1 | """ |
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2 | Sasview model constructor. |
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3 | |
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4 | Given a module defining an OpenCL kernel such as sasmodels.models.cylinder, |
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5 | create a sasview model class to run that kernel as follows:: |
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6 | |
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7 | from sasmodels.sasview_model import make_class |
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8 | from sasmodels.models import cylinder |
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9 | CylinderModel = make_class(cylinder, dtype='single') |
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10 | |
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11 | The model parameters for sasmodels are different from those in sasview. |
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12 | When reloading previously saved models, the parameters should be converted |
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13 | using :func:`sasmodels.convert.convert`. |
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14 | """ |
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15 | from __future__ import print_function |
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16 | |
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17 | import math |
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18 | from copy import deepcopy |
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19 | import collections |
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20 | import traceback |
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21 | import logging |
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22 | |
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23 | import numpy as np # type: ignore |
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24 | |
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25 | from . import core |
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26 | from . import custom |
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27 | from . import generate |
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28 | from . import weights |
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29 | from . import details |
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30 | from . import modelinfo |
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31 | |
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32 | try: |
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33 | from typing import Dict, Mapping, Any, Sequence, Tuple, NamedTuple, List, Optional, Union |
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34 | from .modelinfo import ModelInfo, Parameter |
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35 | from .kernel import KernelModel |
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36 | MultiplicityInfoType = NamedTuple( |
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37 | 'MuliplicityInfo', |
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38 | [("number", int), ("control", str), ("choices", List[str]), |
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39 | ("x_axis_label", str)]) |
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40 | except ImportError: |
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41 | pass |
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42 | |
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43 | # TODO: separate x_axis_label from multiplicity info |
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44 | # The profile x-axis label belongs with the profile generating function |
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45 | MultiplicityInfo = collections.namedtuple( |
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46 | 'MultiplicityInfo', |
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47 | ["number", "control", "choices", "x_axis_label"], |
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48 | ) |
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49 | |
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50 | # TODO: figure out how to say that the return type is a subclass |
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51 | def load_standard_models(): |
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52 | # type: () -> List[type] |
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53 | """ |
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54 | Load and return the list of predefined models. |
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55 | |
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56 | If there is an error loading a model, then a traceback is logged and the |
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57 | model is not returned. |
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58 | """ |
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59 | models = [] |
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60 | for name in core.list_models(): |
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61 | try: |
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62 | models.append(_make_standard_model(name)) |
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63 | except Exception: |
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64 | logging.error(traceback.format_exc()) |
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65 | return models |
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66 | |
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67 | |
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68 | def load_custom_model(path): |
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69 | # type: (str) -> type |
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70 | """ |
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71 | Load a custom model given the model path. |
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72 | """ |
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73 | kernel_module = custom.load_custom_kernel_module(path) |
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74 | model_info = modelinfo.make_model_info(kernel_module) |
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75 | return _make_model_from_info(model_info) |
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76 | |
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77 | |
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78 | def _make_standard_model(name): |
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79 | # type: (str) -> type |
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80 | """ |
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81 | Load the sasview model defined by *name*. |
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82 | |
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83 | *name* can be a standard model name or a path to a custom model. |
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84 | |
