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50  <h1>Source code for sas.fit.expression</h1><div class="highlight"><pre>
51<span class="c"># This program is public domain</span>
52<span class="sd">&quot;&quot;&quot;</span>
53<span class="sd">Parameter expression evaluator.</span>
54
55<span class="sd">For systems in which constraints are expressed as string expressions rather</span>
56<span class="sd">than python code, :func:`compile_constraints` can construct an expression</span>
57<span class="sd">evaluator that substitutes the computed values of the expressions into the</span>
58<span class="sd">parameters.</span>
59
60<span class="sd">The compiler requires a symbol table, an expression set and a context.</span>
61<span class="sd">The symbol table maps strings containing fully qualified names such as</span>
62<span class="sd">&#39;M1.c[3].full_width&#39; to parameter objects with a &#39;value&#39; property that</span>
63<span class="sd">can be queried and set.  The expression set maps symbol names from the</span>
64<span class="sd">symbol table to string expressions.  The context provides additional symbols</span>
65<span class="sd">for the expressions in addition to the usual mathematical functions and</span>
66<span class="sd">constants.</span>
67
68<span class="sd">The expressions are compiled and interpreted by python, with only minimal</span>
69<span class="sd">effort to make sure that they don&#39;t contain bad code.  The resulting</span>
70<span class="sd">constraints function returns 0 so it can be used directly in a fit problem</span>
71<span class="sd">definition.</span>
72
73<span class="sd">Extracting the symbol table from the model depends on the structure of the</span>
74<span class="sd">model.  If fitness.parameters() is set correctly, then this should simply</span>
75<span class="sd">be a matter of walking the parameter data, remembering the path to each</span>
76<span class="sd">parameter in the symbol table.  For compactness, dictionary elements should</span>
77<span class="sd">be referenced by .name rather than [&quot;name&quot;].  Model name can be used as the</span>
78<span class="sd">top level.</span>
79
80<span class="sd">Getting the parameter expressions applied correctly is challenging.</span>
81<span class="sd">The following monkey patch works by overriding model_update in FitProblem</span>
82<span class="sd">so that after setp(p) is called and, the constraints expression can be</span>
83<span class="sd">applied before telling the underlying fitness function that the model</span>
84<span class="sd">is out of date::</span>
85
86<span class="sd">        # Override model update so that parameter constraints are applied</span>
87<span class="sd">        problem._model_update = problem.model_update</span>
88<span class="sd">        def model_update():</span>
89<span class="sd">            constraints()</span>
90<span class="sd">            problem._model_update()</span>
91<span class="sd">        problem.model_update = model_update</span>
92
93<span class="sd">Ideally, this interface will change</span>
94<span class="sd">&quot;&quot;&quot;</span>
95<span class="kn">import</span> <span class="nn">math</span>
96<span class="kn">import</span> <span class="nn">re</span>
97
98<span class="c"># simple pattern which matches symbols.  Note that it will also match</span>
99<span class="c"># invalid substrings such as a3...9, but given syntactically correct</span>
100<span class="c"># input it will only match symbols.</span>
101<span class="n">_symbol_pattern</span> <span class="o">=</span> <span class="n">re</span><span class="o">.</span><span class="n">compile</span><span class="p">(</span><span class="s">&#39;([a-zA-Z_][a-zA-Z_0-9.]*)&#39;</span><span class="p">)</span>
102
103<span class="k">def</span> <span class="nf">_symbols</span><span class="p">(</span><span class="n">expr</span><span class="p">,</span><span class="n">symtab</span><span class="p">):</span>
104    <span class="sd">&quot;&quot;&quot;</span>
105<span class="sd">    Given an expression string and a symbol table, return the set of symbols</span>
106<span class="sd">    used in the expression.  Symbols are only returned once even if they</span>
107<span class="sd">    occur multiple times.  The return value is a set with the elements in</span>
108<span class="sd">    no particular order.</span>
109<span class="sd">    </span>
110<span class="sd">    This is the first step in computing a dependency graph.</span>
111<span class="sd">    &quot;&quot;&quot;</span>
112    <span class="n">matches</span> <span class="o">=</span> <span class="p">[</span><span class="n">m</span><span class="o">.</span><span class="n">group</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">_symbol_pattern</span><span class="o">.</span><span class="n">finditer</span><span class="p">(</span><span class="n">expr</span><span class="p">)]</span>
113    <span class="k">return</span> <span class="nb">set</span><span class="p">([</span><span class="n">symtab</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">matches</span> <span class="k">if</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">symtab</span><span class="p">])</span>
114
115<span class="k">def</span> <span class="nf">_substitute</span><span class="p">(</span><span class="n">expr</span><span class="p">,</span><span class="n">mapping</span><span class="p">):</span>
116    <span class="sd">&quot;&quot;&quot;</span>
117<span class="sd">    Replace all occurrences of symbol s with mapping[s] for s in mapping.</span>
118<span class="sd">    &quot;&quot;&quot;</span>
119    <span class="c"># Find the symbols and the mapping</span>
120    <span class="n">matches</span> <span class="o">=</span> <span class="p">[(</span><span class="n">m</span><span class="o">.</span><span class="n">start</span><span class="p">(),</span><span class="n">m</span><span class="o">.</span><span class="n">end</span><span class="p">(),</span><span class="n">mapping</span><span class="p">[</span><span class="n">m</span><span class="o">.</span><span class="n">group</span><span class="p">(</span><span class="mi">1</span><span class="p">)])</span>
