def test_solver_exact_discrete_solution():
def tilde_w(w, dt):
return (2. / dt) * asin(w * dt / 2.)
def u_numerical_exact(t):
return I * cos(tilde_w(w, dt) * t)
w = 2.5
I = 1.5
# Estimate period and time step
P = 2 * pi / w
num_periods = 4
T = num_periods * P
N = 5 # time steps per period
dt = P / N
u, t = solver(I, w, dt, T)
u_e = u_numerical_exact(t)
error = abs(u_e - u).max()
# Make a plot in a file, but not on the screen
from scitools.std import plot
plot(t,
u,
'bo',
t,
u_e,
'r-',
legend=('numerical', 'exact'),
show=False,
savefig='tmp.png')
assert error < 1E-14
def run_simulations(N, dt0, num_periods):
"""
Run N simulations where the time step is halved in each
simulation, starting with dt0.
Make subdirectories tmp_case0, tmp_case1, etc with plot files
for each simulation (tmp_*.png).
"""
for i in range(N):
dt = dt0 / 2.0**i
u, t = solver(I=1, w=2 * pi, dt=dt, T=num_periods)
# visualize_front removes all old plot files :)
visualize_front(u, t, I=1, w=2 * pi, savefig=True, skip_frames=2**i)
# skip_frames is essential: for N=4 we have to store
# only each 2**4=16-th file to get as many files
# as for the dt0 simulation!
# Move all plot files tmp_*.png for movie to a
# separate directory. Delete that directory if it
# exists and recreate it.
dirname = 'tmp_case%d' % i
if os.path.isdir(dirname):
shutil.rmtree(dirname) # remove directory (tree)
os.mkdir(dirname) # make new directory
for filename in glob.glob('tmp_*.png'):
# Move file to subdirectory dirname
os.rename(filename, os.path.join(dirname, filename))
def test_solver_exact_discrete_solution():
def tilde_w(w, dt):
return (2.0 / dt) * asin(w * dt / 2.0)
def u_numerical_exact(t):
return I * cos(tilde_w(w, dt) * t)
w = 2.5
I = 1.5
# Estimate period and time step
P = 2 * pi / w
num_periods = 4
T = num_periods * P
N = 5 # time steps per period
dt = P / N
u, t = solver(I, w, dt, T)
u_e = u_numerical_exact(t)
error = abs(u_e - u).max()
# Make a plot in a file, but not on the screen
from scitools.std import plot
plot(t, u, "bo", t, u_e, "r-", legend=("numerical", "exact"), show=False, savefig="tmp.png")
assert error < 1e-14
def run_simulations(N, dt0, num_periods):
"""
Run N simulations where the time step is halved in each
simulation, starting with dt0.
Make subdirectories tmp_case0, tmp_case1, etc with plot files
for each simulation (tmp_*.png).
"""
for i in range(N):
dt = dt0/2.0**i
u, t = solver(I=1, w=2*pi, dt=dt, T=num_periods)
# visualize_front removes all old plot files :)
visualize_front(u, t, I=1, w=2*pi, savefig=True,
skip_frames=2**i)
# skip_frames is essential: for N=4 we have to store
# only each 2**4=16-th file to get as many files
# as for the dt0 simulation!
# Move all plot files tmp_*.png for movie to a
# separate directory. Delete that directory if it
# exists and recreate it.
dirname = 'tmp_case%d' % i
if os.path.isdir(dirname):
shutil.rmtree(dirname) # remove directory (tree)
os.mkdir(dirname) # make new directory
for filename in glob.glob('tmp_*.png'):
# Move file to subdirectory dirname
os.rename(filename, os.path.join(dirname, filename))
def test_solver_memsave():
from vib_undamped import solver
_, _ = solver_memsave(I=1, dt=0.1, w=1, T=30)
u_expected, _ = solver (I=1, dt=0.1, w=1, T=30)
data = np.loadtxt('tmp.dat')
u_computed = data[:,1]
diff = np.abs(u_expected - u_computed).max()
assert diff < 5E-13, diff
def test_solver_memsave():
from vib_undamped import solver
_, _ = solver_memsave(I=1, dt=0.1, w=1, T=30)
u_expected, _ = solver(I=1, dt=0.1, w=1, T=30)
data = np.loadtxt('tmp.dat')
u_computed = data[:, 1]
diff = np.abs(u_expected - u_computed).max()
assert diff < 5E-13, diff
def run_solver_and_plot(solver, timesteps_per_period=20,
num_periods=1, I=1, w=2*np.pi):
P = 2*np.pi/w # duration of one period
dt = P/timesteps_per_period
Nt = num_periods*timesteps_per_period
T = Nt*dt
t_mesh = np.linspace(0, T, Nt+1)
solver.set(f_kwargs={'w': w})
solver.set_initial_condition([0, I])
u, t = solver.solve(t_mesh)
from vib_undamped import solver
u2, t2 = solver(I, w, dt, T)
plt.plot(t, u[:,1], 'r-', t2, u2, 'b-')
plt.legend(['Euler-Cromer', '2nd-order ODE'])
plt.xlabel('t'); plt.ylabel('u')
plt.savefig('tmp1.png'); plt.savefig('tmp1.pdf')
def run_solver_and_plot(solver,
timesteps_per_period=20,
num_periods=1,
I=1,
w=2 * np.pi):
P = 2 * np.pi / w # duration of one period
dt = P / timesteps_per_period
Nt = num_periods * timesteps_per_period
T = Nt * dt
t_mesh = np.linspace(0, T, Nt + 1)
solver.set(f_kwargs={'w': w})
solver.set_initial_condition([0, I])
u, t = solver.solve(t_mesh)
from vib_undamped import solver
u2, t2 = solver(I, w, dt, T)
plt.plot(t, u[:, 1], 'r-', t2, u2, 'b-')
plt.legend(['Euler-Cromer', '2nd-order ODE'])
plt.xlabel('t')
plt.ylabel('u')
plt.savefig('tmp1.png')
plt.savefig('tmp1.pdf')
from vib_undamped import solver, plot_empirical_freq_and_amplitude
from math import pi
dt_values = [0.1, 0.05, 0.01]
u_cases = []
t_cases = []
for dt in dt_values:
# Simulate scaled problem for 40 periods
u, t = solver(I=1, w=2 * pi, dt=dt, T=40)
u_cases.append(u)
t_cases.append(t)
plot_empirical_freq_and_amplitude(u_cases, t_cases, I=1, w=2 * pi)
raw_input()
from vib_undamped import solver, plot_empirical_freq_and_amplitude
from math import pi
dt_values = [0.1, 0.05, 0.01]
u_cases = []
t_cases = []
for dt in dt_values:
# Simulate scaled problem for 40 periods
u, t = solver(I=1, w=2*pi, dt=dt, T=40)
u_cases.append(u)
t_cases.append(t)
plot_empirical_freq_and_amplitude(u_cases, t_cases, I=1, w=2*pi)
raw_input()
# -*- coding: utf-8 -*-
from vib_undamped import solver, plot_empirical_freq_and_amplitude
from math import pi
tau_values = [0.1, 0.5, 0.01]
u_cases = []
t_cases = []
for tau in tau_values:
# Расчитываем безразмерную модель для 40 периодов
u, t = solver(U=1, omega=2 * pi, tau=tau, T=40)
u_cases.append(u)
t_cases.append(t)
plot_empirical_freq_and_amplitude(u_cases, t_cases, U=1, omega=2 * pi)
