1 | """ |
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2 | This module implements invariant and its related computations. |
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3 | @author: Gervaise B. Alina/UTK |
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4 | """ |
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5 | #TODO: Need to decide if/how to use smearing for extrapolation |
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6 | import math |
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7 | import numpy |
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8 | |
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9 | from DataLoader.data_info import Data1D as LoaderData1D |
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10 | from DataLoader.qsmearing import smear_selection |
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11 | |
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12 | # The minimum q-value to be used when extrapolating |
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13 | Q_MINIMUM = 1e-5 |
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14 | |
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15 | # The maximum q-value to be used when extrapolating |
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16 | Q_MAXIMUM = 10 |
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17 | |
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18 | # Number of steps in the extrapolation |
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19 | INTEGRATION_NSTEPS = 1000 |
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20 | |
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21 | class Transform(object): |
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22 | """ |
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23 | Define interface that need to compute a function or an inverse |
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24 | function given some x, y |
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25 | """ |
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26 | |
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27 | def linearize_data(self, data): |
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28 | """ |
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29 | Linearize data so that a linear fit can be performed. |
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30 | Filter out the data that can't be transformed. |
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31 | @param data : LoadData1D instance |
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32 | """ |
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33 | # Check that the vector lengths are equal |
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34 | assert(len(data.x)==len(data.y)) |
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35 | if data.dy is not None: |
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36 | assert(len(data.x)==len(data.dy)) |
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37 | dy = data.dy |
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38 | else: |
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39 | #dy = numpy.array([math.sqrt(math.fabs(j)) for j in data.y]) |
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40 | dy = numpy.array([1 for j in data.y]) |
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41 | # Transform smear info |
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42 | dxl_out = None |
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43 | dxw_out = None |
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44 | dx_out = None |
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45 | first_x = data.x#[0] |
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46 | #if first_x == 0: |
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47 | # first_x = data.x[1] |
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48 | |
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49 | |
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50 | data_points = zip(data.x, data.y, dy) |
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51 | |
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52 | # Transform the data |
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53 | output_points = [(self.linearize_q_value(p[0]), |
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54 | math.log(p[1]), |
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55 | p[2]/p[1]) for p in data_points if p[0]>0 and p[1]>0] |
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56 | |
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57 | x_out, y_out, dy_out = zip(*output_points) |
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58 | |
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59 | #Transform smear info |
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60 | if data.dxl is not None and len(data.dxl)>0: |
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61 | dxl_out = self.linearize_dq_value(x=x_out, dx=data.dxl[:len(x_out)]) |
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62 | if data.dxw is not None and len(data.dxw)>0: |
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63 | dxw_out = self.linearize_dq_value(x=x_out, dx=data.dxw[:len(x_out)]) |
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64 | if data.dx is not None and len(data.dx)>0: |
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65 | dx_out = self.linearize_dq_value(x=x_out, dx=data.dx[:len(x_out)]) |
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66 | x_out = numpy.asarray(x_out) |
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67 | y_out = numpy.asarray(y_out) |
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68 | dy_out = numpy.asarray(dy_out) |
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69 | linear_data = LoaderData1D(x=x_out, y=y_out, dx=dx_out, dy=dy_out) |
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70 | linear_data.dxl = dxl_out |
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71 | linear_data.dxw = dxw_out |
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72 | |
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73 | return linear_data |
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74 | def linearize_dq_value(self, x, dx): |
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75 | """ |
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76 | Transform the input dq-value for linearization |
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77 | """ |
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78 | return NotImplemented |
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79 | |
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80 | def linearize_q_value(self, value): |
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81 | """ |
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82 | Transform the input q-value for linearization |
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83 | """ |
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84 | return NotImplemented |
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85 | |
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86 | def extract_model_parameters(self, a, b): |
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87 | """ |
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88 | set private member |
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89 | """ |
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90 | return NotImplemented |
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91 | |
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92 | def evaluate_model(self, x): |
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93 | """ |
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94 | Returns an array f(x) values where f is the Transform function. |
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95 | """ |
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96 | return NotImplemented |
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97 | |
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98 | class Guinier(Transform): |
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99 | """ |
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100 | class of type Transform that performs operations related to guinier |
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101 | function |