121               <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">_symbol_pattern</span><span class="o">.</span><span class="n">finditer</span><span class="p">(</span><span class="n">expr</span><span class="p">)</span>
122               <span class="k">if</span> <span class="n">m</span><span class="o">.</span><span class="n">group</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="ow">in</span> <span class="n">mapping</span><span class="p">]</span>
123
124    <span class="c"># Split the expression in to pieces, with new symbols replacing old</span>
125    <span class="n">pieces</span> <span class="o">=</span> <span class="p">[]</span>
126    <span class="n">offset</span> <span class="o">=</span> <span class="mi">0</span>
127    <span class="k">for</span> <span class="n">start</span><span class="p">,</span><span class="n">end</span><span class="p">,</span><span class="n">text</span> <span class="ow">in</span> <span class="n">matches</span><span class="p">:</span>
128        <span class="n">pieces</span> <span class="o">+=</span> <span class="p">[</span><span class="n">expr</span><span class="p">[</span><span class="n">offset</span><span class="p">:</span><span class="n">start</span><span class="p">],</span><span class="n">text</span><span class="p">]</span>
129        <span class="n">offset</span> <span class="o">=</span> <span class="n">end</span>
130    <span class="n">pieces</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">expr</span><span class="p">[</span><span class="n">offset</span><span class="p">:])</span>
131   
132    <span class="c"># Join the pieces and return them</span>
133    <span class="k">return</span> <span class="s">&quot;&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">pieces</span><span class="p">)</span>
134
135<span class="k">def</span> <span class="nf">_find_dependencies</span><span class="p">(</span><span class="n">symtab</span><span class="p">,</span> <span class="n">exprs</span><span class="p">):</span>
136    <span class="sd">&quot;&quot;&quot;</span>
137<span class="sd">    Returns a list of pair-wise dependencies from the parameter expressions.</span>
138<span class="sd">    </span>
139<span class="sd">    For example, if p3 = p1+p2, then find_dependencies([p1,p2,p3]) will</span>
140<span class="sd">    return [(p3,p1),(p3,p2)].  For base expressions without dependencies,</span>
141<span class="sd">    such as p4 = 2*pi, this should return [(p4, None)]</span>
142<span class="sd">    &quot;&quot;&quot;</span>
143    <span class="n">deps</span> <span class="o">=</span> <span class="p">[(</span><span class="n">target</span><span class="p">,</span><span class="n">source</span><span class="p">)</span>
144            <span class="k">for</span> <span class="n">target</span><span class="p">,</span><span class="n">expr</span> <span class="ow">in</span> <span class="n">exprs</span><span class="o">.</span><span class="n">items</span><span class="p">()</span>
145            <span class="k">for</span> <span class="n">source</span> <span class="ow">in</span> <span class="n">_symbols_or_none</span><span class="p">(</span><span class="n">expr</span><span class="p">,</span><span class="n">symtab</span><span class="p">)]</span>
146    <span class="k">return</span> <span class="n">deps</span>
147
148<span class="c"># Hack to deal with expressions without dependencies --- return a fake</span>
149<span class="c"># dependency of None.</span>
150<span class="c"># The better solution is fix order_dependencies so that it takes a</span>
151<span class="c"># dictionary of {symbol: dependency_list}, for which no dependencies</span>
152<span class="c"># is simply []; fix in parameter_mapping as well</span>
153<span class="k">def</span> <span class="nf">_symbols_or_none</span><span class="p">(</span><span class="n">expr</span><span class="p">,</span><span class="n">symtab</span><span class="p">):</span>
154    <span class="n">syms</span> <span class="o">=</span> <span class="n">_symbols</span><span class="p">(</span><span class="n">expr</span><span class="p">,</span><span class="n">symtab</span><span class="p">)</span>
155    <span class="k">return</span> <span class="n">syms</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">syms</span><span class="p">)</span> <span class="k">else</span> <span class="p">[</span><span class="bp">None</span><span class="p">]</span>
156
157<span class="k">def</span> <span class="nf">_parameter_mapping</span><span class="p">(</span><span class="n">pairs</span><span class="p">):</span>
158    <span class="sd">&quot;&quot;&quot;</span>
159<span class="sd">    Find the parameter substitution we need so that expressions can</span>
160<span class="sd">    be evaluated without having to traverse a chain of </span>
161<span class="sd">    model.layer.parameter.value</span>
162<span class="sd">    &quot;&quot;&quot;</span>
163    <span class="n">left</span><span class="p">,</span><span class="n">right</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">pairs</span><span class="p">)</span>
164    <span class="n">pars</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">p</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="nb">set</span><span class="p">(</span><span class="n">left</span><span class="o">+</span><span class="n">right</span><span class="p">)</span> <span class="k">if</span> <span class="n">p</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">))</span>
165    <span class="n">definition</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span> <span class="p">(</span><span class="s">&#39;P</span><span class="si">%d</span><span class="s">&#39;</span><span class="o">%</span><span class="n">i</span><span class="p">,</span><span class="n">p</span><span class="p">)</span>  <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">p</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">pars</span><span class="p">)</span> <span class="p">)</span>
166    <span class="c"># p is None when there is an expression with no dependencies</span>
167    <span class="n">substitution</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span> <span class="p">(</span><span class="n">p</span><span class="p">,</span><span class="s">&#39;P</span><span class="si">%d</span><span class="s">.value&#39;</span><span class="o">%</span><span class="n">i</span><span class="p">)</span>
