1 | # This program is public domain |
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2 | """ |
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3 | Parameter expression evaluator. |
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4 | |
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5 | For systems in which constraints are expressed as string expressions rather |
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6 | than python code, :func:`compile_constraints` can construct an expression |
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7 | evaluator that substitutes the computed values of the expressions into the |
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8 | parameters. |
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9 | |
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10 | The compiler requires a symbol table, an expression set and a context. |
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11 | The symbol table maps strings containing fully qualified names such as |
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12 | 'M1.c[3].full_width' to parameter objects with a 'value' property that |
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13 | can be queried and set. The expression set maps symbol names from the |
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14 | symbol table to string expressions. The context provides additional symbols |
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15 | for the expressions in addition to the usual mathematical functions and |
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16 | constants. |
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17 | |
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18 | The expressions are compiled and interpreted by python, with only minimal |
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19 | effort to make sure that they don't contain bad code. The resulting |
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20 | constraints function returns 0 so it can be used directly in a fit problem |
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21 | definition. |
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22 | |
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23 | Extracting the symbol table from the model depends on the structure of the |
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24 | model. If fitness.parameters() is set correctly, then this should simply |
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25 | be a matter of walking the parameter data, remembering the path to each |
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26 | parameter in the symbol table. For compactness, dictionary elements should |
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27 | be referenced by .name rather than ["name"]. Model name can be used as the |
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28 | top level. |
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29 | |
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30 | Getting the parameter expressions applied correctly is challenging. |
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31 | The following monkey patch works by overriding model_update in FitProblem |
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32 | so that after setp(p) is called and, the constraints expression can be |
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33 | applied before telling the underlying fitness function that the model |
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34 | is out of date:: |
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35 | |
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36 | # Override model update so that parameter constraints are applied |
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37 | problem._model_update = problem.model_update |
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38 | def model_update(): |
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39 | constraints() |
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40 | problem._model_update() |
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41 | problem.model_update = model_update |
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42 | |
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43 | Ideally, this interface will change |
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44 | """ |
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45 | from __future__ import print_function |
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46 | |
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47 | import math |
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48 | import re |
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49 | |
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50 | # simple pattern which matches symbols. Note that it will also match |
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51 | # invalid substrings such as a3...9, but given syntactically correct |
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52 | # input it will only match symbols. |
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53 | _symbol_pattern = re.compile('([a-zA-Z_][a-zA-Z_0-9.]*)') |
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54 | |
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55 | def _symbols(expr,symtab): |
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56 | """ |
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57 | Given an expression string and a symbol table, return the set of symbols |
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58 | used in the expression. Symbols are only returned once even if they |
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59 | occur multiple times. The return value is a set with the elements in |
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60 | no particular order. |
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61 | |
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62 | This is the first step in computing a dependency graph. |
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63 | """ |
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64 | matches = [m.group(0) for m in _symbol_pattern.finditer(expr)] |
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65 | return set([symtab[m] for m in matches if m in symtab]) |
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66 | |
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67 | def _substitute(expr,mapping): |
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68 | """ |
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69 | Replace all occurrences of symbol s with mapping[s] for s in mapping. |
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70 | """ |
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71 | # Find the symbols and the mapping |
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72 | matches = [(m.start(),m.end(),mapping[m.group(1)]) |
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73 | for m in _symbol_pattern.finditer(expr) |
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74 | if m.group(1) in mapping] |
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75 | |
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76 | # Split the expression in to pieces, with new symbols replacing old |
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77 | pieces = [] |
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78 | offset = 0 |
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79 | for start,end,text in matches: |
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80 | pieces += [expr[offset:start],text] |
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81 | offset = end |
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82 | pieces.append(expr[offset:]) |
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83 | |
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84 | # Join the pieces and return them |
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85 | return "".join(pieces) |
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86 | |
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87 | def _find_dependencies(symtab, exprs): |
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88 | """ |
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89 | Returns a list of pair-wise dependencies from the parameter expressions. |
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90 | |
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91 | For example, if p3 = p1+p2, then find_dependencies([p1,p2,p3]) will |
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92 | return [(p3,p1),(p3,p2)]. For base expressions without dependencies, |
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93 | such as p4 = 2*pi, this should return [(p4, None)] |
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94 | """ |
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95 | deps = [(target,source) |
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96 | for target,expr in exprs.items() |
