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Closure, NumPy
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‎README.md‎

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@@ -840,7 +840,7 @@ import <package>.<module> # Imports a built-in or '<package>/<module>.py'.
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Closure
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-------
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**We have/get a closure in Python when a nested function references a value of its enclosing function and then the enclosing function returns the nested function.**
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**We have/get a closure in Python when a nested function references a value of its enclosing function and then the enclosing function returns its nested function.**
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```python
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def get_multiplier(a):
@@ -2717,50 +2717,49 @@ import numpy as np
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### Broadcasting
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**A set of rules by which NumPy functions operate on arrays of different shapes.**
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```python
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left = [ 0.1 , 0.6 , 0.8 ] # Shape: (3,)
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right = [[0.1], [0.6], [0.8]] # Shape: (3, 1)
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left = np.array([ 0.1, 0.6, 0.8 ]) # `left.shape == (3,)`
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right = np.array([[0.1],[0.6],[0.8]]) # `right.shape == (3, 1)`
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```
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#### 1. If array shapes differ in length, left-pad the shorter shape with ones:
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```python
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left = [[0.1 , 0.6 , 0.8]] # Shape: (1, 3) <- !
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right = [[0.1], [0.6], [0.8]] # Shape: (3, 1)
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left = np.array([[0.1, 0.6, 0.8]]) # `left.shape == (1, 3)`
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right = np.array([[0.1],[0.6],[0.8]]) # `right.shape == (3, 1)`
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```
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#### 2. If any dimensions differ in size, expand the ones that have size 1 by duplicating their elements:
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```python
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left = [[0.1, 0.6, 0.8], # Shape: (3, 3) <- !
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[0.1, 0.6, 0.8],
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[0.1, 0.6, 0.8]]
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```
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left = np.array([[0.1, 0.6, 0.8], # `left.shape == (3, 3)`
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[0.1, 0.6, 0.8],
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[0.1, 0.6, 0.8]])
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```python
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right = [[0.1, 0.1, 0.1], # Shape: (3, 3) <- !
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[0.6, 0.6, 0.6],
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[0.8, 0.8, 0.8]]
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right = np.array([[0.1, 0.1, 0.1], # `right.shape == (3, 3)`
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[0.6, 0.6, 0.6],
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[0.8, 0.8, 0.8]])
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```
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### Example
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#### For each point returns index of its nearest point (`[0.1, 0.6, 0.8] => [1, 2, 1]`):
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```python
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>>> points = np.array([0.1, 0.6, 0.8])
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[ 0.1, 0.6, 0.8 ]
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>>> wrapped_points = points.reshape(3, 1)
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[[0.1], [0.6], [0.8]]
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>>> deltas = points - wrapped_points
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[[ 0. , 0.5, 0.7],
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[-0.5, 0. , 0.2],
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[-0.7, -0.2, 0. ]]
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>>> distances = np.abs(deltas)
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>>> distances[range(3), range(3)] = np.inf
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[[ inf, 0.5, 0.7],
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[ 0.5, inf, 0.2],
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[ 0.7, 0.2, inf]]
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>>> distances.argmin(1)
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[1, 2, 1]
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>>> print(points := np.array([0.1, 0.6, 0.8]))
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[0.1 0.6 0.8]
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>>> print(wrapped_points := points.reshape(3, 1))
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[[0.1]
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[0.6]
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[0.8]]
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>>> print(deltas := points - wrapped_points)
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[[ 0. 0.5 0.7]
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[-0.5 0. 0.2]
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[-0.7 -0.2 0. ]]
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>>> deltas[range(3), range(3)] = np.inf
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>>> print(distances := np.abs(deltas))
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[[inf 0.5 0.7]
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[0.5 inf 0.2]
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[0.7 0.2 inf]]
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>>> print(distances.argmin(axis=1))
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[1 2 1]
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```
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‎index.html‎

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<body>
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<header>
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<aside>December 14, 2024</aside>
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<aside>December 16, 2024</aside>
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<a href="https://gto76.github.io" rel="author">Jure Šorn</a>
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</header>
