def main_operation(self, plot=True):
"""Run the ODE integrator for the system in question and save the
plots."""
torque_index = 0
self._update_torque(self.y0[0], torque_index)
f_baked = h.baker(
c.f_full_torque,
["", "", self.i, self.b, self.k, self._get_recent_torque],
pos_to_pass_through=(0, 1))
# Set initial conditions
dy = c.rk4(f_baked)
times, y, stepsize = *self.t0, self.y0, self.dt[0] / self.divider[0]
results = []
update_counter = 0
while times <= self.t_fin:
results.append(
[times, *y, self.total_torque, self.theta_sim, self.omega_sim])
times, y = times + stepsize, y + dy(times, y, stepsize)
update_counter += 1
# For a fixed step size, we can just repeat the torque
# recalculation every self.divider steps, so there is no
# overshooting.
if update_counter == self.divider:
update_counter = 0
torque_index += 1
if torque_index == self.period_divider:
torque_index = 0
old_theta = n.get_old_theta(times, self.delay, results)
self._update_torque(old_theta, torque_index)
results = np.array(results).squeeze()
# Calculate fourier series first 50 terms.
ind_mag_phi = fourier.get_fourier_series(50, self.w_d, self.dt,
self.g_0)
# fourier theoretical results.
torque_fourier = h.baker(t.calculate_sine_pi, [
"", "", "", "", ind_mag_phi[:, 1], self.w_d * ind_mag_phi[:, 0],
ind_mag_phi[:, 2]
],
pos_to_pass_through=(0, 3))
theory_fourier = t.calc_theory_soln(results[:, 0], self.t0, self.y0,
self.b - self.b_prime,
self.k - self.k_prime, self.i,
torque_fourier)
ss_bit_theory = theory_fourier[:, 1][np.where(
theory_fourier[:, 0] > self.t_fin.squeeze() - 2)]
# Find maximum error over amplitude.
iterator_diffs = np.max(
np.abs(m.calc_norm_errs([results[:, 1], theory_fourier[:, 1]])[1])
/ np.max(ss_bit_theory))
exp_results = pd.DataFrame(
np.array([
self.b, self.k, self.t_fin, self.period_divider,
[iterator_diffs]
]).T,
columns=['b', 'k', 'tfin', 'divider', 'max-frac-err'])
return {'all-mmts': exp_results}
def main_operation(self, plot=True):
"""Read all data from a specific folder and produce real space and
fourier space plots. Use for only one set of b, k, b', k', i,
etc. parameters at a time."""
directory = self.prms['directory'][0]
all_same = self.prms['all_same'][0]
file_list = h.find_files(directory)
filename_roots = r.check_matches(file_list,
num_one='all-mmts',
num_two=None)
all_data = r.read_all_data(directory,
filename_roots,
disps_ext='all-mmts',
torque_ext='all-mmts')
sorted_by_params = r.sort_data(all_data, all_same=all_same)
b = sorted_by_params[0][0]['b']
k = sorted_by_params[0][0]['k']
b_prime = sorted_by_params[0][0]['b\'']
k_prime = sorted_by_params[0][0]['k\'']
i = sorted_by_params[0][0]['i']
# Baked theoretical response function to require wd input only,
# which depends on the range measured.
need_wd = h.baker(t.theory_response,
args=[b, k, i, b_prime, k_prime, ''],
pos_to_pass_through=5)
fft_data = r.match_torques(sorted_by_params,
plot_real=self.prms['plot_real'][0],
savepath=directory + 'plots/')
print(fft_data)
if plot:
r.prepare_to_plot(fft_data, need_wd, savepath=directory + 'plots/')
def main_operation(self):
"""Run the ODE integrator for the system in question."""
