Caleb Madrigalhttps://calebmadrigal.com/2021-02-19T16:00:00-06:00Mad Consulting2021-02-19T16:00:00-06:00Caleb Madrigaltag:calebmadrigal.com,2021-02-19:mad-consulting/<p><img src="/images/madconsulting_logo1.png" width="400px"></p>
<p>Got a crazy project you need done? Looking to build an app? Or a robot? Or start to leverage machine learning in your business? My brother and I recently started offering our services at <a href="https://madconsulting.ai">https://madconsulting.ai</a>. Hit us up!</p>Truthy Graph2017-12-24T16:50:00-06:00Caleb Madrigaltag:calebmadrigal.com,2017-12-24:truthy-graph/<p>One time, I was looking at a graph, and the thought occurred to me, "this graph shows where the two sides of this equation are exactly equal, but what if a graph showed also where they were <em>almost</em> the same?", so I wrote a little graphing web app: <strong><a href="https://truthygraph.github.io/">https://truthygraph.github.io/</a></strong>.</p>
<p>I called it "Truthy Graph", since it shows where the 2 sides of the equation are nearly true. I think some interesting shapes show up. Here's a few screenshots:</p>
<p><img alt="sin(3x)" src="/images/truthygraph_sin.png" /></p>
<p>Another cool thing, is that either side of the equation can use the 'y' or 'x' variables in any way (calling functions like <code>sin</code>, can be squared, etc - the equations need not follow the 'y=' formula). Example:</p>
<p><img alt="Elliptic curve" src="/images/truthygraph_elliptic_curve.png" /></p>
<p>I'm aware there are a few bugs (especially when adjusting the "fuzzy level" or the zoom), but I don't care enough to fix them (I'll accept pull requests though).</p>First musical composition2017-05-02T17:55:00-05:00Caleb Madrigaltag:calebmadrigal.com,2017-05-02:first-musical-composition/<p>I decided to try my hand at musical composition. This is my first piece. I call it "We Spin Together".</p>
<p><img alt="We Spin Together" src="/images/we_spin_together_melody.jpg" />
(This is just the melody)</p>
<p>And here's how it sounds:</p>
<iframe width="100%" height="166" scrolling="no" frameborder="no" src="https://w.soundcloud.com/player/?url=https%3A//api.soundcloud.com/tracks/296051481&color=ff5500&auto_play=false&hide_related=false&show_comments=true&show_user=true&show_reposts=false"></iframe>Digital Radio Signal Generation2016-11-19T23:55:00-06:00Caleb Madrigaltag:calebmadrigal.com,2016-11-19:digital-radio-signal-generation/<p>Recently, I was curious if I could generate a digital radio signal from scratch just using math, and use that signal to control this radio-controlled outlet that I have.</p>
<p>Here's the Github source: <a href="https://github.com/calebmadrigal/radio-hacking-scripts/blob/master/radio_signal_generation.ipynb">https://github.com/calebmadrigal/radio-hacking-scripts/blob/master/radio_signal_generation.ipynb</a></p>
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<h1 id="generating-radio-signals">Generating radio signals</h1>
<p>I want to be able to generate modulated digital signals such as this one...</p>
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<img src="http://calebmadrigal.com/images/original_radio_signal.png" alt="original radio signal" /><p class="caption">original radio signal</p>
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<p>This is a binary signal coded with <a href="https://en.wikipedia.org/wiki/On-off_keying">On-off keying</a> (also known as <a href="https://en.wikipedia.org/wiki/Amplitude-shift_keying">Amplitude-shift keying</a>).</p>
<p>I'm taking the long pulses to mean "1" and the short pulses to mean "0", so this signal is transmitting the digital code, "0110100010000000".</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Imports and boilerplate to make graphs look better</span>
<span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="kn">import</span> <span class="nn">wave</span>
<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">Audio</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h2 id="Basic-wave-functions">Basic wave functions<a class="anchor-link" href="#Basic-wave-functions">¶</a></h2>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">SAMPLE_BITSIZE</span> <span class="o">=</span> <span class="mi">16</span>
<span class="n">MAX_AMP_16BIT</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="n">SAMPLE_BITSIZE</span><span class="o">/</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">generate_wave</span><span class="p">(</span><span class="n">freq</span><span class="p">,</span> <span class="n">len_in_sec</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">samp_rate</span><span class="o">=</span><span class="mi">44100</span><span class="p">,</span> <span class="n">amplitude</span><span class="o">=</span><span class="n">MAX_AMP_16BIT</span><span class="p">):</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">len_in_sec</span><span class="p">,</span> <span class="n">samp_rate</span> <span class="o">*</span> <span class="n">len_in_sec</span><span class="p">)</span>
<span class="n">sig</span> <span class="o">=</span> <span class="n">amplitude</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="k">return</span> <span class="n">sig</span>
<span class="k">def</span> <span class="nf">write_wav_file</span><span class="p">(</span><span class="n">file_path</span><span class="p">,</span> <span class="n">wav_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="o">=</span><span class="mi">44100</span><span class="p">,</span> <span class="n">num_channels</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">wave</span><span class="o">.</span><span class="n">open</span><span class="p">(</span><span class="n">file_path</span><span class="p">,</span> <span class="s">'wb'</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">setparams</span><span class="p">((</span><span class="n">num_channels</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">wav_data</span><span class="p">),</span> <span class="s">"NONE"</span><span class="p">,</span> <span class="s">"Uncompressed"</span><span class="p">))</span>
<span class="n">f</span><span class="o">.</span><span class="n">writeframes</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">wav_data</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">))</span>
<span class="n">f</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">write_pcm_file</span><span class="p">(</span><span class="n">signal_data</span><span class="p">,</span> <span class="n">file_path</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">):</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">signal_data</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">dtype</span><span class="p">)</span><span class="o">.</span><span class="n">tofile</span><span class="p">(</span><span class="n">file_path</span><span class="p">)</span>
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<h1 id="amplitude-modulation">Amplitude modulation</h1>
<p>First, we need to figure out how to modulate the amplitude of the carrier wave to "high amplitude" and "low amplitude" to correspond with the binary"s and 0s.</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">samp_rate</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="n">len_in_sec</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">carrier_freq</span> <span class="o">=</span> <span class="mi">20</span>
<span class="n">low_amp</span> <span class="o">=</span> <span class="mf">0.1</span>
<span class="n">high_amp</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">samp_rate</span> <span class="o">*</span> <span class="n">len_in_sec</span><span class="p">)</span>
<span class="n">carrier</span> <span class="o">=</span> <span class="mi">1</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">carrier_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="c"># Modulate with the binary signal: ['0', '1']</span>
<span class="n">amp_mult</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">low_amp</span><span class="p">]</span><span class="o">*</span><span class="mi">500</span> <span class="o">+</span> <span class="p">[</span><span class="n">high_amp</span><span class="p">]</span><span class="o">*</span><span class="mi">500</span><span class="p">)</span>
<span class="n">sig</span> <span class="o">=</span> <span class="n">amp_mult</span> <span class="o">*</span> <span class="n">carrier</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'sig'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'freq'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">sig</span><span class="p">)</span>
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<p>So looking at the above example, let's see how we calculate the size of the multiplier array...</p>
<ul>
<li>The carrier frequency is 20Hz.</li>
<li>The baud, in this case, is 2 bits per second, which is why we need 1 second to contain the 2 bits.</li>
<li>The size of the multiplier wave to modulate the carrier wave is 1000 in size because it must match the number of samples there are (which in this case, 1 second x 1000 samples per second = 1000).</li>
<li>Note the width of each bit (in terms of samples) is samples_per_second / bits_per_second = 1000 / 2 = 500</li>
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<h2 id="write-function-to-modulate-amplitude-according-to-binary-data">Write function to modulate amplitude according to binary data</h2>
<p>To modulate the carrier wave signal, we will simply: * Generate the carrier wave * Generate a "modulation array" - an array with the LOW or HIGH amplitudes for each data point in the carrier wave array * Multiply the "carrier wave array" with the "modulation array", to result in the "modulated signal"</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">SAMPLE_BITSIZE</span> <span class="o">=</span> <span class="mi">16</span>
<span class="n">MAX_AMP_16BIT</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="n">SAMPLE_BITSIZE</span><span class="o">/</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">DEFAULT_RATIOS</span> <span class="o">=</span> <span class="p">{</span>
<span class="s">'_'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
<span class="s">'0'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
<span class="s">'1'</span><span class="p">:</span> <span class="mi">3</span>
<span class="p">}</span>
<span class="n">DEFAULT_AMP_MAP</span> <span class="o">=</span> <span class="p">{</span>
<span class="s">'0'</span><span class="p">:</span> <span class="n">MAX_AMP_16BIT</span> <span class="o">*</span> <span class="o">.</span><span class="mo">02</span><span class="p">,</span>
<span class="s">'1'</span><span class="p">:</span> <span class="n">MAX_AMP_16BIT</span>
<span class="p">}</span>
<span class="k">def</span> <span class="nf">get_modulation_array</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">data_points_in_bit</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sample_rate</span> <span class="o">*</span> <span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">modulation_array</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">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">)</span>
<span class="k">for</span> <span class="n">bit</span> <span class="ow">in</span> <span class="n">binary_data</span><span class="p">:</span>
<span class="n">bit_amplitude</span> <span class="o">=</span> <span class="n">amp_map</span><span class="p">[</span><span class="n">bit</span><span class="p">]</span>
<span class="n">modulated_bit</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">data_points_in_bit</span><span class="p">,</span> <span class="n">bit_amplitude</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">,</span> <span class="n">modulated_bit</span><span class="p">)</span>
<span class="k">return</span> <span class="n">modulation_array</span>
<span class="k">def</span> <span class="nf">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span>
<span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="o">=</span><span class="n">DEFAULT_RATIOS</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">DEFAULT_AMP_MAP</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">signal_len_secs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">binary_data</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">signal_len_secs</span><span class="p">,</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">signal_len_secs</span><span class="p">)</span>
<span class="n">carrier_wave</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">carrier_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">get_modulation_array</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="p">)</span>
<span class="k">return</span> <span class="n">t</span><span class="p">,</span> <span class="n">carrier_wave</span> <span class="o">*</span> <span class="n">modulation_array</span>
<span class="n">binary_data</span> <span class="o">=</span> <span class="s">'0110100010000000'</span>
<span class="n">carrier_wave_freq</span> <span class="o">=</span> <span class="mi">20</span> <span class="c">#315e6</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">baud</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">t</span><span class="p">,</span> <span class="n">sig</span> <span class="o">=</span> <span class="n">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'sig'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'freq'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">sig</span><span class="p">)</span>
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<p>Sweet! So it looks like it roughly worked. But there is a problem: we have no breaks between bits (so a group of 1's looks like a single pulse). Let's fix that...</p>
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<h2 id="add-the-zero-pulse-and-bit-spacing">Add the zero pulse and bit spacing</h2>
<p>There are 2 problems with the above approach: * Zeros should actually have a short pulse rather than LOW amplitude * Bits should be spaced apart from each other</p>
<p>To accomplish this, we'll just rewrite the <code>get_modulation_array()</code> function so that each "modulated bit" will contain both the "1" or "0" pulse AND a "space" (which will simply be the LOW value).</p>
<p>Also, for simplicity/efficienty, we can just calculate the "1" and "0" modulation arrays once and reuse them.</p>
<p>I'm also going to turn up the sample rate a bit to get a more accurate signal.</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">DEFAULT_AMP_MAP</span> <span class="o">=</span> <span class="p">{</span>
<span class="s">'LOW'</span><span class="p">:</span> <span class="n">MAX_AMP_16BIT</span> <span class="o">*</span> <span class="o">.</span><span class="mo">02</span><span class="p">,</span>
<span class="s">'HIGH'</span><span class="p">:</span> <span class="n">MAX_AMP_16BIT</span>
<span class="p">}</span>
<span class="k">def</span> <span class="nf">get_modulation_array</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">data_points_in_bit</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sample_rate</span> <span class="o">*</span> <span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">modulation_array</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">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">)</span>
<span class="c"># To describe this general algorithms, I'll use the specific concrete pulse ratios:</span>
<span class="c"># '_': 1,</span>
<span class="c"># '0': 1,</span>
<span class="c"># '1': 3</span>
<span class="c"># Meaning that a "1" should be 3x longer than a "0" or a "space" pulse. Now since we need a space</span>
<span class="c"># between "1"s (as well as "0"), we can calculate that the pulse for a "1" should be 3/4 of the bit</span>
<span class="c"># and the pulse for a "0" should be 1/4 of the bit (since for the 1, it's 3 parts "1" and 1 part "space")</span>
<span class="n">one_pulse_len</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="n">sig_ratios</span><span class="p">[</span><span class="s">'1'</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">sig_ratios</span><span class="p">[</span><span class="s">'1'</span><span class="p">]</span> <span class="o">+</span> <span class="n">sig_ratios</span><span class="p">[</span><span class="s">'_'</span><span class="p">]))</span> <span class="o">*</span> <span class="n">data_points_in_bit</span><span class="p">)</span>
<span class="n">one_space_len</span> <span class="o">=</span> <span class="n">data_points_in_bit</span> <span class="o">-</span> <span class="n">one_pulse_len</span>
<span class="n">zero_pulse_len</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="n">sig_ratios</span><span class="p">[</span><span class="s">'0'</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">sig_ratios</span><span class="p">[</span><span class="s">'1'</span><span class="p">]</span> <span class="o">+</span> <span class="n">sig_ratios</span><span class="p">[</span><span class="s">'_'</span><span class="p">]))</span> <span class="o">*</span> <span class="n">data_points_in_bit</span><span class="p">)</span>
<span class="n">zero_space_len</span> <span class="o">=</span> <span class="n">data_points_in_bit</span> <span class="o">-</span> <span class="n">zero_pulse_len</span>
<span class="n">modulated_one_bit</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">one_pulse_len</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">[</span><span class="s">'HIGH'</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">one_space_len</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">[</span><span class="s">'LOW'</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">))</span>
<span class="n">modulated_zero_bit</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">zero_pulse_len</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">[</span><span class="s">'HIGH'</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">zero_space_len</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">[</span><span class="s">'LOW'</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">))</span>
<span class="k">for</span> <span class="n">bit</span> <span class="ow">in</span> <span class="n">binary_data</span><span class="p">:</span>
<span class="n">modulated_bit</span> <span class="o">=</span> <span class="n">modulated_one_bit</span> <span class="k">if</span> <span class="n">bit</span> <span class="o">==</span> <span class="s">'1'</span> <span class="k">else</span> <span class="n">modulated_zero_bit</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">,</span> <span class="n">modulated_bit</span><span class="p">)</span>
<span class="k">return</span> <span class="n">modulation_array</span>
<span class="k">def</span> <span class="nf">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span>
<span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="o">=</span><span class="n">DEFAULT_RATIOS</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">DEFAULT_AMP_MAP</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">signal_len_secs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">binary_data</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">signal_len_secs</span><span class="p">,</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">signal_len_secs</span><span class="p">)</span>
<span class="n">carrier_wave</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">carrier_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">get_modulation_array</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="p">)</span>
<span class="c"># Pad (or trim) the modulation array to match the length of the carrier wave</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o">></span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">):</span>
<span class="n">pad_len</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">pad_len</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">[</span><span class="s">'LOW'</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">))</span>
<span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o"><</span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">):</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">modulation_array</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)]</span>
<span class="k">return</span> <span class="n">t</span><span class="p">,</span> <span class="n">carrier_wave</span> <span class="o">*</span> <span class="n">modulation_array</span>
<span class="n">binary_data</span> <span class="o">=</span> <span class="s">'0110100010000000'</span>
<span class="n">carrier_wave_freq</span> <span class="o">=</span> <span class="mi">20</span> <span class="c">#315e6</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="n">baud</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">t</span><span class="p">,</span> <span class="n">sig</span> <span class="o">=</span> <span class="n">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'sig'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'freq'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">sig</span><span class="p">)</span>
</pre></div>
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Out[6]:</div>
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[<matplotlib.lines.Line2D at 0x10e2b0588>]
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<h2 id="looks-pretty-close-to-the-original">Looks pretty close to the original!</h2>
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<img src="http://calebmadrigal.com/images/original_radio_signal.png" alt="original signal" /><p class="caption">original signal</p>
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<h2 id="Generate-real-wave-and-write-to-file">Generate real wave and write to file<a class="anchor-link" href="#Generate-real-wave-and-write-to-file">¶</a></h2>
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In [7]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Estimating baud</span>
<span class="n">bits_transmitted</span> <span class="o">=</span> <span class="mi">16</span>
<span class="n">viewing_sample_rate</span> <span class="o">=</span> <span class="mi">100000</span> <span class="c"># samples per second</span>
<span class="n">real_sample_rate</span> <span class="o">=</span> <span class="mi">2000000</span> <span class="c"># samples per second</span>
<span class="n">viewing_transmission_time</span> <span class="o">=</span> <span class="mf">8.219</span><span class="o">-</span><span class="mf">6.664</span> <span class="c"># seconds</span>
<span class="n">real_transmission_time</span> <span class="o">=</span> <span class="n">viewing_transmission_time</span> <span class="o">*</span> <span class="p">(</span><span class="n">viewing_sample_rate</span> <span class="o">/</span> <span class="n">real_sample_rate</span><span class="p">)</span>
<span class="n">baud</span> <span class="o">=</span> <span class="n">bits_transmitted</span> <span class="o">/</span> <span class="n">real_transmission_time</span> <span class="c"># bits per second</span>
<span class="k">print</span><span class="p">(</span><span class="s">'Real transmission time: {}</span><span class="se">\n</span><span class="s">Baud: {}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">real_transmission_time</span><span class="p">,</span> <span class="n">baud</span><span class="p">))</span>
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Real transmission time: 0.07774999999999999
Baud: 205.78778135048236
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">binary_data</span> <span class="o">=</span> <span class="s">'0110100010000000'</span>
<span class="n">carrier_wave_freq</span> <span class="o">=</span> <span class="mf">315e6</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mf">2e6</span>
<span class="n">baud</span> <span class="o">=</span> <span class="mi">205</span>
<span class="n">t</span><span class="p">,</span> <span class="n">sig</span> <span class="o">=</span> <span class="n">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'sig'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'freq'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">sig</span><span class="p">)</span>
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[<matplotlib.lines.Line2D at 0x10da2fbe0>]
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">write_pcm_file</span><span class="p">(</span><span class="n">sig</span><span class="p">,</span> <span class="s">'raw_data/generated_sig1.pcm'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'int16'</span><span class="p">)</span>
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<h2 id="now-lets-try-to-replicate-the-full-signal">Now let's try to replicate the full signal</h2>
<p>First, we need a way to generate a HIGH or LOW pulse...</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Generate preamble and repeat pattern</span>
<span class="n">binary_data</span> <span class="o">=</span> <span class="s">'0110100010000000'</span>
<span class="n">carrier_wave_freq</span> <span class="o">=</span> <span class="mf">315e6</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mf">2e6</span>
<span class="n">baud</span> <span class="o">=</span> <span class="mi">205</span>
<span class="k">def</span> <span class="nf">generate_pulse</span><span class="p">(</span><span class="n">bit_val</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">multiple_of_bit_len</span><span class="p">,</span>
<span class="n">amp_map</span><span class="o">=</span><span class="n">DEFAULT_AMP_MAP</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">signal_len_secs</span> <span class="o">=</span> <span class="n">multiple_of_bit_len</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">signal_len_secs</span><span class="p">,</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">signal_len_secs</span><span class="p">)</span>
<span class="n">high_or_low</span> <span class="o">=</span> <span class="s">'HIGH'</span> <span class="k">if</span> <span class="n">bit_val</span> <span class="o">==</span> <span class="s">'1'</span> <span class="k">else</span> <span class="s">'LOW'</span>
<span class="n">pulse</span> <span class="o">=</span> <span class="n">amp_map</span><span class="p">[</span><span class="n">high_or_low</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">carrier_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="k">return</span> <span class="n">t</span><span class="p">,</span> <span class="n">pulse</span>
<span class="n">t1</span><span class="p">,</span> <span class="n">signal_header</span> <span class="o">=</span> <span class="n">generate_pulse</span><span class="p">(</span><span class="s">'1'</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="mf">3.85</span><span class="p">)</span>
<span class="n">t2</span><span class="p">,</span> <span class="n">signal_spacer</span> <span class="o">=</span> <span class="n">generate_pulse</span><span class="p">(</span><span class="s">'0'</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="mf">3.78</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'sig'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'freq'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span> <span class="mi">7</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">signal_spacer</span><span class="p">,</span> <span class="n">signal_header</span><span class="p">))</span>
</pre></div>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">join_all_arrays</span><span class="p">(</span><span class="n">array_list</span><span class="p">):</span>
<span class="n">joined</span> <span class="o">=</span> <span class="n">array_list</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">array_list</span><span class="p">[</span><span class="mi">1</span><span class="p">:]:</span>
<span class="n">joined</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">joined</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
<span class="k">return</span> <span class="n">joined</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">full_signal</span> <span class="o">=</span> <span class="n">join_all_arrays</span><span class="p">([</span><span class="n">signal_header</span><span class="p">]</span> <span class="o">+</span> <span class="p">([</span><span class="n">sig</span><span class="p">,</span> <span class="n">signal_spacer</span><span class="p">]</span> <span class="o">*</span> <span class="mi">12</span><span class="p">))</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'sig'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'samples'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'freq'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span> <span class="mi">7</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">full_signal</span><span class="p">)</span>
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/usr/local/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part
return array(a, dtype, copy=False, order=order)
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[<matplotlib.lines.Line2D at 0x11cb40a58>]
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">write_pcm_file</span><span class="p">(</span><span class="n">full_signal</span><span class="p">,</span> <span class="s">'raw_data/generated_sig2.pcm'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'int16'</span><span class="p">)</span>
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<h2 id="comparison-of-recorded-signal-vs-generated-signal">Comparison of recorded signal vs generated signal</h2>
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<img src="http://calebmadrigal.com/images/recorded_vs_generated.png" alt="comparison" /><p class="caption">comparison</p>
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<h1 id="complex-number-waves">Complex number waves</h1>
<p>It turns out that the HackRF only can transmit complex signals (essentially, a 2-dimensional sine wave, where time is the x axis, and the signal spins around the x axis in a helical shape that would appear like a sine wave when viewed perpendicularly).</p>
<p>So let's generate a complex signal...</p>
<p>There may be a better way, but the best way I know to generate a complex sine wave is with Euler's formula:</p>
<p>e^(i*t) = cos(t) + i sin(t)</p>
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<img src="http://calebmadrigal.com/images/Sine_curve_drawing_animation.gif" alt="Rotation with E animation" /><p class="caption">Rotation with E animation</p>
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<p>For more information on rotation with <code>e</code>, see <a href="https://github.com/calebmadrigal/FourierTalkOSCON/blob/master/05_RotationWithE.ipynb">https://github.com/calebmadrigal/FourierTalkOSCON/blob/master/05_RotationWithE.ipynb</a></p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<span class="n">amp</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">freq</span> <span class="o">=</span> <span class="mi">10</span> <span class="c"># Hz</span>
<span class="n">simple_sig</span> <span class="o">=</span> <span class="n">amp</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">simple_sig</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="kn">import</span> <span class="nn">cmath</span>
<span class="n">complex_sig</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="n">freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="mi">0</span><span class="o">+</span><span class="mi">1j</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">complex_sig</span><span class="p">)</span>
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/usr/local/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part
return array(a, dtype, copy=False, order=order)
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[<matplotlib.lines.Line2D at 0x1239e8470>]
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">simple_sig</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span>
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2.852877874620976
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">complex_sig</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span>
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(2.852877874620976+0.92794818416660674j)
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<div class="highlight-ipynb"><pre class="ipynb"><span class="nb">abs</span><span class="p">(</span><span class="n">complex_sig</span><span class="p">[</span><span class="mi">5</span><span class="p">])</span> <span class="c"># This is the amplitude of the wave</span>
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2.9999999999999996
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<h2 id="Now,-let's-rewrite-the-generation-functions-to-use-complex-math">Now, let's rewrite the generation functions to use complex math<a class="anchor-link" href="#Now,-let's-rewrite-the-generation-functions-to-use-complex-math">¶</a></h2>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span>
<span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="o">=</span><span class="n">DEFAULT_RATIOS</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">DEFAULT_AMP_MAP</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">signal_len_secs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">binary_data</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">signal_len_secs</span><span class="p">,</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">signal_len_secs</span><span class="p">)</span>
<span class="c"># Using Euler's formula to generate a complex sinusoidal wave</span>
<span class="n">carrier_wave</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="n">carrier_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="mi">0</span><span class="o">+</span><span class="mi">1j</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">get_modulation_array</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="p">)</span>
<span class="c"># Pad (or trim) the modulation array to match the length of the carrier wave</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o">></span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">):</span>
<span class="n">pad_len</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">pad_len</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">[</span><span class="s">'LOW'</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">))</span>
<span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o"><</span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">):</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">modulation_array</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)]</span>
<span class="k">return</span> <span class="n">t</span><span class="p">,</span> <span class="n">carrier_wave</span> <span class="o">*</span> <span class="n">modulation_array</span>
<span class="k">def</span> <span class="nf">generate_pulse</span><span class="p">(</span><span class="n">bit_val</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">multiple_of_bit_len</span><span class="p">,</span>
<span class="n">amp_map</span><span class="o">=</span><span class="n">DEFAULT_AMP_MAP</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">signal_len_secs</span> <span class="o">=</span> <span class="n">multiple_of_bit_len</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">signal_len_secs</span><span class="p">,</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">signal_len_secs</span><span class="p">)</span>
<span class="n">high_or_low</span> <span class="o">=</span> <span class="s">'HIGH'</span> <span class="k">if</span> <span class="n">bit_val</span> <span class="o">==</span> <span class="s">'1'</span> <span class="k">else</span> <span class="s">'LOW'</span>
<span class="n">pulse</span> <span class="o">=</span> <span class="n">amp_map</span><span class="p">[</span><span class="n">high_or_low</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="n">carrier_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="mi">0</span><span class="o">+</span><span class="mi">1j</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="k">return</span> <span class="n">t</span><span class="p">,</span> <span class="n">pulse</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">binary_data</span> <span class="o">=</span> <span class="s">'0110100010000000'</span>
<span class="n">carrier_wave_freq</span> <span class="o">=</span> <span class="mf">315e6</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mf">2e6</span>
<span class="n">baud</span> <span class="o">=</span> <span class="mi">205</span>
<span class="n">complex64_amp_map</span> <span class="o">=</span> <span class="p">{</span>
<span class="s">'LOW'</span><span class="p">:</span> <span class="mf">1.4</span> <span class="o">*</span> <span class="o">.</span><span class="mo">02</span><span class="p">,</span>
<span class="s">'HIGH'</span><span class="p">:</span> <span class="mf">1.4</span>
<span class="p">}</span>
<span class="n">t</span><span class="p">,</span> <span class="n">complex_signal</span> <span class="o">=</span> <span class="n">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">complex64_amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
<span class="n">t2</span><span class="p">,</span> <span class="n">signal_header</span> <span class="o">=</span> <span class="n">generate_pulse</span><span class="p">(</span><span class="s">'1'</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="mf">3.85</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">complex64_amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
<span class="n">t3</span><span class="p">,</span> <span class="n">signal_spacer</span> <span class="o">=</span> <span class="n">generate_pulse</span><span class="p">(</span><span class="s">'0'</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="mf">3.78</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">complex64_amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
<span class="n">full_signal</span> <span class="o">=</span> <span class="n">join_all_arrays</span><span class="p">([</span><span class="n">signal_header</span><span class="p">]</span> <span class="o">+</span> <span class="p">([</span><span class="n">complex_signal</span><span class="p">,</span> <span class="n">signal_spacer</span><span class="p">]</span> <span class="o">*</span> <span class="mi">12</span><span class="p">))</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">write_pcm_file</span><span class="p">(</span><span class="n">full_signal</span><span class="p">,</span> <span class="s">'raw_data/generated_sig2.pcm'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
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<h2 id="sadly-this-signal-did-not-trigger-the-outlet">Sadly, this signal did not trigger the outlet</h2>
<p>So what's different? Well, for one, when I play the 2 signals audibly in Audacity, the original signal is pretty loud, whereas, the one I generated sounds really quiet - almost as if there is the waves I'm generating is self-canceling.</p>
<p>Here's a close-up of the wave I generated:</p>
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<img src="http://calebmadrigal.com/images/generated_wave_zoomedin.png" alt="generated zoomed in" /><p class="caption">generated zoomed in</p>
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<p>It almost looks like ther eare equal and opposite waves that would be canceling each other out, but when you look closer, it doesn't seem so:</p>
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<img src="http://calebmadrigal.com/images/generated_wave_zoomedin2.png" alt="generated zoomed in" /><p class="caption">generated zoomed in</p>
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<p>And here's a close-up of the original wave:</p>
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<img src="http://calebmadrigal.com/images/original_wave_zoomedin.png" alt="original zoomed in" /><p class="caption">original zoomed in</p>
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<p>It looks like in the original, the carrier wave is modulated by multiplying by another wave, rather than by unchanging "HIGH" values.</p>
<p>So I'm going to try that now: <strong>to modulate the carrier wave by another wave</strong>, rather than by a static HIGH value...</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span>
<span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="o">=</span><span class="n">DEFAULT_RATIOS</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">DEFAULT_AMP_MAP</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">signal_len_secs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">binary_data</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">signal_len_secs</span><span class="p">,</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">signal_len_secs</span><span class="p">)</span>
<span class="c"># Using Euler's formula to generate a complex sinusoidal wave</span>
<span class="n">carrier_wave</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="n">carrier_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="mi">0</span><span class="o">+</span><span class="mi">1j</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">get_modulation_array</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">sig_ratios</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="p">)</span>
<span class="c"># Pad (or trim) the modulation array to match the length of the carrier wave</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o">></span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">):</span>
<span class="n">pad_len</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">)</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">pad_len</span><span class="p">,</span> <span class="n">amp_map</span><span class="p">[</span><span class="s">'LOW'</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">))</span>
<span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)</span> <span class="o"><</span> <span class="nb">len</span><span class="p">(</span><span class="n">modulation_array</span><span class="p">):</span>
<span class="n">modulation_array</span> <span class="o">=</span> <span class="n">modulation_array</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">carrier_wave</span><span class="p">)]</span>
<span class="c"># Modulate by superwave</span>
<span class="n">super_wave_freq</span> <span class="o">=</span> <span class="n">carrier_wave_freq</span> <span class="o">/</span> <span class="p">(</span><span class="mi">160</span><span class="o">*</span><span class="mi">2</span><span class="p">)</span>
<span class="n">super_wave</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="n">super_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="mi">0</span><span class="o">+</span><span class="mi">1j</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="k">return</span> <span class="n">t</span><span class="p">,</span> <span class="n">carrier_wave</span> <span class="o">*</span> <span class="n">modulation_array</span> <span class="o">*</span> <span class="n">super_wave</span>
<span class="k">def</span> <span class="nf">generate_pulse</span><span class="p">(</span><span class="n">bit_val</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">multiple_of_bit_len</span><span class="p">,</span>
<span class="n">amp_map</span><span class="o">=</span><span class="n">DEFAULT_AMP_MAP</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">):</span>
<span class="n">signal_len_secs</span> <span class="o">=</span> <span class="n">multiple_of_bit_len</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">baud</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">signal_len_secs</span><span class="p">,</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">signal_len_secs</span><span class="p">)</span>
<span class="n">high_or_low</span> <span class="o">=</span> <span class="s">'HIGH'</span> <span class="k">if</span> <span class="n">bit_val</span> <span class="o">==</span> <span class="s">'1'</span> <span class="k">else</span> <span class="s">'LOW'</span>
<span class="n">pulse</span> <span class="o">=</span> <span class="n">amp_map</span><span class="p">[</span><span class="n">high_or_low</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="n">carrier_wave_freq</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="mi">0</span><span class="o">+</span><span class="mi">1j</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span>
<span class="k">return</span> <span class="n">t</span><span class="p">,</span> <span class="n">pulse</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">binary_data</span> <span class="o">=</span> <span class="s">'0110100010000000'</span>
<span class="n">carrier_wave_freq</span> <span class="o">=</span> <span class="mf">315e6</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mf">2e6</span>
<span class="n">baud</span> <span class="o">=</span> <span class="mi">205</span> <span class="o">*</span> <span class="mi">2</span>
<span class="n">complex64_amp_map</span> <span class="o">=</span> <span class="p">{</span>
<span class="s">'LOW'</span><span class="p">:</span> <span class="mf">1.4</span> <span class="o">*</span> <span class="o">.</span><span class="mo">02</span><span class="p">,</span>
<span class="s">'HIGH'</span><span class="p">:</span> <span class="mf">1.4</span>
<span class="p">}</span>
<span class="n">t</span><span class="p">,</span> <span class="n">complex_signal</span> <span class="o">=</span> <span class="n">generate_on_off_key_signal</span><span class="p">(</span><span class="n">binary_data</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">complex64_amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
<span class="n">t2</span><span class="p">,</span> <span class="n">signal_header</span> <span class="o">=</span> <span class="n">generate_pulse</span><span class="p">(</span><span class="s">'1'</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="mf">3.85</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">complex64_amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
<span class="n">t3</span><span class="p">,</span> <span class="n">signal_spacer</span> <span class="o">=</span> <span class="n">generate_pulse</span><span class="p">(</span><span class="s">'0'</span><span class="p">,</span> <span class="n">carrier_wave_freq</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">baud</span><span class="p">,</span> <span class="mf">3.78</span><span class="p">,</span> <span class="n">amp_map</span><span class="o">=</span><span class="n">complex64_amp_map</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
<span class="n">full_signal</span> <span class="o">=</span> <span class="n">join_all_arrays</span><span class="p">([</span><span class="n">signal_header</span><span class="p">]</span> <span class="o">+</span> <span class="p">([</span><span class="n">complex_signal</span><span class="p">,</span> <span class="n">signal_spacer</span><span class="p">]</span> <span class="o">*</span> <span class="mi">12</span><span class="p">))</span>
<span class="n">write_pcm_file</span><span class="p">(</span><span class="n">full_signal</span><span class="p">,</span> <span class="s">'raw_data/generated_sig3.pcm'</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s">'complex64'</span><span class="p">)</span>
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<h1 id="success">Success!</h1>
<p>And this worked. I had to guess at the "super wave" frequency.</p>
<p>Here is what the generated signal looks like zoomed in:</p>
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<img src="http://calebmadrigal.com/images/generated_wave_superwave.png" alt="generated wave superwave" /><p class="caption">generated wave superwave</p>
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<p>And here's the original signal:</p>
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<img src="http://calebmadrigal.com/images/original_wave_superwave.png" alt="original wave superwave" /><p class="caption">original wave superwave</p>
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<p>So there you have it - how to generate a digital radio signal from scratch.</p>
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</div></p>Fourier Transform Notes2016-07-16T17:10:00-05:00Caleb Madrigaltag:calebmadrigal.com,2016-07-16:fourier-transform-notes/<p>The following are my notes from <a href="http://conferences.oreilly.com/oscon/oscon2013/public/schedule/detail/28946">a talk I gave at OSCON 2013</a>. Here is the Github source of these Jupyter/IPython notebooks: <a href="https://github.com/calebmadrigal/FourierTalkOSCON">https://github.com/calebmadrigal/FourierTalkOSCON</a></p>
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<h1 id="sound-analysis-with-the-fourier-transform-and-python">Sound Analysis with the Fourier Transform and Python</h1>
<h3 id="link-to-repo-httptinyurl.comfourierpython">Link to repo: http://tinyurl.com/fourierpython</h3>
<h2 id="intro">Intro</h2>
<ol style="list-style-type: decimal">
<li>Welcome</li>
<li>Format of talk
<ul>
<li>Everything is in iPython Notebook (on Github)</li>
<li>You don't need to take notes</li>
<li>Please save questions for the end</li>
</ul></li>
<li>Why this is interesting
<ul>
<li>Sound processing is big - natural human-machine interfaces (e.g. Siri)</li>
<li>Noise reduction, Compression, feature extraction (e.g. speech)</li>
<li>Understanding our universe better (Superposition, Harmonics, Sound timbre)</li>
</ul></li>
</ol>
<hr />
<h2 id="overview">Overview</h2>
<ul>
<li>The Nature of Waves</li>
<li>The Fourier Transform</li>
<li>Fast Fourier Transform (FFT) in Python</li>
<li>Audio analysis</li>
</ul>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="c"># Graphing helper function</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="the-nature-of-waves">The Nature of Waves</h1>
<p>We're mainly going to talk about sound waves, but many of these things will apply to other types of waves.</p>
<h2 id="how-do-we-represent-waves">How do we represent waves?</h2>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">freq</span> <span class="o">=</span> <span class="mi">1</span> <span class="c">#hz - cycles per second</span>
<span class="n">amplitude</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">time_to_plot</span> <span class="o">=</span> <span class="mi">2</span> <span class="c"># second</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mi">100</span> <span class="c"># samples per second</span>
<span class="n">num_samples</span> <span class="o">=</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">time_to_plot</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">time_to_plot</span><span class="p">,</span> <span class="n">num_samples</span><span class="p">)</span>
<span class="n">signal</span> <span class="o">=</span> <span class="p">[</span><span class="n">amplitude</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">freq</span> <span class="o">*</span> <span class="n">i</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">t</span><span class="p">]</span> <span class="c"># Explain the 2*pi</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'time domain'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">signal</span><span class="p">)</span>
