1 | # pylint: disable=invalid-name |
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2 | """ |
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3 | Module to perform P(r) inversion. |
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4 | The module contains the Invertor class. |
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5 | |
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6 | FIXME: The way the Invertor interacts with its C component should be cleaned up |
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7 | """ |
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8 | |
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9 | import numpy as np |
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10 | import sys |
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11 | import math |
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12 | import time |
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13 | import copy |
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14 | import os |
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15 | import re |
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16 | import logging |
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17 | from numpy.linalg import lstsq |
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18 | from scipy import optimize |
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19 | from sas.sascalc.pr.core.pr_inversion import Cinvertor |
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20 | |
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21 | logger = logging.getLogger(__name__) |
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22 | |
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23 | def help(): |
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24 | """ |
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25 | Provide general online help text |
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26 | Future work: extend this function to allow topic selection |
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27 | """ |
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28 | info_txt = "The inversion approach is based on Moore, J. Appl. Cryst. " |
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29 | info_txt += "(1980) 13, 168-175.\n\n" |
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30 | info_txt += "P(r) is set to be equal to an expansion of base functions " |
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31 | info_txt += "of the type " |
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32 | info_txt += "phi_n(r) = 2*r*sin(pi*n*r/D_max). The coefficient of each " |
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33 | info_txt += "base functions " |
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34 | info_txt += "in the expansion is found by performing a least square fit " |
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35 | info_txt += "with the " |
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36 | info_txt += "following fit function:\n\n" |
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37 | info_txt += "chi**2 = sum_i[ I_meas(q_i) - I_th(q_i) ]**2/error**2 +" |
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38 | info_txt += "Reg_term\n\n" |
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39 | info_txt += "where I_meas(q) is the measured scattering intensity and " |
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40 | info_txt += "I_th(q) is " |
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41 | info_txt += "the prediction from the Fourier transform of the P(r) " |
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42 | info_txt += "expansion. " |
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43 | info_txt += "The Reg_term term is a regularization term set to the second" |
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44 | info_txt += " derivative " |
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45 | info_txt += "d**2P(r)/dr**2 integrated over r. It is used to produce " |
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46 | info_txt += "a smooth P(r) output.\n\n" |
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47 | info_txt += "The following are user inputs:\n\n" |
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48 | info_txt += " - Number of terms: the number of base functions in the P(r)" |
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49 | info_txt += " expansion.\n\n" |
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50 | info_txt += " - Regularization constant: a multiplicative constant " |
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51 | info_txt += "to set the size of " |
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52 | info_txt += "the regularization term.\n\n" |
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53 | info_txt += " - Maximum distance: the maximum distance between any " |
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54 | info_txt += "two points in the system.\n" |
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55 | |
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56 | return info_txt |
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57 | |
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58 | |
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59 | class Invertor(Cinvertor): |
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60 | """ |
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61 | Invertor class to perform P(r) inversion |
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62 | |
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63 | The problem is solved by posing the problem as Ax = b, |
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64 | where x is the set of coefficients we are looking for. |
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65 | |
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66 | Npts is the number of points. |
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67 | |
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68 | In the following i refers to the ith base function coefficient. |
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69 | The matrix has its entries j in its first Npts rows set to :: |
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70 | |
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71 | A[j][i] = (Fourier transformed base function for point j) |
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72 | |
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73 | We then choose a number of r-points, n_r, to evaluate the second |