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85 | Returns a class that can be used directly as a sasview model. |
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86 | """ |
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87 | kernel_module = generate.load_kernel_module(name) |
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88 | model_info = modelinfo.make_model_info(kernel_module) |
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89 | return _make_model_from_info(model_info) |
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90 | |
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91 | |
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92 | def _make_model_from_info(model_info): |
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93 | # type: (ModelInfo) -> type |
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94 | """ |
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95 | Convert *model_info* into a SasView model wrapper. |
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96 | """ |
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97 | def __init__(self, multiplicity=None): |
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98 | SasviewModel.__init__(self, multiplicity=multiplicity) |
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99 | attrs = _generate_model_attributes(model_info) |
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100 | attrs['__init__'] = __init__ |
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101 | ConstructedModel = type(model_info.name, (SasviewModel,), attrs) |
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102 | return ConstructedModel |
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103 | |
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104 | def _generate_model_attributes(model_info): |
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105 | # type: (ModelInfo) -> Dict[str, Any] |
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106 | """ |
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107 | Generate the class attributes for the model. |
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108 | |
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109 | This should include all the information necessary to query the model |
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110 | details so that you do not need to instantiate a model to query it. |
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111 | |
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112 | All the attributes should be immutable to avoid accidents. |
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113 | """ |
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114 | |
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115 | # TODO: allow model to override axis labels input/output name/unit |
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116 | |
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117 | # Process multiplicity |
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118 | non_fittable = [] # type: List[str] |
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119 | xlabel = model_info.profile_axes[0] if model_info.profile is not None else "" |
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120 | variants = MultiplicityInfo(0, "", [], xlabel) |
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121 | for p in model_info.parameters.kernel_parameters: |
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122 | if p.name == model_info.control: |
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123 | non_fittable.append(p.name) |
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124 | variants = MultiplicityInfo( |
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125 | len(p.choices), p.name, p.choices, xlabel |
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126 | ) |
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127 | break |
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128 | elif p.is_control: |
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129 | non_fittable.append(p.name) |
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130 | variants = MultiplicityInfo( |
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131 | int(p.limits[1]), p.name, p.choices, xlabel |
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132 | ) |
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133 | break |
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134 | |
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135 | # Organize parameter sets |
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136 | orientation_params = [] |
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137 | magnetic_params = [] |
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138 | fixed = [] |
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139 | for p in model_info.parameters.user_parameters(): |
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140 | if p.type == 'orientation': |
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141 | orientation_params.append(p.name) |
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142 | orientation_params.append(p.name+".width") |
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143 | fixed.append(p.name+".width") |
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144 | if p.type == 'magnetic': |
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145 | orientation_params.append(p.name) |
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146 | magnetic_params.append(p.name) |
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147 | fixed.append(p.name+".width") |
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148 | |
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149 | # Build class dictionary |
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150 | attrs = {} # type: Dict[str, Any] |
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151 | attrs['_model_info'] = model_info |
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152 | attrs['name'] = model_info.name |
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153 | attrs['id'] = model_info.id |
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154 | attrs['description'] = model_info.description |
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155 | attrs['category'] = model_info.category |
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156 | attrs['is_structure_factor'] = model_info.structure_factor |
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157 | attrs['is_form_factor'] = model_info.ER is not None |
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158 | attrs['is_multiplicity_model'] = variants[0] > 1 |
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159 | attrs['multiplicity_info'] = variants |
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160 | attrs['orientation_params'] = tuple(orientation_params) |
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161 | attrs['magnetic_params'] = tuple(magnetic_params) |
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162 | attrs['fixed'] = tuple(fixed) |
