1 | ##################################################################### |
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2 | # M.M. McKerns, L. Strand, T. Sullivan, A. Fang, M.A.G. Aivazis, |
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3 | # "Building a framework for predictive science", Proceedings of |
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4 | # the 10th Python in Science Conference, (submitted 2011). |
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5 | ##################################################################### |
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6 | |
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7 | # the function to be minimized and initial values |
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8 | from mystic.models import rosen as my_model |
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9 | x0 = [0.8, 1.2, 0.7] |
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10 | |
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11 | # configure the solver and obtain the solution |
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12 | from mystic.solvers import fmin |
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13 | solution = fmin(my_model, x0) |
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14 | |
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15 | ##################################################################### |
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16 | |
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17 | # the function to be minimized and initial values |
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18 | from mystic.models import rosen as my_model |
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19 | x0 = [0.8, 1.2, 0.7] |
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20 | |
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21 | # get monitor and termination condition objects |
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22 | from mystic.monitors import Monitor, VerboseMonitor |
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23 | stepmon = VerboseMonitor(5) |
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24 | evalmon = Monitor() |
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25 | from mystic.termination import ChangeOverGeneration |
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26 | COG = ChangeOverGeneration() |
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27 | |
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28 | # instantiate and configure the solver |
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29 | from mystic.solvers import NelderMeadSimplexSolver |
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30 | solver = NelderMeadSimplexSolver(len(x0)) |
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31 | solver.SetInitialPoints(x0) |
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32 | solver.SetGenerationMonitor(stepmon) |
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33 | solver.SetEvaluationMonitor(evalmon) |
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34 | solver.Solve(my_model, COG) |
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35 | |
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36 | # obtain the solution |
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37 | solution = solver.bestSolution |
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38 | |
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39 | # obtain diagnostic information |
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40 | function_evals = solver.evaluations |
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41 | iterations = solver.generations |
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42 | cost = solver.bestEnergy |
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43 | |
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44 | # modify the solver configuration, and continue |
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45 | COG = ChangeOverGeneration(tolerance=1e-8) |
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46 | solver.Solve(my_model, COG) |
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47 | |
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48 | # obtain the new solution |
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49 | solution = solver.bestSolution |
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50 | |
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51 | ##################################################################### |
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52 | |
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53 | # a user-provided constraints function |
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54 | def constrain(x): |
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55 | x[1] = x[0] |
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56 | return x |
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57 | |
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58 | # the function to be minimized and the bounds |
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59 | from mystic.models import rosen as my_model |
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60 | lb = [0.0, 0.0, 0.0] |
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61 | ub = [2.0, 2.0, 2.0] |
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62 | |
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63 | # get termination condition object |
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64 | from mystic.termination import ChangeOverGeneration |
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65 | COG = ChangeOverGeneration() |
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66 | |
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67 | # instantiate and configure the solver |
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68 | from mystic.solvers import NelderMeadSimplexSolver |
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69 | solver = NelderMeadSimplexSolver(len(x0)) |
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70 | solver.SetRandomInitialPoints(lb, ub) |
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71 | solver.SetStrictRanges(lb, ub) |
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72 | solver.SetConstraints(constrain) |
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73 | solver.Solve(my_model, COG) |
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74 | |
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75 | # obtain the solution |
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76 | solution = solver.bestSolution |
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77 | |
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78 | ##################################################################### |
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79 | |
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80 | # a user-provided constraints function |
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81 | constraints = """ |
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82 | x2 = x1 |
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83 | """ |
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84 | from mystic.constraints import parse |
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85 | constrain = parse(constraints) |
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86 | |
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87 | ##################################################################### |
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88 | |
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89 | # generate a model from a stock 'model factory' |
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90 | from mystic.models.lorentzian import Lorentzian |
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91 | lorentz = Lorentzian(coeffs) |
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92 | |
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93 | # evaluate the model |
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94 | y = lorentz(x) |
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95 | |
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96 | ##################################################################### |
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97 | |
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98 | # a user-provided model function |
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99 | def identify(x) |
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100 | return x |
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101 | |
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102 | # add pathos infrastructure (included in mystic) |
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103 | from mystic.tools import modelFactory, Monitor |
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104 | evalmon = Monitor() |
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105 | my_model = modelFactory(identify, monitor=evalmon) |
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106 | |
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107 | # evaluate the model |
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108 | y = my_model(x) |
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109 | |
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110 | # evaluate the model with a map function |
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111 | from mystic.tools import PythonMap |
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112 | my_map = PythonMap() |
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113 | z = my_map(my_model, range(10)) |
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114 | |
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115 | ##################################################################### |
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116 | |
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117 | # a user-provided model function |
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118 | def identify(x) |
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119 | return x |