168                    <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">p</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">pars</span><span class="p">))</span>
169                    <span class="k">if</span> <span class="n">p</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">)</span>
170    <span class="k">return</span> <span class="n">definition</span><span class="p">,</span> <span class="n">substitution</span>
171
172<div class="viewcode-block" id="no_constraints"><a class="viewcode-back" href="../../../dev/api/sas.fit.html#sas.fit.expression.no_constraints">[docs]</a><span class="k">def</span> <span class="nf">no_constraints</span><span class="p">():</span> 
173    <span class="sd">&quot;&quot;&quot;</span>
174<span class="sd">    This parameter set has no constraints between the parameters.</span>
175<span class="sd">    &quot;&quot;&quot;</span>
176    <span class="k">pass</span>
177</div>
178<div class="viewcode-block" id="compile_constraints"><a class="viewcode-back" href="../../../dev/api/sas.fit.html#sas.fit.expression.compile_constraints">[docs]</a><span class="k">def</span> <span class="nf">compile_constraints</span><span class="p">(</span><span class="n">symtab</span><span class="p">,</span> <span class="n">exprs</span><span class="p">,</span> <span class="n">context</span><span class="o">=</span><span class="p">{}):</span>
179    <span class="sd">&quot;&quot;&quot;</span>
180<span class="sd">    Build and return a function to evaluate all parameter expressions in</span>
181<span class="sd">    the proper order.</span>
182
183<span class="sd">    Input:</span>
184
185<span class="sd">        *symtab* is the symbol table for the model: { &#39;name&#39;: parameter }</span>
186
187<span class="sd">        *exprs* is the set of computed symbols: { &#39;name&#39;: &#39;expression&#39; }</span>
188
189<span class="sd">        *context* is any additional context needed to evaluate the expression</span>
190
191<span class="sd">    Return:</span>
192
193<span class="sd">        updater function which sets parameter.value for each expression</span>
194
195<span class="sd">    Raises:</span>
196
197<span class="sd">       AssertionError - model, parameter or function is missing</span>
198
199<span class="sd">       SyntaxError - improper expression syntax</span>
200
201<span class="sd">       ValueError - expressions have circular dependencies</span>
202
203<span class="sd">    This function is not terribly sophisticated, and it would be easy to</span>
204<span class="sd">    trick.  However it handles the common cases cleanly and generates</span>
205<span class="sd">    reasonable messages for the common errors.</span>
206
207<span class="sd">    This code has not been fully audited for security.  While we have</span>
208<span class="sd">    removed the builtins and the ability to import modules, there may</span>
209<span class="sd">    be other vectors for users to perform more than simple function</span>
210<span class="sd">    evaluations.  Unauthenticated users should not be running this code.</span>
211
212<span class="sd">    Parameter names are assumed to contain only _.a-zA-Z0-9#[]</span>
213<span class="sd">    </span>
214<span class="sd">    Both names are provided for inverse functions, e.g., acos and arccos.</span>
215
216<span class="sd">    Should try running the function to identify syntax errors before</span>
217<span class="sd">    running it in a fit.</span>
218<span class="sd">    </span>
219<span class="sd">    Use help(fn) to see the code generated for the returned function fn.</span>
220<span class="sd">    dis.dis(fn) will show the corresponding python vm instructions.</span>
221<span class="sd">    &quot;&quot;&quot;</span>
222
223    <span class="c"># Sort the parameters in the order they need to be evaluated</span>
224    <span class="n">deps</span> <span class="o">=</span> <span class="n">_find_dependencies</span><span class="p">(</span><span class="n">symtab</span><span class="p">,</span> <span class="n">exprs</span><span class="p">)</span>
225    <span class="k">if</span> <span class="n">deps</span> <span class="o">==</span> <span class="p">[]:</span> <span class="k">return</span> <span class="n">no_constraints</span>
226    <span class="n">order</span> <span class="o">=</span> <span class="n">order_dependencies</span><span class="p">(</span><span class="n">deps</span><span class="p">)</span>
227
228
229    <span class="c"># Rather than using the full path to the parameters in the parameter</span>
230    <span class="c"># expressions, instead use Pn, and substitute Pn.value for each occurrence</span>
231    <span class="c"># of the parameter in the expression.</span>
232    <span class="n">names</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">symtab</span><span class="o">.</span><span class="n">keys</span><span class="p">()))</span>
233    <span class="n">parameters</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">((</span><span class="s">&#39;P</span><span class="si">%d</span><span class="s">&#39;</span><span class="o">%</span><span class="n">i</span><span class="p">,</span> <span class="n">symtab</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">k</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">names</span><span class="p">))</span>
234    <span class="n">mapping</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="s">&#39;P</span><span class="si">%d</span><span class="s">.value&#39;</span><span class="o">%</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">k</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">names</span><span class="p">))</span>
235
236
237    <span class="c"># Initialize dictionary with available functions</span>
238    <span class="nb">globals</span> <span class="o">=</span> <span class="p">{}</span>
239    <span class="nb">globals</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">__dict__</span><span class="p">)</span>
240    <span class="nb">globals</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">arcsin</span><span class="o">=</span><span class="n">math</span><span class="o">.</span><span class="n">asin</span><span class="p">,</span><span class="n">arccos</span><span class="o">=</span><span class="n">math</span><span class="o">.</span><span class="n">acos</span><span class="p">,</span>