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102 | """ |
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103 | def __init__(self, scale=1, radius=60): |
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104 | Transform.__init__(self) |
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105 | self.scale = scale |
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106 | self.radius = radius |
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107 | |
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108 | def linearize_dq_value(self, x, dx): |
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109 | """ |
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110 | Transform the input dq-value for linearization |
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111 | """ |
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112 | return numpy.array([2*x[0]*dx[0] for i in xrange(len(x))]) |
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113 | |
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114 | def linearize_q_value(self, value): |
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115 | """ |
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116 | Transform the input q-value for linearization |
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117 | @param value: q-value |
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118 | @return: q*q |
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119 | """ |
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120 | return value * value |
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121 | |
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122 | def extract_model_parameters(self, a, b): |
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123 | """ |
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124 | assign new value to the scale and the radius |
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125 | """ |
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126 | b = math.sqrt(-3 * b) |
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127 | a = math.exp(a) |
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128 | self.scale = a |
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129 | self.radius = b |
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130 | return a, b |
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131 | |
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132 | def evaluate_model(self, x): |
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133 | """ |
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134 | return F(x)= scale* e-((radius*x)**2/3) |
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135 | """ |
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136 | return self._guinier(x) |
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137 | |
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138 | def _guinier(self, x): |
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139 | """ |
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140 | Retrive the guinier function after apply an inverse guinier function |
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141 | to x |
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142 | Compute a F(x) = scale* e-((radius*x)**2/3). |
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143 | @param x: a vector of q values |
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144 | @param scale: the scale value |
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145 | @param radius: the guinier radius value |
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146 | @return F(x) |
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147 | """ |
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148 | # transform the radius of coming from the inverse guinier function to a |
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149 | # a radius of a guinier function |
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150 | if self.radius <= 0: |
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151 | raise ValueError("Rg expected positive value, but got %s"%self.radius) |
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152 | value = numpy.array([math.exp(-((self.radius * i)**2/3)) for i in x ]) |
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153 | return self.scale * value |
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154 | |
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155 | class PowerLaw(Transform): |
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156 | """ |
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157 | class of type transform that perform operation related to power_law |
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158 | function |
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159 | """ |
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160 | def __init__(self, scale=1, power=4): |
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161 | Transform.__init__(self) |
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162 | self.scale = scale |
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163 | self.power = power |
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164 | |
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165 | def linearize_dq_value(self, x, dx): |
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166 | """ |
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167 | Transform the input dq-value for linearization |
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168 | """ |
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169 | return numpy.array([dx[0]/x[0] for i in xrange(len(x))]) |
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170 | |
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171 | def linearize_q_value(self, value): |
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172 | """ |
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173 | Transform the input q-value for linearization |
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174 | @param value: q-value |
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175 | @return: log(q) |
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176 | """ |
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177 | return math.log(value) |
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178 | |
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179 | def extract_model_parameters(self, a, b): |
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180 | """ |
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181 | Assign new value to the scale and the power |
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182 | """ |
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183 | b = -1 * b |
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184 | a = math.exp(a) |
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185 | self.power = b |
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186 | self.scale = a |
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187 | return a, b |
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188 | |
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189 | def evaluate_model(self, x): |
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190 | """ |
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191 | given a scale and a radius transform x, y using a power_law |
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192 | function |
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193 | """ |
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194 | return self._power_law(x) |
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195 | |
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196 | def _power_law(self, x): |
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197 | """ |
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198 | F(x) = scale* (x)^(-power) |
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199 | when power= 4. the model is porod |
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200 | else power_law |
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201 | The model has three parameters: |
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202 | @param x: a vector of q values |
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203 | @param power: power of the function |
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204 | @param scale : scale factor value |