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<h2 id="in-the-context-of-sound-what-would-a-wave-like-this-represent">In the context of sound, what would a wave like this represent?</h2>
<ul>
<li>Answer: Changes in air pressure</li>
<li>When the graph is above x=0, the pressure of the air is more than "normal" (air is moving toward you)</li>
<li>When the graph is below x=0, the pressure of the air is less than "normal" (air is moving away from you)</li>
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<h1 id="Example-of-a-real-sound-wave">Example of a real sound wave<a class="anchor-link" href="#Example-of-a-real-sound-wave">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="kn">import</span> <span class="nn">scipy.io.wavfile</span>
<span class="p">(</span><span class="n">sample_rate</span><span class="p">,</span> <span class="n">input_signal</span><span class="p">)</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">io</span><span class="o">.</span><span class="n">wavfile</span><span class="o">.</span><span class="n">read</span><span class="p">(</span><span class="s">"audio_files/vowel_ah.wav"</span><span class="p">)</span>
<span class="n">time_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">input_signal</span><span class="p">)</span><span class="o">/</span><span class="n">sample_rate</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">sample_rate</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Ah vowel sound'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time_array</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">4000</span><span class="p">],</span> <span class="n">input_signal</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">4000</span><span class="p">])</span>
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<h1 id="the-superposition-principle">The Superposition Principle</h1>
<ul>
<li>If you add a bunch of waves together, it forms one wave.</li>
<li>Hearing me talk while knocking on the desk</li>
</ul>
<h1 id="example">Example</h1>
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In [27]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Two subplots, the axes array is 1-d</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">y1</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">y2</span> <span class="o">=</span> <span class="mi">0</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
<span class="n">y3</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
<span class="n">y4</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">4</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
<span class="n">f</span><span class="p">,</span> <span class="n">axarr</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">sharex</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">sharey</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y1</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y2</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y3</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y4</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'y1+y2+y3+y4'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">convoluted_wave</span> <span class="o">=</span> <span class="n">y1</span> <span class="o">+</span> <span class="n">y2</span> <span class="o">+</span> <span class="n">y3</span> <span class="o">+</span> <span class="n">y4</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">convoluted_wave</span><span class="p">)</span>
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<h1 id="wave-interference-example">Wave Interference Example</h1>
<h3 id="this-is-how-noise-canceling-headphones-work">This is how noise-canceling headphones work</h3>
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In [29]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">y5</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span>
<span class="n">y6</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span>
<span class="n">f</span><span class="p">,</span> <span class="n">axarr</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">sharex</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">sharey</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y5</span><span class="p">,</span> <span class="s">'b'</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y6</span><span class="p">,</span> <span class="s">'g'</span><span class="p">)</span>
<span class="n">axarr</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y5</span> <span class="o">+</span> <span class="n">y6</span><span class="p">,</span> <span class="s">'r'</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Graphing helper function</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="fourier-transform">Fourier Transform</h1>
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<img src="http://calebmadrigal.com/images/fourier-transform/time_freq_domain.png" alt="Time to Frequency Domain" /><p class="caption">Time to Frequency Domain</p>
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<h2 id="the-fourier-transform-is-like-a-prism-not-the-nsa-one">The Fourier Transform is like a prism (not the NSA one)</h2>
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<img src="http://calebmadrigal.com/images/fourier-transform/prism.png" alt="Prism" /><p class="caption">Prism</p>
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<h2 id="fourier-transform-definition">Fourier Transform Definition</h2>
<p><span class="math">\[G(f) = \int_{-\infty}^\infty g(t) e^{-i 2 \pi f t} dt\]</span></p>
<p><br /> For our purposes, we will just be using the discrete version... <br /><br /></p>
<h2 id="discrete-fourier-transform-dft-definition">Discrete Fourier Transform (DFT) Definition</h2>
<p><span class="math">\[G(\frac{n}{N}) = \sum_{k=0}^{N-1} g(k) e^{-i 2 \pi k \frac{n}{N} }\]</span></p>
<p><strong>Meaning</strong>:</p>
<ul>
<li><span class="math">\(N\)</span> is the total number of samples</li>
<li><span class="math">\(g(k)\)</span> is the kth sample for the time-domain function (i.e. the DFT input)</li>
<li><span class="math">\(G(\frac{n}{N})\)</span> is the output of the DFT for the frequency that is <span class="math">\(\frac{n}{N}\)</span> cycles per sample; so to get the frequency, you have to multiply <span class="math">\(n/N\)</span> by the sample rate.</li>
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<h1 id="How-to-represent-waves">How to represent waves<a class="anchor-link" href="#How-to-represent-waves">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="n">freq</span> <span class="o">=</span> <span class="mi">1</span> <span class="c">#hz - cycles per second</span>
<span class="n">amplitude</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">time_to_plot</span> <span class="o">=</span> <span class="mi">2</span> <span class="c"># second</span>
<span class="n">sample_rate</span> <span class="o">=</span> <span class="mi">100</span> <span class="c"># samples per second</span>
<span class="n">num_samples</span> <span class="o">=</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">time_to_plot</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">time_to_plot</span><span class="p">,</span> <span class="n">num_samples</span><span class="p">)</span>
<span class="n">signal</span> <span class="o">=</span> <span class="p">[</span><span class="n">amplitude</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">freq</span> <span class="o">*</span> <span class="n">i</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">t</span><span class="p">]</span> <span class="c"># Explain the 2*pi</span>
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<h3 id="why-the-2pi">Why the 2*pi?</h3>
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<li>If we want a wave which completes 1 cycle per second, so sine must come back to the same position on a circle as the starting point</li>
<li>So one full rotation about a circle - <span class="math">\(2 \pi\)</span> (in radians)</li>
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<img src="/images/Sine_curve_drawing_animation.gif" alt="sine_curve" /><p class="caption">sine_curve</p>
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<h1 id="Plot-the-wave">Plot the wave<a class="anchor-link" href="#Plot-the-wave">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'time domain'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">signal</span><span class="p">)</span>
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[<matplotlib.lines.Line2D at 0x10f277748>]
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<h1 id="convert-to-the-frequency-domain">Convert to the Frequency Domain</h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">fft_output</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">signal</span><span class="p">)</span>
<span class="n">magnitude_only</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">real</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">i</span><span class="o">.</span><span class="n">imag</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">fft_output</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">fft_output</span><span class="p">]</span>
<span class="n">frequencies</span> <span class="o">=</span> <span class="p">[(</span><span class="n">i</span><span class="o">*</span><span class="mf">1.0</span><span class="o">/</span><span class="n">num_samples</span><span class="p">)</span><span class="o">*</span><span class="n">sample_rate</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_samples</span><span class="o">//</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">)]</span>
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In [23]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'frequency (in Hz)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'frequency domain'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">frequencies</span><span class="p">,</span> <span class="n">magnitude_only</span><span class="p">,</span> <span class="s">'r'</span><span class="p">)</span>
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Out[23]:</div>
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[<matplotlib.lines.Line2D at 0x10eec6160>]
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<h2 id="question-so-what-does-the-fourier-transform-give-us">Question: So what does the Fourier Transform give us?</h2>
<ul>
<li>The amplitudes of simple sine waves</li>
<li>Their starting position - phase (we won't get into this part much)</li>
</ul>
<h2 id="question-what-sine-wave-frequencies-are-used">Question: what sine wave frequencies are used?</h2>
<ul>
<li>Answer: This is determined by how many samples are provided to the Fourier Transform</li>
<li>Frequencies range from 0 to (number of samples) / 2</li>
<li><strong>Example: If your sample rate is 100Hz, and you give the FFT 100 samples, the FFT will return the amplitude of the components with frequencies 0 to 50Hz.</strong></li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="c"># Graphing helper function</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="wave-deconvolution---multiplication-and-addition">Wave Deconvolution - Multiplication and Addition</h1>
<ul>
<li>So a complex wave is made of simple waves.</li>
<li>How can you break a complex wave into it's simple component waves?</li>
</ul>
<h3 id="answer-multiplying-a-wave-by-another-wave-of-frequency-100hz-cancels-out-all-of-the-other-component-waves-and-leaves-only-the-100hz-component-kind-of.">Answer: Multiplying a wave by another wave of frequency 100Hz cancels out all of the other component waves and leaves only the 100Hz component (kind of).</h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">)</span>
<span class="n">freq_1hz_amp_10</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">sin</span><span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">freq_3hz_amp_5</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">complex_wave</span> <span class="o">=</span> <span class="n">freq_1hz_amp_10</span> <span class="o">+</span> <span class="n">freq_3hz_amp_5</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'original wave'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">complex_wave</span><span class="p">)</span>
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<h1 id="Multiply-complex-wave-by-1Hz-wave">Multiply complex wave by 1Hz wave<a class="anchor-link" href="#Multiply-complex-wave-by-1Hz-wave">¶</a></h1>
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In [33]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">freq_1hz</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'original wave * 1Hz wave'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">complex_wave</span> <span class="o">*</span> <span class="n">freq_1hz</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="nb">sum</span><span class="p">(</span><span class="n">complex_wave</span><span class="o">*</span><span class="n">freq_1hz</span><span class="p">)</span>
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994.99999999999977
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">print</span><span class="p">(</span><span class="s">"Amplitude of 1hz component: "</span><span class="p">,</span> <span class="nb">sum</span><span class="p">(</span><span class="n">complex_wave</span><span class="o">*</span><span class="n">freq_1hz</span><span class="p">)</span> <span class="o">*</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="mf">1.0</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">complex_wave</span><span class="p">))</span>
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Amplitude of 1hz component: 9.95
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<h1 id="multiply-complex-wave-by-3hz-wave">Multiply complex wave by 3Hz wave</h1>
<p>Notice that more of the graph is above the x-axis then below it.</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">freq_3hz</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'complex wave * 3Hz wave'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">complex_wave</span> <span class="o">*</span> <span class="n">freq_3hz</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="nb">sum</span><span class="p">(</span><span class="n">complex_wave</span><span class="o">*</span><span class="n">freq_3hz</span><span class="p">)</span>
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497.5
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">print</span><span class="p">(</span><span class="s">"Amplitude of 3hz component: "</span><span class="p">,</span> <span class="nb">sum</span><span class="p">(</span><span class="n">complex_wave</span><span class="o">*</span><span class="n">freq_3hz</span><span class="p">)</span> <span class="o">*</span> <span class="mf">2.0</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">complex_wave</span><span class="p">))</span>
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Amplitude of 3hz component: 4.975
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<h1 id="multiply-complex-wave-by-2hz-wave">Multiply complex wave by 2Hz wave</h1>
<p>Notice that an equal amount of the graph is above the x-axis as below it.</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">freq_2hz</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s">'complex wave * 2Hz wave'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">complex_wave</span> <span class="o">*</span> <span class="n">freq_2hz</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="nb">sum</span><span class="p">(</span><span class="n">complex_wave</span><span class="o">*</span><span class="n">freq_2hz</span><span class="p">)</span>
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1.4549472737712679e-13
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Very close to 0</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Amplitude of 3hz component: "</span><span class="p">,</span> <span class="nb">sum</span><span class="p">(</span><span class="n">complex_wave</span><span class="o">*</span><span class="n">freq_2hz</span><span class="p">)</span> <span class="o">*</span> <span class="mf">2.0</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">complex_wave</span><span class="p">))</span>
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Amplitude of 3hz component: 1.45494727377e-15
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Same with 4Hz - close to 0</span>
<span class="n">freq_4hz</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="nb">sum</span><span class="p">(</span><span class="n">complex_wave</span><span class="o">*</span><span class="n">freq_4hz</span><span class="p">)</span>
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-5.0848214527832113e-14
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<h1 id="so-how-does-this-work">So how does this work?</h1>
<p>The summation of complex wave multiplied by simple wave of a given frequency leaves us with the "power" of that simple wave.</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="c"># Graphing helper function</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="eulers-formula">Euler's Formula</h1>
<p><span class="math">\[e^{ix} = \cos(x) + i \sin(x)\]</span></p>
<p>So raising <span class="math">\(e^{ix}\)</span> produces rotation (in the Complex plane)</p>
<h2 id="related-to-eulers-identity">Related to Euler's Identity</h2>
<p><span class="math">\[e^{i \pi} + 1 = 0\]</span></p>
<ul>
<li>At <span class="math">\(x = \pi\)</span>, <span class="math">\(\sin(\pi) = 0\)</span>, and <span class="math">\(\cos(\pi) = -1\)</span></li>
<li>So <span class="math">\(e^{i \pi} = -1 + 0\)</span></li>
<li>Move the 1 over: <span class="math">\(e^{i \pi} + 1 = 0\)</span></li>
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<h2 id="complex-plane">Complex Plane</h2>
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<img src="http://calebmadrigal.com/images/fourier-transform/complex_plane.jpg" alt="Complex Plane" /><p class="caption">Complex Plane</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Generate some complex numbers, and convert them to (x,y) coordinates</span>
<span class="n">complex_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="mi">1j</span> <span class="o">*</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">16</span><span class="p">)]</span>
<span class="n">real_parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">z</span><span class="o">.</span><span class="n">real</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">complex_points</span><span class="p">]</span>
<span class="n">imag_parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">z</span><span class="o">.</span><span class="n">imag</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">complex_points</span><span class="p">]</span>
<span class="c"># Matplotlib code to draw graph</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s">'left'</span><span class="p">]</span><span class="o">.</span><span class="n">set_position</span><span class="p">(</span><span class="s">'center'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s">'bottom'</span><span class="p">]</span><span class="o">.</span><span class="n">set_position</span><span class="p">(</span><span class="s">'center'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s">'top'</span><span class="p">]</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s">'none'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s">'right'</span><span class="p">]</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s">'none'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">((</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span><span class="mf">1.5</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span><span class="mf">1.5</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">((</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span><span class="mf">1.5</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span><span class="mf">1.5</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s">"{0} + {1}i"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">real_parts</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">imag_parts</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="n">real_parts</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> \
<span class="n">imag_parts</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">),</span> <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s">'black'</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.08</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">real_parts</span><span class="p">,</span> <span class="n">imag_parts</span><span class="p">,</span> <span class="s">'go'</span><span class="p">)</span>
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<h3 id="going-around-a-circle-produces-sine-and-cosine-waves">Going around a circle produces sine and cosine waves</h3>
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<img src="images/Sine_curve_drawing_animation.gif" alt="sine_curve" /><p class="caption">sine_curve</p>
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<h1 id="Circles-produce-sin-(and-cos)-waves">Circles produce sin (and cos) waves<a class="anchor-link" href="#Circles-produce-sin-(and-cos)-waves">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">e_func</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">e</span><span class="o">**</span><span class="p">(</span><span class="mi">1j</span> <span class="o">*</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">t</span><span class="p">]</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'real part (cosine) of e^ix'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude of real part'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="p">[</span><span class="n">i</span><span class="o">.</span><span class="n">real</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">e_func</span><span class="p">])</span>
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In [11]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'imaginary part (sin) of e^ix'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude of imaginary part'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="p">[</span><span class="n">i</span><span class="o">.</span><span class="n">imag</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">e_func</span><span class="p">])</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="c"># Graphing helper function</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="sampling-a-test-function">Sampling a test function</h1>
<p>Wave with:</p>
<ul>
<li>Frequency of 1 Hz</li>
<li>Amplitude of 5</li>
</ul>
<p>We will sample:</p>
<ul>
<li>At 10 samples per second</li>
<li>For 3 seconds</li>
<li>So a total of 30 samples</li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">sample_rate</span> <span class="o">=</span> <span class="mi">10</span> <span class="c"># samples per sec</span>
<span class="n">total_sampling_time</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">num_samples</span> <span class="o">=</span> <span class="n">sample_rate</span> <span class="o">*</span> <span class="n">total_sampling_time</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">total_sampling_time</span><span class="p">,</span> <span class="n">num_samples</span><span class="p">)</span>
<span class="c"># between x = 0 and x = 1, a complete revolution (2 pi) has been made, so this is</span>
<span class="c"># a 1 Hz signal with an amplitude of 5</span>
<span class="n">frequency_in_hz</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">wave_amplitude</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">wave_amplitude</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">frequency_in_hz</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
<span class="n">sampled_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">f</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">t</span><span class="p">]</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'time domain'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">sampled_f</span><span class="p">)</span>
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<h1 id="Take-the-fft">Take the fft<a class="anchor-link" href="#Take-the-fft">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">fft_output</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">sampled_f</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'FFT output'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'FFT bins'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">fft_output</span><span class="p">)</span>
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/usr/local/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part
return array(a, dtype, copy=False, order=order)
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<h1 id="why-is-it-symmetric">Why is it symmetric?</h1>
<ul>
<li>Because it is a complex-input fourier transform, and for real input, the 2nd half will always be a mirror image.</li>
<li>For real-valued input, the fft output is always symmetric.</li>
<li>Since we are only dealing with real input, let's just use a real-input version of the fft.</li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">rfft_output</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">sampled_f</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'rFFT output'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'frequency (in Hz)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rfft_output</span><span class="p">)</span>
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/usr/local/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part
return array(a, dtype, copy=False, order=order)
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<h1 id="get-the-x-axis-labels-correct">Get the x-axis labels correct</h1>
<h2 id="we-want-the-x-axis-to-represent-frequency">We want the x-axis to represent frequency</h2>
<p>In our DFT equation <span class="math">\[G(\frac{n}{N}) = \sum_{k=0}^{N-1} g(k) e^{-i 2 \pi k \frac{n}{N} }\]</span></p>
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<li><span class="math">\(G(\frac{n}{N})\)</span> means the DFT output for the frequency which goes through <span class="math">\(\frac{n}{N}\)</span> cycles per sample.</li>
<li>And we take frequencies from 0 to (the total number of samples divided by 2)</li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Getting frequencies on x-axis right</span>
<span class="n">rfreqs</span> <span class="o">=</span> <span class="p">[(</span><span class="n">i</span><span class="o">*</span><span class="mf">1.0</span><span class="o">/</span><span class="n">num_samples</span><span class="p">)</span><span class="o">*</span><span class="n">sample_rate</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_samples</span><span class="o">//</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">)]</span>
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<h3 id="Frequencies-range-from-0-to-the-Nyquist-Frequency-(sample-rate-/-2)">Frequencies range from 0 to the Nyquist Frequency (sample rate / 2)<a class="anchor-link" href="#Frequencies-range-from-0-to-the-Nyquist-Frequency-(sample-rate-/-2)">¶</a></h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># So you can see, our frequencies go from 0 to 5Hz. 5 is half of the sample rate,</span>
<span class="c"># which is what it should be (Nyquist Frequency).</span>
<span class="n">rfreqs</span>
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[0.0,
0.3333333333333333,
0.6666666666666666,
1.0,
1.3333333333333333,
1.6666666666666665,
2.0,
2.3333333333333335,
2.6666666666666665,
3.0,
3.333333333333333,
3.6666666666666665,
4.0,
4.333333333333334,
4.666666666666667,
5.0]
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Corrected rFFT Output'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'frequency (in Hz)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rfreqs</span><span class="p">,</span> <span class="n">rfft_output</span><span class="p">)</span>
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/usr/local/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part
return array(a, dtype, copy=False, order=order)
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<h1 id="getting-y-axis-labels-correct">Getting y-axis labels correct</h1>
<h2 id="we-want-the-y-axis-to-represent-magnitude">We want the y-axis to represent magnitude</h2>
<p>We are actually getting negative values, and it looks like our amplitude is way larger than what it should be (which is 5).</p>
<p>The magnitude of each component is:</p>
<p><span class="math">\[magnitude(i) = \frac{\sqrt{i.real^2 + i.imag^2}}{N}\]</span></p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">rfft_mag</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">real</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">i</span><span class="o">.</span><span class="n">imag</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">rfft_output</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">rfft_output</span><span class="p">]</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Corrected rFFT Output'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'frequency (in Hz)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'magnitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rfreqs</span><span class="p">,</span> <span class="n">rfft_mag</span><span class="p">)</span>
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<h1 id="inverse-fft">Inverse FFT</h1>
<p>We can take the output of the FFT and perform an Inverse FFT to get back to our original wave (using the Inverse Real FFT - irfft).</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">irfft_output</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">rfft_output</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Inverse rFFT Output'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">irfft_output</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="kn">import</span> <span class="nn">scipy.io.wavfile</span>
<span class="kn">import</span> <span class="nn">IPython</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="Seeing-sound!">Seeing sound!<a class="anchor-link" href="#Seeing-sound!">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># NOTE: This is only works with 1 channel (mono). To record a mono audio sample,</span>
<span class="c"># you can use this command: rec -r 44100 -c 1 -b 16 test.wav</span>
<span class="p">(</span><span class="n">sample_rate</span><span class="p">,</span> <span class="n">input_signal</span><span class="p">)</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">io</span><span class="o">.</span><span class="n">wavfile</span><span class="o">.</span><span class="n">read</span><span class="p">(</span><span class="s">"audio_files/vowel_ah.wav"</span><span class="p">)</span>
<span class="n">time_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">input_signal</span><span class="p">)</span><span class="o">/</span><span class="n">sample_rate</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">sample_rate</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Ah vowel sound'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time_array</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">4000</span><span class="p">],</span> <span class="n">input_signal</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">4000</span><span class="p">])</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c">#IPython.display.Audio("audio_files/vowel_ah.wav")</span>
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In [37]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">fft_out</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">input_signal</span><span class="p">)</span>
<span class="n">fft_mag</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">real</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">i</span><span class="o">.</span><span class="n">imag</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">fft_out</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">fft_out</span><span class="p">]</span>
<span class="n">num_samples</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">input_signal</span><span class="p">)</span>
<span class="n">rfreqs</span> <span class="o">=</span> <span class="p">[(</span><span class="n">i</span><span class="o">*</span><span class="mf">1.0</span><span class="o">/</span><span class="n">num_samples</span><span class="p">)</span><span class="o">*</span><span class="n">sample_rate</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_samples</span><span class="o">//</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">)]</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'FFT of Ah Vowel (first 5000)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'FFT Bins'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'magnitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rfreqs</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">5000</span><span class="p">],</span> <span class="n">fft_mag</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">5000</span><span class="p">])</span>
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<h2 id="few-notes-about-this">Few notes about this</h2>
<ul>
<li>Ratio of harmonics = <strong>timbre</strong> = This is what makes different people's voices sound different (and different from violins)
<ul>
<li>Even if they are singing the same note, and the same volume</li>
</ul></li>
<li>Possible application: synthesizing new sounds (with different harmonic profiles)
<ul>
<li>Example: If you changed the ratio of the harmonics, you could make your voice sound like something else (Darth Vader?)</li>
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<h1 id="spectrogram-fft-over-time">Spectrogram (FFT over time)</h1>
<h3 id="axes">Axes</h3>
<ul>
<li>x-axis: time</li>
<li>y-axis: frequency</li>
<li>z-axis (color): strength of each frequency</li>
</ul>
<h3 id="see-the-harmonics">See the Harmonics!</h3>
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In [38]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="p">(</span><span class="n">doremi_sample_rate</span><span class="p">,</span> <span class="n">doremi</span><span class="p">)</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">io</span><span class="o">.</span><span class="n">wavfile</span><span class="o">.</span><span class="n">read</span><span class="p">(</span><span class="s">"audio_files/do-re-mi.wav"</span><span class="p">)</span>
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In [39]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram of diatonic scale (44100Hz sample rate)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="n">doremi_sample_rate</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">doremi_8000hz</span> <span class="o">=</span> <span class="p">[</span><span class="n">doremi</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">doremi</span><span class="p">),</span> <span class="mi">44100</span><span class="o">//</span><span class="mi">8000</span><span class="p">)]</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (8000Hz sample rate)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="mi">8000</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">doremi_4000hz</span> <span class="o">=</span> <span class="p">[</span><span class="n">doremi</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">doremi</span><span class="p">),</span> <span class="mi">44100</span><span class="o">//</span><span class="mi">4000</span><span class="p">)]</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (4000Hz sample rate)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi_4000hz</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="mi">4000</span><span class="p">)</span>
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<h2 id="a-few-things-to-note">A few things to note</h2>
<ul>
<li>Something that sounds like a single note actually is made up of a bunch of harmonics</li>
<li>Harmonics are integer multiples of the <em>fundamental frequency</em></li>
<li>Notice that the spacing between the harmonics of the first note is about double of the spacing between the harmonics in the last note (1 octave difference)</li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Cleanup to reduce notebook size</span>
<span class="k">del</span> <span class="n">input_signal</span><span class="p">,</span> <span class="n">time_array</span><span class="p">,</span> <span class="n">rfreqs</span><span class="p">,</span> <span class="n">doremi</span><span class="p">,</span> <span class="n">fft_out</span><span class="p">,</span> <span class="n">fft_mag</span><span class="p">,</span> <span class="n">doremi_4000hz</span><span class="p">,</span> <span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">_</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="kn">import</span> <span class="nn">scipy.io.wavfile</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="short-time-fourier-transform-stft">Short-time Fourier Transform (STFT)</h1>
<p>Procedure:</p>
<ul>
<li>Break audio file into (overlapping) chunks</li>
<li>Apply a window to each chunk</li>
<li>Run windowed chunk through the FFT</li>
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<h1 id="Hamming-Window">Hamming Window<a class="anchor-link" href="#Hamming-Window">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">sample_rate</span> <span class="o">=</span> <span class="mi">100</span> <span class="c"># in samples per second</span>
<span class="n">total_time</span> <span class="o">=</span> <span class="mi">10</span> <span class="c"># in seconds</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">total_time</span><span class="p">,</span> <span class="n">total_time</span> <span class="o">*</span> <span class="n">sample_rate</span><span class="p">)</span>
<span class="n">original</span> <span class="o">=</span> <span class="p">[</span><span class="mi">5</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">t</span><span class="p">]</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'f(x) = 5 function'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">original</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">window_size</span> <span class="o">=</span> <span class="mi">100</span> <span class="c"># 100 points (which is 1 second in this case)</span>
<span class="n">hop_size</span> <span class="o">=</span> <span class="n">window_size</span> <span class="o">//</span> <span class="mi">2</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">window</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">hamming</span><span class="p">(</span><span class="n">window_size</span><span class="p">)</span>
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<h1 id="What-the-windows-look-like">What the windows look like<a class="anchor-link" href="#What-the-windows-look-like">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">flatten</span><span class="p">(</span><span class="n">lst</span><span class="p">):</span>
<span class="k">return</span> <span class="p">[</span><span class="n">item</span> <span class="k">for</span> <span class="n">sublist</span> <span class="ow">in</span> <span class="n">lst</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">sublist</span><span class="p">]</span>
<span class="n">window_times</span> <span class="o">=</span> <span class="p">[</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">window_size</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">original</span><span class="p">)</span><span class="o">-</span><span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)]</span>
<span class="n">window_graphs</span> <span class="o">=</span> <span class="p">[[</span><span class="n">wtime</span><span class="p">,</span> <span class="n">window</span><span class="p">]</span> <span class="k">for</span> <span class="n">wtime</span> <span class="ow">in</span> <span class="n">window_times</span><span class="p">]</span>
<span class="n">flattened_window_graphs</span> <span class="o">=</span> <span class="n">flatten</span><span class="p">(</span><span class="n">window_graphs</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Hamming windows'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">*</span><span class="n">flattened_window_graphs</span><span class="p">)</span>
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<h1 id="Break-up-into-chunks-and-apply-window">Break up into chunks and apply window<a class="anchor-link" href="#Break-up-into-chunks-and-apply-window">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">windowed</span> <span class="o">=</span> <span class="p">[</span><span class="n">window</span> <span class="o">*</span> <span class="n">original</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">window_size</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">original</span><span class="p">)</span><span class="o">-</span><span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)]</span>
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<h1 id="put-windowed-chunks-back-together-and-compare-to-original">Put windowed chunks back together (and compare to original)</h1>
<h3 id="this-is-like-what-the-inverse-stft-does">(This is like what the inverse STFT does)</h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">convoluted</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">total_time</span> <span class="o">*</span> <span class="n">sample_rate</span><span class="p">)</span>
<span class="k">for</span> <span class="n">n</span><span class="p">,</span><span class="n">i</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">original</span><span class="p">)</span><span class="o">-</span><span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)):</span>
<span class="n">convoluted</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">window_size</span><span class="p">]</span> <span class="o">+=</span> <span class="n">windowed</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Resynthesized windowed parts (vs original)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">original</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">convoluted</span><span class="p">)</span>
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<h1 id="STFT-Code">STFT Code<a class="anchor-link" href="#STFT-Code">¶</a></h1>
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In [59]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">stft</span><span class="p">(</span><span class="n">input_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">):</span>
<span class="n">window</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">hamming</span><span class="p">(</span><span class="n">window_size</span><span class="p">)</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">scipy</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">window</span><span class="o">*</span><span class="n">input_data</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">window_size</span><span class="p">])</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">input_data</span><span class="p">)</span><span class="o">-</span><span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)])</span>
<span class="k">return</span> <span class="n">output</span>
<span class="k">def</span> <span class="nf">istft</span><span class="p">(</span><span class="n">input_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">,</span> <span class="n">total_time</span><span class="p">):</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">total_time</span><span class="o">*</span><span class="n">sample_rate</span><span class="p">)</span>
<span class="k">for</span> <span class="n">n</span><span class="p">,</span><span class="n">i</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">output</span><span class="p">)</span><span class="o">-</span><span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)):</span>
<span class="n">output</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">window_size</span><span class="p">]</span> <span class="o">+=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">scipy</span><span class="o">.</span><span class="n">ifft</span><span class="p">(</span><span class="n">input_data</span><span class="p">[</span><span class="n">n</span><span class="p">]))</span>
<span class="k">return</span> <span class="n">output</span>
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<h1 id="spectrogram">Spectrogram</h1>
<h3 id="the-frequencytime-uncertainty-principle">The Frequency/Time Uncertainty principle</h3>
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In [60]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="p">(</span><span class="n">doremi_sample_rate</span><span class="p">,</span> <span class="n">doremi</span><span class="p">)</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">io</span><span class="o">.</span><span class="n">wavfile</span><span class="o">.</span><span class="n">read</span><span class="p">(</span><span class="s">"audio_files/do-re-mi.wav"</span><span class="p">)</span>
<span class="n">doremi_8000hz</span> <span class="o">=</span> <span class="p">[</span><span class="n">doremi</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">doremi</span><span class="p">),</span> <span class="mi">44100</span><span class="o">//</span><span class="mi">8000</span><span class="p">)]</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (window size = 256)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="mi">8000</span><span class="p">,</span> <span class="n">NFFT</span><span class="o">=</span><span class="mi">256</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (window size = 512)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="mi">8000</span><span class="p">,</span> <span class="n">NFFT</span><span class="o">=</span><span class="mi">512</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (window size = 1024)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="mi">8000</span><span class="p">,</span> <span class="n">NFFT</span><span class="o">=</span><span class="mi">1024</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (window size = 2048)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="mi">8000</span><span class="p">,</span> <span class="n">NFFT</span><span class="o">=</span><span class="mi">2048</span><span class="p">)</span>
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In [64]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (window size = 8000)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="mi">8000</span><span class="p">,</span> <span class="n">NFFT</span><span class="o">=</span><span class="mi">8000</span><span class="p">)</span>
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<h2 id="meaning">Meaning</h2>
<ul>
<li>So we see that as we take more samples for each FFT, we know more about the frequency</li>
<li>But since we are taking more samples to represent each "block", the time resolution goes down (since the time block is larger)</li>
</ul>
<h2 id="fft-bin-size">FFT Bin Size</h2>
<p><span class="math">\[fft\ bin\ size = \frac{sample\ rate}{window\ size}\]</span></p>
<ul>
<li>So the larger the window size, the smaller the fft bin size (better frequency resolution)</li>
<li>And the smaller the window size, the larger the fft bin size (worse frequency resolution)</li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Cleanup to reduce notebook size</span>
<span class="k">del</span> <span class="n">doremi</span><span class="p">,</span> <span class="n">doremi_8000hz</span><span class="p">,</span> <span class="n">_</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="kn">import</span> <span class="nn">scipy.io.wavfile</span>
<span class="kn">import</span> <span class="nn">IPython</span>
<span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
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<h1 id="audio-filtering">Audio Filtering</h1>
<p>Procedure:</p>
<ul>
<li>Read in audio</li>
<li>Apply STFT (Window and FFT)</li>
<li>Remove a range of frequencies we want out</li>
<li>Apply Inverse STFT (to resynthesize)</li>
<li>Write new audio</li>
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<h1 id="Functions">Functions<a class="anchor-link" href="#Functions">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">stft</span><span class="p">(</span><span class="n">input_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">):</span>
<span class="n">window</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">hamming</span><span class="p">(</span><span class="n">window_size</span><span class="p">)</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">scipy</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">window</span><span class="o">*</span><span class="n">input_data</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">window_size</span><span class="p">])</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">input_data</span><span class="p">)</span><span class="o">-</span><span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)])</span>
<span class="k">return</span> <span class="n">output</span>
<span class="k">def</span> <span class="nf">istft</span><span class="p">(</span><span class="n">input_data</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">,</span> <span class="n">total_time</span><span class="p">):</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">total_time</span><span class="o">*</span><span class="n">sample_rate</span><span class="p">)</span>
<span class="k">for</span> <span class="n">n</span><span class="p">,</span><span class="n">i</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">output</span><span class="p">)</span><span class="o">-</span><span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)):</span>
<span class="n">output</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">window_size</span><span class="p">]</span> <span class="o">+=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">scipy</span><span class="o">.</span><span class="n">ifft</span><span class="p">(</span><span class="n">input_data</span><span class="p">[</span><span class="n">n</span><span class="p">]))</span>
<span class="k">return</span> <span class="n">output</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">low_pass_filter</span><span class="p">(</span><span class="n">max_freq</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">):</span>
<span class="n">fft_bin_width</span> <span class="o">=</span> <span class="n">sample_rate</span> <span class="o">/</span> <span class="n">window_size</span>
<span class="n">max_freq_bin</span> <span class="o">=</span> <span class="n">max_freq</span> <span class="o">/</span> <span class="n">fft_bin_width</span>
<span class="n">filter_block</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">window_size</span><span class="p">)</span>
