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<section><section>
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<h1 id="External-libraries">External libraries<a class="anchor-link" href="#External-libraries">&#182;</a></h1>
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<div class="slide" style="float: left"><div class="full" style="width: 100%; float: left">
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<h2 id="Python">Python<a class="anchor-link" href="#Python">&#182;</a></h2><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">inv</span>
</pre></div>
<ul>
<li>Python interpreter searches modules in the form *.py files, or directories with __init__.py files</li>
<li>Search through standard paths (/usr/lib/python3.6/)</li>
<li>Search through path provided in an environment variable PYTHONPATH (edit .bashrc to extend the list)</li>
<li>can see such a list with:</li>
</ul>
<div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">sys</span>
<span class="k">print</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="p">)</span>
</pre></div>
</div>
</div></div>
</section><section>
<div class="slide" style="float: left"><div class="full" style="width: 100%; float: left">
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<h2 id="Producing-executables">Producing executables<a class="anchor-link" href="#Producing-executables">&#182;</a></h2><ul>
<li>Compilation: produces .o files</li>
<li>Using external libraries first need to include interfaces</li>
</ul>
<div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf">&lt;iostream&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;cmath&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;gsl/gsl_sf_bessel.h&gt;</span><span class="cp"></span>
</pre></div>
<ul>
<li>At compilation, g++ searches through standard paths (such as /usr/bin/include) </li>
<li>Extending the list can be done with the option '-I':<div class="highlight"><pre><span></span>&gt; g++ -c -Imynew_path file.cc
</pre></div>
</li>
</ul>
</div>
</div></div>
</section><section>
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<ul>
<li>Link edition (Linking): produces executables/libraries from .o files and libraries with '-l' option</li>
<li>At compilation, g++ searches through standard paths (such as /usr/lib) </li>
<li>Extend the list can be done with the option '-L' <div class="highlight"><pre><span></span>&gt; g++ file1.o file2.o -L/some_path/ -lmylib -o <span class="nb">exec</span>
</pre></div>
</li>
</ul>
</div>
</div></div>
</section><section>
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<ul>
<li>What is this error about ?</li>
</ul>
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<pre>&gt; g++ tmp.cc
/usr/bin/ld: /usr/lib/gcc/x86_64-linux-gnu/8/../../../x86_64-linux-gnu/Scrt1.o: in function `_start&#39;:
(.text+0x20): undefined reference to `main&#39;
collect2: error: ld returned 1 exit status
</pre>
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</section><section>
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<ul>
<li>What is this error about ?</li>
</ul>
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<div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf">&lt;gsl/gsl_sf_bessel.h&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;iostream&gt;</span><span class="cp"></span>
<span class="kt">int</span> <span class="nf">main</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span> <span class="p">{</span>
<span class="kt">double</span> <span class="n">x</span> <span class="o">=</span> <span class="mf">5.0</span><span class="p">;</span>
<span class="kt">double</span> <span class="n">y</span> <span class="o">=</span> <span class="n">gsl_sf_bessel_J0</span><span class="p">(</span><span class="n">x</span><span class="p">);</span>
<span class="n">std</span><span class="o">::</span><span class="n">cout</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;J0(&quot;</span> <span class="o">&lt;&lt;</span> <span class="n">x</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;) = &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">y</span><span class="p">;</span>
<span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
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<pre>&gt; g++ tmp.cc
/usr/bin/ld: /tmp/ccN3AVEO.o: in function `main&#39;:
tmp.cc:(.text+0x1b): undefined reference to `gsl_sf_bessel_J0&#39;
collect2: error: ld returned 1 exit status
</pre>
</div>
</div>
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</section><section>
<div class="slide" style="float: left"><div class="full" style="width: 100%; float: left">
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<ul>
<li>Need to specify the "library" where the files reside</li>
</ul>
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<pre>&gt; g++ -lgsl tmp.cc
</pre>
</div>
</div>
</div>
</div></div>
</section><section>
<div class="slide" style="float: left"><div class="full" style="width: 100%; float: left">