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205 | @param F(x) |
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206 | """ |
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207 | if self.power <= 0: |
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208 | raise ValueError("Power_law function expected positive power, but got %s"%self.power) |
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209 | if self.scale <= 0: |
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210 | raise ValueError("scale expected positive value, but got %s"%self.scale) |
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211 | |
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212 | value = numpy.array([ math.pow(i, -self.power) for i in x ]) |
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213 | return self.scale * value |
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214 | |
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215 | class Extrapolator: |
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216 | """ |
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217 | Extrapolate I(q) distribution using a given model |
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218 | """ |
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219 | def __init__(self, data): |
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220 | """ |
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221 | Determine a and b given a linear equation y = ax + b |
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222 | @param Data: data containing x and y such as y = ax + b |
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223 | """ |
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224 | self.data = data |
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225 | |
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226 | # Set qmin as the lowest non-zero value |
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227 | self.qmin = Q_MINIMUM |
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228 | for q_value in self.data.x: |
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229 | if q_value > 0: |
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230 | self.qmin = q_value |
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231 | break |
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232 | self.qmax = max(self.data.x) |
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233 | |
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234 | #get the smear object of data |
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235 | self.smearer = smear_selection(self.data) |
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236 | # Set the q-range information to allow smearing |
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237 | self.set_fit_range() |
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238 | |
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239 | def set_fit_range(self, qmin=None, qmax=None): |
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240 | """ to set the fit range""" |
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241 | if qmin is not None: |
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242 | self.qmin = qmin |
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243 | if qmax is not None: |
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244 | self.qmax = qmax |
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245 | |
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246 | # Determine the range needed in unsmeared-Q to cover |
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247 | # the smeared Q range |
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248 | self._qmin_unsmeared = self.qmin |
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249 | self._qmax_unsmeared = self.qmax |
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250 | |
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251 | if self.smearer is not None: |
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252 | self._first_unsmeared_bin, self._last_unsmeared_bin = self.smearer.get_bin_range(self.qmin, self.qmax) |
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253 | self._qmin_unsmeared = self.data.x[self._first_unsmeared_bin] |
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254 | self._qmax_unsmeared = self.data.x[self._last_unsmeared_bin] |
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255 | |
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256 | # Identify the bin range for the unsmeared and smeared spaces |
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257 | self.idx = (self.data.x >= self.qmin) & (self.data.x <= self.qmax) |
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258 | self.idx_unsmeared = (self.data.x >= self._qmin_unsmeared) \ |
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259 | & (self.data.x <= self._qmax_unsmeared) |
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260 | |
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261 | def fit(self, power=None): |
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262 | """ |
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263 | Fit data for y = ax + b return a and b |
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264 | @param power = a fixed, otherwise None |
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265 | """ |
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266 | fx = numpy.zeros(len(self.data.x)) |
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267 | |
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268 | # Uncertainty |
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269 | if type(self.data.dy)==numpy.ndarray and len(self.data.dy)==len(self.data.x)and self.data.dy[0] != 0: |
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270 | sigma = self.data.dy |
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271 | else: |
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272 | sigma = numpy.ones(len(self.data.x)) |
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273 | |
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274 | # Compute theory data f(x) |
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275 | fx[self.idx_unsmeared] = self.data.y[self.idx_unsmeared] |
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276 | ## Smear theory data |
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277 | if self.smearer is not None: |
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278 | fx = self.smearer(fx, self._first_unsmeared_bin,self._last_unsmeared_bin) |
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279 | |
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280 | fx[self.idx_unsmeared] = fx[self.idx_unsmeared]/sigma[self.idx_unsmeared] |
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281 | |
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282 | ##power is given only for function = power_law |
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283 | if power != None: |
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284 | sigma2 = sigma * sigma |
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285 | a = -(power) |
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286 | b = (numpy.sum(fx[self.idx]/sigma[self.idx]) - a*numpy.sum(self.data.x[self.idx]/sigma2[self.idx]))/numpy.sum(numpy.ones(len(sigma2[self.idx]))/sigma2[self.idx]) |
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287 | return a, b |
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288 | else: |
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289 | A = numpy.vstack([ self.data.x[self.idx]/sigma[self.idx], |
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290 | numpy.ones(len(self.data.x[self.idx]))/sigma[self.idx]]).T |
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291 | |
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292 | a, b = numpy.linalg.lstsq(A, fx[self.idx])[0] |
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293 | |
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294 | return a, b |
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295 | |
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296 | |
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297 | class InvariantCalculator(object): |
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298 | """ |
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299 | Compute invariant if data is given. |