<span class="n">filter_block</span><span class="p">[</span><span class="n">max_freq_bin</span><span class="p">:(</span><span class="n">window_size</span><span class="o">-</span><span class="n">max_freq_bin</span><span class="p">)]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">return</span> <span class="n">filter_block</span>
<span class="k">def</span> <span class="nf">high_pass_filter</span><span class="p">(</span><span class="n">min_freq</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">):</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">window_size</span><span class="p">)</span> <span class="o">-</span> <span class="n">low_pass_filter</span><span class="p">(</span><span class="n">min_freq</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">write_audio_file</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="n">filedata</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">):</span>
<span class="n">scipy</span><span class="o">.</span><span class="n">io</span><span class="o">.</span><span class="n">wavfile</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">filedata</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">filter_audio</span><span class="p">(</span><span class="n">input_signal</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">filter_window</span><span class="p">,</span> <span class="n">window_size</span><span class="o">=</span><span class="mi">256</span><span class="p">):</span>
<span class="c"># Setting parameters</span>
<span class="n">hop_size</span> <span class="o">=</span> <span class="n">window_size</span> <span class="o">//</span> <span class="mi">2</span>
<span class="n">total_time</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">input_signal</span><span class="p">)</span> <span class="o">/</span> <span class="n">sample_rate</span>
<span class="c"># Do actual filtering</span>
<span class="n">stft_output</span> <span class="o">=</span> <span class="n">stft</span><span class="p">(</span><span class="n">input_signal</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">)</span>
<span class="n">filtered_result</span> <span class="o">=</span> <span class="p">[</span><span class="n">original</span> <span class="o">*</span> <span class="n">filter_window</span> <span class="k">for</span> <span class="n">original</span> <span class="ow">in</span> <span class="n">stft_output</span><span class="p">]</span>
<span class="n">resynth</span> <span class="o">=</span> <span class="n">istft</span><span class="p">(</span><span class="n">filtered_result</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">hop_size</span><span class="p">,</span> <span class="n">total_time</span><span class="p">)</span>
<span class="k">return</span> <span class="n">resynth</span>
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<h1 id="Perform-filtering">Perform filtering<a class="anchor-link" href="#Perform-filtering">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">infile</span> <span class="o">=</span> <span class="s">"audio_files/ohm_scale.wav"</span>
<span class="n">outfile</span> <span class="o">=</span> <span class="s">"audio_files/high_pass_out.wav"</span>
<span class="n">window_size</span> <span class="o">=</span> <span class="mi">256</span>
<span class="c"># Input</span>
<span class="p">(</span><span class="n">sample_rate</span><span class="p">,</span> <span class="n">input_signal</span><span class="p">)</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">io</span><span class="o">.</span><span class="n">wavfile</span><span class="o">.</span><span class="n">read</span><span class="p">(</span><span class="n">infile</span><span class="p">)</span>
<span class="c"># Create filter window</span>
<span class="n">filter_window</span> <span class="o">=</span> <span class="n">high_pass_filter</span><span class="p">(</span><span class="mi">2500</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">)</span>
<span class="c"># Run filter</span>
<span class="n">resynth</span> <span class="o">=</span> <span class="n">filter_audio</span><span class="p">(</span><span class="n">input_signal</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">filter_window</span><span class="p">,</span> <span class="n">window_size</span><span class="p">)</span>
<span class="c"># Output</span>
<span class="n">write_audio_file</span><span class="p">(</span><span class="n">outfile</span><span class="p">,</span> <span class="n">resynth</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">)</span>
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/usr/local/lib/python3.5/site-packages/ipykernel/__main__.py:5: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
/usr/local/lib/python3.5/site-packages/ipykernel/__main__.py:8: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
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<h1 id="Results">Results<a class="anchor-link" href="#Results">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c">#IPython.display.Audio("audio_files/ohm_scale.wav")</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c">#IPython.display.Audio("audio_files/high_pass_out.wav")</span>
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<h2 id="Spectrogram-Before">Spectrogram Before<a class="anchor-link" href="#Spectrogram-Before">¶</a></h2>
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In [86]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (Before)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">input_signal</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="n">sample_rate</span><span class="p">)</span>
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<h2 id="Spectrogram-After">Spectrogram After<a class="anchor-link" href="#Spectrogram-After">¶</a></h2>
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In [87]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Spectrogram (After)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'frequency'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">specgram</span><span class="p">(</span><span class="n">resynth</span><span class="p">,</span> <span class="n">Fs</span><span class="o">=</span><span class="n">sample_rate</span><span class="p">)</span>
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<h2 id="Sound-Wave-Before">Sound Wave Before<a class="anchor-link" href="#Sound-Wave-Before">¶</a></h2>
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In [88]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Sound wave (Before)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">input_signal</span><span class="p">)</span>
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<h2 id="Sound-Wave-After">Sound Wave After<a class="anchor-link" href="#Sound-Wave-After">¶</a></h2>
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In [89]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Sound wave (After)'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'time (in seconds)'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">7</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">resynth</span><span class="p">)</span>
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<h1 id="A-low-pass-filter-example">A low-pass filter example<a class="anchor-link" href="#A-low-pass-filter-example">¶</a></h1>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">infile</span> <span class="o">=</span> <span class="s">"audio_files/doremi_xylo.wav"</span>
<span class="n">outfile</span> <span class="o">=</span> <span class="s">"audio_files/low_pass_out.wav"</span>
<span class="n">window_size</span> <span class="o">=</span> <span class="mi">256</span>
<span class="c"># Input</span>
<span class="p">(</span><span class="n">sample_rate</span><span class="p">,</span> <span class="n">input_signal</span><span class="p">)</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">io</span><span class="o">.</span><span class="n">wavfile</span><span class="o">.</span><span class="n">read</span><span class="p">(</span><span class="n">infile</span><span class="p">)</span>
<span class="c"># Create filter window</span>
<span class="n">filter_window</span> <span class="o">=</span> <span class="n">low_pass_filter</span><span class="p">(</span><span class="mi">1700</span><span class="p">,</span> <span class="n">window_size</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">)</span>
<span class="c"># Run filter</span>
<span class="n">resynth</span> <span class="o">=</span> <span class="n">filter_audio</span><span class="p">(</span><span class="n">input_signal</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">,</span> <span class="n">filter_window</span><span class="p">,</span> <span class="n">window_size</span><span class="p">)</span>
<span class="c"># Output</span>
<span class="n">write_audio_file</span><span class="p">(</span><span class="n">outfile</span><span class="p">,</span> <span class="n">resynth</span><span class="p">,</span> <span class="n">sample_rate</span><span class="p">)</span>
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/usr/local/lib/python3.5/site-packages/ipykernel/__main__.py:5: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
/usr/local/lib/python3.5/site-packages/ipykernel/__main__.py:8: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c">#IPython.display.Audio("audio_files/doremi_xylo.wav")</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c">#IPython.display.Audio("audio_files/low_pass_out.wav")</span>
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<h3 id="Notice-that-in-the-after-example,-you-can-hear-the-xylophone-mallet,-but-not-the-keys">Notice that in the after example, you can hear the xylophone mallet, but not the keys<a class="anchor-link" href="#Notice-that-in-the-after-example,-you-can-hear-the-xylophone-mallet,-but-not-the-keys">¶</a></h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">del</span> <span class="n">input_signal</span><span class="p">,</span> <span class="n">filter_window</span><span class="p">,</span> <span class="n">resynth</span><span class="p">,</span> <span class="n">_</span>
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<h1 id="conclusion">Conclusion</h1>
<h3 id="we-looked-at">We looked at:</h3>
<ul>
<li>The Nature of Waves</li>
<li>The Fourier Transform</li>
<li>Fast Fourier Transform (FFT) in Python</li>
<li>Audio analysis</li>
</ul>
<h3 id="caveat">Caveat</h3>
<ul>
<li>Audio analysis is difficult (mainly due to harmonics)</li>
</ul>
<h1 id="my-contact-info">My contact info</h1>
<ul>
<li>http://calebmadrigal.com</li>
<li>http://github.com/calebmadrigal</li>
</ul>
<h1 id="questions">Questions?</h1>
</div>
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</div></p>Hackers are the new lawyers2016-05-06T12:30:00-05:00Caleb Madrigaltag:calebmadrigal.com,2016-05-06:hackers-are-the-new-lawyers/<p><strong>Hackers are the new Lawyers are the new Knights.</strong></p>
<p>Back in the feudal days, Lords had Knights to protect them and their possessions from enemies (or to attack their neighbors and plunder their wealth).</p>
<p>In the business world today, lawyers are much like the knights of old. Companies can attack each other with the law, and lawyers are both the attacker and defenders.</p>
<p>In the increasingly computerized world, business are hacking each other to steal their Intellectual Property, understand their strategy, and sometimes, take them down all together (like what happened to <a href="https://en.wikipedia.org/wiki/HBGary">HBGary</a>, though that wasn't caused by another company). Today, these tactics are employed mostly by Chinese companies hacking competitors in other countries, but as multinational corporations continue to grow in power, this tactic might become more ubiquitous. Imagine a world where corporations grow more powerful than governments... cyber attacks might become as common as legal attacks, if there is no government with enough power to catch them or stop them.</p>
<p>In today's world, and very likely even more so in the future, business that have no cyber-firepower will be analogous to peaceful farming villages in the feudal days who had no military capacity, just waiting to be attacked by their militarily superior neighbors.</p>HackRF Replay Attack Jeep2016-04-18T00:20:00-05:00Caleb Madrigaltag:calebmadrigal.com,2016-04-18:hackrf-replay-attack-jeep/<p>I've recently been getting into <a href="https://en.wikipedia.org/wiki/Software-defined_radio">Software-defined Radio</a> (SDR), mostly using a <a href="https://greatscottgadgets.com/hackrf/">HackRF</a> - a radio tranceiver capable of operating from 1MHz to 6GHz (which is a huge range).</p>
<p>One of the most simple (and most interesting attacks) which can be done with SDR is what's called a <a href="https://en.wikipedia.org/wiki/Replay_attack">Replay Attack</a>. It works by simply recording a signal, and then rebroadcasting it. I was able to use this attack to lock and unlock my Jeep Patriot (2006) with my computer. Here's how...</p>
<p>First I recorded the "unlock" and "lock" signals from my <a href="https://en.wikipedia.org/wiki/Remote_keyless_system">keyless entry remote</a> using this "flowgraph" in Gnu Radio Companion:</p>
<p><img alt="Record flowgraph" src="/images/hackrf_replay_attack_jeep/record_flowgraph.png" /></p>
<p>A couple things to note about this flow graph:</p>
<ul>
<li>The frequency is 315 MHz (the frequency at which pretty much all keyless entry)</li>
<li>It records at 2 million samples per second (a piece of data needed for importing into Audacity later)</li>
<li>It saves to this file, 'radio_signal.dat'</li>
<li>It also shows a "waterfall graph" of what it is recording</li>
</ul>
<p>Here is what the waterfall graph of the recording looks like. This is first the "unlock" signal, followed by the "lock" signal:</p>
<p><img alt="Unlock and lock signals waterfall" src="/images/hackrf_replay_attack_jeep/unlock_lock_signals_waterfall.png" /></p>
<p>Now I could simply replay this recording in order to execute a replay attack. But wanted to explore these signals in a bit more detail. So I decided to try to trim them down using <a href="http://www.audacityteam.org/">Audacity</a>. Though Audacity is primarily intended as sound editing software, it can also be used for editing the wave forms of radio signals (which is pretty awesome! Waves are just waves, whether transmitted by sound or radio). I won't go into too many details here, but you can learn more about importing/editing/exporting radio signals in Audacity here: <a href="http://calebmadrigal.com/editing-radio-signals-with-audacity/">http://calebmadrigal.com/editing-radio-signals-with-audacity/</a>.</p>
<p>Here is what the "unlock" and "lock" signals look like in Audacity:</p>
<p><img alt="View signals in audacity" src="/images/hackrf_replay_attack_jeep/audacity_signals1.png" /></p>
<p>So here, you can clearly see the 2 distinct signals: first Unlock, then Lock. From here, I can select and export each of the signals to different files...</p>
<p><img alt="Export signals in audacity" src="/images/hackrf_replay_attack_jeep/audacity_signals2.png" /></p>
<p>So then I had 2 raw signal files:</p>
<div class="highlight"><pre><span class="n">cmbpr</span><span class="o">:</span><span class="n">gnu_radio</span> <span class="n">caleb$</span> <span class="n">ls</span> <span class="o">-</span><span class="n">lh</span> <span class="o">|</span><span class="n">grep</span> <span class="n">raw</span>
<span class="o">-</span><span class="n">rw</span><span class="o">-</span><span class="n">r</span><span class="o">--</span><span class="n">r</span><span class="o">--</span><span class="err">@</span> <span class="mi">1</span> <span class="n">caleb</span> <span class="n">staff</span> <span class="mi">11</span><span class="n">M</span> <span class="n">Apr</span> <span class="mi">16</span> <span class="mi">11</span><span class="o">:</span><span class="mi">09</span> <span class="n">jeep_lock</span><span class="o">.</span><span class="na">raw</span>
<span class="o">-</span><span class="n">rw</span><span class="o">-</span><span class="n">r</span><span class="o">--</span><span class="n">r</span><span class="o">--</span><span class="err">@</span> <span class="mi">1</span> <span class="n">caleb</span> <span class="n">staff</span> <span class="mi">10</span><span class="n">M</span> <span class="n">Apr</span> <span class="mi">16</span> <span class="mi">11</span><span class="o">:</span><span class="mi">09</span> <span class="n">jeep_unlock</span><span class="o">.</span><span class="na">raw</span>
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<p>Note that even after trimming these down, the files are still ~10Mb each.</p>
<p>Finally, the last step was to create a flowgraph to transmit each of the messages. It looked like this:</p>
<p><img alt="Replay flowgraph" src="/images/hackrf_replay_attack_jeep/replay_flowgraph.png" /></p>
<p>In order to make nice command-line scripts, I just modified the <code>top_block.py</code> script which gnuradio-companion outputs, and had one (<code>jeep_unlock.py</code>) transmit the <code>jeep_unlock.raw</code> file, and the other (<code>lock_jeep.py</code>) transmit the <code>jeep_lock.raw</code> file.</p>
<p>Here is a video showing me using these 2 scripts to unlock and lock the jeep:</p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/Q-OlgVLHIDs" frameborder="0" allowfullscreen></iframe>Editing radio signals with Audacity2016-04-18T00:10:00-05:00Caleb Madrigaltag:calebmadrigal.com,2016-04-18:editing-radio-signals-with-audacity/<p>You can capture radio signals with <a href="https://en.wikipedia.org/wiki/Software-defined_radio">Software-defined Radios</a> (SDR), such as the <a href="https://greatscottgadgets.com/hackrf/">HackRF</a>. <a href="https://en.wikipedia.org/wiki/GNU_Radio">Gnu Radio</a> is the main software I use for receiving and transmitting radio signals, but I've found <a href="http://www.audacityteam.org/">Audacity</a>, a program meant primarily for editing sound files, to be a great program for viewing and editing radio signals.</p>
<p>So I had these remote-controlled outlets (which I bought at Home Depot):</p>
<p><img alt="Remote-controlled outlets" src="/images/editing_radio_signals_with_audacity/remote_controlled_outlets.jpg" /></p>
<p>And I wanted to see what their wireless communication looked like...</p>
<p>So first I recorded the signals of the different outlets with this Gnu Radio Companion flowgraph:</p>
<p><img alt="Record flowgraph" src="/images/editing_radio_signals_with_audacity/record_flowgraph.png" /></p>
<p>A few things to note about this flowgraph:</p>
<ul>
<li>It records at around 315 MHz, the frequency at which the remote transmits (which I found by looking up it's FCC ID code online)</li>
<li>It records 2 million samples per second (something needed for importing into Audacity)</li>
<li>It saves the radio signals to a file - <code>/tmp/radio_signal.dat</code></li>
</ul>
<p>I recorded the signal sent by the remote control for both ON and OFF for each of the 3 outlets (so a total of 6 signals).</p>
<h2>Viewing radio signals in Audacity</h2>
<p>The next step was to import the signals into Audacity like this:</p>
<p>Go to <code>File</code> -> <code>Import</code> -> <code>Raw Data...</code>:</p>
<p><img alt="Audacity import 1" src="/images/editing_radio_signals_with_audacity/audacity_import1.png" /></p>
<p>Make sure the sample rate is set to <code>2000000</code> (2 million samples per second), to match the rate at which it was recorded. I also found it's best to set the channels to 1 - Mono. It's also important to set the Encoding (32-bit float in my case) and Byte order (Little endian on Intel) correctly.</p>
<p><img alt="Audacity import 2" src="/images/editing_radio_signals_with_audacity/audacity_import2.png" /></p>
<p>I was then able to see the waves of the signals in Audacity:</p>
<p><img alt="Audacity signal 1" src="/images/editing_radio_signals_with_audacity/audacity_signal1.png" /></p>
<p>Or zooming in:</p>
<p><img alt="Audacity signal 2" src="/images/editing_radio_signals_with_audacity/audacity_signal2.png" /></p>
<p>Further zooming in, I could finally see the individual bits being transmitted:</p>
<p><img alt="Remote channel 1 on signal blob 1" src="/images/editing_radio_signals_with_audacity/remote_chan1_on_blob1.png" /></p>
<p>So this signal is transmitted with what is called <a href="https://en.wikipedia.org/wiki/On-off_keying">On-Off Keying</a>, which is what almost all wireless devices use to communicate. It just transmits signals by sending long or short pulses - just like <a href="https://en.wikipedia.org/wiki/Morse_code">morse code</a>.</p>
<p>I found that the signals sent always start with a long "on", followed by the signal repeated again and again. Here is the "off" signal for outlet 2:</p>
<p><img alt="Remote channel 1 off signal blob 1 and 2" src="/images/editing_radio_signals_with_audacity/remote_chan1_off_blob12.png" /></p>
<p>So here, you can see that the first group has the long "on" followed by a pattern, and that pattern is repeated a 2nd time in the other group.</p>
<p>Eventually, analyzed all 6 signals (3 on signals and 3 off signals), and found that the data transmitted by the remote looks like this:</p>
<div class="highlight"><pre>Channel 1 ON: 0 110 10 0 0 10 0 0 0 0 0 0
Channel 1 OFF: 0 110 10 0 0 0 10 0 0 0 0 0
Channel 2 ON: 0 110 10 0 0 0 0 10 0 0 0 0
Channel 2 OFF: 0 110 10 0 0 0 0 0 10 0 0 0
Channel 3 ON: 0 110 10 0 10 0 0 0 0 0 0 0
Channel 3 OFF: 0 110 10 10 0 0 0 0 0 0 0 0
</pre></div>
<p>Pretty intersting. It looks very possible to brute force :)</p>
<h2>Editing and exporting radio signals with Audacity</h2>
<p>Now, if you want to edit radio signals, that works well in Audacity as well. The only thing I've found this useful for is isolating the signal I'm interested in and saving that to a separate file (like for transmitting later). Here's how to do it:</p>
<p>Select the signal you want to isolate:</p>
<p><img alt="Audacity save signal 1" src="/images/editing_radio_signals_with_audacity/audacity_save_signal1.png" /></p>
<p>Select the format, "Other uncompressed files", and then click the "Options" button...</p>
<p><img alt="Audacity save signal 2" src="/images/editing_radio_signals_with_audacity/audacity_save_signal2.png" /></p>
<p>Select <code>Header</code> to be <code>Raw (header-less)</code> and <code>Encoding</code> to be <code>32 bit float</code>:</p>
<p><img alt="Audacity save signal 3" src="/images/editing_radio_signals_with_audacity/audacity_save_signal3.png" /></p>
<p>And finally, don't set any metadata. And click Ok:</p>
<p><img alt="Audacity save signal 4" src="/images/editing_radio_signals_with_audacity/audacity_save_signal4.png" /></p>
<p>The file this outputs can then be used as an input to a Gnu Radio Companion flowgraph.</p>HackRF Setup OSX 20162016-04-17T22:00:00-05:00Caleb Madrigaltag:calebmadrigal.com,2016-04-17:hackrf-setup-osx-2016/<p>These are some pretty raw notes I took while installing the software for using a HackRF on OSX. This is the software I installed:</p>
<ul>
<li>Gnu Radio (which comes with Gnu Radio Companion)</li>
<li>Osmocom Gnu Radio Blocks</li>
<li>gqrx</li>
</ul>
<h2>Gnu Radio Installation</h2>
<h3>Installed gnuradio via Homebrew</h3>
<div class="highlight"><pre>brew update
brew tap robotastic/homebrew-hackrf
brew install gnuradio --with-qt
brew install hackrf
brew install --HEAD rtlsdr
brew link --overwrite rtlsdr
</pre></div>
<p>This got GNU Radio and GNU Radio Companion installed, but then I needed to install the Osmocom Gnu Radio Blocks so that Gnu Radio could communicate with the HackRF.</p>
<h2>Installing Osmocom Gnu Radio Blocks</h2>
<p>This didn't work:</p>
<div class="highlight"><pre>brew install --HEAD gr-osmosdr
</pre></div>
<p>Build with directions here: <a href="http://sdr.osmocom.org/trac/wiki/GrOsmoSDR">http://sdr.osmocom.org/trac/wiki/GrOsmoSDR</a></p>
<p>Had to add this to /Users/caleb/Documents/gnu_radio/repos/gr-osmosdr/lib/redpitaya/redpitaya_sink_c.cc</p>
<div class="highlight"><pre>#ifndef MSG_NOSIGNAL
#define MSG_NOSIGNAL 0x0 //Don't request NOSIGNAL on systems where this is not implemented.
#endif
</pre></div>
<p>Find python library path:</p>
<div class="highlight"><pre>sudo find /usr -iname libpython*.dylib
# Found python dylib at: /usr/local/Cellar/python/2.7.11/Frameworks/Python.framework/Versions/2.7/lib/libpython2.7.dylib
</pre></div>
<p>Use this library path to build <code>gr-osmosdr</code>:</p>
<div class="highlight"><pre>mkdir build
cd build/
cmake -DPYTHON_LIBRARY=/usr/local/Cellar/python/2.7.11/Frameworks/Python.framework/Versions/2.7/lib/libpython2.7.dylib ../
</pre></div>
<p>Got warning: MACOSX_RPATH is not specified for the following targets: gnuradio-osmosdr</p>
<p>Install it:</p>
<div class="highlight"><pre>make
sudo make install
sudo ldconfig
</pre></div>
<p>At some point, I tried this command to install a collection of Gnu Radio Companion Blocks. I don't remember the result:</p>
<div class="highlight"><pre>brew install gr-baz --HEAD
</pre></div>
<h5>Add config for osmocom blocks:</h5>
<p>Create the ~/.gnuradio/config.conf config file for custom block support and add this into it</p>
<div class="highlight"><pre><span class="k">[grc]</span>
<span class="na">local_blocks_path</span><span class="o">=</span><span class="s">/usr/local/share/gnuradio/grc/blocks</span>
</pre></div>
<h2>Install gqrx</h2>
<p>Installed gqrx with installer from here: <a href="http://gqrx.dk/download">http://gqrx.dk/download</a></p>
<h2>Other Resources</h2>
<p>I found this guide helpful: <a href="https://github.com/robotastic/homebrew-hackrf">https://github.com/robotastic/homebrew-hackrf</a></p>Raspberry Pi Home Security System2016-04-08T23:50:00-05:00Caleb Madrigaltag:calebmadrigal.com,2016-04-08:raspberry-pi-home-security-system/<p>3 Years ago (2013), I built my own home security/automation system with a <a href="https://www.raspberrypi.org/">Raspberry Pi</a>. Here's what it looks like:</p>
<p><img alt="Raspberry Pi Home Security System" src="/images/rpi_security_system/rpi_security_system_complete.jpg" /></p>
<h3>What it does</h3>
<ul>
<li>Allows controlling a couple outlets via a mobile web app</li>
<li>Alarm system enabled/disabled via mobile web app</li>
<li>If alarm enabled, magnetic door sensor would trigger siren and turn on outlets</li>
</ul>
<h3>Hardware used</h3>
<ul>
<li>Raspberry Pi - $35<ul>
<li>Edimax EW-7811Un 150Mbps 11n Wi-Fi USB Adapter - $10</li>
</ul>
</li>
<li>Off-the-shelf remote controlled outlet kit - $20</li>
<li>Off-the-shelf wireless magnetic door sensor/outlet - $25</li>
<li>Car siren - $8</li>
<li>Breadboard, transistors, photoresistor, resistors, wires, soldering iron</li>
</ul>
<p>Total cost of parts: ~$115</p>
<h3>Software used</h3>
<p>I wrote the controller software in Python (with ZeroMQ, Flask, Rpi.GPIO, and jQuery Mobile): <a href="https://github.com/calebmadrigal/rpi-home-automation">https://github.com/calebmadrigal/rpi-home-automation</a>.</p>
<p>It's made of up 3 components:</p>
<ul>
<li><a href="https://github.com/calebmadrigal/rpi-home-automation/blob/master/web_controller.py">Web Controller</a><ul>
<li>This serves a jQuery Mobile front end which allows enabling/disabling the alarm system, and turning on/off outlets.</li>
<li>When the user takes an action, the Web Controller sends a message to the Master Controller via ZeroMQ.</li>
</ul>
</li>
<li><a href="https://github.com/calebmadrigal/rpi-home-automation/blob/master/master_controller.py">Master Controller</a><ul>
<li>The Master Controller handles turning on/off outlets, listening for input from the door sensor, sounding the alarm (if the door sensor is tripped and alarm mode is enabled), and sending notifications (via email).</li>
<li>Whenever an outlet needs to be turned on, the Master Controller sends a message to the GPIO Helper via ZeroMQ.</li>
</ul>
</li>
<li><a href="https://github.com/calebmadrigal/rpi-home-automation/blob/master/gpio_helper.py">GPIO Helper</a><ul>
<li>The GPIO Helper is a process whose sole responsibility is turning outlets on or off. As it turns out, the remote controller must have its switches "pressed" for about 1 second, so the GPIO helper will turn the correct GPIO pin ON, sleep for a second, and then turn it back off.</li>
</ul>
</li>
</ul>
<h3>Development pictures</h3>
<p>Unopened remote-controlled outlet kit</p>
<p><img alt="Unopened remote-controlled outlet kit" src="/images/rpi_security_system/rpi_security_system_01.jpg" /></p>
<p>Remote controller</p>
<p><img alt="Remote controller" src="/images/rpi_security_system/rpi_security_system_02.jpg" /></p>
<p>Board taken out of remote controller</p>
<p><img alt="Board taken out of remote controller" src="/images/rpi_security_system/rpi_security_system_03.jpg" /></p>
<p>Board taken out of remote controller 2</p>
<p><img alt="Board taken out of remote controller 2" src="/images/rpi_security_system/rpi_security_system_04.jpg" /></p>
<p>Initial hookup between Raspberry Pi and remote controller board</p>
<p><img alt="Raspberry pi remote controller hookup" src="/images/rpi_security_system/rpi_security_system_05.jpg" /></p>
<p>Tactile buttons removed from remote</p>
<p><img alt="Tactile buttons removed from remote" src="/images/rpi_security_system/rpi_security_system_06.jpg" /></p>
<p>Here, I soldered wires on to the remote controller board. At this point, connecting each of these sets of wires closes the circuit in the same way the tactile switches used to.</p>
<p><img alt="Soldered remote controller board" src="/images/rpi_security_system/rpi_security_system_07.jpg" /></p>
<p>Transistors added to connect soldered wires. So now, these transistors function like the tactile switches used to. But now, they can be controlled by applying current to the transistor, rather than pressing a button.</p>
<p><img alt="Transistors to connect soldered wires" src="/images/rpi_security_system/rpi_security_system_08.jpg" /></p>
<p>Finished system to hook the Raspberry Pi up to the remote controller board via the breadboard, with transistors and resistors. The Raspberry Pi GPIO pins are used to switch on the transistors, which, in turn, tell the remote to send out a radio signal to turn on the appropriate outlet.</p>
<p><img alt="Finished phase 1" src="/images/rpi_security_system/rpi_security_system_09.jpg" /></p>
<p>At this point, I was able to control the 3 switches (one was hooked up to the siren) via a web app:</p>
<p><img alt="Web app" src="/images/rpi_security_system/rpi_web_ui.png" /></p>
<p>Then it was time for phase 2: to add the door sensor as an input to the Raspberry Pi...</p>
<p>Unopened door sensor/outlet kit.</p>
<p>The kit included a magnetic door sensor, and an outlet which would be turned on when the sensor was tripped. For my purposes, I didn't want the outlet itself, but the LED on the front of it, as an input to the Raspberry Pi. I used a photoresistor in order to "see" when the LED turned on, which indicated the door sensor was tripped.</p>
<p><img alt="Door sensor kit" src="/images/rpi_security_system/door_sensor_01.jpg" /></p>
<p>Testing out reading the photoresistor as an input to the Raspberry Pi</p>
<p><img alt="Photoresistor input test" src="/images/rpi_security_system/door_sensor_02.jpg" /></p>
<p>Here's a video of it:</p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/eReBJl7te-A" frameborder="0" allowfullscreen></iframe>
<p>And here, you can see how it looked to hook up the photoresistor (taped to the door sensor outlet) hooked up to a Raspberry Pi GPIO pin. Another (output) GPIO pin is hooked up a buzzer.</p>
<p><img alt="Door sensor to raspberry pi" src="/images/rpi_security_system/door_sensor_03.jpg" /></p>
<p>Failed test video:</p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/UOkjU6mefhI" frameborder="0" allowfullscreen></iframe>
<p>Successful door sensor test video:</p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/gmZ8WKGPcrA" frameborder="0" allowfullscreen></iframe>
<p>Here's the diagram of how the door sensor was hooked up to the Raspberry Pi:</p>
<p><img alt="Door sensor diagram" src="/images/rpi_security_system/door_trigger_diagram.jpg" /></p>
<p>And again, this is what the finished product looked like:</p>
<p><img alt="Raspberry Pi Home Security System" src="/images/rpi_security_system/rpi_security_system_complete.jpg" /></p>
<p>In the 3 years since I built this, some really nice, low-cost home automation/security systems have come out like <a href="http://www.wink.com/">Wink</a> and <a href="https://www.smartthings.com/">SmartThings</a>. If I wanted a home automation/security system today, I probably wouldn't take this approach; but at the time, I wanted a low-cost system, and I wanted something cool to do with a Raspberry Pi.</p>
<p>For me, this project was a very cool exercise in learning how to control the physical world with code. I loved the feeling of nobody holding my hand, giving me an API, etc. It's a cool feeling hacking hardware into something which I could control with Python code! And it worked out well: 3 years after building it, it's still running as I write this.</p>
<p>Key take-away:</p>
<ul>
<li>Most functions of electronic devices are ultimately controlled by closing some simple contact. Sometimes these are controlled by a tactile switch, sometimes by other things. Either way, it's pretty easy to hack them in a way where you can control them with a computer by using a transistor or relay.</li>
</ul>DNS Tunneling with Iodine2015-10-18T01:20:00-05:00Caleb Madrigaltag:calebmadrigal.com,2015-10-18:dns-tunneling-with-iodine/<p>DNS Tunneling can be useful for getting out of a very restrictive corporate firewall (since almost nobody blocks DNS).</p>
<p>DNS Tunneling works by encoding IP protocol inside of DNS packets. <a href="http://code.kryo.se/iodine/">Iodine</a> is a cross-platform implementation of DNS Tunneling. This mini-guide will walk through the process of setting up a DNS Tunnel with Iodine.</p>
<p><strong>Prerequisite: You will need a server with public IP and domain name</strong></p>
<h2>Setup DNS Tunnel</h2>
<h3>Setup DNS Records</h3>
<p>Add 2 DNS records to your domain's DNS system:</p>
<div class="highlight"><pre>* `<span class="n">A</span> <span class="n">record</span>`: <span class="n">tunnelhost</span> -> <span class="n">your</span> <span class="n">ip</span> (<span class="n">maps</span> <span class="n">tunnelhost</span>.<span class="n">yourdomain</span>.<span class="n">com</span> <span class="nb">to</span> <span class="n">your</span> <span class="n">server's</span> <span class="n">ip</span>)
* `<span class="n">NS</span> <span class="n">record</span>`: <span class="n">tunnel</span> -> <span class="n">tunnelhost</span>.<span class="n">yourdomain</span>.<span class="n">com</span>
</pre></div>
<p>Example:</p>
<p><img alt="DNS Setup" src="/images/dns-tunnel-dns-setup.png" /></p>
<p>So now for me:</p>
<div class="highlight"><pre>* `tunnelhost.calebmadrigal.com` now points to `104.236.122.169`
* `tunnel.calebmadrigal.com` now points to `tunnelhost.calebmadrigal.com`
- **This is the URL I'll use for tunneling**
</pre></div>
<p>When you think you've set your DNS system correctly, you can check it with Iodine's test page: <a href="http://code.kryo.se/iodine/check-it/">http://code.kryo.se/iodine/check-it/</a></p>
<p><img alt="Iodine test page" src="/images/iodine-check-dns.png" /></p>
<h3>Install Iodine on your server</h3>
<p>My server runs Ubuntu, so to install Iodine on linux, I ran:</p>
<div class="highlight"><pre>sudo apt-get install iodine
</pre></div>
<h3>Install Iodine on your client</h3>
<p>My client is a Mac, so to install Iodine on Mac, I ran:</p>
<div class="highlight"><pre>brew install Caskroom/cask/tuntap
brew install iodine
</pre></div>
<p>However, I was unable to get the iodine client on my mac working with the iodine server running on Ubuntu. So I finally decided to just compile iodine on both my server and on my Ubuntu VM. Supposedly, iodine works best with the client and server are the exact same version. So...</p>
<p>Here is how to compile iodine on Ubuntu:</p>
<div class="highlight"><pre>sudo apt-get install zlib1g-dev
git clone https://github.com/yarrick/iodine
cd iodine
make
</pre></div>
<p>This makes <code>bin/iodine</code> and <code>bin/iodined</code>.</p>
<h3>Run Iodine server</h3>
<div class="highlight"><pre>sudo ./iodined -c -f 10.0.0.1 -P secretpassword tunnel.calebmadrigal.com
</pre></div>
<h3>Run Iodine client</h3>
<div class="highlight"><pre>sudo ./iodine -I 50 -f -P secretpassword tunnel.calebmadrigal.com
</pre></div>
<h3>Test DNS Tunnel setup</h3>
<p>To make sure the DNS tunnel is setup correctly, you can:</p>
<p>Run <code>ifconfig</code> (on your client) and make sure there is a <code>tun0</code> entry like this:</p>
<div class="highlight"><pre>(py)iseeyou:~ caleb$ ifconfig
tun0: flags=8851<UP,POINTOPOINT,RUNNING,SIMPLEX,MULTICAST> mtu 1130
inet 10.0.0.2 --> 10.0.0.2 netmask 0xffffffe0
open (pid 53156)
</pre></div>
<p>Ping your server via the subnet IP (through the DNS tunnel):</p>
<div class="highlight"><pre>(py)iseeyou:~ caleb$ ping 10.0.0.1
PING 10.0.0.1 (10.0.0.1): 56 data bytes
64 bytes from 10.0.0.1: icmp_seq=0 ttl=64 time=43.861 ms
64 bytes from 10.0.0.1: icmp_seq=1 ttl=64 time=44.518 ms
</pre></div>
<p>You can also test that you can SSH into your server via the subnet IP, via the DNS tunnel (note that I would typically login by <code>ssh caleb@calebmadrigal.com</code>):</p>
<div class="highlight"><pre><span class="p">(</span><span class="n">py</span><span class="p">)</span><span class="nl">iseeyou</span><span class="p">:</span><span class="o">~</span> <span class="n">caleb</span><span class="err">$</span> <span class="n">ssh</span> <span class="n">caleb</span><span class="mf">@10.0.0.1</span>
<span class="n">Last</span> <span class="nl">login</span><span class="p">:</span> <span class="n">Sat</span> <span class="n">Oct</span> <span class="mi">17</span> <span class="mi">22</span><span class="o">:</span><span class="mi">46</span><span class="o">:</span><span class="mi">23</span> <span class="mi">2015</span> <span class="n">from</span> <span class="n">cpe</span><span class="o">-</span><span class="mi">24</span><span class="o">-</span><span class="mi">167</span><span class="o">-</span><span class="mi">237</span><span class="o">-</span><span class="mf">173.</span><span class="n">wi</span><span class="p">.</span><span class="n">res</span><span class="p">.</span><span class="n">rr</span><span class="p">.</span><span class="n">com</span>
<span class="n">caleb</span><span class="p">@</span><span class="n">calebmadrigal</span><span class="o">-</span><span class="nl">com</span><span class="p">:</span><span class="o">~</span><span class="err">$</span>
</pre></div>
<p><strong>So at this point, you have a fully-functional DNS Tunnel up and running!</strong></p>
<h2>Setup SSH Tunnel inside of DNS Tunnel</h2>
<p>Next, we are going to setup an <a href="calebmadrigal.com/how-to-ssh-tunnel/">SSH tunnel</a> INSIDE of the DNS Tunnel. This will both setup a SOCKS proxy that will allow you to direct your network traffic through, and will secure your network traffic (at least between you and your server). For more information on SSH Tunneling and how it works, check out <a href="calebmadrigal.com/how-to-ssh-tunnel/">this article</a>.</p>
<p>Run (something like) this on your client to setup an SSH Tunnel:</p>
<div class="highlight"><pre><span class="n">ssh</span> <span class="o">-</span><span class="n">D</span> <span class="mi">5000</span> <span class="o">-</span><span class="n">N</span> <span class="n">caleb</span><span class="mf">@10.0.0.1</span>
</pre></div>
<h2>Direct network traffic through tunnel</h2>
<p>The simplest test is to use <code>curl</code> to download something through your SOCKS proxy like this:</p>
<div class="highlight"><pre>curl --socks5-hostname 127.0.0.1:5000 http://httpbin.org/ip
</pre></div>
<p>You can verify that the IP it is returning is the IP of your ssh server.</p>
<p>Alternatively, you can set the proxy for your whole computer like this...</p>
<p>To do this on OSX, go into <code>Settings</code> -> <code>Network</code>, and then:</p>
<p><img alt="OSX Socks Setup" src="/images/osx-socks-setup.png" /></p>
<h2>Proof that it's working</h2>
<p>When you browse the internet through the tunnel, websites will see your IP address as being your server (your "exit node"), so to test that things are working right, check your with and without the tunneling on:</p>
<p>Without Tunneling:</p>
<p><img alt="IP without tunneling" src="/images/whats-my-ip-no-tunneling.png" /></p>
<p>With Tunneling:</p>
<p><img alt="IP with tunneling" src="/images/whats-my-ip-with-tunneling.png" /></p>
<p>Also, if you do a Wireshark capture while browsing the web, you should see a bunch of DNS packets (since all your traffic is tunneling through DNS):</p>
<p><img alt="Wireshark DNS packets" src="/images/dns-tunnel-wireshark-packets.png" /></p>
<p>Now, go enjoy your private and unimpeded internet access right through that corporate or airport firewall!</p>Golden sky painting2015-05-26T00:00:10-05:00Caleb Madrigaltag:calebmadrigal.com,2015-05-26:golden-sky-painting/<p>Just another painting. I did this one earlier this year.</p>
<p><img alt="Golden sky tree" src="/images/golden_sky_tree.jpg" /></p>Calling synchronous code from asyncio2015-05-25T23:59:00-05:00Caleb Madrigaltag:calebmadrigal.com,2015-05-25:calling-sync-code-from-asyncio/<p>I recently needed to call some synchronous code from <a href="https://docs.python.org/3/library/asyncio.html">asyncio</a>. Thankfully, asyncio provides the <a href="https://docs.python.org/3/library/asyncio-eventloop.html#asyncio.BaseEventLoop.run_in_executor"><code>run_in_executor</code></a> function, which runs the specified function in a different thread. Here is an example of using it:</p>
<figure class='code'>
<figcaption><span>call_sync_code.py</span> <a href='/code/python/call_sync_code.py'>download</a></figcaption>
<div class="highlight"><pre><span class="kn">import</span> <span class="nn">asyncio</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">from</span> <span class="nn">urllib.request</span> <span class="kn">import</span> <span class="n">urlopen</span>
<span class="nd">@asyncio.coroutine</span>
<span class="k">def</span> <span class="nf">count_to_10</span><span class="p">():</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">11</span><span class="p">):</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Counter: {}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<span class="k">yield from</span> <span class="n">asyncio</span><span class="o">.</span><span class="n">sleep</span><span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">get_page_len</span><span class="p">(</span><span class="n">url</span><span class="p">):</span>
<span class="c"># This is the blocking sleep (not the async-friendly one)</span>
<span class="n">time</span><span class="o">.</span><span class="n">sleep</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="n">page</span> <span class="o">=</span> <span class="n">urlopen</span><span class="p">(</span><span class="n">url</span><span class="p">)</span><span class="o">.</span><span class="n">read</span><span class="p">()</span>
<span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="n">page</span><span class="p">)</span>
<span class="nd">@asyncio.coroutine</span>
<span class="k">def</span> <span class="nf">run_get_page_len</span><span class="p">():</span>
<span class="n">loop</span> <span class="o">=</span> <span class="n">asyncio</span><span class="o">.</span><span class="n">get_event_loop</span><span class="p">()</span>
<span class="n">future1</span> <span class="o">=</span> <span class="n">loop</span><span class="o">.</span><span class="n">run_in_executor</span><span class="p">(</span><span class="bp">None</span><span class="p">,</span> <span class="n">get_page_len</span><span class="p">,</span> <span class="s">'http://calebmadrigal.com'</span><span class="p">)</span>
<span class="c">#data1 = yield from future1</span>
<span class="k">return</span> <span class="n">future1</span>
<span class="nd">@asyncio.coroutine</span>
<span class="k">def</span> <span class="nf">print_data_size</span><span class="p">():</span>
<span class="n">data</span> <span class="o">=</span> <span class="k">yield from</span> <span class="n">run_get_page_len</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Data size: {}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">data</span><span class="p">))</span>
<span class="n">loop</span> <span class="o">=</span> <span class="n">asyncio</span><span class="o">.</span><span class="n">get_event_loop</span><span class="p">()</span>
<span class="n">tasks</span> <span class="o">=</span> <span class="p">[</span>
<span class="n">asyncio</span><span class="o">.</span><span class="n">async</span><span class="p">(</span><span class="n">count_to_10</span><span class="p">()),</span>
<span class="n">asyncio</span><span class="o">.</span><span class="n">async</span><span class="p">(</span><span class="n">print_data_size</span><span class="p">())]</span>
<span class="n">loop</span><span class="o">.</span><span class="n">run_until_complete</span><span class="p">(</span><span class="n">asyncio</span><span class="o">.</span><span class="n">wait</span><span class="p">(</span><span class="n">tasks</span><span class="p">))</span>
<span class="n">loop</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
</pre></div>
</figure>
<p>And here is the output:</p>
<pre>
Counter: 0
Counter: 1
Counter: 2
Counter: 3
Counter: 4
Counter: 5
Data size: 337581
Counter: 6
Counter: 7
Counter: 8
Counter: 9
Counter: 10
</pre>
<p>As you can see, even while the <code>get_page_len()</code> blocking function is running, the <code>count_to_10()</code> coroutine is still running as desired. Yay.</p>Algorithms in Python2015-05-25T23:45:00-05:00Caleb Madrigaltag:calebmadrigal.com,2015-05-25:algorithms-in-python/<p>I recently decided to brush up on my algorithms and data structures by writing them in Python. Though these are not optimized, they could be helpful for reference. Here is the Github repo: <a href="https://github.com/calebmadrigal/algorithms-in-python">https://github.com/calebmadrigal/algorithms-in-python</a>.</p>
<p>A some of the algorithms included:</p>
<ul>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/mergesort.py">Mergesort in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/quicksort.py">Quicksort in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/depth_first_search.py">Depth-first search in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/breadth_first_search.py">Breadth-first search in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/binary_search_tree.py">Binary search tree algorithms in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/dijkstra.py">Dijkstra's in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/hashtable.py">Hashtable implementation in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/heap.py">Heap in Python</a></li>
<li><a href="https://github.com/calebmadrigal/algorithms-in-python/blob/master/combinatorics.py">Combinatoric algorithms in Python</a></li>
</ul>Recursion with asyncio2015-05-25T23:15:00-05:00Caleb Madrigaltag:calebmadrigal.com,2015-05-25:recursion-with-asyncio/<p>Recursion is awesome, but has the downside of growing the stack, which can limit its usefulness. Some languages like <a href="http://en.wikipedia.org/wiki/Scheme_%28programming_language%29">Scheme</a>, however, have <a href="http://en.wikipedia.org/wiki/Tail_call">Tail-call optimization</a>, which lets programmers write Tail-recursive functions that don't grow the call stack. Python does not have Tail-call optimization (TCO), but with <a href="https://docs.python.org/3/library/asyncio.html">asyncio</a>, we can have something like Tail-call optimization. Basically, this method uses the asyncio event loop like a <a href="http://en.wikipedia.org/wiki/Tail_call#Through_trampolining">trampoline function</a>.</p>
<p>Example:</p>
<figure class='code'>
<figcaption><span>tail_recursion_with_asyncio.py</span> <a href='/code/python/tail_recursion_with_asyncio.py'>download</a></figcaption>
<div class="highlight"><pre><span class="kn">import</span> <span class="nn">asyncio</span>
<span class="c"># Tail-recursive factorial using asyncio event loop as a trampoline to</span>
<span class="c"># keep the stack from growing.</span>
<span class="nd">@asyncio.coroutine</span>
<span class="k">def</span> <span class="nf">factorial</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">callback</span><span class="p">,</span> <span class="n">acc</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">callback</span><span class="p">(</span><span class="n">acc</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">asyncio</span><span class="o">.</span><span class="n">async</span><span class="p">(</span><span class="n">factorial</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">callback</span><span class="p">,</span> <span class="n">acc</span><span class="o">*</span><span class="n">n</span><span class="p">))</span> <span class="c"># async -> ensure_future in Python 3.4.4</span>
<span class="k">def</span> <span class="nf">done_callback</span><span class="p">(</span><span class="n">result</span><span class="p">):</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Result: {}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">result</span><span class="p">))</span>
<span class="n">loop</span> <span class="o">=</span> <span class="n">asyncio</span><span class="o">.</span><span class="n">get_event_loop</span><span class="p">()</span>
<span class="n">loop</span><span class="o">.</span><span class="n">stop</span><span class="p">()</span>
<span class="n">loop</span> <span class="o">=</span> <span class="n">asyncio</span><span class="o">.</span><span class="n">get_event_loop</span><span class="p">()</span>
<span class="n">asyncio</span><span class="o">.</span><span class="n">async</span><span class="p">(</span><span class="n">factorial</span><span class="p">(</span><span class="mi">50000</span><span class="p">,</span> <span class="n">done_callback</span><span class="p">))</span>
<span class="n">loop</span><span class="o">.</span><span class="n">run_forever</span><span class="p">()</span> <span class="c"># Blocking call interrupted by loop.stop()</span>
<span class="n">loop</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
</pre></div>
</figure>
<p>(<a href="https://github.com/calebmadrigal/asyncio-examples/blob/master/tail_recursion_with_asyncio.py">Source on Github</a>)</p>
<p>A few things to note:</p>
<ul>
<li>This will NOT grow the call stack</li>
<li>This is about 2x slower than a loop-based iterative approach (at least for this factorial algorithm)</li>
<li>Notice the use of <code>asyncio.async()</code></li>
<li>Notice that we are using a done callback - this is similar to <a href="http://en.wikipedia.org/wiki/Continuation-passing_style">Continuation-passing style</a>.</li>
</ul>To answer the trees2015-04-20T23:15:00-05:00Caleb Madrigaltag:calebmadrigal.com,2015-04-20:to-answer-the-trees/<pre>
I had to leave -
[or was it "flee"?]
