| 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 | from sas.sascalc.corfunc.transform_thread import FourierThread |
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| 13 | from sas.sascalc.corfunc.transform_thread import HilbertThread |
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| 14 | |
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| 15 | class CorfuncCalculator(object): |
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| 16 | |
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| 17 | class _Interpolator(object): |
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| 18 | """ |
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| 19 | Interpolates between curve f and curve g over the range start:stop and |
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| 20 | caches the result of the function when it's called |
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| 21 | |
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| 22 | :param f: The first curve to interpolate |
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| 23 | :param g: The second curve to interpolate |
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| 24 | :param start: The value at which to start the interpolation |
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| 25 | :param stop: The value at which to stop the interpolation |
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| 26 | """ |
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| 27 | def __init__(self, f, g, start, stop): |
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| 28 | self.f = f |
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| 29 | self.g = g |
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| 30 | self.start = start |
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| 31 | self.stop = stop |
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| 32 | self._lastx = np.empty(0, dtype='d') |
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| 33 | self._lasty = None |
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| 34 | |
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| 35 | def __call__(self, x): |
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| 36 | # If input is a single number, evaluate the function at that number |
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| 37 | # and return a single number |
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| 38 | if isinstance(x, (float, int)): |
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| 39 | return self._smoothed_function(np.array([x]))[0] |
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| 40 | # If input is a list, and is different to the last input, evaluate |
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| 41 | # the function at each point. If the input is the same as last time |
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| 42 | # the function was called, return the result that was calculated |
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| 43 | # last time instead of explicity evaluating the function again. |
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| 44 | if not np.array_equal(x, self._lastx): |
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| 45 | self._lastx, self._lasty = x, self._smoothed_function(x) |
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| 46 | return self._lasty |
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| 47 | |
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| 48 | def _smoothed_function(self,x): |
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| 49 | ys = np.zeros(x.shape) |
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| 50 | ys[x <= self.start] = self.f(x[x <= self.start]) |
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| 51 | ys[x >= self.stop] = self.g(x[x >= self.stop]) |
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| 52 | with warnings.catch_warnings(): |
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| 53 | # Ignore divide by zero error |
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| 54 | warnings.simplefilter('ignore') |
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| 55 | h = 1/(1+(x-self.stop)**2/(self.start-x)**2) |
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| 56 | mask = np.logical_and(x > self.start, x < self.stop) |
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| 57 | ys[mask] = h[mask]*self.g(x[mask])+(1-h[mask])*self.f(x[mask]) |
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| 58 | return ys |
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| 59 | |
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| 60 | |
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| 61 | def __init__(self, data=None, lowerq=None, upperq=None, scale=1): |
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| 62 | """ |
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| 63 | Initialize the class. |
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| 64 | |
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| 65 | :param data: Data of the type DataLoader.Data1D |
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| 66 | :param lowerq: The Q value to use as the boundary for |
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| 67 | Guinier extrapolation |
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| 68 | :param upperq: A tuple of the form (lower, upper). |
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| 69 | Values between lower and upper will be used for Porod extrapolation |
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| 70 | :param scale: Scaling factor for I(q) |
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| 71 | """ |
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| 72 | self._data = None |
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| 73 | self.set_data(data, scale) |
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| 74 | self.lowerq = lowerq |
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| 75 | self.upperq = upperq |
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| 76 | self.background = self.compute_background() |
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| 77 | self._transform_thread = None |
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| 78 | |
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| 79 | def set_data(self, data, scale=1): |
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| 80 | """ |
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| 81 | Prepares the data for analysis |
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| 82 | |
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| 83 | :return: new_data = data * scale - background |
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| 84 | """ |
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| 85 | if data is None: |
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| 86 | return |
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| 87 | # Only process data of the class Data1D |
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| 88 | if not issubclass(data.__class__, Data1D): |
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| 89 | raise ValueError("Correlation function cannot be computed with 2D data.") |
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| 90 | |
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| 91 | # Prepare the data |
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| 92 | new_data = Data1D(x=data.x, y=data.y) |
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| 93 | new_data *= scale |
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| 94 | |
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| 95 | # Ensure the errors are set correctly |
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| 96 | if new_data.dy is None or len(new_data.x) != len(new_data.dy) or \ |
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| 97 | (min(new_data.dy) == 0 and max(new_data.dy) == 0): |
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| 98 | new_data.dy = np.ones(len(new_data.x)) |
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| 99 | |
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| 100 | self._data = new_data |
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| 101 | |
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| 102 | def compute_background(self, upperq=None): |
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| 103 | """ |