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120 | |
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121 | # cast the model as a distributed service |
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122 | from pathos.servers import sshServer |
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123 | id = 'foo.caltech.edu:50000:spike42' |
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124 | my_proxy = sshServer(identify, server=id) |
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125 | |
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126 | # evaluate the model via proxy |
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127 | y = my_proxy(x) |
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128 | |
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129 | ##################################################################### |
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130 | |
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131 | # a user-provided model function |
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132 | def identify(x) |
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133 | return x |
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134 | |
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135 | # select and configure a parallel map |
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136 | from pathos.maps import ipcPool |
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137 | my_map = ipcPool(2, servers=['foo.caltech.edu']) |
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138 | |
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139 | # evaluate the model in parallel |
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140 | z = my_map(identify, range(10)) |
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141 | |
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142 | ##################################################################### |
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143 | |
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144 | # configure and build map |
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145 | from pathos.launchers import ipc |
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146 | from pathos.strategies import pool |
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147 | from pathos.tools import mapFactory |
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148 | my_map = mapFactory(launcher=ipc, strategy=pool) |
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149 | |
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150 | ##################################################################### |
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151 | |
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152 | # establish a tunnel |
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153 | from pathos.tunnel import sshTunnel |
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154 | uid = 'foo.caltech.edu:12345:tunnel69' |
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155 | tunnel_proxy = sshTunnel(uid) |
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156 | |
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157 | # inspect the ports |
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158 | localport = tunnel_proxy.lport |
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159 | remoteport = tunnel_proxy.rport |
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160 | |
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161 | # a user-provided model function |
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162 | def identify(x) |
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163 | return x |
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164 | |
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165 | # cast the model as a distributed service |
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166 | from pathos.servers import ipcServer |
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167 | id = 'localhost:%s:bug01' % localport |
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168 | my_proxy = ipcServer(identify, server=id) |
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169 | |
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170 | # evaluate the model via tunneled proxy |
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171 | y = my_proxy(x) |
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172 | |
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173 | # disconnect the tunnel |
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174 | tunnel_proxy.disconnect() |
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175 | |
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176 | ##################################################################### |
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177 | |
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178 | # configure and build map |
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179 | from pyina.launchers import mpirun |
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180 | from pyina.strategies import carddealer as card |
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181 | from pyina.tools import mapFactory |
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182 | my_map = mapFactory(4, launcher=mpirun, strategy=card) |
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183 | |
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184 | ##################################################################### |
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185 | |
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186 | # the function to be minimized and the bounds |
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187 | from mystic.models import rosen as my_model |
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188 | lb = [0.0, 0.0, 0.0] |
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189 | ub = [2.0, 2.0, 2.0] |
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190 | |
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191 | # get termination condition object |
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192 | from mystic.termination import ChangeOverGeneration |
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193 | COG = ChangeOverGeneration() |
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194 | |
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195 | # select the parallel launch configuration |
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196 | from pyina.maps import MpirunCarddealer |
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197 | my_map = MpirunCarddealer(4) |
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198 | |
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199 | # instantiate and configure the solver |
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200 | from mystic.solvers import DifferentialEvolutionSolver |
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201 | solver = DifferentialEvolutionSolver(len(lb), 20) |
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202 | solver.SetRandomInitialPoints(lb, ub) |
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203 | solver.SetStrictRanges(lb, ub) |
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204 | solver.SetEvaluationMap(my_map) |
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205 | solver.Solve(my_model, COG) |
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206 | |
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207 | # obtain the solution |
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208 | solution = solver.bestSolution |
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209 | |
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210 | ##################################################################### |
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211 | |
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212 | # the function to be minimized and the bounds |
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213 | from mystic.models import rosen as my_model |
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214 | lb = [0.0, 0.0, 0.0] |
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215 | ub = [2.0, 2.0, 2.0] |
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216 | |
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217 | # get monitor and termination condition objects |
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218 | from mystic.monitors import LoggingMonitor |
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219 | stepmon = LoggingMonitor(1, âlog.txtâ) |
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220 | from mystic.termination import ChangeOverGeneration |
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221 | COG = ChangeOverGeneration() |
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222 | |
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223 | # select the parallel launch configuration |
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224 | from pyina.maps import TorqueMpirunCarddealer |
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225 | my_map = TorqueMpirunCarddealer(â5:ppn=4â) |
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226 | |
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227 | # instantiate and configure the nested solver |
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228 | from mystic.solvers import PowellDirectionalSolver |
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229 | my_solver = PowellDirectionalSolver(len(lb)) |
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230 | my_solver.SetStrictRanges(lb, ub) |
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231 | my_solver.SetEvaluationLimits(50) |
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232 | |
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233 | # instantiate and configure the outer solver |
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234 | from mystic.solvers import BuckshotSolver |
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235 | solver = BuckshotSolver(len(lb), 20) |
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236 | solver.SetRandomInitialPoints(lb, ub) |