I felt entrapped by the drywall office halls
[unable to breathe]
The sanitized artwork hanging in the pale florescent haze
reminded me what art should not be -
[what life should not be]
I hate the straight lines in man-made buildings
that make everything feel so...concrete,
[so unbending]
But I love the trees with their curvy lines that say,
"reality can bend -
come bend with us."
So that's why I am here -
[to answer the trees]
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/17/2015</li>
</ul>
<p>This picture by <a href="https://www.flickr.com/photos/melissavincent/9878466196/">Melissa Vincent</a> was part of the inspiration for this poem:
<img alt="Melted Nights by Melissa Vincent" src="/images/melted_nights_melissa_vincent.jpg" /></p>Simple D3 demos2015-02-11T11:35:00-06:00Caleb Madrigaltag:calebmadrigal.com,2015-02-11:simple-d3-demos/<p>I've been playing with <a href="http://d3js.org/">d3</a> recently, and it awesome! I'm especially amazed by the ease of animating <a href="https://github.com/mbostock/d3/wiki/Transitions">transitions</a> with it.</p>
<p>There are plenty of <a href="https://github.com/mbostock/d3/wiki/Gallery">amazing d3 demos</a> out there, but I wanted to write some simpler ones to help me understand the basics of d3. You can find them here:</p>
<p><a href="http://calebmadrigal.github.io/d3-demos/">http://calebmadrigal.github.io/d3-demos/</a></p>
<p>For example, here's how to draw a circle with d3:</p>
<div id="d3-simple-circle"></div>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.3/d3.min.js"></script>
<script type="text/javascript">
var width = 200;
var height = 200;
var x = width/2;
var y = height/2;
var radius = 100;
var fill = '#F012BE';
var svg = d3.select("#d3-simple-circle").append("svg")
.attr("width", width)
.attr("height", height)
.append('circle')
.attr({ r: radius, cx: x, cy: y, fill: fill});
</script>
<p>Code:</p>
<div class="highlight"><pre> <span class="nt">var</span> <span class="nt">width</span> <span class="o">=</span> <span class="nt">200</span><span class="o">;</span>
<span class="nt">var</span> <span class="nt">height</span> <span class="o">=</span> <span class="nt">200</span><span class="o">;</span>
<span class="nt">var</span> <span class="nt">x</span> <span class="o">=</span> <span class="nt">width</span><span class="o">/</span><span class="nt">2</span><span class="o">;</span>
<span class="nt">var</span> <span class="nt">y</span> <span class="o">=</span> <span class="nt">height</span><span class="o">/</span><span class="nt">2</span><span class="o">;</span>
<span class="nt">var</span> <span class="nt">radius</span> <span class="o">=</span> <span class="nt">100</span><span class="o">;</span>
<span class="nt">var</span> <span class="nt">fill</span> <span class="o">=</span> <span class="s1">'#F012BE'</span><span class="o">;</span>
<span class="nt">var</span> <span class="nt">svg</span> <span class="o">=</span> <span class="nt">d3</span><span class="nc">.select</span><span class="o">(</span><span class="s2">"#d3-simple-circle"</span><span class="o">)</span><span class="nc">.append</span><span class="o">(</span><span class="s2">"svg"</span><span class="o">)</span>
<span class="nc">.attr</span><span class="o">(</span><span class="s2">"width"</span><span class="o">,</span> <span class="nt">width</span><span class="o">)</span>
<span class="nc">.attr</span><span class="o">(</span><span class="s2">"height"</span><span class="o">,</span> <span class="nt">height</span><span class="o">)</span>
<span class="nc">.append</span><span class="o">(</span><span class="s1">'circle'</span><span class="o">)</span>
<span class="nc">.attr</span><span class="o">(</span><span class="p">{</span> <span class="n">r</span><span class="o">:</span> <span class="n">radius</span><span class="o">,</span> <span class="n">cx</span><span class="o">:</span> <span class="n">x</span><span class="o">,</span> <span class="n">cy</span><span class="o">:</span> <span class="n">y</span><span class="o">,</span> <span class="n">fill</span><span class="o">:</span> <span class="n">fill</span><span class="p">}</span><span class="o">);</span>
</pre></div>
<p>And here's one of the cooler-looking ones:</p>
<div id="dancing-sin-graph"></div>
<script type="text/javascript">
var width = 700;
var height = 500;
var linspace = function(start, stop, num_samples) {
return d3.range(start, stop * (num_samples / (stop-start)))
.map(function (n) { return n / (num_samples / (stop-start)); });
};
var direction = 1;
var x = linspace(0, 20, 500);
var y = x.map(function (i) { return ((height/2)-50) * direction * Math.sin(i); });
var x_step = width / x.length;
var y_middle = height / 2;
var radius = 100;
var fill = '#F012BE';
var sin_svg = d3.select("#dancing-sin-graph").append("svg")
.attr("width", width)
.attr("height", height);
sin_svg.selectAll('circle')
.data(y)
.enter()
.append('circle')
.attr({r: 2, fill: fill})
.attr('cx', function (d, i) {
return x_step * i;
})
.attr('cy', function (d, i) {
return y_middle - d;
});
function invert() {
direction = direction * -1;
y = x.map(function (i) { return ((height/2)-50) * direction * Math.sin(i); });
d3.select("#dancing-sin-graph").selectAll('circle')
.data(y)
.transition()
.duration(1000)
.attr({r: 2, fill: fill})
.attr('cx', function (d, i) {
return x_step * i;
})
.attr('cy', function (d, i) {
return y_middle - d;
});
}
// Make the interval just less than the transition duration so motion never stops
setInterval(invert, 900);
</script>
<p>Code (granted, this one is a bit more complicated):</p>
<div class="highlight"><pre><span class="kd">var</span> <span class="nx">width</span> <span class="o">=</span> <span class="mi">700</span><span class="p">;</span>
<span class="kd">var</span> <span class="nx">height</span> <span class="o">=</span> <span class="mi">500</span><span class="p">;</span>
<span class="kd">var</span> <span class="nx">linspace</span> <span class="o">=</span> <span class="kd">function</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span> <span class="nx">stop</span><span class="p">,</span> <span class="nx">num_samples</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="nx">d3</span><span class="p">.</span><span class="nx">range</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span> <span class="nx">stop</span> <span class="o">*</span> <span class="p">(</span><span class="nx">num_samples</span> <span class="o">/</span> <span class="p">(</span><span class="nx">stop</span><span class="o">-</span><span class="nx">start</span><span class="p">)))</span>
<span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="kd">function</span> <span class="p">(</span><span class="nx">n</span><span class="p">)</span> <span class="p">{</span> <span class="k">return</span> <span class="nx">n</span> <span class="o">/</span> <span class="p">(</span><span class="nx">num_samples</span> <span class="o">/</span> <span class="p">(</span><span class="nx">stop</span><span class="o">-</span><span class="nx">start</span><span class="p">));</span> <span class="p">});</span>
<span class="p">};</span>
<span class="kd">var</span> <span class="nx">direction</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span>
<span class="kd">var</span> <span class="nx">x</span> <span class="o">=</span> <span class="nx">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">500</span><span class="p">);</span>
<span class="kd">var</span> <span class="nx">y</span> <span class="o">=</span> <span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="kd">function</span> <span class="p">(</span><span class="nx">i</span><span class="p">)</span> <span class="p">{</span> <span class="k">return</span> <span class="p">((</span><span class="nx">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">-</span><span class="mi">50</span><span class="p">)</span> <span class="o">*</span> <span class="nx">direction</span> <span class="o">*</span> <span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span> <span class="p">});</span>
<span class="kd">var</span> <span class="nx">x_step</span> <span class="o">=</span> <span class="nx">width</span> <span class="o">/</span> <span class="nx">x</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<span class="kd">var</span> <span class="nx">y_middle</span> <span class="o">=</span> <span class="nx">height</span> <span class="o">/</span> <span class="mi">2</span><span class="p">;</span>
<span class="kd">var</span> <span class="nx">radius</span> <span class="o">=</span> <span class="mi">100</span><span class="p">;</span>
<span class="kd">var</span> <span class="nx">fill</span> <span class="o">=</span> <span class="s1">'#F012BE'</span><span class="p">;</span>
<span class="kd">var</span> <span class="nx">sin_svg</span> <span class="o">=</span> <span class="nx">d3</span><span class="p">.</span><span class="nx">select</span><span class="p">(</span><span class="s2">"#dancing-sin-graph"</span><span class="p">).</span><span class="nx">append</span><span class="p">(</span><span class="s2">"svg"</span><span class="p">)</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">(</span><span class="s2">"width"</span><span class="p">,</span> <span class="nx">width</span><span class="p">)</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">(</span><span class="s2">"height"</span><span class="p">,</span> <span class="nx">height</span><span class="p">);</span>
<span class="nx">sin_svg</span><span class="p">.</span><span class="nx">selectAll</span><span class="p">(</span><span class="s1">'circle'</span><span class="p">)</span>
<span class="p">.</span><span class="nx">data</span><span class="p">(</span><span class="nx">y</span><span class="p">)</span>
<span class="p">.</span><span class="nx">enter</span><span class="p">()</span>
<span class="p">.</span><span class="nx">append</span><span class="p">(</span><span class="s1">'circle'</span><span class="p">)</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">({</span><span class="nx">r</span><span class="o">:</span> <span class="mi">2</span><span class="p">,</span> <span class="nx">fill</span><span class="o">:</span> <span class="nx">fill</span><span class="p">})</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">(</span><span class="s1">'cx'</span><span class="p">,</span> <span class="kd">function</span> <span class="p">(</span><span class="nx">d</span><span class="p">,</span> <span class="nx">i</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="nx">x_step</span> <span class="o">*</span> <span class="nx">i</span><span class="p">;</span>
<span class="p">})</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">(</span><span class="s1">'cy'</span><span class="p">,</span> <span class="kd">function</span> <span class="p">(</span><span class="nx">d</span><span class="p">,</span> <span class="nx">i</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="nx">y_middle</span> <span class="o">-</span> <span class="nx">d</span><span class="p">;</span>
<span class="p">});</span>
<span class="kd">function</span> <span class="nx">invert</span><span class="p">()</span> <span class="p">{</span>
<span class="nx">direction</span> <span class="o">=</span> <span class="nx">direction</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="p">;</span>
<span class="nx">y</span> <span class="o">=</span> <span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="kd">function</span> <span class="p">(</span><span class="nx">i</span><span class="p">)</span> <span class="p">{</span> <span class="k">return</span> <span class="p">((</span><span class="nx">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">-</span><span class="mi">50</span><span class="p">)</span> <span class="o">*</span> <span class="nx">direction</span> <span class="o">*</span> <span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span> <span class="p">});</span>
<span class="nx">d3</span><span class="p">.</span><span class="nx">select</span><span class="p">(</span><span class="s2">"#dancing-sin-graph"</span><span class="p">).</span><span class="nx">selectAll</span><span class="p">(</span><span class="s1">'circle'</span><span class="p">)</span>
<span class="p">.</span><span class="nx">data</span><span class="p">(</span><span class="nx">y</span><span class="p">)</span>
<span class="p">.</span><span class="nx">transition</span><span class="p">()</span>
<span class="p">.</span><span class="nx">duration</span><span class="p">(</span><span class="mi">1000</span><span class="p">)</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">({</span><span class="nx">r</span><span class="o">:</span> <span class="mi">2</span><span class="p">,</span> <span class="nx">fill</span><span class="o">:</span> <span class="nx">fill</span><span class="p">})</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">(</span><span class="s1">'cx'</span><span class="p">,</span> <span class="kd">function</span> <span class="p">(</span><span class="nx">d</span><span class="p">,</span> <span class="nx">i</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="nx">x_step</span> <span class="o">*</span> <span class="nx">i</span><span class="p">;</span>
<span class="p">})</span>
<span class="p">.</span><span class="nx">attr</span><span class="p">(</span><span class="s1">'cy'</span><span class="p">,</span> <span class="kd">function</span> <span class="p">(</span><span class="nx">d</span><span class="p">,</span> <span class="nx">i</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="nx">y_middle</span> <span class="o">-</span> <span class="nx">d</span><span class="p">;</span>
<span class="p">});</span>
<span class="p">}</span>
<span class="c1">// Make the interval just less than the transition duration so motion never stops</span>
<span class="nx">setInterval</span><span class="p">(</span><span class="nx">invert</span><span class="p">,</span> <span class="mi">900</span><span class="p">);</span>
</pre></div>Spruce Needle Silhouette2015-01-13T23:00:00-06:00Caleb Madrigaltag:calebmadrigal.com,2015-01-13:spruce-needle-silhouette/<p><img alt="Spruce Needle Silhouette" src="/images/spruce-needle-silhouette.jpg" /></p>
<p>This is my 2nd painting (painted 2014-01-10). I like how it came out, but almost gave up while painting it because I was comparing it to the sky God painted:</p>
<p><img alt="Vanilla Sky Sunset Milwaukee WI" src="/images/vanilla-sky-sunset-milwaukee-wi.jpg" /></p>
<p>I took this photo of a beautiful "vanilla sky" outside of our home in Milwaukee, WI. It served as my model for the painting (along with other memories of looking at sunsets from beneath the spruce tree).</p>Dorian Gray Prelude2014-12-22T00:05:00-06:00Caleb Madrigaltag:calebmadrigal.com,2014-12-22:dorian-gray-prelude/<p>This year (2014) has been, for me, a year of art exploration. And to end it, I'd just like to share what I believe to be the greatest prelude ever written: the Prelude to <a href="http://en.wikipedia.org/wiki/The_Picture_of_Dorian_Gray">The Picture of Dorian Gray</a> by <a href="http://en.wikipedia.org/wiki/Oscar_Wilde">Oscar Wilde</a>:</p>
<p><em>"The artist is the creator of beautiful things. To reveal art and conceal the artist is art's aim. The critic is he who can translate into another manner or a new material his impression of beautiful things.</em></p>
<p><em>The highest as the lowest form of criticism is a mode of autobiography. Those who find ugly meanings in beautiful things are corrupt without being charming. This is a fault.</em></p>
<p><em>Those who find beautiful meanings in beautiful things are the cultivated. For these there is hope. They are the elect to whom beautiful things mean only beauty.</em></p>
<p><em>There is no such thing as a moral or an immoral book. Books are well written, or badly written. That is all.</em></p>
<p><em>The nineteenth century dislike of realism is the rage of Caliban seeing his own face in a glass.</em></p>
<p><em>The nineteenth century dislike of romanticism is the rage of Caliban not seeing his own face in a glass. The moral life of man forms part of the subject-matter of the artist, but the morality of art consists in the perfect use of an imperfect medium. No artist desires to prove anything. Even things that are true can be proved. No artist has ethical sympathies. An ethical sympathy in an artist is an unpardonable mannerism of style. No artist is ever morbid. The artist can express everything. Thought and language are to the artist instruments of an art. Vice and virtue are to the artist materials for an art. From the point of view of form, the type of all the arts is the art of the musician. From the point of view of feeling, the actor's craft is the type. All art is at once surface and symbol. Those who go beneath the surface do so at their peril. Those who read the symbol do so at their peril. It is the spectator, and not life, that art really mirrors. Diversity of opinion about a work of art shows that the work is new, complex, and vital. When critics disagree, the artist is in accord with himself. We can forgive a man for making a useful thing as long as he does not admire it. The only excuse for making a useless thing is that one admires it intensely.</em></p>
<p><em>All art is quite useless."</em></p>Phantastes2014-12-21T23:30:00-06:00Caleb Madrigaltag:calebmadrigal.com,2014-12-21:phantastes/<p><img src="/images/phantastes_cover.jpg" style="float:left; margin-right:15px" />
I recently finished reading <a href="http://en.wikipedia.org/wiki/Phantastes"><em>Phantastes</em></a> by <a href="http://en.wikipedia.org/wiki/George_MacDonald">George MacDonald</a> for the 2nd time. The first time I read it, I really liked it. This second time, it became one of my all-time favorites. I've never experience any other work of art which feels so much like being in a dream.</p>
<p>To give you an idea of what it's about, here is the end of the Prelude:</p>
<p><em>"In a genuine fairy-story, everything must be miraculous, mysterious, and interrelated; everything must be alive, each in its own way. The whole of Nature must be wondrously blended with the whole world of the Spirit. In fairy-story the time of anarchy, lawlessness, freedom, the natural state of Nature makes itself felt in the world... The wolrd of the fairy-story is that world which is opposed throughout the world of rational truth, and precisely for that reason it is so throroughly an analogue to it, as Chaos is an analogue to the finished Creation." - NOVALIS</em></p>
<p>And here is how Chapter 1 begins:</p>
<pre>
"A spirit...
The undulating woods, and silent well,
And rippling rivulet, and evening gloom,
Now deepening the dark shades, for speech assuming,
Held commune with him; as if he and it
Were all that was."
</pre>
<p>And here is an excerpt from the middle of the book:</p>
<p><em>Then the woman spoke, but without lifting her head or looking at me: "You had better not open that door." This was uttered quite quietly; and she went on with her reading, partly in silence, partly aloud; but both modes seemed equally intended for herself alone. The prohibition, however, only increased my desire to see...</em></p>
<p>If you are interested in reading <em>Phantastes</em>, it is in the public domain, so it is available for free <a href="http://www.gutenberg.org/ebooks/325">here</a> and there is a free <a href="https://librivox.org/phantastes-by-george-macdonald/">audio book rendition on Librivox</a>.</p>First painting2014-12-14T20:00:00-06:00Caleb Madrigaltag:calebmadrigal.com,2014-12-14:first-painting/<p>Yesterday (12/13/2014), my wife and I went to a painting studio to try our hands at painting. I loved the experience! Here is what I came out with:</p>
<p><img alt="My first painting" src="/images/caleb_painting_2014-12-13.jpg" /></p>
<p>This was my first time painting since I was a kid doing watercolors in school. Definitely plan to try it again!</p>Why I changed my mind about Node.js2014-09-15T22:55:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-09-15:why-i-changed-my-mind-about-nodejs/<h2>Intro</h2>
<p><img src="/images/nodejs-logo.png" style="width:259px; height:141px; float:left; margin-right:15px" />
I first heard of <a href="http://nodejs.org/">Node.js</a> about 4 years ago. I thought it was a ridiculous idea: using JavaScript as your server-side language! JavaScript always felt to me like an inferior language. Why would you use it unless you absolutely had to!? Now of course, you have to do JavaScript if you are writing code which runs in the browser, but on the server, you can use any language you choose. So why choose JavaScript?</p>
<p>I did choose to use JavaScript/Node.js on my current project. I have now been using it for the last several months, and I am quite impressed! Let me tell you what made me change my mind about Node.js.</p>
<h2>Adoption by the Enterprise world</h2>
<p>First, Node.js has been adopted by multiple top-tier companies, with great success. Here are a few companies who have adopted Node.js: <a href="https://www.paypal-engineering.com/2013/11/22/node-js-at-paypal/">PayPal</a>, <a href="http://venturebeat.com/2012/01/24/why-walmart-is-using-node-js/">Walmart</a>, <a href="http://www.ebaytechblog.com/2013/05/17/how-we-built-ebays-first-node-js-application/#.VBe2hi5dV00">Ebay</a>, <a href="http://www.datacenterknowledge.com/archives/2013/12/06/need-speed-groupon-migrated-node-js/">Groupon</a>, and <a href="http://venturebeat.com/2011/08/16/linkedin-node/">LinkedIn</a>. And these companies are not using Node for menial tasks; they’re using it in heavily-used production applications. For example, PayPal wrote about their experience using Node.js on what they call "one of the most trafficked apps on the website”. Here are some of their observations comparing their Node.js version of the app to their Java version of the app:</p>
<ul>
<li>Built <strong>almost twice as fast</strong> with fewer people</li>
<li>Written in <strong>33% fewer lines of code</strong></li>
<li>Constructed with <strong>40% fewer files</strong></li>
<li><strong>Double the requests per second vs. the Java application</strong></li>
<li><strong>35% decrease in the average response time</strong></li>
</ul>
<p>(Source: <a href="https://www.paypal-engineering.com/2013/11/22/node-js-at-paypal/">https://www.paypal-engineering.com/2013/11/22/node-js-at-paypal/</a>)</p>
<p>That’s pretty serious! That’s what got me interested.</p>
<h2>Package manager - NPM</h2>
<p><img src="/images/npm-logo.png" style="width:300px; height:150px; float:left; margin-right:15px" />
So I started looking into Node.js for myself, and found many wonderful things. First, it has a wonderful package management system called <a href="https://www.npmjs.org/">npm</a>. With npm, you can install practically any Node.js package/library by running “npm install package-name”. Node.js also has nice conventions for keeping track of dependencies with a package.json file. With this, you can simply clone a Node.js repo, and run “npm install” to install all of the necessary dependencies.</p>
<h2>Libraries</h2>
<p>These days, having good libraries is crucial to success. And in this regard, Node.js delivers in spades. The Node.js community is incredibly vibrant, and is always turning out new packages. I have found the libraries in Node.js to be so good, that they make JavaScript into a great, productive platform. I’m a long-time Pythonista, and I have a lot of trouble getting excited about other technologies because I just can’t be as productive in them as I can in Python. But I’m excited about Node.js - I feel super productive in it, and I’ve only recently started using it. That’s about the best complement I can give to any language or platform.</p>
<h2>The REPL</h2>
<p>Another thing I loved about Node.js was the <a href="http://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">REPL</a> (read-evaluate-print loop) - or as it is sometimes called, the Node.js command-line. With this, you can just type “node” in the terminal, and be able to test out Node.js one line at a time. This is something that, coming from a strong Python background, I have come to absolutely love! I can easily write a function, and jump into the REPL, import the code, and test it out. Or I sometimes write the function in the REPL, and once it is working well, copy it to my source code file.</p>
<h2>Non-blocking everywhere</h2>
<p>Node.js has another big thing going for it: it was built with an emphasis on non-blocking functions (on the <a href="http://en.wikipedia.org/wiki/Event_loop">Event loop</a> model), and this emphasis has been adopted by the whole Node.js community. This is why you will see a lot of <a href="http://en.wikipedia.org/wiki/Callback_(computer_programming)">callbacks</a> and <a href="https://github.com/kriskowal/q">promises</a> in Node.js code. When you call a function in Node.js, if there is any chance it could take a while, that function will not return it’s value directly; instead, it will return immediately, run the long-running operation "in the background", and call the callback function when complete (passing the return value as a parameter to that callback function). This design pattern is what leads to Node.js’s impressive performance record.</p>
<h2>One language</h2>
<p>Lastly, one of Node.js’s biggest advantages is also what may seem to be a disadvantage: that it is JavaScript. But this is indeed an advantage for a few reasons. The first reason is that everyone knows (or soon will need to know) JavaScript (due to everything moving to the web). So you don’t need to teach anyone a new language to use Node.js. The other reason JavaScript is advantageous is that you can use one language - JavaScript - for everything. JavaScript can obviously run in Browsers, with Node.js, JavaScript can be your server-side code, and with <a href="http://en.wikipedia.org/wiki/Document-oriented_database">Document databases</a> like <a href="http://www.mongodb.org/">MongoDB</a> and <a href="http://couchdb.apache.org/">CouchDB</a> which store JSON objects, JavaScript can be the native format of your data. And having one language for everything can greatly simplify the task of transferring data between your database and UI, and that task often makes up a large portion of the complexity of an application.</p>
<h2>Conclusion</h2>
<p>Use Node.js! It's fun, easy to learn, and (I'm betting) will continue to gain prominence in the upcoming years.</p>
<p><strong>More comments on Hacker News: <a href="https://news.ycombinator.com/item?id=8324890">https://news.ycombinator.com/item?id=8324890</a></strong></p>Sessions in Node.js and Express.js2014-09-15T19:36:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-09-15:sessions-in-nodejs-expressjs/<p>In the process of trying to explain to a friend how sessions work, I decided to write a barebones example to demonstrate how to do sessions in Node.js with Express.js.</p>
<p><strong>Here's a live demo: <a href="http://expressjs-session-example.herokuapp.com/">http://expressjs-session-example.herokuapp.com/</a></strong></p>
<p>And Here's what it looks like:</p>
<p>Before you enter your name:</p>
<p><img src="/images/session_example_1.png" style="width:190px; height:90px" /></p>
<p>After you enter your name:</p>
<p><img src="/images/session_example_2.png" style="width:98px; height:72px" /></p>
<p>And here is the code:</p>
<div class="highlight"><pre><span class="kd">var</span> <span class="nx">express</span> <span class="o">=</span> <span class="nx">require</span><span class="p">(</span><span class="s1">'express'</span><span class="p">);</span>
<span class="kd">var</span> <span class="nx">cookieParser</span> <span class="o">=</span> <span class="nx">require</span><span class="p">(</span><span class="s1">'cookie-parser'</span><span class="p">);</span>
<span class="kd">var</span> <span class="nx">bodyParser</span> <span class="o">=</span> <span class="nx">require</span><span class="p">(</span><span class="s1">'body-parser'</span><span class="p">);</span>
<span class="kd">var</span> <span class="nx">session</span> <span class="o">=</span> <span class="nx">require</span><span class="p">(</span><span class="s1">'cookie-session'</span><span class="p">);</span>
<span class="c1">///////////////////////////////////////////////////////////////////////////////////////// MIDDLEWARE</span>
<span class="kd">var</span> <span class="nx">app</span> <span class="o">=</span> <span class="nx">express</span><span class="p">();</span>
<span class="c1">// Needed to handle JSON posts</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">use</span><span class="p">(</span><span class="nx">bodyParser</span><span class="p">.</span><span class="nx">json</span><span class="p">());</span>
<span class="c1">// Cookie parsing needed for sessions</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">use</span><span class="p">(</span><span class="nx">cookieParser</span><span class="p">(</span><span class="s1">'notsosecretkey'</span><span class="p">));</span>
<span class="c1">// Session framework</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">use</span><span class="p">(</span><span class="nx">session</span><span class="p">({</span><span class="nx">secret</span><span class="o">:</span> <span class="s1">'notsosecretkey123'</span><span class="p">}));</span>
<span class="c1">// Consider all URLs under /public/ as static files, and return them raw.</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">use</span><span class="p">(</span><span class="nx">express</span><span class="p">.</span><span class="kr">static</span><span class="p">(</span><span class="nx">__dirname</span> <span class="o">+</span> <span class="s1">'/public'</span><span class="p">));</span>
<span class="c1">/////////////////////////////////////////////////////////////////////////////////////////// HANDLERS</span>
<span class="kd">function</span> <span class="nx">getName</span><span class="p">(</span><span class="nx">req</span><span class="p">,</span> <span class="nx">res</span><span class="p">)</span> <span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="nx">req</span><span class="p">.</span><span class="nx">session</span><span class="p">.</span><span class="nx">name</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="nx">res</span><span class="p">.</span><span class="nx">json</span><span class="p">({</span> <span class="nx">name</span><span class="o">:</span> <span class="nx">req</span><span class="p">.</span><span class="nx">session</span><span class="p">.</span><span class="nx">name</span> <span class="p">});</span>
<span class="p">}</span>
<span class="k">else</span> <span class="p">{</span>
<span class="k">return</span> <span class="nx">res</span><span class="p">.</span><span class="nx">json</span><span class="p">({</span> <span class="nx">name</span><span class="o">:</span> <span class="s1">''</span> <span class="p">});</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="kd">function</span> <span class="nx">setName</span><span class="p">(</span><span class="nx">req</span><span class="p">,</span> <span class="nx">res</span><span class="p">)</span> <span class="p">{</span>
<span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="nx">req</span><span class="p">.</span><span class="nx">body</span><span class="p">.</span><span class="nx">hasOwnProperty</span><span class="p">(</span><span class="s1">'name'</span><span class="p">))</span> <span class="p">{</span>
<span class="nx">res</span><span class="p">.</span><span class="nx">statusCode</span> <span class="o">=</span> <span class="mi">400</span><span class="p">;</span>
<span class="k">return</span> <span class="nx">res</span><span class="p">.</span><span class="nx">json</span><span class="p">({</span> <span class="nx">error</span><span class="o">:</span> <span class="s1">'Invalid message'</span> <span class="p">});</span>
<span class="p">}</span>
<span class="k">else</span> <span class="p">{</span>
<span class="nx">req</span><span class="p">.</span><span class="nx">session</span><span class="p">.</span><span class="nx">name</span> <span class="o">=</span> <span class="nx">req</span><span class="p">.</span><span class="nx">body</span><span class="p">.</span><span class="nx">name</span><span class="p">;</span>
<span class="k">return</span> <span class="nx">res</span><span class="p">.</span><span class="nx">json</span><span class="p">({</span> <span class="nx">name</span><span class="o">:</span> <span class="nx">req</span><span class="p">.</span><span class="nx">body</span><span class="p">.</span><span class="nx">name</span> <span class="p">});</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="kd">function</span> <span class="nx">logout</span><span class="p">(</span><span class="nx">req</span><span class="p">,</span> <span class="nx">res</span><span class="p">)</span> <span class="p">{</span>
<span class="nx">req</span><span class="p">.</span><span class="nx">session</span> <span class="o">=</span> <span class="kc">null</span><span class="p">;</span>
<span class="k">return</span> <span class="nx">res</span><span class="p">.</span><span class="nx">json</span><span class="p">({});</span>
<span class="p">}</span>
<span class="c1">///////////////////////////////////////////////////////////////////////////////////////////// ROUTES</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="s1">'/name'</span><span class="p">,</span> <span class="nx">getName</span><span class="p">);</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">post</span><span class="p">(</span><span class="s1">'/name'</span><span class="p">,</span> <span class="nx">setName</span><span class="p">);</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="s1">'/logout'</span><span class="p">,</span> <span class="nx">logout</span><span class="p">);</span>
<span class="c1">////////////////////////////////////////////////////////////////////////////////////// SERVER LISTEN</span>
<span class="kd">var</span> <span class="nx">port</span> <span class="o">=</span> <span class="nx">process</span><span class="p">.</span><span class="nx">env</span><span class="p">.</span><span class="nx">PORT</span> <span class="o">||</span> <span class="mi">3000</span><span class="p">;</span>
<span class="nx">app</span><span class="p">.</span><span class="nx">listen</span><span class="p">(</span><span class="nx">port</span><span class="p">,</span> <span class="kd">function</span> <span class="p">()</span> <span class="p">{</span> <span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="s2">"Listening on port "</span> <span class="o">+</span> <span class="nx">port</span><span class="p">);</span> <span class="p">});</span>
</pre></div>
<p>Github repo: <a href="https://github.com/calebmadrigal/expressjs-session-example">https://github.com/calebmadrigal/expressjs-session-example</a></p>On Abstract Art2014-07-12T16:10:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-07-12:on-abstract-art/<p>Too much detail in art is profanity - a vulgar attempt to sum up that which is beyond finite expression.</p>How to SSH Tunnel2014-06-27T19:07:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-06-27:how-to-ssh-tunnel/<h2>When to use an SSH Tunnel?</h2>
<p>An SSH Tunnel is perfect for the following scenarios:</p>
<ul>
<li>You want to get to a website that a corporate network is blocking.</li>
<li>You want to encrypt the network traffic for a non-encrypted protocol.</li>
</ul>
<h2>What is an SSH Tunnel?</h2>
<p>An SSH Tunnel is where you tell your local SSH Client to forward your local computer's traffic to a specified SSH Server (over the encrypted SSH protocol). The SSH Server will then act as a proxy for all requests you make on your local computer.</p>
<p><img alt="SSH Tunnel" src="/images/ssh_tunnel.png" /></p>
<h2>How to set up an SSH Tunnel</h2>
<p>There are 2 steps to set up an SSH Tunnel, and they both happen on your local computer (<strong>no configuration is needed on the SSH server which will be acting as the proxy</strong>).</p>
<h3>Set 1: Open the tunnel</h3>
<p>Run this command on your local computer:</p>
<div class="highlight"><pre>ssh -D 5000 -N user@yourserver.com
</pre></div>
<ul>
<li><code>user@yourserver.com</code> is the user/server you would use for normal SSH (e.g. <code>ssh user@yourserver.com</code>).</li>
<li><code>5000</code> is the port you will hit on <code>localhost</code> to enter the tunnel (see Step 2).</li>
</ul>
<h3>Set 2: Direct your network to use the tunnel</h3>
<p>Open the network settings, find the Network Proxy configuration section, and set <code>localhost:5000</code> as a SOCKS proxy:</p>
<p><img alt="SOCKS proxy network settings" src="/images/ssh_tunnel_proxy_ubuntu.png" /></p>
<h2>Ride the tube!</h2>
<p>If you did it right, all traffic between your computer and <code>yourserver.com</code> should now be encrypted, and <code>yourserver.com</code> should be acting as a proxy on your local computer's behalf.</p>
<p>A <strong>simple test to make sure it is working properly</strong> is to Google for "what's my ip" before and after setting up the Tunnel. The IP should change when the Tunnel is on (and should be your server's IP).</p>Art is a laser2014-06-19T22:54:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-06-19:art-is-a-laser/<p>The best art is more like a laser beam than a flood light - it doesn't hit everyone, but those it hits, it burns.</p>Fuel efficiency difference cost2014-05-21T19:45:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-05-21:fuel-efficiency-difference-cost/<p>I recently was car shopping, and I had the question about gas mileage: "How much does, say, the difference between 25 mpg and 30 mpg cost?" </p>
<p>To answer this question, I did a bit of analysis using IPython Notebook...</p>
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<li>To find how much different fuel efficiencies cost in terms of dollars per year.</li>
<li>I want to estimate this value for the next 10 or so years.</li>
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<li>I'm estimating the average price per gallon of gas (over the next 10 years) to be $4.50. It is around $3.60 now, I adjusted for inflation, and counter-adjusted for the time-value of money.</li>
<li>I'm estimating that we will drive about 14,000 miles per year (based on the last 3 years).</li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">price_per_gallon</span> <span class="o">=</span> <span class="mf">4.50</span> <span class="c"># dollars per gallon</span>
<span class="n">miles_per_year</span> <span class="o">=</span> <span class="mf">14000.0</span> <span class="c"># miles per year</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">price_per_year</span><span class="p">(</span><span class="n">mpg</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">miles_per_year</span> <span class="o">/</span> <span class="n">mpg</span><span class="p">)</span> <span class="o">*</span> <span class="n">price_per_gallon</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Compare fuel efficiencies between 15 mpg and 50 mpg</span>
<span class="n">mpg_list</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">51</span><span class="p">)</span>
<span class="n">price_list</span> <span class="o">=</span> <span class="p">[</span><span class="n">price_per_year</span><span class="p">(</span><span class="n">mpg</span><span class="p">)</span> <span class="k">for</span> <span class="n">mpg</span> <span class="ow">in</span> <span class="n">mpg_list</span><span class="p">]</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">def</span> <span class="nf">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="n">fig_size</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="n">fig_size</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">fig_size</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
<span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Cost per year for each mpg rating'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'mpg'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'price'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">mpg_list</span><span class="p">,</span> <span class="n">price_list</span><span class="p">)</span>
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<h1 id="Example-mpg-differences-in-price">Example mpg differences in price<a class="anchor-link" href="#Example-mpg-differences-in-price">¶</a></h1>
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<h3 id="1-mpg-difference-(29-mpg-to-30-mpg)">1 mpg difference (29 mpg to 30 mpg)<a class="anchor-link" href="#1-mpg-difference-(29-mpg-to-30-mpg)">¶</a></h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">price_per_year</span><span class="p">(</span><span class="mi">29</span><span class="p">)</span> <span class="o">-</span> <span class="n">price_per_year</span><span class="p">(</span><span class="mi">30</span><span class="p">)</span>
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72.41379310344837
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<h3 id="5-mpg-difference-20-mpg-to-25-mpg)">5 mpg difference 20 mpg to 25 mpg)<a class="anchor-link" href="#5-mpg-difference-20-mpg-to-25-mpg)">¶</a></h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">price_per_year</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="o">-</span> <span class="n">price_per_year</span><span class="p">(</span><span class="mi">25</span><span class="p">)</span>
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630.0
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<h3 id="5-mpg-difference-(25-mpg-to-30-mpg)">5 mpg difference (25 mpg to 30 mpg)<a class="anchor-link" href="#5-mpg-difference-(25-mpg-to-30-mpg)">¶</a></h3>
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420.0
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<h3 id="mpg-difference-30-mpg-to-35-mpg">5 mpg difference (30 mpg to 35 mpg)</h3>
<h5 id="note-the-diminishing-returns-as-fuel-efficiency-increases">Note the diminishing returns as fuel efficiency increases</h5>
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300.0
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<h3 id="5-mpg-difference-(35-mpg-to-40-mpg)">5 mpg difference (35 mpg to 40 mpg)<a class="anchor-link" href="#5-mpg-difference-(35-mpg-to-40-mpg)">¶</a></h3>
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225.0
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<h3 id="10-mpg-difference-(20-mpg-to-30-mpg)">10 mpg difference (20 mpg to 30 mpg)<a class="anchor-link" href="#10-mpg-difference-(20-mpg-to-30-mpg)">¶</a></h3>
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1050.0
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<h3 id="10-mpg-difference-(25-mpg-to-35-mpg)">10 mpg difference (25 mpg to 35 mpg)<a class="anchor-link" href="#10-mpg-difference-(25-mpg-to-35-mpg)">¶</a></h3>
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720.0
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525.0
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<h3 id="10-mpg-difference-(40-mpg-to-50-mpg)">10 mpg difference (40 mpg to 50 mpg)<a class="anchor-link" href="#10-mpg-difference-(40-mpg-to-50-mpg)">¶</a></h3>
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315.0
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<p><a href="https://github.com/calebmadrigal/fuel-efficiency-cost-analysis">Github link to this notebook</a></p>Beautiful words2014-03-25T20:30:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-25:beautiful-words/<p>Over the last several years, I've been writing down words (or sets of words) which I consider to be particularly beautiful.</p>
<p>Here is my list:</p>
<ul>
<li>Camp Lejeune</li>
<li>Long Boat Key</li>
<li>Devil May Cry</li>
<li>Effervescent</li>
<li>Cellar Door</li>
<li>Paramore</li>
<li>Nevermore</li>
<li>Evermore</li>
<li>Cognac</li>
<li>vis-à-vis</li>
<li>Commandeer</li>
</ul>Art begets art2014-03-25T20:20:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-25:art-begets-art/<pre>
Art begets art
Hate begets hate
Love begets love
Grace begets grace.
