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<h1>Coverage for <b>navipy/errorprop/__init__.py</b> :
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<p id="t1" class="pln"><span class="str">"""</span><span class="strut"> </span></p>
<p id="t2" class="pln"><span class="str">Numerical error propagation</span><span class="strut"> </span></p>
<p id="t3" class="pln"><span class="strut"> </span></p>
<p id="t4" class="pln"><span class="str">tools to propogate the error by using an estimate</span><span class="strut"> </span></p>
<p id="t5" class="pln"><span class="str">of the jacobian matrix (matrix of derivatives)</span><span class="strut"> </span></p>
<p id="t6" class="pln"><span class="str">"""</span><span class="strut"> </span></p>
<p id="t7" class="stm run hide_run"><span class="key">import</span> <span class="nam">numpy</span> <span class="key">as</span> <span class="nam">np</span><span class="strut"> </span></p>
<p id="t8" class="pln"><span class="strut"> </span></p>
<p id="t9" class="pln"><span class="strut"> </span></p>
<p id="t10" class="stm run hide_run"><span class="key">def</span> <span class="nam">estimate_error</span><span class="op">(</span><span class="nam">markers</span><span class="op">,</span> <span class="nam">rigid_marker_id</span><span class="op">=</span><span class="op">[</span><span class="num">0</span><span class="op">,</span> <span class="num">1</span><span class="op">]</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t11" class="pln"> <span class="str">"""</span><span class="strut"> </span></p>
<p id="t12" class="pln"><span class="str"> Estimate the error by using the deviation from the median</span><span class="strut"> </span></p>
<p id="t13" class="pln"><span class="str">distance between two markers</span><span class="strut"> </span></p>
<p id="t14" class="pln"><span class="str"> """</span><span class="strut"> </span></p>
<p id="t15" class="stm mis"> <span class="key">if</span> <span class="key">not</span> <span class="nam">isinstance</span><span class="op">(</span><span class="nam">rigid_marker_id</span><span class="op">,</span> <span class="nam">list</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t16" class="stm mis"> <span class="key">raise</span> <span class="nam">TypeError</span><span class="op">(</span><span class="str">'rigid_marker_id should be a list'</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t17" class="stm mis"> <span class="key">if</span> <span class="nam">len</span><span class="op">(</span><span class="nam">rigid_marker_id</span><span class="op">)</span> <span class="op">!=</span> <span class="num">2</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t18" class="stm mis"> <span class="key">raise</span> <span class="nam">ValueError</span><span class="op">(</span><span class="str">'rigid_marker_id should be a list with two elements'</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t19" class="stm mis"> <span class="nam">dist</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">sqrt</span><span class="op">(</span><span class="op">(</span><span class="op">(</span><span class="nam">markers</span><span class="op">.</span><span class="nam">loc</span><span class="op">[</span><span class="op">:</span><span class="op">,</span> <span class="nam">rigid_marker_id</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">]</span> <span class="op">-</span><span class="strut"> </span></p>
<p id="t20" class="pln"> <span class="nam">markers</span><span class="op">.</span><span class="nam">loc</span><span class="op">[</span><span class="op">:</span><span class="op">,</span> <span class="nam">rigid_marker_id</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">**</span><span class="num">2</span><span class="op">)</span><span class="op">.</span><span class="nam">sum</span><span class="op">(</span><span class="strut"> </span></p>
<p id="t21" class="pln"> <span class="nam">axis</span><span class="op">=</span><span class="num">1</span><span class="op">,</span> <span class="nam">skipna</span><span class="op">=</span><span class="key">False</span><span class="op">)</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t22" class="stm mis"> <span class="nam">median_dist</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">nanmedian</span><span class="op">(</span><span class="nam">dist</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t23" class="stm mis"> <span class="key">return</span> <span class="nam">np</span><span class="op">.</span><span class="nam">abs</span><span class="op">(</span><span class="nam">dist</span> <span class="op">-</span> <span class="nam">median_dist</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t24" class="pln"><span class="strut"> </span></p>
<p id="t25" class="pln"><span class="strut"> </span></p>
<p id="t26" class="stm run hide_run"><span class="key">def</span> <span class="nam">estimate_jacobian</span><span class="op">(</span><span class="nam">fun</span><span class="op">,</span> <span class="nam">x</span><span class="op">,</span> <span class="nam">args</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">epsilon</span><span class="op">=</span><span class="num">1e-6</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t27" class="pln"> <span class="str">"""Estimate the jacobian matrix</span><span class="strut"> </span></p>
<p id="t28" class="pln"><span class="strut"> </span></p>
<p id="t29" class="pln"><span class="str"> :param fun: The objective function to be derivated. Must be in \</span><span class="strut"> </span></p>
<p id="t30" class="pln"><span class="str">the form f(x, *args). \</span><span class="strut"> </span></p>