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97 | for source in _symbols_or_none(expr,symtab)] |
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98 | return deps |
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99 | |
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100 | # Hack to deal with expressions without dependencies --- return a fake |
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101 | # dependency of None. |
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102 | # The better solution is fix order_dependencies so that it takes a |
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103 | # dictionary of {symbol: dependency_list}, for which no dependencies |
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104 | # is simply []; fix in parameter_mapping as well |
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105 | def _symbols_or_none(expr,symtab): |
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106 | syms = _symbols(expr,symtab) |
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107 | return syms if len(syms) else [None] |
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108 | |
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109 | def _parameter_mapping(pairs): |
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110 | """ |
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111 | Find the parameter substitution we need so that expressions can |
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112 | be evaluated without having to traverse a chain of |
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113 | model.layer.parameter.value |
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114 | """ |
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115 | left,right = zip(*pairs) |
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116 | pars = list(sorted(p for p in set(left+right) if p is not None)) |
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117 | definition = dict( ('P%d'%i,p) for i,p in enumerate(pars) ) |
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118 | # p is None when there is an expression with no dependencies |
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119 | substitution = dict( (p,'P%d.value'%i) |
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120 | for i,p in enumerate(sorted(pars)) |
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121 | if p is not None) |
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122 | return definition, substitution |
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123 | |
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124 | def no_constraints(): |
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125 | """ |
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126 | This parameter set has no constraints between the parameters. |
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127 | """ |
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128 | pass |
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129 | |
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130 | def compile_constraints(symtab, exprs, context={}): |
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131 | """ |
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132 | Build and return a function to evaluate all parameter expressions in |
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133 | the proper order. |
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134 | |
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135 | Input: |
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136 | |
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137 | *symtab* is the symbol table for the model: { 'name': parameter } |
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138 | |
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139 | *exprs* is the set of computed symbols: { 'name': 'expression' } |
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140 | |
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141 | *context* is any additional context needed to evaluate the expression |
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142 | |
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143 | Return: |
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144 | |
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145 | updater function which sets parameter.value for each expression |
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146 | |
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147 | Raises: |
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148 | |
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149 | AssertionError - model, parameter or function is missing |
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150 | |
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151 | SyntaxError - improper expression syntax |
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152 | |
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153 | ValueError - expressions have circular dependencies |
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154 | |
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155 | This function is not terribly sophisticated, and it would be easy to |
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156 | trick. However it handles the common cases cleanly and generates |
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157 | reasonable messages for the common errors. |
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158 | |
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159 | This code has not been fully audited for security. While we have |
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160 | removed the builtins and the ability to import modules, there may |
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161 | be other vectors for users to perform more than simple function |
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162 | evaluations. Unauthenticated users should not be running this code. |
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163 | |
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164 | Parameter names are assumed to contain only _.a-zA-Z0-9#[] |
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165 | |
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166 | Both names are provided for inverse functions, e.g., acos and arccos. |
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167 | |
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168 | Should try running the function to identify syntax errors before |
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169 | running it in a fit. |
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170 | |
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171 | Use help(fn) to see the code generated for the returned function fn. |
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172 | dis.dis(fn) will show the corresponding python vm instructions. |
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173 | """ |
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174 | |
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175 | # Sort the parameters in the order they need to be evaluated |
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176 | deps = _find_dependencies(symtab, exprs) |
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177 | if deps == []: return no_constraints |
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178 | order = order_dependencies(deps) |
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179 | |
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180 | |
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181 | # Rather than using the full path to the parameters in the parameter |
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182 | # expressions, instead use Pn, and substitute Pn.value for each occurrence |
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183 | # of the parameter in the expression. |
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184 | names = list(sorted(symtab.keys())) |
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185 | parameters = dict(('P%d'%i, symtab[k]) for i,k in enumerate(names)) |
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186 | mapping = dict((k, 'P%d.value'%i) for i,k in enumerate(names)) |
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187 | |
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188 | |
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189 | # Initialize dictionary with available functions |
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190 | globals = {} |
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191 | globals.update(math.__dict__) |
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192 | globals.update(dict(arcsin=math.asin,arccos=math.acos, |
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193 | arctan=math.atan,arctan2=math.atan2)) |
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194 | globals.update(context) |
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195 | globals.update(parameters) |
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196 | globals['id'] = id |
