numpy_intro.ipynb



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<div class=" highlight hl-ipython"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span> <span class="o">=</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>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span>
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<pre>[1, 2, 3, 4]</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
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<div class=" highlight hl-ipython"><pre><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
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<pre>[1, 2, 3, 4, 5, 6, 7, 8, 9]</pre>
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<div class=" highlight hl-ipython"><pre><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="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]]</span>
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<pre>[[1, 2, 3], [4, 5, 6], [7, 8, 9]]</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span> <span class="o">=</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="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]]</span>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
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<pre>6</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">:]</span>
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<pre>[5, 6]</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">:]</span>
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<pre>[8, 9]</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span>
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<pre>array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">arr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span>
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<pre>array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">arr</span><span class="p">[</span><span class="mi">1</span><span class="p">:,</span> <span class="p">:</span><span class="mi">2</span><span class="p">]</span>
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<pre>array([[4, 5],
       [7, 8]])</pre>
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<pre>array([1, 2, 3])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">arr</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
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<pre>array([1, 4, 7])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">lst</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">7</span><span class="p">]</span>
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<div class=" highlight hl-ipython"><pre><span class="k">def</span> <span class="nf">sum_list</span><span class="p">(</span><span class="n">lst</span><span class="p">):</span>
    <span class="nb">sum</span> <span class="o">=</span> <span class="mi">0</span>
    <span class="k">for</span> <span class="n">el</span> <span class="ow">in</span> <span class="n">lst</span><span class="p">:</span>
        <span class="nb">sum</span> <span class="o">+=</span> <span class="n">el</span>
    <span class="k">return</span> <span class="nb">sum</span>
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<div class=" highlight hl-ipython"><pre><span class="n">sum_list</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span>
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<pre>12</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">big_lst</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100000</span><span class="p">)</span>
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<div class=" highlight hl-ipython"><pre><span class="o">%</span><span class="k">timeit</span> <span class="n">sum_list</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span>
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<pre>1000000 loops, best of 3: 506 ns per loop</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">big_lst</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100000</span><span class="p">)</span>
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<div class=" highlight hl-ipython"><pre><span class="o">%</span><span class="k">timeit</span> <span class="n">sum_list</span><span class="p">(</span><span class="n">big_lst</span><span class="p">)</span>
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<pre>100 loops, best of 3: 7.01 ms per loop</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">arr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">big_lst</span><span class="p">)</span>
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<div class=" highlight hl-ipython"><pre><span class="o">%</span><span class="k">timeit</span> <span class="n">sum_list</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
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<pre>10 loops, best of 3: 70.7 ms per loop</pre>
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<div class=" highlight hl-ipython"><pre><span class="o">%</span><span class="k">timeit</span> <span class="n">arr</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
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<pre>10000 loops, best of 3: 77.9 us per loop</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
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<pre>4999950000</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">big_lst</span><span class="p">)</span>
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<pre>4999950000</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">big_lst</span><span class="p">)</span>
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<pre>49999.5</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">big_lst</span><span class="p">)</span>
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<pre>28867.513458037916</pre>
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<pre>28867.657796687741</pre>
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<pre>[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
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<pre>array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
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<pre>array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">9</span><span class="p">)</span>
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<pre>array([0, 1, 2, 3, 4, 5, 6, 7, 8])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="err">?</span>
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<div class=" highlight hl-ipython"><pre><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">arange</span><span class="p">(</span><span class="mi">9</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
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<pre>array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
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<pre>array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
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<pre>array([[ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
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<pre>array([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>
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<pre>array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">10</span><span class="p">)))</span>
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<pre>array([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
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<pre>array([[1, 0, 0],
       [0, 6, 0],
       [0, 0, 4]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
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<pre>array([[ 0.45727794,  0.95308707, -0.67349952],
       [ 0.42982752,  1.84326079,  0.88624181],
       [ 0.09784898,  0.65451898,  1.1747724 ],