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<ul>
<li>Why does this show no error at link ?</li>
</ul>
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<div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf">&lt;cmath&gt;</span><span class="cp"></span>
<span class="kt">int</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span> <span class="k">return</span> <span class="kt">int</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">2.</span><span class="p">));</span> <span class="p">}</span>
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<pre>&gt; g++ tmp.cc
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<h2 id="Static-libraries">Static libraries<a class="anchor-link" href="#Static-libraries">&#182;</a></h2><ul>
<li>A <a href="https://en.wikipedia.org/wiki/Static_library">Static libraries</a> is a set of routines, external functions and variables which are resolved by linker/binder to produce a stand-alone executable. </li>
<li>Generally with extension "libXXXX.a" (e.g. /usr/lib/x86_64-linux-gnu/libm.a). </li>
<li>The final executable statically linked includes all the libraries (big executable file)</li>
<li>carry dependencies but not portable</li>
</ul>
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<h2 id="Dynamic-libraries">Dynamic libraries<a class="anchor-link" href="#Dynamic-libraries">&#182;</a></h2><ul>
<li><a href="https://en.wikipedia.org/wiki/Library_(computing">Dynamic/Shared libraries</a>#Shared_libraries) are loaded on demand by executables. </li>
<li>Shared libraries can be statically linked or dynamically loaded.</li>
<li>libXXX.so (or libXXX.dll on windows). e.g. /usr/lib/x86_64-linux-gnu/libm.so</li>
</ul>
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<div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf">&lt;cmath&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;gsl/gsl_sf_bessel.h&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;iostream&gt;</span><span class="cp"></span>
<span class="kt">int</span> <span class="nf">main</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span> <span class="p">{</span>
<span class="kt">double</span> <span class="n">x</span> <span class="o">=</span> <span class="mf">5.0</span><span class="p">;</span>
<span class="kt">double</span> <span class="n">y</span> <span class="o">=</span> <span class="n">gsl_sf_bessel_J0</span><span class="p">(</span><span class="n">x</span><span class="p">);</span>
<span class="n">std</span><span class="o">::</span><span class="n">cout</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;J0(&quot;</span> <span class="o">&lt;&lt;</span> <span class="n">x</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;) = &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">y</span><span class="p">;</span>
<span class="k">return</span> <span class="kt">int</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">2.</span><span class="p">));</span>
<span class="p">}</span>
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<pre>&gt; ldd exe
linux-vdso.so.1 (0x00007ffe0acfa000)
libgsl.so.23 =&gt; /lib/x86_64-linux-gnu/libgsl.so.23 (0x00007f434ca37000)
libstdc++.so.6 =&gt; /lib/x86_64-linux-gnu/libstdc++.so.6 (0x00007f434c8b4000)
libm.so.6 =&gt; /lib/x86_64-linux-gnu/libm.so.6 (0x00007f434c720000)
libgcc_s.so.1 =&gt; /lib/x86_64-linux-gnu/libgcc_s.so.1 (0x00007f434c706000)
libc.so.6 =&gt; /lib/x86_64-linux-gnu/libc.so.6 (0x00007f434c549000)
libgslcblas.so.0 =&gt; /lib/x86_64-linux-gnu/libgslcblas.so.0 (0x00007f434c508000)
/lib64/ld-linux-x86-64.so.2 (0x00007f434ccf1000)
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<h2 id="Scrutinizing-a-library">Scrutinizing a library<a class="anchor-link" href="#Scrutinizing-a-library">&#182;</a></h2><ul>
<li>What to do if you have a link error <strong>Undefined symbol</strong></li>
<li>For an <strong>internal</strong> symbol: check missing <em>inline</em>, check missing implementation</li>
<li>For an <strong>external</strong> symbol: search the library file !</li>
</ul>
<p>Listing the <strong>Symbols</strong> from a library:</p>
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<pre>&gt; nm -DAC /lib/x86_64-linux-gnu/libm.so.6
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<ul>
<li>option "-A": precede the symbol with library name</li>
<li>option "-D": for dynamic libraries (not needed if .o or .a files)</li>
<li>option "-C": demangle C++ symbols</li>
</ul>
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<pre>&gt; nm -DAC /lib/x86_64-linux-gnu/libm.so.6
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<pre>/lib/x86_64-linux-gnu/libm.so.6:000000000000e910 W acos
/lib/x86_64-linux-gnu/libm.so.6:0000000000011f40 W acosf
/lib/x86_64-linux-gnu/libm.so.6:0000000000074b30 W acosf128
/lib/x86_64-linux-gnu/libm.so.6:0000000000056b30 T __acosf128_finite
/lib/x86_64-linux-gnu/libm.so.6:0000000000011f40 W acosf32
...
