About Guaranteed Automatic Integration Library (GAIL)

GAIL is a suite of algorithms for integration problems in one and many dimensions, and whose answers are guaranteed to be correct.

GAIL is created, developed, and maintained by http://mypages.iit.edu/~hickernell/'>Fred Hickernell (Illinois Institute of Technology), http://home.uchicago.edu/sctchoi'>Sou-Cheng Choi (NORC at the University of Chicago and IIT), and their collaborators including Yuhan Ding (IIT), Lan Jiang (IIT), Lluís Antoni Jiménez Rugama (IIT), Xin Tong (UIC), Yizhi Zhang (IIT), and Xuan Zhou (IIT). It is a free software and could be downloaded via the link below.

To download the latest version of GAIL, follow one of the links below to:

           Get zip file            OR   run the MATLAB installation script

http://math.iit.edu/~openscholar/sites/default/files/meshfree/files/gail_2_1_1.zip'>https://raw.githubusercontent.com/harryzyz/GAILPubPic/master/downloadzip.png'> http://math.iit.edu/~openscholar/sites/default/files/meshfree/files/downloadinstallgail_2_1_2.m'>https://raw.githubusercontent.com/harryzyz/GAILPubPic/master/downloadscript.png'>

News

• We have migrated this project website to GitHub starting July 12, 2015.
  
• GAIL version 2.1 is released on March 14, 2015 (Super Pi Day and Albert Einstein's Birthday)
  
• GAIL's GitHub repository is open to public at https://github.com/GailGithub/GAIL_Dev starting February 6, 2015.
  
• GAIL version 2.0 is released on November 1, 2014 (All Saints' Day).
  
• GAIL version 1.3 is released on February 14, 2014 (Valentine's Day, for our love of the package).
  
• GAIL version 1.0 is released on September 3, 2013.
  
  
  

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If you find GAIL helpful in your work, please support us by citing the
following papers and software.

Free GAIL Software

• Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, Lluis Antoni Jimenez Rugama, Xin Tong, Yizhi Zhang, and Xuan Zhou. GAIL: Guaranteed Automatic Integration Library (Version 2.1), MATLAB Software, 2015. (Download zip, or download and run Matlab script, or clone repository. HTML documentation and PDF documentation. Bibtex.)

• Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, Lluis Antoni Jimenez Rugama, Xin Tong, Yizhi Zhang, and Xuan Zhou. GAIL: Guaranteed Automatic Integration Library (Version 2.0), MATLAB Software, 2014. (Download zip, or download and run Matlab script, or clone repository. Documentation. Bibtex.)

• Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, and Yizhi Zhang. GAIL: Guaranteed Automatic Integration Library (Version 1.3.1), MATLAB Software, 2014. (Download zip, or download and run Matlab script, or clone repository. Documentation. Bibtex.)

• Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, and Yizhi Zhang. GAIL: Guaranteed Automatic Integration Library (Version 1.3), MATLAB Software, 2014. (Download zip, or download and run Matlab script, or clone repository. Documentation. Bibtex.)

• Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, and Yizhi Zhang. GAIL: Guaranteed Automatic Integration Library (Version 1), MATLAB Software, 2013. (Download zip, or download and run Matlab script, or clone repository. Documentation. Bibtex.)

Papers and Reports

2015

• Daniel S. Katz, Sou-Cheng T. Choi, Nancy Wilkins-Diehr, Neil Chue Hong, Colin C. Venters, James Howison, Frank Seinstra, Matthew Jones, Karen Cranston, Thomas L. Clune, Miguel de Val-Borro, Richard Littauer, Report on the Second Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE2), submitted, 2015.

• Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, Lluis Antoni Jimenez Rugama, Xin Tong, Yizhi Zhang, and Xuan Zhou, GAIL---Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1, Technical Report, Illinois Institute of Technology, 2015.

2014

• Fred J. Hickernell and Lluís Antoni Jiménez Rugama, Reliable Adaptive Cubature Using Digital Sequences, submitted.

• Xuan Zhou and Fred J. Hickernell, Tractability of the function approximation problem in terms of the kernel's shape and scale parameters, submitted.

• Lan Jiang and Fred J. Hickernell, Guaranteed Monte Carlo Methods for Bernoulli Random Variables, submitted.

• Lluís Antoni Jiménez Rugama and Fred J. Hickernell, Adaptive Multidimensional Integration Based on Rank-1 Lattices, submitted.

