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Morten Hjorth-Jensen
2024-09-22 21:21:59 +02:00
parent 0a6ba7c08d
commit 80f0f2ffab
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@@ -298,6 +298,16 @@ const thebe_selector_output = ".output, .cell_output"
Week 38: Logistic Regression and Optimization
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek39.html">
Exercises week 39
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week39.html">
Week 39: Optimization and Gradient Methods
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
@@ -2577,83 +2587,11 @@ Using TensorFlow results in a much better execution time. Try it!</p>
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
<span class="ne">---&gt; </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:28,</span> in <span class="ni">grad</span><span class="nt">(fun, x)</span>
<span class="g g-Whitespace"> </span><span class="mi">21</span> <span class="nd">@unary_to_nary</span>
<span class="g g-Whitespace"> </span><span class="mi">22</span> <span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">23</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="g g-Whitespace"> </span><span class="mi">24</span><span class="sd"> Returns a function which computes the gradient of `fun` with respect to</span>
<span class="g g-Whitespace"> </span><span class="mi">25</span><span class="sd"> positional argument number `argnum`. The returned function takes the same</span>
<span class="g g-Whitespace"> </span><span class="mi">26</span><span class="sd"> arguments as `fun`, but returns the gradient instead. The function `fun`</span>
<span class="g g-Whitespace"> </span><span class="mi">27</span><span class="sd"> should be scalar-valued. The gradient has the same type as the argument.&quot;&quot;&quot;</span>
<span class="ne">---&gt; </span><span class="mi">28</span> <span class="n">vjp</span><span class="p">,</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">_make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">29</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">30</span> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Grad only applies to real scalar-output functions. &quot;</span>
<span class="g g-Whitespace"> </span><span class="mi">31</span> <span class="s2">&quot;Try jacobian, elementwise_grad or holomorphic_grad.&quot;</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10,</span> in <span class="ni">make_vjp</span><span class="nt">(fun, x)</span>
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">def</span> <span class="nf">make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">start_node</span> <span class="o">=</span> <span class="n">VJPNode</span><span class="o">.</span><span class="n">new_root</span><span class="p">()</span>
<span class="ne">---&gt; </span><span class="mi">10</span> <span class="n">end_value</span><span class="p">,</span> <span class="n">end_node</span> <span class="o">=</span> <span class="n">trace</span><span class="p">(</span><span class="n">start_node</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">11</span> <span class="k">if</span> <span class="n">end_node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">12</span> <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">zeros</span><span class="p">()</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10,</span> in <span class="ni">trace</span><span class="nt">(start_node, fun, x)</span>
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">with</span> <span class="n">trace_stack</span><span class="o">.</span><span class="n">new_trace</span><span class="p">()</span> <span class="k">as</span> <span class="n">t</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">start_box</span> <span class="o">=</span> <span class="n">new_box</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">start_node</span><span class="p">)</span>
<span class="ne">---&gt; </span><span class="mi">10</span> <span class="n">end_box</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="n">start_box</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">11</span> <span class="k">if</span> <span class="n">isbox</span><span class="p">(</span><span class="n">end_box</span><span class="p">)</span> <span class="ow">and</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_trace</span> <span class="o">==</span> <span class="n">start_box</span><span class="o">.</span><span class="n">_trace</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">12</span> <span class="k">return</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_value</span><span class="p">,</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_node</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f.&lt;locals&gt;.unary_f</span><span class="nt">(x)</span>
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="k">else</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">14</span> <span class="n">subargs</span> <span class="o">=</span> <span class="n">subvals</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">zip</span><span class="p">(</span><span class="n">argnum</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
<span class="ne">---&gt; </span><span class="mi">15</span> <span class="k">return</span> <span class="n">fun</span><span class="p">(</span><span class="o">*</span><span class="n">subargs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="nn">Cell In[9], line 80,</span> in <span class="ni">cost_function</span><span class="nt">(P, x, t)</span>
