Matrix cascade equation core code
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MCEq - Matrix cascade equation (Release Candidate 1)

This version was previously known as 'dev' branch.

This scientific package might be useful fo all who deal with high-energy inclusive atmospheric fluxes of muons and neutrinos. In particular it might be useful for astroparticle physics experiments, for example IceCube or MINOS, for calculations of systematic uncertainties and atmospheric backgrounds.

Status (Updated)

This is release candiate of the final version 1.0. It has several new features including: - extended energy range (1 GeV - 10^11 GeV) - new interaction models, SIBYLL 2.3 + 2.3c, EPOS-LHC and DPMJET-III 17.1 - compact (=very fast) mode - low-energy extension (with DPMJET-III) of high-energy interaction models - computation of hadron and lepton yields along an air-shower trajectory (average air-shower) - energy loss for muons - a generalized target mode, with arbitrary density profiles of target material (experimental and physics is not yet accurate)

Documentation (updated)

The latest version of the documentation can be found here.

Please cite our work

If you are using this code in your scientific work, please cite the code AND the physical models. A complete list of references can be found in the Citations section of the docs.

System requirements

  • Some kind of modern CPU with FPU unit
  • 2GB (8GB of RAM is recommended)
  • ~2GB of disk space
  • OS: Linux, Mac or Windows 10

Software requirements

The majority of the code is pure Python. Some functions are accelerated through Just-In-Time (JIT) compilation using numba, which requires the llvmlite package.


  • python-2.7
  • numpy
  • scipy
  • numba
  • matplotlib
  • jupyter notebook (optional, but needed for examples)
  • progressbar

Additional dependencies are required for the C implementation of the NRLMSISE-00 atmosphere:

  • a C compiler (GNU gcc, for example)
  • make
  • ctypes


The installation simplest method relies on the Python package manager Anaconda/Miniconda by Continuum Analytics. It doesn't just improve your life, but also provides most of the scientific computing packages by default. It also distributes a numpy version integrated with Intel's Math Kernel Library (MKL). It will not spoil your system Python paths and will install itself into a specified directory. The only action which is needed for activation, is to add this directory to your system $PATH variable. To uninstall just delete this directory.

  1. Download one of the installers for your system architecure from here:

    • Anaconda - larger download, already containing most of the scientific packages and the package manager conda itself
    • Miniconda - minimal download, which contains the minimum requirements for the package manager conda.
  2. Run the installer and follow the instructions:

    $ bash

    Open a new terminal window to reload your new $PATH variable.

  3. Cd to you desired working directory. And clone (note the `--recursive`) this project including submodules:

    $ git clone --recursive

    It will clone this github repository into a folder called MCEq and download all files. Enter this directory.

  4. To install all dependencies into you new conda environment

    $ conda install --file conda_req.txt

    This will ask conda to download and install all needed packages into its default environment.

  5. (Optional) If you know what a virtualenv is, the corresponding commands to download and install all packages in a newly created environment mceq_env are

    $ conda create -n mceq_env --file conda_req.txt
    $ source activate mceq_env

    To quit this environment just

    $ deactivate
  6. Run some example

    $ jupyter notebook

    click on the examples directory and select basic_flux.ipynb. Click through the blocks and see what happens.


You might run into problems with Anaconda if you have previous Python installations. A workaround is to set the environement variable


Thanks to F.C. Penha for pointing this out.


Anatoli Fedynitch

Copyright and license

Code and documentation copyright 2014-2017 Anatoli Fedynitch. Code released under the MIT license.