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300 | Can provide volume fraction and surface area if the user provides |
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301 | Porod constant and contrast values. |
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302 | @precondition: the user must send a data of type DataLoader.Data1D |
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303 | the user provide background and scale values. |
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304 | |
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305 | @note: Some computations depends on each others. |
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306 | """ |
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307 | def __init__(self, data, background=0, scale=1 ): |
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308 | """ |
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309 | Initialize variables |
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310 | @param data: data must be of type DataLoader.Data1D |
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311 | @param background: Background value. The data will be corrected before processing |
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312 | @param scale: Scaling factor for I(q). The data will be corrected before processing |
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313 | """ |
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314 | # Background and scale should be private data member if the only way to |
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315 | # change them are by instantiating a new object. |
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316 | self._background = background |
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317 | self._scale = scale |
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318 | |
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319 | # The data should be private |
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320 | self._data = self._get_data(data) |
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321 | |
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322 | # Since there are multiple variants of Q*, you should force the |
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323 | # user to use the get method and keep Q* a private data member |
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324 | self._qstar = None |
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325 | |
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326 | # You should keep the error on Q* so you can reuse it without |
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327 | # recomputing the whole thing. |
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328 | self._qstar_err = 0 |
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329 | |
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330 | # Extrapolation parameters |
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331 | self._low_extrapolation_npts = 4 |
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332 | self._low_extrapolation_function = Guinier() |
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333 | self._low_extrapolation_power = None |
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334 | |
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335 | self._high_extrapolation_npts = 4 |
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336 | self._high_extrapolation_function = PowerLaw() |
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337 | self._high_extrapolation_power = None |
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338 | |
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339 | def _get_data(self, data): |
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340 | """ |
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341 | @note this function must be call before computing any type |
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342 | of invariant |
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343 | @return data= self._scale *data - self._background |
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344 | """ |
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345 | if not issubclass(data.__class__, LoaderData1D): |
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346 | #Process only data that inherited from DataLoader.Data_info.Data1D |
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347 | raise ValueError,"Data must be of type DataLoader.Data1D" |
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348 | new_data = (self._scale * data) - self._background |
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349 | new_data.dy[new_data.dy==0] = 1 |
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350 | new_data.dxl = data.dxl |
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351 | new_data.dxw = data.dxw |
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352 | return new_data |
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353 | |
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354 | def _fit(self, model, qmin=Q_MINIMUM, qmax=Q_MAXIMUM, power=None): |
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355 | """ |
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356 | fit data with function using |
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357 | data= self._get_data() |
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358 | fx= Functor(data , function) |
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359 | y = data.y |
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360 | slope, constant = linalg.lstsq(y,fx) |
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361 | @param qmin: data first q value to consider during the fit |
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362 | @param qmax: data last q value to consider during the fit |
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363 | @param power : power value to consider for power-law |
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364 | @param function: the function to use during the fit |
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365 | @return a: the scale of the function |
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366 | @return b: the other parameter of the function for guinier will be radius |
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367 | for power_law will be the power value |
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368 | """ |
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369 | # Linearize the data in preparation for fitting |
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370 | fit_data = model.linearize_data(self._data) |
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371 | qmin = model.linearize_q_value(qmin) |
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372 | qmax = model.linearize_q_value(qmax) |
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373 | # Get coefficient cmoning out of the fit |
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374 | extrapolator = Extrapolator(data=fit_data) |
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375 | extrapolator.set_fit_range(qmin=qmin, qmax=qmax) |
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376 | b, a = extrapolator.fit(power=power) |
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377 | |
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378 | return model.extract_model_parameters(a=a, b=b) |
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379 | |
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380 | def _get_qstar(self, data): |
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381 | """ |
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382 | Compute invariant for data |
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383 | @param data: data to use to compute invariant. |
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384 | |
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385 | """ |
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386 | if data is None: |
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387 | return 0 |
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388 | if data.is_slit_smeared(): |
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389 | return self._get_qstar_smear(data) |
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390 | else: |
