1 | """ |
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2 | Product model |
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3 | ------------- |
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4 | |
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5 | The product model multiplies the structure factor by the form factor, |
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6 | modulated by the effective radius of the form. The resulting model |
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7 | has a attributes of both the model description (with parameters, etc.) |
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8 | and the module evaluator (with call, release, etc.). |
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9 | |
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10 | To use it, first load form factor P and structure factor S, then create |
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11 | *make_product_info(P, S)*. |
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12 | """ |
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13 | from __future__ import print_function, division |
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14 | |
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15 | from collections import OrderedDict |
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16 | |
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17 | from copy import copy |
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18 | import numpy as np # type: ignore |
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19 | |
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20 | from .modelinfo import ParameterTable, ModelInfo, parse_parameter |
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21 | from .kernel import KernelModel, Kernel |
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22 | from .details import make_details |
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23 | |
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24 | # pylint: disable=unused-import |
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25 | try: |
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26 | from typing import Tuple, Callable, Union |
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27 | except ImportError: |
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28 | pass |
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29 | else: |
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30 | from .modelinfo import ParameterSet, Parameter |
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31 | # pylint: enable=unused-import |
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32 | |
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33 | # TODO: make estimates available to constraints |
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34 | #ESTIMATED_PARAMETERS = [ |
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35 | # ["est_radius_effective", "A", 0.0, [0, np.inf], "", "Estimated effective radius"], |
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36 | # ["est_volume_ratio", "", 1.0, [0, np.inf], "", "Estimated volume ratio"], |
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37 | #] |
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38 | |
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39 | STRUCTURE_MODE_ID = "structure_factor_mode" |
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40 | RADIUS_MODE_ID = "radius_effective_mode" |
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41 | RADIUS_ID = "radius_effective" |
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42 | VOLFRAC_ID = "volfraction" |
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43 | def make_extra_pars(p_info): |
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44 | # type: (ModelInfo) -> List[Parameter] |
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45 | """ |
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46 | Create parameters for structure_factor_mode and radius_effective_mode. |
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47 | """ |
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48 | pars = [] |
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49 | if p_info.have_Fq: |
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50 | par = parse_parameter( |
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51 | STRUCTURE_MODE_ID, |
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52 | "", |
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53 | 0, |
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54 | [["P*S", "P*(1+beta*(S-1))"]], |
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55 | "", |
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56 | "Structure factor calculation") |
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57 | pars.append(par) |
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58 | if p_info.effective_radius_type is not None: |
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59 | par = parse_parameter( |
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60 | RADIUS_MODE_ID, |
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61 | "", |
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62 | 1, |
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63 | [["unconstrained"] + p_info.effective_radius_type], |
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64 | "", |
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65 | "Effective radius calculation") |
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66 | pars.append(par) |
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67 | return pars |
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68 | |
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69 | def make_product_info(p_info, s_info): |
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70 | # type: (ModelInfo, ModelInfo) -> ModelInfo |
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71 | """ |
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72 | Create info block for product model. |
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73 | """ |
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74 | # Make sure effective radius is the first parameter and |
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75 | # make sure volume fraction is the second parameter of the |
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76 | # structure factor calculator. Structure factors should not |
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77 | # have any magnetic parameters |
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78 | if not len(s_info.parameters.kernel_parameters) >= 2: |
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79 | raise TypeError("S needs {} and {} as its first parameters".format(RADIUS_ID, VOLFRAC_ID)) |
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80 | if not s_info.parameters.kernel_parameters[0].id == RADIUS_ID: |
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81 | raise TypeError("S needs {} as first parameter".format(RADIUS_ID)) |
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82 | if not s_info.parameters.kernel_parameters[1].id == VOLFRAC_ID: |
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83 | raise TypeError("S needs {} as second parameter".format(VOLFRAC_ID)) |
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84 | if not s_info.parameters.magnetism_index == []: |
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85 | raise TypeError("S should not have SLD parameters") |
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86 | p_id, p_name, p_pars = p_info.id, p_info.name, p_info.parameters |
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87 | s_id, s_name, s_pars = s_info.id, s_info.name, s_info.parameters |
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88 | |
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89 | # Create list of parameters for the combined model. If there |
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90 | # are any names in P that overlap with those in S, modify the name in S |
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91 | # to distinguish it. |
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92 | p_set = set(p.id for p in p_pars.kernel_parameters) |
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93 | s_list = [(_tag_parameter(par) if par.id in p_set else par) |
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94 | for par in s_pars.kernel_parameters] |
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95 | # Check if still a collision after renaming. This could happen if for |
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96 | # example S has volfrac and P has both volfrac and volfrac_S. |
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97 | if any(p.id in p_set for p in s_list): |
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98 | raise TypeError("name collision: P has P.name and P.name_S while S has S.name") |
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99 | |