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74 | derivative of P(r) at. This is used as our regularization term. |
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75 | For a vector r of length n_r, the following n_r rows are set to :: |
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76 | |
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77 | A[j+Npts][i] = (2nd derivative of P(r), d**2(P(r))/d(r)**2, |
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78 | evaluated at r[j]) |
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79 | |
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80 | The vector b has its first Npts entries set to :: |
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81 | |
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82 | b[j] = (I(q) observed for point j) |
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83 | |
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84 | The following n_r entries are set to zero. |
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85 | |
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86 | The result is found by using scipy.linalg.basic.lstsq to invert |
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87 | the matrix and find the coefficients x. |
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88 | |
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89 | Methods inherited from Cinvertor: |
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90 | |
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91 | * ``get_peaks(pars)``: returns the number of P(r) peaks |
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92 | * ``oscillations(pars)``: returns the oscillation parameters for the output P(r) |
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93 | * ``get_positive(pars)``: returns the fraction of P(r) that is above zero |
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94 | * ``get_pos_err(pars)``: returns the fraction of P(r) that is 1-sigma above zero |
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95 | """ |
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96 | ## Chisqr of the last computation |
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97 | chi2 = 0 |
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98 | ## Time elapsed for last computation |
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99 | elapsed = 0 |
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100 | ## Alpha to get the reg term the same size as the signal |
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101 | suggested_alpha = 0 |
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102 | ## Last number of base functions used |
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103 | nfunc = 10 |
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104 | ## Last output values |
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105 | out = None |
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106 | ## Last errors on output values |
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107 | cov = None |
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108 | ## Background value |
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109 | background = 0 |
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110 | ## Information dictionary for application use |
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111 | info = {} |
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112 | |
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113 | def __init__(self): |
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114 | Cinvertor.__init__(self) |
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115 | |
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116 | def __setstate__(self, state): |
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117 | """ |
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118 | restore the state of invertor for pickle |
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119 | """ |
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120 | (self.__dict__, self.alpha, self.d_max, |
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121 | self.q_min, self.q_max, |
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122 | self.x, self.y, |
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123 | self.err, self.est_bck, |
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124 | self.slit_height, self.slit_width) = state |
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125 | |
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126 | def __reduce_ex__(self, proto): |
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127 | """ |
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128 | Overwrite the __reduce_ex__ |
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129 | """ |
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130 | |
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131 | state = (self.__dict__, |
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132 | self.alpha, self.d_max, |
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133 | self.q_min, self.q_max, |
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134 | self.x, self.y, |
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135 | self.err, self.est_bck, |
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136 | self.slit_height, self.slit_width, |
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137 | ) |
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138 | return (Invertor, tuple(), state, None, None) |
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139 | |
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140 | def __setattr__(self, name, value): |
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141 | """ |
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142 | Set the value of an attribute. |
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143 | Access the parent class methods for |
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144 | x, y, err, d_max, q_min, q_max and alpha |
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145 | """ |
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146 | if name == 'x': |
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147 | if 0.0 in value: |
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148 | msg = "Invertor: one of your q-values is zero. " |
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149 | msg += "Delete that entry before proceeding" |
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150 | raise ValueError(msg) |
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151 | return self.set_x(value) |
