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50  <h1>Source code for sas.data_util.uncertainty</h1><div class="highlight"><pre>
51<span class="sd">&quot;&quot;&quot;</span>
52
53<span class="sd">Uncertainty propagation class, and log() and exp() functions.</span>
54
55<span class="sd">Based on scalars or numpy vectors, this class allows you to store and </span>
56<span class="sd">manipulate values+uncertainties, with propagation of gaussian error for</span>
57<span class="sd">addition, subtraction, multiplication, division, power, exp() and log().</span>
58
59<span class="sd">Storage properties are determined by the numbers used to set the value</span>
60<span class="sd">and uncertainty.  Be sure to use floating point uncertainty vectors </span>
61<span class="sd">for inplace operations since numpy does not do automatic type conversion.</span>
62<span class="sd">Normal operations can use mixed integer and floating point.  In place</span>
63<span class="sd">operations (a *= b, etc.) create at most one extra copy for each operation.</span>
64<span class="sd">c = a*b by contrast uses four intermediate vectors, so shouldn&#39;t be used</span>
65<span class="sd">for huge arrays.</span>
66<span class="sd">&quot;&quot;&quot;</span>
67
68<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
69
70<span class="kn">import</span> <span class="nn">numpy</span>
71<span class="kn">import</span> <span class="nn">err1d</span>
72<span class="kn">from</span> <span class="nn">formatnum</span> <span class="kn">import</span> <span class="n">format_uncertainty</span>
73
74<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;Uncertainty&#39;</span><span class="p">]</span>
75
76<span class="c"># TODO: rename to Measurement and add support for units?</span>
77<span class="c"># TODO: C implementation of *,/,**?</span>
78<div class="viewcode-block" id="Uncertainty"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.uncertainty.Uncertainty">[docs]</a><span class="k">class</span> <span class="nc">Uncertainty</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
79    <span class="c"># Make standard deviation available</span>
80    <span class="k">def</span> <span class="nf">_getdx</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span>
81    <span class="k">def</span> <span class="nf">_setdx</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span><span class="n">dx</span><span class="p">):</span> 
82        <span class="c"># Direct operation</span>
83        <span class="c">#    variance = dx**2</span>
84        <span class="c"># Indirect operation to avoid temporaries</span>
85        <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">dx</span>
86        <span class="bp">self</span><span class="o">.</span><span class="n">variance</span> <span class="o">**=</span> <span class="mi">2</span>
87    <span class="n">dx</span> <span class="o">=</span> <span class="nb">property</span><span class="p">(</span><span class="n">_getdx</span><span class="p">,</span><span class="n">_setdx</span><span class="p">,</span><span class="n">doc</span><span class="o">=</span><span class="s">&quot;standard deviation&quot;</span><span class="p">)</span>
88
89    <span class="c"># Constructor</span>
90    <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">x</span><span class="p">,</span> <span class="n">variance</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
91        <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span> <span class="o">=</span> <span class="n">x</span><span class="p">,</span> <span class="n">variance</span>   
92 
93    <span class="c"># Numpy array slicing operations</span>
94    <span class="k">def</span> <span class="nf">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> 
95        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
96    <span class="k">def</span> <span class="nf">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span><span class="n">key</span><span class="p">):</span> 
97        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">key</span><span class="p">],</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
98    <span class="k">def</span> <span class="nf">__setitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span><span class="n">key</span><span class="p">,</span><span class="n">value</span><span class="p">):</span>
99        <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="n">value</span><span class="o">.</span><span class="n">x</span>
100        <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="n">value</span><span class="o">.</span><span class="n">variance</span>
101    <span class="k">def</span> <span class="nf">__delitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
102        <span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">key</span><span class="p">]</span>
103        <span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">[</span><span class="n">key</span><span class="p">]</span>
104    <span class="c">#def __iter__(self): pass # Not sure we need iter</span>
105
106    <span class="c"># Normal operations: may be of mixed type</span>
107    <span class="k">def</span> <span class="nf">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
108        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
109            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">*</span><span class="n">err1d</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
110        <span class="k">else</span><span class="p">:</span>
111            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">+</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="o">+</span><span class="mi">0</span><span class="p">)</span> <span class="c"># Force copy</span>
112    <span class="k">def</span> <span class="nf">__sub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
113        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
114            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">*</span><span class="n">err1d</span><span class="o">.</span><span class="n">sub</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
115        <span class="k">else</span><span class="p">:</span>
116            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">-</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="o">+</span><span class="mi">0</span><span class="p">)</span> <span class="c"># Force copy</span>
117    <span class="k">def</span> <span class="nf">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
118        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
119            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">*</span><span class="n">err1d</span><span class="o">.</span><span class="n">mul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
120        <span class="k">else</span><span class="p">:</span>
121            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">*</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="o">*</span><span class="n">other</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
122    <span class="k">def</span> <span class="nf">__truediv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
123        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
124            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">*</span><span class="n">err1d</span><span class="o">.</span><span class="n">div</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
125        <span class="k">else</span><span class="p">:</span>