# Set parameters.
i = self.prms['i']
b = self.prms['b']
k = self.prms['k']
y0 = np.array([self.prms['theta_0'], self.prms['omega_0']]).squeeze()
t0 = self.prms['t0']
t_fin = self.prms['tfin']
r = ode(c.f_full_torque) #.set_integrator('dop853')
self._update_torque(y0[0])
r.set_initial_value(y0, t0).set_f_params(
i, b, k, self._get_recent_torque).set_jac_params(i, b, k)
results = [[*t0, *y0]]
while r.successful() and r.t < t_fin:
y = np.real(r.integrate(r.t + self.display_dt))
data_point = [*(r.t + self.display_dt), *y]
results.append(data_point)
print("Time-theta-omega", data_point)
# Recalculate the reset the torque every dt seconds.
# get the last set of consecutive points where the digitised
# torque (-6th column) has the same value as the current one
# every cycle. If the corresponding times have a range greater
# than or equal to dt, re-measure the torque.
matching_indices = h.find_consec_indices(self.torques[:, -6])
if self.torques[-1, 1] - min(self.torques[matching_indices,
1]) >= self.dt:
self._update_torque(y[0])
print("triggered")
r.set_initial_value(r.y,
r.t).set_f_params(i, b, k,
self._get_recent_torque)
results = np.array(results).squeeze()
sines_torque = h.baker(t.calculate_sine_pi, [
"", "", "", "", self.prms['g_0_mag'], self.prms['w_d'],
np.array([0])
],
pos_to_pass_through=(0, 3))
theory = t.calc_theory_soln(np.linspace(0, 2, 1000), t0[0], y0,
(b - self.prms['b\''])[0],
(k - self.prms['k\''])[0], i[0],
sines_torque)
print(
"Init parameters: dt: {}, display_dt: {}, b: {}, b': {}, k: {}, "
"k': {}, I: {}, y0: {}, t0: {}, tfin: {}, g0: {}, w_d: {}".format(
self.dt, self.display_dt, b, self.prms['b\''], k,
self.prms['k\''], i, y0, t0, t_fin, self.prms['g_0_mag'],
self.prms['w_d']))
print("Parameters from the C code: k': {}, b': {}, g0: {}".format(
talk.get_k_prime(), talk.get_b_prime(), talk.get_amp()))
plt.plot(theory[:, 0], theory[:, 1])
plt.plot(results[:, 0], results[:, 1])
plt.show()
def _single_operation(self, times, b, k, i, b_prime, k_prime, w_d, g_0_mag,
phase, n_frq_peak, t0, y0):
"""One run for one value of b, k, i, b_prime, k_prime,
torque_amplitude, torque_phase, torque_frequency and noise. t is a time
array."""
times = m.check_nyquist(times, w_d, b, b_prime, k, k_prime, i)
decimal_periods = np.abs(5.231 * 2 * np.pi / w_d)
time_index = 0
num = 1
# The index for 5.231 periods of time being elapsed is used to
# calculate the number per segment to use for the autocorrelation.
while time_index < 10:
time_index = np.abs(times - num * decimal_periods).argmin()
num += 1
torque = g_0_mag * np.sin(w_d * times + phase)
pi_contr = h.baker(t.calculate_sine_pi,
["", "", "", "", g_0_mag, w_d, phase],
pos_to_pass_through=(0, 3))
theory = t.calc_theory_soln(times, t0, y0, b - b_prime, k - k_prime, i,
pi_contr)
w_res = t.w_res_gamma(b - b_prime, k - k_prime, i)[0]
if b - b_prime >= 0:
if b - b_prime == 0 and np.isreal(w_res):
# filter out the transient frequency.
theory[:, 1] = m.remove_one_frequency(times, theory[:, 1],
w_res)
theory[:, 2] = m.remove_one_frequency(times, theory[:, 2],
w_res)
# Will only reach steady state if this is the case, otherwise no
# point making a response curve. Measure one point. b - b' = 0
# has two steady state frequencies, the transient and PI.
ss_times = m.identify_ss(theory[:, 0],
theory[:, 1],
n_per_segment=time_index)
if ss_times is not False:
self._log('before fft')
frq, fft_theta = m.calc_fft(
times[(times >= ss_times[0]) * (times <= ss_times[1])],
theory[:,
1][(times >= ss_times[0]) * (times <= ss_times[1])])
# For low frequencies, the length of time of the signal must
# also be sufficiently wrong for the peak position to be
# measured properly.
freq = m.calc_freqs(np.absolute(fft_theta),
frq,
n_peaks=n_frq_peak)
amp = m.calc_one_amplitude(theory[:,
1][(times >= ss_times[0]) *
(times <= ss_times[1])])
phase = m.calc_phase(theory[:, 1], torque)
return True, theory, np.array([freq, amp, phase])
else:
return False, theory
else:
return False, theory
def ode_integrator(y0, t0, i, b_prime, k_prime, b, k, g_0_mags, w_ds, phases,
t_fin, dt, torque_func):
"""Test function for ODE integration."""