241                        <span class="n">arctan</span><span class="o">=</span><span class="n">math</span><span class="o">.</span><span class="n">atan</span><span class="p">,</span><span class="n">arctan2</span><span class="o">=</span><span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">))</span>
242    <span class="nb">globals</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">context</span><span class="p">)</span>
243    <span class="nb">globals</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
244    <span class="nb">globals</span><span class="p">[</span><span class="s">&#39;id&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="nb">id</span>
245    <span class="nb">locals</span> <span class="o">=</span> <span class="p">{}</span>
246
247    <span class="c"># Define the constraints function</span>
248    <span class="n">assignments</span> <span class="o">=</span> <span class="p">[</span><span class="s">&quot;=&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">((</span><span class="n">p</span><span class="p">,</span><span class="n">exprs</span><span class="p">[</span><span class="n">p</span><span class="p">]))</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">order</span><span class="p">]</span>
249    <span class="n">code</span> <span class="o">=</span> <span class="p">[</span><span class="n">_substitute</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">mapping</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">assignments</span><span class="p">]</span>
250    <span class="n">functiondef</span> <span class="o">=</span> <span class="s">&quot;&quot;&quot;</span>
251<span class="s">def eval_expressions():</span>
252<span class="s">    &#39;&#39;&#39;</span>
253<span class="s">    </span><span class="si">%s</span><span class="s"></span>
254<span class="s">    &#39;&#39;&#39;</span>
255<span class="s">    </span><span class="si">%s</span><span class="s"></span>
256<span class="s">    return 0</span>
257<span class="s">&quot;&quot;&quot;</span><span class="o">%</span><span class="p">(</span><span class="s">&quot;</span><span class="se">\n</span><span class="s">    &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">assignments</span><span class="p">),</span><span class="s">&quot;</span><span class="se">\n</span><span class="s">    &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">code</span><span class="p">))</span>
258
259    <span class="c">#print(&quot;Function: &quot;+functiondef)</span>
260    <span class="k">exec</span> <span class="n">functiondef</span> <span class="ow">in</span> <span class="nb">globals</span><span class="p">,</span><span class="nb">locals</span>
261    <span class="n">retfn</span> <span class="o">=</span> <span class="nb">locals</span><span class="p">[</span><span class="s">&#39;eval_expressions&#39;</span><span class="p">]</span>
262
263    <span class="c"># Remove garbage added to globals by exec</span>
264    <span class="nb">globals</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="s">&#39;__doc__&#39;</span><span class="p">,</span><span class="bp">None</span><span class="p">)</span>
265    <span class="nb">globals</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="s">&#39;__name__&#39;</span><span class="p">,</span><span class="bp">None</span><span class="p">)</span>
266    <span class="nb">globals</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="s">&#39;__file__&#39;</span><span class="p">,</span><span class="bp">None</span><span class="p">)</span>
267    <span class="nb">globals</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="s">&#39;__builtins__&#39;</span><span class="p">)</span>
268    <span class="c">#print globals.keys()</span>
269
270    <span class="k">return</span> <span class="n">retfn</span>
271</div>
272<div class="viewcode-block" id="order_dependencies"><a class="viewcode-back" href="../../../dev/api/sas.fit.html#sas.fit.expression.order_dependencies">[docs]</a><span class="k">def</span> <span class="nf">order_dependencies</span><span class="p">(</span><span class="n">pairs</span><span class="p">):</span>
273    <span class="sd">&quot;&quot;&quot;</span>
274<span class="sd">    Order elements from pairs so that b comes before a in the</span>
275<span class="sd">    ordered list for all pairs (a,b).</span>
276<span class="sd">    &quot;&quot;&quot;</span>
277    <span class="c">#print &quot;order_dependencies&quot;,pairs</span>
278    <span class="n">emptyset</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
279    <span class="n">order</span> <span class="o">=</span> <span class="p">[]</span>
280
281    <span class="c"># Break pairs into left set and right set</span>
282    <span class="n">left</span><span class="p">,</span><span class="n">right</span> <span class="o">=</span> <span class="p">[</span><span class="nb">set</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">pairs</span><span class="p">)]</span> <span class="k">if</span> <span class="n">pairs</span> <span class="o">!=</span> <span class="p">[]</span> <span class="k">else</span> <span class="p">([],[])</span>
283    <span class="k">while</span> <span class="n">pairs</span> <span class="o">!=</span> <span class="p">[]:</span>
284        <span class="c">#print &quot;within&quot;,pairs</span>
285        <span class="c"># Find which items only occur on the right</span>
286        <span class="n">independent</span> <span class="o">=</span> <span class="n">right</span> <span class="o">-</span> <span class="n">left</span>
287        <span class="k">if</span> <span class="n">independent</span> <span class="o">==</span> <span class="n">emptyset</span><span class="p">:</span>
288            <span class="n">cycleset</span> <span class="o">=</span> <span class="s">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">left</span><span class="p">)</span>
289            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">,</span><span class="s">&quot;Cyclic dependencies amongst </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="n">cycleset</span>
290
291        <span class="c"># The possibly resolvable items are those that depend on the independents</span>