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152 | elif name == 'y': |
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153 | return self.set_y(value) |
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154 | elif name == 'err': |
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155 | value2 = abs(value) |
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156 | return self.set_err(value2) |
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157 | elif name == 'd_max': |
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158 | if value <= 0.0: |
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159 | msg = "Invertor: d_max must be greater than zero." |
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160 | msg += "Correct that entry before proceeding" |
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161 | raise ValueError(msg) |
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162 | return self.set_dmax(value) |
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163 | elif name == 'q_min': |
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164 | if value is None: |
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165 | return self.set_qmin(-1.0) |
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166 | return self.set_qmin(value) |
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167 | elif name == 'q_max': |
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168 | if value is None: |
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169 | return self.set_qmax(-1.0) |
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170 | return self.set_qmax(value) |
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171 | elif name == 'alpha': |
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172 | return self.set_alpha(value) |
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173 | elif name == 'slit_height': |
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174 | return self.set_slit_height(value) |
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175 | elif name == 'slit_width': |
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176 | return self.set_slit_width(value) |
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177 | elif name == 'est_bck': |
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178 | if value == True: |
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179 | return self.set_est_bck(1) |
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180 | elif value == False: |
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181 | return self.set_est_bck(0) |
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182 | else: |
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183 | raise ValueError("Invertor: est_bck can only be True or False") |
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184 | |
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185 | return Cinvertor.__setattr__(self, name, value) |
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186 | |
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187 | def __getattr__(self, name): |
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188 | """ |
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189 | Return the value of an attribute |
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190 | """ |
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191 | #import numpy |
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192 | if name == 'x': |
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193 | out = np.ones(self.get_nx()) |
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194 | self.get_x(out) |
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195 | return out |
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196 | elif name == 'y': |
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197 | out = np.ones(self.get_ny()) |
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198 | self.get_y(out) |
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199 | return out |
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200 | elif name == 'err': |
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201 | out = np.ones(self.get_nerr()) |
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202 | self.get_err(out) |
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203 | return out |
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204 | elif name == 'd_max': |
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205 | return self.get_dmax() |
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206 | elif name == 'q_min': |
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207 | qmin = self.get_qmin() |
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208 | if qmin < 0: |
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209 | return None |
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210 | return qmin |
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211 | elif name == 'q_max': |
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212 | qmax = self.get_qmax() |
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213 | if qmax < 0: |
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214 | return None |
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215 | return qmax |
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216 | elif name == 'alpha': |
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217 | return self.get_alpha() |
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218 | elif name == 'slit_height': |
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219 | return self.get_slit_height() |
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220 | elif name == 'slit_width': |
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221 | return self.get_slit_width() |
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222 | elif name == 'est_bck': |
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223 | value = self.get_est_bck() |
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224 | return value == 1 |
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225 | elif name in self.__dict__: |
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226 | return self.__dict__[name] |
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227 | return None |
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228 | |
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229 | def add_errors(self, yvalues): |
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230 | """ |
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231 | Adds errors to data set is they are not avaialble |
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232 | :return: |
