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