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163 | attrs['non_fittable'] = tuple(non_fittable) |
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164 | |
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165 | return attrs |
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166 | |
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167 | class SasviewModel(object): |
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168 | """ |
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169 | Sasview wrapper for opencl/ctypes model. |
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170 | """ |
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171 | # Model parameters for the specific model are set in the class constructor |
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172 | # via the _generate_model_attributes function, which subclasses |
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173 | # SasviewModel. They are included here for typing and documentation |
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174 | # purposes. |
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175 | _model = None # type: KernelModel |
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176 | _model_info = None # type: ModelInfo |
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177 | #: load/save name for the model |
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178 | id = None # type: str |
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179 | #: display name for the model |
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180 | name = None # type: str |
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181 | #: short model description |
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182 | description = None # type: str |
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183 | #: default model category |
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184 | category = None # type: str |
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185 | |
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186 | #: names of the orientation parameters in the order they appear |
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187 | orientation_params = None # type: Sequence[str] |
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188 | #: names of the magnetic parameters in the order they appear |
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189 | magnetic_params = None # type: Sequence[str] |
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190 | #: names of the fittable parameters |
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191 | fixed = None # type: Sequence[str] |
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192 | # TODO: the attribute fixed is ill-named |
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193 | |
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194 | # Axis labels |
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195 | input_name = "Q" |
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196 | input_unit = "A^{-1}" |
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197 | output_name = "Intensity" |
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198 | output_unit = "cm^{-1}" |
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199 | |
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200 | #: default cutoff for polydispersity |
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201 | cutoff = 1e-5 |
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202 | |
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203 | # Note: Use non-mutable values for class attributes to avoid errors |
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204 | #: parameters that are not fitted |
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205 | non_fittable = () # type: Sequence[str] |
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206 | |
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207 | #: True if model should appear as a structure factor |
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208 | is_structure_factor = False |
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209 | #: True if model should appear as a form factor |
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210 | is_form_factor = False |
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211 | #: True if model has multiplicity |
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212 | is_multiplicity_model = False |
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213 | #: Mulitplicity information |
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214 | multiplicity_info = None # type: MultiplicityInfoType |
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215 | |
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216 | # Per-instance variables |
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217 | #: parameter {name: value} mapping |
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218 | params = None # type: Dict[str, float] |
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219 | #: values for dispersion width, npts, nsigmas and type |
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220 | dispersion = None # type: Dict[str, Any] |
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221 | #: units and limits for each parameter |
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222 | details = None # type: Mapping[str, Tuple[str, float, float]] |
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223 | #: multiplicity value, or None if no multiplicity on the model |
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224 | multiplicity = None # type: Optional[int] |
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225 | #: memory for polydispersity array if using ArrayDispersion (used by sasview). |
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226 | _persistency_dict = None # type: Dict[str, Tuple[np.ndarray, np.ndarray]] |
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227 | |
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228 | def __init__(self, multiplicity=None): |
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229 | # type: (Optional[int]) -> None |
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230 | |
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231 | # TODO: _persistency_dict to persistency_dict throughout sasview |
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232 | # TODO: refactor multiplicity to encompass variants |
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233 | # TODO: dispersion should be a class |
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234 | # TODO: refactor multiplicity info |
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235 | # TODO: separate profile view from multiplicity |
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236 | # The button label, x and y axis labels and scale need to be under |
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237 | # the control of the model, not the fit page. Maximum flexibility, |
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238 | # the fit page would supply the canvas and the profile could plot |
