def main(argv=None):
if argv is None:
argv = sys.argv
file_prefix = None
a = 16.0
r = 45.0
b = 4.0
suffixed = lambda s, suf: None if s is None else '{0}{1}'.format(s, suf)
try:
options, args = getopt.getopt(argv[1:], 'a:r:b:f:')
for opt, arg in options:
if opt == '-a':
a = float(arg)
elif opt == '-r':
r = float(arg)
elif opt == '-b':
b = float(arg)
elif opt == '-f':
file_prefix = arg
except getopt.GetoptError as err:
print str(err)
return 2
x0 = numpy.array([-13, -12, 52], dtype=numpy.float64)
lfunc = lorenz(a, r, b)
ts, xs = rungekutta.ark4(lfunc, 0.0, x0, 20000.0, 0.00001)
plot.render3d(xs[0, :],
xs[1, :],
xs[2, :],
'b.',
xlabel='x',
ylabel='y',
zlabel='z',
markersize=0.2,
title='Lorenz Attractor',
file_prefix=suffixed(file_prefix, '_2a'))
ts1, xs1 = rungekutta.ark4(lfunc, 0.0, x0, 2.0, 0.01)
ts2, xs2 = rungekutta.rk4(lfunc, 0.0, x0, 0.001, 2000)
def _lorenz_2b_callback(axes):
axes.plot(xs1[0, :], xs1[1, :], xs1[2, :], 'b', label='ARK4')
axes.plot(xs2[0, :], xs2[1, :], xs2[2, :], 'r', label='RK4')
axes.legend()
plot.render3d(xlabel='x',
ylabel='y',
zlabel='z',
title='RK4 vs. ARK4 Overlay',
ax_callback=_lorenz_2b_callback,
file_prefix=suffixed(file_prefix, '_2b'))
return 0
def main(argv=None):
if argv is None:
argv=sys.argv
file_prefix = None
a = 16.0
r = 45.0
b = 4.0
suffixed = lambda s, suf: None if s is None else '{0}{1}'.format(s, suf)
try:
options, args = getopt.getopt(argv[1:], 'a:r:b:f:')
for opt, arg in options:
if opt == '-a':
a = float(arg)
elif opt == '-r':
r = float(arg)
elif opt == '-b':
b = float(arg)
elif opt == '-f':
file_prefix = arg
except getopt.GetoptError as err:
print str(err)
return 2
x0 = numpy.array([-13, -12, 52], dtype=numpy.float64)
lfunc = lorenz(a, r, b)
ts, xs = rungekutta.ark4(lfunc, 0.0, x0, 20000.0, 0.00001)
plot.render3d(
xs[0,:], xs[1,:], xs[2,:], 'b.',
xlabel='x',
ylabel='y',
zlabel='z',
markersize=0.2,
title='Lorenz Attractor',
file_prefix=suffixed(file_prefix, '_2a')
)
ts1, xs1 = rungekutta.ark4(lfunc, 0.0, x0, 2.0, 0.01)
ts2, xs2 = rungekutta.rk4(lfunc, 0.0, x0, 0.001, 2000)
def _lorenz_2b_callback(axes):
axes.plot(xs1[0,:], xs1[1,:], xs1[2,:], 'b', label='ARK4')
axes.plot(xs2[0,:], xs2[1,:], xs2[2,:], 'r', label='RK4')
axes.legend()
plot.render3d(
xlabel='x',
ylabel='y',
zlabel='z',
title='RK4 vs. ARK4 Overlay',
ax_callback=_lorenz_2b_callback,
file_prefix=suffixed(file_prefix, '_2b')
)
return 0
def main(argv=None):
if argv is None:
argv = sys.argv
file_prefix = None
x = 0.0001
y = 0.0001
z = 0.0001
a = 0.398
b = 2.0
c = 4.0
try:
options, args = getopt.getopt(argv[1:], 'f:x:y:z:a:b:c:')
for opt, arg in options:
if opt == '-f':
file_prefix = arg
elif opt == '-x':
x = float(arg)
elif opt == '-y':
y = float(arg)
elif opt == '-z':
z = float(arg)
elif opt == '-a':
a = float(arg)
elif opt == '-b':
b = float(arg)
elif opt == '-c':
c = float(arg)
except getopt.GetoptError as err:
print str(err)
return 2
rfunc = rossler(a, b, c)
x0 = numpy.array([x, y, z], numpy.float64)
_, xs = rungekutta.ark4(rfunc, 0.0, x0, 20000.0, 0.00001)
plot.render3d(xs[0, :],
xs[1, :],
xs[2, :],
'r.',
xlabel='x',
ylabel='y',
zlabel='z',
markersize=0.2,
title='Rossler Attractor',
file_prefix=file_prefix)
return 0
def plot_dtol(tstep, **kwargs):
'''
Makes a plot with a parameterized tolerance.
'''
lfunc = lorenz(16.0, 45.0, 4.0)
x0 = numpy.array([-13, -12, 52], dtype=numpy.float64)
_, xs = rungekutta.ark4(lfunc, 0.0, x0, 20.0, tstep)
plot_args = dict(kwargs)
plot_args.update({
'xlabel': 'x',
'ylabel': 'y',
'zlabel': 'z',
'title': 'Lorenz Attractor (Tol = {0})'.format(tstep),
})
plot.render3d(xs[0, :], xs[1, :], xs[2, :], **plot_args)
def plot_dtol(tstep, **kwargs):
'''
Makes a plot with a parameterized tolerance.
'''
lfunc = lorenz(16.0, 45.0, 4.0)
x0 = numpy.array([-13, -12, 52], dtype=numpy.float64)
_, xs = rungekutta.ark4(lfunc, 0.0, x0, 20.0, tstep)
plot_args = dict(kwargs)
plot_args.update({
'xlabel': 'x',
'ylabel': 'y',
'zlabel': 'z',
'title': 'Lorenz Attractor (Tol = {0})'.format(tstep),
})
plot.render3d(xs[0,:], xs[1,:], xs[2,:], **plot_args)
def main(argv=None):
if argv is None:
argv = sys.argv
file_prefix = None
x = 0.0001
y = 0.0001
z = 0.0001
a = 0.398
b = 2.0
c = 4.0
try:
options, args = getopt.getopt(argv[1:], 'f:x:y:z:a:b:c:')
for opt, arg in options:
if opt == '-f':
file_prefix = arg
elif opt == '-x':
x = float(arg)
elif opt == '-y':
y = float(arg)
elif opt == '-z':
z = float(arg)
elif opt == '-a':
a = float(arg)
elif opt == '-b':
b = float(arg)
elif opt == '-c':
c = float(arg)
except getopt.GetoptError as err:
print str(err)
return 2
rfunc = rossler(a, b, c)
x0 = numpy.array([x, y, z], numpy.float64)
_, xs = rungekutta.ark4(rfunc, 0.0, x0, 20000.0, 0.00001)
plot.render3d(xs[0,:], xs[1,:], xs[2,:], 'r.',
xlabel='x',
ylabel='y',
zlabel='z',
markersize=0.2,
title='Rossler Attractor',
file_prefix=file_prefix
)
return 0