self.q = 0
y = lorenz.lorenz(num_steps=2000000)
self.data = y.astype('float32')
self.newdata = False
def extrema():
lfunc = lorenz.lorenz(16, 45, 4)
ts, xxs = rungekutta.rk4(
lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64),
0.0001, 300000)
xs = xxs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.mutual('-D', 16000, input=data)
tau = first_min(ms)
print 'Tau: {0:.6f}'.format(tau)
ws = tispy.delay('-d', int(tau), '-m', 7, input=data)
zs = ws[100000:, :]
mins = numpy.empty(7, dtype=numpy.float64)
maxs = numpy.empty(7, dtype=numpy.float64)
for i in xrange(7):
mins[i] = min(zs[:, i])
maxs[i] = max(zs[:, i])
print 'Mins: {0}'.format(mins)
print 'Maxs: {0}'.format(maxs)
def pr6(file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, vs = rungekutta.rk4(lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64), 0.001, 30000)
xs = vs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.mutual("-D", 1600, input=data)
tau = first_min(ms)
ws = tispy.delay("-d", int(tau), "-m", 7, input=data)
col1 = 0
col2 = 5
plot.render(
ws[:, col1],
ws[:, col2],
"k.",
markersize=0.6,
title=r"Delay Coordinate Embedding: {0}, $\tau={1}$ s".format(r"lorenz", 0.001 * tau),
xlabel=r"$x(t+{0:.3f})$".format(col1 * 0.001 * tau),
ylabel=r"$x(t+{0:.3f})$".format(col2 * 0.001 * tau),
file_prefix=suffixed(file_prefix, "_6"),
)
return tau
def pr6(file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, vs = rungekutta.rk4(
lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64),
0.001, 30000)
xs = vs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.mutual('-D', 1600, input=data)
tau = first_min(ms)
ws = tispy.delay('-d', int(tau), '-m', 7, input=data)
col1 = 0
col2 = 5
plot.render(ws[:, col1],
ws[:, col2],
'k.',
markersize=0.6,
title=r'Delay Coordinate Embedding: {0}, $\tau={1}$ s'.format(
r'lorenz', 0.001 * tau),
xlabel=r'$x(t+{0:.3f})$'.format(col1 * 0.001 * tau),
ylabel=r'$x(t+{0:.3f})$'.format(col2 * 0.001 * tau),
file_prefix=suffixed(file_prefix, '_6'))
return tau
def lorenz(reservoir_size, spectral_radius, train_len, future):
# Load in mackey-glass numpy array
data_full = lz.lorenz()
data = data_full[0]
#Initialize ESN
esn = ESN(n_inputs=1,
n_outputs=1,
n_reservoir=reservoir_size,
spectral_radius=spectral_radius,
random_state=42)
# Fit the model
pred_training = esn.fit(np.ones(train_len), data[:train_len])
# Predict and find the error
prediction = esn.predict(np.ones(future))
error = np.sqrt(
np.mean(
(prediction.flatten() - data[train_len:train_len + future])**2))
return error, prediction, reservoir_size, spectral_radius, train_len, future
def pr6x1(tau, file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, vs = rungekutta.rk4(
lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64),
0.001, 30000)
xs = vs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.lyap_k('-d', int(tau), '-m', 7, '-M', 7, input=data)
pargs = cut(ms[:, 0], ms[:, 1])
total = 0.0
count = len(pargs) / 2
for i in xrange(0, len(pargs), 2):
xs = 0.31 * pargs[i][:50]
ys = pargs[i + 1][:50]
ps = numpy.polyfit(xs, ys, 1)
total += ps[0]
print 'Lorenz lyapunov exponent: {0}'.format(total / count)
plot.render(*pargs,
xlabel='Iterations',
ylabel='Logarithm of the Stretching Factor',
title='Calculating the Lyapunov Exponent',
file_prefix=suffixed(file_prefix, '_7'))
def pr6x1(tau, file_prefix=None):
lfunc = lorenz.lorenz(16, 45, 4)
ts, vs = rungekutta.rk4(lfunc, 0.0, numpy.array([-13.0, -12.0, 52.0], dtype=numpy.float64), 0.001, 30000)
xs = vs.transpose()[:, 0]
data = numpy.array(zip(xs, ts), dtype=numpy.float64)
ms = tispy.lyap_k("-d", int(tau), "-m", 7, "-M", 7, input=data)
pargs = cut(ms[:, 0], ms[:, 1])
total = 0.0
count = len(pargs) / 2
for i in xrange(0, len(pargs), 2):
xs = 0.31 * pargs[i][:50]
ys = pargs[i + 1][:50]
ps = numpy.polyfit(xs, ys, 1)
total += ps[0]
print "Lorenz lyapunov exponent: {0}".format(total / count)
plot.render(
*pargs,
xlabel="Iterations",
ylabel="Logarithm of the Stretching Factor",
title="Calculating the Lyapunov Exponent",
file_prefix=suffixed(file_prefix, "_7")
)
# -------------------------------------------------------------------------
#
# PYTHON for DUMMIES 18-19
# Problème 7
#
# Script de test
# Vincent Legat
#
# -------------------------------------------------------------------------
#
from numpy import *
from matplotlib import pyplot as plt
from lorenz import lorenz
plt.figure("Lorenz Equations")
Xstart = 0
Xend = 100
Ustart = [0, 1, 0]
n = 10000
X, U = lorenz(Xstart, Xend, Ustart, n)
plt.plot(U[:, 0], U[:, 2], '-r', linewidth=0.5)
plt.show()