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239 | # how it wants, but this assumes matplotlib. Next level is that |
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240 | # we provide some sort of data description including title, labels |
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241 | # and lines to plot. |
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242 | |
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243 | # Get the list of hidden parameters given the mulitplicity |
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244 | # Don't include multiplicity in the list of parameters |
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245 | self.multiplicity = multiplicity |
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246 | if multiplicity is not None: |
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247 | hidden = self._model_info.get_hidden_parameters(multiplicity) |
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248 | hidden |= set([self.multiplicity_info.control]) |
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249 | else: |
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250 | hidden = set() |
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251 | |
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252 | self._persistency_dict = {} |
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253 | self.params = collections.OrderedDict() |
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254 | self.dispersion = {} |
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255 | self.details = {} |
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256 | for p in self._model_info.parameters.user_parameters(): |
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257 | if p.name in hidden: |
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258 | continue |
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259 | self.params[p.name] = p.default |
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260 | self.details[p.id] = [p.units, p.limits[0], p.limits[1]] |
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261 | if p.polydisperse: |
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262 | self.details[p.id+".width"] = [ |
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263 | "", 0.0, 1.0 if p.relative_pd else np.inf |
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264 | ] |
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265 | self.dispersion[p.name] = { |
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266 | 'width': 0, |
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267 | 'npts': 35, |
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268 | 'nsigmas': 3, |
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269 | 'type': 'gaussian', |
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270 | } |
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271 | |
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272 | def __get_state__(self): |
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273 | # type: () -> Dict[str, Any] |
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274 | state = self.__dict__.copy() |
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275 | state.pop('_model') |
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276 | # May need to reload model info on set state since it has pointers |
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277 | # to python implementations of Iq, etc. |
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278 | #state.pop('_model_info') |
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279 | return state |
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280 | |
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281 | def __set_state__(self, state): |
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282 | # type: (Dict[str, Any]) -> None |
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283 | self.__dict__ = state |
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284 | self._model = None |
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285 | |
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286 | def __str__(self): |
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287 | # type: () -> str |
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288 | """ |
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289 | :return: string representation |
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290 | """ |
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291 | return self.name |
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292 | |
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293 | def is_fittable(self, par_name): |
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294 | # type: (str) -> bool |
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295 | """ |
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296 | Check if a given parameter is fittable or not |
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297 | |
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298 | :param par_name: the parameter name to check |
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299 | """ |
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300 | return par_name.lower() in self.fixed |
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301 | #For the future |
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302 | #return self.params[str(par_name)].is_fittable() |
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303 | |
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304 | |
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305 | def getProfile(self): |
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306 | # type: () -> (np.ndarray, np.ndarray) |
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307 | """ |
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308 | Get SLD profile |
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309 | |
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310 | : return: (z, beta) where z is a list of depth of the transition points |
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311 | beta is a list of the corresponding SLD values |
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312 | """ |
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313 | args = [] |
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314 | for p in self._model_info.parameters.kernel_parameters: |
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315 | if p.id == self.multiplicity_info.control: |
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316 | args.append(self.multiplicity) |
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317 | elif p.length == 1: |
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318 | args.append(self.params.get(p.id, np.NaN)) |
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319 | else: |
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320 | args.append([self.params.get(p.id+str(k), np.NaN) |
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321 | for k in range(1,p.length+1)]) |
