Added exercices and the disrt 5 stars
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Nicolas Rougier
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README.html
58
README.html
@ -664,6 +664,32 @@ combinations of every item) (★★★☆☆)</p>
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<span class="keyword">print</span> <span class="punctuation">(</span><span class="name">cartesian</span><span class="punctuation">(([</span><span class="literal number integer">1</span><span class="punctuation">,</span> <span class="literal number integer">2</span><span class="punctuation">,</span> <span class="literal number integer">3</span><span class="punctuation">],</span> <span class="punctuation">[</span><span class="literal number integer">4</span><span class="punctuation">,</span> <span class="literal number integer">5</span><span class="punctuation">],</span> <span class="punctuation">[</span><span class="literal number integer">6</span><span class="punctuation">,</span> <span class="literal number integer">7</span><span class="punctuation">])))</span>
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</pre>
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</li>
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<li><p class="first">How to create a record array from a regular array ? (★★★☆☆)</p>
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<pre class="code python literal-block">
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<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">array</span><span class="punctuation">([(</span><span class="literal string">"Hello"</span><span class="punctuation">,</span> <span class="literal number float">2.5</span><span class="punctuation">,</span> <span class="literal number integer">3</span><span class="punctuation">),</span>
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<span class="punctuation">(</span><span class="literal string">"World"</span><span class="punctuation">,</span> <span class="literal number float">3.6</span><span class="punctuation">,</span> <span class="literal number integer">2</span><span class="punctuation">)])</span>
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<span class="name">R</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">core</span><span class="operator">.</span><span class="name">records</span><span class="operator">.</span><span class="name">fromarrays</span><span class="punctuation">(</span><span class="name">Z</span><span class="operator">.</span><span class="name">T</span><span class="punctuation">,</span>
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<span class="name">names</span><span class="operator">=</span><span class="literal string">'col1, col2, col3'</span><span class="punctuation">,</span>
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<span class="name">formats</span> <span class="operator">=</span> <span class="literal string">'S8, f8, i8'</span><span class="punctuation">)</span>
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</pre>
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</li>
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<li><p class="first">Comsider a large vector Z, compute Z to the power of 3 using 3 different
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methods (★★★☆☆)</p>
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<pre class="code python literal-block">
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<span class="name">Author</span><span class="punctuation">:</span> <span class="name">Ryan</span> <span class="name">G</span><span class="operator">.</span>
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<span class="name">x</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">rand</span><span class="punctuation">(</span><span class="literal number float">5e7</span><span class="punctuation">)</span>
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<span class="operator">%</span><span class="name">timeit</span> <span class="name">np</span><span class="operator">.</span><span class="name">power</span><span class="punctuation">(</span><span class="name">x</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">)</span>
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<span class="literal number integer">1</span> <span class="name">loops</span><span class="punctuation">,</span> <span class="name">best</span> <span class="name">of</span> <span class="literal number integer">3</span><span class="punctuation">:</span> <span class="literal number integer">574</span> <span class="name">ms</span> <span class="name">per</span> <span class="name">loop</span>
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<span class="operator">%</span><span class="name">timeit</span> <span class="name">x</span><span class="operator">*</span><span class="name">x</span><span class="operator">*</span><span class="name">x</span>
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<span class="literal number integer">1</span> <span class="name">loops</span><span class="punctuation">,</span> <span class="name">best</span> <span class="name">of</span> <span class="literal number integer">3</span><span class="punctuation">:</span> <span class="literal number integer">429</span> <span class="name">ms</span> <span class="name">per</span> <span class="name">loop</span>
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<span class="operator">%</span><span class="name">timeit</span> <span class="name">np</span><span class="operator">.</span><span class="name">einsum</span><span class="punctuation">(</span><span class="literal string">'i,i,i->i'</span><span class="punctuation">,</span><span class="name">x</span><span class="punctuation">,</span><span class="name">x</span><span class="punctuation">,</span><span class="name">x</span><span class="punctuation">)</span>
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<span class="literal number integer">1</span> <span class="name">loops</span><span class="punctuation">,</span> <span class="name">best</span> <span class="name">of</span> <span class="literal number integer">3</span><span class="punctuation">:</span> <span class="literal number integer">244</span> <span class="name">ms</span> <span class="name">per</span> <span class="name">loop</span>
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</pre>
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</li>
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<li><p class="first">Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A
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that contain elements of each row of B regardless of the order of the elements
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in B ? (★★★★☆)</p>
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@ -703,7 +729,7 @@ in B ? (★★★★☆)</p>