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197 | locals = {} |
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198 | |
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199 | # Define the constraints function |
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200 | assignments = ["=".join((p,exprs[p])) for p in order] |
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201 | code = [_substitute(s, mapping) for s in assignments] |
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202 | functiondef = """ |
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203 | def eval_expressions(): |
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204 | ''' |
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205 | %s |
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206 | ''' |
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207 | %s |
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208 | return 0 |
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209 | """%("\n ".join(assignments),"\n ".join(code)) |
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210 | |
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211 | #print("Function: "+functiondef) |
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212 | exec (functiondef in globals,locals) |
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213 | retfn = locals['eval_expressions'] |
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214 | |
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215 | # Remove garbage added to globals by exec |
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216 | globals.pop('__doc__',None) |
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217 | globals.pop('__name__',None) |
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218 | globals.pop('__file__',None) |
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219 | globals.pop('__builtins__') |
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220 | #print globals.keys() |
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221 | |
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222 | return retfn |
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223 | |
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224 | def order_dependencies(pairs): |
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225 | """ |
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226 | Order elements from pairs so that b comes before a in the |
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227 | ordered list for all pairs (a,b). |
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228 | """ |
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229 | #print "order_dependencies",pairs |
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230 | emptyset = set() |
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231 | order = [] |
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232 | |
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233 | # Break pairs into left set and right set |
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234 | left,right = [set(s) for s in zip(*pairs)] if pairs != [] else ([],[]) |
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235 | while pairs != []: |
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236 | #print "within",pairs |
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237 | # Find which items only occur on the right |
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238 | independent = right - left |
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239 | if independent == emptyset: |
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240 | cycleset = ", ".join(str(s) for s in left) |
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241 | raise ValueError("Cyclic dependencies amongst %s"%cycleset) |
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242 | |
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243 | # The possibly resolvable items are those that depend on the independents |
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244 | dependent = set([a for a,b in pairs if b in independent]) |
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245 | pairs = [(a,b) for a,b in pairs if b not in independent] |
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246 | if pairs == []: |
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247 | resolved = dependent |
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248 | else: |
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249 | left,right = [set(s) for s in zip(*pairs)] |
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250 | resolved = dependent - left |
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251 | #print "independent",independent,"dependent",dependent,"resolvable",resolved |
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252 | order += resolved |
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253 | #print "new order",order |
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254 | order.reverse() |
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255 | return order |
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256 | |
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257 | # ========= Test code ======== |
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258 | def _check(msg,pairs): |
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259 | """ |
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260 | Verify that the list n contains the given items, and that the list |
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261 | satisfies the partial ordering given by the pairs in partial order. |
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262 | """ |
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263 | left,right = zip(*pairs) if pairs != [] else ([],[]) |
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264 | items = set(left) |
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265 | n = order_dependencies(pairs) |
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266 | if set(n) != items or len(n) != len(items): |
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267 | n.sort() |
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268 | items = list(items); items.sort() |
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269 | raise ValueError("%s expect %s to contain %s for %s"%(msg,n,items,pairs)) |
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270 | for lo,hi in pairs: |
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271 | if lo in n and hi in n and n.index(lo) >= n.index(hi): |
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272 | raise ValueError("%s expect %s before %s in %s for %s"%(msg,lo,hi,n,pairs)) |
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273 | |
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274 | def test_deps(): |
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275 | import numpy as np |
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276 | |
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277 | # Null case |
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278 | _check("test empty",[]) |
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279 | |
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280 | # Some dependencies |
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281 | _check("test1",[(2,7),(1,5),(1,4),(2,1),(3,1),(5,6)]) |
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282 | _check("test1 renumbered",[(6,1),(7,3),(7,4),(6,7),(5,7),(3,2)]) |
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283 | _check("test1 numpy",np.array([(2,7),(1,5),(1,4),(2,1),(3,1),(5,6)])) |
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284 | |
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285 | # No dependencies |
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286 | _check("test2",[(4,1),(3,2),(8,4)]) |
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287 | |
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288 | # Cycle test |
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289 | pairs = [(1,4),(4,3),(4,5),(5,1)] |
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290 | try: |
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291 | n = order_dependencies(pairs) |
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292 | except ValueError: |
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293 | pass |
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294 | else: |
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295 | raise ValueError("test3 expect ValueError exception for %s"%(pairs,)) |
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296 | |
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297 | # large test for gross speed check |
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298 | A = np.random.randint(4000,size=(1000,2)) |
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299 | A[:,1] += 4000 # Avoid cycles |
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300 | _check("test-large",A) |
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301 | |