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322 | return self._model_info.profile(*args) |
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323 | |
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324 | def setParam(self, name, value): |
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325 | # type: (str, float) -> None |
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326 | """ |
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327 | Set the value of a model parameter |
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328 | |
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329 | :param name: name of the parameter |
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330 | :param value: value of the parameter |
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331 | |
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332 | """ |
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333 | # Look for dispersion parameters |
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334 | toks = name.split('.') |
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335 | if len(toks) == 2: |
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336 | for item in self.dispersion.keys(): |
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337 | if item.lower() == toks[0].lower(): |
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338 | for par in self.dispersion[item]: |
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339 | if par.lower() == toks[1].lower(): |
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340 | self.dispersion[item][par] = value |
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341 | return |
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342 | else: |
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343 | # Look for standard parameter |
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344 | for item in self.params.keys(): |
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345 | if item.lower() == name.lower(): |
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346 | self.params[item] = value |
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347 | return |
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348 | |
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349 | raise ValueError("Model does not contain parameter %s" % name) |
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350 | |
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351 | def getParam(self, name): |
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352 | # type: (str) -> float |
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353 | """ |
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354 | Set the value of a model parameter |
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355 | |
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356 | :param name: name of the parameter |
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357 | |
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358 | """ |
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359 | # Look for dispersion parameters |
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360 | toks = name.split('.') |
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361 | if len(toks) == 2: |
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362 | for item in self.dispersion.keys(): |
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363 | if item.lower() == toks[0].lower(): |
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364 | for par in self.dispersion[item]: |
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365 | if par.lower() == toks[1].lower(): |
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366 | return self.dispersion[item][par] |
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367 | else: |
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368 | # Look for standard parameter |
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369 | for item in self.params.keys(): |
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370 | if item.lower() == name.lower(): |
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371 | return self.params[item] |
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372 | |
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373 | raise ValueError("Model does not contain parameter %s" % name) |
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374 | |
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375 | def getParamList(self): |
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376 | # type: () -> Sequence[str] |
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377 | """ |
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378 | Return a list of all available parameters for the model |
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379 | """ |
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380 | param_list = list(self.params.keys()) |
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381 | # WARNING: Extending the list with the dispersion parameters |
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382 | param_list.extend(self.getDispParamList()) |
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383 | return param_list |
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384 | |
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385 | def getDispParamList(self): |
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386 | # type: () -> Sequence[str] |
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387 | """ |
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388 | Return a list of polydispersity parameters for the model |
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389 | """ |
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390 | # TODO: fix test so that parameter order doesn't matter |
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391 | ret = ['%s.%s' % (p.name.lower(), ext) |
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392 | for p in self._model_info.parameters.user_parameters() |
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393 | for ext in ('npts', 'nsigmas', 'width') |
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394 | if p.polydisperse] |
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395 | #print(ret) |
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396 | return ret |
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397 | |
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398 | def clone(self): |
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399 | # type: () -> "SasviewModel" |
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400 | """ Return a identical copy of self """ |
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401 | return deepcopy(self) |
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402 | |
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403 | def run(self, x=0.0): |
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404 | # type: (Union[float, (float, float), List[float]]) -> float |
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405 | """ |
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406 | Evaluate the model |