       [ 0.72163378, -0.02091747, -1.01356388]])</pre>
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<pre>array([[-0.2567363 , -0.01732275,  1.41093738],
       [ 1.07042878, -0.21508292, -0.54726137],
       [ 0.12873854, -0.79321983,  0.15202132],
       [ 0.19978042, -1.87479486, -0.75646302]])</pre>
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<pre>array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">mat</span><span class="p">)</span>
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<pre>36</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">mat</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<pre>array([ 9, 12, 15])</pre>
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<pre>array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">mat</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
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<pre>array([ 3, 12, 21])</pre>
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<pre>array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])</pre>
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<pre>array([[ 5,  6,  7],
       [ 8,  9, 10],
       [11, 12, 13]])</pre>
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<pre>array([[ 0, 10, 20],
       [30, 40, 50],
       [60, 70, 80]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">mat2</span> <span class="o">=</span> <span class="n">mat</span><span class="o">**</span><span class="mi">3</span>
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<pre>array([[  0,   1,   8],
       [ 27,  64, 125],
       [216, 343, 512]])</pre>
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<pre>array([[  0,   2,  10],
       [ 30,  68, 130],
       [222, 350, 520]])</pre>
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<pre>array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])</pre>
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<pre>
<span class="ansired">---------------------------------------------------------------------------</span>
<span class="ansired">ValueError</span>                                Traceback (most recent call last)
<span class="ansigreen">/Users/ely/Downloads/classes/pydata_workshop_20121216/&lt;ipython-input-69-6b2e1601ecfe&gt;</span> in <span class="ansicyan">&lt;module&gt;</span><span class="ansiblue">()</span>
<span class="ansigreen">----&gt; 1</span><span class="ansired"> </span>mat<span class="ansiblue">[</span><span class="ansicyan">1</span><span class="ansiblue">:</span><span class="ansiblue">,</span> <span class="ansicyan">1</span><span class="ansiblue">:</span><span class="ansiblue">]</span> <span class="ansiblue">+</span> mat2<span class="ansiblue"></span>

<span class="ansired">ValueError</span>: operands could not be broadcast together with shapes (2,2) (3,3) </pre>
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<pre>array([0, 3, 6])</pre>
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<pre>array([[  0,   1,   8],
       [ 27,  64, 125],
       [216, 343, 512]])</pre>
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<pre>array([[  0,   4,  14],
       [ 27,  67, 131],
       [216, 346, 518]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">mat2</span><span class="o">.</span><span class="n">T</span>
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<pre>array([[  0,  27, 216],
       [  1,  64, 343],
       [  8, 125, 512]])</pre>
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<pre>array([0, 3, 6])</pre>
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<pre>(3, 3)</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">mat3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">)])</span>
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<pre>array([[0, 1, 2],
       [0, 1, 2]])</pre>
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<pre>(2, 3)</pre>
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<pre>[1, 4, 7]</pre>
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<pre>False</pre>
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<pre>array([1, 4, 7])</pre>
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<pre>array([False,  True, False], dtype=bool)</pre>
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<pre>4</pre>
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<pre>array([1, 4])</pre>
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<pre>array([4])</pre>
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<pre>array([False,  True, False], dtype=bool)</pre>
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<pre>array([False,  True,  True], dtype=bool)</pre>
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<pre>array([4, 7])</pre>
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<div class=" highlight hl-ipython"><pre><span class="c">#1: create 4x4 identity matrix, and set the 2nd row to be all 10s</span>
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<div class=" highlight hl-ipython"><pre><span class="n">ex_one</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
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<pre>array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  1.]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">ex_one</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span><span class="o">.</span><span class="n">shape</span>
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<pre>(4,)</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">ex_one</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">ex_one</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
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<pre>array([[  1.,   0.,   0.,   0.],
       [ 10.,  10.,  10.,  10.],
       [  0.,   0.,   1.,   0.],
       [  0.,   0.,   0.,   1.]])</pre>
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<pre>array([[  1.,   0.,   0.,   0.],
       [ 10.,  10.,  10.,  10.],
       [  0.,   0.,   1.,   0.],
       [  0.,   0.,   0.,   1.]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">m2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
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<pre>array([[-0.99288657,  2.29884659,  1.23340896],
       [ 1.20568734,  0.58893783, -1.19805267],
       [ 0.01238457, -0.89575218, -0.32703349],
       [-1.33648817, -1.41533797, -0.78696767],
       [-0.311132  , -1.35272218,  0.29392369],
       [-1.02919624, -0.01262656,  0.11126516]])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">m2</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="n">ddof</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
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<pre>array([ 0.93596566,  1.42572445,  0.86093872])</pre>
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<div class=" highlight hl-ipython"><pre><span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">mat</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">mat</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="n">ddof</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
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<span class="n">mat</span>
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<pre>array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])</pre>
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<span class="n">means</span>
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<pre>array([ 3.,  4.,  5.])</pre>
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<div class=" highlight hl-ipython"><pre><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">se</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="o">/</span> <span class="p">(</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
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<pre>array([ 9.,  9.,  9.])</pre>
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