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<span class="keyword">print</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">unpackbits</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">[:,</span> <span class="name">np</span><span class="operator">.</span><span class="name">newaxis</span><span class="punctuation">],</span> <span class="name">axis</span><span class="operator">=</span><span class="literal number integer">1</span><span class="punctuation">))</span>
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</pre>
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</li>
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<li><p class="first">Given a two dimensional array, how to extract unique rows ? (★★★★☆)</p>
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<li><p class="first">Given a two dimensional array, how to extract unique rows ? (★★★★☆)</p>
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<div class="note">
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<p class="first admonition-title">Note</p>
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<p class="last">See <a class="reference external" href="http://stackoverflow.com/questions/16970982/find-unique-rows-in-numpy-array/">stackoverflow</a> for explanations.</p>
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@ -718,6 +744,36 @@ in B ? (★★★★☆)</p>
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<span class="keyword">print</span><span class="punctuation">(</span><span class="name">uZ</span><span class="punctuation">)</span>
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</pre>
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</li>
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<li><p class="first">Considering 2 vectors A & B, write the einsum equivalent of inner, outer,
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sum, and mul function (★★★★☆)</p>
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<pre class="code python literal-block">
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<span class="comment"># Author: Alex Riley</span>
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<span class="comment"># Make sure to read: http://ajcr.net/Basic-guide-to-einsum/</span>
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<span class="name">np</span><span class="operator">.</span><span class="name">einsum</span><span class="punctuation">(</span><span class="literal string">'i->'</span><span class="punctuation">,</span> <span class="name">A</span><span class="punctuation">)</span> <span class="comment"># np.sum(A)</span>
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<span class="name">np</span><span class="operator">.</span><span class="name">einsum</span><span class="punctuation">(</span><span class="literal string">'i,i->i'</span><span class="punctuation">,</span> <span class="name">A</span><span class="punctuation">,</span> <span class="name">B</span><span class="punctuation">)</span> <span class="comment"># A * B</span>
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<span class="name">np</span><span class="operator">.</span><span class="name">einsum</span><span class="punctuation">(</span><span class="literal string">'i,i'</span><span class="punctuation">,</span> <span class="name">A</span><span class="punctuation">,</span> <span class="name">B</span><span class="punctuation">)</span> <span class="comment"># np.inner(A, B)</span>
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<span class="name">np</span><span class="operator">.</span><span class="name">einsum</span><span class="punctuation">(</span><span class="literal string">'i,j'</span><span class="punctuation">,</span> <span class="name">A</span><span class="punctuation">,</span> <span class="name">B</span><span class="punctuation">)</span> <span class="comment"># np.outer(A, B)</span>
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</pre>
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</li>
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<li><p class="first">Considering a path described by two vectors (X,Y), how to sample it using
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equidistant samples (★★★★★) ?</p>
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<pre class="code python literal-block">
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<span class="comment"># Author: Bas Swinckels</span>
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<span class="name">phi</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span> <span class="literal number integer">10</span><span class="operator">*</span><span class="name">np</span><span class="operator">.</span><span class="name">pi</span><span class="punctuation">,</span> <span class="literal number float">0.1</span><span class="punctuation">)</span>
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<span class="name">a</span> <span class="operator">=</span> <span class="literal number integer">1</span>
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<span class="name">x</span> <span class="operator">=</span> <span class="name">a</span><span class="operator">*</span><span class="name">phi</span><span class="operator">*</span><span class="name">np</span><span class="operator">.</span><span class="name">cos</span><span class="punctuation">(</span><span class="name">phi</span><span class="punctuation">)</span>
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<span class="name">y</span> <span class="operator">=</span> <span class="name">a</span><span class="operator">*</span><span class="name">phi</span><span class="operator">*</span><span class="name">np</span><span class="operator">.</span><span class="name">sin</span><span class="punctuation">(</span><span class="name">phi</span><span class="punctuation">)</span>
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<span class="name">dr</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">diff</span><span class="punctuation">(</span><span class="name">x</span><span class="punctuation">)</span><span class="operator">**</span><span class="literal number integer">2</span> <span class="operator">+</span> <span class="name">np</span><span class="operator">.</span><span class="name">diff</span><span class="punctuation">(</span><span class="name">y</span><span class="punctuation">)</span><span class="operator">**</span><span class="literal number integer">2</span><span class="punctuation">)</span><span class="operator">**.</span><span class="literal number integer">5</span> <span class="comment"># segment lengths</span>
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<span class="name">r</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros_like</span><span class="punctuation">(</span><span class="name">x</span><span class="punctuation">)</span>
