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 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 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 pr4(file_prefix=None):
data = numpy.loadtxt("data/ps8/data2.first250sec", dtype=numpy.float64)
vs = tispy.delay("-d", "155", "-m", "8", input=data)
plot.embedded(
vs,
0,
2,
"k.",
markersize=0.6,
ybound=(0, 2 * numpy.pi),
yticks=(0, numpy.pi / 2, numpy.pi, 3 * numpy.pi / 2, 2 * numpy.pi),
yticklabels=("0", r"$\frac{\pi}{2}$", r"$\pi$", r"$\frac{3\pi}{2}$", r"$2\pi$"),
title=r"Delay Coordinate Embedding: {0}, $\tau={1}$ s".format("data2", _get_actual_delay("data2", 1, 155)),
xlabel=r"$\theta(t + {0})$".format(_get_actual_delay("data2", 0, 155)),
ylabel=r"$\theta(t + {0})$".format(_get_actual_delay("data2", 2, 155)),
aspect="equal",
file_prefix=suffixed(file_prefix, "_3"),
)
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 pr4(file_prefix=None):
data = numpy.loadtxt('data/ps8/data2.first250sec', dtype=numpy.float64)
vs = tispy.delay('-d', '155', '-m', '8', input=data)
plot.embedded(
vs,
0,
2,
'k.',
markersize=0.6,
ybound=(0, 2 * numpy.pi),
yticks=(0, numpy.pi / 2, numpy.pi, 3 * numpy.pi / 2, 2 * numpy.pi),
yticklabels=('0', r'$\frac{\pi}{2}$', r'$\pi$', r'$\frac{3\pi}{2}$',
r'$2\pi$'),
title=r'Delay Coordinate Embedding: {0}, $\tau={1}$ s'.format(
'data2', _get_actual_delay('data2', 1, 155)),
xlabel=r'$\theta(t + {0})$'.format(_get_actual_delay('data2', 0, 155)),
ylabel=r'$\theta(t + {0})$'.format(_get_actual_delay('data2', 2, 155)),
aspect='equal',
file_prefix=suffixed(file_prefix, '_3'))
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