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233 | """ |
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234 | stats_errors = np.zeros(len(yvalues)) |
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235 | for i in range(len(yvalues)): |
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236 | # Scale the error so that we can fit over several decades of Q |
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237 | scale = 0.05 * np.sqrt(yvalues[i]) |
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238 | min_err = 0.01 * yvalues[i] |
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239 | stats_errors[i] = scale * np.sqrt(np.fabs(yvalues[i])) + min_err |
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240 | logger.warning("Simulated errors have been added to the data set\n") |
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241 | return stats_errors |
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242 | |
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243 | def clone(self): |
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244 | """ |
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245 | Return a clone of this instance |
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246 | """ |
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247 | #import copy |
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248 | |
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249 | invertor = Invertor() |
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250 | invertor.chi2 = self.chi2 |
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251 | invertor.elapsed = self.elapsed |
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252 | invertor.nfunc = self.nfunc |
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253 | invertor.alpha = self.alpha |
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254 | invertor.d_max = self.d_max |
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255 | invertor.q_min = self.q_min |
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256 | invertor.q_max = self.q_max |
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257 | |
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258 | invertor.x = self.x |
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259 | invertor.y = self.y |
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260 | if np.size(self.err) == 0 or np.all(self.err) == 0: |
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261 | invertor.err = self.add_errors(self.y) |
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262 | else: |
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263 | invertor.err = self.err |
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264 | invertor.est_bck = self.est_bck |
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265 | invertor.background = self.background |
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266 | invertor.slit_height = self.slit_height |
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267 | invertor.slit_width = self.slit_width |
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268 | |
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269 | invertor.info = copy.deepcopy(self.info) |
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270 | |
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271 | return invertor |
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272 | |
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273 | def invert(self, nfunc=10, nr=20): |
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274 | """ |
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275 | Perform inversion to P(r) |
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276 | |
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277 | The problem is solved by posing the problem as Ax = b, |
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278 | where x is the set of coefficients we are looking for. |
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279 | |
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280 | Npts is the number of points. |
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281 | |
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282 | In the following i refers to the ith base function coefficient. |
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283 | The matrix has its entries j in its first Npts rows set to :: |
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284 | |
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285 | A[i][j] = (Fourier transformed base function for point j) |
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286 | |
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287 | We then choose a number of r-points, n_r, to evaluate the second |
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288 | derivative of P(r) at. This is used as our regularization term. |
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289 | For a vector r of length n_r, the following n_r rows are set to :: |
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290 | |
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291 | A[i+Npts][j] = (2nd derivative of P(r), d**2(P(r))/d(r)**2, evaluated at r[j]) |
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292 | |
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293 | The vector b has its first Npts entries set to :: |
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294 | |
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295 | b[j] = (I(q) observed for point j) |
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296 | |
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297 | The following n_r entries are set to zero. |
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298 | |
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299 | The result is found by using scipy.linalg.basic.lstsq to invert |
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300 | the matrix and find the coefficients x. |
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301 | |
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302 | :param nfunc: number of base functions to use. |
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303 | :param nr: number of r points to evaluate the 2nd derivative at for the reg. term. |
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304 | :return: c_out, c_cov - the coefficients with covariance matrix |
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305 | """ |
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306 | # Reset the background value before proceeding |
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307 | # self.background = 0.0 |
