def pr5b2(dim, cutoff):
data = numpy.loadtxt("data/ps8/data2", dtype=numpy.float64)
ms = tispy.lyap_k("-d", 155, "-m", dim, "-M", dim, 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][:cutoff]
ys = pargs[i + 1][:cutoff]
ps = numpy.polyfit(xs, ys, 1)
total += ps[0]
print "Found Lyapunov exponent: {0:.6f}".format(total / count)
def pr5b2(dim, cutoff):
data = numpy.loadtxt('data/ps8/data2', dtype=numpy.float64)
ms = tispy.lyap_k('-d', 155, '-m', dim, '-M', dim, 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][:cutoff]
ys = pargs[i + 1][:cutoff]
ps = numpy.polyfit(xs, ys, 1)
total += ps[0]
print 'Found Lyapunov exponent: {0:.6f}'.format(total / count)
def pr5(dim=8, file_prefix=None):
data = numpy.loadtxt('data/ps8/data2', dtype=numpy.float64)
ms = tispy.lyap_k('-d', 155, '-m', dim, '-M', dim, input=data)
pargs = cut(ms[:, 0], ms[:, 1])
# Find the average slope of the first two points.
total = 0.0
count = len(pargs) / 2
for i in xrange(0, len(pargs), 2):
[x1, x2] = pargs[i][:2]
[y1, y2] = pargs[i + 1][:2]
total += (y2 - y1) / (0.31 * (x2 - x1))
print 'Found Lyapunov exponent: {0:.6f}'.format(total / count)
plot.render(*pargs,
xlabel='Iterations',
ylabel='Logarithm of the Stretching Factor',
title='Calculating the Lyapunov Exponent',
file_prefix=suffixed(file_prefix, '_4'))
def pr5(dim=8, file_prefix=None):
data = numpy.loadtxt("data/ps8/data2", dtype=numpy.float64)
ms = tispy.lyap_k("-d", 155, "-m", dim, "-M", dim, input=data)
pargs = cut(ms[:, 0], ms[:, 1])
# Find the average slope of the first two points.
total = 0.0
count = len(pargs) / 2
for i in xrange(0, len(pargs), 2):
[x1, x2] = pargs[i][:2]
[y1, y2] = pargs[i + 1][:2]
total += (y2 - y1) / (0.31 * (x2 - x1))
print "Found Lyapunov exponent: {0:.6f}".format(total / count)
plot.render(
*pargs,
xlabel="Iterations",
ylabel="Logarithm of the Stretching Factor",
title="Calculating the Lyapunov Exponent",
file_prefix=suffixed(file_prefix, "_4")
)
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")
)
def pr5b1(dim):
data = numpy.loadtxt('data/ps8/data2', dtype=numpy.float64)
ms = tispy.lyap_k('-d', 155, '-m', dim, '-M', dim, input=data)
pargs = tuple([xs[:11] for xs in cut(ms[:, 0], ms[:, 1])])
plot.render(*pargs)
def pr5b1(dim):
data = numpy.loadtxt("data/ps8/data2", dtype=numpy.float64)
ms = tispy.lyap_k("-d", 155, "-m", dim, "-M", dim, input=data)
pargs = tuple([xs[:11] for xs in cut(ms[:, 0], ms[:, 1])])
plot.render(*pargs)
