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, radians |
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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, Tuple, Sequence |
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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 | from .modelinfo import ParameterTable |
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37 | |
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38 | |
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39 | class CallDetails(object): |
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40 | """ |
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41 | Manage the polydispersity information for the kernel call. |
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42 | |
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43 | Conceptually, a polydispersity calculation is an integral over a mesh |
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44 | in n-D space where n is the number of polydisperse parameters. In order |
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45 | to keep the program responsive, and not crash the GPU, only a portion |
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46 | of the mesh is computed at a time. Meshes with a large number of points |
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47 | will therefore require many calls to the polydispersity loop. Restarting |
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48 | a nested loop in the middle requires that the indices of the individual |
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49 | mesh dimensions can be computed for the current loop location. This |
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50 | is handled by the *pd_stride* vector, with n//stride giving the loop |
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51 | index and n%stride giving the position in the sub loops. |
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52 | |
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53 | One of the parameters may be the latitude. When integrating in polar |
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54 | coordinates, the total circumference decreases as latitude varies from |
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55 | pi r^2 at the equator to 0 at the pole, and the weight associated |
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56 | with a range of latitude values needs to be scaled by this circumference. |
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57 | This scale factor needs to be updated each time the theta value |
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58 | changes. *theta_par* indicates which of the values in the parameter |
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59 | vector is the latitude parameter, or -1 if there is no latitude |
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60 | parameter in the model. In practice, the normalization term cancels |
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61 | if the latitude is not a polydisperse parameter. |
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62 | """ |
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63 | parts = None # type: List["CallDetails"] |
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64 | def __init__(self, model_info): |
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65 | # type: (ModelInfo) -> None |
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66 | parameters = model_info.parameters |
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67 | max_pd = parameters.max_pd |
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68 | |
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69 | # Structure of the call details buffer: |
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70 | # pd_par[max_pd] pd params in order of length |
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71 | # pd_length[max_pd] length of each pd param |
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72 | # pd_offset[max_pd] offset of pd values in parameter array |
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73 | # pd_stride[max_pd] index of pd value in loop = n//stride[k] |
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74 | # num_eval total length of pd loop |
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75 | # num_weights total length of the weight vector |
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76 | # num_active number of pd params |
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77 | # theta_par parameter number for theta parameter |
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78 | self.buffer = np.empty(4*max_pd + 4, 'i4') |
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79 | |
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80 | # generate views on different parts of the array |
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81 | self._pd_par = self.buffer[0 * max_pd:1 * max_pd] |
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82 | self._pd_length = self.buffer[1 * max_pd:2 * max_pd] |
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83 | self._pd_offset = self.buffer[2 * max_pd:3 * max_pd] |
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84 | self._pd_stride = self.buffer[3 * max_pd:4 * max_pd] |
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85 | |
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86 | # theta_par is fixed |
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87 | self.theta_par = parameters.theta_offset |
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88 | |
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89 | # offset and length are for all parameters, not just pd parameters |
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90 | # They are not sent to the kernel function, though they could be. |
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91 | # They are used by the composite models (sum and product) to |
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92 | # figure out offsets into the combined value list. |
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93 | self.offset = None # type: np.ndarray |
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94 | self.length = None # type: np.ndarray |
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95 | |
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96 | # keep hold of ifno show() so we can break a values vector |
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97 | # into the individual components |
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98 | self.info = model_info |
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99 | |
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100 | @property |
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101 | def pd_par(self): |
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102 | """List of polydisperse parameters""" |
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103 | return self._pd_par |
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104 | |
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105 | @property |
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106 | def pd_length(self): |
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107 | """Number of weights for each polydisperse parameter""" |
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108 | return self._pd_length |
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109 | |
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110 | @property |
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111 | def pd_offset(self): |
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112 | """Offsets for the individual weight vectors in the set of weights""" |
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113 | return self._pd_offset |
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114 | |
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115 | @property |
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116 | def pd_stride(self): |
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117 | """Stride in the pd mesh for each pd dimension""" |
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118 | return self._pd_stride |
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119 | |
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120 | @property |
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121 | def num_eval(self): |
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122 | """Total size of the pd mesh""" |
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123 | return self.buffer[-4] |
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124 | |
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125 | @num_eval.setter |
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126 | def num_eval(self, v): |
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127 | """Total size of the pd mesh""" |
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128 | self.buffer[-4] = v |
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129 | |
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130 | @property |
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131 | def num_weights(self): |
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132 | """Total length of all the weight vectors""" |
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133 | return self.buffer[-3] |
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134 | |
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135 | @num_weights.setter |
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136 | def num_weights(self, v): |