126            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">/</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="o">/</span><span class="n">other</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
127    <span class="k">def</span> <span class="nf">__pow__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
128        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
129            <span class="c"># Haven&#39;t calcuated variance in (a+/-da) ** (b+/-db)</span>
130            <span class="k">return</span> <span class="bp">NotImplemented</span>
131        <span class="k">else</span><span class="p">:</span>
132            <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">*</span><span class="n">err1d</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="p">))</span>
133
134    <span class="c"># Reverse operations</span>
135    <span class="k">def</span> <span class="nf">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
136        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">+</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="o">+</span><span class="mi">0</span><span class="p">)</span> <span class="c"># Force copy</span>
137    <span class="k">def</span> <span class="nf">__rsub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
138        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="n">other</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="o">+</span><span class="mi">0</span><span class="p">)</span>
139    <span class="k">def</span> <span class="nf">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
140        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">*</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="o">*</span><span class="n">other</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
141    <span class="k">def</span> <span class="nf">__rtruediv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
142        <span class="n">x</span><span class="p">,</span><span class="n">variance</span> <span class="o">=</span> <span class="n">err1d</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
143        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="n">x</span><span class="o">*</span><span class="n">other</span><span class="p">,</span><span class="n">variance</span><span class="o">*</span><span class="n">other</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
144    <span class="k">def</span> <span class="nf">__rpow__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
145
146    <span class="c"># In-place operations: may be of mixed type</span>
147    <span class="k">def</span> <span class="nf">__iadd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
148        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
149            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span> \
150                <span class="o">=</span> <span class="n">err1d</span><span class="o">.</span><span class="n">add_inplace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span>
151        <span class="k">else</span><span class="p">:</span>
152            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">+=</span><span class="n">other</span>
153        <span class="k">return</span> <span class="bp">self</span>
154    <span class="k">def</span> <span class="nf">__isub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
155        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
156            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span> \
157                <span class="o">=</span> <span class="n">err1d</span><span class="o">.</span><span class="n">sub_inplace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span>
158        <span class="k">else</span><span class="p">:</span>
159            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">-=</span><span class="n">other</span>
160        <span class="k">return</span> <span class="bp">self</span>
161    <span class="k">def</span> <span class="nf">__imul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
162        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
163            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span> \
164                <span class="o">=</span> <span class="n">err1d</span><span class="o">.</span><span class="n">mul_inplace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span>
165        <span class="k">else</span><span class="p">:</span>
166            <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">*=</span> <span class="n">other</span>
167            <span class="bp">self</span><span class="o">.</span><span class="n">variance</span> <span class="o">*=</span> <span class="n">other</span><span class="o">**</span><span class="mi">2</span>
168        <span class="k">return</span> <span class="bp">self</span>
169    <span class="k">def</span> <span class="nf">__itruediv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
170        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
171            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span> \
172                <span class="o">=</span> <span class="n">err1d</span><span class="o">.</span><span class="n">div_inplace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">other</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span>
173        <span class="k">else</span><span class="p">:</span>
174            <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">/=</span> <span class="n">other</span>
175            <span class="bp">self</span><span class="o">.</span><span class="n">variance</span> <span class="o">/=</span> <span class="n">other</span><span class="o">**</span><span class="mi">2</span>
176        <span class="k">return</span> <span class="bp">self</span>
177    <span class="k">def</span> <span class="nf">__ipow__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
178        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span><span class="n">Uncertainty</span><span class="p">):</span>
179            <span class="c"># Haven&#39;t calcuated variance in (a+/-da) ** (b+/-db)</span>
180            <span class="k">return</span> <span class="bp">NotImplemented</span>
181        <span class="k">else</span><span class="p">:</span>
182            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span> <span class="o">=</span> <span class="n">err1d</span><span class="o">.</span><span class="n">pow_inplace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">,</span> <span class="n">other</span><span class="p">)</span>
183        <span class="k">return</span> <span class="bp">self</span>
184
185    <span class="c"># Use true division instead of integer division</span>
186    <span class="k">def</span> <span class="nf">__div__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__truediv__</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
187    <span class="k">def</span> <span class="nf">__rdiv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__rtruediv__</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
188    <span class="k">def</span> <span class="nf">__idiv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__itruediv__</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
189
190       
191    <span class="c"># Unary ops</span>
192    <span class="k">def</span> <span class="nf">__neg__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
193        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span>
194    <span class="k">def</span> <span class="nf">__pos__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
195        <span class="k">return</span> <span class="bp">self</span>
