Presentation given at a MATRIX workshop in Australia on June 5, proposing that the quasi-Monte Carlo community develop a shared software

1. A Proposal for Community (Quasi-) Monte Carlo Software
Fred J. Hickernell
Department of Applied Mathematics
Center for Interdisciplinary Scientific Computation
Illinois Institute of Technology
hickernell@iit.edu mypages.iit.edu/~hickernell
Thanks to the workshop organizers, the GAIL team
NSF-DMS-1522687 and NSF-DMS-1638521 (SAMSI)
Matrix Worskshop on the Frontiers of High Dimensional Computation, June 4-15, 2018

2. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
2/7

3. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
Where can I find demos or use cases that show me how to employ qMC methods?
2/7

4. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
Where can I find demos or use cases that show me how to employ qMC methods?
How can I try that qMC method developed by X’s group for my problem?
2/7

5. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
Where can I find demos or use cases that show me how to employ qMC methods?
How can I try that qMC method developed by X’s group for my problem?
How can I try my QMC method on the example shown by Y’s group?
2/7

6. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
Where can I find demos or use cases that show me how to employ qMC methods?
How can I try that qMC method developed by X’s group for my problem?
How can I try my QMC method on the example shown by Y’s group?
How can my student get results without writing code from scratch?
2/7

7. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
Where can I find demos or use cases that show me how to employ qMC methods?
How can I try that qMC method developed by X’s group for my problem?
How can I try my QMC method on the example shown by Y’s group?
How can my student get results without writing code from scratch?
How can the code that I use benefit from recent developments?
2/7

8. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
Where can I find demos or use cases that show me how to employ qMC methods?
How can I try that qMC method developed by X’s group for my problem?
How can I try my QMC method on the example shown by Y’s group?
How can my student get results without writing code from scratch?
How can the code that I use benefit from recent developments?
How can my work receive wider recognition?
2/7

9. Motivation Landscape Big Questions Next Steps References
Questions that I Ask or Hear Asked
Where can I find quality, free quasi-Monte Carlo software?
Where can I find demos or use cases that show me how to employ qMC methods?
How can I try that qMC method developed by X’s group for my problem?
How can I try my QMC method on the example shown by Y’s group?
How can my student get results without writing code from scratch?
How can the code that I use benefit from recent developments?
How can my work receive wider recognition?
My initial attempts in this direction over the past 5 years have produced GAIL1
1Choi, S.-C. T. et al. GAIL: Guaranteed Automatic Integration Library (Versions 1.0–2.2) MATLAB software.
2013–2017. <http://gailgithub.github.io/GAIL_Dev/>. 2/7

10. Motivation Landscape Big Questions Next Steps References
Can We Have a QMC Community Software that Grows Up to Be Like ...
Chebfun Computing with Chebyhsev polynomials chebfun.org
Clawpack Solution of conservation laws clawpack.org
FEniCS Finite-elements fenicsproject.org
Trilinos Multiphysics computations trilinos.org
Gromacs Molecular dynamics gromacs.org
Developed and supported by multiple research groups
Used beyond the research groups that develop it
A recognized standard in its field
3/7

11. Motivation Landscape Big Questions Next Steps References
What Is Available
John Burkhardt Variety of qMC Software in C++, Fortran, MATLAB, and Python
people.sc.fsu.edu/~jburkardt//
Mike Giles Multi-Level Monte Carlo Software in C++, MATLAB, Python, and R,
people.maths.ox.ac.uk/gilesm/mlmc/
Fred Hickernell Guaranteed Automatic Integration Library (GAIL) in MATLAB
gailgithub.github.io/GAIL_Dev/
Stephen Joe and Frances Kuo Sobol’ generators in C++
web.maths.unsw.edu.au/~fkuo/sobol/index.html, Generating vectors for
lattices web.maths.unsw.edu.au/~fkuo/lattice/index.html
Pierre L’Ecuyer Random number generators, Stochastic Simulation, Lattice Builder in C/C++
and Java simul.iro.umontreal.ca
Dirk Nuyens Magic Point Shop, QMC4PDE, etc. in MATLAB, Python, and C++
people.cs.kuleuven.be/~dirk.nuyens/
Art Owen Various code statweb.stanford.edu/~owen/code/
MATLAB Sobol’ and Halton sequences
R randtoolbox Sobol’, lattice, and Halton sequences 4/7

12. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
5/7

13. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
Sequence generators—with inputs d, coordinate indices, and index range
5/7

14. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
Sequence generators—with inputs d, coordinate indices, and index range
Discrepancy measures—various kernels and domains
5/7

15. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
Sequence generators—with inputs d, coordinate indices, and index range
Discrepancy measures—various kernels and domains
Variable transformations to accommodate non-uniform distributions and
domains other than the unit cube
5/7

16. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
Sequence generators—with inputs d, coordinate indices, and index range
Discrepancy measures—various kernels and domains
Variable transformations to accommodate non-uniform distributions and
domains other than the unit cube
Functions, but not all need to be included
5/7

17. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
Sequence generators—with inputs d, coordinate indices, and index range
Discrepancy measures—various kernels and domains
Variable transformations to accommodate non-uniform distributions and
domains other than the unit cube
Functions, but not all need to be included
Approximate integrators, including multilevel and multivariate decomposition
methods
5/7

18. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
Sequence generators—with inputs d, coordinate indices, and index range
Discrepancy measures—various kernels and domains
Variable transformations to accommodate non-uniform distributions and
domains other than the unit cube
Functions, but not all need to be included
Approximate integrators, including multilevel and multivariate decomposition
methods
Compelling use cases
5/7

19. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Key Elements
Sequences—IID, Sobol’, lattice, ..., including randomization; fixed length
and extensible; constructions using optimization
Sequence generators—with inputs d, coordinate indices, and index range
Discrepancy measures—various kernels and domains
Variable transformations to accommodate non-uniform distributions and
domains other than the unit cube
Functions, but not all need to be included
Approximate integrators, including multilevel and multivariate decomposition
methods
Compelling use cases
Stopping criteria
5/7

20. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Languages and Architectures
How do we balance performance, developer time, and portability?
5/7

21. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Languages and Architectures
How do we balance performance, developer time, and portability?
How will users connect the software with other software packages and
environments?
5/7

22. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Languages and Architectures
How do we balance performance, developer time, and portability?
How will users connect the software with other software packages and
environments?
How will parallel computing be supported?
5/7

23. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Good Development Practices
Start small, with good skeleton
5/7

24. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Good Development Practices
Start small, with good skeleton
Version control on Git or equivalent
5/7

25. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Good Development Practices
Start small, with good skeleton
Version control on Git or equivalent
Ownership of routines, changes requiring the owners to approve pull
requests
5/7

26. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Good Development Practices
Start small, with good skeleton
Version control on Git or equivalent
Ownership of routines, changes requiring the owners to approve pull
requests
Comprehensive tests run regularly
5/7

27. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Good Development Practices
Start small, with good skeleton
Version control on Git or equivalent
Ownership of routines, changes requiring the owners to approve pull
requests
Comprehensive tests run regularly
Reasonable license
5/7

28. Motivation Landscape Big Questions Next Steps References
Big Questions If We Want to Succeed
Good Development Practices
Start small, with good skeleton
Version control on Git or equivalent
Ownership of routines, changes requiring the owners to approve pull
requests
Comprehensive tests run regularly
Reasonable license
Marketing on websites and at conferences
5/7

29. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
6/7

30. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
6/7

31. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
Determine what we can agree on as initial answers to the big questions
6/7

32. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
Determine what we can agree on as initial answers to the big questions
Design a skeleton and give ourselves a deadline for putting it into place
6/7

33. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
Determine what we can agree on as initial answers to the big questions
Design a skeleton and give ourselves a deadline for putting it into place
An initial language
6/7

34. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
Determine what we can agree on as initial answers to the big questions
Design a skeleton and give ourselves a deadline for putting it into place
An initial language
An initial version control platform, and a model for collaboration
6/7

35. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
Determine what we can agree on as initial answers to the big questions
Design a skeleton and give ourselves a deadline for putting it into place
An initial language
An initial version control platform, and a model for collaboration
A few initial routines
6/7

36. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
Determine what we can agree on as initial answers to the big questions
Design a skeleton and give ourselves a deadline for putting it into place
An initial language
An initial version control platform, and a model for collaboration
A few initial routines
An initial use case
6/7

37. Motivation Landscape Big Questions Next Steps References
Next Steps This Week
If you are interested, let’s sit down and talk
Discuss what you agree or disagree with, would add or subtract, etc.
Determine what we can agree on as initial answers to the big questions
Design a skeleton and give ourselves a deadline for putting it into place
An initial language
An initial version control platform, and a model for collaboration
A few initial routines
An initial use case
Invite others to join us
6/7

38. Thank you
Slides available on SlideShare at
www.slideshare.net/fjhickernell/qmc-community-software
on Overleaf at www.overleaf.com/read/cbdmywrqyvpt
on Github at git.overleaf.com/16270995qmbvpwsxkfxk

39. Motivation Landscape Big Questions Next Steps References
Choi, S.-C. T. et al. GAIL: Guaranteed Automatic Integration Library (Versions 1.0–2.2)
MATLAB software. 2013–2017. <http://gailgithub.github.io/GAIL_Dev/>.
7/7