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137 | """Total length of all the weight vectors""" |
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138 | self.buffer[-3] = v |
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139 | |
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140 | @property |
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141 | def num_active(self): |
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142 | """Number of active polydispersity loops""" |
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143 | return self.buffer[-2] |
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144 | |
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145 | @num_active.setter |
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146 | def num_active(self, v): |
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147 | """Number of active polydispersity loops""" |
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148 | self.buffer[-2] = v |
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149 | |
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150 | @property |
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151 | def theta_par(self): |
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152 | """Location of the theta parameter in the parameter vector""" |
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153 | return self.buffer[-1] |
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154 | |
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155 | @theta_par.setter |
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156 | def theta_par(self, v): |
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157 | """Location of the theta parameter in the parameter vector""" |
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158 | self.buffer[-1] = v |
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159 | |
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160 | def show(self, values=None): |
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161 | """Print the polydispersity call details to the console""" |
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162 | print("===== %s details ===="%self.info.name) |
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163 | print("num_active:%d num_eval:%d num_weights:%d theta=%d" |
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164 | % (self.num_active, self.num_eval, self.num_weights, self.theta_par)) |
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165 | if self.pd_par.size: |
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166 | print("pd_par", self.pd_par) |
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167 | print("pd_length", self.pd_length) |
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168 | print("pd_offset", self.pd_offset) |
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169 | print("pd_stride", self.pd_stride) |
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170 | if values is not None: |
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171 | nvalues = self.info.parameters.nvalues |
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172 | print("scale, background", values[:2]) |
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173 | print("val", values[2:nvalues]) |
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174 | print("pd", values[nvalues:nvalues+self.num_weights]) |
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175 | print("wt", values[nvalues+self.num_weights:nvalues+2*self.num_weights]) |
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176 | print("offsets", self.offset) |
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177 | |
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178 | |
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179 | def make_details(model_info, length, offset, num_weights): |
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180 | # type: (ModelInfo, np.ndarray, np.ndarray, int) -> CallDetails |
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181 | """ |
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182 | Return a :class:`CallDetails` object for a polydisperse calculation |
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183 | of the model defined by *model_info*. Polydispersity is defined by |
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184 | the *length* of the polydispersity distribution for each parameter |
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185 | and the *offset* of the distribution in the polydispersity array. |
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186 | Monodisperse parameters should use a polydispersity length of one |
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187 | with weight 1.0. *num_weights* is the total length of the polydispersity |
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188 | array. |
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189 | """ |
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190 | #pars = model_info.parameters.call_parameters[2:model_info.parameters.npars+2] |
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191 | #print(", ".join(str(i)+"-"+p.id for i,p in enumerate(pars))) |
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192 | #print("len:",length) |
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193 | #print("off:",offset) |
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194 | |
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195 | # Check that we aren't using too many polydispersity loops |
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196 | num_active = np.sum(length > 1) |
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197 | max_pd = model_info.parameters.max_pd |
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198 | if num_active > max_pd: |
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199 | raise ValueError("Too many polydisperse parameters") |
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200 | |
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201 | # Decreasing list of polydpersity lengths |
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202 | # Note: the reversing view, x[::-1], does not require a copy |
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203 | idx = np.argsort(length)[::-1][:max_pd] |
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204 | pd_stride = np.cumprod(np.hstack((1, length[idx]))) |
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205 | |
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206 | call_details = CallDetails(model_info) |
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207 | call_details.pd_par[:max_pd] = idx |
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208 | call_details.pd_length[:max_pd] = length[idx] |
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209 | call_details.pd_offset[:max_pd] = offset[idx] |
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210 | call_details.pd_stride[:max_pd] = pd_stride[:-1] |
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211 | call_details.num_eval = pd_stride[-1] |
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212 | call_details.num_weights = num_weights |
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213 | call_details.num_active = num_active |
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214 | call_details.length = length |
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215 | call_details.offset = offset |
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216 | #call_details.show() |
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217 | return call_details |
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218 | |
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219 | |
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220 | ZEROS = tuple([0.]*31) |
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221 | def make_kernel_args(kernel, mesh): |
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222 | # type: (Kernel, Tuple[List[np.ndarray], List[np.ndarray]]) -> Tuple[CallDetails, np.ndarray, bool] |
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223 | """ |
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224 | Converts (value, dispersity, weight) for each parameter into kernel pars. |
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225 | |
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226 | Returns a CallDetails object indicating the polydispersity, a data object |
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227 | containing the different values, and the magnetic flag indicating whether |
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228 | any magnetic magnitudes are non-zero. Magnetic vectors (M0, phi, theta) are |
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229 | converted to rectangular coordinates (mx, my, mz). |
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230 | """ |
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231 | npars = kernel.info.parameters.npars |
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232 | nvalues = kernel.info.parameters.nvalues |
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233 | scalars = [value for value, dispersity, weight in mesh] |
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234 | # skipping scale and background when building values and weights |
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235 | values, dispersity, weights = zip(*mesh[2:npars+2]) if npars else ((), (), ()) |
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236 | #weights = correct_theta_weights(kernel.info.parameters, dispersity, weights) |
