mhjensen
325 lines
20 KiB
HTML
325 lines
20 KiB
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'sections': [('Overview of first week', 2, None, '___sec0'),
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('Lectures and ComputerLab', 2, None, '___sec2'),
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('Matrices in Python', 2, None, '___sec26'),
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('Meet the Pandas', 2, None, '___sec27'),
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('Friday August 21', 2, None, '___sec28'),
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('Reading Data and fitting', 2, None, '___sec29'),
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<a class="navbar-brand" href="week34-bs.html">Week 34: Introduction to the course, Logistics and Practicalities</a>
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<!-- navigation toc: --> <li><a href="._week34-bs001.html#___sec0" style="font-size: 80%;"><b>Overview of first week</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs002.html#___sec1" style="font-size: 80%;"><b>Thursday August 20</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs003.html#___sec2" style="font-size: 80%;"><b>Lectures and ComputerLab</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs007.html#___sec6" style="font-size: 80%;"><b>Recommended textbooks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs008.html#___sec7" style="font-size: 80%;"><b>Prerequisites</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs009.html#___sec8" style="font-size: 80%;"><b>Learning outcomes</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs010.html#___sec9" style="font-size: 80%;"><b>Topics covered in this course: Statistical analysis and optimization of data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs011.html#___sec10" style="font-size: 80%;"><b>Topics covered in this course: Machine Learning</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs012.html#___sec11" style="font-size: 80%;"><b>Extremely useful tools, strongly recommended</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs013.html#___sec12" style="font-size: 80%;"><b>Other courses on Data science and Machine Learning at UiO</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs014.html#___sec13" style="font-size: 80%;"><b>Introduction</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs015.html#___sec14" style="font-size: 80%;"><b>What is Machine Learning?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs016.html#___sec15" style="font-size: 80%;"><b>Types of Machine Learning</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs017.html#___sec16" style="font-size: 80%;"><b>Software and needed installations</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs018.html#___sec17" style="font-size: 80%;"><b>Python installers</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs019.html#___sec18" style="font-size: 80%;"><b>Useful Python libraries</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs020.html#___sec19" style="font-size: 80%;"><b>Installing R, C++, cython or Julia</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs021.html#___sec20" style="font-size: 80%;"><b>Installing R, C++, cython, Numba etc</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs022.html#___sec21" style="font-size: 80%;"><b>Numpy examples and Important Matrix and vector handling packages</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs023.html#___sec22" style="font-size: 80%;"><b>Basic Matrix Features</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs024.html#___sec23" style="font-size: 80%;"> Some famous Matrices</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs025.html#___sec24" style="font-size: 80%;"> More Basic Matrix Features</a></li>
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<!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;"><b>Numpy and arrays</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs027.html#___sec26" style="font-size: 80%;"><b>Matrices in Python</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs028.html#___sec27" style="font-size: 80%;"><b>Meet the Pandas</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs029.html#___sec28" style="font-size: 80%;"><b>Friday August 21</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs030.html#___sec29" style="font-size: 80%;"><b>Reading Data and fitting</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs031.html#___sec30" style="font-size: 80%;"><b>Friday August 21</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec31" style="font-size: 80%;"> Simple linear regression model using <b>scikit-learn</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec32" style="font-size: 80%;"> To our real data: nuclear binding energies. Brief reminder on masses and binding energies</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec33" style="font-size: 80%;"> Organizing our data</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec34" style="font-size: 80%;"> Seeing the wood for the trees</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec35" style="font-size: 80%;"> And what about using neural networks?</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec36" style="font-size: 80%;"><b>A first summary</b></a></li>
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<a name="part0026"></a>
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<!-- !split -->
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<h2 id="___sec25" class="anchor">Numpy and arrays </h2>
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<a href="http://www.numpy.org/" target="_self">Numpy</a> provides an easy way to handle arrays in Python. The standard way to import this library is as
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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</pre></div>
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<p>
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Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution,
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>n <span style="color: #666666">=</span> <span style="color: #666666">10</span>
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x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>normal(size<span style="color: #666666">=</span>n)
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<span style="color: #008000; font-weight: bold">print</span>(x)
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</pre></div>
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<p>
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We defined a vector \( x \) with \( n=10 \) elements with its values given by the Normal distribution \( N(0,1) \).
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Another alternative is to declare a vector as follows
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1</span>, <span style="color: #666666">2</span>, <span style="color: #666666">3</span>])
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<span style="color: #008000; font-weight: bold">print</span>(x)
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</pre></div>
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<p>
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Here we have defined a vector with three elements, with \( x_0=1 \), \( x_1=2 \) and \( x_2=3 \). Note that both Python and C++
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start numbering array elements from \( 0 \) and on. This means that a vector with \( n \) elements has a sequence of entities \( x_0, x_1, x_2, \dots, x_{n-1} \). We could also let (recommended) Numpy to compute the logarithms of a specific array as
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>log(np<span style="color: #666666">.</span>array([<span style="color: #666666">4</span>, <span style="color: #666666">7</span>, <span style="color: #666666">8</span>]))
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<span style="color: #008000; font-weight: bold">print</span>(x)
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</pre></div>
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<p>
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In the last example we used Numpy's unary function \( np.log \). This function is
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highly tuned to compute array elements since the code is vectorized
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and does not require looping. We normaly recommend that you use the
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Numpy intrinsic functions instead of the corresponding <b>log</b> function
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from Python's <b>math</b> module. The looping is done explicitely by the
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<b>np.log</b> function. The alternative, and slower way to compute the
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logarithms of a vector would be to write
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">math</span> <span style="color: #008000; font-weight: bold">import</span> log
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x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">4</span>, <span style="color: #666666">7</span>, <span style="color: #666666">8</span>])
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<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">0</span>, <span style="color: #008000">len</span>(x)):
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x[i] <span style="color: #666666">=</span> log(x[i])
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<span style="color: #008000; font-weight: bold">print</span>(x)
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</pre></div>
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<p>
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We note that our code is much longer already and we need to import the <b>log</b> function from the <b>math</b> module.
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The attentive reader will also notice that the output is \( [1, 1, 2] \). Python interprets automagically our numbers as integers (like the <b>automatic</b> keyword in C++). To change this we could define our array elements to be double precision numbers as
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>log(np<span style="color: #666666">.</span>array([<span style="color: #666666">4</span>, <span style="color: #666666">7</span>, <span style="color: #666666">8</span>], dtype <span style="color: #666666">=</span> np<span style="color: #666666">.</span>float64))
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<span style="color: #008000; font-weight: bold">print</span>(x)
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</pre></div>
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<p>
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or simply write them as double precision numbers (Python uses 64 bits as default for floating point type variables), that is
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>log(np<span style="color: #666666">.</span>array([<span style="color: #666666">4.0</span>, <span style="color: #666666">7.0</span>, <span style="color: #666666">8.0</span>])
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<span style="color: #008000; font-weight: bold">print</span>(x)
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</pre></div>
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<p>
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To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the <b>itemsize</b> functionality (the array \( x \) is actually an object which inherits the functionalities defined in Numpy) as
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>log(np<span style="color: #666666">.</span>array([<span style="color: #666666">4.0</span>, <span style="color: #666666">7.0</span>, <span style="color: #666666">8.0</span>])
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<span style="color: #008000; font-weight: bold">print</span>(x<span style="color: #666666">.</span>itemsize)
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</pre></div>
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<p>
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<p>
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<li><a href="._week34-bs023.html">24</a></li>
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