<p id="t31" class="pln"><span class="str">The argument, x, is a 1-D array of points, and args is a tuple of \</span><span class="strut"> </span></p>
<p id="t32" class="pln"><span class="str">any additional \</span><span class="strut"> </span></p>
<p id="t33" class="pln"><span class="str">fixed parameters needed to completely specify the function.</span><span class="strut"> </span></p>
<p id="t34" class="pln"><span class="str"> :param x: values at which the jacobian should be calculated</span><span class="strut"> </span></p>
<p id="t35" class="pln"><span class="str"> :param args: Extra arguments passed to the objective function</span><span class="strut"> </span></p>
<p id="t36" class="pln"><span class="str"> :param epsilon: step used to estimate the jacobian</span><span class="strut"> </span></p>
<p id="t37" class="pln"><span class="str"> :returns: An estimated jacobian matrix</span><span class="strut"> </span></p>
<p id="t38" class="pln"><span class="str"> """</span><span class="strut"> </span></p>
<p id="t39" class="stm run hide_run"> <span class="key">if</span> <span class="nam">isinstance</span><span class="op">(</span><span class="nam">x</span><span class="op">,</span> <span class="op">(</span><span class="nam">list</span><span class="op">,</span> <span class="nam">tuple</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">ndarray</span><span class="op">)</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t40" class="stm run hide_run"> <span class="nam">jacobian_matrix</span> <span class="op">=</span> <span class="nam">list</span><span class="op">(</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t41" class="stm run hide_run"> <span class="key">for</span> <span class="nam">vari</span><span class="op">,</span> <span class="nam">_</span> <span class="key">in</span> <span class="nam">enumerate</span><span class="op">(</span><span class="nam">x</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t42" class="stm run hide_run"> <span class="nam">x_minus</span> <span class="op">=</span> <span class="nam">x</span><span class="op">.</span><span class="nam">copy</span><span class="op">(</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t43" class="stm run hide_run"> <span class="nam">x_plus</span> <span class="op">=</span> <span class="nam">x</span><span class="op">.</span><span class="nam">copy</span><span class="op">(</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t44" class="stm run hide_run"> <span class="nam">x_minus</span><span class="op">[</span><span class="nam">vari</span><span class="op">]</span> <span class="op">-=</span> <span class="nam">epsilon</span><span class="strut"> </span></p>
<p id="t45" class="stm run hide_run"> <span class="nam">x_plus</span><span class="op">[</span><span class="nam">vari</span><span class="op">]</span> <span class="op">+=</span> <span class="nam">epsilon</span><span class="strut"> </span></p>
<p id="t46" class="pln"><span class="strut"> </span></p>
<p id="t47" class="stm run hide_run"> <span class="key">if</span> <span class="nam">args</span> <span class="key">is</span> <span class="key">None</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t48" class="stm run hide_run"> <span class="nam">dfs1</span> <span class="op">=</span> <span class="nam">fun</span><span class="op">(</span><span class="nam">x_minus</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t49" class="stm run hide_run"> <span class="nam">dfs2</span> <span class="op">=</span> <span class="nam">fun</span><span class="op">(</span><span class="nam">x_plus</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t50" class="pln"> <span class="key">else</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t51" class="stm mis"> <span class="nam">dfs1</span> <span class="op">=</span> <span class="nam">fun</span><span class="op">(</span><span class="nam">x_minus</span><span class="op">,</span> <span class="nam">args</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t52" class="stm mis"> <span class="nam">dfs2</span> <span class="op">=</span> <span class="nam">fun</span><span class="op">(</span><span class="nam">x_plus</span><span class="op">,</span> <span class="nam">args</span><span class="op">)</span><span class="strut"> </span></p><p id="t53" class="stm run hide_run"> <span class="nam">dfs1</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="nam">dfs1</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t54" class="stm run hide_run"> <span class="nam">dfs2</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="nam">dfs2</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t55" class="stm run hide_run"> <span class="nam">deriv</span> <span class="op">=</span> <span class="op">(</span><span class="nam">dfs2</span> <span class="op">-</span> <span class="nam">dfs1</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="num">2</span> <span class="op">*</span> <span class="nam">epsilon</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t56" class="stm run hide_run"> <span class="nam">jacobian_matrix</span><span class="op">.</span><span class="nam">append</span><span class="op">(</span><span class="nam">deriv</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t57" class="stm run hide_run"> <span class="key">return</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="nam">jacobian_matrix</span><span class="op">)</span><span class="op">.</span><span class="nam">transpose</span><span class="op">(</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t58" class="pln"> <span class="key">else</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t59" class="stm run hide_run"> <span class="nam">x_minus</span> <span class="op">=</span> <span class="nam">x</span> <span class="op">-</span> <span class="nam">epsilon</span><span class="strut"> </span></p>
