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 Tests & internals
 =================
 
 Unit tests
 ----------
 .. image:: https://travis-ci.org/Duke-QCD/trento.svg?branch=master
     :target: https://travis-ci.org/Duke-QCD/trento
     :width: 90px
 
 T\ :sub:`R`\ ENTo has a thorough `test suite <https://github.com/Duke-QCD/trento/tree/master/test>`_.
 To run the tests, build the code in debug mode::
 
    mkdir build-debug && cd build-debug
    cmake .. -DCMAKE_BUILD_TYPE=Debug
    make tests
 
 Tests rely on the `Catch <https://github.com/philsquared/Catch>`_ C++ test framework, which CMake downloads automatically during the build process.
 If for some reason this fails, manually download the header `catch.hpp <https://raw.githubusercontent.com/philsquared/Catch/master/single_include/catch.hpp>`_ and place it in the ``test`` directory.
 
 If `gcovr <http://gcovr.com>`_ is installed a code coverage report will be generated.
 
 If any `sanitizers <https://github.com/google/sanitizers>`_ are available they will run.
 The sanitizers check for runtime errors such as memory leaks.
 They are included in recent versions of GCC and Clang.
 
 Fitting the cross section
 -------------------------
 It is vital that the model reproduce the inelastic nucleon-nucleon cross section `\sigma_{NN}`.
 This condition may be written
 
 .. math::
 
       \sigma_{NN} = \int d^2b \, P_\text{coll}(b),
 
 where
 
 .. math::
 
    P_\text{coll}(b) = 1 - \exp[-\sigma_{gg}T_{AB}(b)]
 
 is the probability of two nucleons colliding at impact parameter `b`.
 
 `T_{AB}` is the overlap integral of the two nucleons' thickness functions, easily computed given Gaussian nucleons of width `w`:
 
 .. math::
 
    \begin{align*}
       T_A(x, y) &= \frac{1}{2\pi w^2} \exp\biggl( -\frac{x^2 + y^2}{2w^2} \biggr), \\[1em]
       T_{AB}(b) &= \int dx \, dy \, T_A(x - b/2, y) T_B(x + b/2, y) \\
                 &= \frac{1}{4\pi w^2} \exp\biggl( -\frac{b^2}{4w^2} \biggr).
    \end{align*}
 
 `\sigma_{gg}` is an effective parton-parton cross section now determined by the relation
 
 .. math::
 
    \sigma_{NN} = \int_0^{b_\text{max}} 2\pi b \, db \,
       \biggl\{
          1 - \exp\biggl[
             -\frac{\sigma_{gg}}{4\pi w^2}
             \exp\biggl( -\frac{b^2}{4w^2} \biggr)
          \biggr]
       \biggr\},
 
 where `b_\text{max}` is the maximum impact parameter for a collision.
 Let `b_\text{max} = Aw`, i.e. some number of nucleon widths (the actual code uses `A = 6`).
 
 After appropriate change of variables, this relation may be written
 
 .. math::
 
    \frac{\sigma_{NN}}{4\pi w^2} =
       \frac{A^2}{4} +
       \text{Ei}\biggl( -e^{-A^2/4} \frac{\sigma_{gg}}{4\pi w^2} \biggr) -
       \text{Ei}\biggl( -\frac{\sigma_{gg}}{4\pi w^2} \biggr)
 
 where `\text{Ei}` is the `exponential integral <https://en.wikipedia.org/wiki/Exponential_integral>`_.
 This is still a transcendental equation but it can be quickly solved numerically for a given cross section and nucleon width.
 
 The code determines `\sigma_{gg}` at runtime by solving this equation using a standard root finding algorithm.
 The relevant function is ``compute_cross_sec_param`` in `nucleon.cxx <https://github.com/Duke-QCD/trento/blob/master/src/nucleon.cxx>`_.
 Note that it actually optimizes over the dimensionless variable `\log({\sigma_{gg}/4\pi w^2})`.
 
 The nucleon unit test verifies that the cross section is accurately reproduced.
 
 List of classes
 ---------------
 This section is automatically generated from the source code by `Doxygen <http://www.stack.nl/~dimitri/doxygen>`_ and converted into `Sphinx <http://sphinx-doc.org>`_ format by `Breathe <https://breathe.readthedocs.org>`_.
 In order to emphasize functionality---rather than implementation details---private class methods are not shown.
 
 .. highlight:: cpp
 
 Collider
 ~~~~~~~~
 .. doxygenclass:: trento::Collider
    :members: Collider, run_events
 
 Event
 ~~~~~
 .. doxygenclass:: trento::Event
    :members:
 
 Output
 ~~~~~~
 .. doxygenclass:: trento::Output
    :members:
 
 Nucleus
 ~~~~~~~
 .. doxygenfunction:: trento::Nucleus::create
 
 .. doxygenclass:: trento::Nucleus
    :members: radius, sample_nucleons, ~Nucleus
    :protected-members:
 
 Nucleus types
 '''''''''''''
 .. doxygenclass:: trento::Proton
 .. doxygenclass:: trento::Deuteron
 .. doxygenclass:: trento::WoodsSaxonNucleus
 .. doxygenclass:: trento::DeformedWoodsSaxonNucleus
 .. doxygenclass:: trento::ManualNucleus
 
 Nucleon
 ~~~~~~~
 .. doxygenclass:: trento::Nucleon
    :members: Nucleon, x, y, z, is_participant, set_position, set_participant
 
 Nucleon profile
 ~~~~~~~~~~~~~~~
 .. doxygenclass:: trento::NucleonProfile
    :members:
 
 Fast exponential
 ~~~~~~~~~~~~~~~~
 .. doxygenclass:: trento::FastExp
    :members:

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