196    <span class="k">def</span> <span class="nf">__abs__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
197        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="n">numpy</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">),</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span>
198
199    <span class="k">def</span> <span class="nf">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
200        <span class="c">#return str(self.x)+&quot; +/- &quot;+str(numpy.sqrt(self.variance))</span>
201        <span class="k">if</span> <span class="n">numpy</span><span class="o">.</span><span class="n">isscalar</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">):</span>
202            <span class="k">return</span> <span class="n">format_uncertainty</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">numpy</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
203        <span class="k">else</span><span class="p">:</span>
204            <span class="k">return</span> <span class="p">[</span><span class="n">format_uncertainty</span><span class="p">(</span><span class="n">v</span><span class="p">,</span><span class="n">dv</span><span class="p">)</span> 
205                    <span class="k">for</span> <span class="n">v</span><span class="p">,</span><span class="n">dv</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="n">numpy</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">))]</span>
206    <span class="k">def</span> <span class="nf">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
207        <span class="k">return</span> <span class="s">&quot;Uncertainty(</span><span class="si">%s</span><span class="s">,</span><span class="si">%s</span><span class="s">)&quot;</span><span class="o">%</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">),</span><span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
208
209    <span class="c"># Not implemented</span>
210    <span class="k">def</span> <span class="nf">__floordiv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
211    <span class="k">def</span> <span class="nf">__mod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
212    <span class="k">def</span> <span class="nf">__divmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
213    <span class="k">def</span> <span class="nf">__mod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
214    <span class="k">def</span> <span class="nf">__lshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
215    <span class="k">def</span> <span class="nf">__rshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
216    <span class="k">def</span> <span class="nf">__and__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
217    <span class="k">def</span> <span class="nf">__xor__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
218    <span class="k">def</span> <span class="nf">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
219
220    <span class="k">def</span> <span class="nf">__rfloordiv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
221    <span class="k">def</span> <span class="nf">__rmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
222    <span class="k">def</span> <span class="nf">__rdivmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
223    <span class="k">def</span> <span class="nf">__rmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
224    <span class="k">def</span> <span class="nf">__rlshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
225    <span class="k">def</span> <span class="nf">__rrshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
226    <span class="k">def</span> <span class="nf">__rand__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
227    <span class="k">def</span> <span class="nf">__rxor__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
228    <span class="k">def</span> <span class="nf">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
229
230    <span class="k">def</span> <span class="nf">__ifloordiv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
231    <span class="k">def</span> <span class="nf">__imod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
232    <span class="k">def</span> <span class="nf">__idivmod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
233    <span class="k">def</span> <span class="nf">__imod__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
234    <span class="k">def</span> <span class="nf">__ilshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
235    <span class="k">def</span> <span class="nf">__irshift__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
236    <span class="k">def</span> <span class="nf">__iand__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
237    <span class="k">def</span> <span class="nf">__ixor__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
238    <span class="k">def</span> <span class="nf">__ior__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="bp">NotImplemented</span>
239
240    <span class="k">def</span> <span class="nf">__invert__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>  <span class="c"># For ~x</span>
241    <span class="k">def</span> <span class="nf">__complex__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
242    <span class="k">def</span> <span class="nf">__int__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
243    <span class="k">def</span> <span class="nf">__long__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
244    <span class="k">def</span> <span class="nf">__float__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
245    <span class="k">def</span> <span class="nf">__oct__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
246    <span class="k">def</span> <span class="nf">__hex__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
247    <span class="k">def</span> <span class="nf">__index__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
248    <span class="k">def</span> <span class="nf">__coerce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="k">return</span> <span class="n">NotImplmented</span>
249
250<div class="viewcode-block" id="Uncertainty.log"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.uncertainty.Uncertainty.log">[docs]</a>    <span class="k">def</span> <span class="nf">log</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
251        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">*</span><span class="n">err1d</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
252</div>
253<div class="viewcode-block" id="Uncertainty.exp"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.uncertainty.Uncertainty.exp">[docs]</a>    <span class="k">def</span> <span class="nf">exp</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
254        <span class="k">return</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="o">*</span><span class="n">err1d</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span><span class="bp">self</span><span class="o">.</span><span class="n">variance</span><span class="p">))</span>
255</div></div>
256<span class="k">def</span> <span class="nf">log</span><span class="p">(</span><span class="n">val</span><span class="p">):</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">log</span><span class="p">()</span>
257<span class="k">def</span> <span class="nf">exp</span><span class="p">(</span><span class="n">val</span><span class="p">):</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">exp</span><span class="p">()</span>
258
259<span class="k">def</span> <span class="nf">test</span><span class="p">():</span>