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100 | # make sure effective radius is not a polydisperse parameter in product |
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101 | s_list[0] = copy(s_list[0]) |
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102 | s_list[0].polydisperse = False |
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103 | |
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104 | translate_name = dict((old.id, new.id) for old, new |
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105 | in zip(s_pars.kernel_parameters, s_list)) |
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106 | combined_pars = p_pars.kernel_parameters + s_list + make_extra_pars(p_info) |
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107 | parameters = ParameterTable(combined_pars) |
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108 | parameters.max_pd = p_pars.max_pd + s_pars.max_pd |
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109 | def random(): |
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110 | """Random set of model parameters for product model""" |
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111 | combined_pars = p_info.random() |
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112 | s_names = set(par.id for par in s_pars.kernel_parameters) |
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113 | combined_pars.update((translate_name[k], v) |
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114 | for k, v in s_info.random().items() |
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115 | if k in s_names) |
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116 | return combined_pars |
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117 | |
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118 | model_info = ModelInfo() |
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119 | model_info.id = '@'.join((p_id, s_id)) |
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120 | model_info.name = '@'.join((p_name, s_name)) |
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121 | model_info.filename = None |
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122 | model_info.title = 'Product of %s and %s'%(p_name, s_name) |
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123 | model_info.description = model_info.title |
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124 | model_info.docs = model_info.title |
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125 | model_info.category = "custom" |
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126 | model_info.parameters = parameters |
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127 | model_info.random = random |
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128 | #model_info.single = p_info.single and s_info.single |
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129 | model_info.structure_factor = False |
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130 | model_info.variant_info = None |
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131 | #model_info.tests = [] |
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132 | #model_info.source = [] |
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133 | # Remember the component info blocks so we can build the model |
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134 | model_info.composition = ('product', [p_info, s_info]) |
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135 | model_info.hidden = p_info.hidden |
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136 | if getattr(p_info, 'profile', None) is not None: |
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137 | profile_pars = set(p.id for p in p_info.parameters.kernel_parameters) |
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138 | def profile(**kwargs): |
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139 | """Return SLD profile of the form factor as a function of radius.""" |
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140 | # extract the profile args |
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141 | kwargs = dict((k, v) for k, v in kwargs.items() if k in profile_pars) |
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142 | return p_info.profile(**kwargs) |
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143 | else: |
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144 | profile = None |
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145 | model_info.profile = profile |
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146 | model_info.profile_axes = p_info.profile_axes |
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147 | |
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148 | # TODO: delegate random to p_info, s_info |
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149 | #model_info.random = lambda: {} |
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150 | |
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151 | ## Show the parameter table |
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152 | #from .compare import get_pars, parlist |
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153 | #print("==== %s ====="%model_info.name) |
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154 | #values = get_pars(model_info) |
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155 | #print(parlist(model_info, values, is2d=True)) |
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156 | return model_info |
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157 | |
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158 | def _tag_parameter(par): |
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159 | """ |
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160 | Tag the parameter name with _S to indicate that the parameter comes from |
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161 | the structure factor parameter set. This is only necessary if the |
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162 | form factor model includes a parameter of the same name as a parameter |
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163 | in the structure factor. |
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164 | """ |
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165 | par = copy(par) |
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166 | # Protect against a vector parameter in S by appending the vector length |
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167 | # to the renamed parameter. Note: haven't tested this since no existing |
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168 | # structure factor models contain vector parameters. |
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169 | vector_length = par.name[len(par.id):] |
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170 | par.id = par.id + "_S" |
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171 | par.name = par.id + vector_length |
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172 | return par |
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173 | |
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174 | def _intermediates( |
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175 | F1, # type: np.ndarray |
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176 | F2, # type: np.ndarray |
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177 | S, # type: np.ndarray |
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178 | scale, # type: float |
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179 | effective_radius, # type: float |
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180 | beta_mode, # type: bool |
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181 | ): |
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182 | # type: (...) -> OrderedDict[str, Union[np.ndarray, float]] |
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183 | """ |
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184 | Returns intermediate results for beta approximation-enabled product. |
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185 | The result may be an array or a float. |
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186 | """ |
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187 | if beta_mode: |
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188 | # TODO: 1. include calculated Q vector |
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189 | # TODO: 2. consider implications if there are intermediate results in P(Q) |
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190 | parts = OrderedDict(( |
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191 | ("P(Q)", scale*F2), |
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192 | ("S(Q)", S), |
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193 | ("beta(Q)", F1**2 / F2), |
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194 | ("S_eff(Q)", 1 + (F1**2 / F2)*(S-1)), |
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195 | ("effective_radius", effective_radius), |
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196 | # ("I(Q)", scale*(F2 + (F1**2)*(S-1)) + bg), |