r = ode(f_analytic).set_integrator('vode')
baked_g_0 = h.baker(torque_func, args=['', w_ds, g_0_mags, phases])
r.set_initial_value(y0, t0).set_f_params(i, baked_g_0, b, b_prime, k,
k_prime)
results = [[t0, *y0]]
while r.successful() and r.t < t_fin:
data_point = [r.t + dt, *np.real(r.integrate(r.t + dt))]
results.append(data_point)
exp_results = np.array(results)
return exp_results
def main_operation(self, plot=True):
"""Run the ODE integrator for the system in question and save the
plots."""
torque_index = 0
self._update_torque(self.y0[0], torque_index)
f_baked = h.baker(
c.f_full_torque,
["", "", self.i, self.b, self.k, self._get_recent_torque],
pos_to_pass_through=(0, 1))
# Set initial conditions
dy = c.rk4(f_baked)
times, y, stepsize = *self.t0, self.y0, self.dt[0] / self.divider[0]
results = []
update_counter = 0
while times <= self.t_fin:
results.append(
[times, *y, self.total_torque, self.theta_sim, self.omega_sim])
times, y = times + stepsize, y + dy(times, y, stepsize)
update_counter += 1
# For a fixed step size, we can just repeat the torque
# recalculation every self.divider steps, so there is no
# overshooting.
if update_counter == self.divider:
update_counter = 0
torque_index += 1
if torque_index == self.period_divider:
torque_index = 0
old_theta = n.get_old_theta(times, self.delay, results)
self._update_torque(old_theta, torque_index)
results = np.array(results).squeeze()
# Calculate fourier series first num_terms terms.
ind_mag_phi = fourier.get_fourier_series(self.num_terms, self.w_d,
self.dt, self.g_0)
# fourier theoretical results.
torque_fourier = h.baker(t.calculate_sine_pi, [
"", "", "", "", ind_mag_phi[:, 1], self.w_d * ind_mag_phi[:, 0],
ind_mag_phi[:, 2]
],
pos_to_pass_through=(0, 3))
theory_fourier = t.calc_theory_soln(results[:, 0], self.t0, self.y0,
self.b - self.b_prime,
self.k - self.k_prime, self.i,
torque_fourier)
f_torque = fourier.get_torque(results[:, 0], ind_mag_phi[:, 0],
ind_mag_phi[:, 1], ind_mag_phi[:, 2],
self.w_d)
if plot:
times = m.check_nyquist(results[:, 0], self.w_d, self.b,
self.b_prime, self.k, self.k_prime, self.i)
decimal_periods = np.abs(5.231 * 2 * np.pi / self.w_d)
time_index = 0
num = 1
# The index for 5.231 periods of time being elapsed is used to
# calculate the number per segment to use for the auto-correlation.
while time_index < 10:
time_index = np.abs(times - num * decimal_periods).argmin()
num += 1
print(
"Init parameters: dt: {}, b: {}, b': {}, k: {}, k': {}, I: {}, "
"y0: {}, t0: {}, tfin: {}, g0: {}, w_d: {}".format(
self.dt, self.b, self.b_prime, self.k, self.k_prime,
self.i, self.y0, self.t0, self.t_fin, self.g_0, self.w_d))
# Find absolute errors and plot.
iterator_diffs = m.calc_norm_errs(
[results[:, 1], theory_fourier[:, 1]],
[results[:, 2], theory_fourier[:, 2]])[1]
simu_diffs = m.calc_norm_errs([results[:, 4], results[:, 1]],
[results[:, 5], results[:, 2]])[1]
real_space_data = \
[[[[theory_fourier[:, 0], theory_fourier[:, 1]],
[results[:, 0], results[:, 1]],
[results[:, 0], results[:, 4]]],
[[results[:, 0], iterator_diffs[0]],
[results[:, 0], simu_diffs[0]]]],
[[[theory_fourier[:, 0], theory_fourier[:, 2]],
[results[:, 0], results[:, 2]],
[results[:, 0], results[:, 5]]],
[[results[:, 0], iterator_diffs[1]],
[results[:, 0], simu_diffs[1]]]]]
p.two_by_n_plotter(
real_space_data,
self.filename,
self.prms,
tag='fourier-added',
savepath=self.savepath,
show=True,
x_axes_labels=['t/s', 't/s'],
y_top_labels=[r'$\theta$/rad', r'$\dot{\theta}$/rad/s'],
y_bottom_labels=[
r'$\Delta\theta$/rad', r'$\Delta\dot{\theta}$/rad/s'
])
results = np.hstack((results, np.array([f_torque]).T))
exp_results = pd.DataFrame(results,
columns=[
't', 'theta', 'omega', 'total-torque',
'theta-sim', 'omega-sim', 'sine-torque'
])
return {'all-mmts': exp_results}
def _one_run(self,
theta_0,
omega_0,
t0,
i,
b_prime,
k_prime,
b,
k,
g_0_mag,
w_d,
phase,
t_fin,
dt,
num_terms,
create_plot=False):
"""Compare experiment to theory for one set of parameters and return the
difference between the two. Uses only Fourier torque expression."""
