artiq/examples/fit_image.py

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2016-04-02 22:43:37 +08:00
"""Image processing with SciPy example"""
2016-03-24 03:05:52 +08:00
import numpy as np
from scipy.optimize import least_squares
from scipy import constants
class Fit:
variables = [] # fixed ordering
def build(self, data, meta):
self.data = data
self.meta = meta
def variables_dict(self, param):
return dict(zip(self.variables, param))
def guess(self):
raise NotImplementedError
def model(self, *param, **kwargs):
raise NotImplementedError
def fit(self, *param, **kwargs):
def fun(x, *args, **kwargs):
return (self.model(x, *args, **kwargs) - self.data).ravel()
try:
mjac = self.model_jacobian
def jac(x, *args, **kwargs):
return mjac(x, *args, **kwargs).reshape(-1, x.size)
except AttributeError:
jac = "2-point"
res = least_squares(fun, param, jac, **kwargs)
_, s, v = np.linalg.svd(res.jac, full_matrices=False)
threshold = np.finfo(float).eps * max(res.jac.shape) * s[0]
s = s[s > threshold]
v = v[:s.size]
pcov = np.dot(v.T/s**2, v)
return res.x, pcov
def process(self, cov, *param):
return self.variables_dict(param)
def run(self, data, meta, **kwargs):
self.build(data, meta)
param = self.guess()
param, cov = self.fit(*param, **kwargs)
results = self.process(cov, *param)
return param, results
def od_to_n(od, meta):
return (od*meta["pitch_x"]*meta["pitch_x"] *
(1.+4.*meta["detuning"]**2)/meta["sigma0"])
def area_gauss(p, h, w):
return 2.*np.pi*p*abs(w*h)
def area_parabola(p, h, w):
return p*2/5.*np.pi/abs(w*h)**.5
def t_gauss(mass, omega, width, tof):
return mass/constants.Boltzmann*(omega*width)**2/(1. + (tof*omega)**2)
class Fit2DGaussParabola(Fit):
variables = ["i_offset", "x_center", "y_center",
"a_parabola", "v_parabola", "w_parabola",
"a_gauss", "v_gauss", "w_gauss"]
def build(self, data, meta):
super(Fit2DGaussParabola, self).build(data, meta)
self.xy = np.ogrid[:data.shape[0], :data.shape[1]]
def guess(self):
# TODO: this is usually smarter, based on self.data and self.meta
return [1000, 100, 100, 2000, 4, 4, 2000, 20, 20]
def model(self, param):
p = self.variables_dict(param)
x, y = self.xy
x2 = (x - p["x_center"])**2
y2 = (y - p["y_center"])**2
gauss = p["a_gauss"]*np.exp(
-(x2/p["v_gauss"]**2 + y2/p["w_gauss"]**2)/2)
r = 1 - p["v_parabola"]*x2 - p["w_parabola"]*y2
parabola = p["a_parabola"]*np.where(r > 0, r, 0)**1.5
return p["i_offset"] + gauss + parabola
def process(self, cov, *param):
r = self.variables_dict(param)
r["cov"] = np.diag(cov)
# TODO: handle cov, compute confidence intervals
r["n_condensate"] = area_parabola(od_to_n(r["a_parabola"], self.meta),
r["v_parabola"], r["w_parabola"])
r["n_thermal"] = area_gauss(od_to_n(r["a_gauss"], self.meta),
r["v_gauss"], r["w_gauss"])
r["t_x"] = t_gauss(self.meta["mass"], self.meta["omega_x"],
r["v_gauss"]*self.meta["pitch_x"], self.meta["tof"])
r["t_y"] = t_gauss(self.meta["mass"], self.meta["omega_y"],
r["w_gauss"]*self.meta["pitch_y"], self.meta["tof"])
r["t"] = (r["t_x"] + r["t_y"])/2
return r
if __name__ == "__main__":
# generate some test data
f = Fit2DGaussParabola()
f.xy = np.ogrid[:300, :300]
i = f.model(f.guess())
# make it noisy
i += 100 + np.random.randn(*i.shape)*200 + i*np.random.randn(*i.shape)*.1
meta = dict(mass=constants.atomic_mass*87, tof=25e-3,
omega_x=2*np.pi*30, omega_y=2*np.pi*100,
pitch_x=2e-6, pitch_y=2e-6,
detuning=0, sigma0=1e-12)
# fit it
f = Fit2DGaussParabola()
p, r = f.run(i, meta)
print(r)
from timeit import timeit
print(timeit("f.model(p)", globals=globals(), number=10))
import matplotlib.pyplot as plt
fig, ax = plt.subplots(2, 2)
for axi, ii in zip(ax.ravel(),
(i, f.model(f.guess()),
f.model(p), (f.model(p) - i) + 1000)):
axi.imshow(ii, cmap=plt.cm.Greys, vmin=0, vmax=5000)
plt.show()