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197 | )) |
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198 | else: |
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199 | parts = OrderedDict(( |
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200 | ("P(Q)", scale*F2), |
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201 | ("S(Q)", S), |
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202 | ("effective_radius", effective_radius), |
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203 | )) |
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204 | return parts |
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205 | |
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206 | class ProductModel(KernelModel): |
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207 | """ |
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208 | Model definition for product model. |
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209 | """ |
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210 | def __init__(self, model_info, P, S): |
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211 | # type: (ModelInfo, KernelModel, KernelModel) -> None |
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212 | #: Combined info plock for the product model |
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213 | self.info = model_info |
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214 | #: Form factor modelling individual particles. |
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215 | self.P = P |
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216 | #: Structure factor modelling interaction between particles. |
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217 | self.S = S |
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218 | |
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219 | #: Model precision. This is not really relevant, since it is the |
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220 | #: individual P and S models that control the effective dtype, |
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221 | #: converting the q-vectors to the correct type when the kernels |
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222 | #: for each are created. Ideally this should be set to the more |
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223 | #: precise type to avoid loss of precision, but precision in q is |
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224 | #: not critical (single is good enough for our purposes), so it just |
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225 | #: uses the precision of the form factor. |
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226 | self.dtype = P.dtype # type: np.dtype |
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227 | |
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228 | def make_kernel(self, q_vectors): |
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229 | # type: (List[np.ndarray]) -> Kernel |
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230 | # Note: may be sending the q_vectors to the GPU twice even though they |
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231 | # are only needed once. It would mess up modularity quite a bit to |
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232 | # handle this optimally, especially since there are many cases where |
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233 | # separate q vectors are needed (e.g., form in python and structure |
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234 | # in opencl; or both in opencl, but one in single precision and the |
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235 | # other in double precision). |
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236 | |
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237 | p_kernel = self.P.make_kernel(q_vectors) |
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238 | s_kernel = self.S.make_kernel(q_vectors) |
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239 | return ProductKernel(self.info, p_kernel, s_kernel) |
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240 | make_kernel.__doc__ = KernelModel.make_kernel.__doc__ |
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241 | |
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242 | def release(self): |
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243 | # type: (None) -> None |
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244 | """ |
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245 | Free resources associated with the model. |
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246 | """ |
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247 | self.P.release() |
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248 | self.S.release() |
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249 | |
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250 | |
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251 | class ProductKernel(Kernel): |
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252 | """ |
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253 | Instantiated kernel for product model. |
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254 | """ |
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255 | def __init__(self, model_info, p_kernel, s_kernel): |
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256 | # type: (ModelInfo, Kernel, Kernel) -> None |
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257 | self.info = model_info |
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258 | self.p_kernel = p_kernel |
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259 | self.s_kernel = s_kernel |
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260 | self.dtype = p_kernel.dtype |
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261 | self.results = [] # type: List[np.ndarray] |
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262 | |
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263 | def Iq(self, call_details, values, cutoff, magnetic): |
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264 | # type: (CallDetails, np.ndarray, float, bool) -> np.ndarray |
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265 | |
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266 | p_info, s_info = self.info.composition[1] |
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267 | p_npars = p_info.parameters.npars |
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268 | p_length = call_details.length[:p_npars] |
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269 | p_offset = call_details.offset[:p_npars] |
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270 | s_npars = s_info.parameters.npars |
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271 | s_length = call_details.length[p_npars:p_npars+s_npars] |
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272 | s_offset = call_details.offset[p_npars:p_npars+s_npars] |
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273 | |
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274 | # Beta mode parameter is the first parameter after P and S parameters |
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275 | have_beta_mode = p_info.have_Fq |
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276 | beta_mode_offset = 2+p_npars+s_npars |
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277 | beta_mode = (values[beta_mode_offset] > 0) if have_beta_mode else False |
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278 | if beta_mode and self.p_kernel.dim == '2d': |
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279 | raise NotImplementedError("beta not yet supported for 2D") |
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280 | |
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281 | # R_eff type parameter is the second parameter after P and S parameters |
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282 | # unless the model doesn't support beta mode, in which case it is first |
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283 | have_radius_type = p_info.effective_radius_type is not None |
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284 | radius_type_offset = 2+p_npars+s_npars + (1 if have_beta_mode else 0) |
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285 | radius_type = int(values[radius_type_offset]) if have_radius_type else 0 |
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286 | |
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287 | # Retrieve the volume fraction, which is the second of the |
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288 | # 'S' parameters in the parameter list, or 2+np in 0-origin, |
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289 | # as well as the scale and background. |
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290 | volfrac = values[3+p_npars] |
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291 | scale, background = values[0], values[1] |