y0 = np.array([theta_0, omega_0]).squeeze()
times = np.arange(t0, t_fin, dt / self.divider)
try:
w_d = t.w_res_gamma(b - b_prime, k - k_prime, i)[0]
except ValueError:
return []
# Standard sine calculation.
# Calculate fourier series first num_terms terms.
ind_mag_phi = fourier.get_fourier_series(num_terms, w_d, dt, g_0_mag)
f_torque = fourier.get_torque(times, ind_mag_phi[:, 0],
ind_mag_phi[:, 1], ind_mag_phi[:,
2], w_d)
# Calculate theoretical results.
torque_sine = h.baker(
t.calculate_sine_pi,
["", "", "", "", g_0_mag, w_d, phase - dt * w_d / 2],
pos_to_pass_through=(0, 3))
theory = t.calc_theory_soln(times, t0, y0, b - b_prime, k - k_prime, i,
torque_sine)
# fourier theoretical results.
torque_fourier = h.baker(t.calculate_sine_pi, [
"", "", "", "", ind_mag_phi[:, 1], w_d * ind_mag_phi[:, 0],
ind_mag_phi[:, 2]
],
pos_to_pass_through=(0, 3))
theory_fourier = t.calc_theory_soln(times, t0, y0, b - b_prime,
k - k_prime, i, torque_fourier)
# Normalise error by amplitude
max_theta_diff = np.max(np.abs(theory_fourier[:, 1] - theory[:, 1]))
max_omega_diff = np.max(np.abs(theory_fourier[:, 2] - theory[:, 2]))
norm_theta_diff = (theory_fourier[:, 1] - theory[:, 1]) / np.max(
theory_fourier[:, 1])
norm_omega_diff = (theory_fourier[:, 2] - theory[:, 2]) / np.max(
theory_fourier[:, 2])
max_theta_norm = np.max(np.abs(norm_theta_diff))
max_omega_norm = np.max(np.abs(norm_omega_diff))
# Plotting - for 4 subplots on 1 figure.
if create_plot:
self._update_filename()
plotting_data = \
[
[
[[theory_fourier[:, 0], theory_fourier[:, 1],
r'Digitised'],
[theory[:, 0], theory[:, 1], r'Analogue']],
[[theory_fourier[:, 0], norm_theta_diff]],
],
[
[[theory_fourier[:, 0], theory_fourier[:, 2],
r'Digitised'],
[theory[:, 0], theory[:, 2], r'Analogue']],
[[theory_fourier[:, 0], norm_omega_diff]],
]
]
params = {
'theta_0': theta_0,
'omega_0': omega_0,
't0': t0,
'I': i,
'b\'': b_prime,
'k\'': k_prime,
'b': b,
'k': k,
'g_0_mag': g_0_mag,
'w_d': w_d,
'phi': phase,
't_fin': t_fin,
'dt': dt
}
p.two_by_n_plotter(
plotting_data,
self.filename,
params,
savepath=self.plotpath,
show=True,
x_axes_labels=['t/s', 't/s'],
tag='with-uniform-noise-torque-over-100',
y_top_labels=[r'$\theta$/rad', r'$\dot{\theta}$/rad/s'],
y_bottom_labels=[
r'$(\theta_{sim}-\theta_{an})/|\theta_{max}|$',
r'$(\dot{\theta}_{sim}-\dot{\theta}_{an})/'
r'|\dot{\theta}_{max}|$'
],
legend={
'loc': 'upper center',
'bbox_to_anchor': (0.5, 1),
'ncol': 2
})
print(b, k, i, num_terms, max_theta_norm, max_omega_norm)
return [
b, k, i, num_terms, max_theta_diff, max_omega_diff, max_theta_norm,
max_omega_norm
]
def main_operation(self, plot=False):
