def demo():
"""
Demonstrate difference between Euler-Cromer and the
scheme for the corresponding 2nd-order ODE.
"""
I = 1.2
V = 0.2
m = 4
b = 0.2
s = lambda u: 2 * u
F = lambda t: 0
w = np.sqrt(2.0 / 4) # approx freq
dt = 0.9 * 2 / w # longest possible time step
w = 0.5
P = 2 * pi / w
T = 4 * P
from vib import solver as solver2
import scitools.std as plt
for k in range(4):
u2, t2 = solver2(I, V, m, b, s, F, dt, T, "quadratic")
u, v, t = solver(I, V, m, b, s, F, dt, T, "quadratic")
plt.figure()
plt.plot(t, u, "r-", t2, u2, "b-")
plt.legend(["Euler-Cromer", "centered scheme"])
plt.title("dt=%.3g" % dt)
raw_input()
plt.savefig("tmp_%d" % k + ".png")
plt.savefig("tmp_%d" % k + ".pdf")
dt /= 2
def demo():
"""
Demonstrate difference between Euler-Cromer and the
scheme for the corresponding 2nd-order ODE.
"""
I = 1.2
V = 0.2
m = 4
b = 0.2
s = lambda u: 2 * u
F = lambda t: 0
w = np.sqrt(2. / 4) # approx freq
dt = 0.9 * 2 / w # longest possible time step
w = 0.5
P = 2 * pi / w
T = 4 * P
from vib import solver as solver2
import scitools.std as plt
for k in range(4):
u2, t2 = solver2(I, V, m, b, s, F, dt, T, 'quadratic')
u, v, t = solver(I, V, m, b, s, F, dt, T, 'quadratic')
plt.figure()
plt.plot(t, u, 'r-', t2, u2, 'b-')
plt.legend(['Euler-Cromer', 'centered scheme'])
plt.title('dt=%.3g' % dt)
raw_input()
plt.savefig('tmp_%d' % k + '.png')
plt.savefig('tmp_%d' % k + '.pdf')
dt /= 2
def main():
import argparse
parser = argparse.ArgumentParser()
parser.add_argument('--I', type=float, default=1.0)
parser.add_argument('--V', type=float, default=0.0)
parser.add_argument('--m', type=float, default=1.0)
parser.add_argument('--b', type=float, default=0.0)
parser.add_argument('--s', type=str, default='4*pi**2*u')
parser.add_argument('--F', type=str, default='0')
parser.add_argument('--dt', type=float, default=0.05)
parser.add_argument('--T', type=float, default=20)
parser.add_argument('--window_width',
type=float,
default=30.,
help='Number of periods in a window')
parser.add_argument('--damping', type=str, default='linear')
parser.add_argument('--savefig', action='store_true')
# Hack to allow --SCITOOLS options
# (scitools.std reads this argument at import)
parser.add_argument('--SCITOOLS_easyviz_backend', default='matplotlib')
a = parser.parse_args()
from scitools.std import StringFunction
s = StringFunction(a.s, independent_variable='u')
F = StringFunction(a.F, independent_variable='t')
I, V, m, b, dt, T, window_width, savefig, damping = \
a.I, a.V, a.m, a.b, a.dt, a.T, a.window_width, a.savefig, \
a.damping
# compute u by both methods and then visualize the difference
u, t = solver2(I, V, m, b, s, F, dt, T, damping)
u_bw, _ = solver_bwdamping(I, V, m, b, s, F, dt, T, damping)
u_diff = u - u_bw
num_periods = plot_empirical_freq_and_amplitude(u_diff, t)
if num_periods <= 40:
plt.figure()
legends = [
'1st-2nd order method', '2nd order method', '1st order method'
]
visualize([(u_diff, t), (u, t), (u_bw, t)], legends)
else:
visualize_front(u_diff, t, window_width, savefig)
#visualize_front_ascii(u_diff, t)
plt.show()
def main():
import argparse
parser = argparse.ArgumentParser()
parser.add_argument('--I', type=float, default=1.0)
parser.add_argument('--V', type=float, default=0.0)
parser.add_argument('--m', type=float, default=1.0)
parser.add_argument('--b', type=float, default=0.0)
parser.add_argument('--s', type=str, default='4*pi**2*u')
parser.add_argument('--F', type=str, default='0')
parser.add_argument('--dt', type=float, default=0.05)
parser.add_argument('--T', type=float, default=20)
parser.add_argument('--window_width', type=float, default=30.,
help='Number of periods in a window')
parser.add_argument('--damping', type=str, default='linear')
parser.add_argument('--savefig', action='store_true')
# Hack to allow --SCITOOLS options
# (scitools.std reads this argument at import)
parser.add_argument('--SCITOOLS_easyviz_backend',
default='matplotlib')
a = parser.parse_args()
from scitools.std import StringFunction
s = StringFunction(a.s, independent_variable='u')
F = StringFunction(a.F, independent_variable='t')
I, V, m, b, dt, T, window_width, savefig, damping = \
a.I, a.V, a.m, a.b, a.dt, a.T, a.window_width, a.savefig, \
a.damping
# compute u by both methods and then visualize the difference
u, t = solver2(I, V, m, b, s, F, dt, T, damping)
u_bw, _ = solver_bwdamping(I, V, m, b, s, F, dt, T, damping)
u_diff = u - u_bw
num_periods = plot_empirical_freq_and_amplitude(u_diff, t)
if num_periods <= 40:
plt.figure()
legends = ['1st-2nd order method',
'2nd order method',
'1st order method']
visualize([(u_diff, t), (u, t), (u_bw, t)], legends)
else:
visualize_front(u_diff, t, window_width, savefig)
#visualize_front_ascii(u_diff, t)
plt.show()
