[8d79a87] | 1 | """ |
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| 2 | This module implements corfunc |
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| 3 | """ |
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| 4 | import warnings |
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| 5 | import numpy as np |
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| 6 | from scipy.optimize import curve_fit |
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| 7 | from scipy.interpolate import interp1d |
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| 8 | from scipy.fftpack import dct |
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| 9 | from scipy.signal import argrelextrema |
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| 10 | from numpy.linalg import lstsq |
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| 11 | from sas.sascalc.dataloader.data_info import Data1D |
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| 12 | |
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| 13 | class CorfuncCalculator(object): |
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| 14 | |
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| 15 | # Helper class |
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| 16 | class _Struct: |
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| 17 | def __init__(self, **entries): |
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| 18 | self.__dict__.update(entries) |
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| 19 | |
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| 20 | class _Interpolator(object): |
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| 21 | """ |
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| 22 | Interpolates between curve f and curve g over the range start:stop and |
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| 23 | caches the result of the function when it's called |
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| 24 | |
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| 25 | :param f: The first curve to interpolate |
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| 26 | :param g: The second curve to interpolate |
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| 27 | :param start: The value at which to start the interpolation |
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| 28 | :param stop: The value at which to stop the interpolation |
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| 29 | """ |
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| 30 | def __init__(self, f, g, start, stop): |
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| 31 | self.f = f |
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| 32 | self.g = g |
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| 33 | self.start = start |
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| 34 | self.stop = stop |
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| 35 | self._lastx = [] |
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| 36 | self._lasty = [] |
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| 37 | |
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| 38 | def __call__(self, x): |
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| 39 | if self._lastx == [] or x.tolist() != self._lastx.tolist(): |
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| 40 | self._lasty = self._smoothed_function(x) |
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| 41 | self._lastx = x |
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| 42 | return self._lasty |
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| 43 | |
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| 44 | def _smoothed_function(self,x): |
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| 45 | ys = np.zeros(x.shape) |
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| 46 | ys[x <= self.start] = self.f(x[x <= self.start]) |
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| 47 | ys[x >= self.stop] = self.g(x[x >= self.stop]) |
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| 48 | with warnings.catch_warnings(): |
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| 49 | # Ignore divide by zero error |
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| 50 | warnings.simplefilter('ignore') |
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| 51 | h = 1/(1+(x-self.stop)**2/(self.start-x)**2) |
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| 52 | mask = np.logical_and(x > self.start, x < self.stop) |
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| 53 | ys[mask] = h[mask]*self.g(x[mask])+(1-h[mask])*self.f(x[mask]) |
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| 54 | return ys |
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| 55 | |
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| 56 | |
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| 57 | def __init__(self, data, lowerq, upperq, background=0, scale=1): |
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| 58 | """ |
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| 59 | Initialize the class. |
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| 60 | |
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| 61 | :param data: Data of the type DataLoader.Data1D |
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| 62 | :param background: Background value. Will be subtracted from the data |
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| 63 | before processing |
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| 64 | :param scale: Scaling factor for I(q) |
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| 65 | """ |
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| 66 | print "Before: {}".format(data.y[0]) |
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| 67 | self._data = self._get_data(data, background, scale) |
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| 68 | print "After: {}".format(self._data.y[0]) |
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| 69 | self.lowerq = lowerq |
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| 70 | self.upperq = upperq |
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| 71 | |
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| 72 | def compute_extrapolation(self): |
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| 73 | q = self._data.x |
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| 74 | iq = self._data.y |
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| 75 | |
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| 76 | s2 = self._fit_data(q, iq) |
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| 77 | qs = np.arange(0, q[-1]*100, (q[1]-q[0])) |
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| 78 | iqs = s2(qs) |
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| 79 | |
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| 80 | extrapolation = Data1D(qs, iqs) |