292        <span class="n">dependent</span> <span class="o">=</span> <span class="nb">set</span><span class="p">([</span><span class="n">a</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span><span class="n">b</span> <span class="ow">in</span> <span class="n">pairs</span> <span class="k">if</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">independent</span><span class="p">])</span>
293        <span class="n">pairs</span> <span class="o">=</span> <span class="p">[(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span><span class="n">b</span> <span class="ow">in</span> <span class="n">pairs</span> <span class="k">if</span> <span class="n">b</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">independent</span><span class="p">]</span>
294        <span class="k">if</span> <span class="n">pairs</span> <span class="o">==</span> <span class="p">[]:</span>
295            <span class="n">resolved</span> <span class="o">=</span> <span class="n">dependent</span>
296        <span class="k">else</span><span class="p">:</span>
297            <span class="n">left</span><span class="p">,</span><span class="n">right</span> <span class="o">=</span> <span class="p">[</span><span class="nb">set</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">pairs</span><span class="p">)]</span>
298            <span class="n">resolved</span> <span class="o">=</span> <span class="n">dependent</span> <span class="o">-</span> <span class="n">left</span>
299        <span class="c">#print &quot;independent&quot;,independent,&quot;dependent&quot;,dependent,&quot;resolvable&quot;,resolved</span>
300        <span class="n">order</span> <span class="o">+=</span> <span class="n">resolved</span>
301        <span class="c">#print &quot;new order&quot;,order</span>
302    <span class="n">order</span><span class="o">.</span><span class="n">reverse</span><span class="p">()</span>
303    <span class="k">return</span> <span class="n">order</span>
304
305<span class="c"># ========= Test code ========</span></div>
306<span class="k">def</span> <span class="nf">_check</span><span class="p">(</span><span class="n">msg</span><span class="p">,</span><span class="n">pairs</span><span class="p">):</span>
307    <span class="sd">&quot;&quot;&quot;</span>
308<span class="sd">    Verify that the list n contains the given items, and that the list</span>
309<span class="sd">    satisfies the partial ordering given by the pairs in partial order.</span>
310<span class="sd">    &quot;&quot;&quot;</span>
311    <span class="n">left</span><span class="p">,</span><span class="n">right</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">pairs</span><span class="p">)</span> <span class="k">if</span> <span class="n">pairs</span> <span class="o">!=</span> <span class="p">[]</span> <span class="k">else</span> <span class="p">([],[])</span>
312    <span class="n">items</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">left</span><span class="p">)</span>
313    <span class="n">n</span> <span class="o">=</span> <span class="n">order_dependencies</span><span class="p">(</span><span class="n">pairs</span><span class="p">)</span>
314    <span class="k">if</span> <span class="nb">set</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">!=</span> <span class="n">items</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">items</span><span class="p">):</span>
315        <span class="n">n</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
316        <span class="n">items</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">items</span><span class="p">);</span> <span class="n">items</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
317        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">,</span><span class="s">&quot;</span><span class="si">%s</span><span class="s"> expect </span><span class="si">%s</span><span class="s"> to contain </span><span class="si">%s</span><span class="s"> for </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">msg</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">items</span><span class="p">,</span><span class="n">pairs</span><span class="p">)</span>
318    <span class="k">for</span> <span class="n">lo</span><span class="p">,</span><span class="n">hi</span> <span class="ow">in</span> <span class="n">pairs</span><span class="p">:</span>
319        <span class="k">if</span> <span class="n">lo</span> <span class="ow">in</span> <span class="n">n</span> <span class="ow">and</span> <span class="n">hi</span> <span class="ow">in</span> <span class="n">n</span> <span class="ow">and</span> <span class="n">n</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="n">lo</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="n">n</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="n">hi</span><span class="p">):</span>
320            <span class="k">raise</span> <span class="ne">Exception</span><span class="p">,</span><span class="s">&quot;</span><span class="si">%s</span><span class="s"> expect </span><span class="si">%s</span><span class="s"> before </span><span class="si">%s</span><span class="s"> in </span><span class="si">%s</span><span class="s"> for </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">msg</span><span class="p">,</span><span class="n">lo</span><span class="p">,</span><span class="n">hi</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">pairs</span><span class="p">)</span>
321
322<div class="viewcode-block" id="test_deps"><a class="viewcode-back" href="../../../dev/api/sas.fit.html#sas.fit.expression.test_deps">[docs]</a><span class="k">def</span> <span class="nf">test_deps</span><span class="p">():</span>
323    <span class="kn">import</span> <span class="nn">numpy</span>
324
325    <span class="c"># Null case</span>
326    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;test empty&quot;</span><span class="p">,[])</span>
327
328    <span class="c"># Some dependencies</span>
329    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;test1&quot;</span><span class="p">,[(</span><span class="mi">2</span><span class="p">,</span><span class="mi">7</span><span class="p">),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">5</span><span class="p">),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">),(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">),(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">),(</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">)])</span>
