| 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, Parameter, parse_parameter |
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| 21 | from .kernel import KernelModel, Kernel |
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| 22 | from .details import make_details, dispersion_mesh |
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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 |
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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 |
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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 | ER_ID = "radius_effective" |
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| 40 | VF_ID = "volfraction" |
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| 41 | |
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| 42 | def make_extra_pars(p_info): |
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| 43 | pars = [] |
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| 44 | if p_info.have_Fq: |
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| 45 | par = parse_parameter( |
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| 46 | "structure_factor_mode", |
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| 47 | "", |
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| 48 | 0, |
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| 49 | [["P*S","P*(1+beta*(S-1))"]], |
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| 50 | "", |
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| 51 | "Structure factor calculation") |
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| 52 | pars.append(par) |
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| 53 | return pars |
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| 54 | |
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| 55 | # TODO: core_shell_sphere model has suppressed the volume ratio calculation |
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| 56 | # revert it after making VR and ER available at run time as constraints. |
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| 57 | def make_product_info(p_info, s_info): |
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| 58 | # type: (ModelInfo, ModelInfo) -> ModelInfo |
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| 59 | """ |
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| 60 | Create info block for product model. |
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| 61 | """ |
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| 62 | # Make sure effective radius is the first parameter and |
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| 63 | # make sure volume fraction is the second parameter of the |
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| 64 | # structure factor calculator. Structure factors should not |
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| 65 | # have any magnetic parameters |
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| 66 | if not len(s_info.parameters.kernel_parameters) >= 2: |
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| 67 | raise TypeError("S needs {} and {} as its first parameters".format(ER_ID, VF_ID)) |
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| 68 | if not s_info.parameters.kernel_parameters[0].id == ER_ID: |
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| 69 | raise TypeError("S needs {} as first parameter".format(ER_ID)) |
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| 70 | if not s_info.parameters.kernel_parameters[1].id == VF_ID: |
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| 71 | raise TypeError("S needs {} as second parameter".format(VF_ID)) |
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| 72 | if not s_info.parameters.magnetism_index == []: |
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| 73 | raise TypeError("S should not have SLD parameters") |
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| 74 | p_id, p_name, p_pars = p_info.id, p_info.name, p_info.parameters |
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| 75 | s_id, s_name, s_pars = s_info.id, s_info.name, s_info.parameters |
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| 76 | |
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| 77 | # Create list of parameters for the combined model. Skip the first |
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| 78 | # parameter of S, which we verified above is effective radius. If there |
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| 79 | # are any names in P that overlap with those in S, modify the name in S |
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| 80 | # to distinguish it. |
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| 81 | p_set = set(p.id for p in p_pars.kernel_parameters) |
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| 82 | s_list = [(_tag_parameter(par) if par.id in p_set else par) |
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| 83 | for par in s_pars.kernel_parameters[1:]] |
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| 84 | # Check if still a collision after renaming. This could happen if for |
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| 85 | # example S has volfrac and P has both volfrac and volfrac_S. |
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| 86 | if any(p.id in p_set for p in s_list): |
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| 87 | raise TypeError("name collision: P has P.name and P.name_S while S has S.name") |
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| 88 | |
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| 89 | translate_name = dict((old.id, new.id) for old, new |
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| 90 | in zip(s_pars.kernel_parameters[1:], s_list)) |
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| 91 | combined_pars = p_pars.kernel_parameters + s_list + make_extra_pars(p_info) |
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| 92 | parameters = ParameterTable(combined_pars) |
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| 93 | parameters.max_pd = p_pars.max_pd + s_pars.max_pd |
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| 94 | def random(): |
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| 95 | combined_pars = p_info.random() |
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| 96 | s_names = set(par.id for par in s_pars.kernel_parameters[1:]) |
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| 97 | combined_pars.update((translate_name[k], v) |
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| 98 | for k, v in s_info.random().items() |
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| 99 | if k in s_names) |
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| 100 | return combined_pars |
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| 101 | |
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| 102 | model_info = ModelInfo() |
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| 103 | model_info.id = '@'.join((p_id, s_id)) |
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| 104 | model_info.name = '@'.join((p_name, s_name)) |
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| 105 | model_info.filename = None |
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| 106 | model_info.title = 'Product of %s and %s'%(p_name, s_name) |
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| 107 | model_info.description = model_info.title |
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| 108 | model_info.docs = model_info.title |
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| 109 | model_info.category = "custom" |
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| 110 | model_info.parameters = parameters |
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| 111 | model_info.random = random |
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| 112 | #model_info.single = p_info.single and s_info.single |
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| 113 | model_info.structure_factor = False |
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| 114 | model_info.variant_info = None |
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| 115 | #model_info.tests = [] |