# feed in fixed b - b', k - k', torque, i, noise level and type,
# but a range of driving frequencies to test.
b_s = self.prms['b_s']
k_s = self.prms['k_s']
i_s = self.prms['i_s']
b_primes = self.prms['b\'s']
k_primes = self.prms['k\'s']
w_ds = np.arange(self.prms['w_d_start'], self.prms['w_d_final'],
self.prms['w_d_step'])
g_0_mags = self.prms['g0s']
phases = self.prms['phis']
t0 = self.prms['t0'].squeeze()
y0 = np.array([self.prms['theta_0'], self.prms['omega_0']]).squeeze()
times = np.arange(t0, self.prms['tfin'], self.prms['dt'])
# Get the theoretical position of the peak and generate a finely
# spaced set of frequency points around it to measure with greater
# resolution here.
w2_res = (k_s - k_primes) / i_s - (b_s - b_primes)**2 / (2 * i_s**2)
gamma = (b_s - b_primes) / i_s
# 5 * bandwidth on either side
gamma = np.absolute(gamma)
width = 5 * gamma if gamma != 0 else self.prms['w_d_step']
if w2_res >= 0:
w_res = np.sqrt(w2_res)
else:
w_res = 0
w_range = np.linspace(w_res - width if w_res - width > 2 else 2,
w_res + width, 100)
single_run = h.baker(
self._single_operation,
[times, '', '', '', '', '', '', '', '', '', t0, y0],
pos_to_pass_through=(1, 9))
ws = [w_ds, w_range]
for j in range(len(ws)):
all_times = h.all_combs(single_run, b_s, k_s, i_s, b_primes,
k_primes, ws[j], g_0_mags, phases, 1)
# final argument 1/2 for 1 frequency peak expected.
fft_data = []
real_data = []
for i in range(len(all_times)):
real_data.append(all_times[i][-1][1])
if all_times[i][-1][0]:
fft_data.append(all_times[i][-1][-1])
if j == 0:
fft_mmts = np.array(fft_data)
else:
fft_mmts = np.append(fft_mmts, np.array(fft_data), axis=0)
fft_mmts = fft_mmts[fft_mmts[:, 0, 0].argsort()]
ang_freqs = np.array([fft_mmts[:, 0, 0], fft_mmts[:, 0, 1]
]).T * 2 * np.pi
amps = np.array([fft_mmts[:, 1, 0], fft_mmts[:, 1, 1]]).T / g_0_mags
phases = np.array([fft_mmts[:, 2, 0], fft_mmts[:, 2, 1]]).T
# For a single set of data, get the transfer function once only. This
# allows error to be calculated as specifically the experimental
# ang_freqs are used.
fft_theory = np.array(
h.all_combs(t.theory_response, b_s, k_s, i_s, b_primes, k_primes,
ang_freqs[:, 0]))
theory_amps = np.absolute(fft_theory[:, -1])
theory_phases = np.angle(fft_theory[:, -1])
amp_err, phase_err = m.calc_norm_errs([amps[:, 0], theory_amps],
[phases[:, 0], theory_phases])[1]
theory_n_mmt = \
[[[[ang_freqs, theory_amps], [ang_freqs, amps]],
[[ang_freqs, amp_err / np.max(amps[:, 0])]]],
[[[ang_freqs, theory_phases], [ang_freqs, phases]],
[[ang_freqs, phase_err / np.max(np.absolute(phases[:, 0]))]]]]
p.two_by_n_plotter(theory_n_mmt,
self.filename,
self.prms,
savepath=self.plotpath,
show=False,
x_axes_labels=['$\omega$/rad/s', '$\omega$/rad/s'],
y_top_labels=[
r'$\left|R(\omega)\right|$/rad/(Nm)',
r'arg[$R(\omega)$]/rad'
],
y_bottom_labels=[
r'Normalised error in $\left|R(\omega)\right|$',
r'Normalised error in arg[$R(\omega)$]'
])