1 | """ |
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2 | Kernel Call Details |
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3 | =================== |
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4 | |
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5 | When calling sas computational kernels with polydispersity there are a |
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6 | number of details that need to be sent to the caller. This includes the |
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7 | list of polydisperse parameters, the number of points in the polydispersity |
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8 | weight distribution, and which parameter is the "theta" parameter for |
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9 | polar coordinate integration. The :class:`CallDetails` object maintains |
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10 | this data. Use :func:`build_details` to build a *details* object which |
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11 | can be passed to one of the computational kernels. |
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12 | """ |
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13 | |
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14 | from __future__ import print_function |
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15 | |
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16 | import numpy as np # type: ignore |
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17 | from numpy import pi, cos, sin |
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18 | |
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19 | try: |
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20 | np.meshgrid([]) |
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21 | meshgrid = np.meshgrid |
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22 | except Exception: |
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23 | # CRUFT: np.meshgrid requires multiple vectors |
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24 | def meshgrid(*args): |
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25 | if len(args) > 1: |
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26 | return np.meshgrid(*args) |
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27 | else: |
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28 | return [np.asarray(v) for v in args] |
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29 | |
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30 | try: |
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31 | from typing import List |
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32 | except ImportError: |
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33 | pass |
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34 | else: |
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35 | from .modelinfo import ModelInfo |
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36 | |
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37 | |
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38 | class CallDetails(object): |
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39 | """ |
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40 | Manage the polydispersity information for the kernel call. |
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41 | |
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42 | Conceptually, a polydispersity calculation is an integral over a mesh |
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43 | in n-D space where n is the number of polydisperse parameters. In order |
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44 | to keep the program responsive, and not crash the GPU, only a portion |
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45 | of the mesh is computed at a time. Meshes with a large number of points |
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46 | will therefore require many calls to the polydispersity loop. Restarting |
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47 | a nested loop in the middle requires that the indices of the individual |
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48 | mesh dimensions can be computed for the current loop location. This |
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49 | is handled by the *pd_stride* vector, with n//stride giving the loop |
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50 | index and n%stride giving the position in the sub loops. |
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51 | |
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52 | One of the parameters may be the latitude. When integrating in polar |
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53 | coordinates, the total circumference decreases as latitude varies from |
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54 | pi r^2 at the equator to 0 at the pole, and the weight associated |
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55 | with a range of phi values needs to be scaled by this circumference. |
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56 | This scale factor needs to be updated each time the theta value |
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57 | changes. *theta_par* indicates which of the values in the parameter |
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58 | vector is the latitude parameter, or -1 if there is no latitude |
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59 | parameter in the model. In practice, the normalization term cancels |
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60 | if the latitude is not a polydisperse parameter. |
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61 | """ |
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62 | parts = None # type: List["CallDetails"] |
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63 | def __init__(self, model_info): |
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64 | # type: (ModelInfo) -> None |
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65 | parameters = model_info.parameters |
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66 | max_pd = parameters.max_pd |
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67 | |
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68 | # Structure of the call details buffer: |
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69 | # pd_par[max_pd] pd params in order of length |
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70 | # pd_length[max_pd] length of each pd param |
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71 | # pd_offset[max_pd] offset of pd values in parameter array |
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72 | # pd_stride[max_pd] index of pd value in loop = n//stride[k] |
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73 | # num_eval total length of pd loop |
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74 | # num_weights total length of the weight vector |
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75 | # num_active number of pd params |
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76 | # theta_par parameter number for theta parameter |
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77 | self.buffer = np.empty(4*max_pd + 4, 'i4') |
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78 | |
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79 | # generate views on different parts of the array |
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80 | self._pd_par = self.buffer[0 * max_pd:1 * max_pd] |
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81 | self._pd_length = self.buffer[1 * max_pd:2 * max_pd] |
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82 | self._pd_offset = self.buffer[2 * max_pd:3 * max_pd] |
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83 | self._pd_stride = self.buffer[3 * max_pd:4 * max_pd] |
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84 | |
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85 | # theta_par is fixed |
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86 | self.theta_par = parameters.theta_offset |
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87 | |
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88 | # offset and length are for all parameters, not just pd parameters |
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89 | # They are not sent to the kernel function, though they could be. |
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90 | # They are used by the composite models (sum and product) to |
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91 | # figure out offsets into the combined value list. |
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92 | self.offset = None # type: np.ndarray |
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93 | self.length = None # type: np.ndarray |
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94 | |