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391 | return self._get_qstar_unsmear(data) |
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392 | |
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393 | def _get_qstar_unsmear(self, data): |
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394 | """ |
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395 | Compute invariant for pinhole data. |
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396 | This invariant is given by: |
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397 | |
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398 | q_star = x0**2 *y0 *dx0 +x1**2 *y1 *dx1 |
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399 | + ..+ xn**2 *yn *dxn |
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400 | |
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401 | where n >= len(data.x)-1 |
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402 | dxi = 1/2*(xi+1 - xi) + (xi - xi-1) |
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403 | dx0 = (x1 - x0)/2 |
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404 | dxn = (xn - xn-1)/2 |
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405 | @param data: the data to use to compute invariant. |
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406 | @return q_star: invariant value for pinhole data. q_star > 0 |
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407 | """ |
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408 | if len(data.x) <= 1 or len(data.y) <= 1 or len(data.x)!= len(data.y): |
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409 | msg = "Length x and y must be equal" |
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410 | msg += " and greater than 1; got x=%s, y=%s"%(len(data.x), len(data.y)) |
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411 | raise ValueError, msg |
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412 | else: |
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413 | n = len(data.x)- 1 |
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414 | #compute the first delta q |
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415 | dx0 = (data.x[1] - data.x[0])/2 |
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416 | #compute the last delta q |
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417 | dxn = (data.x[n] - data.x[n-1])/2 |
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418 | sum = 0 |
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419 | sum += data.x[0] * data.x[0] * data.y[0] * dx0 |
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420 | sum += data.x[n] * data.x[n] * data.y[n] * dxn |
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421 | |
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422 | if len(data.x) == 2: |
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423 | return sum |
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424 | else: |
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425 | #iterate between for element different from the first and the last |
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426 | for i in xrange(1, n-1): |
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427 | dxi = (data.x[i+1] - data.x[i-1])/2 |
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428 | sum += data.x[i] * data.x[i] * data.y[i] * dxi |
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429 | return sum |
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430 | |
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431 | def _get_qstar_smear(self, data): |
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432 | """ |
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433 | Compute invariant for slit-smeared data. |
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434 | This invariant is given by: |
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435 | q_star = x0*dxl *y0*dx0 + x1*dxl *y1 *dx1 |
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436 | + ..+ xn*dxl *yn *dxn |
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437 | where n >= len(data.x)-1 |
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438 | dxi = 1/2*(xi+1 - xi) + (xi - xi-1) |
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439 | dx0 = (x1 - x0)/2 |
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440 | dxn = (xn - xn-1)/2 |
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441 | dxl: slit smear value |
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442 | |
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443 | @return q_star: invariant value for slit smeared data. |
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444 | """ |
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445 | if not data.is_slit_smeared(): |
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446 | msg = "_get_qstar_smear need slit smear data " |
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447 | msg += "Hint :dxl= %s , dxw= %s"%(str(data.dxl), str(data.dxw)) |
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448 | raise ValueError, msg |
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449 | |
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450 | if len(data.x) <= 1 or len(data.y) <= 1 or len(data.x) != len(data.y)\ |
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451 | or len(data.x)!= len(data.dxl): |
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452 | msg = "x, dxl, and y must be have the same length and greater than 1" |
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453 | msg +=" len x=%s, y=%s, dxl=%s"%(len(data.x),len(data.y),len(data.dxl)) |
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454 | raise ValueError, msg |
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455 | else: |
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456 | n = len(data.x)-1 |
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457 | #compute the first delta |
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458 | dx0 = (data.x[1] - data.x[0])/2 |
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459 | #compute the last delta |
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460 | dxn = (data.x[n] - data.x[n-1])/2 |
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461 | sum = 0 |
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462 | sum += data.x[0] * data.dxl[0] * data.y[0] * dx0 |
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463 | sum += data.x[n] * data.dxl[n] * data.y[n] * dxn |
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464 | |
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465 | if len(data.x)==2: |
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466 | return sum |
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467 | else: |
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468 | #iterate between for element different from the first and the last |
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469 | for i in xrange(1, n-1): |
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470 | dxi = (data.x[i+1] - data.x[i-1])/2 |
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471 | sum += data.x[i] * data.dxl[i] * data.y[i] * dxi |
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472 | return sum |
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473 | |
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474 | def _get_qstar_uncertainty(self, data=None): |
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475 | """ |
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476 | Compute uncertainty of invariant value |
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477 | Implementation: |
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478 | if data is None: |
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479 | data = self.data |
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480 | |
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481 | if data.slit smear: |
---|
482 | return self._get_qstar_smear_uncertainty(data) |
---|
483 | else: |
---|
484 | return self._get_qstar_unsmear_uncertainty(data) |
---|
485 | |
---|
486 | @param: data use to compute the invariant which allow uncertainty |
---|
487 | computation. |
---|
488 | @return: uncertainty |
---|
489 | """ |
---|
490 | if data is None: |
---|
491 | data = self._data |
---|
492 | if data.is_slit_smeared(): |
---|
493 | return self._get_qstar_smear_uncertainty(data) |
---|