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308 | if not self.est_bck: |
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309 | self.y -= self.background |
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310 | out, cov = self.lstsq(nfunc, nr=nr) |
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311 | if not self.est_bck: |
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312 | self.y += self.background |
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313 | return out, cov |
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314 | |
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315 | def iq(self, out, q): |
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316 | """ |
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317 | Function to call to evaluate the scattering intensity |
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318 | |
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319 | :param args: c-parameters, and q |
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320 | :return: I(q) |
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321 | |
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322 | """ |
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323 | return Cinvertor.iq(self, out, q) + self.background |
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324 | |
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325 | def invert_optimize(self, nfunc=10, nr=20): |
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326 | """ |
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327 | Slower version of the P(r) inversion that uses scipy.optimize.leastsq. |
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328 | |
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329 | This probably produce more reliable results, but is much slower. |
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330 | The minimization function is set to |
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331 | sum_i[ (I_obs(q_i) - I_theo(q_i))/err**2 ] + alpha * reg_term, |
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332 | where the reg_term is given by Svergun: it is the integral of |
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333 | the square of the first derivative |
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334 | of P(r), d(P(r))/dr, integrated over the full range of r. |
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335 | |
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336 | :param nfunc: number of base functions to use. |
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337 | :param nr: number of r points to evaluate the 2nd derivative at |
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338 | for the reg. term. |
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339 | |
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340 | :return: c_out, c_cov - the coefficients with covariance matrix |
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341 | |
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342 | """ |
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343 | self.nfunc = nfunc |
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344 | # First, check that the current data is valid |
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345 | if self.is_valid() <= 0: |
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346 | msg = "Invertor.invert: Data array are of different length" |
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347 | raise RuntimeError(msg) |
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348 | |
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349 | p = np.ones(nfunc) |
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350 | t_0 = time.time() |
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351 | out, cov_x, _, _, _ = optimize.leastsq(self.residuals, p, full_output=1) |
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352 | |
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353 | # Compute chi^2 |
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354 | res = self.residuals(out) |
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355 | chisqr = 0 |
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356 | for i in range(len(res)): |
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357 | chisqr += res[i] |
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358 | |
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359 | self.chi2 = chisqr |
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360 | |
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361 | # Store computation time |
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362 | self.elapsed = time.time() - t_0 |
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363 | |
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364 | if cov_x is None: |
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365 | cov_x = np.ones([nfunc, nfunc]) |
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366 | cov_x *= math.fabs(chisqr) |
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367 | return out, cov_x |
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368 | |
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369 | def pr_fit(self, nfunc=5): |
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370 | """ |
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371 | This is a direct fit to a given P(r). It assumes that the y data |
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372 | is set to some P(r) distribution that we are trying to reproduce |
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373 | with a set of base functions. |
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374 | |
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375 | This method is provided as a test. |
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376 | """ |
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377 | # First, check that the current data is valid |
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378 | if self.is_valid() <= 0: |
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379 | msg = "Invertor.invert: Data arrays are of different length" |
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380 | raise RuntimeError(msg) |
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381 | |
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382 | p = np.ones(nfunc) |
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383 | t_0 = time.time() |
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384 | out, cov_x, _, _, _ = optimize.leastsq(self.pr_residuals, p, full_output=1) |
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385 | |