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| 104 | Compute the background level from the Porod region of the data |
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| 105 | """ |
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| 106 | if self._data is None: return 0 |
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| 107 | elif upperq is None and self.upperq is not None: upperq = self.upperq |
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| 108 | elif upperq is None and self.upperq is None: return 0 |
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| 109 | q = self._data.x |
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| 110 | mask = np.logical_and(q > upperq[0], q < upperq[1]) |
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| 111 | _, _, bg = self._fit_porod(q[mask], self._data.y[mask]) |
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| 112 | |
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| 113 | return bg |
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| 114 | |
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| 115 | def compute_extrapolation(self): |
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| 116 | """ |
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| 117 | Extrapolate and interpolate scattering data |
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| 118 | |
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| 119 | :return: The extrapolated data |
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| 120 | """ |
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| 121 | q = self._data.x |
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| 122 | iq = self._data.y |
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| 123 | |
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| 124 | params, s2 = self._fit_data(q, iq) |
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| 125 | # Extrapolate to 100*Qmax in experimental data |
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| 126 | qs = np.arange(0, q[-1]*100, (q[1]-q[0])) |
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| 127 | iqs = s2(qs) |
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| 128 | |
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| 129 | extrapolation = Data1D(qs, iqs) |
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| 130 | |
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| 131 | return params, extrapolation, s2 |
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| 132 | |
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| 133 | def compute_transform(self, extrapolation, trans_type, background=None, |
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| 134 | completefn=None, updatefn=None): |
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| 135 | """ |
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| 136 | Transform an extrapolated scattering curve into a correlation function. |
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| 137 | |
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| 138 | :param extrapolation: The extrapolated data |
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| 139 | :param background: The background value (if not provided, previously |
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| 140 | calculated value will be used) |
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| 141 | :param extrap_fn: A callable function representing the extraoplated data |
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| 142 | :param completefn: The function to call when the transform calculation |
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| 143 | is complete |
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| 144 | :param updatefn: The function to call to update the GUI with the status |
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| 145 | of the transform calculation |
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| 146 | :return: The transformed data |
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| 147 | """ |
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| 148 | if self._transform_thread is not None: |
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| 149 | if self._transform_thread.isrunning(): return |
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| 150 | |
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| 151 | if background is None: background = self.background |
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| 152 | |
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| 153 | if trans_type == 'fourier': |
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| 154 | self._transform_thread = FourierThread(self._data, extrapolation, |
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| 155 | background, completefn=completefn, |
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| 156 | updatefn=updatefn) |
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| 157 | elif trans_type == 'hilbert': |
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| 158 | self._transform_thread = HilbertThread(self._data, extrapolation, |
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| 159 | background, completefn=completefn, updatefn=updatefn) |
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| 160 | else: |
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| 161 | err = ("Incorrect transform type supplied, must be 'fourier'", |
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| 162 | " or 'hilbert'") |
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| 163 | raise ValueError(err) |
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| 164 | |
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| 165 | self._transform_thread.queue() |
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| 166 | |
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| 167 | def transform_isrunning(self): |
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| 168 | if self._transform_thread is None: return False |
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| 169 | return self._transform_thread.isrunning() |
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| 170 | |
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| 171 | def stop_transform(self): |
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| 172 | if self._transform_thread.isrunning(): |
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| 173 | self._transform_thread.stop() |
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| 174 | |
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| 175 | def extract_parameters(self, transformed_data): |
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| 176 | """ |
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| 177 | Extract the interesting measurements from a correlation function |
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| 178 | |
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| 179 | :param transformed_data: Fourier transformation of the extrapolated data |
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| 180 | """ |
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| 181 | # Calculate indexes of maxima and minima |
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| 182 | x = transformed_data.x |
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| 183 | y = transformed_data.y |
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| 184 | maxs = argrelextrema(y, np.greater)[0] |
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| 185 | mins = argrelextrema(y, np.less)[0] |
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| 186 | |
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| 187 | # If there are no maxima, return None |
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| 188 | if len(maxs) == 0: |
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| 189 | return None |
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| 190 | |
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| 191 | GammaMin = y[mins[0]] # The value at the first minimum |
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| 192 | |
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| 193 | ddy = (y[:-2]+y[2:]-2*y[1:-1])/(x[2:]-x[:-2])**2 # 2nd derivative of y |
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| 194 | dy = (y[2:]-y[:-2])/(x[2:]-x[:-2]) # 1st derivative of y |
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| 195 | # Find where the second derivative goes to zero |