<span class="g g-Whitespace"> </span><span class="mi">78</span> <span class="n">g_t</span> <span class="o">=</span> <span class="n">g_trial</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">79</span> <span class="n">g_t_jacobian</span> <span class="o">=</span> <span class="n">g_t_jacobian_func</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
<span class="ne">---&gt; </span><span class="mi">80</span> <span class="n">g_t_hessian</span> <span class="o">=</span> <span class="n">g_t_hessian_func</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">82</span> <span class="n">g_t_dt</span> <span class="o">=</span> <span class="n">g_t_jacobian</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="n">g_t_d2x</span> <span class="o">=</span> <span class="n">g_t_hessian</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f</span><span class="nt">(*args, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
<span class="ne">---&gt; </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:81,</span> in <span class="ni">hessian</span><span class="nt">(fun, x)</span>
<span class="g g-Whitespace"> </span><span class="mi">78</span> <span class="nd">@unary_to_nary</span>
<span class="g g-Whitespace"> </span><span class="mi">79</span> <span class="k">def</span> <span class="nf">hessian</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">80</span> <span class="s2">&quot;Returns a function that computes the exact Hessian.&quot;</span>
<span class="ne">---&gt; </span><span class="mi">81</span> <span class="k">return</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">fun</span><span class="p">))(</span><span class="n">x</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f</span><span class="nt">(*args, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
<span class="ne">---&gt; </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:64,</span> in <span class="ni">jacobian</span><span class="nt">(fun, x)</span>
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="n">jacobian_shape</span> <span class="o">=</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">shape</span>
<span class="g g-Whitespace"> </span><span class="mi">63</span> <span class="n">grads</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">vjp</span><span class="p">,</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">standard_basis</span><span class="p">())</span>
<span class="ne">---&gt; </span><span class="mi">64</span> <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">grads</span><span class="p">),</span> <span class="n">jacobian_shape</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88,</span> in <span class="ni">stack</span><span class="nt">(arrays, axis)</span>
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="k">def</span> <span class="nf">stack</span><span class="p">(</span><span class="n">arrays</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">84</span> <span class="c1"># this code is basically copied from numpy/core/shape_base.py&#39;s stack</span>
<span class="g g-Whitespace"> </span><span class="mi">85</span> <span class="c1"># we need it here because we want to re-implement stack in terms of the</span>
<span class="g g-Whitespace"> </span><span class="mi">86</span> <span class="c1"># primitives defined in this file</span>
<span class="ne">---&gt; </span><span class="mi">88</span> <span class="n">arrays</span> <span class="o">=</span> <span class="p">[</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">arr</span> <span class="ow">in</span> <span class="n">arrays</span><span class="p">]</span>
<span class="g g-Whitespace"> </span><span class="mi">89</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">arrays</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">90</span> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;need at least one array to stack&#39;</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88,</span> in <span class="ni">&lt;listcomp&gt;</span><span class="nt">(.0)</span>
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="k">def</span> <span class="nf">stack</span><span class="p">(</span><span class="n">arrays</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">84</span> <span class="c1"># this code is basically copied from numpy/core/shape_base.py&#39;s stack</span>
<span class="g g-Whitespace"> </span><span class="mi">85</span> <span class="c1"># we need it here because we want to re-implement stack in terms of the</span>
<span class="g g-Whitespace"> </span><span class="mi">86</span> <span class="c1"># primitives defined in this file</span>
<span class="ne">---&gt; </span><span class="mi">88</span> <span class="n">arrays</span> <span class="o">=</span> <span class="p">[</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">arr</span> <span class="ow">in</span> <span class="n">arrays</span><span class="p">]</span>
<span class="g g-Whitespace"> </span><span class="mi">89</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">arrays</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">90</span> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;need at least one array to stack&#39;</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:32,</span> in <span class="ni">grad</span><span class="nt">(fun, x)</span>
<span class="g g-Whitespace"> </span><span class="mi">29</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">30</span> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Grad only applies to real scalar-output functions. &quot;</span>
<span class="g g-Whitespace"> </span><span class="mi">31</span> <span class="s2">&quot;Try jacobian, elementwise_grad or holomorphic_grad.&quot;</span><span class="p">)</span>
