Kodiak, a C++ Library for Rigorous Branch and Bound Computation
Kodiak is a C++ library that implements a generic branch and bound algorithm for rigorous numerical approximations. Particular instances of the branch and bound algorithm allow the user to refine and isolate solutions to systems of nonlinear equations and inequalities, global optimization problems, and bifurcation sets for systems of ODEs. Kodiak utilizes interval arithmetic (via the filib++ library) and Bernstein enclosure (for polynomials and rational functions) as self-validating enclosure methods. Symbolic operations support procedures such as automatic partial differentiation.
Marco A. Feliu (firstname.lastname@example.org), National Institute of Aerospace
Aaron M. Dutle (email@example.com), NASA Langley Research Center, US.
Cesar A. Munoz, formerly at NASA Langley Research Center, US.
Andrew P. Smith, formerly at National Institute of Aerospace, US.
Anthony Narkawicz, formerly at NASA Langley Research Center, US.
Mantas Markevicius, formerly at University of York, UK.
Currently, the main documentation is contained in this file. Publications concerning the library and associated algorithms are in preparation. There are also numerous comments in the source code.
Support and Contribution
See the instructions in this file and the linked resources. For further assistance, or to report problems and bugs, please contact the authors. Contributions to the library are welcomed.
The repository is located at: https://github.com/nasa/Kodiak/
The Kodiak C++ Library is released under NASA's Open Source Agreement.
See the files
see also the copyright notice at the end of this file.
Installation and Usage Options
Kodiak is installed from source code. Kodiak is run by encoding a problem in a C++ program file, then compiling and running it.
It is recommended to run Kodiak on a Linux or Mac computer with the GNU C++ compiler; so far it has been successfully tested on Ubuntu Linux and Mac OS X. Use of Windows is not supported, although it ought to be feasible, and the authors would welcome any report of successfully running the software on Windows or any other system.
The following software should firstly be installed, if not already present (please follow the links for instructions and support):
C++ compiler (standard
CMake build tool (version
filib++ interval library (version
3.0.2required) configured with the following options:
$ ./configure CFLAGS=-fPIC CPPFLAGS=-fPIC CXXFLAGS=-fPIC
before invoking the
$ make $ make install
Boost libraries (only for debugging): http://www.boost.org/users/download/ In addition to the headers, you need at least the library
2. Build Library and Examples
If necessary, unzip the zip file in order to extract the files. The following files and directories should be present:
- In the working directory: this
README.mdfile and a
LICENSES: licenses and copyrights for Kodiak
logo: Kodiak's logo and credits
src: source code for the library
examples: example C++ files (
.cpp) containing several problems
If any of the prerequisite libraries were installed in non-standard
directories, then the file
CMakeLists.txt should be modified accordingly.
build directory to keep the compiled libraries and make it
the current working directory:
$ mkdir build $ cd build
Now, run CMake for creating the build scripts:
$ cmake ..
If this command fails because CMake cannot find FILIB, add the
FILIB_ROOT environment variable with the path to the FILIB source code directory used during the installation.
$ FILIB_ROOT=<FILIB-directory> cmake ..
Finally, build all targets by invoking the CMake build command:
$ cmake --build .
Using the Library
The Kodiak library is used in your own C/C++ programs.
A good way to start is to take one of the existing
files in the
examples directory and adapt it to your purposes.
You can either invoke the compiler directly with a link to the
filib++ and Kodiak libraries, or else add a new entry to
For C programs, please use the
src/Adapters/Codiak.h header file to invoke Kodiak's routines.
Be aware that care must be taken with the order in which commands are invoked. All variables should be declared before any variable resolutions are set.
Kodiak ver. 2.0.3, January 2022
The Kodiak logo was designed by Mahyar Malekpour (NASA).
License and Copyright Notice
The code in this repository is released under NASA's Open Source
Agreement. See the directory
Notices: Copyright 2017 United States Government as represented by the Administrator of the National Aeronautics and Space Administration. All Rights Reserved. Disclaimers: No Warranty: THE SUBJECT SOFTWARE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY OF ANY KIND, EITHER EXPRESSED, IMPLIED, OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, ANY WARRANTY THAT THE SUBJECT SOFTWARE WILL CONFORM TO SPECIFICATIONS, ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR FREEDOM FROM INFRINGEMENT, ANY WARRANTY THAT THE SUBJECT SOFTWARE WILL BE ERROR FREE, OR ANY WARRANTY THAT DOCUMENTATION, IF PROVIDED, WILL CONFORM TO THE SUBJECT SOFTWARE. THIS AGREEMENT DOES NOT, IN ANY MANNER, CONSTITUTE AN ENDORSEMENT BY GOVERNMENT AGENCY OR ANY PRIOR RECIPIENT OF ANY RESULTS, RESULTING DESIGNS, HARDWARE, SOFTWARE PRODUCTS OR ANY OTHER APPLICATIONS RESULTING FROM USE OF THE SUBJECT SOFTWARE. FURTHER, GOVERNMENT AGENCY DISCLAIMS ALL WARRANTIES AND LIABILITIES REGARDING THIRD-PARTY SOFTWARE, IF PRESENT IN THE ORIGINAL SOFTWARE, AND DISTRIBUTES IT "AS IS." Waiver and Indemnity: RECIPIENT AGREES TO WAIVE ANY AND ALL CLAIMS AGAINST THE UNITED STATES GOVERNMENT, ITS CONTRACTORS AND SUBCONTRACTORS, AS WELL AS ANY PRIOR RECIPIENT. IF RECIPIENT'S USE OF THE SUBJECT SOFTWARE RESULTS IN ANY LIABILITIES, DEMANDS, DAMAGES, EXPENSES OR LOSSES ARISING FROM SUCH USE, INCLUDING ANY DAMAGES FROM PRODUCTS BASED ON, OR RESULTING FROM, RECIPIENT'S USE OF THE SUBJECT SOFTWARE, RECIPIENT SHALL INDEMNIFY AND HOLD HARMLESS THE UNITED STATES GOVERNMENT, ITS CONTRACTORS AND SUBCONTRACTORS, AS WELL AS ANY PRIOR RECIPIENT, TO THE EXTENT PERMITTED BY LAW. RECIPIENT'S SOLE REMEDY FOR ANY SUCH MATTER SHALL BE THE IMMEDIATE, UNILATERAL TERMINATION OF THIS AGREEMENT.