330    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;test1 renumbered&quot;</span><span class="p">,[(</span><span class="mi">6</span><span class="p">,</span><span class="mi">1</span><span class="p">),(</span><span class="mi">7</span><span class="p">,</span><span class="mi">3</span><span class="p">),(</span><span class="mi">7</span><span class="p">,</span><span class="mi">4</span><span class="p">),(</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">),(</span><span class="mi">5</span><span class="p">,</span><span class="mi">7</span><span class="p">),(</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">)])</span>
331    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;test1 numpy&quot;</span><span class="p">,</span><span class="n">numpy</span><span class="o">.</span><span class="n">array</span><span class="p">([(</span><span class="mi">2</span><span class="p">,</span><span class="mi">7</span><span class="p">),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">5</span><span class="p">),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">),(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">),(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">),(</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">)]))</span>
332
333    <span class="c"># No dependencies</span>
334    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;test2&quot;</span><span class="p">,[(</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">),(</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">),(</span><span class="mi">8</span><span class="p">,</span><span class="mi">4</span><span class="p">)])</span>
335
336    <span class="c"># Cycle test</span>
337    <span class="n">pairs</span> <span class="o">=</span> <span class="p">[(</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">),(</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">),(</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">),(</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">)]</span>
338    <span class="k">try</span><span class="p">:</span> <span class="n">n</span> <span class="o">=</span> <span class="n">order_dependencies</span><span class="p">(</span><span class="n">pairs</span><span class="p">)</span>
339    <span class="k">except</span> <span class="ne">ValueError</span><span class="p">:</span> <span class="k">pass</span>
340    <span class="k">else</span><span class="p">:</span> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">,</span><span class="s">&quot;test3 expect ValueError exception for </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">pairs</span><span class="p">,)</span>
341
342    <span class="c"># large test for gross speed check</span>
343    <span class="n">A</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">4000</span><span class="p">,</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">1000</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
344    <span class="n">A</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">4000</span>  <span class="c"># Avoid cycles</span>
345    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;test-large&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
346
347    <span class="c"># depth tests</span>
348    <span class="n">k</span> <span class="o">=</span> <span class="mi">200</span>
349    <span class="n">A</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">k</span><span class="p">),</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">k</span><span class="o">+</span><span class="mi">1</span><span class="p">)])</span><span class="o">.</span><span class="n">T</span>
350    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;depth-1&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
351
352    <span class="n">A</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">k</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">k</span><span class="p">)])</span><span class="o">.</span><span class="n">T</span>
353    <span class="n">_check</span><span class="p">(</span><span class="s">&quot;depth-2&quot;</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
354</div>
355<div class="viewcode-block" id="test_expr"><a class="viewcode-back" href="../../../dev/api/sas.fit.html#sas.fit.expression.test_expr">[docs]</a><span class="k">def</span> <span class="nf">test_expr</span><span class="p">():</span>
356    <span class="kn">import</span> <span class="nn">inspect</span><span class="o">,</span> <span class="nn">dis</span>
357    <span class="kn">import</span> <span class="nn">math</span>
358   
359    <span class="n">symtab</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;a.b.x&#39;</span><span class="p">:</span><span class="mi">1</span><span class="p">,</span> <span class="s">&#39;a.c&#39;</span><span class="p">:</span><span class="mi">2</span><span class="p">,</span> <span class="s">&#39;a.b&#39;</span><span class="p">:</span><span class="mi">3</span><span class="p">,</span> <span class="s">&#39;b.x&#39;</span><span class="p">:</span><span class="mi">4</span><span class="p">}</span>
360    <span class="n">expr</span> <span class="o">=</span> <span class="s">&#39;a.b.x + sin(4*pi*a.c) + a.b.x/a.b&#39;</span>
361   
362    <span class="c"># Check symbol lookup</span>
363    <span class="k">assert</span> <span class="n">_symbols</span><span class="p">(</span><span class="n">expr</span><span class="p">,</span> <span class="n">symtab</span><span class="p">)</span> <span class="o">==</span> <span class="nb">set</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
364
365    <span class="c"># Check symbol rename</span>
366    <span class="k">assert</span> <span class="n">_substitute</span><span class="p">(</span><span class="n">expr</span><span class="p">,{</span><span class="s">&#39;a.b.x&#39;</span><span class="p">:</span><span class="s">&#39;Q&#39;</span><span class="p">})</span> <span class="o">==</span> <span class="s">&#39;Q + sin(4*pi*a.c) + Q/a.b&#39;</span>
367    <span class="k">assert</span> <span class="n">_substitute</span><span class="p">(</span><span class="n">expr</span><span class="p">,{</span><span class="s">&#39;a.b&#39;</span><span class="p">:</span><span class="s">&#39;Q&#39;</span><span class="p">})</span> <span class="o">==</span> <span class="s">&#39;a.b.x + sin(4*pi*a.c) + a.b.x/Q&#39;</span>