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@@ -701,7 +701,7 @@
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<li><strong>Directory of the file that is passed to python command serves as a root of local imports.</strong></li>
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<li><strong>For relative imports use <code class="python hljs"><span class="hljs-string">'from .[…][&lt;pkg/module&gt;[.…]] import &lt;obj&gt;'</span></code>.</strong></li>
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</ul>
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<div><h2 id="closure"><a href="#closure" name="closure">#</a>Closure</h2><p><strong>We have/get a closure in Python when a nested function references a value of its enclosing function and then the enclosing function returns the nested function.</strong></p><pre><code class="python language-python hljs"><span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">get_multiplier</span><span class="hljs-params">(a)</span>:</span>
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<div><h2 id="closure"><a href="#closure" name="closure">#</a>Closure</h2><p><strong>We have/get a closure in Python when a nested function references a value of its enclosing function and then the enclosing function returns its nested function.</strong></p><pre><code class="python language-python hljs"><span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">get_multiplier</span><span class="hljs-params">(a)</span>:</span>
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<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">out</span><span class="hljs-params">(b)</span>:</span>
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<span class="hljs-keyword">return</span> a * b
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<span class="hljs-keyword">return</span> out
@@ -2216,39 +2216,41 @@ <h3 id="format-2">Format</h3><div><h4 id="forstandardtypesizesandmanualalignment
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<li><strong><code class="python hljs"><span class="hljs-string">'ix_([1, 2], [3, 4])'</span></code> returns <code class="python hljs"><span class="hljs-string">'[[1], [2]]'</span></code> and <code class="python hljs"><span class="hljs-string">'[[3, 4]]'</span></code>. Due to broadcasting rules, this is the same as using <code class="python hljs"><span class="hljs-string">'[[1, 1], [2, 2]]'</span></code> and <code class="python hljs"><span class="hljs-string">'[[3, 4], [3, 4]]'</span></code>.</strong></li>
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<li><strong>Any value that is broadcastable to the indexed shape can be assigned to the selection.</strong></li>
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</ul>
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<div><h3 id="broadcasting">Broadcasting</h3><p><strong>A set of rules by which NumPy functions operate on arrays of different shapes.</strong></p><pre><code class="python language-python hljs">left = [ <span class="hljs-number">0.1</span> , <span class="hljs-number">0.6</span> , <span class="hljs-number">0.8</span> ] <span class="hljs-comment"># Shape: (3,)</span>
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right = [[<span class="hljs-number">0.1</span>], [<span class="hljs-number">0.6</span>], [<span class="hljs-number">0.8</span>]] <span class="hljs-comment"># Shape: (3, 1)</span>
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<div><h3 id="broadcasting">Broadcasting</h3><p><strong>A set of rules by which NumPy functions operate on arrays of different shapes.</strong></p><pre><code class="python language-python hljs">left = np.array([ <span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span> ]) <span class="hljs-comment"># `left.shape == (3,)`</span>
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right = np.array([[<span class="hljs-number">0.1</span>],[<span class="hljs-number">0.6</span>],[<span class="hljs-number">0.8</span>]]) <span class="hljs-comment"># `right.shape == (3, 1)`</span>
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</code></pre></div>
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<div><h4 id="1ifarrayshapesdifferinlengthleftpadtheshortershapewithones">1. If array shapes differ in length, left-pad the shorter shape with ones:</h4><pre><code class="python language-python hljs">left = [[<span class="hljs-number">0.1</span> , <span class="hljs-number">0.6</span> , <span class="hljs-number">0.8</span>]] <span class="hljs-comment"># Shape: (1, 3) &lt;- !</span>
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right = [[<span class="hljs-number">0.1</span>], [<span class="hljs-number">0.6</span>], [<span class="hljs-number">0.8</span>]] <span class="hljs-comment"># Shape: (3, 1)</span>
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<div><h4 id="1ifarrayshapesdifferinlengthleftpadtheshortershapewithones">1. If array shapes differ in length, left-pad the shorter shape with ones:</h4><pre><code class="python language-python hljs">left = np.array([[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>]]) <span class="hljs-comment"># `left.shape == (1, 3)`</span>
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right = np.array([[<span class="hljs-number">0.1</span>],[<span class="hljs-number">0.6</span>],[<span class="hljs-number">0.8</span>]]) <span class="hljs-comment"># `right.shape == (3, 1)`</span>
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</code></pre></div>
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<div><h4 id="2ifanydimensionsdifferinsizeexpandtheonesthathavesize1byduplicatingtheirelements">2. If any dimensions differ in size, expand the ones that have size 1 by duplicating their elements:</h4><pre><code class="python language-python hljs">left = [[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>], <span class="hljs-comment"># Shape: (3, 3) &lt;- !</span>
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[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>],
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[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>]]
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<div><h4 id="2ifanydimensionsdifferinsizeexpandtheonesthathavesize1byduplicatingtheirelements">2. If any dimensions differ in size, expand the ones that have size 1 by duplicating their elements:</h4><pre><code class="python language-python hljs">left = np.array([[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>], <span class="hljs-comment"># `left.shape == (3, 3)`</span>
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[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>],
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[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>]])
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right = np.array([[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.1</span>, <span class="hljs-number">0.1</span>], <span class="hljs-comment"># `right.shape == (3, 3)`</span>
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[<span class="hljs-number">0.6</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.6</span>],