<span class="ne">---&gt; </span><span class="mi">32</span> <span class="k">return</span> <span class="n">vjp</span><span class="p">(</span><span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">ones</span><span class="p">())</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14,</span> in <span class="ni">make_vjp.&lt;locals&gt;.vjp</span><span class="nt">(g)</span>
<span class="ne">---&gt; </span><span class="mi">14</span> <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">backward_pass</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">end_node</span><span class="p">)</span>
@@ -2678,12 +2616,30 @@ Using TensorFlow results in a much better execution time. Try it!</p>
<span class="g g-Whitespace"> </span><span class="mi">659</span> <span class="n">target_meta</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">metadata</span><span class="p">(</span><span class="n">target</span><span class="p">)</span>
<span class="ne">--&gt; </span><span class="mi">660</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">unbroadcast</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">g</span><span class="p">),</span> <span class="n">target_meta</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:651,</span> in <span class="ni">unbroadcast</span><span class="nt">(x, target_meta, broadcast_idx)</span>
<span class="g g-Whitespace"> </span><span class="mi">649</span> <span class="k">while</span> <span class="n">anp</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">target_ndim</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">650</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">broadcast_idx</span><span class="p">)</span>
<span class="ne">--&gt; </span><span class="mi">651</span> <span class="k">for</span> <span class="n">axis</span><span class="p">,</span> <span class="n">size</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">target_shape</span><span class="p">):</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:653,</span> in <span class="ni">unbroadcast</span><span class="nt">(x, target_meta, broadcast_idx)</span>
<span class="g g-Whitespace"> </span><span class="mi">651</span> <span class="k">for</span> <span class="n">axis</span><span class="p">,</span> <span class="n">size</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">target_shape</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">652</span> <span class="k">if</span> <span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">653</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">axis</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="ne">--&gt; </span><span class="mi">653</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">axis</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">654</span> <span class="k">if</span> <span class="n">anp</span><span class="o">.</span><span class="n">iscomplexobj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">target_iscomplex</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">655</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48,</span> in <span class="ni">primitive.&lt;locals&gt;.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">46</span> <span class="k">return</span> <span class="n">new_box</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">trace</span><span class="p">,</span> <span class="n">node</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">47</span> <span class="k">else</span><span class="p">:</span>
<span class="ne">---&gt; </span><span class="mi">48</span> <span class="k">return</span> <span class="n">f_raw</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="nn">File &lt;__array_function__ internals&gt;:180,</span> in <span class="ni">sum</span><span class="nt">(*args, **kwargs)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:2296,</span> in <span class="ni">sum</span><span class="nt">(a, axis, dtype, out, keepdims, initial, where)</span>
<span class="g g-Whitespace"> </span><span class="mi">2293</span> <span class="k">return</span> <span class="n">out</span>
<span class="g g-Whitespace"> </span><span class="mi">2294</span> <span class="k">return</span> <span class="n">res</span>
<span class="ne">-&gt; </span><span class="mi">2296</span> <span class="k">return</span> <span class="n">_wrapreduction</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="s1">&#39;sum&#39;</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="n">keepdims</span><span class="p">,</span>
<span class="g g-Whitespace"> </span><span class="mi">2297</span> <span class="n">initial</span><span class="o">=</span><span class="n">initial</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="n">where</span><span class="p">)</span>
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:86,</span> in <span class="ni">_wrapreduction</span><span class="nt">(obj, ufunc, method, axis, dtype, out, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">83</span> <span class="k">else</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">84</span> <span class="k">return</span> <span class="n">reduction</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="n">axis</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">out</span><span class="p">,</span> <span class="o">**</span><span class="n">passkwargs</span><span class="p">)</span>
<span class="ne">---&gt; </span><span class="mi">86</span> <span class="k">return</span> <span class="n">ufunc</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="o">**</span><span class="n">passkwargs</span><span class="p">)</span>
<span class="ne">KeyboardInterrupt</span>:
</pre></div>