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<ul>
<li>U: undefined symbol $\Rightarrow$ used in the library not defined</li>
<li>T: text symbol $\Rightarrow$ used in the library and defined in the library</li>
<li>W: weak symbol $\Rightarrow$ used in the library, defined but can be overloaded with a T symbol</li>
</ul>
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<h2 id="Finding-a-symbol-from-a-list-of-files">Finding a symbol from a list of files<a class="anchor-link" href="#Finding-a-symbol-from-a-list-of-files">&#182;</a></h2>
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<pre>&gt; find /usr/lib/x86_64-linux-gnu/ -name &#39;*.so&#39; -exec nm -DAC &#39;{}&#39; &#39;;&#39; | grep &#39;gsl_sf_bessel_J0&#39;
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<pre>/usr/lib/x86_64-linux-gnu/libgsl.so:0000000000164250 T gsl_sf_bessel_J0
/usr/lib/x86_64-linux-gnu/libgsl.so:0000000000163dd0 T gsl_sf_bessel_J0_e
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<h1 id="Advanced-CMake">Advanced <a href="https://cmake.org/cmake/help/v3.13/">CMake</a><a class="anchor-link" href="#Advanced-CMake">&#182;</a></h1>
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<h2 id="Creating-an-executable">Creating an executable<a class="anchor-link" href="#Creating-an-executable">&#182;</a></h2><div class="highlight"><pre><span></span><span class="nb">cmake_minimum_required</span> <span class="p">(</span><span class="s">VERSION</span> <span class="s">3.1</span><span class="p">)</span>
<span class="nb">project</span> <span class="p">(</span><span class="s">Wonderland</span><span class="p">)</span>
<span class="nb">add_executable</span><span class="p">(</span><span class="s">exe</span> <span class="s">file1.cc</span> <span class="s">file2.cc</span><span class="p">)</span>
</pre></div>
<ul>
<li>compiles <em>file1.o</em> and <em>file2.o</em> and link into an executable <em>exe</em></li>
</ul>
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<h2 id="Variables">Variables<a class="anchor-link" href="#Variables">&#182;</a></h2><div class="highlight"><pre><span></span><span class="nb">set</span><span class="p">(</span><span class="s">VAR_NAME</span> <span class="s2">&quot;my variable&quot;</span><span class="p">)</span>
<span class="c"># example: setting version number </span>
<span class="nb">set</span><span class="p">(</span><span class="s">Wonderland_VERSION_MAJOR</span> <span class="s">1</span><span class="p">)</span>
<span class="nb">set</span><span class="p">(</span><span class="s">Wonderland_VERSION_MINOR</span> <span class="s">0</span><span class="p">)</span><span class="err">)</span>
<span class="c"># variable appearing in the ccmake menu</span>
<span class="nb">set</span><span class="p">(</span><span class="s">CACHED_VARIABLE</span> <span class="s">CACHE</span> <span class="s">STRING</span> <span class="s2">&quot;a variable appearing in cmake menu&quot;</span><span class="p">)</span>
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<ul>
<li>types are BOOL, FILEPATH, PATH, STRING</li>
<li>using variables</li>
</ul>
<div class="highlight"><pre><span></span><span class="nb">message</span><span class="p">(</span><span class="s2">&quot;VAR_NAME = ${VAR_NAME}&quot;</span><span class="p">)</span>
</pre></div>
<ul>
<li><a href="https://cmake.org/cmake/help/v3.13/manual/cmake-variables.7.html">special variables</a></li>
</ul>
<pre><code>example: ${PROJECT_BINARY_DIR} ${PROJECT_SOURCE_DIR}</code></pre>