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407 | |
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408 | :param x: input q, or [q,phi] |
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409 | |
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410 | :return: scattering function P(q) |
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411 | |
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412 | **DEPRECATED**: use calculate_Iq instead |
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413 | """ |
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414 | if isinstance(x, (list, tuple)): |
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415 | # pylint: disable=unpacking-non-sequence |
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416 | q, phi = x |
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417 | return self.calculate_Iq([q * math.cos(phi)], |
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418 | [q * math.sin(phi)])[0] |
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419 | else: |
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420 | return self.calculate_Iq([float(x)])[0] |
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421 | |
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422 | |
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423 | def runXY(self, x=0.0): |
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424 | # type: (Union[float, (float, float), List[float]]) -> float |
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425 | """ |
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426 | Evaluate the model in cartesian coordinates |
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427 | |
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428 | :param x: input q, or [qx, qy] |
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429 | |
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430 | :return: scattering function P(q) |
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431 | |
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432 | **DEPRECATED**: use calculate_Iq instead |
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433 | """ |
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434 | if isinstance(x, (list, tuple)): |
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435 | return self.calculate_Iq([float(x[0])], [float(x[1])])[0] |
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436 | else: |
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437 | return self.calculate_Iq([float(x)])[0] |
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438 | |
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439 | def evalDistribution(self, qdist): |
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440 | # type: (Union[np.ndarray, Tuple[np.ndarray, np.ndarray], List[np.ndarray]]) -> np.ndarray |
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441 | r""" |
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442 | Evaluate a distribution of q-values. |
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443 | |
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444 | :param qdist: array of q or a list of arrays [qx,qy] |
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445 | |
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446 | * For 1D, a numpy array is expected as input |
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447 | |
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448 | :: |
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449 | |
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450 | evalDistribution(q) |
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451 | |
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452 | where *q* is a numpy array. |
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453 | |
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454 | * For 2D, a list of *[qx,qy]* is expected with 1D arrays as input |
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455 | |
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456 | :: |
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457 | |
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458 | qx = [ qx[0], qx[1], qx[2], ....] |
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459 | qy = [ qy[0], qy[1], qy[2], ....] |
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460 | |
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461 | If the model is 1D only, then |
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462 | |
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463 | .. math:: |
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464 | |
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465 | q = \sqrt{q_x^2+q_y^2} |
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466 | |
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467 | """ |
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468 | if isinstance(qdist, (list, tuple)): |
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469 | # Check whether we have a list of ndarrays [qx,qy] |
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470 | qx, qy = qdist |
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471 | if not self._model_info.parameters.has_2d: |
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472 | return self.calculate_Iq(np.sqrt(qx ** 2 + qy ** 2)) |
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473 | else: |
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474 | return self.calculate_Iq(qx, qy) |
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475 | |
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476 | elif isinstance(qdist, np.ndarray): |
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477 | # We have a simple 1D distribution of q-values |
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478 | return self.calculate_Iq(qdist) |
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479 | |
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480 | else: |
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481 | raise TypeError("evalDistribution expects q or [qx, qy], not %r" |
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482 | % type(qdist)) |
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483 | |
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484 | def calculate_Iq(self, qx, qy=None): |
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485 | # type: (Sequence[float], Optional[Sequence[float]]) -> np.ndarray |
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486 | """ |
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487 | Calculate Iq for one set of q with the current parameters. |
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488 | |
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489 | If the model is 1D, use *q*. If 2D, use *qx*, *qy*. |
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490 | |
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491 | This should NOT be used for fitting since it copies the *q* vectors |
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492 | to the card for each evaluation. |