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292 | |
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293 | # if there are magnetic parameters, they will only be on the |
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294 | # form factor P, not the structure factor S. |
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295 | nmagnetic = len(self.info.parameters.magnetism_index) |
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296 | if nmagnetic: |
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297 | spin_index = self.info.parameters.npars + 2 |
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298 | magnetism = values[spin_index: spin_index+3+3*nmagnetic] |
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299 | else: |
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300 | magnetism = [] |
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301 | nvalues = self.info.parameters.nvalues |
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302 | nweights = call_details.num_weights |
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303 | weights = values[nvalues:nvalues + 2*nweights] |
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304 | |
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305 | # Construct the calling parameters for P. |
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306 | p_details = make_details(p_info, p_length, p_offset, nweights) |
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307 | p_values = [ |
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308 | [1., 0.], # scale=1, background=0, |
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309 | values[2:2+p_npars], |
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310 | magnetism, |
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311 | weights] |
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312 | spacer = (32 - sum(len(v) for v in p_values)%32)%32 |
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313 | p_values.append([0.]*spacer) |
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314 | p_values = np.hstack(p_values).astype(self.p_kernel.dtype) |
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315 | |
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316 | # Construct the calling parameters for S. |
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317 | if radius_type > 0: |
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318 | # If R_eff comes from form factor, make sure it is monodisperse. |
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319 | # weight is set to 1 later, after the value array is created |
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320 | s_length[0] = 1 |
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321 | s_details = make_details(s_info, s_length, s_offset, nweights) |
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322 | s_values = [ |
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323 | [1., 0.], # scale=1, background=0, |
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324 | values[2+p_npars:2+p_npars+s_npars], |
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325 | weights, |
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326 | ] |
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327 | spacer = (32 - sum(len(v) for v in s_values)%32)%32 |
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328 | s_values.append([0.]*spacer) |
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329 | s_values = np.hstack(s_values).astype(self.s_kernel.dtype) |
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330 | |
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331 | # Call the form factor kernel to compute <F> and <F^2>. |
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332 | # If the model doesn't support Fq the returned <F> will be None. |
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333 | F1, F2, effective_radius, shell_volume, volume_ratio = self.p_kernel.Fq( |
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334 | p_details, p_values, cutoff, magnetic, radius_type) |
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335 | |
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336 | # Call the structure factor kernel to compute S. |
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337 | # Plug R_eff from the form factor into structure factor parameters |
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338 | # and scale volume fraction by form:shell volume ratio. These changes |
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339 | # needs to be both in the initial value slot as well as the |
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340 | # polydispersity distribution slot in the values array due to |
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341 | # implementation details in kernel_iq.c. |
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342 | #print("R_eff=%d:%g, volfrac=%g, volume ratio=%g" |
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343 | # % (radius_type, effective_radius, volfrac, volume_ratio)) |
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344 | if radius_type > 0: |
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345 | # set the value to the model R_eff and set the weight to 1 |
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346 | s_values[2] = s_values[2+s_npars+s_offset[0]] = effective_radius |
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347 | s_values[2+s_npars+s_offset[0]+nweights] = 1.0 |
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348 | s_values[3] = s_values[2+s_npars+s_offset[1]] = volfrac*volume_ratio |
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349 | S = self.s_kernel.Iq(s_details, s_values, cutoff, False) |
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350 | |
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351 | # Determine overall scale factor. Hollow shapes are weighted by |
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352 | # shell_volume, so that is needed for volume normalization. For |
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353 | # solid shapes we can use shell_volume as well since it is equal |
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354 | # to form volume. |
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355 | combined_scale = scale*volfrac/shell_volume |
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356 | |
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357 | # Combine form factor and structure factor |
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358 | #print("beta", beta_mode, F1, F2, S) |
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359 | PS = F2 + F1**2*(S-1) if beta_mode else F2*S |
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360 | final_result = combined_scale*PS + background |
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361 | |
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362 | # Capture intermediate values so user can see them. These are |
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363 | # returned as a lazy evaluator since they are only needed in the |
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364 | # GUI, and not for each evaluation during a fit. |
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365 | # TODO: return the results structure with the final results |
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366 | # That way the model calcs are idempotent. Further, we can |
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367 | # generalize intermediates to various other model types if we put it |
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368 | # kernel calling interface. Could do this as an "optional" |
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369 | # return value in the caller, though in that case we could return |
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370 | # the results directly rather than through a lazy evaluator. |
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371 | self.results = lambda: _intermediates( |
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372 | F1, F2, S, combined_scale, effective_radius, beta_mode) |
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373 | |
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374 | return final_result |
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375 | |
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376 | Iq.__doc__ = Kernel.Iq.__doc__ |
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377 | __call__ = Iq |
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378 | |
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379 | def release(self): |
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380 | # type: () -> None |
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381 | """Free resources associated with the kernel.""" |
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382 | self.p_kernel.release() |
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383 | self.s_kernel.release() |
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