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Apache Commons Math includes the following code provided to the ASF under the
Apache License 2.0:

 - The inverse error function implementation in the Erf class is based on CUDA
   code developed by Mike Giles, Oxford-Man Institute of Quantitative Finance,
   and published in GPU Computing Gems, volume 2, 2010 (grant received on
   March 23th 2013)
 - The LinearConstraint, LinearObjectiveFunction, LinearOptimizer,
   RelationShip, SimplexSolver and SimplexTableau classes in package
   org.apache.commons.math3.optimization.linear include software developed by
   Benjamin McCann (http://www.benmccann.com) and distributed with
   the following copyright: Copyright 2009 Google Inc. (grant received on
   March 16th 2009)
 - The class "org.apache.commons.math3.exception.util.LocalizedFormatsTest" which
   is an adapted version of "OrekitMessagesTest" test class for the Orekit library
 - The "org.apache.commons.math3.analysis.interpolation.HermiteInterpolator"
   has been imported from the Orekit space flight dynamics library.

===============================================================================
 


APACHE COMMONS MATH DERIVATIVE WORKS: 

The Apache commons-math library includes a number of subcomponents
whose implementation is derived from original sources written
in C or Fortran.  License terms of the original sources
are reproduced below.

===============================================================================
For the lmder, lmpar and qrsolv Fortran routine from minpack and translated in
the LevenbergMarquardtOptimizer class in package
org.apache.commons.math3.optimization.general 
Original source copyright and license statement:

Minpack Copyright Notice (1999) University of Chicago.  All rights reserved

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the
following conditions are met:

1. Redistributions of source code must retain the above
copyright notice, this list of conditions and the following
disclaimer.

2. Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials
provided with the distribution.

3. The end-user documentation included with the
redistribution, if any, must include the following
acknowledgment:

   "This product includes software developed by the
   University of Chicago, as Operator of Argonne National
   Laboratory.

Alternately, this acknowledgment may appear in the software
itself, if and wherever such third-party acknowledgments
normally appear.

4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
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THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
BE CORRECTED.

5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
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PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
POSSIBILITY OF SUCH LOSS OR DAMAGES.
===============================================================================

Copyright and license statement for the odex Fortran routine developed by
E. Hairer and G. Wanner and translated in GraggBulirschStoerIntegrator class
in package org.apache.commons.math3.ode.nonstiff:


Copyright (c) 2004, Ernst Hairer

Redistribution and use in source and binary forms, with or without 
modification, are permitted provided that the following conditions are 
met:

- Redistributions of source code must retain the above copyright 
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright 
notice, this list of conditions and the following disclaimer in the 
documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS 
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED 
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A 
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR 
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
===============================================================================

Copyright and license statement for the original Mersenne twister C
routines translated in MersenneTwister class in package 
org.apache.commons.math3.random:

   Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
   All rights reserved.                          

   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions
   are met:

     1. Redistributions of source code must retain the above copyright
        notice, this list of conditions and the following disclaimer.

     2. Redistributions in binary form must reproduce the above copyright
        notice, this list of conditions and the following disclaimer in the
        documentation and/or other materials provided with the distribution.

     3. The names of its contributors may not be used to endorse or promote 
        products derived from this software without specific prior written 
        permission.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
   A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

===============================================================================

The initial code for shuffling an array (originally in class
"org.apache.commons.math3.random.RandomDataGenerator", now replaced by
a method in class "org.apache.commons.math3.util.MathArrays") was
inspired from the algorithm description provided in
"Algorithms", by Ian Craw and John Pulham (University of Aberdeen 1999).
The textbook (containing a proof that the shuffle is uniformly random) is
available here:
  http://citeseerx.ist.psu.edu/viewdoc/download;?doi=10.1.1.173.1898&rep=rep1&type=pdf

===============================================================================
License statement for the direction numbers in the resource files for Sobol sequences.

-----------------------------------------------------------------------------
Licence pertaining to sobol.cc and the accompanying sets of direction numbers

-----------------------------------------------------------------------------
Copyright (c) 2008, Frances Y. Kuo and Stephen Joe
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.

    * Redistributions in binary form must reproduce the above copyright
      notice, this list of conditions and the following disclaimer in the
      documentation and/or other materials provided with the distribution.

    * Neither the names of the copyright holders nor the names of the
      University of New South Wales and the University of Waikato
      and its contributors may be used to endorse or promote products derived
      from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
===============================================================================

The initial commit of package "org.apache.commons.math3.ml.neuralnet" is
an adapted version of code developed in the context of the Data Processing
and Analysis Consortium (DPAC) of the "Gaia" project of the European Space
Agency (ESA).
===============================================================================

The initial commit of the class "org.apache.commons.math3.special.BesselJ" is
an adapted version of code translated from the netlib Fortran program, rjbesl
http://www.netlib.org/specfun/rjbesl by R.J. Cody at Argonne National
Laboratory (USA).  There is no license or copyright statement included with the
original Fortran sources.
===============================================================================


The BracketFinder (package org.apache.commons.math3.optimization.univariate)
and PowellOptimizer (package org.apache.commons.math3.optimization.general)
classes are based on the Python code in module "optimize.py" (version 0.5)
developed by Travis E. Oliphant for the SciPy library (http://www.scipy.org/)
Copyright © 2003-2009 SciPy Developers.

SciPy license
Copyright © 2001, 2002 Enthought, Inc.
All rights reserved.

Copyright © 2003-2013 SciPy Developers.
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.

    * Redistributions in binary form must reproduce the above copyright
      notice, this list of conditions and the following disclaimer in the
      documentation and/or other materials provided with the distribution.

    * Neither the name of Enthought nor the names of the SciPy Developers may
      be used to endorse or promote products derived from this software without
      specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
===============================================================================