<p id="t60" class="stm run hide_run"> <span class="nam">x_plus</span> <span class="op">=</span> <span class="nam">x</span> <span class="op">+</span> <span class="nam">epsilon</span><span class="strut"> </span></p>
<p id="t61" class="stm run hide_run"> <span class="key">if</span> <span class="nam">args</span> <span class="key">is</span> <span class="key">None</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t62" class="stm run hide_run"> <span class="nam">deriv</span> <span class="op">=</span> <span class="op">(</span><span class="nam">fun</span><span class="op">(</span><span class="nam">x_plus</span><span class="op">)</span> <span class="op">-</span> <span class="nam">fun</span><span class="op">(</span><span class="nam">x_minus</span><span class="op">)</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="num">2</span> <span class="op">*</span> <span class="nam">epsilon</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t63" class="pln"> <span class="key">else</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t64" class="stm mis"> <span class="nam">deriv</span> <span class="op">=</span> <span class="op">(</span><span class="nam">fun</span><span class="op">(</span><span class="nam">x_plus</span><span class="op">,</span> <span class="nam">args</span><span class="op">)</span> <span class="op">-</span> <span class="nam">fun</span><span class="op">(</span><span class="nam">x_minus</span><span class="op">,</span> <span class="nam">args</span><span class="op">)</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="num">2</span> <span class="op">*</span> <span class="nam">epsilon</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t65" class="stm run hide_run"> <span class="key">return</span> <span class="nam">deriv</span><span class="strut"> </span></p>
<p id="t66" class="pln"><span class="strut"> </span></p>
<p id="t67" class="pln"><span class="strut"> </span></p>
<p id="t68" class="stm run hide_run"><span class="key">def</span> <span class="nam">propagate_error</span><span class="op">(</span><span class="nam">fun</span><span class="op">,</span> <span class="nam">x</span><span class="op">,</span> <span class="nam">covar</span><span class="op">,</span> <span class="nam">args</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">epsilon</span><span class="op">=</span><span class="num">1e-6</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t69" class="pln"> <span class="str">"""Estimate the jacobian matrix</span><span class="strut"> </span></p>
<p id="t70" class="pln"><span class="strut"> </span></p>
<p id="t71" class="pln"><span class="str"> :param fun: The objective function to be error propagated. \</span><span class="strut"> </span></p>
<p id="t72" class="pln"><span class="str">Must be in the form f(x, *args). \</span><span class="strut"> </span></p>
<p id="t73" class="pln"><span class="str">The argument, x, is a 1-D array of points, and args is a tuple of \</span><span class="strut"> </span></p>
<p id="t74" class="pln"><span class="str">any additional \</span><span class="strut"> </span></p>
<p id="t75" class="pln"><span class="str">fixed parameters needed to completely specify the function.</span><span class="strut"> </span></p>
<p id="t76" class="pln"><span class="str"> :param x: values at which the error should be calculated</span><span class="strut"> </span></p>
<p id="t77" class="pln"><span class="str"> :param covar: variance-covariance matrix</span><span class="strut"> </span></p>
<p id="t78" class="pln"><span class="str"> :param args: Extra arguments passed to the objective function</span><span class="strut"> </span></p>
<p id="t79" class="pln"><span class="str"> :param epsilon: step used to estimate the jacobian</span><span class="strut"> </span></p>
<p id="t80" class="pln"><span class="str"> :returns: An estimated jacobian matrix</span><span class="strut"> </span></p>
<p id="t81" class="pln"><span class="str"> """</span><span class="strut"> </span></p>
<p id="t82" class="stm run hide_run"> <span class="nam">jacobian_matrix</span> <span class="op">=</span> <span class="nam">estimate_jacobian</span><span class="op">(</span><span class="nam">fun</span><span class="op">,</span> <span class="nam">x</span><span class="op">,</span> <span class="nam">args</span><span class="op">,</span> <span class="nam">epsilon</span><span class="op">=</span><span class="num">1e-6</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t83" class="stm run hide_run"> <span class="key">if</span> <span class="nam">isinstance</span><span class="op">(</span><span class="nam">x</span><span class="op">,</span> <span class="op">(</span><span class="nam">list</span><span class="op">,</span> <span class="nam">tuple</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">ndarray</span><span class="op">)</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t84" class="stm run hide_run"> <span class="key">return</span> <span class="nam">jacobian_matrix</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">covar</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">jacobian_matrix</span><span class="op">.</span><span class="nam">transpose</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t85" class="pln"> <span class="key">else</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t86" class="stm run hide_run"> <span class="key">return</span> <span class="nam">np</span><span class="op">.</span><span class="nam">abs</span><span class="op">(</span><span class="nam">jacobian_matrix</span><span class="op">)</span> <span class="op">*</span> <span class="nam">covar</span><span class="strut"> </span></p>
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