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386 | # Compute chi^2 |
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387 | res = self.pr_residuals(out) |
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388 | chisqr = 0 |
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389 | for i in range(len(res)): |
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390 | chisqr += res[i] |
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391 | |
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392 | self.chisqr = chisqr |
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393 | |
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394 | # Store computation time |
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395 | self.elapsed = time.time() - t_0 |
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396 | |
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397 | return out, cov_x |
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398 | |
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399 | def pr_err(self, c, c_cov, r): |
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400 | """ |
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401 | Returns the value of P(r) for a given r, and base function |
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402 | coefficients, with error. |
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403 | |
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404 | :param c: base function coefficients |
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405 | :param c_cov: covariance matrice of the base function coefficients |
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406 | :param r: r-value to evaluate P(r) at |
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407 | |
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408 | :return: P(r) |
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409 | |
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410 | """ |
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411 | return self.get_pr_err(c, c_cov, r) |
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412 | |
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413 | def _accept_q(self, q): |
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414 | """ |
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415 | Check q-value against user-defined range |
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416 | """ |
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417 | if self.q_min is not None and q < self.q_min: |
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418 | return False |
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419 | if self.q_max is not None and q > self.q_max: |
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420 | return False |
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421 | return True |
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422 | |
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423 | def lstsq(self, nfunc=5, nr=20): |
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424 | """ |
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425 | The problem is solved by posing the problem as Ax = b, |
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426 | where x is the set of coefficients we are looking for. |
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427 | |
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428 | Npts is the number of points. |
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429 | |
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430 | In the following i refers to the ith base function coefficient. |
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431 | The matrix has its entries j in its first Npts rows set to :: |
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432 | |
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433 | A[i][j] = (Fourier transformed base function for point j) |
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434 | |
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435 | We them choose a number of r-points, n_r, to evaluate the second |
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436 | derivative of P(r) at. This is used as our regularization term. |
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437 | For a vector r of length n_r, the following n_r rows are set to :: |
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438 | |
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439 | A[i+Npts][j] = (2nd derivative of P(r), d**2(P(r))/d(r)**2, |
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440 | evaluated at r[j]) |
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441 | |
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442 | The vector b has its first Npts entries set to :: |
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443 | |
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444 | b[j] = (I(q) observed for point j) |
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445 | |
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446 | The following n_r entries are set to zero. |
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447 | |
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448 | The result is found by using scipy.linalg.basic.lstsq to invert |
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449 | the matrix and find the coefficients x. |
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450 | |
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451 | :param nfunc: number of base functions to use. |
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452 | :param nr: number of r points to evaluate the 2nd derivative at for the reg. term. |
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453 | |
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454 | If the result does not allow us to compute the covariance matrix, |
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455 | a matrix filled with zeros will be returned. |
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456 | |
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457 | """ |
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458 | # Note: To make sure an array is contiguous: |
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459 | # blah = np.ascontiguousarray(blah_original) |
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460 | # ... before passing it to C |
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461 | |
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462 | if self.is_valid() < 0: |