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<h2 id="Adding-paths-to-the-include-search-list">Adding paths to the include search list<a class="anchor-link" href="#Adding-paths-to-the-include-search-list">&#182;</a></h2><div class="highlight"><pre><span></span><span class="nb">include_directories</span><span class="p">(</span><span class="s">&#39;/my_preferred_path&#39;</span><span class="p">)</span>
<span class="nb">include_directories</span><span class="p">(</span><span class="s2">&quot;${PROJECT_BINARY_DIR}&quot;</span><span class="p">)</span>
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<h2 id="Adding-an-external-library">Adding an external library<a class="anchor-link" href="#Adding-an-external-library">&#182;</a></h2><div class="highlight"><pre><span></span><span class="nb">add_executable</span><span class="p">(</span><span class="s">exe</span> <span class="s">file1.cc</span> <span class="s">file2.cc</span><span class="p">)</span>
<span class="nb">target_link_libraries</span> <span class="p">(</span><span class="s">exe</span> <span class="s">gsl</span><span class="p">)</span>
<span class="c"># or with full path</span>
<span class="nb">target_link_libraries</span> <span class="p">(</span><span class="s">exe</span> <span class="s">/usr/lib/x86_64-linux-gnu/libgsl.so</span><span class="p">)</span>
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<h2 id="Creating-a-library">Creating a library<a class="anchor-link" href="#Creating-a-library">&#182;</a></h2><div class="highlight"><pre><span></span><span class="nb">add_library</span><span class="p">(</span><span class="s">mylib</span> <span class="s">file1.cc</span> <span class="s">file2.cc</span><span class="p">)</span>
<span class="nb">add_executable</span><span class="p">(</span><span class="s">exe</span> <span class="s">main.cc</span><span class="p">)</span>
<span class="nb">target_link_libraries</span> <span class="p">(</span><span class="s">exe</span> <span class="s">gsl</span> <span class="s">mylib</span><span class="p">)</span>
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<h2 id="Making-options">Making options<a class="anchor-link" href="#Making-options">&#182;</a></h2><div class="highlight"><pre><span></span><span class="c"># should we use our own math functions?</span>
<span class="nb">option</span> <span class="p">(</span><span class="s">USE_GSL</span> <span class="s2">&quot;Use gsl library&quot;</span> <span class="s">ON</span><span class="p">)</span>
<span class="nb">if</span> <span class="p">(</span><span class="s">USE_GSL</span><span class="p">)</span>
<span class="nb">target_link_libraries</span> <span class="p">(</span><span class="s">exe</span> <span class="s">gsl</span> <span class="s">mylib</span><span class="p">)</span>
<span class="nb">endif</span> <span class="p">(</span><span class="s">USE_GSL</span><span class="p">)</span>
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<h2 id="Finding-libraries">Finding libraries<a class="anchor-link" href="#Finding-libraries">&#182;</a></h2><ul>
<li>For the library files</li>
</ul>
<div class="highlight"><pre><span></span><span class="nb">set</span><span class="p">(</span><span class="s">GSL_LIBRARY_PATH</span> <span class="s">CACHE</span> <span class="s">PATH</span> <span class="s2">&quot;library where to search libgsl&quot;</span><span class="p">)</span>
<span class="nb">find_library</span> <span class="p">(</span><span class="s">GSL_LIBRARY</span> <span class="s">libgsl</span> <span class="o">${</span><span class="nv">GSL_LIBRARY_PATH</span><span class="o">}</span> <span class="s">/usr/lib</span><span class="p">)</span>