494 | else: |
---|
495 | return self._get_qstar_unsmear_uncertainty(data) |
---|
496 | |
---|
497 | def _get_qstar_unsmear_uncertainty(self, data): |
---|
498 | """ |
---|
499 | Compute invariant uncertainty with with pinhole data. |
---|
500 | This uncertainty is given as follow: |
---|
501 | dq_star = math.sqrt[(x0**2*(dy0)*dx0)**2 + |
---|
502 | (x1**2 *(dy1)*dx1)**2 + ..+ (xn**2 *(dyn)*dxn)**2 ] |
---|
503 | where n >= len(data.x)-1 |
---|
504 | dxi = 1/2*(xi+1 - xi) + (xi - xi-1) |
---|
505 | dx0 = (x1 - x0)/2 |
---|
506 | dxn = (xn - xn-1)/2 |
---|
507 | dyn: error on dy |
---|
508 | |
---|
509 | @param data: |
---|
510 | note: if data doesn't contain dy assume dy= math.sqrt(data.y) |
---|
511 | """ |
---|
512 | if len(data.x) <= 1 or len(data.y) <= 1 or \ |
---|
513 | len(self.data.x) != len(self.data.y): |
---|
514 | msg = "Length of data.x and data.y must be equal" |
---|
515 | msg += " and greater than 1; got x=%s, y=%s"%(len(data.x), |
---|
516 | len(data.y)) |
---|
517 | raise ValueError, msg |
---|
518 | else: |
---|
519 | #Create error for data without dy error |
---|
520 | if (data.dy is None) or (not data.dy): |
---|
521 | dy = math.sqrt(y) |
---|
522 | else: |
---|
523 | dy = data.dy |
---|
524 | |
---|
525 | n = len(data.x) - 1 |
---|
526 | #compute the first delta |
---|
527 | dx0 = (data.x[1] - data.x[0])/2 |
---|
528 | #compute the last delta |
---|
529 | dxn= (data.x[n] - data.x[n-1])/2 |
---|
530 | sum = 0 |
---|
531 | sum += (data.x[0] * data.x[0] * dy[0] * dx0)**2 |
---|
532 | sum += (data.x[n] * data.x[n] * dy[n] * dxn)**2 |
---|
533 | if len(data.x) == 2: |
---|
534 | return math.sqrt(sum) |
---|
535 | else: |
---|
536 | #iterate between for element different from the first and the last |
---|
537 | for i in xrange(1, n-1): |
---|
538 | dxi = (data.x[i+1] - data.x[i-1])/2 |
---|
539 | sum += (data.x[i] * data.x[i] * dy[i] * dxi)**2 |
---|
540 | return math.sqrt(sum) |
---|
541 | |
---|
542 | def _get_qstar_smear_uncertainty(self, data): |
---|
543 | """ |
---|
544 | Compute invariant uncertainty with slit smeared data. |
---|
545 | This uncertainty is given as follow: |
---|
546 | dq_star = x0*dxl *dy0 *dx0 + x1*dxl *dy1 *dx1 |
---|
547 | + ..+ xn*dxl *dyn *dxn |
---|
548 | where n >= len(data.x)-1 |
---|
549 | dxi = 1/2*(xi+1 - xi) + (xi - xi-1) |
---|
550 | dx0 = (x1 - x0)/2 |
---|
551 | dxn = (xn - xn-1)/2 |
---|
552 | dxl: slit smearing value |
---|
553 | dyn : error on dy |
---|
554 | @param data: data of type Data1D where the scale is applied |
---|
555 | and the background is subtracted. |
---|
556 | |
---|
557 | note: if data doesn't contain dy assume dy= math.sqrt(data.y) |
---|
558 | """ |
---|
559 | if not data.is_slit_smeared(): |
---|
560 | msg = "_get_qstar_smear_uncertainty need slit smear data " |
---|
561 | msg += "Hint :dxl= %s , dxw= %s"%(str(data.dxl), str(data.dxw)) |
---|
562 | raise ValueError, msg |
---|
563 | |
---|
564 | if len(data.x) <= 1 or len(data.y) <= 1 or len(data.x) != len(data.y)\ |
---|
565 | or len(data.x) != len(data.dxl): |
---|
566 | msg = "x, dxl, and y must be have the same length and greater than 1" |
---|
567 | raise ValueError, msg |
---|
568 | else: |
---|
569 | #Create error for data without dy error |
---|
570 | if (data.dy is None) or (not data.dy): |
---|
571 | dy = math.sqrt(y) |
---|
572 | else: |
---|
573 | dy = data.dy |
---|
574 | |
---|
575 | n = len(data.x) - 1 |
---|
576 | #compute the first delta |
---|
577 | dx0 = (data.x[1] - data.x[0])/2 |
---|
578 | #compute the last delta |
---|
579 | dxn = (data.x[n] - data.x[n-1])/2 |
---|
580 | sum = 0 |
---|
581 | sum += (data.x[0] * data.dxl[0] * dy[0] * dx0)**2 |
---|
582 | sum += (data.x[n] * data.dxl[n] * dy[n] * dxn)**2 |
---|
583 | |
---|
584 | if len(data.x) == 2: |
---|
585 | return math.sqrt(sum) |
---|
586 | else: |
---|
587 | #iterate between for element different from the first and the last |
---|
588 | for i in xrange(1, n-1): |
---|
589 | dxi = (data.x[i+1] - data.x[i-1])/2 |
---|
590 | sum += (data.x[i] * data.dxl[i] * dy[i] * dxi)**2 |
---|
591 | return math.sqrt(sum) |
---|
592 | |
---|
593 | def _get_extrapolated_data(self, model, npts=INTEGRATION_NSTEPS, |
---|
594 | q_start=Q_MINIMUM, q_end=Q_MAXIMUM): |
---|
595 | """ |
---|
596 | @return extrapolate data create from data |
---|
597 | """ |
---|
598 | #create new Data1D to compute the invariant |
---|
599 | q = numpy.linspace(start=q_start, |
---|
600 | stop=q_end, |
---|
601 | num=npts, |
---|
602 | endpoint=True) |
---|
603 | iq = model.evaluate_model(q) |
---|
604 | |
---|
605 | # Determine whether we are extrapolating to high or low q-values |
---|
606 | # If the data is slit smeared, get the index of the slit dimension array entry |
---|
607 | # that we will use to smear the extrapolated data. |
---|
608 | dxl = None |
---|
609 | dxw = None |
---|
610 | |
---|
611 | if self._data.is_slit_smeared(): |
---|
612 | if q_start<min(self._data.x): |
---|
613 | smear_index = 0 |
---|
614 | elif q_end>max(self._data.x): |
---|
615 | smear_index = len(self._data.x)-1 |
---|
616 | else: |
---|
617 | raise RuntimeError, "Extrapolation can only be evaluated for points outside the data Q range" |
---|
618 | |
---|
619 | if self._data.dxl is not None : |
---|
620 | dxl = numpy.ones(INTEGRATION_NSTEPS) |
---|
621 | dxl = dxl * self._data.dxl[smear_index] |
---|
622 | |
---|
623 | if self._data.dxw is not None : |
---|
624 | dxw = numpy.ones(INTEGRATION_NSTEPS) |
---|
625 | dxw = dxw * self._data.dxw[smear_index] |
---|
626 | |
---|
627 | result_data = LoaderData1D(x=q, y=iq) |
---|
628 | result_data.dxl = dxl |
---|
629 | result_data.dxw = dxw |
---|
630 | return result_data |
---|
631 | |
---|
632 | def _get_extra_data_low(self): |
---|
633 | """ |
---|
634 | This method creates a new data set from the invariant calculator. |
---|
635 | |
---|
636 | It will use the extrapolation parameters kept as private data members. |
---|
637 | |
---|
638 | self._low_extrapolation_npts is the number of data points to use in to fit. |
---|
639 | self._low_extrapolation_function will be used as the fit function. |
---|
640 | |
---|
641 | |
---|
642 | |
---|
643 | It takes npts first points of data, fits them with a given model |
---|
644 | then uses the new parameters resulting from the fit to create a new data set. |
---|
645 | |
---|
646 | The new data first point is Q_MINIMUM. |
---|
647 | |
---|
648 | The last point of the new data is the first point of the original data. |
---|
649 | the number of q points of this data is INTEGRATION_NSTEPS. |
---|
650 | |
---|
651 | @return: a new data of type Data1D |
---|
652 | """ |
---|
653 | |
---|
654 | # Data boundaries for fitting |
---|
655 | qmin = self._data.x[0] |
---|
656 | qmax = self._data.x[self._low_extrapolation_npts - 1] |
---|
657 | |
---|
658 | # Extrapolate the low-Q data |
---|
659 | a, b = self._fit(model=self._low_extrapolation_function, |
---|
660 | qmin=qmin, |
---|
661 | qmax=qmax, |
---|
662 | power=self._low_extrapolation_power) |
---|
663 | q_start = Q_MINIMUM |
---|
664 | #q_start point |
---|
665 | if Q_MINIMUM >= qmin: |
---|
666 | q_start = qmin/10 |
---|
667 | |
---|
668 | data_min = self._get_extrapolated_data(model=self._low_extrapolation_function, |
---|
669 | npts=INTEGRATION_NSTEPS, |
---|
670 | q_start=q_start, q_end=qmin) |
---|
671 | return data_min |
---|
672 | |
---|
673 | def _get_extra_data_high(self): |
---|
674 | """ |
---|
675 | This method creates a new data from the invariant calculator. |
---|
676 | |
---|
677 | It takes npts last points of data, fits them with a given model |
---|
678 | (for this function only power_law will be use), then uses |
---|
679 | the new parameters resulting from the fit to create a new data set. |
---|
680 | The first point is the last point of data. |
---|
681 | The last point of the new data is Q_MAXIMUM. |
---|
682 | The number of q points of this data is INTEGRATION_NSTEPS. |
---|
683 | |
---|
684 | |
---|
685 | @return: a new data of type Data1D |
---|
686 | """ |
---|
687 | # Data boundaries for fitting |
---|
688 | x_len = len(self._data.x) - 1 |
---|
689 | qmin = self._data.x[x_len - (self._high_extrapolation_npts - 1)] |
---|
690 | qmax = self._data.x[x_len] |
---|
691 | q_end = Q_MAXIMUM |
---|
692 | |
---|
693 | # fit the data with a model to get the appropriate parameters |
---|
694 | a, b = self._fit(model=self._high_extrapolation_function, |
---|
695 | qmin=qmin, |
---|
696 | qmax=qmax, |
---|
697 | power=self._high_extrapolation_power) |
---|
698 | |
---|