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463 | msg = "Invertor: invalid data; incompatible data lengths." |
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464 | raise RuntimeError(msg) |
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465 | |
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466 | self.nfunc = nfunc |
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467 | # a -- An M x N matrix. |
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468 | # b -- An M x nrhs matrix or M vector. |
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469 | npts = len(self.x) |
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470 | nq = nr |
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471 | sqrt_alpha = math.sqrt(math.fabs(self.alpha)) |
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472 | if sqrt_alpha < 0.0: |
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473 | nq = 0 |
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474 | |
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475 | # If we need to fit the background, add a term |
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476 | if self.est_bck: |
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477 | nfunc_0 = nfunc |
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478 | nfunc += 1 |
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479 | |
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480 | a = np.zeros([npts + nq, nfunc]) |
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481 | b = np.zeros(npts + nq) |
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482 | err = np.zeros([nfunc, nfunc]) |
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483 | |
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484 | # Construct the a matrix and b vector that represent the problem |
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485 | t_0 = time.time() |
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486 | try: |
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487 | self._get_matrix(nfunc, nq, a, b) |
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488 | except Exception as exc: |
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489 | raise RuntimeError("Invertor: could not invert I(Q)\n %s" % str(exc)) |
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490 | |
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491 | # Perform the inversion (least square fit) |
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492 | c, chi2, _, _ = lstsq(a, b) |
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493 | # Sanity check |
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494 | try: |
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495 | float(chi2) |
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496 | except: |
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497 | chi2 = -1.0 |
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498 | self.chi2 = chi2 |
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499 | |
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500 | inv_cov = np.zeros([nfunc, nfunc]) |
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501 | # Get the covariance matrix, defined as inv_cov = a_transposed * a |
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502 | self._get_invcov_matrix(nfunc, nr, a, inv_cov) |
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503 | |
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504 | # Compute the reg term size for the output |
---|
505 | sum_sig, sum_reg = self._get_reg_size(nfunc, nr, a) |
---|
506 | |
---|
507 | if math.fabs(self.alpha) > 0: |
---|
508 | new_alpha = sum_sig / (sum_reg / self.alpha) |
---|
509 | else: |
---|
510 | new_alpha = 0.0 |
---|
511 | self.suggested_alpha = new_alpha |
---|
512 | |
---|
513 | try: |
---|
514 | cov = np.linalg.pinv(inv_cov) |
---|
515 | err = math.fabs(chi2 / float(npts - nfunc)) * cov |
---|
516 | except: |
---|
517 | # We were not able to estimate the errors |
---|
518 | # Return an empty error matrix |
---|
519 | logger.error(sys.exc_value) |
---|
520 | |
---|
521 | # Keep a copy of the last output |
---|
522 | if not self.est_bck: |
---|
523 | self.out = c |
---|
524 | self.cov = err |
---|
525 | else: |
---|
526 | self.background = c[0] |
---|
527 | |
---|
528 | err_0 = np.zeros([nfunc, nfunc]) |
---|
529 | c_0 = np.zeros(nfunc) |
---|
530 | |
---|
531 | for i in range(nfunc_0): |
---|
532 | c_0[i] = c[i + 1] |
---|
533 | for j in range(nfunc_0): |
---|
534 | err_0[i][j] = err[i + 1][j + 1] |
---|
535 | |
---|
536 | self.out = c_0 |
---|
537 | self.cov = err_0 |
---|
538 | |
---|
539 | # Store computation time |
---|
540 | self.elapsed = time.time() - t_0 |
---|
541 | |
---|
542 | return self.out, self.cov |
---|
543 | |
---|
544 | def estimate_numterms(self, isquit_func=None): |
---|
545 | """ |
---|
546 | Returns a reasonable guess for the |
---|
547 | number of terms |
---|
548 | |
---|
549 | :param isquit_func: |
---|
550 | reference to thread function to call to check whether the computation needs to |
---|
551 | be stopped. |
---|
552 | |
---|
553 | :return: number of terms, alpha, message |
---|
554 | |
---|
555 | """ |
---|
556 | from .num_term import NTermEstimator |
---|
557 | estimator = NTermEstimator(self.clone()) |
---|
558 | try: |
---|
559 | return estimator.num_terms(isquit_func) |
---|
560 | except: |
---|
561 | # If we fail, estimate alpha and return the default |
---|
562 | # number of terms |
---|
563 | best_alpha, _, _ = self.estimate_alpha(self.nfunc) |
---|
564 | logger.warning("Invertor.estimate_numterms: %s" % sys.exc_value) |
---|
565 | return self.nfunc, best_alpha, "Could not estimate number of terms" |
---|
566 | |
---|
567 | def estimate_alpha(self, nfunc): |
---|
568 | """ |
---|
569 | Returns a reasonable guess for the |
---|
570 | regularization constant alpha |
---|
571 | |
---|
572 | :param nfunc: number of terms to use in the expansion. |
---|
573 | |
---|
574 | :return: alpha, message, elapsed |
---|
575 | |
---|
576 | where alpha is the estimate for alpha, |
---|
577 | message is a message for the user, |
---|
578 | elapsed is the computation time |
---|
579 | """ |
---|
580 | #import time |
---|
581 | try: |
---|
582 | pr = self.clone() |
---|
583 | |
---|
584 | # T_0 for computation time |
---|
585 | starttime = time.time() |
---|
586 | elapsed = 0 |
---|
587 | |
---|
588 | # If the current alpha is zero, try |
---|
589 | # another value |
---|
590 | if pr.alpha <= 0: |
---|
591 | pr.alpha = 0.0001 |
---|
592 | |
---|
593 | # Perform inversion to find the largest alpha |
---|
594 | out, _ = pr.invert(nfunc) |
---|
595 | elapsed = time.time() - starttime |
---|
596 | initial_alpha = pr.alpha |
---|
597 | initial_peaks = pr.get_peaks(out) |