Before we depart
We do place
A lasting mark
On others' fate.
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/18/2014</li>
<li>Inspiration: I've found that taking in good art makes me want to write.</li>
<li>Note: This isn't so much a poem as a truth put into a rhythmic format. It's a bit too "teachy" to be real poetry, in my opinion. Real poetry should not try to teach directly, but rather, should convey feelings (which may indirectly teach something).</li>
</ul>Analogies are like functions2014-03-24T00:07:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-24:analogies-are-like-functions/<p>Analogies are to functions as facts are to variables - facts are data which the mind can reference, but analogies change the way the mind works.</p>
<p>Whenever possible, I try to explain things with analogies.</p>Gray2014-03-17T22:37:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-17:gray/<pre>
Gray
I feel gray
Cannot stay
In this daze.
Even pain -
Let it rain!
Anything…
but this haze.
I need light
Or even night.
These gray skies
Glaze my eyes.
Stimulation!
Exhumation!
Must awaken
To elation.
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/17/2014</li>
<li>Inspiration: I was in a gray mood today, and when I looked outside and saw the gray skies, I thought, “the weather matches my mood… or does my mood match the weather?” I didn’t feel like staying in this gray mood.</li>
</ul>On the words of a song2014-03-12T23:32:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:on-the-words-of-a-song/<pre>
Carried along
On the words of a song,
We let ourselves go
In the waves as they roll.
This ebb and flow
Entraps our souls.
Enraptured so,
As our feelings grow.
And into this torrent,
Reason forfeit,
Our hearts implore us
To join the chorus.
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/10/2014</li>
<li>Inspiration: Music is universal. We enjoy it; we cannot help ourselves. And we want to join with it.</li>
</ul>The deep ocean skies2014-03-12T23:30:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:the-deep-ocean-skies/<pre>
Stay away! Stay away!
Keep away from the bay!
You know that at night,
Will in come the tide,
Sweeping out the mind
That is near the seaside.
And into this sky
You'll sink and you'll fly,
Fish floating by,
Enchanting your eyes,
No more to rise
From the deep ocean skies.
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<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/10/2014</li>
<li>Inspiration: Sometimes, when I need to get work done, I have to stay away from things which will get me into an artistic, or I'll be swept up in it for hours.</li>
</ul>
<p>I think <a href="https://www.flickr.com/photos/alijardine/11360839004/">Ali Jardine</a> was going for the same idea in this beautiful picture:</p>
<p><img alt="Ali Jardine ocean sky" src="/images/ali_jardine_ocean_sky.jpg" /></p>The right side of my mind2014-03-12T23:25:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:the-right-side-of-my-mind/<pre>
Oft on cold and starry nights,
He raises arms, and the battle fights.
And storms the castle of my mind,
Removing from the throne my logical side.
And having the ship commandeered,
Into the stormy winds he steers,
And brings us into crashing waves -
Deep oceans are within his gaze.
And rejoicing on the captain's deck,
Tiring of appointments to respect,
He does not care if we should wreck
But only in beauty does he invest.
Careless and wild - this side of mine.
Roaring through life, not glancing behind
"Behold! the sails are filled with wind!
Onward towards the moon again!"
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<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/10/2014</li>
<li>Inspiration: What it feels like when my right-brain takes control. Often, starry nights and moonlight provoke me.</li>
</ul>The stars as they shine2014-03-12T23:19:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:the-stars-as-they-shine/<pre>
The stars as they shine
Will begin to divide
And in the sky
The Morning’s alive
Which never will die,
And then we ride
To eternal life
And to find our time
Was not lived a lie,
And to meet His smile
And to see His face
To bask in His grace
And to in love, embrace.
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/9/2014</li>
<li>Inspiration: Riding on a bus, looking at the beautiful sky, and thinking about meeting God.</li>
</ul>That romantic flow2014-03-12T23:11:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:that-romantic-flow/<pre>
Life is beautiful
I feel it inside
But how can I express
The inner mind?
I suppose I can try
Let’s take a ride…
Heart overflowing
No need to hide
Love is a real thing
And there’s a spiritual side.
There is magic
Hidden from our eyes
Yet felt with the soul
That romantic flow.
And to this goal
I continue to stroll
Seeking that beacon
My spirit to strengthen.
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/9/2014</li>
<li>Inspiration: Looking at the sunrise in Chicago over the lake, after a night casually dressed and deep in conversation.</li>
</ul>Passion not spent2014-03-12T23:07:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:passion-not-spent/<pre>
What's my great fear?
I'll tell you; come near.
To lay down in death
with so much left.
Passion not spent -
Oh cowardly regret!
For fear of others?
The thousand deaths.
I'm afraid to die
With no twinkle in my eye
To pass meagerly by
Yet hidden inside.
To walk through life
Not truly alive
And to pass in the night
With an unfelt "goodbye".
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/7/2014</li>
<li>Inspiration: An explanation of why living from my heart is so important to me.</li>
</ul>Experiencing fully the beautiful present2014-03-12T22:57:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:experiencing-fully-the-beautiful-present/<pre>
He views the world through an unfiltered mind -
No defenses built up, layers over time.
He sees it in all its shining brilliance
Experiencing fully the beautiful present.
</pre>
<ul>
<li>Author: Caleb Madrigal</li>
<li>Date written: 3/4/2014</li>
<li>Inspiration: Rafe (my son) - when I look at his eyes, it looks like he is just driniking everything in.</li>
</ul>Poetic Mood2014-03-12T18:00:00-05:00Caleb Madrigaltag:calebmadrigal.com,2014-03-12:poetic-mood/<p>In the last week or so (starting Monday, March 3, 2014) I've been in a very poetic mood. It has been so interesting - it was light a light switch flipping on. I haven't been sitting down and trying to write poetry, they've just been coming to me. Often, as soon as one ends, another begins. It has been so pleasurable. I hope people enjoy them, but even if they don't, it has been so worth it to me!</p>NodeJS on Heroku2014-02-08T15:45:00-06:00Caleb Madrigaltag:calebmadrigal.com,2014-02-08:nodejs-on-heroku/<p>I've recently tried both <a href="http://heroku.com">Heroku</a> and <a href="http://nodejs.org/">Node.js</a> for the first time. Both are very simple, and work very nicely together. This is a quick guide to deploying a Node.js app to Heroku. To make it simple, I'll walk through deploying a Node.js <a href="https://github.com/calebmadrigal/expressjs-messageboard">sample project I created</a>. It is a very simple message board.</p>
<p>Here are the steps to getting this simple app up and running on Heroku...</p>
<h4>Get Heroku account</h4>
<ul>
<li>Go to <a href="http://heroku.com">Heroku</a>, and click Sign Up</li>
<li>Download and install the Heroku Toolbeld for your operating system (which gives you the <code>heroku</code> command in your terminal)<ul>
<li><a href="https://toolbelt.heroku.com/">Installation details</a></li>
</ul>
</li>
<li>Open your terminal and run <code>heroku login</code>, and enter your heroku credentials and the prompts</li>
</ul>
<h4>Deploy your app to heroku</h4>
<p>In your terminal, do the following:</p>
<ul>
<li><code>git clone https://github.com/calebmadrigal/expressjs-messageboard</code><ul>
<li>Clone the sample message board app</li>
</ul>
</li>
<li><code>cd expressjs-messageboard</code><ul>
<li>It is important to be in the top-level directory of the repository</li>
</ul>
</li>
<li><code>heroku apps:create expressjs-messageboard</code><ul>
<li>Adds a git remote for heroku</li>
<li>At this point, you should be able to see the app listed in your Heroku dashboard</li>
</ul>
</li>
<li><code>git push heroku master</code><ul>
<li>Pushes your repo out to heroku, which causes heroku to deploy your app</li>
</ul>
</li>
<li><code>heroku ps:scale web=1</code><ul>
<li>Ensures that at least 1 "dyno" is allocated to the app</li>
</ul>
</li>
</ul>
<h4>Bask in the glory</h4>
<ul>
<li><code>heroku open</code><ul>
<li>Attempts to open your app in a browser window</li>
</ul>
</li>
</ul>Display List as Table in IPython Notebook2013-08-29T22:42:00-05:00Caleb Madrigaltag:calebmadrigal.com,2013-08-29:display-list-as-table-in-ipython-notebook/<p>IPython Notebook provides hook methods like <code>_repr_html_</code> which can be defined by Python objects to allow richer representations. Here's an example:</p>
<p>
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<span class="sd">""" Overridden list class which takes a 2-dimensional list of </span>
<span class="sd"> the form [[1,2,3],[4,5,6]], and renders an HTML Table in </span>
<span class="sd"> IPython Notebook. """</span>
<span class="k">def</span> <span class="nf">_repr_html_</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">html</span> <span class="o">=</span> <span class="p">[</span><span class="s">"<table>"</span><span class="p">]</span>
<span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">:</span>
<span class="n">html</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s">"<tr>"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">row</span><span class="p">:</span>
<span class="n">html</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s">"<td>{0}</td>"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">col</span><span class="p">))</span>
<span class="n">html</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s">"</tr>"</span><span class="p">)</span>
<span class="n">html</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s">"</table>"</span><span class="p">)</span>
<span class="k">return</span> <span class="s">''</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">html</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="kn">import</span> <span class="nn">random</span>
<span class="n">table</span> <span class="o">=</span> <span class="n">ListTable</span><span class="p">()</span>
<span class="n">table</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="s">'x'</span><span class="p">,</span> <span class="s">'y'</span><span class="p">,</span> <span class="s">'x-y'</span><span class="p">,</span> <span class="s">'(x-y)^2'</span><span class="p">])</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">7</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">table</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">-</span><span class="n">y</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">y</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">])</span>
<span class="n">table</span>
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<table><tr><td>x</td><td>y</td><td>x-y</td><td>(x-y)^2</td></tr><tr><td>7.13100115096</td><td>6.41454890689</td><td>0.716452244068</td><td>0.51330381803</td></tr><tr><td>2.20510983649</td><td>9.08155522913</td><td>-6.87644539264</td><td>47.285501238</td></tr><tr><td>6.02880950267</td><td>0.452385399979</td><td>5.5764241027</td><td>31.0965057731</td></tr><tr><td>2.40055115069</td><td>4.26670665801</td><td>-1.86615550732</td><td>3.48253637751</td></tr><tr><td>8.04537815742</td><td>9.77588474573</td><td>-1.73050658831</td><td>2.99465305217</td></tr><tr><td>8.01528822253</td><td>1.95724789666</td><td>6.05804032587</td><td>36.6998525898</td></tr><tr><td>0.905518153536</td><td>1.91330142109</td><td>-1.00778326755</td><td>1.01562711436</td></tr></table>
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<p>The 6 rich representions currently supported by IPython Notebook are: </p>
<ul>
<li>HTML</li>
<li>JSON</li>
<li>PNG</li>
<li>JPEG</li>
<li>SVG</li>
<li>LaTeX</li>
</ul>
<p>For more information, check out <a href="http://nbviewer.ipython.org/url/github.com/ipython/ipython/raw/master/examples/notebooks/Custom%20Display%20Logic.ipynb">this IPython Notebook</a> (by the IPython team).</p>How To Draw Lines With Matplotlib2013-08-27T22:00:00-05:00Caleb Madrigaltag:calebmadrigal.com,2013-08-27:draw-lines-with-matplotlib/<p>Simple example to show how to draw lines with Matplotlib (in IPython Notebook).</p>
<div class="highlight"><pre>ipython notebook --pylab inline
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<div class="highlight-ipynb"><pre class="ipynb"><span class="kn">import</span> <span class="nn">matplotlib.lines</span> <span class="kn">as</span> <span class="nn">lines</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="mi">6</span><span class="p">)</span> <span class="c"># Make graph square</span>
<span class="n">scatter</span><span class="p">([</span><span class="o">-</span><span class="mf">0.1</span><span class="p">],[</span><span class="o">-</span><span class="mf">0.1</span><span class="p">],</span><span class="n">s</span><span class="o">=</span><span class="mf">0.01</span><span class="p">)</span> <span class="c"># Move graph window a little left and down</span>
<span class="n">line1</span> <span class="o">=</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">)]</span>
<span class="n">line2</span> <span class="o">=</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">)]</span>
<span class="c"># Note that the Line2D takes a list of x values and a list of y values,</span>
<span class="c"># not 2 points as one might expect. So we have to convert our points</span>
<span class="c"># an x-list and a y-list.</span>
<span class="p">(</span><span class="n">line1_xs</span><span class="p">,</span> <span class="n">line1_ys</span><span class="p">)</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">line1</span><span class="p">)</span>
<span class="p">(</span><span class="n">line2_xs</span><span class="p">,</span> <span class="n">line2_ys</span><span class="p">)</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">line2</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">add_line</span><span class="p">(</span><span class="n">Line2D</span><span class="p">(</span><span class="n">line1_xs</span><span class="p">,</span> <span class="n">line1_ys</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'blue'</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">add_line</span><span class="p">(</span><span class="n">Line2D</span><span class="p">(</span><span class="n">line2_xs</span><span class="p">,</span> <span class="n">line2_ys</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'red'</span><span class="p">))</span>
<span class="n">plot</span><span class="p">()</span>
<span class="n">show</span><span class="p">()</span>
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</div></p>Opposite of zip function in Python2013-08-26T15:30:00-05:00Caleb Madrigaltag:calebmadrigal.com,2013-08-26:opposite-of-zip-function/<p>Is there a way to do the opposite of what the <code>zip()</code> function does? It turns out, there is - the <code>zip()</code> function with list unpacking...</p>
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<h3 id="normal-zip-usage">Normal <code>zip()</code> usage</h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">x</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><span class="mi">5</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="mi">30</span><span class="p">,</span><span class="mi">40</span><span class="p">,</span><span class="mi">50</span><span class="p">]</span>
<span class="n">points</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span>
<span class="n">points</span>
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[(1, 10), (2, 20), (3, 30), (4, 40), (5, 50)]
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<h3 id="reverse-of-normal-zip-with-list-unpacking">Reverse of normal <code>zip()</code> with list unpacking</h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">)</span>
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[(1, 2, 3, 4, 5), (10, 20, 30, 40, 50)]
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<div class="highlight-ipynb"><pre class="ipynb"><span class="kn">import</span> <span class="nn">random</span>
<span class="n">rand</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">random</span><span class="o">.</span><span class="n">gauss</span><span class="p">(</span><span class="n">mu</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">points</span> <span class="o">=</span> <span class="p">[(</span><span class="n">rand</span><span class="p">(),</span> <span class="n">rand</span><span class="p">())</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">1000</span><span class="p">)]</span>
<span class="c"># Make the graph square</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">7</span><span class="p">,</span><span class="mi">7</span><span class="p">)</span>
<span class="c"># The scatter function takes an x-list and a y-list, NOT a list of points</span>
<span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">)</span>
<span class="n">scatter</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span>
<span class="n">show</span><span class="p">()</span>
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</div></p>Monte Carlo In Python2013-08-20T13:00:00-05:00Caleb Madrigaltag:calebmadrigal.com,2013-08-20:monte-carlo-in-python/<p><img alt="Monte Carlo Estimation of Area" src="/images/MonteCarloEstimationArea.png" /></p>
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<h1 id="monte-carlo-estimation">Monte Carlo Estimation</h1>
<p><a href="http://en.wikipedia.org/wiki/Monte_Carlo_method">Monte Carlo Estimation</a> is a method of numerically estimating things which we don't (or can't) calculate numerically by randomly generating samples. In this IPython Notebook, I'm going to use Monte Carlo Estimation to estimate:</p>
<ol style="list-style-type: decimal">
<li><a href="#area">The area under a curve</a></li>
<li><a href="#pi">The value of <span class="math">\(\pi\)</span></a></li>
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<h2 id="monte-carlo-estimation-of-area"><a name="area">Monte Carlo Estimation of Area</a></h2>
<p>Let's use <a href="http://en.wikipedia.org/wiki/Monte_Carlo_method">Monte Carlo Estimation</a> to estimate the area onder this curve (from 0 to 10):</p>
<p><span class="math">\[y = 5 * \sin(6~x) + \sin(2~x) + 7\]</span></p>
<h3 id="here-are-the-basic-steps">Here are the basic steps:</h3>
<ol style="list-style-type: decimal">
<li>Define a rectangle which encloses the part of the curve for which we want to find area.</li>
<li>Randomly generate points within that region.</li>
<li>Find which of the randomly generated points are under the curve by checking them against the equation of the function; for a point (x,y), it is under the curve if y <= f(x).</li>
<li>Find the ratio of the points under the curve to the points all the randomly generated points, and multipy that number by the area of the enclosing rectangle (see below for why).</li>
</ol>
<h4 id="why-do-we-need-to-multiply-by-the-area-of-the-rectangle">Why do we need to multiply by the area of the rectangle?</h4>
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<li><p><span class="math">\[\frac{area\ under\ curve}{area\ of\ rectangle} = \frac{points\ under\ curve}{points\ in\ rectangle}\]</span></p></li>
<li><p><span class="math">\[area\ under\ curve\ =\ {area\ of\ rectangle}~(\frac{points\ under\ curve}{points\ in\ rectangle})\]</span></p></li>
</ol>
<h3 id="lets-do-it">Let's do it:</h3>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="mi">6</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="mi">7</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span>
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In [4]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">rect_width</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">rect_height</span> <span class="o">=</span> <span class="mi">14</span>
<span class="n">rand_x</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">rect_width</span><span class="p">)</span>
<span class="n">rand_y</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">rect_height</span><span class="p">)</span>
<span class="n">points</span> <span class="o">=</span> <span class="p">[(</span><span class="n">rand_x</span><span class="p">(),</span> <span class="n">rand_y</span><span class="p">())</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">NUM_POINTS</span><span class="p">)]</span>
<span class="n">points_under</span> <span class="o">=</span> <span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">point</span><span class="p">:</span> <span class="n">point</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o"><=</span> <span class="n">f</span><span class="p">(</span><span class="n">point</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">points</span><span class="p">)</span>
<span class="n">points_above</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">points</span><span class="p">)</span> <span class="o">-</span> <span class="nb">set</span><span class="p">(</span><span class="n">points_under</span><span class="p">))</span>
<span class="c"># Separate x's and y's to pass to scatter function.</span>
<span class="p">(</span><span class="n">under_x</span><span class="p">,</span> <span class="n">under_y</span><span class="p">)</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">points_under</span><span class="p">)</span>
<span class="p">(</span><span class="n">over_x</span><span class="p">,</span> <span class="n">over_y</span><span class="p">)</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">points_above</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">scatter</span><span class="p">(</span><span class="n">under_x</span><span class="p">,</span> <span class="n">under_y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'red'</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">scatter</span><span class="p">(</span><span class="n">over_x</span><span class="p">,</span> <span class="n">over_y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'green'</span><span class="p">)</span>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Area = area of domain rectangle * num_points_under/num_points_total</span>
<span class="n">area</span> <span class="o">=</span> <span class="n">rect_width</span> <span class="o">*</span> <span class="n">rect_height</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">points_under</span><span class="p">)</span><span class="o">*</span><span class="mf">1.0</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">points</span><span class="p">)</span>
<span class="k">print</span> <span class="s">"Estimate of area under the curve:"</span><span class="p">,</span> <span class="n">area</span>
<span class="c"># Sanity check: it looks like the area under is about half of the rectangle, and the rectangle</span>
<span class="c"># area is 10*14 = 140, so it should be around 70.</span>
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Estimate of area under the curve: 73.346
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<h2 id="monte-carlo-estimation-of-pi"><a name="pi">Monte Carlo Estimation of <span class="math">\(\pi\)</span></a></h2>
<p>Let's draw a circle by randomly generating points in the space (<span class="math">\(x\)</span>,<span class="math">\(y\)</span>) such that <span class="math">\(x^{2}+y^{2}\leq1\)</span></p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="kn">import</span> <span class="nn">random</span>
<span class="n">NUM_POINTS</span> <span class="o">=</span> <span class="mi">10000</span>
<span class="c"># Randomly generate points (x[i], y[i]) such that -1 <= x[i] = 1 and -1 <= y[i] <= 1.</span>
<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">NUM_POINTS</span><span class="p">)]</span>
<span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">NUM_POINTS</span><span class="p">)]</span>
<span class="n">circle_x</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">circle_y</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">outsiders_x</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">outsiders_y</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c"># Determine which points are inside the circle (and for visualization purposes, also</span>
<span class="c"># determine which are outside the circle).</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">NUM_POINTS</span><span class="p">):</span>
<span class="k">if</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">circle_x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="n">circle_y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">outsiders_x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="n">outsiders_y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="c"># Plot it.</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">scatter</span><span class="p">(</span><span class="n">outsiders_x</span><span class="p">,</span> <span class="n">outsiders_y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'green'</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">scatter</span><span class="p">(</span><span class="n">circle_x</span><span class="p">,</span> <span class="n">circle_y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'red'</span><span class="p">)</span>
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<h2 id="now-lets-estimate-pi">Now let's estimate <span class="math">\(\pi\)</span></h2>
<p>Here's a few facts:</p>
<ul>
<li>The area of a circle is <span class="math">\(\pi r^2\)</span>.</li>
<li>Since our circle only has a radius of 1, its area is <span class="math">\(\pi\)</span>.</li>
<li>The area of the square is <span class="math">\(2*2 = 4\)</span>.</li>
<li>The ratio of the <strong>area of the circle</strong> to the <strong>area of the square</strong> should be the same as the ratio of the <strong>points inside the circle</strong> to the <strong>points inside the square</strong></li>
<li>So the ratio of <span class="math">\(\frac{\pi}{4} = \frac{circle\ points}{total\ points}\)</span>. So <span class="math">\(\pi = 4~\frac{circle\ points}{total\ points}\)</span></li>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="k">print</span> <span class="s">"Estimate of area of circle (pi):"</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">circle_x</span><span class="p">)</span><span class="o">*</span><span class="mf">1.0</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
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<pre>
Estimate of area of circle (pi): 3.148
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</div></p>Wordpress to Pelican Reasons2013-08-06T13:00:00-05:00Caleb Madrigaltag:calebmadrigal.com,2013-08-06:wordpress-to-pelican-reasons/<p>I recently migrated my blog from <a href="http://wordpress.org/">Wordpress</a> to <a href="http://docs.getpelican.com/en/3.2/">Pelican</a>. Pelican is a static-site generating blog system which is written in Python and uses <a href="http://jinja.pocoo.org/docs/">Jinja2</a> for templating. I'll probably do a post about the migration process later, but for now, I'll just give <strong>my reasons for moving to Pelican...</strong></p>
<h3>Data Longevity</h3>
<p>I didn't want my blog data stored in a database; I vastly prefer it being stored in version-controlled Markdown format.</p>
<h3>Markdown</h3>
<ul>
<li>I wanted to write blog posts in <a href="http://en.wikipedia.org/wiki/Markdown">Markdown</a> (which is possible in Wordpress, but Wordpress isn't designed to use Markdown).</li>
<li>I also get to use <code>vim</code> to write my blog posts now, which is much nicer than the Wordpress editor.</li>
</ul>
<h3>Language</h3>
<ul>
<li>I hate PHP, but love Python. It worried me that my blog was sitting on a giant, ugly PHP stack.</li>
<li>Also, because Pelican is in Python, the code base is much, much cleaner and customizations are much easier.</li>
</ul>
<h3>Security</h3>
<ul>
<li>Pelican outputs a static HTML/JS/CSS site, which exposes a much smaller attack surface than the large Wordpress stack.</li>
<li>I had my Wordpress site hosted on a shared hosting environment, on which I didn't have HTTPS for my blog (so my Wordpress admin password was being transmitted in plain text). With Pelican, I log in over ssh.</li>
</ul>
<h3>Version Control</h3>
<ul>
<li>With Pelican, my blog content and configuration is <a href="https://github.com/calebmadrigal/calebmadrigal-blog">stored in Github</a>, so I have full version control over everything.</li>
<li>It's true that Wordpress has it's own version control, but I trust (and enjoy) git a lot more.</li>
</ul>
<h3>Mobility</h3>
<p>Because everything is in git, and because I only need basic static HTML webserver capabilities, I can host my site just about anywhere. So I can easily change hosts if I see fit.</p>
<h3>Nice Octopress theme</h3>
<p>The default Pelican theme is pretty bad, but I love the <a href="http://octopress.org">Octopress</a> theme, which has been <a href="https://github.com/duilio/pelican-octopress-theme">ported</a> to Pelican.</p>
<h3>Speed</h3>
<p><a href="http://nginx.org/en/">nginx</a> serving static HTML/JS/CSS files is <strong>very fast</strong>. Preliminary tests showed that my site would load <strong>3-10x</strong> faster than with wordpress.</p>
<h3>Staging changes and easy deployment</h3>
<ul>
<li>In Pelican, I can make large changes to the entire blog, regenerate it, and run a staging server to verify that my changes work before ever deploying them.</li>
<li>Pelican comes with a Makefile to make blog generation, testing, and deployment very easy</li>
<li>The command to regenerate the blog is <code>make html</code></li>
<li>The command to run a staging server is <code>make serve</code> or <code>make devserver</code></li>
<li>The command to deploy is <code>make ssh_upload</code></li>
</ul>
<h3>Nicer syntax highlighting</h3>
<p>Pelican has very nice <code>syntax highlighting</code> with <a href="http://pygments.org/">Pygments</a></p>
<p>See:</p>
<div class="highlight"><pre># Result: 1.6180339887498947
reduce(lambda acc,_: (acc+1.0)/acc, xrange(100), 1)
</pre></div>
<h3>Easy code file inclusion</h3>
<p>Include code syntax:</p>
<div class="highlight"><pre>{% include_code python/liquid_tags_test.py lang:python %}
</pre></div>
<p>Result:</p>
<figure class='code'>
<figcaption><span>liquid_tags_test.py</span> <a href='/code/python/liquid_tags_test.py'>download</a></figcaption>
<div class="highlight"><pre><span class="kn">from</span> <span class="nn">urllib2</span> <span class="kn">import</span> <span class="n">urlopen</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">urlopen</span><span class="p">(</span><span class="s">"http://calebmadrigal.com/static/code/python/liquid_tags_test.py"</span><span class="p">)</span><span class="o">.</span><span class="n">read</span><span class="p">()</span>
<span class="k">print</span> <span class="n">data</span>
</pre></div>
</figure>
<h3>Ability to embed IPython Notebooks</h3>
<p>Thanks to <a href="http://jakevdp.github.io/blog/2013/05/07/migrating-from-octopress-to-pelican/#This-Is-An-IPython-Notebook">Jake VanderPlas</a> <a href="https://github.com/jakevdp/pelican-plugins/tree/liquid_tags/liquid_tags">liquid_tags plugin</a>, I can embed an IPython Notebook like this:</p>
<div class="highlight"><pre>{% notebook ipython_notebook/EmbedNotebookExample.ipynb %}
</pre></div>
<p>Which looks like this:</p>
<p>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">
In [5]:
</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight-ipynb"><pre class="ipynb"><span class="n">x</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="o">*</span><span class="n">pi</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span><span class="s">'ro'</span><span class="p">)</span>
</pre></div>
</div>
</div>
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<p>Another nice benefit of being able to embed IPython Notebooks is that they can render mathematics formulas with <a href="http://www.mathjax.org/">MathJax</a>:</p>
<p><span class="math">\[x^2 + y^2 = \pi\]</span></p>
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</div></p>IPython Notebook on a VPS2013-07-31T21:12:04-05:00Caleb Madrigaltag:calebmadrigal.com,2013-07-31:ipython-notebook-vps/<h2>Overview</h2>
<p>This is a guide to set up IPython Notebook on a Server - specifically, on a <a href="https://www.digitalocean.com/">DigitalOcean</a> VPS. This will allow you to access your <a href="http://ipython.org/ipython-doc/dev/interactive/htmlnotebook.html">iPython Notebooks</a> from anywhere.</p>
<h3>Overview of Steps:</h3>
<ul>
<li>Set up a domain name</li>
<li>Get a VPS</li>
<li>Install IPython Notebook (and all dependencies)</li>
<li>Configure IPython Notebook to run in a server mode</li>
<li>Add SSL</li>
<li>Make IPython Notebook start automatically</li>
</ul>
<h2>Create a domain</h2>
<p><strong>Go to <a href="http://freedns.afraid.org">http://freedns.afraid.org</a></strong> and click <strong>"Setup an account here"</strong> Go through the signup form Click on the activation link they send to your email This will bring you back to their site; Click the link you see there called <strong>"Add a subdomain"</strong> Here is how I filled out the form:</p>
<p><img alt="Create Domain" src="/images/00_create_domain.png" /></p>
<h3>Notes:</h3>
<ul>
<li>Leave the Destination alone for now, and leave the page open, as we will come back and change the destination in a minute.</li>
<li>You the domain name you select may be taken; if so, just click on the "Subdomains" link and try a different name.</li>
</ul>
<h2>Get a VPS (Virtual Private Server)</h2>
<p>For the tutorial, I'm using <a href="https://www.digitalocean.com/">Digital Ocean</a>, since it is what I use personally. It is only $5/month for an SSD-based VPS (as of August 2013).</p>
<p><strong>Create an account</strong> on <a href="https://www.digitalocean.com/">Digital Ocean</a>, including putting in a credit card</p>
<p>Go to the Droplets tab and hit the button: "Create Droplet" ("Droplet" is how DigitalOcean refers to their VPSs):</p>
<p><img alt="Create Droplet" src="/images/01_create_droplet.png" /></p>
<p><strong>Enter the hostname</strong> as the domain name you just set up above</p>
<p><img alt="Set hostname, size" src="/images/02_create_droplet_size.png" /></p>
<p>Make sure you have <strong>Ubuntu 12.04 x32</strong> selected. You should be able to keep all the other default settings.</p>
<p><img alt="Select Ubuntu OS" src="/images/03_create_droplet_os.png" /></p>
<p>Click <strong>"Create Droplet"</strong> and then wait for it to be created. When it is done, you should see a screen like this:</p>
<p><img alt="Droplet created" src="/images/04_droplet_created.png" /></p>
<p><strong>Make a note of the IP Address</strong></p>
<p>You will also receive an email that gives you the password for the root user on this Droplet (VPS). When you get that email, you will have all the information you need to log in to the new VPS:</p>
<div class="highlight"><pre><span class="n">IP</span><span class="o">:</span> <span class="mf">192.241</span><span class="o">.</span><span class="mf">162.4</span> <span class="o">(</span><span class="k">in</span> <span class="n">my</span> <span class="k">case</span><span class="o">)</span>
<span class="n">Username</span><span class="o">:</span> <span class="n">root</span>
<span class="n">Password</span><span class="o">:</span> <span class="n">mysecretpassword</span>
</pre></div>
<p>If you are on mac or linux, you can just type the command:</p>
<div class="highlight"><pre><span class="n">ssh</span> <span class="n">root</span><span class="mf">@192.241.162.4</span> <span class="err">#</span> <span class="p">(</span><span class="n">of</span> <span class="n">course</span><span class="p">,</span> <span class="n">with</span> <span class="n">your</span> <span class="n">Droplet</span><span class="err">'</span><span class="n">s</span> <span class="n">IP</span> <span class="n">Address</span><span class="p">)</span>
</pre></div>
<p><strong>If you are on windows, you can use <a href="http://www.chiark.greenend.org.uk/~sgtatham/putty/download.html">Putty</a>.</strong></p>
<p>Once you are logged in, you should see a prompt that looks something like this:</p>
<p><img alt="SSH" src="/images/05_ssh.png" /></p>
<p>I recommend <strong>changing your password</strong>. To do this, just type <code>passwd</code>, and it will prompt you for a new password. If you do this, then you will login with that password from then on (instead of the one that was emailed to you).</p>
<h2>Set domain to point to this server</h2>
<p>Now that you can login, let's set up DNS to point your domain name to this server.</p>
<p><strong>Go back into the freedns.afraid.org</strong>, and click on the domain link, and <strong>change the Destination</strong> to the IP Address of your Server/Droplet/VPS.</p>
<p>Now you may have to wait for a few minutes (or hours) before you are able to access your server by this name, and you can move on to the other steps without this, but here is how you see if it is ready:</p>
<p>Do this on a command-line (<strong>Terminal</strong> if on mac, <strong>cmd</strong> in windows, if you're on linux, then you know it :) ).</p>
<div class="highlight"><pre>ping ipynb.mooo.com # (or whatever your domain is).
</pre></div>
<p>You will know if the DNS change has propagated to you if you see your server's IP address in there. When I first tried it, the IP was still out of date:</p>
<p><img alt="Ping domain" src="/images/06_ping.png" /></p>
<h2>Install IPython Notebook and its dependencies</h2>
<div class="highlight"><pre>apt-get update # To update the repository
apt-get install python-pip python-virtualenv python-numpy python-scipy
pip install tornado pyzmq ipython
</pre></div>
<h2>Create an SSL Certificate</h2>
<p>You will need an SSL Certificate below; to create it, enter the command below, and set the prompts as see fit to you:</p>
<div class="highlight"><pre>openssl req -x509 -nodes -newkey rsa:1024 -keyout ipython_cert.pem -out ipython_cert.pem
</pre></div>
<p>It should ask you a few questions, and look something like this:</p>
<div class="highlight"><pre>Generating a 1024 bit RSA private key
.............++++++
......................................++++++
writing new private key to 'ipython_cert.pem'
-----
You are about to be asked to enter information that will be incorporated
into your certificate request.
What you are about to enter is what is called a Distinguished Name or a DN.
There are quite a few fields but you can leave some blank
For some fields there will be a default value,
If you enter '.', the field will be left blank.
