mhjensen
263 lines
16 KiB
HTML
263 lines
16 KiB
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'sections': [('What is Machine Learning?', 2, None, '___sec0'),
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('Types of Machine Learning', 2, None, '___sec1'),
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('Different algorithms', 2, None, '___sec2'),
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('Software and needed installations', 2, None, '___sec3'),
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('Python installers', 2, None, '___sec4'),
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('Introduction to Jupyter notebook and available tools',
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('Representing data, more examples', 2, None, '___sec8'),
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('Predator-Prey model from ecology', 2, None, '___sec9'),
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('Case study from Hudson bay', 2, None, '___sec10'),
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('Hudson bay data', 2, None, '___sec11'),
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('Plotting the data', 2, None, '___sec12'),
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('Hares and lynx in Hudson bay from 1900 to 1920',
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2,
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None,
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'___sec13'),
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('Why now create a computer model for the hare and lynx '
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'populations?',
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2,
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None,
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'___sec14'),
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('The traditional (top-down) approach', 2, None, '___sec15'),
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('Basic mathematics notation', 2, None, '___sec16'),
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('Basic dynamics of the population of hares',
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2,
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None,
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'___sec17'),
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('Basic dynamics of the population of lynx', 2, None, '___sec18'),
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('Evolution equations', 2, None, '___sec19'),
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('Adapt the model to the Hudson Bay case', 2, None, '___sec20'),
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('The program', 2, None, '___sec21'),
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('The plot', 2, None, '___sec22'),
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('Linear regression in Python', 2, None, '___sec23'),
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('Linear Least squares in R', 2, None, '___sec24'),
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('Non-Linear Least squares in R', 2, None, '___sec25')]}
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs001.html#___sec0" style="font-size: 80%;">What is Machine Learning?</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs002.html#___sec1" style="font-size: 80%;">Types of Machine Learning</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs003.html#___sec2" style="font-size: 80%;">Different algorithms</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs006.html#___sec5" style="font-size: 80%;">Installing R, C++, cython or Julia</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs007.html#___sec6" style="font-size: 80%;">Installing R, C++, cython or Julia</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs008.html#___sec7" style="font-size: 80%;">Introduction to Jupyter notebook and available tools</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs009.html#___sec8" style="font-size: 80%;">Representing data, more examples</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs010.html#___sec9" style="font-size: 80%;">Predator-Prey model from ecology</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs011.html#___sec10" style="font-size: 80%;">Case study from Hudson bay</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs012.html#___sec11" style="font-size: 80%;">Hudson bay data</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs013.html#___sec12" style="font-size: 80%;">Plotting the data</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs014.html#___sec13" style="font-size: 80%;">Hares and lynx in Hudson bay from 1900 to 1920</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs015.html#___sec14" style="font-size: 80%;">Why now create a computer model for the hare and lynx populations?</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs016.html#___sec15" style="font-size: 80%;">The traditional (top-down) approach</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs017.html#___sec16" style="font-size: 80%;">Basic mathematics notation</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs018.html#___sec17" style="font-size: 80%;">Basic dynamics of the population of hares</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs019.html#___sec18" style="font-size: 80%;">Basic dynamics of the population of lynx</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs020.html#___sec19" style="font-size: 80%;">Evolution equations</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs021.html#___sec20" style="font-size: 80%;">Adapt the model to the Hudson Bay case</a></li>
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<!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;">The program</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs023.html#___sec22" style="font-size: 80%;">The plot</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs024.html#___sec23" style="font-size: 80%;">Linear regression in Python</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs025.html#___sec24" style="font-size: 80%;">Linear Least squares in R</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs026.html#___sec25" style="font-size: 80%;">Non-Linear Least squares in R</a></li>
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<h2 id="___sec21" class="anchor">The program </h2>
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<!-- code=python (!bc pypro) 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">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">solver</span>(m, H0, L0, dt, a, b, c, d, t0):