260    <span class="n">a</span> <span class="o">=</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
261    <span class="n">b</span> <span class="o">=</span> <span class="n">Uncertainty</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
262
263    <span class="c"># Scalar operations</span>
264    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">4</span>
265    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">+</span><span class="mi">4</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span>
266    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">-</span><span class="mi">4</span>
267    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">-</span><span class="mi">4</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span>
268    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="mi">4</span>
269    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">*</span><span class="mi">4</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span><span class="o">*</span><span class="mi">4</span><span class="o">**</span><span class="mi">2</span>
270    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">/</span><span class="mi">4</span>
271    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mf">5.</span><span class="o">/</span><span class="mi">4</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mf">3.</span><span class="o">/</span><span class="mi">4</span><span class="o">**</span><span class="mi">2</span>
272   
273    <span class="c"># Reverse scalar operations</span>
274    <span class="n">z</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="n">a</span>
275    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">4</span><span class="o">+</span><span class="mi">5</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span>
276    <span class="n">z</span> <span class="o">=</span> <span class="mi">4</span><span class="o">-</span><span class="n">a</span>
277    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">4</span><span class="o">-</span><span class="mi">5</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span>
278    <span class="n">z</span> <span class="o">=</span> <span class="mi">4</span><span class="o">*</span><span class="n">a</span>
279    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">4</span><span class="o">*</span><span class="mi">5</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span><span class="o">*</span><span class="mi">4</span><span class="o">**</span><span class="mi">2</span>
280    <span class="n">z</span> <span class="o">=</span> <span class="mi">4</span><span class="o">/</span><span class="n">a</span>
281    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mf">4.</span><span class="o">/</span><span class="mi">5</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">-</span> <span class="mf">3.</span><span class="o">/</span><span class="mi">5</span><span class="o">**</span><span class="mi">4</span> <span class="o">*</span> <span class="mi">4</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
282   
283    <span class="c"># Power operations</span>
284    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span>
285    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">**</span><span class="mi">2</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">4</span><span class="o">*</span><span class="mi">3</span><span class="o">*</span><span class="mi">5</span><span class="o">**</span><span class="mi">2</span>
286    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">1</span>
287    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">**</span><span class="mi">1</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span>
288    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">0</span>
289    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">**</span><span class="mi">0</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">0</span>
290    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">**-</span><span class="mi">1</span>
291    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">**-</span><span class="mi">1</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">-</span> <span class="mf">3.</span><span class="o">/</span><span class="mi">5</span><span class="o">**</span><span class="mi">4</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
292
293    <span class="c"># Binary operations</span>
294    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span>
295    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">+</span><span class="mi">4</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span><span class="o">+</span><span class="mi">2</span>
296    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span>
297    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">-</span><span class="mi">4</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span><span class="o">+</span><span class="mi">2</span>
298    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span>
299    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">*</span><span class="mi">4</span> <span class="ow">and</span> <span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="p">(</span><span class="mi">5</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">4</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="mi">3</span><span class="p">)</span>
300    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">/</span><span class="n">b</span>
301    <span class="k">assert</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mf">5.</span><span class="o">/</span><span class="mi">4</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">-</span> <span class="p">(</span><span class="mf">3.</span><span class="o">/</span><span class="mi">5</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">2.</span><span class="o">/</span><span class="mi">4</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="mf">5.</span><span class="o">/</span><span class="mi">4</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
302
303    <span class="c"># ===== Inplace operations =====    </span>
304    <span class="c"># Scalar operations</span>
305    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">+=</span> <span class="mi">4</span>
306    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">4</span>
307    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
308    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">-=</span> <span class="mi">4</span>
309    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">-</span><span class="mi">4</span>
310    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
311    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">*=</span> <span class="mi">4</span>
312    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="mi">4</span>
313    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
314    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">/=</span> <span class="mi">4</span>
315    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">/</span><span class="mi">4</span>
316    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
317
318    <span class="c"># Power operations</span>
319    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">**=</span> <span class="mi">4</span>
320    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">4</span>
321    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
322
323    <span class="c"># Binary operations</span>
324    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">+=</span> <span class="n">b</span>