699 | #create new Data1D to compute the invariant |
---|
700 | data_max = self._get_extrapolated_data(model=self._high_extrapolation_function, |
---|
701 | npts=INTEGRATION_NSTEPS, |
---|
702 | q_start=qmax, q_end=q_end) |
---|
703 | return data_max |
---|
704 | |
---|
705 | def get_qstar_low(self): |
---|
706 | """ |
---|
707 | Compute the invariant for extrapolated data at low q range. |
---|
708 | |
---|
709 | Implementation: |
---|
710 | data = self._get_extra_data_low() |
---|
711 | return self._get_qstar() |
---|
712 | |
---|
713 | @return q_star: the invariant for data extrapolated at low q. |
---|
714 | """ |
---|
715 | data = self._get_extra_data_low() |
---|
716 | |
---|
717 | return self._get_qstar(data=data) |
---|
718 | |
---|
719 | def get_qstar_high(self): |
---|
720 | """ |
---|
721 | Compute the invariant for extrapolated data at high q range. |
---|
722 | |
---|
723 | Implementation: |
---|
724 | data = self._get_extra_data_high() |
---|
725 | return self._get_qstar() |
---|
726 | |
---|
727 | @return q_star: the invariant for data extrapolated at high q. |
---|
728 | """ |
---|
729 | data = self._get_extra_data_high() |
---|
730 | return self._get_qstar(data=data) |
---|
731 | |
---|
732 | def get_extra_data_low(self, npts_in=None, q_start=Q_MINIMUM, nsteps=INTEGRATION_NSTEPS): |
---|
733 | """ |
---|
734 | This method generates 2 data sets , the first is a data created during |
---|
735 | low extrapolation . its y is generated from x in [ Q_MINIMUM - the minimum of |
---|
736 | data.x] and the outputs of the extrapolator . |
---|
737 | (data is the data used to compute invariant) |
---|
738 | the second is also data produced during the fit but the x range considered |
---|
739 | is within the reel range of data x. |
---|
740 | x uses is in [minimum of data.x up to npts_in points] |
---|
741 | @param npts_in: the number of first points of data to consider for computing |
---|
742 | y's coming out of the fit. |
---|
743 | @param q_start: is the minimum value to uses for extrapolated data |
---|
744 | @param npts: the number of point used to create extrapolated data |
---|
745 | |
---|
746 | """ |
---|
747 | #Create a data from result of the fit for a range outside of the data |
---|
748 | # at low q range |
---|
749 | data_out_range = self._get_extra_data_low() |
---|
750 | |
---|
751 | if q_start != Q_MINIMUM or nsteps != INTEGRATION_NSTEPS: |
---|
752 | qmin = min(self._data.x) |
---|
753 | if q_start < Q_MINIMUM: |
---|
754 | q_start = Q_MINIMUM |
---|
755 | elif q_start >= qmin: |
---|
756 | q_start = qmin/10 |
---|
757 | |
---|
758 | #compute the new data with the proper result of the fit for different |
---|
759 | #boundary and step, outside of data |
---|
760 | data_out_range = self._get_extrapolated_data(model=self._low_extrapolation_function, |
---|
761 | npts=nsteps, |
---|
762 | q_start=q_start, q_end=qmin) |
---|
763 | #Create data from the result of the fit for a range inside data q range for |
---|
764 | #low q |
---|
765 | if npts_in is None : |
---|
766 | npts_in = self._low_extrapolation_npts |
---|
767 | |
---|
768 | x = self._data.x[:npts_in] |
---|
769 | y = self._low_extrapolation_function.evaluate_model(x=x) |
---|
770 | dy = None |
---|
771 | dx = None |
---|
772 | dxl = None |
---|
773 | dxw = None |
---|
774 | if self._data.dx is not None: |
---|
775 | dx = self._data.dx[:npts_in] |
---|
776 | if self._data.dy is not None: |
---|
777 | dy = self._data.dy[:npts_in] |
---|
778 | if self._data.dxl is not None and len(self._data.dxl)>0: |
---|
779 | dxl = self._data.dxl[:npts_in] |
---|
780 | if self._data.dxw is not None and len(self._data.dxw)>0: |
---|
781 | dxw = self._data.dxw[:npts_in] |
---|
782 | #Crate new data |
---|
783 | data_in_range = LoaderData1D(x=x, y=y, dx=dx, dy=dy) |
---|
784 | data_in_range.clone_without_data(clone=self._data) |
---|
785 | data_in_range.dxl = dxl |
---|
786 | data_in_range.dxw = dxw |
---|
787 | |
---|
788 | return data_out_range, data_in_range |
---|
789 | |
---|
790 | def get_extra_data_high(self, npts_in=None, q_end=Q_MAXIMUM, nsteps=INTEGRATION_NSTEPS ): |
---|
791 | """ |
---|
792 | This method generates 2 data sets , the first is a data created during |
---|
793 | low extrapolation . its y is generated from x in [ the maximum of |
---|
794 | data.x to Q_MAXIMUM] and the outputs of the extrapolator . |
---|
795 | (data is the data used to compute invariant) |
---|
796 | the second is also data produced during the fit but the x range considered |
---|
797 | is within the reel range of data x. |
---|
798 | x uses is from maximum of data.x up to npts_in points before data.x maximum. |
---|
799 | @param npts_in: the number of first points of data to consider for computing |
---|
800 | y's coming out of the fit. |
---|
801 | @param q_end: is the maximum value to uses for extrapolated data |
---|
802 | @param npts: the number of point used to create extrapolated data |
---|
803 | |
---|
804 | """ |
---|
805 | #Create a data from result of the fit for a range outside of the data |
---|
806 | # at low q range |
---|
807 | data_out_range = self._get_extra_data_high() |
---|
808 | qmax = max(self._data.x) |
---|
809 | if q_end != Q_MAXIMUM or nsteps != INTEGRATION_NSTEPS: |
---|
810 | if q_end > Q_MAXIMUM: |
---|
811 | q_end = Q_MAXIMUM |
---|
812 | elif q_end <= qmax: |
---|
813 | q_end = qmax * 10 |
---|
814 | |
---|
815 | #compute the new data with the proper result of the fit for different |
---|
816 | #boundary and step, outside of data |
---|
817 | data_out_range = self._get_extrapolated_data(model=self._high_extrapolation_function, |
---|
818 | npts=nsteps, |
---|
819 | q_start=qmax, q_end=q_end) |
---|
820 | #Create data from the result of the fit for a range inside data q range for |
---|
821 | #high q |
---|
822 | if npts_in is None : |
---|
823 | npts_in = self._high_extrapolation_npts |
---|
824 | |
---|
825 | x_len = len(self._data.x) |
---|
826 | x = self._data.x[(x_len-npts_in):] |
---|
827 | y = self._high_extrapolation_function.evaluate_model(x=x) |
---|
828 | dy = None |
---|
829 | dx = None |
---|
830 | dxl = None |
---|
831 | dxw = None |
---|
832 | |
---|
833 | if self._data.dx is not None: |
---|
834 | dx = self._data.dx[(x_len-npts_in):] |
---|
835 | if self._data.dy is not None: |
---|
836 | dy = self._data.dy[(x_len-npts_in):] |
---|
837 | if self._data.dxl is not None and len(self._data.dxl)>0: |
---|
838 | dxl = self._data.dxl[(x_len-npts_in):] |
---|
839 | if self._data.dxw is not None and len(self._data.dxw)>0: |
---|
840 | dxw = self._data.dxw[(x_len-npts_in):] |
---|
841 | #Crate new data |
---|
842 | data_in_range = LoaderData1D(x=x, y=y, dx=dx, dy=dy) |
---|
843 | data_in_range.clone_without_data(clone=self._data) |
---|
844 | data_in_range.dxl = dxl |
---|
845 | data_in_range.dxw = dxw |
---|
846 | |
---|
847 | return data_out_range, data_in_range |
---|
848 | |
---|
849 | |
---|
850 | def set_extrapolation(self, range, npts=4, function=None, power=None): |
---|
851 | """ |
---|
852 | Set the extrapolation parameters for the high or low Q-range. |
---|
853 | Note that this does not turn extrapolation on or off. |
---|
854 | @param range: a keyword set the type of extrapolation . type string |
---|
855 | @param npts: the numbers of q points of data to consider for extrapolation |
---|
856 | @param function: a keyword to select the function to use for extrapolation. |
---|
857 | of type string. |
---|
858 | @param power: an power to apply power_low function |
---|
859 | |
---|
860 | """ |
---|
861 | range = range.lower() |
---|
862 | if range not in ['high', 'low']: |
---|
863 | raise ValueError, "Extrapolation range should be 'high' or 'low'" |
---|
864 | function = function.lower() |
---|
865 | if function not in ['power_law', 'guinier']: |
---|
866 | raise ValueError, "Extrapolation function should be 'guinier' or 'power_law'" |
---|
867 | |
---|
868 | if range == 'high': |
---|
869 | if function != 'power_law': |
---|
870 | raise ValueError, "Extrapolation only allows a power law at high Q" |
---|
871 | self._high_extrapolation_npts = npts |
---|
872 | self._high_extrapolation_power = power |
---|
873 | else: |
---|
874 | if function == 'power_law': |
---|
875 | self._low_extrapolation_function = PowerLaw() |
---|
876 | else: |
---|
877 | self._low_extrapolation_function = Guinier() |
---|
878 | self._low_extrapolation_npts = npts |
---|
879 | self._low_extrapolation_power = power |
---|
880 | |
---|
881 | def get_qstar(self, extrapolation=None): |
---|
882 | """ |
---|