-----
Country Name (2 letter code) [AU]:US
State or Province Name (full name) [Some-State]:Wisconsin
Locality Name (eg, city) []:Milwaukee
Organization Name (eg, company) [Internet Widgits Pty Ltd]:CalebMadrigal
Organizational Unit Name (eg, section) []:
Common Name (e.g. server FQDN or YOUR name) []:Caleb
Email Address []:caleb.madrigal@gmail.com
</pre></div>
<p>Move the certificate to the .ssl directory:</p>
<div class="highlight"><pre>mkdir /root/.ssl
mv ipython_cert.pem /root/.ssl
</pre></div>
<h2>Create a password hash</h2>
<p>You will need a password to protect you IPython Notebook from other people. So choose a password, and then follow these steps to get the hash of the password (which you will use below).</p>
<p>On the command-line, run:</p>
<div class="highlight"><pre>ipython
</pre></div>
<p>And type in the following (and enter your desired password at the "Enter password" prompt):</p>
<div class="highlight"><pre><span class="n">In</span> <span class="p">[</span><span class="mi">1</span><span class="p">]:</span> <span class="kn">from</span> <span class="nn">IPython.lib</span> <span class="kn">import</span> <span class="n">passwd</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">2</span><span class="p">]:</span> <span class="n">passwd</span><span class="p">()</span>
<span class="n">Enter</span> <span class="n">password</span><span class="p">:</span>
<span class="n">Verify</span> <span class="n">password</span><span class="p">:</span>
<span class="n">Out</span><span class="p">[</span><span class="mi">4</span><span class="p">]:</span> <span class="s">'sha1:1219a393391f:5e453a30e31c69641678aba65e2e91aeadeb1068'</span>
</pre></div>
<p>That output string, <strong>'sha1:1219a393391f:5e453a30e31c6...'</strong> is your hash. Save it, as you will use it below.</p>
<h2>Configure IPython Notebook</h2>
<p>Create a directory to hold your IPython Notebook files (*.ipynb)</p>
<div class="highlight"><pre>cd /root
mkdir pynb
</pre></div>
<p>Create a IPython Notebook profile</p>
<div class="highlight"><pre>ipython profile create nbserver
</pre></div>
<p>Edit the config file for IPython notebook for the newly created profile; NOTE: you can use nano place of vim if you don't know vim.</p>
<div class="highlight"><pre>vim /root/.ipython/profile_nbserver/ipython_notebook_config.py
</pre></div>
<p>Add the following lines to the top:</p>
<div class="highlight"><pre>c = get_config()
c.IPKernalApp.pylab = 'inline'
c.NotebookApp.certfile = u'/root/.ssl/ipython_cert.pem'
c.NotebookApp.ip = '*'
c.NotebookApp.open_browser = False
c.NotebookApp.password = u'REPLACE ME'
c.NotebookApp.port = 4096
c.NotebookManager.notebook_dir = u'/root/pynb'
</pre></div>
<p><strong>Make sure to replace the 'REPLACE ME' string with the password hash which you generated above</strong></p>
<p>Now, to run IPython Notebook with all of these settings, you this command:</p>
<div class="highlight"><pre>ipython notebook --profile nbserver --pylab inline
</pre></div>
<p>And finally, you should be able to access your IPython Notebook server from anywhere from a URL like this (but with your own hostname instead of mine): https://ipython.mooo.com:4096/</p>
<p>And it should look like this:</p>
<p><img alt="IPython Notebook running" src="/images/07_signature_check.png" /></p>
<h2>How to check that your certificate is correct</h2>
<p>Since you are not using a certificate signed by a certificate authority, you will need to be able to verify that the certificate is correct when you go to the IPython Notebook site. To do this, I recommend downloading the Chrome extension put out by <a href="https://www.signaturecheck.org/">https://www.signaturecheck.org/</a>. Just Google for "Google Chrome Signature Check"</p>
<p>You can see me using it in the <strong>image above</strong>. Just memorize at least some of the digits in the MD5 or SHA1 Thumbprint. Else, you can write them down somewhere. It's okay if someone finds them; these numbers are meant to be public.</p>
<h2>Set up IPython Notebook to start automatically</h2>
<p>So that you don't have to log in to SSH to get IPython Notebook running, you can set up supervisord to start it for you:</p>
<p>Find the path of ipython:</p>
<div class="highlight"><pre>root@ipynb:~# which ipython
/usr/local/bin/ipython
</pre></div>
<p>Add this line to the file: <code>/etc/rc.local</code></p>
<div class="highlight"><pre>/usr/local/bin/ipython notebook --profile nbserver --pylab inline
</pre></div>
<p>Now you should be able to reboot, and you should be able to access your IPython Notebook as before. So at this point, even if the server reboots, iPython Notebook will be started again.</p>
<p>To test this, type <code>reboot</code> into the command-line. This will boot you out of SSH, but you should be able to reconnect in a minute or 2. After the server has had time to reboot, you should see if you can access your IPython Notebook server (as done above). If so, everything is working.</p>
<h2>Final Notes</h2>
<ul>
<li>Remember to always check the SSL signature before typing your passoword in. If you don't, then it is possible that there is a Man-in-the-Middle attack going on, and someone evil could see your password</li>
<li>You are typically encouraged not to run things with root, but if IPython Notebook is all you are using this VPS for, then it should be fine.</li>
<li>You are typically encouraged to run python stuff in a virtualenv. That is typically good, but for simplicity, I didn't include it in this tutorial.</li>
<li>For now, you cannot organize IPython Notebooks in subdirectories (and access them all with a single running instance of iPython Notebook). But that should be coming in the future: https://github.com/ipython/ipython/wiki/IPEP-16%3A-Notebook-multi-directory-dashboard-and-URL-mapping</li>
</ul>
<h2>THE END</h2>Big graphs in IPython Notebook2013-07-29T21:20:15-05:00Caleb Madrigaltag:calebmadrigal.com,2013-07-29:big-graphs-ipython-notebook/<p>I've been doing a good bit of <a href="https://github.com/calebmadrigal/FourierTalkOSCON">graphing</a> in IPython Notebook recently, and I often wanted to make the graphs larger. I also often wanted to label the graph axes. So I wrote this simple function and have been using it a lot.</p>
<div class="highlight"><pre><span class="err">#</span> <span class="nx">Graphing</span> <span class="nx">helper</span> <span class="kd">function</span>
<span class="nx">def</span> <span class="nx">setup_graph</span><span class="p">(</span><span class="nx">title</span><span class="o">=</span><span class="s1">''</span><span class="p">,</span> <span class="nx">x_label</span><span class="o">=</span><span class="s1">''</span><span class="p">,</span> <span class="nx">y_label</span><span class="o">=</span><span class="s1">''</span><span class="p">,</span> <span class="nx">fig_size</span><span class="o">=</span><span class="nx">None</span><span class="p">)</span><span class="o">:</span>
<span class="nx">fig</span> <span class="o">=</span> <span class="nx">plt</span><span class="p">.</span><span class="nx">figure</span><span class="p">()</span>
<span class="k">if</span> <span class="nx">fig_size</span> <span class="o">!=</span> <span class="nx">None</span><span class="o">:</span>
<span class="nx">fig</span><span class="p">.</span><span class="nx">set_size_inches</span><span class="p">(</span><span class="nx">fig_size</span><span class="cp">[</span><span class="mi">0</span><span class="cp">]</span><span class="p">,</span> <span class="nx">fig_size</span><span class="cp">[</span><span class="mi">1</span><span class="cp">]</span><span class="p">)</span>
<span class="nx">ax</span> <span class="o">=</span> <span class="nx">fig</span><span class="p">.</span><span class="nx">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="nx">ax</span><span class="p">.</span><span class="nx">set_title</span><span class="p">(</span><span class="nx">title</span><span class="p">)</span>
<span class="nx">ax</span><span class="p">.</span><span class="nx">set_xlabel</span><span class="p">(</span><span class="nx">x_label</span><span class="p">)</span>
<span class="nx">ax</span><span class="p">.</span><span class="nx">set_ylabel</span><span class="p">(</span><span class="nx">y_label</span><span class="p">)</span>
</pre></div>
<p>Here's a demo of using it...</p>
<p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">x</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">pi</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
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<h2 id="without-setup_graph">Without setup_graph()</h2>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">_</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
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<h2 id="with-setup_graph">With setup_graph()</h2>
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In [26]:
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">setup_graph</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s">'Pretty graph'</span><span class="p">,</span> <span class="n">x_label</span><span class="o">=</span><span class="s">'Time'</span><span class="p">,</span> <span class="n">y_label</span><span class="o">=</span><span class="s">'Amplitude'</span><span class="p">,</span> <span class="n">fig_size</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
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</div>
</div>
</div></p>Pandas Into2013-05-11T19:01:01-05:00Caleb Madrigaltag:calebmadrigal.com,2013-05-11:pandas_intro/<p>I've recently been playing with the <a href="http://pandas.pydata.org/">pandas</a> Python data analysis framework while reading the <a href="http://shop.oreilly.com/product/0636920023784.do">Python for Data Analysis book</a> (which is written by the author of the pandas library). Here are 2 of my IPython Notebooks that demonstrate some of the basics:</p>
<ul>
<li><a href="http://nbviewer.ipython.org/urls/raw.github.com/calebmadrigal/ipython_notebooks/master/PandasTesting1.ipynb">IPython Notebook Viewer</a></li>
<li><a href="http://nbviewer.ipython.org/urls/raw.github.com/calebmadrigal/ipython_notebooks/master/PandasBabyNameAnalysis.ipynb">US Names Examples</a><ul>
<li>This is an example from the book which I've made some modifications to.</li>
</ul>
</li>
</ul>
<p>And here's a little screenshot of what it looks like in IPython Notebook:</p>
<p><img alt="ipython notebook screenshot" src="/images/pandas_intro_screenshot.png" /></p>Finding the Golden Ratio2013-03-01T19:52:27-06:00Caleb Madrigaltag:calebmadrigal.com,2013-03-01:finding-golden-ratio/<p>I recently was exploring the <a href="http://en.wikipedia.org/wiki/Golden_ratio">Golden Ratio</a>. I was really surprised what a simple (and recursive) relationship it comes from:</p>
<p><img alt="golden_ratio" src="/images/golden_ratio.png" /></p>
<p>Starting with this this image, here is the derivation of the golden ratio...</p>
<p>
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<p>From this relationship we see in this image, we can derive this equation: <span class="math">\[\frac{a}{b} = \frac{a+b}{a}\]</span></p>
<p>And if we then let b=1 (so we can find the ratio of a to 1), we get: <span class="math">\[a = \frac{a+1}{a}\]</span></p>
<p>Then, with this formula, we can define a function: <span class="math">\[f(a) = \frac{a+1}{a}\]</span></p>
<p>If we then find the <strong>fixed-point in this function</strong> (so that f(x) = x), then we will have found a solution to <span class="math">\[a = \frac{a+1}{a}\]</span></p>
<p>A simple way to think about the fixed-point of this function is this: it is the place where <span class="math">\(y=x\)</span> (or <span class="math">\(f(x) = x\)</span> ) intersects with our function. And that intersction point should be the golden ratio.</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="c"># Plot y=(x+1)/x and y=x</span>
<span class="n">x</span><span class="o">=</span><span class="n">numpy</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1000</span><span class="p">)</span>
<span class="n">y</span><span class="o">=</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">a</span><span class="p">:</span> <span class="p">(</span><span class="n">a</span><span class="o">+</span><span class="mf">1.0</span><span class="p">)</span><span class="o">/</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="n">y2</span><span class="o">=</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">a</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="s">'r'</span><span class="p">)</span>
<span class="c"># Make graph square</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">matplotlib</span><span class="o">.</span><span class="n">pyplot</span><span class="o">.</span><span class="n">gcf</span><span class="p">()</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_size_inches</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
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<p>Another way to find the golden ratio is to use <a href="http://en.wikipedia.org/wiki/Fixed-point_iteration">Fixed-point iteration</a> - again, since we know that finding the fixed point of the function:</p>
<p><span class="math">\[f(a) = \frac{a+1}{a}\]</span></p>
<p>is the golden ratio.</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">golden_ratio</span> <span class="o">=</span> <span class="nb">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">acc</span><span class="p">,</span><span class="n">_</span><span class="p">:</span> <span class="p">(</span><span class="n">acc</span><span class="o">+</span><span class="mf">1.0</span><span class="p">)</span><span class="o">/</span><span class="n">acc</span><span class="p">,</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">100</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">print</span> <span class="n">golden_ratio</span>
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<pre>
1.61803398875
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</div></p>How to graph with IPython Notebook2013-01-21T22:04:23-06:00Caleb Madrigaltag:calebmadrigal.com,2013-01-21:graph-ipython-notebook/<p>IPython Notebook / Matplotlib / Pylab / Numpy is great for graphing (among other things). Below is a simple demo of how to graph with it.</p>
<p>To run IPython Notebook, use this command: <code>ipython notebook --pylab inline</code></p>
<p>Here's a screenshot:</p>
<p><img alt="IPython Notebook Example" src="/images/ipython_notebook_example.png" /></p>
<p>Here's an embedded IPython Notebook showing a slightly easier way:</p>
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<div class="highlight-ipynb"><pre class="ipynb"><span class="n">x</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">,</span> <span class="mi">42</span><span class="p">)</span>
<span class="n">f1</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">f2</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
<span class="n">f3</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f1</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f2</span><span class="p">,</span> <span class="s">'ro'</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f3</span><span class="p">,</span> <span class="s">'g--'</span><span class="p">)</span>
<span class="n">show</span><span class="p">()</span>
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/LjoUPSSkJCAyMhIuLu7IzAwEHv37kWfPn1Eh2WwihUrAuBLZHTt2hVHjx4VHJF+3Nzc4ObmhoYN
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k5Ysie+//x5+fn7Iz8/HgAED4OnpKcelZBEYGIj4+Hjcv38flStXxpQpU9CvXz/RYent0KFDWL16
9fMyMACYPn062rZtKzgy/dy6dQt9+/aFVquFVqvFp59+ilatWokOyyhq7E68c+cOunbtCoB3SfTq
1Qtt2rQRHJX+IiIi0KtXL+Tk5ECj0WDlypWiQzJIRkYG9uzZo9fYg9ETeQghhIil3mFyQgixcpTA
CSFEpSiBE0KISlECJ4QQlaIETgghKkUJnBBCVOr/AeB42cOMzzWiAAAAAElFTkSuQmCC
"
>
</div>
</div>
</div>
</div>
</div></p>
<p>Note: using the <code>--pylab</code> argument makes python automatically import a number of modeules, so that I can do things like just writing <code>pi</code> instead of <code>math.pi</code>. Also, <code>sin()</code> is the <code>scipy.sin()</code> function, which can take a numpy array as an argument, so that I don't have to do a <code>map()</code> or list comprehension to apply the function to each item in <code>x</code>.</p>Running Ubuntu on VirtualBox in Windows2012-11-28T18:48:27-06:00Caleb Madrigaltag:calebmadrigal.com,2012-11-28:running-ubuntu-virtualbox/<p>I'm mostly a Mac user and I also really like Linux (especially Ubuntu), but I hate Windows. However, I'm occasionally required to use Windows at work, so I've found a way to make using Windows more enjoyable: to use Ubuntu (installed on VirtualBox inside of Windows) instead of Windows for everything except for the few tasks which require Windows.</p>
<p>So I have made this little <strong>How to Install Ubuntu on VirtualBox in Windows</strong> setup guide:</p>
<h2>Contents</h2>
<ul>
<li>Install VirtualBox</li>
<li>Download Ubuntu 12.04 ISO file</li>
<li>Create and configure a Virtual Machine</li>
<li>Tweak Virtual Machine hardware settings</li>
<li>Install Ubuntu in the Virtual Machine</li>
<li>Make Ubuntu nicer to use in VirtualBox</li>
<li>Using your new Virtual Ubuntu system</li>
</ul>
<h2>Install VirtualBox</h2>
<ul>
<li>Download installer from: https://www.virtualbox.org/wiki/Downloads</li>
<li>The version I am using is 4.2.4: <a href="http://download.virtualbox.org/virtualbox/4.2.4/VirtualBox-4.2.4-81684-Win.exe">http://download.virtualbox.org/virtualbox/4.2.4/VirtualBox-4.2.4-81684-Win.exe</a></li>
</ul>
<h2>Download Ubuntu 12.04 ISO file</h2>
<ul>
<li>Download 12.04 LTS (12.10 is VERY SLOW in VirtualBox): <a href="http://www.ubuntu.com/download/desktop/questions?distro=desktop&bits=32&release=lts">http://www.ubuntu.com/download/desktop/questions?distro=desktop&bits;=32&release;=lts</a></li>
</ul>
<h2>Create a virtual machine</h2>
<h4>Hit New:</h4>
<p><img alt="Virtualbox New" src="/images/virtualbox_new.png" /></p>
<h4>Type: Linux, Version: Ubuntu</h4>
<p><img alt="Virtualbox Create VM" src="/images/virtualbox_create_vm.png" /></p>
<h4>2 Gb memory (At least that's what I used on an 8Gb machine)</h4>
<p><img alt="Virtualbox Ram" src="/images/virtualbox_ram.png" /></p>
<h4>Create a virtual hard drive</h4>
<p><img alt="Virtualbox HD" src="/images/virtualbox_hd.png" /></p>
<h4>Use VID Format</h4>
<p><img alt="Virtualbox HD Format" src="/images/virtualbox_hd_format.png" /></p>
<h4>Create a Fixed size hard drive - they are faster</h4>
<p><img alt="Virtualbox HD Fixed Size" src="/images/virtualbox_hd_fixed_size.png" /></p>
<h4>I allocated 10 Gb for my virtual hard drive</h4>
<p><img alt="Virtualbox HD Size" src="/images/virtualbox_hd_size.png" /></p>
<h4>Select the Ubuntu ISO as a CD; Go to Settings -> Storage</h4>
<p><img alt="Virtualbox CD" src="/images/virtualbox_cd.png" /></p>
<h4>Click "Choose Disk"</h4>
<p><img alt="Virtualbox choose disk" src="/images/virtualbox_choose_disk.png" /></p>
<h4>Choose the Ubuntu ISO file</h4>
<p><img alt="Virtualbox choose disk2" src="/images/virtualbox_choose_disk2.png" /></p>
<p>Then finish out the wizard</p>
<h2>Tweak Virtual Machine hardware settings</h2>
<h4>Open the Settings</h4>
<p><img alt="Virtualbox Settings" src="/images/virtualbox_settings.png" /></p>
<h4>Add more Video memory and enable 3d acceleration</h4>
<p><img alt="Virtualbox video memory" src="/images/virtualbox_video_mem.png" /></p>
<h4>Default network settings worked for me</h4>
<p><img alt="Virtualbox networking" src="/images/virtualbox_network.png" /></p>
<h4>Add shared host drive. Later, this will allow you to mount your entire windows hard drive from Ubuntu</h4>
<p><img alt="Virtualbox shared folders" src="/images/virtualbox_shared_folders.png" /></p>
<h4>Enable copy/paste between Linux and Windows</h4>
<p>Go to Settings - General - Advanced and set Shared Clipboard to be "Bidirectional".</p>
<p><img alt="Virtualbox shared clipboard" src="/images/virtualbox_shared_clipboard.png" /></p>
<p>Now exit out of the settings. Time to install Ubuntu.</p>
<h2>Install Ubuntu in the Virtual Machine</h2>
<h4>Click "Start" to start the Virtual Machine</h4>
<p><img alt="Virtualbox start" src="/images/virtualbox_start.png" /></p>
<h4>The Virtual Machine should see the "bootable" Ubuntu ISO image and run it automatically. If this works, you will soon see the Ubuntu installation screen</h4>
<p><img alt="Ubuntu install screen" src="/images/ubuntu_install_screen.png" /></p>
<h4>Ubuntu Installation Steps</h4>
<p>The wizard will walk you through these, but here are the basic steps:</p>
<ul>
<li>Click "Install Ubuntu"</li>
<li>Check "Download updates while installing" and Check "Install this third-party software" (and then click "Continue")</li>
<li>Select "Erase disk and install Ubuntu" (and then click Continue)<ul>
<li>Note that this erases your virtual hard drive created just for Ubuntu (not your entire real computer hard drive)</li>
</ul>
</li>
<li>Click "Install Now"</li>
<li>While installing, it will prompt you for some basic info like timezone, keyboard layout, etc. Just do what is best for you.</li>
<li>Also, while installing, it will prompt you for "Who you are?" Make sure to pick a username and password which you will remember.</li>
<li>Also, click "Require password on startup", because you will need this later when you switch to Xubuntu (assuming you want to switch - I recommend it for speed).</li>
<li>When complete, click restart</li>
<li>Right click on the CD looking thing near the bottom right of the VirtualBox window to remove the installation disk (the Ubuntu ISO) from the Virtual drive.</li>
<li>Login when it restarts.</li>
</ul>
<h2>Make Ubuntu nicer to use in VirtualBox</h2>
<h4>Install "Guest Additions"</h4>
<p>The Guest Additions allow Ubuntu to behave better inside of Virtualbox; for example, you can resize the VirtualBox window and Ubuntu will appropriately resize. Here are the steps:</p>
<ul>
<li>Click on Devices - Install Guest Additions (in the VitualBox window).</li>
<li>Click "Run" on the window that pops up.</li>
<li>Enter your password on the box that pops up and click "Authenticate"</li>
</ul>
<h4>Install Updates</h4>
<p>You should get a popup asking if you want to install updates. If you do, install them.</p>
<h4>Install Xubuntu</h4>
<p>Xubuntu is a customized XFCE packages. It is much more lightweight than the default Unity window manager. I also prefer it to Unity</p>
<ul>
<li>Open the Terminal</li>
<li>sudo apt-get install xubuntu-desktop</li>
<li>Once that finishes installing, log out</li>
<li>Click the Ubuntu button to switch to the Xubuntu window manage:</li>
</ul>
<p><img alt="Ubuntu change wm" src="/images/ubuntu_change_wm.png" /></p>
<ul>
<li>Select "Xubuntu Session"</li>
</ul>
<p><img alt="Ubuntu change wm2" src="/images/ubuntu_change_wm2.png" /></p>
<ul>
<li>Then log back in, and you should have a Xubuntu desktop</li>
</ul>
<h4>Add access to your entire Windows hard drive within Ubuntu</h4>
<p>Run this command at the Terminal (the Terminal can be found under Accessories):</p>
<div class="highlight"><pre>sudo mount -t vboxsf C_DRIVE /media/windows
</pre></div>
<p>This command must be run each time you start the Virtual Machine. I decided to write a script called mountw to run this script:</p>
<div class="highlight"><pre>sudo cat "sudo mount -t vboxsf C_DRIVE /media/windows" > /usr/bin/mountw
sudo chmod a+x /usr/bin/mountw
</pre></div>
<p>Now I can just run "mountw" from the terminal when I want full access to my Windows hard drive.</p>
<p><strong>The installation/configuration is complete!</strong></p>
<h2>Using your new Virtual Ubuntu system</h2>
<p>You can, of course, just keep Ubuntu running in the VirtualBox window (which is what I do most of the time):</p>
<p><img alt="Ubuntu in windows" src="/images/ubuntu_in_window.png" /></p>
<p>Or, you can also use "Seemless mode" by clicking "Host-L" ("Host" is typically the Right Control key, so Right Control+L), which lets you have mesh Linux and Windows windows right beside each other (without having the containing VirtualBox window). You can click Right Control+L again to get out of Seamless mode:</p>
<p><img alt="Ubuntu in seamless" src="/images/ubuntu_in_seamless.png" /></p>
<p>Lastly, if you want to stop using your Virtual Machine for a little while but don't want to turn it off, you can just hit "Right Control+P" to pause it.</p>
<p>Special thanks to <a href="http://www.wisdomandwonder.com/">Grant Rettke</a> for helping me compile this guide.</p>Pyknon Intro, Chords, and Intervals2012-11-26T06:19:53-06:00Caleb Madrigaltag:calebmadrigal.com,2012-11-26:pyknon-intro-chords-intervals/<p>I've continued on my (hopefully) short-term fascination with music+math (it's fun, but really bad for productivity). So I found this great library for generating music in Python called <a href="http://kroger.github.com/pyknon/">Pyknon</a>. And it can be installed using pip: <code>pip install pyknon</code>.</p>
<p>I wrote a little python script just to help me understand some concepts in music theory like intervals and chords. It is meant to be read top to bottom (which is why I intersperse functions and variables throughout). It is NOT written in good modular form (in general, I don't recommend writing python like this). This code can also be used as an intro to the pyknon library.</p>
<p>Behold:</p>
<div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyknon.genmidi</span> <span class="kn">import</span> <span class="n">Midi</span>
<span class="kn">from</span> <span class="nn">pyknon.music</span> <span class="kn">import</span> <span class="n">NoteSeq</span><span class="p">,</span> <span class="n">Note</span><span class="p">,</span> <span class="n">Rest</span>
<span class="c">####### First we'll generate all piano notes</span>
<span class="c"># Pyknon dubs C5 as the value 0, so Note(0) give you C5</span>
<span class="c"># (C in the 5th octave). So we have to move 51 keys to the</span>
<span class="c"># left to get the far left key on a piano.</span>
<span class="n">first_note</span> <span class="o">=</span> <span class="n">Note</span><span class="p">(</span><span class="s">"A,,,,,"</span><span class="p">)</span> <span class="c"># The far-left key on the piano</span>
<span class="k">def</span> <span class="nf">key_number</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="k">return</span> <span class="n">n</span><span class="o">.</span><span class="n">octave</span> <span class="o">*</span> <span class="mi">12</span> <span class="o">+</span> <span class="n">n</span><span class="o">.</span><span class="n">value</span> <span class="o">-</span> <span class="n">first_note</span><span class="o">.</span><span class="n">value</span>
<span class="k">def</span> <span class="nf">note_from_key_number</span><span class="p">(</span><span class="n">k</span><span class="p">):</span>
<span class="k">return</span> <span class="n">Note</span><span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">51</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">intervals</span><span class="p">(</span><span class="n">notes</span><span class="p">):</span>
<span class="n">interval</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">notes</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<span class="n">interval</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">notes</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">notes</span><span class="p">[</span><span class="n">n</span><span class="p">])</span>
<span class="k">return</span> <span class="n">interval</span>
<span class="n">piano_notes</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">note_from_key_number</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="mi">88</span><span class="p">))</span>
<span class="n">midi</span> <span class="o">=</span> <span class="n">Midi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">tempo</span><span class="o">=</span><span class="mi">80</span><span class="p">)</span>
<span class="n">midi</span><span class="o">.</span><span class="n">seq_notes</span><span class="p">(</span><span class="n">piano_notes</span><span class="p">,</span> <span class="n">track</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">midi</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s">"piano_keys.mid"</span><span class="p">)</span>
<span class="c">####### Next we'll examine a major and minor scale, and look at the intervals between</span>
<span class="c">####### each of their notes</span>
<span class="n">middle_c</span> <span class="o">=</span> <span class="n">Note</span><span class="p">(</span><span class="s">"C,"</span><span class="p">)</span> <span class="c"># key_number=39</span>
<span class="n">note_nums</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">key_number</span><span class="p">,</span> <span class="n">piano_notes</span><span class="p">)</span>
<span class="k">print</span> <span class="s">"All piano notes:"</span><span class="p">,</span> <span class="n">note_nums</span>
<span class="k">print</span> <span class="s">"Middle C key number:"</span><span class="p">,</span> <span class="n">key_number</span><span class="p">(</span><span class="n">middle_c</span><span class="p">)</span>
<span class="c"># A, means drop the octave, C' means raise the octave.</span>
<span class="c"># Also, in a NoteSeq, Pyknon stays in the same octave unless explicitly</span>
<span class="c"># changed by using either , or '.</span>
<span class="n">C_major</span> <span class="o">=</span> <span class="n">NoteSeq</span><span class="p">(</span><span class="s">"C D E F G A B C'' "</span><span class="p">)</span>
<span class="n">A_minor</span> <span class="o">=</span> <span class="n">NoteSeq</span><span class="p">(</span><span class="s">"A, B C' D E F G A"</span><span class="p">)</span>
<span class="c"># Note, when defining a NoteSeq, all notes are by default in the same </span>
<span class="c"># octave as the starting note.</span>
<span class="k">print</span> <span class="s">"C major (staring with middle C):"</span><span class="p">,</span> <span class="nb">map</span><span class="p">(</span><span class="n">key_number</span><span class="p">,</span> <span class="n">NoteSeq</span><span class="p">(</span><span class="s">"C, D E F G A B"</span><span class="p">))</span>
<span class="k">print</span> <span class="s">"C major:"</span><span class="p">,</span> <span class="nb">map</span><span class="p">(</span><span class="n">key_number</span><span class="p">,</span> <span class="n">C_major</span><span class="p">)</span>
<span class="k">print</span> <span class="s">"Intervals for C major:"</span><span class="p">,</span> <span class="n">intervals</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">key_number</span><span class="p">,</span> <span class="n">C_major</span><span class="p">))</span>
<span class="k">print</span> <span class="s">"A minor:"</span><span class="p">,</span> <span class="nb">map</span><span class="p">(</span><span class="n">key_number</span><span class="p">,</span> <span class="n">A_minor</span><span class="p">)</span>
<span class="k">print</span> <span class="s">"Intervals A minor:"</span><span class="p">,</span> <span class="n">intervals</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">key_number</span><span class="p">,</span> <span class="n">A_minor</span><span class="p">))</span>
<span class="c">####### Last we'll generate some chords in a major and minor keys.</span>
<span class="k">def</span> <span class="nf">major_chord</span><span class="p">(</span><span class="n">root</span><span class="p">):</span>
<span class="n">root_key_num</span> <span class="o">=</span> <span class="n">key_number</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">map</span><span class="p">(</span><span class="n">note_from_key_number</span><span class="p">,</span> <span class="p">[</span><span class="n">root_key_num</span><span class="p">,</span> <span class="n">root_key_num</span><span class="o">+</span><span class="mi">4</span><span class="p">,</span> <span class="n">root_key_num</span><span class="o">+</span><span class="mi">7</span><span class="p">])</span>
<span class="k">def</span> <span class="nf">minor_chord</span><span class="p">(</span><span class="n">root</span><span class="p">):</span>
<span class="n">root_key_num</span> <span class="o">=</span> <span class="n">key_number</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">map</span><span class="p">(</span><span class="n">note_from_key_number</span><span class="p">,</span> <span class="p">[</span><span class="n">root_key_num</span><span class="p">,</span> <span class="n">root_key_num</span><span class="o">+</span><span class="mi">3</span><span class="p">,</span> <span class="n">root_key_num</span><span class="o">+</span><span class="mi">7</span><span class="p">])</span>
<span class="k">def</span> <span class="nf">dim_chord</span><span class="p">(</span><span class="n">root</span><span class="p">):</span>
<span class="n">root_key_num</span> <span class="o">=</span> <span class="n">key_number</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">map</span><span class="p">(</span><span class="n">note_from_key_number</span><span class="p">,</span> <span class="p">[</span><span class="n">root_key_num</span><span class="p">,</span> <span class="n">root_key_num</span><span class="o">+</span><span class="mi">3</span><span class="p">,</span> <span class="n">root_key_num</span><span class="o">+</span><span class="mi">6</span><span class="p">])</span>
<span class="c"># Chord qualities: M m m M M m d (M)</span>
<span class="n">major_chord_progression</span> <span class="o">=</span> <span class="p">[</span><span class="n">major_chord</span><span class="p">,</span> <span class="n">minor_chord</span><span class="p">,</span> <span class="n">minor_chord</span><span class="p">,</span> <span class="n">major_chord</span><span class="p">,</span> \
<span class="n">major_chord</span><span class="p">,</span> <span class="n">minor_chord</span><span class="p">,</span> <span class="n">dim_chord</span><span class="p">]</span>
<span class="c"># Chord qualities: m d M m m M M (m)</span>
<span class="n">minor_chord_progression</span> <span class="o">=</span> <span class="p">[</span><span class="n">minor_chord</span><span class="p">,</span> <span class="n">dim_chord</span><span class="p">,</span> <span class="n">major_chord</span><span class="p">,</span> <span class="n">minor_chord</span><span class="p">,</span> \
<span class="n">minor_chord</span><span class="p">,</span> <span class="n">major_chord</span><span class="p">,</span> <span class="n">major_chord</span><span class="p">]</span>
<span class="c">####### Generate C major chords ###</span>
<span class="n">C_maj_chords</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">major_chord_progression</span><span class="p">)):</span>
<span class="n">C_maj_chords</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">major_chord_progression</span><span class="p">[</span><span class="n">i</span><span class="p">](</span><span class="n">C_major</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
<span class="c"># Throw a "mistake" in there to hear the difference</span>
<span class="n">C_maj_chords</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">Note</span><span class="p">(</span><span class="s">"C"</span><span class="p">),</span> <span class="n">Note</span><span class="p">(</span><span class="s">"F#"</span><span class="p">),</span> <span class="n">Note</span><span class="p">(</span><span class="s">"Bb"</span><span class="p">)])</span>
<span class="k">print</span> <span class="s">"C major chords:"</span><span class="p">,</span> <span class="n">C_maj_chords</span>
<span class="n">midi</span> <span class="o">=</span> <span class="n">Midi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">tempo</span><span class="o">=</span><span class="mi">80</span><span class="p">)</span>
<span class="n">midi</span><span class="o">.</span><span class="n">seq_chords</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">NoteSeq</span><span class="p">,</span> <span class="n">C_maj_chords</span><span class="p">))</span>
<span class="n">midi</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s">"c_major_chords.mid"</span><span class="p">)</span>
<span class="c">####### Generate G minor chords ###</span>
<span class="n">G_minor</span> <span class="o">=</span> <span class="n">NoteSeq</span><span class="p">(</span><span class="s">"G, A Bb C' D Eb F"</span><span class="p">)</span>
<span class="n">G_min_chords</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">minor_chord_progression</span><span class="p">)):</span>
<span class="n">G_min_chords</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">minor_chord_progression</span><span class="p">[</span><span class="n">i</span><span class="p">](</span><span class="n">G_minor</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
<span class="k">print</span> <span class="s">"G minor chords:"</span><span class="p">,</span> <span class="n">G_min_chords</span>
<span class="n">midi</span> <span class="o">=</span> <span class="n">Midi</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">tempo</span><span class="o">=</span><span class="mi">80</span><span class="p">)</span>
<span class="n">midi</span><span class="o">.</span><span class="n">seq_chords</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">NoteSeq</span><span class="p">,</span> <span class="n">G_min_chords</span><span class="p">))</span>
<span class="n">midi</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s">"g_minor_chords.mid"</span><span class="p">)</span>
</pre></div>
<p>And here is the output (excluding the MIDI files it writes):</p>
<div class="highlight"><pre><span class="n">localhost</span><span class="o">:</span><span class="n">music</span> <span class="n">caleb$</span> <span class="n">python</span> <span class="n">piano_notes</span><span class="o">.</span><span class="na">py</span>
<span class="n">All</span> <span class="n">piano</span> <span class="n">notes</span><span class="o">:</span> <span class="o">[</span><span class="mi">0</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">3</span><span class="o">,</span> <span class="mi">4</span><span class="o">,</span> <span class="mi">5</span><span class="o">,</span> <span class="mi">6</span><span class="o">,</span> <span class="mi">7</span><span class="o">,</span> <span class="mi">8</span><span class="o">,</span> <span class="mi">9</span><span class="o">,</span> <span class="mi">10</span><span class="o">,</span> <span class="mi">11</span><span class="o">,</span> <span class="mi">12</span><span class="o">,</span> <span class="mi">13</span><span class="o">,</span> <span class="mi">14</span><span class="o">,</span> <span class="mi">15</span><span class="o">,</span> <span class="mi">16</span><span class="o">,</span> <span class="mi">17</span><span class="o">,</span> <span class="mi">18</span><span class="o">,</span> <span class="mi">19</span><span class="o">,</span> <span class="mi">20</span><span class="o">,</span>
<span class="mi">21</span><span class="o">,</span> <span class="mi">22</span><span class="o">,</span> <span class="mi">23</span><span class="o">,</span> <span class="mi">24</span><span class="o">,</span> <span class="mi">25</span><span class="o">,</span> <span class="mi">26</span><span class="o">,</span> <span class="mi">27</span><span class="o">,</span> <span class="mi">28</span><span class="o">,</span> <span class="mi">29</span><span class="o">,</span> <span class="mi">30</span><span class="o">,</span> <span class="mi">31</span><span class="o">,</span> <span class="mi">32</span><span class="o">,</span> <span class="mi">33</span><span class="o">,</span> <span class="mi">34</span><span class="o">,</span> <span class="mi">35</span><span class="o">,</span> <span class="mi">36</span><span class="o">,</span> <span class="mi">37</span><span class="o">,</span> <span class="mi">38</span><span class="o">,</span> <span class="mi">39</span><span class="o">,</span> <span class="mi">40</span><span class="o">,</span> <span class="mi">41</span><span class="o">,</span> <span class="mi">42</span><span class="o">,</span> <span class="mi">43</span><span class="o">,</span>
<span class="mi">44</span><span class="o">,</span> <span class="mi">45</span><span class="o">,</span> <span class="mi">46</span><span class="o">,</span> <span class="mi">47</span><span class="o">,</span> <span class="mi">48</span><span class="o">,</span> <span class="mi">49</span><span class="o">,</span> <span class="mi">50</span><span class="o">,</span> <span class="mi">51</span><span class="o">,</span> <span class="mi">52</span><span class="o">,</span> <span class="mi">53</span><span class="o">,</span> <span class="mi">54</span><span class="o">,</span> <span class="mi">55</span><span class="o">,</span> <span class="mi">56</span><span class="o">,</span> <span class="mi">57</span><span class="o">,</span> <span class="mi">58</span><span class="o">,</span> <span class="mi">59</span><span class="o">,</span> <span class="mi">60</span><span class="o">,</span> <span class="mi">61</span><span class="o">,</span> <span class="mi">62</span><span class="o">,</span> <span class="mi">63</span><span class="o">,</span> <span class="mi">64</span><span class="o">,</span> <span class="mi">65</span><span class="o">,</span> <span class="mi">66</span><span class="o">,</span>
<span class="mi">67</span><span class="o">,</span> <span class="mi">68</span><span class="o">,</span> <span class="mi">69</span><span class="o">,</span> <span class="mi">70</span><span class="o">,</span> <span class="mi">71</span><span class="o">,</span> <span class="mi">72</span><span class="o">,</span> <span class="mi">73</span><span class="o">,</span> <span class="mi">74</span><span class="o">,</span> <span class="mi">75</span><span class="o">,</span> <span class="mi">76</span><span class="o">,</span> <span class="mi">77</span><span class="o">,</span> <span class="mi">78</span><span class="o">,</span> <span class="mi">79</span><span class="o">,</span> <span class="mi">80</span><span class="o">,</span> <span class="mi">81</span><span class="o">,</span> <span class="mi">82</span><span class="o">,</span> <span class="mi">83</span><span class="o">,</span> <span class="mi">84</span><span class="o">,</span> <span class="mi">85</span><span class="o">,</span> <span class="mi">86</span><span class="o">,</span> <span class="mi">87</span><span class="o">]</span>
<span class="n">Middle</span> <span class="n">C</span> <span class="n">key</span> <span class="n">number</span><span class="o">:</span> <span class="mi">39</span>
<span class="n">C</span> <span class="n">major</span> <span class="o">(</span><span class="n">staring</span> <span class="k">with</span> <span class="n">middle</span> <span class="n">C</span><span class="o">):</span> <span class="o">[</span><span class="mi">39</span><span class="o">,</span> <span class="mi">41</span><span class="o">,</span> <span class="mi">43</span><span class="o">,</span> <span class="mi">44</span><span class="o">,</span> <span class="mi">46</span><span class="o">,</span> <span class="mi">48</span><span class="o">,</span> <span class="mi">50</span><span class="o">]</span>
<span class="n">C</span> <span class="n">major</span><span class="o">:</span> <span class="o">[</span><span class="mi">51</span><span class="o">,</span> <span class="mi">53</span><span class="o">,</span> <span class="mi">55</span><span class="o">,</span> <span class="mi">56</span><span class="o">,</span> <span class="mi">58</span><span class="o">,</span> <span class="mi">60</span><span class="o">,</span> <span class="mi">62</span><span class="o">,</span> <span class="mi">63</span><span class="o">]</span>
<span class="n">Intervals</span> <span class="k">for</span> <span class="n">C</span> <span class="n">major</span><span class="o">:</span> <span class="o">[</span><span class="mi">2</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">1</span><span class="o">]</span>
<span class="n">A</span> <span class="n">minor</span><span class="o">:</span> <span class="o">[</span><span class="mi">48</span><span class="o">,</span> <span class="mi">50</span><span class="o">,</span> <span class="mi">51</span><span class="o">,</span> <span class="mi">53</span><span class="o">,</span> <span class="mi">55</span><span class="o">,</span> <span class="mi">56</span><span class="o">,</span> <span class="mi">58</span><span class="o">,</span> <span class="mi">60</span><span class="o">]</span>
<span class="n">Intervals</span> <span class="n">A</span> <span class="n">minor</span><span class="o">:</span> <span class="o">[</span><span class="mi">2</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">2</span><span class="o">]</span>
<span class="n">C</span> <span class="n">major</span> <span class="n">chords</span><span class="o">:</span> <span class="o">[[<</span><span class="n">c</span><span class="o">>,</span> <span class="o"><</span><span class="n">e</span><span class="o">>,</span> <span class="o"><</span><span class="n">g</span><span class="o">>],</span> <span class="o">[<</span><span class="n">d</span><span class="o">>,</span> <span class="o"><</span><span class="n">f</span><span class="o">>,</span> <span class="o"><</span><span class="n">a</span><span class="o">>],</span> <span class="o">[<</span><span class="n">e</span><span class="o">>,</span> <span class="o"><</span><span class="n">g</span><span class="o">>,</span> <span class="o"><</span><span class="n">b</span><span class="o">>],</span> <span class="o">[<</span><span class="n">f</span><span class="o">>,</span> <span class="o"><</span><span class="n">a</span><span class="o">>,</span> <span class="o"><</span><span class="n">c</span><span class="o">>],</span>
<span class="o">[<</span><span class="n">g</span><span class="o">>,</span> <span class="o"><</span><span class="n">b</span><span class="o">>,</span> <span class="o"><</span><span class="n">d</span><span class="o">>],</span> <span class="o">[<</span><span class="n">a</span><span class="o">>,</span> <span class="o"><</span><span class="n">c</span><span class="o">>,</span> <span class="o"><</span><span class="n">e</span><span class="o">>],</span> <span class="o">[<</span><span class="n">b</span><span class="o">>,</span> <span class="o"><</span><span class="n">d</span><span class="o">>,</span> <span class="o"><</span><span class="n">f</span><span class="o">>],</span> <span class="o">[<</span><span class="n">c</span><span class="o">>,</span> <span class="o"><</span><span class="n">F</span><span class="err">#</span><span class="o">>,</span> <span class="o"><</span><span class="n">A</span><span class="err">#</span><span class="o">>]]</span>
<span class="n">G</span> <span class="n">minor</span> <span class="n">chords</span><span class="o">:</span> <span class="o">[[<</span><span class="n">g</span><span class="o">>,</span> <span class="o"><</span><span class="n">A</span><span class="err">#</span><span class="o">>,</span> <span class="o"><</span><span class="n">d</span><span class="o">>],</span> <span class="o">[<</span><span class="n">a</span><span class="o">>,</span> <span class="o"><</span><span class="n">c</span><span class="o">>,</span> <span class="o"><</span><span class="n">D</span><span class="err">#</span><span class="o">>],</span> <span class="o">[<</span><span class="n">A</span><span class="err">#</span><span class="o">>,</span> <span class="o"><</span><span class="n">d</span><span class="o">>,</span> <span class="o"><</span><span class="n">f</span><span class="o">>],</span> <span class="o">[<</span><span class="n">c</span><span class="o">>,</span> <span class="o"><</span><span class="n">D</span><span class="err">#</span><span class="o">>,</span> <span class="o"><</span><span class="n">g</span><span class="o">>],</span>
<span class="o">[<</span><span class="n">d</span><span class="o">>,</span> <span class="o"><</span><span class="n">f</span><span class="o">>,</span> <span class="o"><</span><span class="n">a</span><span class="o">>],</span> <span class="o">[<</span><span class="n">D</span><span class="err">#</span><span class="o">>,</span> <span class="o"><</span><span class="n">g</span><span class="o">>,</span> <span class="o"><</span><span class="n">A</span><span class="err">#</span><span class="o">>],</span> <span class="o">[<</span><span class="n">f</span><span class="o">>,</span> <span class="o"><</span><span class="n">a</span><span class="o">>,</span> <span class="o"><</span><span class="n">c</span><span class="o">>]]</span>
</pre></div>Music Theory and Math Notes2012-11-23T23:11:39-06:00Caleb Madrigaltag:calebmadrigal.com,2012-11-23:music-theory-notes/<p>For the last day, I've done some reading on music theory (trying to understand why things are the way they are in terms of math). Here are my raw unedited notes:</p>
<h2>Important musical ratios:</h2>
<ul>
<li>Unison: 1:1 frequency</li>
<li>Octave: 2:1 frequency<ul>
<li>12 semitone increase</li>
</ul>
</li>
<li>Fifth: 3:2 frequency (i.e. multiply by 1.5)<ul>
<li>7 semitone increase</li>
</ul>
</li>
<li>Semitone: 2^(1./12) (12th root of 2) - about 1.059 - this is the "half-step" distance, so you can multiply the frequency of F by 1.059 to get the frequency for F#</li>
</ul>
<h2>Scales and keys</h2>
<ul>
<li>Chromatic scale: 12 notes (list of all semitones in an octave)</li>
<li>Diatomic scale: 7 notes</li>
<li>To be in a "key" (like C-major) means to select 7 notes from the 12 notes in the chromatic scale<ul>
<li>In theory, these notes sound good together</li>
</ul>
</li>
<li>C-major is the white keys on the piano staring on C<ul>
<li>There is no E# or B# notes on the piano (because the notes in the diatonic scale are determined by going up fifths). So the interval between the white keys (which don't have a black key in between them) are half-tones (i.e. "semitones"). Each key increase is a "half tone" increase (including black keys).<ul>
<li>See python program below to generate chromatic scale</li>
</ul>
</li>
</ul>
</li>
<li>Major key intervals can be derived by starting on C and hitting 7 white key<ul>
<li>Intervals: whole whole half whole whole whole half</li>
</ul>
</li>
<li>Minor key intervals can be derived by starting on A and hitting 7 white keys<ul>
<li>Intervals: whole half whole whole half whole whole</li>
</ul>
</li>
</ul>
<h2>Chords</h2>
<ul>
<li>Major chord ratios: 4:5:6<ul>
<li>The original note</li>
<li>A major 3rd</li>
<li>A perfect fifth (notice that 4 * 1.5 = 6)</li>
</ul>
</li>
<li>Minor chord ratios: 10:12:15<ul>
<li>The original note</li>
<li>A minor 3rd</li>
<li>A perfect fifth (notice that 10 * 1.5 = 15)</li>
</ul>
</li>
<li>In a "key", there are 7 chords (numbered I, II, III, IV, V, VI, VII).<ul>
<li>To determine if which chords (major or minor) are in a key, start at each of the 7 notes in the key and see which chords "fit" into that key (all notes in the chords must be in the key as well).</li>
</ul>
</li>
</ul>
<h2>Note generation example with python</h2>
<p>Python to generate the 12 basic notes (starting with the note F1 = 43.65Hz):</p>
<div class="highlight"><pre>>>> notes = []
>>> acc = f1
>>> for i in range(12):
... notes.append(acc)
... acc = acc * 1.5
...