368
369
370    <span class="c"># Check dependency builder</span>
371    <span class="c"># Fake parameter class</span>
372    <span class="k">class</span> <span class="nc">Parameter</span><span class="p">:</span>
373        <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">expression</span><span class="o">=</span><span class="s">&#39;&#39;</span><span class="p">):</span>
374            <span class="bp">self</span><span class="o">.</span><span class="n">path</span> <span class="o">=</span> <span class="n">name</span>
375            <span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">=</span> <span class="n">value</span>
376            <span class="bp">self</span><span class="o">.</span><span class="n">expression</span> <span class="o">=</span> <span class="n">expression</span>
377        <span class="k">def</span> <span class="nf">iscomputed</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">expression</span> <span class="o">!=</span> <span class="s">&#39;&#39;</span><span class="p">)</span>
378        <span class="k">def</span> <span class="nf">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">path</span>
379    <span class="k">def</span> <span class="nf">world</span><span class="p">(</span><span class="o">*</span><span class="n">pars</span><span class="p">):</span>
380        <span class="n">symtab</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">((</span><span class="n">p</span><span class="o">.</span><span class="n">path</span><span class="p">,</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">pars</span><span class="p">)</span>
381        <span class="n">exprs</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">((</span><span class="n">p</span><span class="o">.</span><span class="n">path</span><span class="p">,</span><span class="n">p</span><span class="o">.</span><span class="n">expression</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">pars</span> <span class="k">if</span> <span class="n">p</span><span class="o">.</span><span class="n">iscomputed</span><span class="p">())</span>
382        <span class="k">return</span> <span class="n">symtab</span><span class="p">,</span> <span class="n">exprs</span>
383    <span class="n">p1</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="s">&#39;G0.sigma&#39;</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
384    <span class="n">p2</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="s">&#39;other&#39;</span><span class="p">,</span><span class="n">expression</span><span class="o">=</span><span class="s">&#39;2*pi*sin(G0.sigma/.1875) + M1.G1&#39;</span><span class="p">)</span>
385    <span class="n">p3</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="s">&#39;M1.G1&#39;</span><span class="p">,</span><span class="mi">6</span><span class="p">)</span>
386    <span class="n">p4</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="s">&#39;constant&#39;</span><span class="p">,</span><span class="n">expression</span><span class="o">=</span><span class="s">&#39;2*pi*35&#39;</span><span class="p">)</span>
387    <span class="c"># Simple chain</span>
388    <span class="k">assert</span> <span class="nb">set</span><span class="p">(</span><span class="n">_find_dependencies</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="n">p2</span><span class="p">,</span><span class="n">p3</span><span class="p">)))</span> <span class="o">==</span> <span class="nb">set</span><span class="p">([(</span><span class="n">p2</span><span class="o">.</span><span class="n">path</span><span class="p">,</span><span class="n">p1</span><span class="p">),(</span><span class="n">p2</span><span class="o">.</span><span class="n">path</span><span class="p">,</span><span class="n">p3</span><span class="p">)])</span>
389    <span class="c"># Constant expression</span>
390    <span class="k">assert</span> <span class="nb">set</span><span class="p">(</span><span class="n">_find_dependencies</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="n">p4</span><span class="p">)))</span> <span class="o">==</span> <span class="nb">set</span><span class="p">([(</span><span class="n">p4</span><span class="o">.</span><span class="n">path</span><span class="p">,</span><span class="bp">None</span><span class="p">)])</span>
391    <span class="c"># No dependencies</span>
392    <span class="k">assert</span> <span class="nb">set</span><span class="p">(</span><span class="n">_find_dependencies</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="n">p3</span><span class="p">)))</span> <span class="o">==</span> <span class="nb">set</span><span class="p">([])</span>
393
394    <span class="c"># Check function builder</span>
395    <span class="n">fn</span> <span class="o">=</span> <span class="n">compile_constraints</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="n">p2</span><span class="p">,</span><span class="n">p3</span><span class="p">))</span>
396
397    <span class="c"># Inspect the resulting function</span>
398    <span class="k">if</span> <span class="mi">0</span><span class="p">:</span>
399        <span class="k">print</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getdoc</span><span class="p">(</span><span class="n">fn</span><span class="p">))</span>
400        <span class="k">print</span><span class="p">(</span><span class="n">dis</span><span class="o">.</span><span class="n">dis</span><span class="p">(</span><span class="n">fn</span><span class="p">))</span>
401
402    <span class="c"># Evaluate the function and see if it updates the</span>
403    <span class="c"># target value as expected</span>
404    <span class="n">fn</span><span class="p">()</span>
405    <span class="n">expected</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">5</span><span class="o">/.</span><span class="mi">1875</span><span class="p">)</span> <span class="o">+</span> <span class="mi">6</span>
406    <span class="k">assert</span> <span class="n">p2</span><span class="o">.</span><span class="n">value</span> <span class="o">==</span> <span class="n">expected</span><span class="p">,</span><span class="s">&quot;Value was </span><span class="si">%s</span><span class="s">, not </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">p2</span><span class="o">.</span><span class="n">value</span><span class="p">,</span><span class="n">expected</span><span class="p">)</span>