325    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span>
326    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
327    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">-=</span> <span class="n">b</span>
328    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span>
329    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
330    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">*=</span> <span class="n">b</span>
331    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span>
332    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
333    <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">+</span><span class="mi">0</span><span class="p">;</span> <span class="n">y</span> <span class="o">/=</span> <span class="n">b</span>
334    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">/</span><span class="n">b</span>
335    <span class="k">assert</span> <span class="n">y</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">variance</span><span class="o">-</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span>
336
337
338    <span class="c"># =============== vector operations ================</span>
339    <span class="c"># Slicing</span>
340    <span class="n">z</span> <span class="o">=</span> <span class="n">Uncertainty</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">1</span><span class="p">,</span><span class="mi">2</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="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">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">]))</span>
341    <span class="k">assert</span> <span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">3</span> <span class="ow">and</span> <span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">2</span>
342    <span class="k">assert</span> <span class="p">(</span><span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">]</span><span class="o">.</span><span class="n">x</span> <span class="o">==</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="o">.</span><span class="n">all</span><span class="p">()</span>
343    <span class="k">assert</span> <span class="p">(</span><span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">]</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span><span class="o">.</span><span class="n">all</span><span class="p">()</span>
344    <span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="n">Uncertainty</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">8</span><span class="p">,</span><span class="mi">7</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">4</span><span class="p">,</span><span class="mi">5</span><span class="p">]))</span>
345    <span class="k">assert</span> <span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">8</span> <span class="ow">and</span> <span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">4</span>
346    <span class="n">A</span> <span class="o">=</span> <span class="n">Uncertainty</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="n">a</span><span class="o">.</span><span class="n">x</span><span class="p">]</span><span class="o">*</span><span class="mi">2</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="n">a</span><span class="o">.</span><span class="n">variance</span><span class="p">]</span><span class="o">*</span><span class="mi">2</span><span class="p">))</span>
347    <span class="n">B</span> <span class="o">=</span> <span class="n">Uncertainty</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="n">b</span><span class="o">.</span><span class="n">x</span><span class="p">]</span><span class="o">*</span><span class="mi">2</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="n">b</span><span class="o">.</span><span class="n">variance</span><span class="p">]</span><span class="o">*</span><span class="mi">2</span><span class="p">))</span>
348
349    <span class="c"># TODO complete tests of copy and inplace operations for vectors and slices.</span>
350
351    <span class="c"># Binary operations</span>
352    <span class="n">z</span> <span class="o">=</span> <span class="n">A</span><span class="o">+</span><span class="n">B</span>
353    <span class="k">assert</span> <span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">+</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">()</span> <span class="ow">and</span> <span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">()</span>
354    <span class="n">z</span> <span class="o">=</span> <span class="n">A</span><span class="o">-</span><span class="n">B</span>
355    <span class="k">assert</span> <span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">-</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">()</span> <span class="ow">and</span> <span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="mi">3</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">()</span>
356    <span class="n">z</span> <span class="o">=</span> <span class="n">A</span><span class="o">*</span><span class="n">B</span>
357    <span class="k">assert</span> <span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mi">5</span><span class="o">*</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">()</span> <span class="ow">and</span> <span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">==</span> <span class="p">(</span><span class="mi">5</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">4</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="mi">3</span><span class="p">))</span><span class="o">.</span><span class="n">all</span><span class="p">()</span>
358    <span class="n">z</span> <span class="o">=</span> <span class="n">A</span><span class="o">/</span><span class="n">B</span>
359    <span class="k">assert</span> <span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">x</span> <span class="o">==</span> <span class="mf">5.</span><span class="o">/</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">()</span>
360    <span class="k">assert</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">variance</span> <span class="o">-</span> <span class="p">(</span><span class="mf">3.</span><span class="o">/</span><span class="mi">5</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">2.</span><span class="o">/</span><span class="mi">4</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="mf">5.</span><span class="o">/</span><span class="mi">4</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-15</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">()</span>
361   
362    <span class="c"># printing; note that sqrt(3) ~ 1.7</span>
363    <span class="k">assert</span> <span class="nb">str</span><span class="p">(</span><span class="n">Uncertainty</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span> <span class="o">==</span> <span class="s">&quot;5.0(17)&quot;</span>
364    <span class="k">assert</span> <span class="nb">str</span><span class="p">(</span><span class="n">Uncertainty</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span> <span class="o">==</span> <span class="s">&quot;15.0(17)&quot;</span>
365    <span class="k">assert</span> <span class="nb">str</span><span class="p">(</span><span class="n">Uncertainty</span><span class="p">(</span><span class="mf">151.23356</span><span class="p">,</span><span class="mf">0.324185</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> <span class="o">==</span> <span class="s">&quot;151.23(32)&quot;</span>
366
367<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> <span class="n">test</span><span class="p">()</span>
368</pre></div>
369
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