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493 | """ |
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494 | if self._model is None: |
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495 | self._model = core.build_model(self._model_info) |
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496 | if qy is not None: |
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497 | q_vectors = [np.asarray(qx), np.asarray(qy)] |
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498 | else: |
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499 | q_vectors = [np.asarray(qx)] |
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500 | kernel = self._model.make_kernel(q_vectors) |
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501 | pairs = [self._get_weights(p) |
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502 | for p in self._model_info.parameters.call_parameters] |
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503 | call_details, weight, value = details.build_details(kernel, pairs) |
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504 | result = kernel(call_details, weight, value, cutoff=self.cutoff) |
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505 | kernel.release() |
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506 | return result |
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507 | |
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508 | def calculate_ER(self): |
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509 | # type: () -> float |
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510 | """ |
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511 | Calculate the effective radius for P(q)*S(q) |
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512 | |
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513 | :return: the value of the effective radius |
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514 | """ |
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515 | if self._model_info.ER is None: |
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516 | return 1.0 |
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517 | else: |
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518 | value, weight = self._dispersion_mesh() |
---|
519 | fv = self._model_info.ER(*value) |
---|
520 | #print(values[0].shape, weights.shape, fv.shape) |
---|
521 | return np.sum(weight * fv) / np.sum(weight) |
---|
522 | |
---|
523 | def calculate_VR(self): |
---|
524 | # type: () -> float |
---|
525 | """ |
---|
526 | Calculate the volf ratio for P(q)*S(q) |
---|
527 | |
---|
528 | :return: the value of the volf ratio |
---|
529 | """ |
---|
530 | if self._model_info.VR is None: |
---|
531 | return 1.0 |
---|
532 | else: |
---|
533 | value, weight = self._dispersion_mesh() |
---|
534 | whole, part = self._model_info.VR(*value) |
---|
535 | return np.sum(weight * part) / np.sum(weight * whole) |
---|
536 | |
---|
537 | def set_dispersion(self, parameter, dispersion): |
---|
538 | # type: (str, weights.Dispersion) -> Dict[str, Any] |
---|
539 | """ |
---|
540 | Set the dispersion object for a model parameter |
---|
541 | |
---|
542 | :param parameter: name of the parameter [string] |
---|
543 | :param dispersion: dispersion object of type Dispersion |
---|
544 | """ |
---|
545 | if parameter.lower() in (s.lower() for s in self.params.keys()): |
---|
546 | # TODO: Store the disperser object directly in the model. |
---|
547 | # The current method of creating one on the fly whenever it is |
---|
548 | # needed is kind of funky. |
---|
549 | # Note: can't seem to get disperser parameters from sasview |
---|
550 | # (1) Could create a sasview model that has not yet # been |
---|
551 | # converted, assign the disperser to one of its polydisperse |
---|
552 | # parameters, then retrieve the disperser parameters from the |
---|
553 | # sasview model. (2) Could write a disperser parameter retriever |
---|
554 | # in sasview. (3) Could modify sasview to use sasmodels.weights |
---|
555 | # dispersers. |
---|
556 | # For now, rely on the fact that the sasview only ever uses |
---|
557 | # new dispersers in the set_dispersion call and create a new |
---|
558 | # one instead of trying to assign parameters. |
---|
559 | from . import weights |
---|
560 | disperser = weights.dispersers[dispersion.__class__.__name__] |
---|
561 | dispersion = weights.MODELS[disperser]() |
---|
562 | self.dispersion[parameter] = dispersion.get_pars() |
---|
563 | else: |
---|
564 | raise ValueError("%r is not a dispersity or orientation parameter") |
---|
565 | |
---|
566 | def _dispersion_mesh(self): |
---|
567 | # type: () -> List[Tuple[np.ndarray, np.ndarray]] |
---|
568 | """ |
---|
569 | Create a mesh grid of dispersion parameters and weights. |
---|
570 | |
---|
571 | Returns [p1,p2,...],w where pj is a vector of values for parameter j |
---|
572 | and w is a vector containing the products for weights for each |
---|
573 | parameter set in the vector. |
---|
574 | """ |
---|
575 | pars = [self._get_weights(p) |
---|
576 | for p in self._model_info.parameters.call_parameters |
---|
577 | if p.type == 'volume'] |
---|
578 | return details.dispersion_mesh(self._model_info, pars) |
---|
579 | |
---|
580 | def _get_weights(self, par): |
---|
581 | # type: (Parameter) -> Tuple[np.ndarray, np.ndarray] |
---|
582 | """ |
---|
583 | Return dispersion weights for parameter |
---|
584 | """ |
---|
585 | if par.name not in self.params: |
---|
586 | if par.name == self.multiplicity_info.control: |
---|
587 | return [self.multiplicity], [] |
---|
588 | else: |
---|
589 | return [np.NaN], [] |
---|
590 | elif par.polydisperse: |
---|
591 | dis = self.dispersion[par.name] |
---|
592 | value, weight = weights.get_weights( |
---|
593 | dis['type'], dis['npts'], dis['width'], dis['nsigmas'], |
---|
594 | self.params[par.name], par.limits, par.relative_pd) |
---|
595 | return value, weight / np.sum(weight) |
---|
596 | else: |
---|
597 | return [self.params[par.name]], [] |
---|
598 | |
---|
599 | def test_model(): |
---|
600 | # type: () -> float |
---|
601 | """ |
---|
602 | Test that a sasview model (cylinder) can be run. |
---|
603 | """ |
---|
604 | Cylinder = _make_standard_model('cylinder') |
---|
605 | cylinder = Cylinder() |
---|
606 | return cylinder.evalDistribution([0.1,0.1]) |
---|
607 | |
---|
608 | def test_rpa(): |
---|
609 | # type: () -> float |
---|
610 | """ |
---|
611 | Test that a sasview model (cylinder) can be run. |
---|
612 | """ |
---|
613 | RPA = _make_standard_model('rpa') |
---|
614 | rpa = RPA(3) |
---|
615 | return rpa.evalDistribution([0.1,0.1]) |
---|
616 | |
---|
617 | |
---|
618 | def test_model_list(): |
---|
619 | # type: () -> None |
---|
620 | """ |
---|
621 | Make sure that all models build as sasview models. |
---|
622 | """ |
---|
623 | from .exception import annotate_exception |
---|
624 | for name in core.list_models(): |
---|
625 | try: |
---|
626 | _make_standard_model(name) |
---|
627 | except: |
---|
628 | annotate_exception("when loading "+name) |
---|
629 | raise |
---|
630 | |
---|
631 | if __name__ == "__main__": |
---|
632 | print("cylinder(0.1,0.1)=%g"%test_model()) |
---|