examples: add fit_image

examples/fit_image.py

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+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()