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| 81 | |
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| 82 | return extrapolation |
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| 83 | |
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| 84 | def compute_transform(self, extrapolation): |
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| 85 | """ |
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| 86 | Transform an extrapolated scattering curve into a correlation function. |
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| 87 | """ |
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| 88 | qs = extrapolation.x |
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| 89 | iqs = extrapolation.y |
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| 90 | |
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| 91 | gamma = dct(iqs*qs**2) |
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| 92 | gamma = gamma / gamma.max() |
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| 93 | xs = np.pi*np.arange(len(qs),dtype=np.float32)/(q[1]-q[0])/len(qs) |
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| 94 | |
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| 95 | transform = Data1D(xs, gamma) |
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| 96 | |
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| 97 | return transform |
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| 98 | |
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| 99 | def _porod(self, q, K, sigma): |
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| 100 | """Equation for the Porod region of the data""" |
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| 101 | return (K*q**(-4))*np.exp(-q**2*sigma**2) |
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| 102 | |
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| 103 | def _fit_guinier(self, q, iq): |
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| 104 | """Fit the Guinier region of the curve""" |
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| 105 | A = np.vstack([q**2, np.ones(q.shape)]).T |
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| 106 | return lstsq(A, np.log(iq)) |
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| 107 | |
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| 108 | def _get_data(self, data, background, scale): |
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| 109 | """ |
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| 110 | Prepares the data for analysis |
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| 111 | |
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| 112 | :return: new_data = data * scale - background |
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| 113 | """ |
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| 114 | # Only process data of the class Data1D |
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| 115 | if not issubclass(data.__class__, Data1D): |
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| 116 | raise ValueError, "Data must be of the type DataLoader.Data1D" |
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| 117 | |
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| 118 | # Prepare the data |
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| 119 | new_data = (scale * data) |
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| 120 | new_data.y -= background |
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| 121 | |
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| 122 | # Check the vector lengths are equal |
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| 123 | assert len(new_data.x) == len(new_data.y) |
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| 124 | |
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| 125 | # Ensure the errors are set correctly |
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| 126 | if new_data.dy is None or len(new_data.x) != len(new_data.dy) or \ |
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| 127 | (min(new_data.dy) == 0 and max(new_data.dy) == 0): |
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| 128 | new_data.dy = np.ones(len(new_data.x)) |
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| 129 | |
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| 130 | return new_data |
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| 131 | |
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| 132 | def _fit_data(self, q, iq): |
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| 133 | """Given a data set, extrapolate out to large q with Porod |
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| 134 | and to q=0 with Guinier""" |
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| 135 | mask = np.logical_and(q > self.upperq[0], q < self.upperq[1]) |
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| 136 | |
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| 137 | # Returns an array where the 1st and 2nd elements are the values of k |
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| 138 | # and sigma for the best-fit Porod function |
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| 139 | fitp = curve_fit(lambda q, k, sig: self._porod(q, k, sig)*q**2, |
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| 140 | q[mask], iq[mask]*q[mask]**2)[0] |
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| 141 | |
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| 142 | # Smooths between the best-fit porod function and the data to produce a |
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| 143 | # better fitting curve |
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| 144 | data = interp1d(q, iq) |
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[a9b7a8f] | 145 | s1 = self._Interpolator(data, |
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| 146 | lambda x: self._porod(x, fitp[0], fitp[1]), self.upperq[0], q[-1]) |
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[8d79a87] | 147 | |
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| 148 | mask = np.logical_and(q < self.lowerq, 0 < q) |
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| 149 | |
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| 150 | # Returns parameters for the best-fit Guinier function |
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| 151 | g = self._fit_guinier(q[mask], iq[mask])[0] |
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| 152 | |
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| 153 | # Smooths between the best-fit Guinier function and the Porod curve |
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| 154 | s2 = self._Interpolator((lambda x: (np.exp(g[1]+g[0]*x**2))), s1, q[0], |
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| 155 | self.lowerq) |
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| 156 | |
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| 157 | return s2 |
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