import numpy as np from scipy.optimize import least_squares from scipy import constants # from numba import jit 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] # @jit 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()