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237 | solver.SetGenerationMonitor(stepmon) |
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238 | solver.SetNestedSolver(my_solver) |
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239 | solver.SetSolverMap(my_map) |
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240 | solver.Solve(my_model, COG) |
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241 | |
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242 | # obtain the solution |
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243 | solution = solver.bestSolution |
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244 | |
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245 | ##################################################################### |
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246 | |
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247 | # prepare a (F(X) - G)**2 a metric |
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248 | def costFactory(my_model, my_data): |
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249 | def cost(param): |
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250 | |
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251 | # compute the cost |
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252 | return ( my_model(param) - my_data )**2 |
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253 | |
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254 | return cost |
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255 | |
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256 | ##################################################################### |
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257 | ''' |
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258 | The calculation of the diameter is performed as a nested |
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259 | optimization, as shown above for the BuckshotSolver. Each |
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260 | inner optimization is a calculation of a component |
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261 | suboscillation, using the a global optimizer |
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262 | (such as DifferentialEvolutionSolver) and the cost |
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263 | metric shown above. |
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264 | ''' |
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265 | |
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266 | # prepare a (F(X) - F(X'))**2 cost metric |
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267 | def suboscillationFactory(my_model, i): |
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268 | def cost(param): |
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269 | |
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270 | # get X and X' (Xi' is appended to X at param[-1]) |
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271 | x = param[:-1] |
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272 | x_prime = param[:i] + param[-1:] + param[i+1:-1] |
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273 | |
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274 | # compute the suboscillation |
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275 | return -( my_model(x) - my_model(x_prime) )**2 |
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276 | |
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277 | return cost |
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278 | |
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279 | ##################################################################### |
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280 | ''' |
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281 | Global optimizations used in solving OUQ problems are |
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282 | composed in the same manner as shown above for the |
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283 | DifferentialEvolutionSolver. |
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284 | ''' |
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285 | |
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286 | # OUQ requires bounds in a very specific form... |
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287 | # param = [wxi]*nx + [xi]*nx + [wyi]*ny + [yi]*ny + [wzi]*nz + [zi]*nz |
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288 | npts = (nx,ny,nz) |
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289 | lb = (nx * w_lower) + (nx * x_lower) \ |
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290 | + (ny * w_lower) + (ny * y_lower) \ |
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291 | + (nz * w_lower) + (nz * z_lower) |
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292 | ub = (nx * w_upper) + (nx * x_upper) \ |
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293 | + (ny * w_upper) + (ny * y_upper) \ |
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294 | + (nz * w_upper) + (nz * z_upper) |
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295 | |
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296 | from mystic.math.measures import split_param |
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297 | from mystic.math.dirac_measure import product_measure |
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298 | from mystic.math import almostEqual |
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299 | |
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300 | # split bounds into weight-only & sample-only |
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301 | w_lb, m_lb = split_param(lb, npts) |
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302 | w_ub, m_ub = split_param(ub, npts) |
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303 | |
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304 | # generate constraints function |
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305 | def constraints(param): |
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306 | prodmeasure = product_measure() |
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307 | prodmeasure.load(param, npts) |
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308 | |
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309 | # impose norm on measures |
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310 | for measure in prodmeasure: |
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311 | if not almostEqual(float(measure.mass), 1.0): |
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312 | measure.normalize() |
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313 | |
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314 | # impose expectation on product measure |
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315 | E = float(prodmeasure.get_expect(my_model)) |
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316 | if not (E <= float(target_mean + error)) \ |
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317 | or not (float(target_mean - error) <= E): |
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318 | prodmeasure.set_expect((target_mean, error), my_model, (m_lb, m_ub)) |
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319 | |
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320 | # extract weights and positions |
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321 | return prodmeasure.flatten() |
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322 | |
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323 | # generate maximizing function |
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324 | def cost(param): |
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325 | prodmeasure = product_measure() |
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326 | prodmeasure.load(param, npts) |
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327 | return MINMAX * prodmeasure.pof(my_model) |
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328 | |
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329 | ##################################################################### |
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330 | """ |
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331 | DIRECT: |
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332 | * Add more python optimizers: scipy, OpenOpt, PARK (snobfit) |
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333 | * Allow for derivative and gradient capture -> use Sow? |
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334 | * get "handler" to work in parallel |
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335 | * Better 'programmatic' interface for handler |
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336 | * Add more options to handler (i.e. toggle_verbosity?, get_cost?, ...?) |
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337 | * Allow sigint_callback to take a list (i.e. provide call[i]) |
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338 | * Add "constraints" to models (design similar to pyre.inventory and validators) |
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339 | |
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340 | INDIRECT: |
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341 | * Build a failure test suite, and a proper test suite |
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342 | * Try one of the VTF apps... or Sean's "cain" library |
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343 | |
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344 | REFERENCE: |
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345 | * Look at PARK's rangemap.py for bounds and range mapping |
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346 | * Look at PARK's parameter.py, deps.py, expression.py, & assembly.py |
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347 | * <-- Find OpenOpt's model & optimizer API --> |
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348 | * <-- Find DAKOTA's model & optimizer API --> |
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349 | """ |
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