---|
598 | |
---|
599 | # Try the inversion with the estimated alpha |
---|
600 | pr.alpha = pr.suggested_alpha |
---|
601 | out, _ = pr.invert(nfunc) |
---|
602 | |
---|
603 | npeaks = pr.get_peaks(out) |
---|
604 | # if more than one peak to start with |
---|
605 | # just return the estimate |
---|
606 | if npeaks > 1: |
---|
607 | #message = "Your P(r) is not smooth, |
---|
608 | #please check your inversion parameters" |
---|
609 | message = None |
---|
610 | return pr.suggested_alpha, message, elapsed |
---|
611 | else: |
---|
612 | |
---|
613 | # Look at smaller values |
---|
614 | # We assume that for the suggested alpha, we have 1 peak |
---|
615 | # if not, send a message to change parameters |
---|
616 | alpha = pr.suggested_alpha |
---|
617 | best_alpha = pr.suggested_alpha |
---|
618 | found = False |
---|
619 | for i in range(10): |
---|
620 | pr.alpha = (0.33) ** (i + 1) * alpha |
---|
621 | out, _ = pr.invert(nfunc) |
---|
622 | |
---|
623 | peaks = pr.get_peaks(out) |
---|
624 | if peaks > 1: |
---|
625 | found = True |
---|
626 | break |
---|
627 | best_alpha = pr.alpha |
---|
628 | |
---|
629 | # If we didn't find a turning point for alpha and |
---|
630 | # the initial alpha already had only one peak, |
---|
631 | # just return that |
---|
632 | if not found and initial_peaks == 1 and \ |
---|
633 | initial_alpha < best_alpha: |
---|
634 | best_alpha = initial_alpha |
---|
635 | |
---|
636 | # Check whether the size makes sense |
---|
637 | message = '' |
---|
638 | |
---|
639 | if not found: |
---|
640 | message = None |
---|
641 | elif best_alpha >= 0.5 * pr.suggested_alpha: |
---|
642 | # best alpha is too big, return a |
---|
643 | # reasonable value |
---|
644 | message = "The estimated alpha for your system is too " |
---|
645 | message += "large. " |
---|
646 | message += "Try increasing your maximum distance." |
---|
647 | |
---|
648 | return best_alpha, message, elapsed |
---|
649 | |
---|
650 | except: |
---|
651 | message = "Invertor.estimate_alpha: %s" % sys.exc_value |
---|
652 | return 0, message, elapsed |
---|
653 | |
---|
654 | def to_file(self, path, npts=100): |
---|
655 | """ |
---|
656 | Save the state to a file that will be readable |
---|
657 | by SliceView. |
---|
658 | |
---|
659 | :param path: path of the file to write |
---|
660 | :param npts: number of P(r) points to be written |
---|
661 | |
---|
662 | """ |
---|
663 | file = open(path, 'w') |
---|
664 | file.write("#d_max=%g\n" % self.d_max) |
---|
665 | file.write("#nfunc=%g\n" % self.nfunc) |
---|
666 | file.write("#alpha=%g\n" % self.alpha) |
---|
667 | file.write("#chi2=%g\n" % self.chi2) |
---|
668 | file.write("#elapsed=%g\n" % self.elapsed) |
---|
669 | file.write("#qmin=%s\n" % str(self.q_min)) |
---|
670 | file.write("#qmax=%s\n" % str(self.q_max)) |
---|
671 | file.write("#slit_height=%g\n" % self.slit_height) |
---|
672 | file.write("#slit_width=%g\n" % self.slit_width) |
---|
673 | file.write("#background=%g\n" % self.background) |
---|
674 | if self.est_bck: |
---|
675 | file.write("#has_bck=1\n") |
---|
676 | else: |
---|
677 | file.write("#has_bck=0\n") |
---|
678 | file.write("#alpha_estimate=%g\n" % self.suggested_alpha) |
---|
679 | if self.out is not None: |
---|
680 | if len(self.out) == len(self.cov): |
---|
681 | for i in range(len(self.out)): |
---|
682 | file.write("#C_%i=%s+-%s\n" % (i, str(self.out[i]), |
---|
683 | str(self.cov[i][i]))) |
---|
684 | file.write("<r> <Pr> <dPr>\n") |
---|
685 | r = np.arange(0.0, self.d_max, self.d_max / npts) |
---|
686 | |
---|
687 | for r_i in r: |
---|
688 | (value, err) = self.pr_err(self.out, self.cov, r_i) |
---|
689 | file.write("%g %g %g\n" % (r_i, value, err)) |
---|
690 | |
---|
691 | file.close() |
---|
692 | |
---|
693 | def from_file(self, path): |
---|
694 | """ |
---|
695 | Load the state of the Invertor from a file, |
---|
696 | to be able to generate P(r) from a set of |
---|
697 | parameters. |
---|
698 | |
---|
699 | :param path: path of the file to load |
---|
700 | |
---|
701 | """ |
---|
702 | #import os |
---|
703 | #import re |
---|
704 | if os.path.isfile(path): |
---|
705 | try: |
---|
706 | fd = open(path, 'r') |
---|
707 | |
---|
708 | buff = fd.read() |
---|
709 | lines = buff.split('\n') |
---|
710 | for line in lines: |
---|
711 | if line.startswith('#d_max='): |
---|
712 | toks = line.split('=') |
---|
713 | self.d_max = float(toks[1]) |
---|
714 | elif line.startswith('#nfunc='): |
---|
715 | toks = line.split('=') |
---|
716 | self.nfunc = int(toks[1]) |
---|
717 | self.out = np.zeros(self.nfunc) |
---|
718 | self.cov = np.zeros([self.nfunc, self.nfunc]) |
---|
719 | elif line.startswith('#alpha='): |
---|
720 | toks = line.split('=') |
---|
721 | self.alpha = float(toks[1]) |
---|
722 | elif line.startswith('#chi2='): |
---|
723 | toks = line.split('=') |
---|
724 | self.chi2 = float(toks[1]) |
---|
725 | elif line.startswith('#elapsed='): |
---|
726 | toks = line.split('=') |
---|
727 | self.elapsed = float(toks[1]) |
---|
728 | elif line.startswith('#alpha_estimate='): |
---|
729 | toks = line.split('=') |
---|
730 | self.suggested_alpha = float(toks[1]) |
---|
731 | elif line.startswith('#qmin='): |
---|
732 | toks = line.split('=') |
---|
733 | try: |
---|
734 | self.q_min = float(toks[1]) |
---|
735 | except: |
---|
736 | self.q_min = None |
---|
737 | elif line.startswith('#qmax='): |
---|
738 | toks = line.split('=') |
---|
739 | try: |
---|
740 | self.q_max = float(toks[1]) |
---|
741 | except: |
---|
742 | self.q_max = None |
---|
743 | elif line.startswith('#slit_height='): |
---|
744 | toks = line.split('=') |
---|
745 | self.slit_height = float(toks[1]) |
---|
746 | elif line.startswith('#slit_width='): |
---|
747 | toks = line.split('=') |
---|
748 | self.slit_width = float(toks[1]) |
---|
749 | elif line.startswith('#background='): |
---|
750 | toks = line.split('=') |
---|
751 | self.background = float(toks[1]) |
---|
752 | elif line.startswith('#has_bck='): |
---|
753 | toks = line.split('=') |
---|
754 | self.est_bck = int(toks[1]) == 1 |
---|
755 | |
---|
756 | # Now read in the parameters |
---|
757 | elif line.startswith('#C_'): |
---|
758 | toks = line.split('=') |
---|
759 | p = re.compile('#C_([0-9]+)') |
---|
760 | m = p.search(toks[0]) |
---|
761 | toks2 = toks[1].split('+-') |
---|
762 | i = int(m.group(1)) |
---|
763 | self.out[i] = float(toks2[0]) |
---|
764 | |
---|
765 | self.cov[i][i] = float(toks2[1]) |
---|
766 | |
---|
767 | except: |
---|
768 | msg = "Invertor.from_file: corrupted file\n%s" % sys.exc_value |
---|
769 | raise RuntimeError(msg) |
---|
770 | else: |
---|
771 | msg = "Invertor.from_file: '%s' is not a file" % str(path) |
---|
772 | raise RuntimeError(msg) |
---|