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| 116 | #model_info.source = [] |
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| 117 | # Iq, Iqxy, form_volume, ER, VR and sesans |
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| 118 | # Remember the component info blocks so we can build the model |
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| 119 | model_info.composition = ('product', [p_info, s_info]) |
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| 120 | model_info.control = p_info.control |
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| 121 | model_info.hidden = p_info.hidden |
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| 122 | if getattr(p_info, 'profile', None) is not None: |
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| 123 | profile_pars = set(p.id for p in p_info.parameters.kernel_parameters) |
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| 124 | def profile(**kwargs): |
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| 125 | # extract the profile args |
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| 126 | kwargs = dict((k, v) for k, v in kwargs.items() if k in profile_pars) |
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| 127 | return p_info.profile(**kwargs) |
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| 128 | else: |
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| 129 | profile = None |
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| 130 | model_info.profile = profile |
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| 131 | model_info.profile_axes = p_info.profile_axes |
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| 132 | |
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| 133 | # TODO: delegate random to p_info, s_info |
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| 134 | #model_info.random = lambda: {} |
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| 135 | |
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| 136 | ## Show the parameter table |
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| 137 | #from .compare import get_pars, parlist |
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| 138 | #print("==== %s ====="%model_info.name) |
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| 139 | #values = get_pars(model_info) |
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| 140 | #print(parlist(model_info, values, is2d=True)) |
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| 141 | return model_info |
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| 142 | |
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| 143 | def _tag_parameter(par): |
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| 144 | """ |
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| 145 | Tag the parameter name with _S to indicate that the parameter comes from |
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| 146 | the structure factor parameter set. This is only necessary if the |
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| 147 | form factor model includes a parameter of the same name as a parameter |
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| 148 | in the structure factor. |
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| 149 | """ |
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| 150 | par = copy(par) |
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| 151 | # Protect against a vector parameter in S by appending the vector length |
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| 152 | # to the renamed parameter. Note: haven't tested this since no existing |
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| 153 | # structure factor models contain vector parameters. |
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| 154 | vector_length = par.name[len(par.id):] |
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| 155 | par.id = par.id + "_S" |
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| 156 | par.name = par.id + vector_length |
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| 157 | return par |
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| 158 | |
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| 159 | def _intermediates(P, S): |
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| 160 | # type: (np.ndarray, np.ndarray) -> OrderedDict[str, np.ndarray] |
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| 161 | """ |
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| 162 | Returns intermediate results for standard product (P(Q)*S(Q)) |
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| 163 | """ |
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| 164 | return OrderedDict(( |
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| 165 | ("P(Q)", P), |
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| 166 | ("S(Q)", S), |
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| 167 | )) |
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| 168 | |
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| 169 | def _intermediates_beta(F1, F2, S, scale, bg): |
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| 170 | # type: (np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray) -> OrderedDict[str, np.ndarray] |
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| 171 | """ |
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| 172 | Returns intermediate results for beta approximation-enabled product |
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| 173 | """ |
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| 174 | # TODO: 1. include calculated Q vector |
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| 175 | # TODO: 2. consider implications if there are intermediate results in P(Q) |
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| 176 | return OrderedDict(( |
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| 177 | ("P(Q)", scale*F2), |
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| 178 | ("S(Q)", S), |
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| 179 | ("beta(Q)", F1**2 / F2), |
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| 180 | ("S_eff(Q)", 1 + (F1**2 / F2)*(S-1)), |
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| 181 | # ("I(Q)", scale*(F2 + (F1**2)*(S-1)) + bg), |
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| 182 | )) |
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| 183 | |
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| 184 | class ProductModel(KernelModel): |
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| 185 | def __init__(self, model_info, P, S): |
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| 186 | # type: (ModelInfo, KernelModel, KernelModel) -> None |
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| 187 | #: Combined info plock for the product model |
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| 188 | self.info = model_info |
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| 189 | #: Form factor modelling individual particles. |
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| 190 | self.P = P |
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| 191 | #: Structure factor modelling interaction between particles. |
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| 192 | self.S = S |
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| 193 | |
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| 194 | #: Model precision. This is not really relevant, since it is the |
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| 195 | #: individual P and S models that control the effective dtype, |
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| 196 | #: converting the q-vectors to the correct type when the kernels |
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| 197 | #: for each are created. Ideally this should be set to the more |
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| 198 | #: precise type to avoid loss of precision, but precision in q is |
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| 199 | #: not critical (single is good enough for our purposes), so it just |
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| 200 | #: uses the precision of the form factor. |
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| 201 | self.dtype = P.dtype # type: np.dtype |