• Xin Tong, A Guaranteed, Adaptive, Automatic Algorithm for Univariate Function Minimization, M.S. Thesis, Illinois Institute of Technology, 2014.

• Fred J. Hickernell, Lan Jiang, Yuewei Liu, and Art B. Owen, Guaranteed conservative fixed width confidence intervals via Monte Carlo sampling, Monte Carlo and Quasi-Monte Carlo Methods 2012 (J. Dick, F. Y. Kuo, G. W. Peters, and I. H. Sloan, eds.), pp. 105-128, Springer-Verlag, Berlin, 2014, DOI: 10.1007/978-3-642-41095-6_5. (PDF)

• N. Clancy, Y. Ding, C. Hamilton, F. J. Hickernell, and Y. Zhang, The complexity of guaranteed automatic algorithms: Cones, not balls, Journal of Complexity, 30, pp. 21-45, 2014, DOI: 10.1016/j.bbr.2011.03.031. (PDF)

• Sou-Cheng T. Choi, MINRES-QLP Pack and Reliable Reproducible Research via Supportable Scientific Software, Journal of Open Research Software, 2014.

• Daniel S. Katz, Sou-Cheng T. Choi, Hilmar Lapp, Ketan Maheshwari, Frank Löffler, Matthew Turk, Marcus D. Hanwell, Nancy Wilkins-Diehr, James Hetherington, James Howison, Shel Swenson, Gabrielle D. Allen, Anne C. Elster, Bruce Berriman, Colin Venters, Summary of the First Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE1), Journal of Open Research Software, 2014
  
  
  

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Courses and Notes

Sou-Cheng T. Choi and Fred J. Hickernell, IIT MATH-573 Reliable Mathematical Software Slides, Illinois Institute of Technology, Chicago, IL, 2013. (http://mypages.iit.edu/~schoi32/MATH573Slides.pdf'>slides)

Presentations and Slides

2015

• Meshfree Methods Seminar, Illinois Institute of Technology, Chicago, IL, Jan 9-May 12, 2015:
  
  o A New Guaranteed Adaptive Trapezoidal Rule Algorithm

• Adaptive Algorithms for Computing Expectations and Integrals, 2015 Joint Math Meetings, San Antonio, TX, Jan 10-13,2015

• A Guaranteed, Adaptive, Automatic, Algorithm for Univariate Function Minimization, ACNW Optimization Workshop, Chicago, Illinois, Jun 8, 2015.

2014

• Meshfree Methods Seminar, Illinois Institute of Technology, Chicago, IL, Aug 23-Dec 12, 2014:
  
  o Interpolation Using Kernel Methods With Guaranteed Error Bounds
  o Some Thoughts on Guaranteed Function Approximation Satisfying Relative Error
  o Deterministic Guaranteed Automatic Local-Adaptive Algorithm for Univariate Function Approximation

• Reliable Error Estimation for Monte Carlo and Quasi-Monte Carlo Simulation, IEMS Department Seminars, Northwestern University, Evanston, IL, Oct 7, 2014

• Guaranteed Monte Carlo Methods for Bernoulli Random Variables (Poster), Approximation, Integration, and Optimization Workshop, ICERM at Brown University, Providence, RI, Sep 29-Oct 3, 2014

• Information-Based Complexity and Stochastic Computation Workshop, ICERM at Brown University, Providence, RI, Sep 15-19, 2014:
  
  o Adaptive Algorithms for Stochastic Computation (Slides)
  o Generalizing the Tolerance for Guaranteed QMC Algorithms (Poster)
  o Tractability of Function Approximation Problems With Kernels of a Product Form (Poster)
  o Deterministic Guaranteed Automatic Algorithms in Univariate Approximation (Poster)

• Minisymposium on Reliable Computational Science, part I, part II, SIAM Annual Meeting, Chicago, July 7-11, 2014:
  
  o A Survey of Issues in Reliable Computational Science
  o The Scholarly Work of Reliable and Well-Designed Mathematical Software
  o Generation of Appropriate Publication Citations by Numerical Software Libraries
  o A Deterministic Guaranteed Automatic Algorithm for Univariate Function Approximation
  o Towards Verifiable Publications
  o Improving Computing Skills of STEM Graduates
  o Constructing Guaranteed Automatic Numerical Algorithms for Univariate Integration
  o What Is Worth Reproducing in Computational Science?