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95 | # keep hold of ifno show() so we can break a values vector |
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96 | # into the individual components |
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97 | self.info = model_info |
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98 | |
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99 | @property |
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100 | def pd_par(self): |
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101 | """List of polydisperse parameters""" |
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102 | return self._pd_par |
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103 | |
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104 | @property |
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105 | def pd_length(self): |
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106 | """Number of weights for each polydisperse parameter""" |
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107 | return self._pd_length |
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108 | |
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109 | @property |
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110 | def pd_offset(self): |
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111 | """Offsets for the individual weight vectors in the set of weights""" |
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112 | return self._pd_offset |
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113 | |
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114 | @property |
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115 | def pd_stride(self): |
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116 | """Stride in the pd mesh for each pd dimension""" |
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117 | return self._pd_stride |
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118 | |
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119 | @property |
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120 | def num_eval(self): |
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121 | """Total size of the pd mesh""" |
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122 | return self.buffer[-4] |
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123 | |
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124 | @num_eval.setter |
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125 | def num_eval(self, v): |
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126 | """Total size of the pd mesh""" |
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127 | self.buffer[-4] = v |
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128 | |
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129 | @property |
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130 | def num_weights(self): |
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131 | """Total length of all the weight vectors""" |
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132 | return self.buffer[-3] |
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133 | |
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134 | @num_weights.setter |
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135 | def num_weights(self, v): |
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136 | """Total length of all the weight vectors""" |
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137 | self.buffer[-3] = v |
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138 | |
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139 | @property |
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140 | def num_active(self): |
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141 | """Number of active polydispersity loops""" |
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142 | return self.buffer[-2] |
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143 | |
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144 | @num_active.setter |
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145 | def num_active(self, v): |
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146 | """Number of active polydispersity loops""" |
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147 | self.buffer[-2] = v |
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148 | |
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149 | @property |
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150 | def theta_par(self): |
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151 | """Location of the theta parameter in the parameter vector""" |
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152 | return self.buffer[-1] |
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153 | |
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154 | @theta_par.setter |
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155 | def theta_par(self, v): |
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156 | """Location of the theta parameter in the parameter vector""" |
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157 | self.buffer[-1] = v |
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158 | |
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159 | def show(self, values=None): |
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160 | """Print the polydispersity call details to the console""" |
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161 | print("===== %s details ===="%self.info.name) |
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162 | print("num_active:%d num_eval:%d num_weights:%d theta=%d" |
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163 | % (self.num_active, self.num_eval, self.num_weights, self.theta_par)) |
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164 | if self.pd_par.size: |
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165 | print("pd_par", self.pd_par) |
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166 | print("pd_length", self.pd_length) |
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167 | print("pd_offset", self.pd_offset) |
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168 | print("pd_stride", self.pd_stride) |
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169 | if values is not None: |
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170 | nvalues = self.info.parameters.nvalues |
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171 | print("scale, background", values[:2]) |
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172 | print("val", values[2:nvalues]) |
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173 | print("pd", values[nvalues:nvalues+self.num_weights]) |
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174 | print("wt", values[nvalues+self.num_weights:nvalues+2*self.num_weights]) |
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175 | print("offsets", self.offset) |
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176 | |
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177 | |
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178 | def make_details(model_info, length, offset, num_weights): |
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179 | # type: (ModelInfo, np.ndarray, np.ndarray, int) -> CallDetails |
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180 | """ |
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181 | Return a :class:`CallDetails` object for a polydisperse calculation |
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182 | of the model defined by *model_info*. Polydispersity is defined by |
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183 | the *length* of the polydispersity distribution for each parameter |
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184 | and the *offset* of the distribution in the polydispersity array. |
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185 | Monodisperse parameters should use a polydispersity length of one |
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186 | with weight 1.0. *num_weights* is the total length of the polydispersity |
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187 | array. |
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188 | """ |
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189 | #pars = model_info.parameters.call_parameters[2:model_info.parameters.npars+2] |
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190 | #print(", ".join(str(i)+"-"+p.id for i,p in enumerate(pars))) |
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191 | #print("len:",length) |
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192 | #print("off:",offset) |
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193 | |
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194 | # Check that we arn't using too many polydispersity loops |
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195 | num_active = np.sum(length > 1) |
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196 | max_pd = model_info.parameters.max_pd |