>>> notes
[43.65, 65.475, 98.21249999999999, 147.31875, 220.97812499999998, 331.46718749999997, 497.20078125, 745.8011718749999, 1118.7017578124999, 1678.05263671875, 2517.0789550781246, 3775.618432617187]
>>> note_names = ['f', 'c', 'g', 'd', 'a', 'e', 'b', 'f#', 'c#', 'g#', 'd#', 'a#']
>>> 3729 * 1.5
5593.5
>>> 5593.5 / f1
128.1443298969072
>>> # f8 should equal 5587 Hz. So from A#, if we go up a fifth, we are at F8,
>>> # which is a 7 octaves higher than F1 (2^7 = 128). 128* F1 = F8.
</pre></div>
<h2>Sources</h2>
<ul>
<li><a href="http://en.wikipedia.org/wiki/Piano_key_frequencies">http://en.wikipedia.org/wiki/Piano_key_frequencies</a></li>
<li><a href="http://www.pianoworld.com/forum/ubbthreads.php/topics/988787/E%20Sharp,%20B%20Sharp.html">http://www.pianoworld.com/forum/ubbthreads.php/topics/988787/E%20Sharp,%20B%20Sharp.html</a></li>
<li><a href="http://www.phy.mtu.edu/~suits/chords.html">http://www.phy.mtu.edu/~suits/chords.html</a></li>
<li>Michael New's video tutorials:<ul>
<li><a href="http://www.youtube.com/watch?v=5Y01jIorpeA">http://www.youtube.com/watch?v=5Y01jIorpeA</a></li>
<li><a href="http://www.youtube.com/watch?v=rHlWP-nc4tM">http://www.youtube.com/watch?v=rHlWP-nc4tM</a></li>
<li><a href="http://www.youtube.com/watch?v=xLaw0CLTNfA&feature=relmfu">http://www.youtube.com/watch?v=xLaw0CLTNfA&feature=relmfu</a></li>
</ul>
</li>
</ul>Reduce with Python and Clojure2012-09-06T04:30:29-05:00Caleb Madrigaltag:calebmadrigal.com,2012-09-06:reduce-awesomeness/<p>I was just playing around writing an annuity calculator function. Here is my first version:</p>
<div class="highlight"><pre>def calculate_annuity(years, interest=0, addition_per_year=0, starting_amount=0):
result = []
running_total = starting_amount
for year in range(years+1):
result.append(running_total)
running_total = (running_total + addition_per_year) * (1 + interest)
return result
</pre></div>
<p>Here is a 2nd version, written using reduce instead of a loop:</p>
<div class="highlight"><pre>def calculate_annuity2(years, interest=0, addition_per_year=0, starting_amount=0):
return reduce(lambda result,addition: result + [(result[-1] + addition) * (1 + interest)],
[addition_per_year] * years, [starting_amount])
</pre></div>
<p>And here is a version in Clojure (basically a direct translation of the Python one:</p>
<div class="highlight"><pre><span class="p">(</span><span class="kd">defn </span><span class="nv">annuity</span> <span class="p">[</span><span class="nv">years</span> <span class="nv">interest</span> <span class="nv">addition_per_year</span> <span class="nv">init</span><span class="p">]</span>
<span class="p">(</span><span class="nb">reduce</span>
<span class="o">#</span><span class="p">(</span><span class="nf">conj</span> <span class="nv">%1</span> <span class="p">(</span><span class="nf">*</span> <span class="p">(</span><span class="nf">+</span> <span class="p">(</span><span class="nf">last</span> <span class="nv">%1</span><span class="p">)</span> <span class="nv">%2</span><span class="p">)</span> <span class="p">(</span><span class="nf">+</span> <span class="mi">1</span> <span class="nv">interest</span><span class="p">)))</span>
<span class="p">[</span><span class="nv">starting_amount</span><span class="p">]</span>
<span class="p">(</span><span class="k">for</span> <span class="p">[</span><span class="nv">i</span> <span class="p">(</span><span class="nb">range</span> <span class="nv">years</span><span class="p">)]</span> <span class="nv">addition_per_year</span><span class="p">)))</span>
</pre></div>
<p>Here are some example use cases:</p>
<div class="highlight"><pre>; Find investment returns by year for a $1000 investment at 7% interest
; for 10 years.
(println (annuity 10 0.07 0 1000))
; Find annuity value if contributing $1000 each month and starting with $7777
; with 10% interest for 10 years.
(println (annuity 10 0.10 1000 7777))
; Find annuity value if contributing $1000 each month and starting with $777
; with 10% interest for 10 years.
(println (annuity 10 0.07 0 1000))
; Test perpetuity annuity that pays out $6000 per year, given a $100000
; at 6.4% interest.
(println (annuity 30 0.064 -6000 100000))
</pre></div>Vim run current file2012-08-16T16:02:05-05:00Caleb Madrigaltag:calebmadrigal.com,2012-08-16:vim-run-current-file/<p>I just added a nice command to my .vimrc file to allow me to run the current file I am working on by typing <code>:R</code>:</p>
<div class="highlight"><pre>command R !./%
</pre></div>
<p>On the VIM note, here is a link to my current vim config (.vimrc file and .vim directory) on github: <a href="https://github.com/calebmadrigal/caleb-vim-config">Vim config</a>.</p>Barcamp Milwaukee 20122012-08-15T14:44:29-05:00Caleb Madrigaltag:calebmadrigal.com,2012-08-15:barcamp-milwaukee-2012/<p><a href="https://barcampmilwaukee.org/">Barcamp Milwaukee</a> 2012 is being held October 6th-7th. I had a good time last year, so I can definitely recommend it :)</p>Secret to not having road rage2012-08-08T04:11:38-05:00Caleb Madrigaltag:calebmadrigal.com,2012-08-08:secret-road-rage/<p>I have found the secret to not getting road rage: <strong>audiobooks</strong>. Try it. Right now, I'm listening to Dune by Frank Herbert.</p>Facial Detection with OpenCV and Python2012-07-06T05:09:57-05:00Caleb Madrigaltag:calebmadrigal.com,2012-07-06:facial-detection-opencv-python/<p>I was able to get some basic facial detection working in OpenCV with Python. Here's what it looks like:</p>
<p><img alt="Facial recognition with OpenCV" src="/images/facial_recognition.png" /></p>
<p>And here is the 34-line python script to draw boxes around all detected faces in live video:</p>
<div class="highlight"><pre><span class="kn">import</span> <span class="nn">cv</span>
<span class="n">HAAR_CASCADE_PATH</span> <span class="o">=</span> <span class="s">"/opt/local/share/OpenCV/haarcascades/haarcascade_frontalface_default.xml"</span>
<span class="n">CAMERA_INDEX</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">def</span> <span class="nf">detect_faces</span><span class="p">(</span><span class="n">image</span><span class="p">):</span>
<span class="n">faces</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">detected</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">HaarDetectObjects</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="n">cascade</span><span class="p">,</span> <span class="n">storage</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">cv</span><span class="o">.</span><span class="n">CV_HAAR_DO_CANNY_PRUNING</span><span class="p">,</span> <span class="p">(</span><span class="mi">100</span><span class="p">,</span><span class="mi">100</span><span class="p">))</span>
<span class="k">if</span> <span class="n">detected</span><span class="p">:</span>
<span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span><span class="n">w</span><span class="p">,</span><span class="n">h</span><span class="p">),</span><span class="n">n</span> <span class="ow">in</span> <span class="n">detected</span><span class="p">:</span>
<span class="n">faces</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span><span class="n">w</span><span class="p">,</span><span class="n">h</span><span class="p">))</span>
<span class="k">return</span> <span class="n">faces</span>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">"__main__"</span><span class="p">:</span>
<span class="n">cv</span><span class="o">.</span><span class="n">NamedWindow</span><span class="p">(</span><span class="s">"Video"</span><span class="p">,</span> <span class="n">cv</span><span class="o">.</span><span class="n">CV_WINDOW_AUTOSIZE</span><span class="p">)</span>
<span class="n">capture</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">CaptureFromCAM</span><span class="p">(</span><span class="n">CAMERA_INDEX</span><span class="p">)</span>
<span class="n">storage</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">CreateMemStorage</span><span class="p">()</span>
<span class="n">cascade</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">Load</span><span class="p">(</span><span class="n">HAAR_CASCADE_PATH</span><span class="p">)</span>
<span class="n">faces</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="bp">True</span><span class="p">:</span>
<span class="n">image</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">QueryFrame</span><span class="p">(</span><span class="n">capture</span><span class="p">)</span>
<span class="c"># Only run the Detection algorithm every 5 frames to improve performance</span>
<span class="k">if</span> <span class="n">i</span><span class="o">%</span><span class="mi">5</span><span class="o">==</span><span class="mi">0</span><span class="p">:</span>
<span class="n">faces</span> <span class="o">=</span> <span class="n">detect_faces</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
<span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span><span class="n">w</span><span class="p">,</span><span class="n">h</span><span class="p">)</span> <span class="ow">in</span> <span class="n">faces</span><span class="p">:</span>
<span class="n">cv</span><span class="o">.</span><span class="n">Rectangle</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> <span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">w</span><span class="p">,</span><span class="n">y</span><span class="o">+</span><span class="n">h</span><span class="p">),</span> <span class="mi">255</span><span class="p">)</span>
<span class="n">cv</span><span class="o">.</span><span class="n">ShowImage</span><span class="p">(</span><span class="s">"w1"</span><span class="p">,</span> <span class="n">image</span><span class="p">)</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
</pre></div>Intro to OpenCV with Python2012-07-06T02:45:23-05:00Caleb Madrigaltag:calebmadrigal.com,2012-07-06:intro-opencv-python/<p>I have started my journey into the world of OpenCV using Python on my Mac. These are my first steps with it.</p>
<h1>Installing OpenCV for Python on the Mac</h1>
<div class="highlight"><pre># Install numpy as a prerequisite
sudo port install numpy
# Install OpenCV with the Python API
sudo port install opencv +python27
</pre></div>
<p>(The <code>port</code> command is part of <a href="http://www.macports.org/">Macports</a>)</p>
<h1>Capturing an images from a webcam</h1>
<table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre> 1
2
3
4
5
6
7
8
9
10</pre></div></td><td class="code"><div class="highlight"><pre><span class="c">#!/usr/bin/env python2.7</span>
<span class="kn">import</span> <span class="nn">cv</span>
<span class="n">cv</span><span class="o">.</span><span class="n">NamedWindow</span><span class="p">(</span><span class="s">"w1"</span><span class="p">,</span> <span class="n">cv</span><span class="o">.</span><span class="n">CV_WINDOW_AUTOSIZE</span><span class="p">)</span>
<span class="n">camera_index</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">capture</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">CaptureFromCAM</span><span class="p">(</span><span class="n">camera_index</span><span class="p">)</span>
<span class="n">frame</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">QueryFrame</span><span class="p">(</span><span class="n">capture</span><span class="p">)</span>
<span class="n">cv</span><span class="o">.</span><span class="n">SaveImage</span><span class="p">(</span><span class="s">"pic.jpg"</span><span class="p">,</span> <span class="n">frame</span><span class="p">)</span>
</pre></div>
</td></tr></table>
<p>(I tested this with the iSight camera on my Macbook Pro)</p>
<h1>Displaying live video</h1>
<table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre> 1
2
3
4
5
6
7
8
9
10
11</pre></div></td><td class="code"><div class="highlight"><pre><span class="c">#!/usr/bin/env python2.7</span>
<span class="kn">import</span> <span class="nn">cv</span>
<span class="n">CAMERA_INDEX</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">cv</span><span class="o">.</span><span class="n">NamedWindow</span><span class="p">(</span><span class="s">"Video"</span><span class="p">,</span> <span class="n">cv</span><span class="o">.</span><span class="n">CV_WINDOW_AUTOSIZE</span><span class="p">)</span>
<span class="n">capture</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">CaptureFromCAM</span><span class="p">(</span><span class="n">CAMERA_INDEX</span><span class="p">)</span>
<span class="k">while</span> <span class="bp">True</span><span class="p">:</span>
<span class="n">frame</span> <span class="o">=</span> <span class="n">cv</span><span class="o">.</span><span class="n">QueryFrame</span><span class="p">(</span><span class="n">capture</span><span class="p">)</span>
<span class="n">cv</span><span class="o">.</span><span class="n">ShowImage</span><span class="p">(</span><span class="s">"w1"</span><span class="p">,</span> <span class="n">frame</span><span class="p">)</span>
</pre></div>
</td></tr></table>NSArray+FP2012-06-26T23:31:24-05:00Caleb Madrigaltag:calebmadrigal.com,2012-06-26:nsarrayfp/<p>I realized that I utilize the <code>[NSArray head]</code> and <code>[NSArray tail]</code> functions in various code snippets, but haven.t shared the actual code for that category. So here is my <code>NSArray+FPcode</code>.</p>
<p>NSArray+FP.h</p>
<div class="highlight"><pre><span class="cp">#import <Foundation/Foundation.h></span>
<span class="k">typedef</span> <span class="nf">id</span><span class="p">(</span><span class="o">^</span><span class="n">MapBlock</span><span class="p">)(</span><span class="kt">id</span><span class="p">);</span>
<span class="k">@interface</span> <span class="bp">NSArray</span> <span class="nl">(FP)</span>
<span class="p">-</span> <span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nf">map:</span><span class="p">(</span><span class="n">MapBlock</span><span class="p">)</span><span class="nv">block</span><span class="p">;</span>
<span class="p">-</span> <span class="p">(</span><span class="kt">id</span><span class="p">)</span><span class="nf">head</span><span class="p">;</span>
<span class="p">-</span> <span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nf">tail</span><span class="p">;</span>
<span class="k">@end</span>
</pre></div>
<p>NSArray+FP.m</p>
<div class="highlight"><pre><span class="cp">#import "NSArray+FP.h"</span>
<span class="k">@implementation</span> <span class="bp">NSArray</span> <span class="nl">(FP)</span>
<span class="p">-</span> <span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nf">map:</span><span class="p">(</span><span class="n">MapBlock</span><span class="p">)</span><span class="nv">block</span> <span class="p">{</span>
<span class="bp">NSMutableArray</span> <span class="o">*</span><span class="n">resultArray</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">NSMutableArray</span> <span class="n">alloc</span><span class="p">]</span> <span class="n">init</span><span class="p">];</span>
<span class="k">for</span> <span class="p">(</span><span class="kt">id</span> <span class="n">object</span> <span class="k">in</span> <span class="nb">self</span><span class="p">)</span> <span class="p">{</span>
<span class="p">[</span><span class="n">resultArray</span> <span class="nl">addObject</span><span class="p">:</span><span class="n">block</span><span class="p">(</span><span class="n">object</span><span class="p">)];</span>
<span class="p">}</span>
<span class="k">return</span> <span class="n">resultArray</span><span class="p">;</span>
<span class="p">}</span>
<span class="p">-</span> <span class="p">(</span><span class="kt">id</span><span class="p">)</span><span class="nf">head</span>
<span class="p">{</span>
<span class="k">return</span> <span class="p">[</span><span class="nb">self</span> <span class="nl">objectAtIndex</span><span class="p">:</span><span class="mi">0</span><span class="p">];</span>
<span class="p">}</span>
<span class="p">-</span> <span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nf">tail</span>
<span class="p">{</span>
<span class="n">NSRange</span> <span class="n">tailRange</span><span class="p">;</span>
<span class="n">tailRange</span><span class="p">.</span><span class="n">location</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span>
<span class="n">tailRange</span><span class="p">.</span><span class="n">length</span> <span class="o">=</span> <span class="p">[</span><span class="nb">self</span> <span class="n">count</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">;</span>
<span class="k">return</span> <span class="p">[</span><span class="nb">self</span> <span class="nl">subarrayWithRange</span><span class="p">:</span><span class="n">tailRange</span><span class="p">];</span>
<span class="p">}</span>
<span class="k">@end</span>
</pre></div>Eye movement on web pages2012-06-22T16:07:57-05:00Caleb Madrigaltag:calebmadrigal.com,2012-06-22:eye-movement-web-pages/<ul>
<li>I've always preferred bulleted lists (and the like) over flat paragraph formats</li>
<li>I believe they can be visually parsed much faster than paragraphs</li>
<li>Now I have <strong>evidence</strong>: <a href="http://www.useit.com/alertbox/reading_pattern.html">F-shaped reading pattern study</a> :)</li>
</ul>
<p>Here is an image which shows the eye movement of users on web pages (where red means more time was spent looking there):
<img alt="F Reading Pattern" src="/images/f_reading_pattern_eyetracking.jpg" /></p>Functional programming to deal with asynchronicity in Objective-C2012-05-30T21:05:43-05:00Caleb Madrigaltag:calebmadrigal.com,2012-05-30:functional-programming-deal-asynchronicity-objective-c/<p>In the last few weeks, I've used the <code>[ALAssetsLibrary loadImages:callback:]</code> method to load a list of images. For what I was doing, I wanted to wait till all the images were loaded before proceeding. I found that I could solve this problem very elegantly using a recursive solution:</p>
<div class="highlight"><pre><span class="p">-</span> <span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="nf">loadImages:</span><span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nv">imageUrls</span> <span class="nf">loadedImages:</span><span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nv">loadedImages</span>
<span class="nf">callback:</span><span class="p">(</span><span class="kt">void</span><span class="p">(</span><span class="o">^</span><span class="p">)(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">))</span><span class="nv">callback</span>
<span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="n">imageUrls</span> <span class="o">==</span> <span class="nb">nil</span> <span class="o">||</span> <span class="p">[</span><span class="n">imageUrls</span> <span class="n">count</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span> <span class="p">{</span>
<span class="n">callback</span><span class="p">(</span><span class="n">loadedImages</span><span class="p">);</span>
<span class="p">}</span>
<span class="k">else</span> <span class="p">{</span>
<span class="bp">NSURL</span> <span class="o">*</span><span class="n">head</span> <span class="o">=</span> <span class="p">[</span><span class="n">imageUrls</span> <span class="n">head</span><span class="p">];</span>
<span class="n">__unsafe_unretained</span> <span class="kt">id</span> <span class="n">unretained_self</span> <span class="o">=</span> <span class="nb">self</span><span class="p">;</span>
<span class="bp">ALAssetsLibrary</span><span class="o">*</span> <span class="n">library</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">ALAssetsLibrary</span> <span class="n">alloc</span><span class="p">]</span> <span class="n">init</span><span class="p">];</span>
<span class="p">[</span><span class="n">library</span> <span class="nl">assetForURL</span><span class="p">:</span><span class="n">head</span> <span class="nl">resultBlock</span><span class="p">:</span><span class="o">^</span><span class="p">(</span><span class="bp">ALAsset</span> <span class="o">*</span><span class="n">asset</span><span class="p">)</span> <span class="p">{</span>
<span class="bp">ALAssetRepresentation</span> <span class="o">*</span><span class="n">assetRepresentation</span> <span class="o">=</span> <span class="n">asset</span><span class="p">.</span><span class="n">defaultRepresentation</span><span class="p">;</span>
<span class="bp">UIImage</span> <span class="o">*</span><span class="n">image</span> <span class="o">=</span> <span class="p">[</span><span class="bp">UIImage</span> <span class="nl">imageWithCGImage</span><span class="p">:</span><span class="n">assetRepresentation</span><span class="p">.</span><span class="n">fullResolutionImage</span>
<span class="nl">scale</span><span class="p">:</span><span class="n">assetRepresentation</span><span class="p">.</span><span class="n">scale</span>
<span class="nl">orientation</span><span class="p">:(</span><span class="n">UIImageOrientation</span><span class="p">)</span><span class="n">assetRepresentation</span><span class="p">.</span><span class="n">orientation</span><span class="p">];</span>
<span class="p">[</span><span class="n">unretained_self</span> <span class="nl">loadImages</span><span class="p">:[</span><span class="n">imageUrls</span> <span class="n">tail</span><span class="p">]</span> <span class="nl">loadedImages</span><span class="p">:[</span><span class="n">loadedImages</span>
<span class="nl">arrayByAddingObject</span><span class="p">:</span><span class="n">image</span><span class="p">]</span> <span class="nl">callback</span><span class="p">:</span><span class="n">callback</span><span class="p">];</span>
<span class="p">}</span> <span class="nl">failureBlock</span><span class="p">:</span><span class="o">^</span><span class="p">(</span><span class="bp">NSError</span> <span class="o">*</span><span class="n">error</span><span class="p">)</span> <span class="p">{</span>
<span class="p">[</span><span class="n">unretained_self</span> <span class="nl">loadImages</span><span class="p">:[</span><span class="n">imageUrls</span> <span class="n">tail</span><span class="p">]</span> <span class="nl">loadedImages</span><span class="p">:</span><span class="n">loadedImages</span> <span class="nl">callback</span><span class="p">:</span><span class="n">callback</span><span class="p">];</span>
<span class="p">}];</span>
<span class="p">}</span>
<span class="p">}</span>
</pre></div>
<p>In general, this scenario where you want to call a blocking method over a list of items seems to be better handled by recursion. This is just another place where functional programming proves superior in handling asynchronous tasks.</p>
<p>By the way, <a href="http://calebmadrigal.com/nsarrayfp/">here</a> is a reference to my NSArray+FP category which defines the <code>head</code> and <code>tail</code> code I use above.</p>First look at Pylab/Matplotlib2012-05-17T20:04:04-05:00Caleb Madrigaltag:calebmadrigal.com,2012-05-17:first-look-at-pylab-matplotlib/<p>Since I've been getting into Machine Learning/Artificial Intelligence recently, I've been looking at various computing environments recently. Some of the contenders are:</p>
<ul>
<li><a href="http://en.wikipedia.org/wiki/MATLAB">MATLAB</a> - The traditional software stack for doing machine learning and statistical analysis</li>
<li><a href="http://en.wikipedia.org/wiki/GNU_Octave">GNU Octave</a> - An open-source MATLAB clone.</li>
<li><a href="http://en.wikipedia.org/wiki/R_(programming_language)">R</a> - An open source clone of a statistical computing environment called S.</li>
<li><a href="http://julialang.org/">Julia</a> - A language for doing statistical analysis. The goals are to compete with Matlab and R.</li>
<li><a href="http://matplotlib.sourceforge.net/">Matplotlib/Pylab/SciPy/NumPy</a> - see below</li>
</ul>
<p>Of these, I've tried Octave and Matplotlib. Matplotlib/Pylab is the software stack consisting of:</p>
<ul>
<li><a href="http://ipython.org/">IPython</a> - an interactive REPL for Python with things like tab completion</li>
<li><a href="http://matplotlib.sourceforge.net/">Matplotlib</a> - a graphical plotting library</li>
<li><a href="http://numpy.scipy.org/">NumPy</a> - a matrix library</li>
<li><a href="http://www.scipy.org/">SciPy</a> - a collection of scientific and mathematical algorithms</li>
</ul>
<p>I've only played with Matplotlib/Pylab a little bit, but I like what I've seen so far. Here's 2 quick examples:</p>
<h2>1. Displaying a Histogram of a gaussian distribution</h2>
<p>First, make sure to run <code>from matplotlib import *</code> and <code>from numpy import *</code></p>
<p><img alt="Gaussian Histogram" src="/images/gaussian_histogram.png" /></p>
<p>(I love how there are bell-shaped curves in the array representation of the histogram) :)</p>
<h2>2. Plotting a function (y=x^2+10):</h2>
<p><img alt="Matplotlib Quadratic" src="/images/matplotlib_quadratic1.png" /></p>
<p>Also, there is a really good video from PyCon 2012 on Matplotlib: <a href="http://pyvideo.org/video/617/plotting-with-matplotlib">Plotting with Matplotlib</a>.</p>How to reference self in a block in Objective-C2012-05-08T16:14:15-05:00Caleb Madrigaltag:calebmadrigal.com,2012-05-08:reference-self-in-block/<p>When using ARC (automatic reference counting) in Objective-C, you need to be careful to avoid causing retain cycles. One place where a retain cycle can occur is where self is referenced in a block. To avoid a retain cycle, you can use the <code>__unsafe_unretained</code> modifier as such:</p>
<div class="highlight"><pre><span class="n">__unsafe_unretained</span> <span class="kt">id</span> <span class="n">unretained_self</span> <span class="o">=</span> <span class="nb">self</span><span class="p">;</span>
<span class="n">reachability</span> <span class="o">=</span> <span class="p">[</span><span class="n">Reachability</span> <span class="nl">reachabilityWithHostname</span><span class="p">:</span><span class="s">@"maps.google.com"</span><span class="p">];</span>
<span class="n">reachability</span><span class="p">.</span><span class="n">reachableBlock</span> <span class="o">=</span> <span class="o">^</span><span class="p">(</span><span class="n">Reachability</span> <span class="o">*</span><span class="n">r</span><span class="p">)</span> <span class="p">{</span>
<span class="n">dispatch_async</span><span class="p">(</span><span class="n">dispatch_get_main_queue</span><span class="p">(),</span> <span class="o">^</span><span class="p">{</span>
<span class="n">SurveyFormController</span> <span class="o">*</span><span class="n">myself</span> <span class="o">=</span> <span class="n">unretained_self</span><span class="p">;</span>
<span class="nb">self</span><span class="p">.</span><span class="n">mapView</span><span class="p">.</span><span class="n">reachable</span> <span class="o">=</span> <span class="nb">YES</span><span class="p">;</span>
<span class="p">[</span><span class="n">myself</span> <span class="n">configureView</span><span class="p">];</span>
<span class="p">});</span>
<span class="p">};</span>
</pre></div>Probability and Statistics book for Python programmers2012-05-04T20:22:08-05:00Caleb Madrigaltag:calebmadrigal.com,2012-05-04:probability-statistics-book-python-programmers/<p>This seems like a nice, concise book on probability and statistics for Python programmers: <a href="http://greenteapress.com/thinkstats/thinkstats.pdf">Think Stats</a>.</p>Premature generalization is the new premature optimization2012-04-30T20:05:16-05:00Caleb Madrigaltag:calebmadrigal.com,2012-04-30:premature-generalization-premature-optimization/<p>A <a href="http://www.wisdomandwonder.com/">co-worker</a> was just showing me a situation where another developer had written a validation framework which was only used on 2 pages. I've seen this pattern again and again, and I've put a phrase to the thought:</p>
<div class="highlight"><pre>Premature generalization is the new premature optimization.