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302 | # depth tests |
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303 | k = 200 |
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304 | A = np.array([range(0,k),range(1,k+1)]).T |
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305 | _check("depth-1",A) |
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306 | |
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307 | A = np.array([range(1,k+1),range(0,k)]).T |
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308 | _check("depth-2",A) |
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309 | |
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310 | def test_expr(): |
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311 | import inspect, dis |
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312 | import math |
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313 | |
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314 | symtab = {'a.b.x':1, 'a.c':2, 'a.b':3, 'b.x':4} |
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315 | expr = 'a.b.x + sin(4*pi*a.c) + a.b.x/a.b' |
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316 | |
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317 | # Check symbol lookup |
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318 | assert _symbols(expr, symtab) == set([1,2,3]) |
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319 | |
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320 | # Check symbol rename |
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321 | assert _substitute(expr,{'a.b.x':'Q'}) == 'Q + sin(4*pi*a.c) + Q/a.b' |
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322 | assert _substitute(expr,{'a.b':'Q'}) == 'a.b.x + sin(4*pi*a.c) + a.b.x/Q' |
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323 | |
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324 | |
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325 | # Check dependency builder |
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326 | # Fake parameter class |
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327 | class Parameter: |
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328 | def __init__(self, name, value=0, expression=''): |
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329 | self.path = name |
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330 | self.value = value |
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331 | self.expression = expression |
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332 | def iscomputed(self): return (self.expression != '') |
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333 | def __repr__(self): return self.path |
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334 | def world(*pars): |
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335 | symtab = dict((p.path,p) for p in pars) |
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336 | exprs = dict((p.path,p.expression) for p in pars if p.iscomputed()) |
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337 | return symtab, exprs |
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338 | p1 = Parameter('G0.sigma',5) |
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339 | p2 = Parameter('other',expression='2*pi*sin(G0.sigma/.1875) + M1.G1') |
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340 | p3 = Parameter('M1.G1',6) |
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341 | p4 = Parameter('constant',expression='2*pi*35') |
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342 | # Simple chain |
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343 | assert set(_find_dependencies(*world(p1,p2,p3))) == set([(p2.path,p1),(p2.path,p3)]) |
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344 | # Constant expression |
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345 | assert set(_find_dependencies(*world(p1,p4))) == set([(p4.path,None)]) |
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346 | # No dependencies |
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347 | assert set(_find_dependencies(*world(p1,p3))) == set([]) |
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348 | |
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349 | # Check function builder |
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350 | fn = compile_constraints(*world(p1,p2,p3)) |
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351 | |
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352 | # Inspect the resulting function |
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353 | if 0: |
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354 | print(inspect.getdoc(fn)) |
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355 | print(dis.dis(fn)) |
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356 | |
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357 | # Evaluate the function and see if it updates the |
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358 | # target value as expected |
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359 | fn() |
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360 | expected = 2*math.pi*math.sin(5/.1875) + 6 |
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361 | assert p2.value == expected,"Value was %s, not %s"%(p2.value,expected) |
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362 | |
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363 | # Check empty dependency set doesn't crash |
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364 | fn = compile_constraints(*world(p1,p3)) |
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365 | fn() |
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366 | |
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367 | # Check that constants are evaluated properly |
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368 | fn = compile_constraints(*world(p4)) |
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369 | fn() |
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370 | assert p4.value == 2*math.pi*35 |
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371 | |
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372 | # Check additional context example; this also tests multiple |
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373 | # expressions |
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374 | class Table: |
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375 | Si = 2.09 |
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376 | values = {'Si': 2.07} |
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377 | tbl = Table() |
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378 | p5 = Parameter('lookup',expression="tbl.Si") |
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379 | fn = compile_constraints(*world(p1,p2,p3,p5),context=dict(tbl=tbl)) |
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380 | fn() |
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381 | assert p5.value == 2.09,"Value for %s was %s"%(p5.expression,p5.value) |
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382 | p5.expression = "tbl.values['Si']" |
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383 | fn = compile_constraints(*world(p1,p2,p3,p5),context=dict(tbl=tbl)) |
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384 | fn() |
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385 | assert p5.value == 2.07,"Value for %s was %s"%(p5.expression,p5.value) |
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386 | |
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387 | |
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388 | # Verify that we capture invalid expressions |
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389 | for expr in ['G4.cage', 'M0.cage', 'M1.G1 + *2', |
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390 | 'piddle', |
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391 | '5; import sys; print "p0wned"', |
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392 | '__import__("sys").argv']: |
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393 | try: |
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394 | p6 = Parameter('broken',expression=expr) |
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395 | fn = compile_constraints(*world(p6)) |
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396 | fn() |
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397 | except Exception as msg: |
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398 | #print(msg) |
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399 | pass |
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400 | else: |
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401 | raise "Failed to raise error for %s"%expr |
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402 | |
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403 | if __name__ == "__main__": |
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404 | test_expr() |
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405 | test_deps() |
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