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<span class="name">r</span><span class="punctuation">[</span><span class="literal number integer">1</span><span class="punctuation">:]</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">cumsum</span><span class="punctuation">(</span><span class="name">dr</span><span class="punctuation">)</span> <span class="comment"># integrate path</span>
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<span class="name">r_int</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span> <span class="name">r</span><span class="operator">.</span><span class="name">max</span><span class="punctuation">(),</span> <span class="literal number integer">200</span><span class="punctuation">)</span> <span class="comment"># regular spaced path</span>
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<span class="name">x_int</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">interp</span><span class="punctuation">(</span><span class="name">r_int</span><span class="punctuation">,</span> <span class="name">r</span><span class="punctuation">,</span> <span class="name">x</span><span class="punctuation">)</span> <span class="comment"># integrate path</span>
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<span class="name">y_int</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">interp</span><span class="punctuation">(</span><span class="name">r_int</span><span class="punctuation">,</span> <span class="name">r</span><span class="punctuation">,</span> <span class="name">y</span><span class="punctuation">)</span>
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</pre>
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</li>
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</ol>
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</div>
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</body>
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67
README.rst
67
README.rst
@ -780,7 +780,36 @@ Thanks to Michiaki Ariga, there is now a
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print (cartesian(([1, 2, 3], [4, 5], [6, 7])))
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#. How to create a record array from a regular array ? (★★★☆☆)
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.. code-block:: python
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Z = np.array([("Hello", 2.5, 3),
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("World", 3.6, 2)])
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R = np.core.records.fromarrays(Z.T,
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names='col1, col2, col3',
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formats = 'S8, f8, i8')
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#. Comsider a large vector Z, compute Z to the power of 3 using 3 different
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methods (★★★☆☆)
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.. code-block:: python
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Author: Ryan G.
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x = np.random.rand(5e7)
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%timeit np.power(x,3)
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1 loops, best of 3: 574 ms per loop
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%timeit x*x*x
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1 loops, best of 3: 429 ms per loop
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%timeit np.einsum('i,i,i->i',x,x,x)
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1 loops, best of 3: 244 ms per loop
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#. Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A
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that contain elements of each row of B regardless of the order of the elements
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in B ? (★★★★☆)
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@ -826,7 +855,7 @@ Thanks to Michiaki Ariga, there is now a
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print(np.unpackbits(I[:, np.newaxis], axis=1))
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#. Given a two dimensional array, how to extract unique rows ? (★★★★☆)
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#. Given a two dimensional array, how to extract unique rows ? (★★★★☆)
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.. note:: See `stackoverflow <http://stackoverflow.com/questions/16970982/find-unique-rows-in-numpy-array/>`_ for explanations.
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@ -839,3 +868,37 @@ Thanks to Michiaki Ariga, there is now a
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_, idx = np.unique(T, return_index=True)
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uZ = Z[idx]
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print(uZ)
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#. Considering 2 vectors A & B, write the einsum equivalent of inner, outer,
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sum, and mul function (★★★★☆)
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.. code-block:: python
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# Author: Alex Riley
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# Make sure to read: http://ajcr.net/Basic-guide-to-einsum/
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np.einsum('i->', A) # np.sum(A)
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np.einsum('i,i->i', A, B) # A * B
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np.einsum('i,i', A, B) # np.inner(A, B)
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np.einsum('i,j', A, B) # np.outer(A, B)
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#. Considering a path described by two vectors (X,Y), how to sample it using
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equidistant samples (★★★★★) ?
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.. code-block:: python
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# Author: Bas Swinckels
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phi = np.arange(0, 10*np.pi, 0.1)
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a = 1
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x = a*phi*np.cos(phi)
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y = a*phi*np.sin(phi)
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dr = (np.diff(x)**2 + np.diff(y)**2)**.5 # segment lengths
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r = np.zeros_like(x)
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r[1:] = np.cumsum(dr) # integrate path
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r_int = np.linspace(0, r.max(), 200) # regular spaced path
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x_int = np.interp(r_int, r, x) # integrate path
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y_int = np.interp(r_int, r, y)
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