</pre></div>
<ul>
<li>For the include files</li>
</ul>
<div class="highlight"><pre><span></span><span class="nb">set</span><span class="p">(</span><span class="s">GSL_INCLUDE_PATH</span> <span class="s">CACHE</span> <span class="s">PATH</span> <span class="s2">&quot;path where to search gsl include files&quot;</span><span class="p">)</span>
<span class="nb">find_path</span><span class="p">(</span><span class="s">GSL_INCLUDE</span> <span class="s">gsl_root.h</span> <span class="o">${</span><span class="nv">GSL_INCLUDE_PATH</span><span class="o">}</span> <span class="s">/usr/include/</span><span class="p">)</span>
</pre></div>
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<h1 id="Discrete-Fourier-Transform"><a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">Discrete Fourier Transform</a><a class="anchor-link" href="#Discrete-Fourier-Transform">&#182;</a></h1><ul>
<li>Taking a signal (vector of points) $(x_i)$, the Discrete Fourier Transform is gien as the signal:</li>
</ul>
$$[DFT(x)]_k = \hat{x}_k = \sum_{i=0}^{N-1} x_i \cdot e^{-\frac{2\pi i kn}{N}}$$<ul>
<li>It forms an approximation of Fourier series complex coefficients</li>
<li>The inverse DFT is given with</li>
</ul>
$$[DFT^{-1}(\hat{x})]_i = x_i = \frac{1}{N}\sum_{i=0}^{N-1} \hat{x}_k \cdot e^{\frac{2\pi kin}{N}}$$
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<h1 id="Fast-Fourier-Transform"><a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform">Fast Fourier Transform</a><a class="anchor-link" href="#Fast-Fourier-Transform">&#182;</a></h1><ul>
<li>Hierarchical algorithm ($N \log N$)</li>
<li><a href="http://www.fftw.org/">FFTW</a> library: mainstream library implementating the FFT transform (Fastest Fourier Transform in the West)</li>
<li><a href="http://www.fftw.org/fftw3_doc/">Documentation</a></li>
<li>example<div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf">&lt;fftw3.h&gt;</span><span class="cp"></span>
<span class="p">{</span>
<span class="n">fftw_complex</span> <span class="o">*</span><span class="n">in</span><span class="p">,</span> <span class="o">*</span><span class="n">out</span><span class="p">;</span>
<span class="n">fftw_plan</span> <span class="n">p</span><span class="p">;</span>
<span class="p">...</span>
<span class="n">in</span> <span class="o">=</span> <span class="k">new</span> <span class="n">fftw_complex</span><span class="p">[</span><span class="n">N</span><span class="p">];</span>
<span class="n">out</span> <span class="o">=</span> <span class="k">new</span> <span class="n">fftw_complex</span><span class="p">[</span><span class="n">N</span><span class="p">];</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">fftw_plan_dft_1d</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">in</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="n">FFTW_FORWARD</span><span class="p">,</span> <span class="n">FFTW_ESTIMATE</span><span class="p">);</span>
<span class="p">...</span>
<span class="n">fftw_execute</span><span class="p">(</span><span class="n">p</span><span class="p">);</span> <span class="cm">/* repeat as needed */</span>
<span class="p">...</span>
<span class="n">fftw_destroy_plan</span><span class="p">(</span><span class="n">p</span><span class="p">);</span>
<span class="k">delete</span> <span class="p">[]</span> <span class="n">in</span><span class="p">;</span>
<span class="k">delete</span> <span class="p">[]</span> <span class="n">out</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
</li>
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