• Contributed talks, SIAM Annual Meeting, Chicago, July 7-11, 2014:
  
  o Tractability of Function Approximation Problems with General Kernels
  o A Guaranteed Automatic Integration Library for Monte Carlo Simulation
  o Reliable Error Estimation for Quasi-Monte Carlo Methods

• Constructing Numerical Algorithms that Can Be Trusted, BNU-HKBU United International College, Zhuhai, China, June 20, 2014. News, Poster.

• Reliable Reproducible Research in Computational Sciences through Sustainable Software Practices, Chinese Academy of Sciences, Beijing, China, June 19, 2014.

• Meshfree Methods Seminar, Illinois Institute of Technology, Chicago, IL, May 19-Aug 10, 2014:
  
  o Automatic Algorithms
  o A Guaranteed, Adaptive, Automatic Algorithm for
  Univariate Function Minimization
  o Guaranteed Quasi-Monte Carlo Methods
  o Good Practices for Mathematical Software Developing
  o A Deterministic Guaranteed Automatic Algorithm for Univariate Function Approximation
  o Constructing Guaranteed Automatic Numerical Algorithms for Univariate Integration
  o Reliable Error Estimation for Quasi-Monte Carlo Methods
  o Generalizing the tolerance function for guaranteed algorithms.

• Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2014), Leuven, Belgium, April 6-11, 2014:
  
  o Reliable Error Estimation for Cubature Using Sobol' sequences
  o A Guaranteed Automatic Integration Library
  o Tractability of Function Approximation Problems with General Kernels
  o Error Estimation for Multidimensional Integration Based on Rank-1 Lattices

• Guaranteed Adaptive, Automatic, Quadrature, Joint Mathematics Meetings (JMM 2014), Baltimore, MD, Jan 16, 2014.

2013

• GAIL: Guaranteed Automatic Integration Library, Math Tea and Talk, SIAM Student Chapter, Illinois Institute of Technology, Chicago, IL, Nov 20, 2013.

• Constructing Reliable Automatic Numerical Algorithms, Departmental Colloquium, Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, Nov 18, 2013.

• Guaranteed Automatic Integration Library (GAIL), Meshfree Methods Seminar, Illinois Institute of Technology, Chicago, IL, Aug 8, 2013.

• Guaranteed Automatic Integration Library (GAIL) Version 1---before and after, Meshfree Methods Seminar, Illinois Institute of Technology, Chicago, IL, Aug 6, 2013.

• Constructing Trustworthy Automatic Numerical Integration Algorithms, Midwest Numerical Analysis Day, University of Chicago, Chicago, IL, May 25, 2013.

• Reliable Reproducible Research & Staunch Scientific Software—A Proposal for CubMC: Guaranteed MC Quadrature, Meshfree Methods Seminar, Illinois Institute of Technology, Chicago, IL, Feb 5, 2013.

2012

• Automatic Numerical Algorithms with Performance Guarantees, LANS Informal Seminar, Argonne National Laboratory, Argonne, IL, Jul 25, 2012.

• Monte Carlo algorithms where the integrand size is unknown, The Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC), Sydney, Australia, Feb 16, 2012.

• The Reliability of Error Estimates for Multivariate Numerical Integration, Joint Mathematics Meetings AMS Special Session, Boston, MA, Jan 4, 2012.

2011

• Recent Developments in Quasi-Monte Carlo Methods, Summer Seminar Series, Department of Statistics, University of Chicago, Chicago, IL, Sep 6, 2011.
  
  
  

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Events of Interest

• SIAM Annual Meeting 2014

• Meshfree Methods Seminars

• A seminal course Reliable Mathematical Software offered at IIT in fall 2013. Here are the syllabus and slides.

• First Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE1), held in conjunction with SC13, 17 November 2013, Denver, CO, USA

For Help

• Refer to our Wiki pages for information and frequently asked questions.
  
• Review and search Issues for your questions about GAIL. If it does not help, you may file a new issue ticket and we will respond as soon as we can.
  
• Email questions and comments to gail-users@googlegroups.com.

To Help

The GAIL routines come with comprehensive online documentation and their implementation is driven by rigorous unit tests. If you would like to contribute to the software development or documentation of the library, please contact gail-users@googlegroups.com

Acknowledgement

Our work was supported in part by grants from

• the National Science Foundation under grant NSF-DMS-1115392, and
  
• the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under contract DE-AC02-06CH11357.

We thank the contributions of Xincheng Sheng, Xuan Zhou, and the class of Math 573 Reliable Mathematical Software, Fall 2013.