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[<span class="hljs-number">0.8</span>, <span class="hljs-number">0.8</span>, <span class="hljs-number">0.8</span>]])
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</code></pre></div>
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<pre><code class="python language-python hljs">right = [[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.1</span>, <span class="hljs-number">0.1</span>], <span class="hljs-comment"># Shape: (3, 3) &lt;- !</span>
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[<span class="hljs-number">0.6</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.6</span>],
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[<span class="hljs-number">0.8</span>, <span class="hljs-number">0.8</span>, <span class="hljs-number">0.8</span>]]
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</code></pre>
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<div><h3 id="example-3">Example</h3><div><h4 id="foreachpointreturnsindexofitsnearestpoint010608121">For each point returns index of its nearest point (<code class="python hljs">[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>] =&gt; [<span class="hljs-number">1</span>, <span class="hljs-number">2</span>, <span class="hljs-number">1</span>]</code>):</h4><pre><code class="python language-python hljs"><span class="hljs-meta">&gt;&gt;&gt; </span>points = np.array([<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>])
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[ <span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span> ]
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<span class="hljs-meta">&gt;&gt;&gt; </span>wrapped_points = points.reshape(<span class="hljs-number">3</span>, <span class="hljs-number">1</span>)
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[[<span class="hljs-number">0.1</span>], [<span class="hljs-number">0.6</span>], [<span class="hljs-number">0.8</span>]]
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<span class="hljs-meta">&gt;&gt;&gt; </span>deltas = points - wrapped_points
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[[ <span class="hljs-number">0.</span> , <span class="hljs-number">0.5</span>, <span class="hljs-number">0.7</span>],
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[<span class="hljs-number">-0.5</span>, <span class="hljs-number">0.</span> , <span class="hljs-number">0.2</span>],
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[<span class="hljs-number">-0.7</span>, <span class="hljs-number">-0.2</span>, <span class="hljs-number">0.</span> ]]
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<span class="hljs-meta">&gt;&gt;&gt; </span>distances = np.abs(deltas)
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<span class="hljs-meta">&gt;&gt;&gt; </span>distances[range(<span class="hljs-number">3</span>), range(<span class="hljs-number">3</span>)] = np.inf
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[[ inf, <span class="hljs-number">0.5</span>, <span class="hljs-number">0.7</span>],
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[ <span class="hljs-number">0.5</span>, inf, <span class="hljs-number">0.2</span>],
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[ <span class="hljs-number">0.7</span>, <span class="hljs-number">0.2</span>, inf]]
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<span class="hljs-meta">&gt;&gt;&gt; </span>distances.argmin(<span class="hljs-number">1</span>)
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[<span class="hljs-number">1</span>, <span class="hljs-number">2</span>, <span class="hljs-number">1</span>]
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<div><h3 id="example-3">Example</h3><div><h4 id="foreachpointreturnsindexofitsnearestpoint010608121">For each point returns index of its nearest point (<code class="python hljs">[<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>] =&gt; [<span class="hljs-number">1</span>, <span class="hljs-number">2</span>, <span class="hljs-number">1</span>]</code>):</h4><pre><code class="python language-python hljs"><span class="hljs-meta">&gt;&gt;&gt; </span>print(points := np.array([<span class="hljs-number">0.1</span>, <span class="hljs-number">0.6</span>, <span class="hljs-number">0.8</span>]))
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[<span class="hljs-number">0.1</span> <span class="hljs-number">0.6</span> <span class="hljs-number">0.8</span>]
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<span class="hljs-meta">&gt;&gt;&gt; </span>print(wrapped_points := points.reshape(<span class="hljs-number">3</span>, <span class="hljs-number">1</span>))
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[[<span class="hljs-number">0.1</span>]
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[<span class="hljs-number">0.6</span>]
2242+
[<span class="hljs-number">0.8</span>]]
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<span class="hljs-meta">&gt;&gt;&gt; </span>print(deltas := points - wrapped_points)
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[[ <span class="hljs-number">0.</span> <span class="hljs-number">0.5</span> <span class="hljs-number">0.7</span>]
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[<span class="hljs-number">-0.5</span> <span class="hljs-number">0.</span> <span class="hljs-number">0.2</span>]
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[<span class="hljs-number">-0.7</span> <span class="hljs-number">-0.2</span> <span class="hljs-number">0.</span> ]]
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<span class="hljs-meta">&gt;&gt;&gt; </span>deltas[range(<span class="hljs-number">3</span>), range(<span class="hljs-number">3</span>)] = np.inf
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<span class="hljs-meta">&gt;&gt;&gt; </span>print(distances := np.abs(deltas))
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[[inf <span class="hljs-number">0.5</span> <span class="hljs-number">0.7</span>]
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[<span class="hljs-number">0.5</span> inf <span class="hljs-number">0.2</span>]
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[<span class="hljs-number">0.7</span> <span class="hljs-number">0.2</span> inf]]
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<span class="hljs-meta">&gt;&gt;&gt; </span>print(distances.argmin(axis=<span class="hljs-number">1</span>))
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[<span class="hljs-number">1</span> <span class="hljs-number">2</span> <span class="hljs-number">1</span>]
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</code></pre></div></div>
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<footer>
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<aside>December 14, 2024</aside>
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<aside>December 16, 2024</aside>
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<a href="https://gto76.github.io" rel="author">Jure Šorn</a>
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</footer>
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