def __init__(self):
OscillatorModel.__init__(self)
self.oscillator = NormalOscillator()
self.control_params = dict()
self.control_params['alpha'] = ControlParameter('alpha', [-1.25, 0.20], -0.41769)
self.control_params['beta'] = ControlParameter('beta', [-0.75, 0.75], -0.346251775)
def find_admissible_controls(output_file=None,
alphamin=-1.25,
alphamax=0.25,
alphastep=0.01,
betamin=-1.50,
betamax=1.50,
betastep=0.01):
no = NormalOscillator()
stime = time.time()
alpharng = np.arange(alphamin, alphamax, alphastep)
betarng = np.arange(betamin, betamax, betastep)
nrows = len(alpharng)
ncols = len(betarng)
print '# of (alpha,beta) pairs: %d' % (nrows * ncols)
all_pairs = np.zeros([nrows, ncols, 2])
all_dv_rms = np.zeros([nrows, ncols]) * np.nan
all_ff = np.zeros([nrows, ncols]) * np.nan
sim_duration = 0.010
step_size = 1e-6
steady_state_point = 0.005
steady_state_index = int(steady_state_point / step_size)
for i, alpha in enumerate(alpharng):
for j, beta in enumerate(betarng):
all_pairs[i, j, :] = [alpha, beta]
output = no.simulate(0.0,
0.0,
duration=sim_duration,
dt=step_size,
alpha=alpha,
beta=beta)
dv = np.diff(output[:, 1])
dv_rms = dv[steady_state_index:].std(ddof=1)
all_dv_rms[i, j] = dv_rms
#compute power spectrum
fftx = fft(output[:, 0])
ps_f = fftfreq(len(output[:, 0]), d=step_size)
findx = (ps_f > 100.0) & (ps_f < 8000.0)
#estimate fundamental frequency from log power spectrum in the simplest way possible
ps = np.abs(fftx[findx])
peak_index = ps.argmax()
all_ff[i, j] = ps_f[findx][peak_index]
etime = time.time() - stime
print 'Elapsed Time: %0.2f s' % etime
if output_file is not None:
hf = h5py.File(output_file, 'w')
hf['all_pairs'] = all_pairs
hf['all_dv_rms'] = all_dv_rms
hf['all_ff'] = all_ff
hf.close()
def __init__(self):
self.oscillator = NormalOscillator()
self.sample_rate = 1000.0
self.waveform_sample_rate = 1e5
self.alpha = list()
self.beta = list()
self.mu = list()
self.sigma1 = list()
self.sigma2 = list()
def find_fixedpoints_normal(xmin=-10.0,
xmax=10.0,
xstep=1e-3,
alpha=-0.41769,
beta=-0.346251775,
plot=False):
no = NormalOscillator()
xrng = np.arange(xmin, xmax + xstep, xstep)
nullx = np.array([no.nullcline_x(xval, alpha, beta) for xval in xrng])
xp = zip(xrng, nullx, np.abs(nullx))
xp.sort(key=operator.itemgetter(-1))
top3 = np.array(xp[:3])
f = lambda x: no.nullcline_x(x, alpha, beta)
df = lambda x: no.nullcline_dx(x, alpha, beta)
zero_tol = 1e-6
x_tol = 1e-4
roots = list()
for k, xi in enumerate(top3[:, 0]):
try:
xz = newton(f, xi, fprime=df, maxiter=100)
except RuntimeError:
continue
xz_val = no.nullcline_x(xz, alpha, beta)
#print 'xz=%0.9f, xz_val=%0.9f' % (xz, xz_val)
if np.abs(xz_val) < zero_tol:
is_duplicate = False
for x, xv in roots:
if np.abs(x - xz) < x_tol:
is_duplicate = True
if not is_duplicate:
#print 'Root: x=%0.6f, f(x)=%0.6f' % (xz, xz_val)
roots.append([xz, xz_val])
roots = np.array(roots)
if plot:
plt.figure()
plt.plot(xrng, nullx, 'k-')
plt.plot(top3[:, 0], top3[:, 1], 'rx')
plt.plot(roots[:, 0], roots[:, 1], 'go')
plt.title('Fixed Point Surface for dv')
plt.xlabel('x')
plt.axis('tight')
return roots
def control_oscillator(self, states, dt=1e-3, oscillator_dt=1e-6):
no = NormalOscillator()
output = list()
oscillator_x = 0.0
oscillator_v = 0.0
for alpha, beta in states:
params = {'alpha': alpha, 'beta': beta}
ostates = no.run_simulation(params,
dt,
oscillator_dt,
initial_x=oscillator_x,
initial_v=oscillator_v)
oscillator_x = ostates[-1, 0]
oscillator_v = ostates[-1, 1]
output.extend(ostates[:, 0])
return output