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| 202 | |
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| 203 | def make_kernel(self, q_vectors): |
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| 204 | # type: (List[np.ndarray]) -> Kernel |
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| 205 | # Note: may be sending the q_vectors to the GPU twice even though they |
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| 206 | # are only needed once. It would mess up modularity quite a bit to |
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| 207 | # handle this optimally, especially since there are many cases where |
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| 208 | # separate q vectors are needed (e.g., form in python and structure |
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| 209 | # in opencl; or both in opencl, but one in single precision and the |
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| 210 | # other in double precision). |
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| 211 | |
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| 212 | p_kernel = self.P.make_kernel(q_vectors) |
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| 213 | s_kernel = self.S.make_kernel(q_vectors) |
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| 214 | return ProductKernel(self.info, p_kernel, s_kernel) |
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| 215 | |
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| 216 | def release(self): |
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| 217 | # type: (None) -> None |
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| 218 | """ |
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| 219 | Free resources associated with the model. |
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| 220 | """ |
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| 221 | self.P.release() |
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| 222 | self.S.release() |
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| 223 | |
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| 224 | |
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| 225 | class ProductKernel(Kernel): |
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| 226 | def __init__(self, model_info, p_kernel, s_kernel): |
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| 227 | # type: (ModelInfo, Kernel, Kernel) -> None |
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| 228 | self.info = model_info |
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| 229 | self.p_kernel = p_kernel |
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| 230 | self.s_kernel = s_kernel |
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| 231 | self.dtype = p_kernel.dtype |
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| 232 | self.results = [] # type: List[np.ndarray] |
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| 233 | |
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| 234 | def __call__(self, call_details, values, cutoff, magnetic): |
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| 235 | # type: (CallDetails, np.ndarray, float, bool) -> np.ndarray |
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| 236 | p_info, s_info = self.info.composition[1] |
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| 237 | |
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| 238 | # if there are magnetic parameters, they will only be on the |
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| 239 | # form factor P, not the structure factor S. |
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| 240 | nmagnetic = len(self.info.parameters.magnetism_index) |
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| 241 | if nmagnetic: |
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| 242 | spin_index = self.info.parameters.npars + 2 |
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| 243 | magnetism = values[spin_index: spin_index+3+3*nmagnetic] |
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| 244 | else: |
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| 245 | magnetism = [] |
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| 246 | nvalues = self.info.parameters.nvalues |
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| 247 | nweights = call_details.num_weights |
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| 248 | weights = values[nvalues:nvalues + 2*nweights] |
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| 249 | |
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| 250 | # Construct the calling parameters for P. |
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| 251 | p_npars = p_info.parameters.npars |
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| 252 | p_length = call_details.length[:p_npars] |
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| 253 | p_offset = call_details.offset[:p_npars] |
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| 254 | p_details = make_details(p_info, p_length, p_offset, nweights) |
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| 255 | |
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| 256 | # Set p scale to the volume fraction in s, which is the first of the |
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| 257 | # 'S' parameters in the parameter list, or 2+np in 0-origin. |
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| 258 | volfrac = values[2+p_npars] |
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| 259 | p_values = [[volfrac, 0.0], values[2:2+p_npars], magnetism, weights] |
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| 260 | spacer = (32 - sum(len(v) for v in p_values)%32)%32 |
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| 261 | p_values.append([0.]*spacer) |
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| 262 | p_values = np.hstack(p_values).astype(self.p_kernel.dtype) |
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| 263 | |
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| 264 | # Call ER and VR for P since these are needed for S. |
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| 265 | p_er, p_vr = calc_er_vr(p_info, p_details, p_values) |
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| 266 | s_vr = (volfrac/p_vr if p_vr != 0. else volfrac) |
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| 267 | #print("volfrac:%g p_er:%g p_vr:%g s_vr:%g"%(volfrac,p_er,p_vr,s_vr)) |
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| 268 | |
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| 269 | # Construct the calling parameters for S. |
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| 270 | # The effective radius is not in the combined parameter list, so |
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| 271 | # the number of 'S' parameters is one less than expected. The |
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| 272 | # computed effective radius needs to be added into the weights |
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| 273 | # vector, especially since it is a polydisperse parameter in the |
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| 274 | # stand-alone structure factor models. We will added it at the |
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| 275 | # end so the remaining offsets don't need to change. |
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| 276 | s_npars = s_info.parameters.npars-1 |
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| 277 | s_length = call_details.length[p_npars:p_npars+s_npars] |
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| 278 | s_offset = call_details.offset[p_npars:p_npars+s_npars] |
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| 279 | s_length = np.hstack((1, s_length)) |
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| 280 | s_offset = np.hstack((nweights, s_offset)) |
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| 281 | s_details = make_details(s_info, s_length, s_offset, nweights+1) |
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| 282 | v, w = weights[:nweights], weights[nweights:] |
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| 283 | s_values = [ |
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| 284 | # scale=1, background=0, radius_effective=p_er, volfraction=s_vr |