407   
408    <span class="c"># Check empty dependency set doesn&#39;t crash</span>
409    <span class="n">fn</span> <span class="o">=</span> <span class="n">compile_constraints</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="n">p3</span><span class="p">))</span>
410    <span class="n">fn</span><span class="p">()</span>
411
412    <span class="c"># Check that constants are evaluated properly</span>
413    <span class="n">fn</span> <span class="o">=</span> <span class="n">compile_constraints</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p4</span><span class="p">))</span>
414    <span class="n">fn</span><span class="p">()</span>
415    <span class="k">assert</span> <span class="n">p4</span><span class="o">.</span><span class="n">value</span> <span class="o">==</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="mi">35</span>
416
417    <span class="c"># Check additional context example; this also tests multiple</span>
418    <span class="c"># expressions</span>
419    <span class="k">class</span> <span class="nc">Table</span><span class="p">:</span>
420        <span class="n">Si</span> <span class="o">=</span> <span class="mf">2.09</span>
421        <span class="n">values</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;Si&#39;</span><span class="p">:</span> <span class="mf">2.07</span><span class="p">}</span>
422    <span class="n">tbl</span> <span class="o">=</span> <span class="n">Table</span><span class="p">()</span>
423    <span class="n">p5</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="s">&#39;lookup&#39;</span><span class="p">,</span><span class="n">expression</span><span class="o">=</span><span class="s">&quot;tbl.Si&quot;</span><span class="p">)</span>
424    <span class="n">fn</span> <span class="o">=</span> <span class="n">compile_constraints</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="n">p2</span><span class="p">,</span><span class="n">p3</span><span class="p">,</span><span class="n">p5</span><span class="p">),</span><span class="n">context</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">tbl</span><span class="o">=</span><span class="n">tbl</span><span class="p">))</span>
425    <span class="n">fn</span><span class="p">()</span>
426    <span class="k">assert</span> <span class="n">p5</span><span class="o">.</span><span class="n">value</span> <span class="o">==</span> <span class="mf">2.09</span><span class="p">,</span><span class="s">&quot;Value for </span><span class="si">%s</span><span class="s"> was </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">p5</span><span class="o">.</span><span class="n">expression</span><span class="p">,</span><span class="n">p5</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
427    <span class="n">p5</span><span class="o">.</span><span class="n">expression</span> <span class="o">=</span> <span class="s">&quot;tbl.values[&#39;Si&#39;]&quot;</span>
428    <span class="n">fn</span> <span class="o">=</span> <span class="n">compile_constraints</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="n">p2</span><span class="p">,</span><span class="n">p3</span><span class="p">,</span><span class="n">p5</span><span class="p">),</span><span class="n">context</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">tbl</span><span class="o">=</span><span class="n">tbl</span><span class="p">))</span>
429    <span class="n">fn</span><span class="p">()</span>
430    <span class="k">assert</span> <span class="n">p5</span><span class="o">.</span><span class="n">value</span> <span class="o">==</span> <span class="mf">2.07</span><span class="p">,</span><span class="s">&quot;Value for </span><span class="si">%s</span><span class="s"> was </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">p5</span><span class="o">.</span><span class="n">expression</span><span class="p">,</span><span class="n">p5</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
431   
432
433    <span class="c"># Verify that we capture invalid expressions</span>
434    <span class="k">for</span> <span class="n">expr</span> <span class="ow">in</span> <span class="p">[</span><span class="s">&#39;G4.cage&#39;</span><span class="p">,</span> <span class="s">&#39;M0.cage&#39;</span><span class="p">,</span> <span class="s">&#39;M1.G1 + *2&#39;</span><span class="p">,</span> 
435                 <span class="s">&#39;piddle&#39;</span><span class="p">,</span>
436                 <span class="s">&#39;5; import sys; print &quot;p0wned&quot;&#39;</span><span class="p">,</span>
437                 <span class="s">&#39;__import__(&quot;sys&quot;).argv&#39;</span><span class="p">]:</span>
438        <span class="k">try</span><span class="p">:</span>
439            <span class="n">p6</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="s">&#39;broken&#39;</span><span class="p">,</span><span class="n">expression</span><span class="o">=</span><span class="n">expr</span><span class="p">)</span>
440            <span class="n">fn</span> <span class="o">=</span> <span class="n">compile_constraints</span><span class="p">(</span><span class="o">*</span><span class="n">world</span><span class="p">(</span><span class="n">p6</span><span class="p">))</span>
441            <span class="n">fn</span><span class="p">()</span>
442        <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">msg</span><span class="p">:</span>
443            <span class="c">#print(msg)</span>
444            <span class="k">pass</span>
445        <span class="k">else</span><span class="p">:</span>
446            <span class="k">raise</span> <span class="s">&quot;Failed to raise error for </span><span class="si">%s</span><span class="s">&quot;</span><span class="o">%</span><span class="n">expr</span>
447</div>
448<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">&quot;__main__&quot;</span><span class="p">:</span>
449    <span class="n">test_expr</span><span class="p">()</span>
450    <span class="n">test_deps</span><span class="p">()</span>
451</pre></div>
452
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