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197 | if num_active > max_pd: |
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198 | raise ValueError("Too many polydisperse parameters") |
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199 | |
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200 | # Decreasing list of polydpersity lengths |
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201 | # Note: the reversing view, x[::-1], does not require a copy |
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202 | idx = np.argsort(length)[::-1][:max_pd] |
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203 | pd_stride = np.cumprod(np.hstack((1, length[idx]))) |
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204 | |
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205 | call_details = CallDetails(model_info) |
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206 | call_details.pd_par[:max_pd] = idx |
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207 | call_details.pd_length[:max_pd] = length[idx] |
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208 | call_details.pd_offset[:max_pd] = offset[idx] |
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209 | call_details.pd_stride[:max_pd] = pd_stride[:-1] |
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210 | call_details.num_eval = pd_stride[-1] |
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211 | call_details.num_weights = num_weights |
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212 | call_details.num_active = num_active |
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213 | call_details.length = length |
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214 | call_details.offset = offset |
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215 | #call_details.show() |
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216 | return call_details |
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217 | |
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218 | |
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219 | ZEROS = tuple([0.]*31) |
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220 | def make_kernel_args(kernel, pairs): |
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221 | # type: (Kernel, Tuple[List[np.ndarray], List[np.ndarray]]) -> Tuple[CallDetails, np.ndarray, bool] |
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222 | """ |
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223 | Converts (value, weight) pairs into parameters for the kernel call. |
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224 | |
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225 | Returns a CallDetails object indicating the polydispersity, a data object |
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226 | containing the different values, and the magnetic flag indicating whether |
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227 | any magnetic magnitudes are non-zero. Magnetic vectors (M0, phi, theta) are |
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228 | converted to rectangular coordinates (mx, my, mz). |
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229 | """ |
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230 | npars = kernel.info.parameters.npars |
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231 | nvalues = kernel.info.parameters.nvalues |
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232 | scalars = [(v[0] if len(v) else np.NaN) for v, w in pairs] |
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233 | values, weights = zip(*pairs[2:npars+2]) if npars else ((),()) |
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234 | length = np.array([len(w) for w in weights]) |
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235 | offset = np.cumsum(np.hstack((0, length))) |
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236 | call_details = make_details(kernel.info, length, offset[:-1], offset[-1]) |
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237 | # Pad value array to a 32 value boundaryd |
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238 | data_len = nvalues + 2*sum(len(v) for v in values) |
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239 | extra = (32 - data_len%32)%32 |
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240 | data = np.hstack((scalars,) + values + weights + ZEROS[:extra]) |
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241 | data = data.astype(kernel.dtype) |
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242 | is_magnetic = convert_magnetism(kernel.info.parameters, data) |
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243 | #call_details.show() |
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244 | return call_details, data, is_magnetic |
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245 | |
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246 | |
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247 | def convert_magnetism(parameters, values): |
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248 | """ |
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249 | Convert magnetism values from polar to rectangular coordinates. |
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250 | |
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251 | Returns True if any magnetism is present. |
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252 | """ |
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253 | mag = values[parameters.nvalues-3*parameters.nmagnetic:parameters.nvalues] |
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254 | mag = mag.reshape(-1, 3) |
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255 | scale = mag[:,0] |
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256 | if np.any(scale): |
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257 | theta, phi = mag[:, 1]*pi/180., mag[:, 2]*pi/180. |
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258 | cos_theta = cos(theta) |
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259 | mag[:, 0] = scale*cos_theta*cos(phi) # mx |
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260 | mag[:, 1] = scale*sin(theta) # my |
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261 | mag[:, 2] = -scale*cos_theta*sin(phi) # mz |
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262 | return True |
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263 | else: |
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264 | return False |
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265 | |
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266 | |
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267 | def dispersion_mesh(model_info, pars): |
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268 | # type: (ModelInfo) -> Tuple[List[np.ndarray], List[np.ndarray]] |
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269 | """ |
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270 | Create a mesh grid of dispersion parameters and weights. |
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271 | |
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272 | Returns [p1,p2,...],w where pj is a vector of values for parameter j |
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273 | and w is a vector containing the products for weights for each |
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274 | parameter set in the vector. |
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275 | """ |
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276 | value, weight = zip(*pars) |
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277 | #weight = [w if len(w)>0 else [1.] for w in weight] |
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278 | weight = np.vstack([v.flatten() for v in meshgrid(*weight)]) |
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279 | weight = np.prod(weight, axis=0) |
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280 | value = [v.flatten() for v in meshgrid(*value)] |
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281 | lengths = [par.length for par in model_info.parameters.kernel_parameters |
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282 | if par.type == 'volume'] |
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283 | if any(n > 1 for n in lengths): |
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284 | pars = [] |
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285 | offset = 0 |
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286 | for n in lengths: |
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287 | pars.append(np.vstack(value[offset:offset+n]) |
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288 | if n > 1 else value[offset]) |
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289 | offset += n |
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290 | value = pars |
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291 | return value, weight |
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