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| 285 | [1., 0., p_er, s_vr], |
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| 286 | # structure factor parameters start after scale, background and |
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| 287 | # all the form factor parameters. Skip the volfraction parameter |
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| 288 | # as well, since it is computed elsewhere, and go to the end of the |
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| 289 | # parameter list. |
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| 290 | values[2+p_npars+1:2+p_npars+s_npars], |
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| 291 | # no magnetism parameters to include for S |
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| 292 | # add er into the (value, weights) pairs |
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| 293 | v, [p_er], w, [1.0] |
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| 294 | ] |
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| 295 | spacer = (32 - sum(len(v) for v in s_values)%32)%32 |
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| 296 | s_values.append([0.]*spacer) |
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| 297 | s_values = np.hstack(s_values).astype(self.s_kernel.dtype) |
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| 298 | |
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| 299 | # beta mode is the first parameter after the structure factor pars |
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| 300 | beta_index = 2+p_npars+s_npars |
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| 301 | beta_mode = values[beta_index] |
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| 302 | |
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| 303 | # Call the kernels |
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| 304 | s_result = self.s_kernel.Iq(s_details, s_values, cutoff, False) |
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| 305 | scale, background = values[0], values[1] |
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| 306 | if beta_mode: |
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| 307 | F1, F2, volume_avg = self.p_kernel.beta(p_details, p_values, cutoff, magnetic) |
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| 308 | combined_scale = scale*volfrac/volume_avg |
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| 309 | |
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| 310 | self.results = lambda: _intermediates_beta(F1, F2, s_result, volfrac/volume_avg, background) |
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| 311 | final_result = combined_scale*(F2 + (F1**2)*(s_result - 1)) + background |
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| 312 | |
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| 313 | else: |
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| 314 | p_result = self.p_kernel.Iq(p_details, p_values, cutoff, magnetic) |
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| 315 | |
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| 316 | self.results = lambda: _intermediates(p_result, s_result) |
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| 317 | final_result = scale*(p_result*s_result) + background |
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| 318 | |
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| 319 | #call_details.show(values) |
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| 320 | #print("values", values) |
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| 321 | #p_details.show(p_values) |
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| 322 | #print("=>", p_result) |
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| 323 | #s_details.show(s_values) |
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| 324 | #print("=>", s_result) |
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| 325 | #import pylab as plt |
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| 326 | #plt.subplot(211); plt.loglog(self.p_kernel.q_input.q, p_result, '-') |
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| 327 | #plt.subplot(212); plt.loglog(self.s_kernel.q_input.q, s_result, '-') |
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| 328 | #plt.figure() |
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| 329 | return final_result |
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| 330 | |
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| 331 | def release(self): |
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| 332 | # type: () -> None |
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| 333 | self.p_kernel.release() |
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| 334 | self.s_kernel.release() |
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| 335 | |
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| 336 | |
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| 337 | def calc_er_vr(model_info, call_details, values): |
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| 338 | # type: (ModelInfo, ParameterSet) -> Tuple[float, float] |
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| 339 | |
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| 340 | if model_info.ER is None and model_info.VR is None: |
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| 341 | return 1.0, 1.0 |
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| 342 | |
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| 343 | nvalues = model_info.parameters.nvalues |
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| 344 | value = values[nvalues:nvalues + call_details.num_weights] |
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| 345 | weight = values[nvalues + call_details.num_weights: nvalues + 2*call_details.num_weights] |
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| 346 | npars = model_info.parameters.npars |
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| 347 | # Note: changed from pairs ([v], [w]) to triples (p, [v], [w]), but the |
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| 348 | # dispersion mesh code doesn't actually care about the nominal parameter |
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| 349 | # value, p, so set it to None. |
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| 350 | pairs = [(None, value[offset:offset+length], weight[offset:offset+length]) |
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| 351 | for p, offset, length |
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| 352 | in zip(model_info.parameters.call_parameters[2:2+npars], |
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| 353 | call_details.offset, |
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| 354 | call_details.length) |
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| 355 | if p.type == 'volume'] |
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| 356 | value, weight = dispersion_mesh(model_info, pairs) |
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| 357 | |
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| 358 | if model_info.ER is not None: |
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| 359 | individual_radii = model_info.ER(*value) |
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| 360 | radius_effective = np.sum(weight*individual_radii) / np.sum(weight) |
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| 361 | else: |
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| 362 | radius_effective = 1.0 |
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| 363 | |
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| 364 | if model_info.VR is not None: |
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| 365 | whole, part = model_info.VR(*value) |
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| 366 | volume_ratio = np.sum(weight*part)/np.sum(weight*whole) |
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| 367 | else: |
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| 368 | volume_ratio = 1.0 |
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| 369 | |
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| 370 | return radius_effective, volume_ratio |
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