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<span style="color: #BA2121; font-style: italic">"""Solve the difference equations for H and L over m years</span>
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<span style="color: #BA2121; font-style: italic"> with time step dt (measured in years."""</span>
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num_intervals <span style="color: #666666">=</span> <span style="color: #008000">int</span>(m<span style="color: #666666">/</span><span style="color: #008000">float</span>(dt))
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t <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(t0, t0 <span style="color: #666666">+</span> m, num_intervals<span style="color: #666666">+1</span>)
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H <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(t<span style="color: #666666">.</span>size)
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L <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(t<span style="color: #666666">.</span>size)
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'Init:'</span>, H0, L0, dt)
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H[<span style="color: #666666">0</span>] <span style="color: #666666">=</span> H0
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L[<span style="color: #666666">0</span>] <span style="color: #666666">=</span> L0
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<span style="color: #008000; font-weight: bold">for</span> n <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>(t)<span style="color: #666666">-1</span>):
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H[n<span style="color: #666666">+1</span>] <span style="color: #666666">=</span> H[n] <span style="color: #666666">+</span> a<span style="color: #666666">*</span>dt<span style="color: #666666">*</span>H[n] <span style="color: #666666">-</span> b<span style="color: #666666">*</span>dt<span style="color: #666666">*</span>H[n]<span style="color: #666666">*</span>L[n]
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L[n<span style="color: #666666">+1</span>] <span style="color: #666666">=</span> L[n] <span style="color: #666666">+</span> d<span style="color: #666666">*</span>dt<span style="color: #666666">*</span>H[n]<span style="color: #666666">*</span>L[n] <span style="color: #666666">-</span> c<span style="color: #666666">*</span>dt<span style="color: #666666">*</span>L[n]
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<span style="color: #008000; font-weight: bold">return</span> H, L, t
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<span style="color: #408080; font-style: italic"># Load in data file</span>
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data <span style="color: #666666">=</span> np<span style="color: #666666">.</span>loadtxt(<span style="color: #BA2121">'src/Hudson_Bay.csv'</span>, delimiter<span style="color: #666666">=</span><span style="color: #BA2121">','</span>, skiprows<span style="color: #666666">=1</span>)
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<span style="color: #408080; font-style: italic"># Make arrays containing x-axis and hares and lynx populations</span>
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t_e <span style="color: #666666">=</span> data[:,<span style="color: #666666">0</span>]
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H_e <span style="color: #666666">=</span> data[:,<span style="color: #666666">1</span>]
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L_e <span style="color: #666666">=</span> data[:,<span style="color: #666666">2</span>]
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<span style="color: #408080; font-style: italic"># Simulate using the model</span>
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H, L, t <span style="color: #666666">=</span> solver(m<span style="color: #666666">=20</span>, H0<span style="color: #666666">=34.91</span>, L0<span style="color: #666666">=3.857</span>, dt<span style="color: #666666">=0.1</span>,
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a<span style="color: #666666">=0.4807</span>, b<span style="color: #666666">=0.02482</span>, c<span style="color: #666666">=0.9272</span>, d<span style="color: #666666">=0.02756</span>,
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t0<span style="color: #666666">=1900</span>)
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<span style="color: #408080; font-style: italic"># Visualize simulations and data</span>
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plt<span style="color: #666666">.</span>plot(t_e, H_e, <span style="color: #BA2121">'b-+'</span>, t_e, L_e, <span style="color: #BA2121">'r-o'</span>, t, H, <span style="color: #BA2121">'m--'</span>, t, L, <span style="color: #BA2121">'k--'</span>)
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plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'Year'</span>)
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plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'Numbers of hares and lynx'</span>)
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plt<span style="color: #666666">.</span>axis([<span style="color: #666666">1900</span>, <span style="color: #666666">1920</span>, <span style="color: #666666">0</span>, <span style="color: #666666">140</span>])
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plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r'Population of hares and lynx 1900-1920 (x1000)'</span>)
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plt<span style="color: #666666">.</span>legend((<span style="color: #BA2121">'H_e'</span>, <span style="color: #BA2121">'L_e'</span>, <span style="color: #BA2121">'H'</span>, <span style="color: #BA2121">'L'</span>), loc<span style="color: #666666">=</span><span style="color: #BA2121">'upper left'</span>)
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plt<span style="color: #666666">.</span>savefig(<span style="color: #BA2121">'Hudson_Bay_sim.pdf'</span>)
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plt<span style="color: #666666">.</span>savefig(<span style="color: #BA2121">'Hudson_Bay_sim.png'</span>)
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plt<span style="color: #666666">.</span>show()
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</pre></div>
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