</pre></div>
<p>And it, too, is evil.</p>Linear Regression with Gradient Descent2012-04-26T20:15:23-05:00Caleb Madrigaltag:calebmadrigal.com,2012-04-26:linear-regression/<p>I'm taking the <a href="http://class.coursera.org/ml/">Stanford Machine Learning class</a>. The first algorithm we covered is Linear Regression using <a href="http://en.wikipedia.org/wiki/Gradient_descent">Gradient Descent</a>. I implemented this algorithm is Python. Here's what it looks like:</p>
<div class="highlight"><pre><span class="kn">import</span> <span class="nn">subprocess</span>
<span class="k">def</span> <span class="nf">create_hypothesis</span><span class="p">(</span><span class="n">slope</span><span class="p">,</span> <span class="n">y0</span><span class="p">):</span>
<span class="k">return</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">slope</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">y0</span>
<span class="k">def</span> <span class="nf">linear_regression</span><span class="p">(</span><span class="n">data_points</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">variance</span><span class="o">=</span><span class="mf">0.001</span><span class="p">):</span>
<span class="sd">""" Takes a set of data points in the form: [(1,1), (2,2), ...] and outputs (slope, y0). """</span>
<span class="n">slope_guess</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="n">y0_guess</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="n">last_slope</span> <span class="o">=</span> <span class="mf">1000.</span>
<span class="n">last_y0</span> <span class="o">=</span> <span class="mf">1000.</span>
<span class="n">num_points</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data_points</span><span class="p">)</span>
<span class="k">while</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">slope_guess</span><span class="o">-</span><span class="n">last_slope</span><span class="p">)</span> <span class="o">></span> <span class="n">variance</span> <span class="ow">or</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y0_guess</span> <span class="o">-</span> <span class="n">last_y0</span><span class="p">)</span> <span class="o">></span> <span class="n">variance</span><span class="p">):</span>
<span class="n">last_slope</span> <span class="o">=</span> <span class="n">slope_guess</span>
<span class="n">last_y0</span> <span class="o">=</span> <span class="n">y0_guess</span>
<span class="n">hypothesis</span> <span class="o">=</span> <span class="n">create_hypothesis</span><span class="p">(</span><span class="n">slope_guess</span><span class="p">,</span> <span class="n">y0_guess</span><span class="p">)</span>
<span class="n">y0_guess</span> <span class="o">=</span> <span class="n">y0_guess</span> <span class="o">-</span> <span class="n">learning_rate</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="n">num_points</span><span class="p">)</span> <span class="o">*</span> <span class="nb">sum</span><span class="p">([</span><span class="n">hypothesis</span><span class="p">(</span><span class="n">point</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">point</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="n">data_points</span><span class="p">])</span>
<span class="n">slope_guess</span> <span class="o">=</span> <span class="n">slope_guess</span> <span class="o">-</span> <span class="n">learning_rate</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="n">num_points</span><span class="p">)</span> <span class="o">*</span> <span class="nb">sum</span><span class="p">([</span> <span class="p">(</span><span class="n">hypothesis</span><span class="p">(</span><span class="n">point</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">point</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="n">point</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="n">data_points</span><span class="p">])</span>
<span class="k">return</span> <span class="p">(</span><span class="n">slope_guess</span><span class="p">,</span> <span class="n">y0_guess</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_data_and_line</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">data_file</span><span class="p">):</span>
<span class="c"># Plot with gnuplot</span>
<span class="n">plot</span> <span class="o">=</span> <span class="n">subprocess</span><span class="o">.</span><span class="n">Popen</span><span class="p">([</span><span class="s">'gnuplot'</span><span class="p">],</span> <span class="n">stdin</span><span class="o">=</span><span class="n">subprocess</span><span class="o">.</span><span class="n">PIPE</span><span class="p">)</span>
<span class="n">line_eq</span> <span class="o">=</span> <span class="s">"</span><span class="si">%f</span><span class="s">*x+</span><span class="si">%f</span><span class="s">"</span> <span class="o">%</span> <span class="n">line</span>
<span class="n">plot</span><span class="o">.</span><span class="n">communicate</span><span class="p">(</span><span class="s">"plot </span><span class="si">%s</span><span class="s">, '</span><span class="si">%s</span><span class="s">' with points;"</span> <span class="o">%</span> <span class="p">(</span><span class="n">line_eq</span><span class="p">,</span><span class="n">data_file</span><span class="p">))</span>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">"__main__"</span><span class="p">:</span>
<span class="n">data_file</span> <span class="o">=</span> <span class="s">"points.dat"</span>
<span class="n">points_str</span> <span class="o">=</span> <span class="p">[</span><span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">'</span><span class="se">\t</span><span class="s">'</span><span class="p">)</span> <span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="nb">open</span><span class="p">(</span><span class="n">data_file</span><span class="p">,</span><span class="s">'r'</span><span class="p">)</span><span class="o">.</span><span class="n">readlines</span><span class="p">()]</span>
<span class="n">points</span> <span class="o">=</span> <span class="p">[(</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="nb">float</span><span class="p">(</span><span class="n">y</span><span class="p">))</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">points_str</span><span class="p">]</span>
<span class="n">line</span> <span class="o">=</span> <span class="n">linear_regression</span><span class="p">(</span><span class="n">points</span><span class="p">)</span>
<span class="k">print</span> <span class="n">line</span>
<span class="n">plot_data_and_line</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">data_file</span><span class="p">)</span>
</pre></div>
<p>This code takes in a data file with a data point on each line with the x and y separated by a TAB; Example:</p>
<div class="highlight"><pre>0.000000 95.364693
1.000000 97.217205
2.000000 75.195834
3.000000 60.105519
</pre></div>
<p>This code also plots the data points and the resulting best-fit line in <a href="http://en.wikipedia.org/wiki/Gnuplot">gnuplot</a>. For example:</p>
<p><img alt="Linear Regression" src="/images/linear_regression_example.png" /></p>
<p>This code, along with helper files, is on <a href="https://github.com/calebmadrigal/machine-learning-algorithms/tree/master/univariate_linear_regression">my github repo</a>.</p>Embedding an XSLT in an XML document2012-04-11T19:36:30-05:00Caleb Madrigaltag:calebmadrigal.com,2012-04-11:embedding-xslt-xml-document/<p>Today, I had this XML document which I was wanting to make viewable in a browser. My plan was to run the XML document through an XSLT engine to transform it into an HTML document (which could then be opened in a browser).</p>
<p>Instead, I found that I could just embed the XSLT directly in the XML document. Then, when this file is opened in a browser, the XSLT executes and spits out HTML, which is then rendered into the browser window. This is great because I now have the original XML file (which we wanted to keep further analysis purposes) which can also be rendered nicely in a browser.</p>
<p>Here's an example:</p>
<div class="highlight"><pre><span class="cp"><?xml version="1.0" encoding="ISO-8859-1"?></span>
<span class="cp"><?xml-stylesheet type="text/xml" href="#stylesheet"?></span>
<span class="cp"><!DOCTYPE catelog [</span>
<span class="cp"><!ATTLIST xsl:stylesheet</span>
<span class="cp"> id ID #REQUIRED></span>
]>
<span class="nt"><catalog></span>
<span class="k"><xsl:stylesheet</span> <span class="na">id=</span><span class="s">"stylesheet"</span> <span class="na">version=</span><span class="s">"1.0"</span> <span class="na">xmlns:xsl=</span><span class="s">"http://www.w3.org/1999/XSL/Transform"</span><span class="nt">></span>
<span class="k"><xsl:template</span> <span class="na">match=</span><span class="s">"/"</span><span class="nt">></span>
<span class="nt"><html></span>
<span class="nt"><body></span>
<span class="nt"><h2></span>My CD Collection<span class="nt"></h2></span>
<span class="nt"><table</span> <span class="na">border=</span><span class="s">"1"</span><span class="nt">></span>
<span class="nt"><tr</span> <span class="na">bgcolor=</span><span class="s">"#9acd32"</span><span class="nt">></span>
<span class="nt"><th></span>Title<span class="nt"></th></span>
<span class="nt"><th></span>Artist<span class="nt"></th></span>
<span class="nt"></tr></span>
<span class="k"><xsl:for-each</span> <span class="na">select=</span><span class="s">"catalog/cd"</span><span class="nt">></span>
<span class="nt"><tr></span>
<span class="nt"><td></span><span class="k"><xsl:value-of</span> <span class="na">select=</span><span class="s">"title"</span><span class="nt">/></td></span>
<span class="nt"><td></span><span class="k"><xsl:value-of</span> <span class="na">select=</span><span class="s">"artist"</span><span class="nt">/></td></span>
<span class="nt"></tr></span>
<span class="k"></xsl:for-each></span>
<span class="nt"></table></span>
<span class="nt"></body></span>
<span class="nt"></html></span>
<span class="k"></xsl:template></span>
<span class="k"></xsl:stylesheet></span>
<span class="nt"><cd></span>
<span class="nt"><title></span>Empire Burlesque<span class="nt"></title></span>
<span class="nt"><artist></span>Bob Dylan<span class="nt"></artist></span>
<span class="nt"><country></span>USA<span class="nt"></country></span>
<span class="nt"><company></span>Columbia<span class="nt"></company></span>
<span class="nt"><price></span>10.90<span class="nt"></price></span>
<span class="nt"><year></span>1985<span class="nt"></year></span>
<span class="nt"></cd></span>
<span class="nt"><cd></span>
<span class="nt"><title></span>Hide your heart<span class="nt"></title></span>
<span class="nt"><artist></span>Bonnie Tyler<span class="nt"></artist></span>
<span class="nt"><country></span>UK<span class="nt"></country></span>
<span class="nt"><company></span>CBS Records<span class="nt"></company></span>
<span class="nt"><price></span>9.90<span class="nt"></price></span>
<span class="nt"><year></span>1988<span class="nt"></year></span>
<span class="nt"></cd></span>
<span class="nt"></catalog></span>
</pre></div>
<p>And this renders as such:</p>
<p><img alt="XSLT Render" src="/images/embedded_xslt_screenshot.png" /></p>
<p>Please note that this doesn't work for Internet Explorer. For IE, the XSL document must be referenced like this:</p>
<div class="highlight"><pre><span class="cp"><?xml-stylesheet type="text/xml" href="report.xsl"?></span>
</pre></div>Resampling Wheel Algorithm2012-03-12T14:45:40-05:00Caleb Madrigaltag:calebmadrigal.com,2012-03-12:resampling-wheel-algorithm/<p>I've been taking the Udacity CS373 (Robotic Car) class, and this week the topic was <a href="http://en.wikipedia.org/wiki/Particle_filter">Particle filters</a>. Particle filters are basically a localization algorithm that accounts for error in measurements and sensors.</p>
<p>Anyway, part of the Particle Filter algorithm requires the generation of a new set of these things called "particles" based on the particles' weights. So to accomplish this task, the Resample Wheel algorithm was presented in class. It is a particularly elegant method of generating a new set of particles by randomly drawing from an old set of particles (with replacement). The particle weight determines the likelihood of it being picked.</p>
<p>Here is the algorithm (with print statements - I used these to help me understand how the algorithm works):</p>
<div class="highlight"><pre><span class="kn">import</span> <span class="nn">random</span>
<span class="k">def</span> <span class="nf">generate_new_particles</span><span class="p">(</span><span class="n">old_particles</span><span class="p">,</span> <span class="n">weights</span><span class="p">):</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">old_particles</span><span class="p">)</span>
<span class="n">new_particles</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">index</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span> <span class="o">*</span> <span class="n">N</span><span class="p">)</span>
<span class="n">beta</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="n">mw</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">weights</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>
<span class="n">beta</span> <span class="o">+=</span> <span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span> <span class="o">*</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">mw</span>
<span class="k">print</span> <span class="s">"beta ="</span><span class="p">,</span> <span class="n">beta</span>
<span class="k">while</span> <span class="n">beta</span> <span class="o">></span> <span class="n">weights</span><span class="p">[</span><span class="n">index</span><span class="p">]:</span>
<span class="n">beta</span> <span class="o">-=</span> <span class="n">weights</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
<span class="n">index</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="n">N</span>
<span class="k">print</span> <span class="s">"</span><span class="se">\t</span><span class="s">beta= </span><span class="si">%f</span><span class="s">, index = </span><span class="si">%d</span><span class="s">, weight = </span><span class="si">%f</span><span class="s">"</span> <span class="o">%</span> <span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">index</span><span class="p">,</span> <span class="n">weights</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
<span class="n">new_particles</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">old_particles</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
<span class="k">return</span> <span class="n">new_particles</span>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">"__main__"</span><span class="p">:</span>
<span class="n">old_particles</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>
<span class="n">weights</span> <span class="o">=</span> <span class="p">[</span><span class="o">.</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">.</span><span class="mi">4</span><span class="p">,</span> <span class="o">.</span><span class="mi">3</span><span class="p">]</span>
<span class="n">new_particles</span> <span class="o">=</span> <span class="n">generate_new_particles</span><span class="p">(</span><span class="n">old_particles</span><span class="p">,</span> <span class="n">weights</span><span class="p">)</span>
<span class="k">print</span> <span class="s">"old particles ="</span><span class="p">,</span> <span class="n">old_particles</span>
<span class="k">print</span> <span class="s">"weights ="</span><span class="p">,</span> <span class="n">old_particles</span>
<span class="k">print</span> <span class="s">"new particles ="</span><span class="p">,</span> <span class="n">new_particles</span>
</pre></div>
<p>And here is a sample run (with my debug print statements):</p>
<div class="highlight"><pre>beta = 0.536313558942
beta= 0.236314, index = 0, weight = 0.300000
beta = 0.510275914962
beta= 0.210276, index = 1, weight = 0.000000
beta= 0.210276, index = 2, weight = 0.400000
beta = 0.954824882947
beta= 0.554825, index = 3, weight = 0.300000
beta= 0.254825, index = 0, weight = 0.300000
beta = 0.678700538951
beta= 0.378701, index = 1, weight = 0.000000
beta= 0.378701, index = 2, weight = 0.400000
old particles = [1, 2, 3, 4]
weights = [1, 2, 3, 4]
new particles = [1, 3, 1, 3]
</pre></div>JSONP for cross-origin AJAX2012-03-05T18:27:30-06:00Caleb Madrigaltag:calebmadrigal.com,2012-03-05:jsonp-for-cross-origin-ajax/<p>I was recently wanting to enable a webpage to utilize some server-side functionality which was on a different server than the one serving the original page. Traditionally, this has been problematic due to browsers' <a href="http://en.wikipedia.org/wiki/Same_origin_policy">Same origin policy</a>. JSONP is a solution to this problem. Here is how to do it with jQuery...</p>
<p>This webpage can be saved locally to any machine, opened in a browser, and can then load data from my web server:</p>
<div class="highlight"><pre><span class="nt"><html><head></span>
<span class="nt"><script</span> <span class="na">src=</span><span class="s">"http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"</span> <span class="na">type=</span><span class="s">"text/javascript"</span><span class="nt">></script></span>
<span class="nt"><script</span> <span class="na">type=</span><span class="s">"text/javascript"</span><span class="nt">></span>
$(document).ready(function(){
$("button").click(function(){
$.ajax({
url:"http://test.calebmadrigal.com/javascript/jsonp_test.json",
dataType:'jsonp',
jsonpCallback: "jsonp_load",
success:function(result){
$("#outputdiv").html(result);
}
});
});
});
<span class="nt"></script></span>
<span class="nt"></head><body></span>
<span class="nt"><button></span>Load data<span class="nt"></button></span>
<span class="nt"><div</span> <span class="na">id=</span><span class="s">"outputdiv"</span><span class="nt">></div></span>
<span class="nt"></body></html></span>
</pre></div>
<p>Here is what the server-side looks like:</p>
<div class="highlight"><pre>jsonp_load("<span class="nt"><h4></span>This text was loaded from http://test.calebmadrigal.com/javascript/jsonp_test.json<span class="nt"></h4></span>");
</pre></div>Tail call optimization in Python2012-03-03T04:50:36-06:00Caleb Madrigaltag:calebmadrigal.com,2012-03-03:tail-call-optimization-in-python/<p>Since I've been getting into functional programming more recently, the fact that Python doesn't do tail-call optimization has been bothering me. So I did a bit of searching, and found this gem: <a href="http://code.activestate.com/recipes/474088/">Tail Call Optimization Decorator</a>.</p>
<p>Here is a snippet from it:</p>
<div class="highlight"><pre><span class="kn">import</span> <span class="nn">sys</span>
<span class="k">class</span> <span class="nc">TailRecurseException</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">args</span> <span class="o">=</span> <span class="n">args</span>
<span class="bp">self</span><span class="o">.</span><span class="n">kwargs</span> <span class="o">=</span> <span class="n">kwargs</span>
<span class="k">def</span> <span class="nf">tail_call_optimized</span><span class="p">(</span><span class="n">g</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> This function decorates a function with tail call</span>
<span class="sd"> optimization. It does this by throwing an exception</span>
<span class="sd"> if it is it's own grandparent, and catching such</span>
<span class="sd"> exceptions to fake the tail call optimization.</span>
<span class="sd"> This function fails if the decorated</span>
<span class="sd"> function recurses in a non-tail context.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">sys</span><span class="o">.</span><span class="n">_getframe</span><span class="p">()</span>
<span class="k">if</span> <span class="n">f</span><span class="o">.</span><span class="n">f_back</span> <span class="ow">and</span> <span class="n">f</span><span class="o">.</span><span class="n">f_back</span><span class="o">.</span><span class="n">f_back</span> \
<span class="ow">and</span> <span class="n">f</span><span class="o">.</span><span class="n">f_back</span><span class="o">.</span><span class="n">f_back</span><span class="o">.</span><span class="n">f_code</span> <span class="o">==</span> <span class="n">f</span><span class="o">.</span><span class="n">f_code</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">TailRecurseException</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">while</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span>
<span class="k">return</span> <span class="n">g</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">except</span> <span class="n">TailRecurseException</span><span class="p">,</span> <span class="n">e</span><span class="p">:</span>
<span class="n">args</span> <span class="o">=</span> <span class="n">e</span><span class="o">.</span><span class="n">args</span>
<span class="n">kwargs</span> <span class="o">=</span> <span class="n">e</span><span class="o">.</span><span class="n">kwargs</span>
<span class="n">func</span><span class="o">.</span><span class="n">__doc__</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">__doc__</span>
<span class="k">return</span> <span class="n">func</span>
<span class="nd">@tail_call_optimized</span>
<span class="k">def</span> <span class="nf">factorial</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">acc</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="s">"calculate a factorial"</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="n">acc</span>
<span class="k">return</span> <span class="n">factorial</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="o">*</span><span class="n">acc</span><span class="p">)</span>
</pre></div>
<p>So it is a decorator that you place on a tail-call recursive function. This basically lets the function continue executing rather than throwing the <code>RuntimeError: maximum recursion depth exceeded</code> exception. Note however, that this is not still not very optimal. But is does kind of simulate TCO.</p>Standard Deviation in Python2012-03-01T16:43:12-06:00Caleb Madrigaltag:calebmadrigal.com,2012-03-01:standard-deviation-in-python/<p>I just wanted to go through the process of calculating standard deviation today, and this is how I did it in Python. Python makes such a nice calculator :)</p>
<div class="highlight"><pre><span class="o">>>></span> <span class="n">s</span> <span class="o">=</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">4</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">5</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">9</span><span class="p">]</span>
<span class="o">>>></span> <span class="k">def</span> <span class="nf">average</span><span class="p">(</span><span class="n">s</span><span class="p">):</span> <span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="o">...</span>
<span class="o">>>></span> <span class="n">avg</span> <span class="o">=</span> <span class="n">average</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="o">>>></span> <span class="n">avg</span>
<span class="mf">5.0</span>
<span class="o">>>></span> <span class="n">variance</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">avg</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
<span class="o">>>></span> <span class="n">variance</span>
<span class="p">[</span><span class="mf">9.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">16.0</span><span class="p">]</span>
<span class="o">>>></span> <span class="n">average</span><span class="p">(</span><span class="n">variance</span><span class="p">)</span>
<span class="mf">4.0</span>
<span class="o">>>></span> <span class="kn">import</span> <span class="nn">math</span>
<span class="o">>>></span> <span class="n">standard_deviation</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">average</span><span class="p">(</span><span class="n">variance</span><span class="p">))</span>
<span class="o">>>></span> <span class="n">standard_deviation</span>
<span class="mf">2.0</span>
<span class="o">>>></span>
</pre></div>Django on Hostmonster2012-02-21T00:05:37-06:00Caleb Madrigaltag:calebmadrigal.com,2012-02-21:django-on-hostmonster/<p>I just finished going through the process of installing and configuring Django (with FastCGI) on Hostmonster's Shared hosting. It was more painful than I expected, so I decided write a post about how I got it working...</p>
<p>First, I wanted to create a subdomain which would host my django stuff. In order to do this, I created a subdomain using the cPanel (the item is called "Subdomains"). This created the directory and a basic .htaccess file (along with a few error pages).</p>
<p>I then went through the basic processes described on these pages:</p>
<ul>
<li><a href="http://www.infoinfoc.us/django/hostmonster">http://www.infoinfoc.us/django/hostmonster</a></li>
<li><a href="http://www.techgeekguy.com/2011/01/how-to-install-python-svn-django-osqa-web-hosting-server-hostmonster-dreamhost-bluehost-godaddy-hostgator/">http://www.techgeekguy.com/2011/01/how-to-install-python-svn-django-osqa-web-hosting-server-hostmonster-dreamhost-bluehost-godaddy-hostgator/</a></li>
</ul>
<p>When I finished these guides, I kept getting a 500 error. I eventually found that I can access the error log through cPanel (maybe there is a more direct way?). Then I went through and fixed error by error. Hostmonster's helpdesk has a great <a href="https://my.hostmonster.com/cgi/help/585">Troubleshooting Django</a> page which was helpful once the error log started showing python-related errors.</p>
<p>So after all this pain, I finally got it working. I now present to you my basic setup:</p>
<p><strong>Directory structure:</strong></p>
<div class="highlight"><pre>/home4/questiq1/
|
|-- django/
| |-- django_src/
| |-- django_projects/
| | |-- mysite/
| | | |-- manage.py
| | | |-- mysite/
| | | | |-- __init__.py
| | | | |-- settings.py
| | | | |-- urls.py
| | | | |-- wsgi.py
|
|-- python/
| |-- bin/
| |-- include/
| |-- lib/
| |-- share/
|
|-- public_html/
| |-- highaltitudescience/
| | |-- .htaccess
| | |-- django.fcgi
</pre></div>
<p>A few things to note about the directory structure:</p>
<ul>
<li><code>~/django/django_src</code> is a direct svn checkout of the django project (<code>svn co http://code.djangoproject.com/svn/django/trunk/ django_src</code>)</li>
<li><code>~/django/django_projects</code> contains the actual django code (rather than it living under <code>public_html</code>).</li>
<li><code>django.fcgi</code> must be executable (<code>chmod a+x django.fcgi</code>)</li>
</ul>
<p><strong>django.fcgi file:</strong></p>
<table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre> 1
2
3
4
5
6
7
8
9
10
11
12
13</pre></div></td><td class="code"><div class="highlight"><pre><span class="c">#!/home4/questiq1/python/bin/python</span>
<span class="kn">import</span> <span class="nn">sys</span><span class="o">,</span> <span class="nn">os</span>
<span class="c"># Add a custom Python path.</span>
<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="s">"/home4/questiq1/django/django_src"</span><span class="p">)</span>
<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="s">"/home4/questiq1/django/django_projects"</span><span class="p">)</span>
<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="s">"/home4/questiq1/django/django_projects/mysite"</span><span class="p">)</span>
<span class="c"># Set the DJANGO_SETTINGS_MODULE environment variable.</span>
<span class="n">os</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s">'DJANGO_SETTINGS_MODULE'</span><span class="p">]</span> <span class="o">=</span> <span class="s">"mysite.settings"</span>
<span class="kn">from</span> <span class="nn">django.core.servers.fastcgi</span> <span class="kn">import</span> <span class="n">runfastcgi</span>
<span class="n">runfastcgi</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s">"threaded"</span><span class="p">,</span> <span class="n">daemonize</span><span class="o">=</span><span class="s">"false"</span><span class="p">)</span>
</pre></div>
</td></tr></table>
<p>Notice that I use a custom python path for <code>django.fcgi</code> (to force FastCGI to use my custom-installed version of python rather than the older, pre-installed one).</p>
<p><strong>.htaccess file:</strong></p>
<div class="highlight"><pre>Options +SymLinksIfOwnerMatch
AddHandler fcgid-script .fcgi
RewriteEngine On
RewriteCond %{HTTP_HOST} ^(www.)?highaltitudescience.calebmadrigal.com$
RewriteCond %{REQUEST_FILENAME} !-f [NC]
RewriteRule ^(.*)$ django.fcgi/$1 [QSA,L]
</pre></div>
<p><strong>.bashrc file:</strong></p>
<div class="highlight"><pre><span class="x">if [ -f /etc/bashrc ]; then</span>
<span class="x"> . /etc/bashrc</span>
<span class="x">fi</span>
<span class="x">export PATH=~/python/bin:</span><span class="p">$</span><span class="nv">PATH</span><span class="x"></span>
<span class="x">export PATH=~/django/django_src/django/bin:</span><span class="p">$</span><span class="nv">PATH</span><span class="x"></span>
<span class="x">export PYTHONPATH=~/django/django_src:</span><span class="p">$</span><span class="nv">PYTHONPATH</span><span class="x"></span>
<span class="x">export PYTHONPATH=~/django/django_projects:</span><span class="p">$</span><span class="nv">PYTHONPATH</span><span class="x"></span>
</pre></div>String to Base64 String in Objective-C2012-02-08T17:11:48-06:00Caleb Madrigaltag:calebmadrigal.com,2012-02-08:string-to-base64-string-in-objective-c/<p>Today, I needed to convert an ASCII-encoded NSString to a base64 NSString. I found a number of methods that convert from an NSString to a Base64 NSData, or from NSData to a Base64 string, but couldn't find one that did exactly what I needed. So here is a method that simply converts an NSString to a Base64 NSString:</p>
<div class="highlight"><pre><span class="p">+</span> <span class="p">(</span><span class="bp">NSString</span> <span class="o">*</span><span class="p">)</span><span class="nf">base64String:</span><span class="p">(</span><span class="bp">NSString</span> <span class="o">*</span><span class="p">)</span><span class="nv">str</span>
<span class="p">{</span>
<span class="bp">NSData</span> <span class="o">*</span><span class="n">theData</span> <span class="o">=</span> <span class="p">[</span><span class="n">str</span> <span class="nl">dataUsingEncoding</span><span class="p">:</span> <span class="n">NSASCIIStringEncoding</span><span class="p">];</span>
<span class="k">const</span> <span class="kt">uint8_t</span><span class="o">*</span> <span class="n">input</span> <span class="o">=</span> <span class="p">(</span><span class="k">const</span> <span class="kt">uint8_t</span><span class="o">*</span><span class="p">)[</span><span class="n">theData</span> <span class="n">bytes</span><span class="p">];</span>
<span class="n">NSInteger</span> <span class="n">length</span> <span class="o">=</span> <span class="p">[</span><span class="n">theData</span> <span class="n">length</span><span class="p">];</span>
<span class="k">static</span> <span class="kt">char</span> <span class="n">table</span><span class="p">[]</span> <span class="o">=</span> <span class="s">"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/="</span><span class="p">;</span>
<span class="bp">NSMutableData</span><span class="o">*</span> <span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="bp">NSMutableData</span> <span class="nl">dataWithLength</span><span class="p">:((</span><span class="n">length</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="mi">4</span><span class="p">];</span>
<span class="kt">uint8_t</span><span class="o">*</span> <span class="n">output</span> <span class="o">=</span> <span class="p">(</span><span class="kt">uint8_t</span><span class="o">*</span><span class="p">)</span><span class="n">data</span><span class="p">.</span><span class="n">mutableBytes</span><span class="p">;</span>
<span class="n">NSInteger</span> <span class="n">i</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span> <span class="n">i</span> <span class="o"><</span> <span class="n">length</span><span class="p">;</span> <span class="n">i</span> <span class="o">+=</span> <span class="mi">3</span><span class="p">)</span> <span class="p">{</span>
<span class="n">NSInteger</span> <span class="n">value</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span>
<span class="n">NSInteger</span> <span class="n">j</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="n">j</span> <span class="o">=</span> <span class="n">i</span><span class="p">;</span> <span class="n">j</span> <span class="o"><</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">3</span><span class="p">);</span> <span class="n">j</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
<span class="n">value</span> <span class="o"><<=</span> <span class="mi">8</span><span class="p">;</span>
<span class="k">if</span> <span class="p">(</span><span class="n">j</span> <span class="o"><</span> <span class="n">length</span><span class="p">)</span> <span class="p">{</span>
<span class="n">value</span> <span class="o">|=</span> <span class="p">(</span><span class="mh">0xFF</span> <span class="o">&</span> <span class="n">input</span><span class="p">[</span><span class="n">j</span><span class="p">]);</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="n">NSInteger</span> <span class="n">theIndex</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="mi">4</span><span class="p">;</span>
<span class="n">output</span><span class="p">[</span><span class="n">theIndex</span> <span class="o">+</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">table</span><span class="p">[(</span><span class="n">value</span> <span class="o">>></span> <span class="mi">18</span><span class="p">)</span> <span class="o">&</span> <span class="mh">0x3F</span><span class="p">];</span>
<span class="n">output</span><span class="p">[</span><span class="n">theIndex</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">table</span><span class="p">[(</span><span class="n">value</span> <span class="o">>></span> <span class="mi">12</span><span class="p">)</span> <span class="o">&</span> <span class="mh">0x3F</span><span class="p">];</span>
<span class="n">output</span><span class="p">[</span><span class="n">theIndex</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o"><</span> <span class="n">length</span> <span class="o">?</span> <span class="n">table</span><span class="p">[(</span><span class="n">value</span> <span class="o">>></span> <span class="mi">6</span><span class="p">)</span> <span class="o">&</span> <span class="mh">0x3F</span><span class="p">]</span> <span class="o">:</span> <span class="sc">'='</span><span class="p">;</span>
<span class="n">output</span><span class="p">[</span><span class="n">theIndex</span> <span class="o">+</span> <span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="o"><</span> <span class="n">length</span> <span class="o">?</span> <span class="n">table</span><span class="p">[(</span><span class="n">value</span> <span class="o">>></span> <span class="mi">0</span><span class="p">)</span> <span class="o">&</span> <span class="mh">0x3F</span><span class="p">]</span> <span class="o">:</span> <span class="sc">'='</span><span class="p">;</span>
<span class="p">}</span>
<span class="k">return</span> <span class="p">[[</span><span class="bp">NSString</span> <span class="n">alloc</span><span class="p">]</span> <span class="nl">initWithData</span><span class="p">:</span><span class="n">data</span> <span class="nl">encoding</span><span class="p">:</span><span class="n">NSASCIIStringEncoding</span><span class="p">];</span>
<span class="p">}</span>
</pre></div>
<p>Note that the base code (which I slightly modified) was taken from this <a href="http://stackoverflow.com/questions/6006823/how-to-get-base64-nsstring-from-nsdata">Stackoverflow answer</a>.</p>Function application and function composition in Haskell2012-01-22T22:57:42-06:00Caleb Madrigaltag:calebmadrigal.com,2012-01-22:function-application-and-function-composition-in-haskell/<p>In the process of learning haskell, I've been trying to become comfortable with the function applicator (<code>$</code>) and function composition (<code>.</code>). Here is some code to show how they relate (and how they relate to using parenthesis to enforce order of operations):</p>
<div class="highlight"><pre>let dict = [(1,'a'),(2,'b'),(3,'c')]
-- The following 3 lines of code are equivalent...
snd . head . filter (\item@(k,v) -> k == 2) $ dict -- returns 'b'
snd $ head $ filter (\item@(k,v) -> k == 2) dict -- returns 'b'
snd (head (filter (\item@(k,v) -> k == 2) dict)) -- return 'b'
</pre></div>Map in Objective-C2012-01-20T23:22:36-06:00Caleb Madrigaltag:calebmadrigal.com,2012-01-20:map-in-objective-c/<p>Today, I was faced with an issue several times where I had an array of items of one type, and had to convert this into an array of items of a different type. This made me really want a <code>map()</code> function. So I added one to <code>NSArray</code> like so:</p>
<p>NSArray+FP.h</p>
<div class="highlight"><pre><span class="cp">#import <Foundation/Foundation.h></span>
<span class="k">typedef</span> <span class="nf">id</span><span class="p">(</span><span class="o">^</span><span class="n">MapBlock</span><span class="p">)(</span><span class="kt">id</span><span class="p">);</span>
<span class="k">@interface</span> <span class="bp">NSArray</span> <span class="nl">(FP)</span>
<span class="p">-</span> <span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nf">map:</span><span class="p">(</span><span class="n">MapBlock</span><span class="p">)</span><span class="nv">block</span><span class="p">;</span>
<span class="k">@end</span>
</pre></div>
<p>NSArray+FP.m</p>
<div class="highlight"><pre><span class="cp">#import "NSArray+FP.h"</span>
<span class="k">@implementation</span> <span class="bp">NSArray</span> <span class="nl">(FP)</span>
<span class="p">-</span> <span class="p">(</span><span class="bp">NSArray</span> <span class="o">*</span><span class="p">)</span><span class="nf">map:</span><span class="p">(</span><span class="n">MapBlock</span><span class="p">)</span><span class="nv">block</span> <span class="p">{</span>
<span class="bp">NSMutableArray</span> <span class="o">*</span><span class="n">resultArray</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">NSMutableArray</span> <span class="n">alloc</span><span class="p">]</span> <span class="n">init</span><span class="p">];</span>
<span class="k">for</span> <span class="p">(</span><span class="kt">id</span> <span class="n">object</span> <span class="k">in</span> <span class="nb">self</span><span class="p">)</span> <span class="p">{</span>
<span class="p">[</span><span class="n">resultArray</span> <span class="nl">addObject</span><span class="p">:</span><span class="n">block</span><span class="p">(</span><span class="n">object</span><span class="p">)];</span>
<span class="p">}</span>
<span class="k">return</span> <span class="n">resultArray</span><span class="p">;</span>
<span class="p">}</span>
<span class="k">@end</span>
</pre></div>
<p>So now, I can do this!</p>
<div class="highlight"><pre><span class="bp">NSArray</span> <span class="o">*</span><span class="n">strArray</span> <span class="o">=</span> <span class="p">[</span><span class="bp">NSArray</span> <span class="nl">arrayWithObjects</span><span class="p">:</span><span class="s">@"1"</span><span class="p">,</span><span class="s">@"1"</span><span class="p">,</span><span class="s">@"2"</span><span class="p">,</span><span class="s">@"3"</span><span class="p">,</span><span class="s">@"5"</span><span class="p">,</span><span class="s">@"8"</span><span class="p">,</span><span class="nb">nil</span><span class="p">];</span>
<span class="bp">NSArray</span> <span class="o">*</span><span class="n">numArray</span> <span class="o">=</span> <span class="p">[</span><span class="n">strArray</span> <span class="nl">map</span><span class="p">:</span><span class="o">^</span><span class="kt">id</span><span class="p">(</span><span class="kt">id</span> <span class="n">object</span><span class="p">)</span> <span class="p">{</span>
<span class="bp">NSString</span> <span class="o">*</span><span class="n">str</span> <span class="o">=</span> <span class="n">object</span><span class="p">;</span>
<span class="k">return</span> <span class="p">[</span><span class="bp">NSNumber</span> <span class="nl">numberWithInt</span><span class="p">:[</span><span class="n">str</span> <span class="n">intValue</span><span class="p">]];</span>
<span class="p">}];</span>
</pre></div>How to place custom image in UITextField in iOS2012-01-19T18:02:16-06:00Caleb Madrigaltag:calebmadrigal.com,2012-01-19:how-to-place-custom-image-in-uitextfield-in-ios/<p>Here is how to put an image in the right portion of a <code>UITextField</code>:</p>
<div class="highlight"><pre><span class="bp">UITextField</span> <span class="o">*</span><span class="n">textField</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">UITextField</span> <span class="n">alloc</span><span class="p">]</span> <span class="nl">initWithFrame</span><span class="p">:</span><span class="n">CGRectMake</span><span class="p">(</span><span class="mi">55</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">660</span><span class="p">,</span> <span class="mi">30</span><span class="p">)];</span>
<span class="n">textField</span><span class="p">.</span><span class="n">rightViewMode</span> <span class="o">=</span> <span class="n">UITextFieldViewModeWhileEditing</span><span class="p">;</span>
<span class="bp">UIImageView</span> <span class="o">*</span><span class="n">imageView</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">UIImageView</span> <span class="n">alloc</span><span class="p">]</span> <span class="nl">initWithFrame</span><span class="p">:</span><span class="n">CGRectMake</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">15</span><span class="p">)];</span>
<span class="n">imageView</span><span class="p">.</span><span class="n">image</span> <span class="o">=</span> <span class="p">[</span><span class="bp">UIImage</span> <span class="nl">imageNamed</span><span class="p">:</span><span class="s">@"invalidFieldCircle"</span><span class="p">];</span>
<span class="n">textField</span><span class="p">.</span><span class="n">rightView</span> <span class="o">=</span> <span class="n">imageView</span><span class="p">;</span>
</pre></div>
<p>This also assumes that an image called "invalidFieldCircle.png" is in your project's "Resources" directory, which should be located just below the main project directory (you may have to create it).</p>Force weak reference in Objective-C2012-01-10T20:14:27-06:00Caleb Madrigaltag:calebmadrigal.com,2012-01-10:force-weak-reference-in-objective-c/<p>Today, I was trying to add an object to an <code>NSDictionary</code> and force it to be a weak reference. This can be done with the <code>[NSValue valueWithNonretainedObject]</code> call:</p>
<div class="highlight"><pre><span class="bp">NSValue</span> <span class="o">*</span><span class="n">weakRef</span> <span class="o">=</span> <span class="p">[</span><span class="bp">NSValue</span> <span class="nl">valueWithNonretainedObject</span><span class="p">:</span><span class="n">loadDelegate</span><span class="p">];</span>
<span class="bp">NSDictionary</span> <span class="o">*</span><span class="n">userInfo</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">NSDictionary</span> <span class="n">alloc</span><span class="p">]</span> <span class="nl">initWithObjectsAndKeys</span><span class="p">:</span><span class="n">weakRef</span><span class="p">,</span> <span class="s">@"loadDelegate"</span><span class="p">,</span> <span class="nb">nil</span><span class="p">];</span>
</pre></div>First steps in haskell2012-01-09T02:30:39-06:00Caleb Madrigaltag:calebmadrigal.com,2012-01-09:first-steps-in-haskell/<p>Just started looking into the Haskell programming language by going through the first few chapters of the awesome book: <a href="http://learnyouahaskell.com/">Learn You a Haskell</a> which is free to read online. Here are some things I really like about what I have seen of Haskell so far:</p>
<ul>
<li>Type inference allows you to have static typing but not all the verbosity of most other statically-typed languages.</li>
<li>Lazy evaluation is huge in Haskell, and it lets you do things like this: <code>let factorial n = product (take n [1..])</code> So here, we have an infinite list (<code>[1..]</code> creates a infinite list from 1 to infinity!) which from which the first <code>n</code> items are taken and passed to the <code>product</code> function. Awesomeness...</li>
<li>Nice REPL</li>
</ul>Consuming web service in Python with SUDS2012-01-02T20:25:08-06:00Caleb Madrigaltag:calebmadrigal.com,2012-01-02:consuming-web-service-in-python-with-suds/<div class="highlight"><pre><span class="kn">import</span> <span class="nn">datetime</span>
<span class="kn">from</span> <span class="nn">suds.client</span> <span class="kn">import</span> <span class="n">Client</span>
<span class="n">url</span> <span class="o">=</span> <span class="s">"http://localhost:9080/dataplanws/DataPlanWebService/WEB-INF/wsdl/DataPlanWebService.wsdl"</span>
<span class="n">client</span> <span class="o">=</span> <span class="n">Client</span><span class="p">(</span><span class="n">url</span><span class="p">)</span>
<span class="k">print</span> <span class="n">client</span><span class="o">.</span><span class="n">service</span><span class="o">.</span><span class="n">hello</span><span class="p">(</span><span class="s">"Caleb"</span><span class="p">)</span>
</pre></div>Periods in Powershell2012-01-02T20:21:30-06:00Caleb Madrigaltag:calebmadrigal.com,2012-01-02:periods-in-powershell/<p>For running most commands, powershell and CMD work the same. One big difference I've found is that, when you use periods (<code>.</code>) in a command, they must be surrounded by quotation marks. For instance, this won't work:</p>
<div class="highlight"><pre>mvn clean install -U -Docns.web.dynamic.content.version=2.6.0
</pre></div>
<p>But this will work:</p>
<div class="highlight"><pre>mvn clean install -U "-Docns.web.dynamic.content.version=2.6.0"
</pre></div>