883 | Compute the invariant of the local copy of data. |
---|
884 | Implementation: |
---|
885 | if slit smear: |
---|
886 | qstar_0 = self._get_qstar_smear() |
---|
887 | else: |
---|
888 | qstar_0 = self._get_qstar_unsmear() |
---|
889 | if extrapolation is None: |
---|
890 | return qstar_0 |
---|
891 | if extrapolation==low: |
---|
892 | return qstar_0 + self.get_qstar_low() |
---|
893 | elif extrapolation==high: |
---|
894 | return qstar_0 + self.get_qstar_high() |
---|
895 | elif extrapolation==both: |
---|
896 | return qstar_0 + self.get_qstar_low() + self.get_qstar_high() |
---|
897 | |
---|
898 | @param extrapolation: string to apply optional extrapolation |
---|
899 | @return q_star: invariant of the data within data's q range |
---|
900 | |
---|
901 | @warning: When using setting data to Data1D , the user is responsible of |
---|
902 | checking that the scale and the background are properly apply to the data |
---|
903 | |
---|
904 | @warning: if error occur self.get_qstar_low() or self.get_qstar_low() |
---|
905 | their returned value will be ignored |
---|
906 | """ |
---|
907 | qstar_0 = self._get_qstar(data=self._data) |
---|
908 | |
---|
909 | if extrapolation is None: |
---|
910 | self._qstar = qstar_0 |
---|
911 | return self._qstar |
---|
912 | # Compute invariant plus invaraint of extrapolated data |
---|
913 | extrapolation = extrapolation.lower() |
---|
914 | if extrapolation == "low": |
---|
915 | self._qstar = qstar_0 + self.get_qstar_low() |
---|
916 | return self._qstar |
---|
917 | elif extrapolation == "high": |
---|
918 | self._qstar = qstar_0 + self.get_qstar_high() |
---|
919 | return self._qstar |
---|
920 | elif extrapolation == "both": |
---|
921 | self._qstar = qstar_0 + self.get_qstar_low() + self.get_qstar_high() |
---|
922 | return self._qstar |
---|
923 | |
---|
924 | def get_surface(self,contrast, porod_const): |
---|
925 | """ |
---|
926 | Compute the surface of the data. |
---|
927 | |
---|
928 | Implementation: |
---|
929 | V= self.get_volume_fraction(contrast) |
---|
930 | |
---|
931 | Compute the surface given by: |
---|
932 | surface = (2*pi *V(1- V)*porod_const)/ q_star |
---|
933 | |
---|
934 | @param contrast: contrast value to compute the volume |
---|
935 | @param porod_const: Porod constant to compute the surface |
---|
936 | @return: specific surface |
---|
937 | """ |
---|
938 | if contrast is None or porod_const is None: |
---|
939 | return None |
---|
940 | #Check whether we have Q star |
---|
941 | if self._qstar is None: |
---|
942 | self._qstar = self.get_star() |
---|
943 | if self._qstar == 0: |
---|
944 | raise RuntimeError("Cannot compute surface, invariant value is zero") |
---|
945 | # Compute the volume |
---|
946 | volume = self.get_volume_fraction(contrast) |
---|
947 | return 2 * math.pi * volume *(1 - volume) * float(porod_const)/self._qstar |
---|
948 | |
---|
949 | def get_volume_fraction(self, contrast): |
---|
950 | """ |
---|
951 | Compute volume fraction is deduced as follow: |
---|
952 | |
---|
953 | q_star = 2*(pi*contrast)**2* volume( 1- volume) |
---|
954 | for k = 10^(-8)*q_star/(2*(pi*|contrast|)**2) |
---|
955 | we get 2 values of volume: |
---|
956 | with 1 - 4 * k >= 0 |
---|
957 | volume1 = (1- sqrt(1- 4*k))/2 |
---|
958 | volume2 = (1+ sqrt(1- 4*k))/2 |
---|
959 | |
---|
960 | q_star: the invariant value included extrapolation is applied |
---|
961 | unit 1/A^(3)*1/cm |
---|
962 | q_star = self.get_qstar() |
---|
963 | |
---|
964 | the result returned will be 0<= volume <= 1 |
---|
965 | |
---|
966 | @param contrast: contrast value provides by the user of type float. |
---|
967 | contrast unit is 1/A^(2)= 10^(16)cm^(2) |
---|
968 | @return: volume fraction |
---|
969 | @note: volume fraction must have no unit |
---|
970 | """ |
---|
971 | if contrast is None: |
---|
972 | return None |
---|
973 | if contrast < 0: |
---|
974 | raise ValueError, "contrast must be greater than zero" |
---|
975 | |
---|
976 | if self._qstar is None: |
---|
977 | self._qstar = self.get_qstar() |
---|
978 | |
---|
979 | if self._qstar < 0: |
---|
980 | raise RuntimeError, "invariant must be greater than zero" |
---|
981 | |
---|
982 | # Compute intermediate constant |
---|
983 | k = 1.e-8 * self._qstar/(2 * (math.pi * math.fabs(float(contrast)))**2) |
---|
984 | #Check discriminant value |
---|
985 | discrim = 1 - 4 * k |
---|
986 | |
---|
987 | # Compute volume fraction |
---|
988 | if discrim < 0: |
---|
989 | raise RuntimeError, "could not compute the volume fraction: negative discriminant" |
---|
990 | elif discrim == 0: |
---|
991 | return 1/2 |
---|
992 | else: |
---|
993 | volume1 = 0.5 * (1 - math.sqrt(discrim)) |
---|
994 | volume2 = 0.5 * (1 + math.sqrt(discrim)) |
---|
995 | |
---|
996 | if 0 <= volume1 and volume1 <= 1: |
---|
997 | return volume1 |
---|
998 | elif 0 <= volume2 and volume2 <= 1: |
---|
999 | return volume2 |
---|
1000 | raise RuntimeError, "could not compute the volume fraction: inconsistent results" |
---|
1001 | |
---|
1002 | def get_qstar_with_error(self, extrapolation=None): |
---|
1003 | """ |
---|
1004 | Compute the invariant uncertainty. |
---|
1005 | This uncertainty computation depends on whether or not the data is |
---|
1006 | smeared. |
---|
1007 | @return: invariant, the invariant uncertainty |
---|
1008 | return self._get_qstar(), self._get_qstar_smear_uncertainty() |
---|
1009 | """ |
---|
1010 | if self._qstar is None: |
---|
1011 | self._qstar = self.get_qstar(extrapolation=extrapolation) |
---|
1012 | if self._qstar_err is None: |
---|
1013 | self._qstar_err = self._get_qstar_smear_uncertainty() |
---|
1014 | |
---|
1015 | return self._qstar, self._qstar_err |
---|
1016 | |
---|
1017 | def get_volume_fraction_with_error(self, contrast): |
---|
1018 | """ |
---|
1019 | Compute uncertainty on volume value as well as the volume fraction |
---|
1020 | This uncertainty is given by the following equation: |
---|
1021 | dV = 0.5 * (4*k* dq_star) /(2* math.sqrt(1-k* q_star)) |
---|
1022 | |
---|
1023 | for k = 10^(-8)*q_star/(2*(pi*|contrast|)**2) |
---|
1024 | |
---|
1025 | q_star: the invariant value including extrapolated value if existing |
---|
1026 | dq_star: the invariant uncertainty |
---|
1027 | dV: the volume uncertainty |
---|
1028 | @param contrast: contrast value |
---|
1029 | @return: V, dV = self.get_volume_fraction_with_error(contrast), dV |
---|
1030 | """ |
---|
1031 | if contrast is None: |
---|
1032 | return None, None |
---|
1033 | self._qstar, self._qstar_err = self.get_qstar_with_error() |
---|
1034 | |
---|
1035 | volume = self.get_volume_fraction(contrast) |
---|
1036 | if self._qstar < 0: |
---|
1037 | raise ValueError, "invariant must be greater than zero" |
---|
1038 | |
---|
1039 | k = 1.e-8 * self._qstar /(2 * (math.pi* math.fabs(float(contrast)))**2) |
---|
1040 | #check value inside the sqrt function |
---|
1041 | value = 1 - k * self._qstar |
---|
1042 | if (value) <= 0: |
---|
1043 | raise ValueError, "Cannot compute incertainty on volume" |
---|
1044 | # Compute uncertainty |
---|
1045 | uncertainty = (0.5 * 4 * k * self._qstar_err)/(2 * math.sqrt(1 - k * self._qstar)) |
---|
1046 | |
---|
1047 | return volume, math.fabs(uncertainty) |
---|
1048 | |
---|
1049 | def get_surface_with_error(self, contrast, porod_const): |
---|
1050 | """ |
---|
1051 | Compute uncertainty of the surface value as well as thesurface value |
---|
1052 | this uncertainty is given as follow: |
---|
1053 | |
---|
1054 | dS = porod_const *2*pi[( dV -2*V*dV)/q_star |
---|
1055 | + dq_star(v-v**2) |
---|
1056 | |
---|
1057 | q_star: the invariant value including extrapolated value if existing |
---|
1058 | dq_star: the invariant uncertainty |
---|
1059 | V: the volume fraction value |
---|
1060 | dV: the volume uncertainty |
---|
1061 | |
---|
1062 | @param contrast: contrast value |
---|
1063 | @param porod_const: porod constant value |
---|
1064 | @return S, dS: the surface, with its uncertainty |
---|
1065 | """ |
---|
1066 | if contrast is None or porod_const is None: |
---|
1067 | return None, None |
---|
1068 | v, dv = self.get_volume_fraction_with_error(contrast) |
---|
1069 | self._qstar, self._qstar_err = self.get_qstar_with_error() |
---|
1070 | if self._qstar <= 0: |
---|
1071 | raise ValueError, "invariant must be greater than zero" |
---|
1072 | ds = porod_const * 2 * math.pi * (( dv - 2 * v * dv)/ self._qstar\ |
---|
1073 | + self._qstar_err * ( v - v**2)) |
---|
1074 | s = self.get_surface(contrast=contrast, porod_const=porod_const) |
---|
1075 | return s, ds |
---|