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| 196 | zeros = argrelextrema(np.abs(ddy), np.less)[0] |
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| 197 | # locate the first inflection point |
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| 198 | linear_point = zeros[0] |
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| 199 | |
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| 200 | # Try to calculate slope around linear_point using 80 data points |
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| 201 | lower = linear_point - 40 |
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| 202 | upper = linear_point + 40 |
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| 203 | |
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| 204 | # If too few data points to the left, use linear_point*2 data points |
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| 205 | if lower < 0: |
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| 206 | lower = 0 |
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| 207 | upper = linear_point * 2 |
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| 208 | # If too few to right, use 2*(dy.size - linear_point) data points |
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| 209 | elif upper > len(dy): |
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| 210 | upper = len(dy) |
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| 211 | width = len(dy) - linear_point |
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| 212 | lower = 2*linear_point - dy.size |
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| 213 | |
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| 214 | m = np.mean(dy[lower:upper]) # Linear slope |
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| 215 | b = y[1:-1][linear_point]-m*x[1:-1][linear_point] # Linear intercept |
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| 216 | |
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| 217 | Lc = (GammaMin-b)/m # Hard block thickness |
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| 218 | |
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| 219 | # Find the data points where the graph is linear to within 1% |
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| 220 | mask = np.where(np.abs((y-(m*x+b))/y) < 0.01)[0] |
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| 221 | if len(mask) == 0: # Return garbage for bad fits |
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| 222 | return { 'max': self._round_sig_figs(x[maxs[0]], 6) } |
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| 223 | dtr = x[mask[0]] # Beginning of Linear Section |
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| 224 | d0 = x[mask[-1]] # End of Linear Section |
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| 225 | GammaMax = y[mask[-1]] |
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| 226 | A = np.abs(GammaMin/GammaMax) # Normalized depth of minimum |
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| 227 | |
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| 228 | params = { |
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| 229 | 'max': x[maxs[0]], |
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| 230 | 'dtr': dtr, |
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| 231 | 'Lc': Lc, |
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| 232 | 'd0': d0, |
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| 233 | 'A': A, |
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| 234 | 'fill': Lc/x[maxs[0]] |
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| 235 | } |
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| 236 | |
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| 237 | return params |
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| 238 | |
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| 239 | |
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| 240 | def _porod(self, q, K, sigma, bg): |
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| 241 | """Equation for the Porod region of the data""" |
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| 242 | return bg + (K*q**(-4))*np.exp(-q**2*sigma**2) |
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| 243 | |
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| 244 | def _fit_guinier(self, q, iq): |
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| 245 | """Fit the Guinier region of the curve""" |
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| 246 | A = np.vstack([q**2, np.ones(q.shape)]).T |
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| 247 | # CRUFT: numpy>=1.14.0 allows rcond=None for the following default |
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| 248 | rcond = np.finfo(float).eps * max(A.shape) |
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| 249 | return lstsq(A, np.log(iq), rcond=rcond) |
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| 250 | |
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| 251 | def _fit_porod(self, q, iq): |
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| 252 | """Fit the Porod region of the curve""" |
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| 253 | fitp = curve_fit(lambda q, k, sig, bg: self._porod(q, k, sig, bg)*q**2, |
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| 254 | q, iq*q**2, bounds=([-np.inf, 0, -np.inf], [np.inf, np.inf, np.inf]))[0] |
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| 255 | k, sigma, bg = fitp |
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| 256 | return k, sigma, bg |
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| 257 | |
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| 258 | def _fit_data(self, q, iq): |
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| 259 | """ |
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| 260 | Given a data set, extrapolate out to large q with Porod and |
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| 261 | to q=0 with Guinier |
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| 262 | """ |
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| 263 | mask = np.logical_and(q > self.upperq[0], q < self.upperq[1]) |
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| 264 | |
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| 265 | # Returns an array where the 1st and 2nd elements are the values of k |
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| 266 | # and sigma for the best-fit Porod function |
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| 267 | k, sigma, _ = self._fit_porod(q[mask], iq[mask]) |
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| 268 | bg = self.background |
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| 269 | |
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| 270 | # Smooths between the best-fit porod function and the data to produce a |
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| 271 | # better fitting curve |
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| 272 | data = interp1d(q, iq) |
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| 273 | s1 = self._Interpolator(data, |
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| 274 | lambda x: self._porod(x, k, sigma, bg), self.upperq[0], q[-1]) |
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| 275 | |
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| 276 | mask = np.logical_and(q < self.lowerq, 0 < q) |
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| 277 | |
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| 278 | # Returns parameters for the best-fit Guinier function |
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| 279 | g = self._fit_guinier(q[mask], iq[mask])[0] |
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| 280 | |
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| 281 | # Smooths between the best-fit Guinier function and the Porod curve |
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| 282 | s2 = self._Interpolator((lambda x: (np.exp(g[1]+g[0]*x**2))), s1, q[0], |
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| 283 | self.lowerq) |
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| 284 | |
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| 285 | params = {'A': g[1], 'B': g[0], 'K': k, 'sigma': sigma} |
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| 286 | |
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| 287 | return params, s2 |
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