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237 | length = np.array([len(w) for w in weights]) |
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238 | offset = np.cumsum(np.hstack((0, length))) |
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239 | call_details = make_details(kernel.info, length, offset[:-1], offset[-1]) |
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240 | # Pad value array to a 32 value boundaryd |
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241 | data_len = nvalues + 2*sum(len(v) for v in dispersity) |
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242 | extra = (32 - data_len%32)%32 |
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243 | data = np.hstack((scalars,) + dispersity + weights + ZEROS[:extra]) |
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244 | data = data.astype(kernel.dtype) |
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245 | is_magnetic = convert_magnetism(kernel.info.parameters, data) |
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246 | #call_details.show() |
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247 | return call_details, data, is_magnetic |
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248 | |
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249 | def correct_theta_weights(parameters, dispersity, weights): |
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250 | # type: (ParameterTable, Sequence[np.ndarray], Sequence[np.ndarray]) -> Sequence[np.ndarray] |
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251 | """ |
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252 | If there is a theta parameter, update the weights of that parameter so that |
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253 | the cosine weighting required for polar integration is preserved. |
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254 | |
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255 | Avoid evaluation strictly at the pole, which would otherwise send the |
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256 | weight to zero. This is probably not a problem in practice (if dispersity |
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257 | is +/- 90, then you probably should be using a 1-D model of the circular |
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258 | average). |
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259 | |
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260 | Note: scale and background parameters are not include in the tuples for |
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261 | dispersity and weights, so index is parameters.theta_offset, not |
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262 | parameters.theta_offset+2 |
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263 | |
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264 | Returns updated weights vectors |
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265 | """ |
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266 | # TODO: explain in a comment why scale and background are missing |
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267 | # Apparently the parameters.theta_offset similarly skips scale and |
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268 | # and background, so the indexing works out, but they are still shipped |
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269 | # to the kernel, so we need to add two there. |
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270 | if parameters.theta_offset >= 0: |
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271 | index = parameters.theta_offset |
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272 | theta = dispersity[index] |
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273 | # TODO: modify the dispersity vector to avoid the theta=-90,90,270,... |
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274 | theta_weight = abs(cos(radians(theta))) |
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275 | weights = tuple(theta_weight*w if k == index else w |
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276 | for k, w in enumerate(weights)) |
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277 | return weights |
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278 | |
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279 | |
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280 | def convert_magnetism(parameters, values): |
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281 | # type: (ParameterTable, Sequence[np.ndarray]) -> bool |
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282 | """ |
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283 | Convert magnetism values from polar to rectangular coordinates. |
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284 | |
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285 | Returns True if any magnetism is present. |
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286 | """ |
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287 | mag = values[parameters.nvalues-3*parameters.nmagnetic:parameters.nvalues] |
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288 | mag = mag.reshape(-1, 3) |
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289 | scale = mag[:,0] |
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290 | if np.any(scale): |
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291 | theta, phi = radians(mag[:, 1]), radians(mag[:, 2]) |
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292 | cos_theta = cos(theta) |
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293 | mag[:, 0] = scale*cos_theta*cos(phi) # mx |
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294 | mag[:, 1] = scale*sin(theta) # my |
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295 | mag[:, 2] = -scale*cos_theta*sin(phi) # mz |
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296 | return True |
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297 | else: |
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298 | return False |
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299 | |
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300 | |
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301 | def dispersion_mesh(model_info, mesh): |
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302 | # type: (ModelInfo) -> Tuple[List[np.ndarray], List[np.ndarray]] |
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303 | """ |
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304 | Create a mesh grid of dispersion parameters and weights. |
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305 | |
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306 | *mesh* is a list of (value, dispersity, weights), where the values |
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307 | are the individual parameter values, and (dispersity, weights) is |
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308 | the distribution of parameter values. |
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309 | |
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310 | Only the volume parameters should be included in this list. Orientation |
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311 | parameters do not affect the calculation of effective radius or volume |
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312 | ratio. This is convenient since it avoids the distinction between |
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313 | value and dispersity that is present in orientation parameters but not |
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314 | shape parameters. |
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315 | |
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316 | Returns [p1,p2,...],w where pj is a vector of values for parameter j |
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317 | and w is a vector containing the products for weights for each |
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318 | parameter set in the vector. |
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319 | """ |
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320 | _, dispersity, weight = zip(*mesh) |
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321 | #weight = [w if len(w)>0 else [1.] for w in weight] |
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322 | weight = np.vstack([v.flatten() for v in meshgrid(*weight)]) |
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323 | weight = np.prod(weight, axis=0) |
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324 | dispersity = [v.flatten() for v in meshgrid(*dispersity)] |
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325 | lengths = [par.length for par in model_info.parameters.kernel_parameters |
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326 | if par.type == 'volume'] |
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327 | if any(n > 1 for n in lengths): |
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328 | pars = [] |
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329 | offset = 0 |
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330 | for n in lengths: |
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331 | pars.append(np.vstack(dispersity[offset:offset+n]) |
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332 | if n > 1 else dispersity[offset]) |
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333 | offset += n |
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334 | dispersity = pars |
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335 | return dispersity, weight |
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