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Expand Up @@ -9,7 +9,7 @@ Quasi-Monte Carlo (QMC) methods are used to approximate multivariate integrals.

<center><img src="https://github.com/QMCSoftware/QMCSoftware/blob/master/sphinx/logo/qmcpy_logo.png?raw=true" alt="QMCPy logo" height=200px width=200px/>

[Homepage](https://qmcsoftware.github.io/QMCSoftware/) | [GitHub](https://github.com/QMCSoftware/QMCSoftware) | [Read the Docs](https://qmcpy.readthedocs.io/en/latest/) | [PyPI](https://pypi.org/project/qmcpy/) | [Blogs](http://qmcpy.wordpress.com/) | [Contributing](https://github.com/QMCSoftware/QMCSoftware/blob/master/CONTRIBUTING.md) | [Issues](https://github.com/QMCSoftware/QMCSoftware/issues)</center>
[Homepage](https://qmcsoftware.github.io/QMCSoftware/) | [GitHub](https://github.com/QMCSoftware/QMCSoftware) | [Read the Docs](https://qmcpy.readthedocs.io/en/latest/) | [PyPI](https://pypi.org/project/qmcpy/) | [Blogs](http://qmcpy.wordpress.com/) | [Contributing](https://github.com/QMCSoftware/QMCSoftware/blob/master/CONTRIBUTING.md) | [Issues](https://github.com/QMCSoftware/QMCSoftware/issues) | [Citations](https://github.com/QMCSoftware/QMCSoftware/blob/master/citations.md)</center>

----

Expand Down Expand Up @@ -84,83 +84,6 @@ A more detailed quickstart can be found in our GitHub repo at `QMCSoftware/demos

----

## Citation

If you find QMCPy helpful in your work, please support us by citing the following work:

**BibTex**

~~~
@misc{QMCPy,
Author = {S.-C. T. Choi and F. J. Hickernell and M. McCourt and A. Sorokin},
Date-Added = {2020-04-15 15:19:14 -0500},
Date-Modified = {2020-04-26 17:13:25 -0500},
Title = {{QMCPy}: A quasi-{M}onte {C}arlo {P}ython Library},
Url = {https://github.com/QMCSoftware/QMCSoftware},
Year = {2020+},
Bdsk-Url-1 = {https://github.com/QMCSoftware/QMCSoftware}}
~~~

**Plain Text**

~~~
Choi, S.-C. T., Hickernell, F. J., McCourt, M., Rathinavel, J. & Sorokin, A.
QMCPy: A quasi-Monte Carlo Python Library. Working. 2020.
https://qmcsoftware.github.io/QMCSoftware/
~~~

----

## References

<b>[1]</b> F. Y. Kuo and D. Nuyens. "Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation," Foundations of Computational Mathematics, 16(6):1631-1696, 2016. ([springer link](https://link.springer.com/article/10.1007/s10208-016-9329-5), [arxiv link](https://arxiv.org/abs/1606.06613))

<b>[2]</b> 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

<b>[3]</b> Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, Lluis Antoni Jimenez Rugama, Da Li, Jagadeeswaran Rathinavel, Xin Tong, Kan Zhang, Yizhi Zhang, and Xuan Zhou, GAIL: Guaranteed Automatic Integration Library (Version 2.3.1) [MATLAB Software], 2020. Available from [http://gailgithub.github.io/GAIL_Dev/](http://gailgithub.github.io/GAIL_Dev/).

<b>[4]</b> Sou-Cheng T. Choi, "MINRES-QLP Pack and Reliable Reproducible Research via Supportable Scientific Software," Journal of Open Research Software, Volume 2, Number 1, e22, pp. 1-7, 2014.

<b>[5]</b> Sou-Cheng T. Choi and Fred J. Hickernell, "IIT MATH-573 Reliable Mathematical Software" [Course Slides], Illinois Institute of Technology, Chicago, IL, 2013. Available from [http://gailgithub.github.io/GAIL_Dev/](http://gailgithub.github.io/GAIL_Dev/).

<b>[6]</b> Daniel S. Katz, Sou-Cheng T. Choi, Hilmar Lapp, Ketan Maheshwari, Frank Loffler, 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, Volume 2, Number 1, e6, pp. 1-21, 2014.

<b>[7]</b> Fang, K.-T., and Wang, Y. (1994). Number-theoretic Methods in Statistics. London, UK: CHAPMAN & HALL

<b>[8]</b> Lan Jiang, Guaranteed Adaptive Monte Carlo Methods for Estimating Means of Random Variables, PhD Thesis, Illinois Institute of Technology, 2016.

<b>[9]</b> Lluis Antoni Jimenez Rugama and Fred J. Hickernell, "Adaptive multidimensional integration based on rank-1 lattices," Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014 (R. Cools and D. Nuyens, eds.), Springer Proceedings in Mathematics and Statistics, vol. 163, Springer-Verlag, Berlin, 2016, arXiv:1411.1966, pp. 407-422.

<b>[10]</b> Kai-Tai Fang and Yuan Wang, Number-theoretic Methods in Statistics, Chapman & Hall, London, 1994.

<b>[11]</b> Fred J. Hickernell and Lluis Antoni Jimenez Rugama, "Reliable adaptive cubature using digital sequences," Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014 (R. Cools and D. Nuyens, eds.), Springer Proceedings in Mathematics and Statistics, vol. 163, Springer-Verlag, Berlin, 2016, arXiv:1410.8615 [math.NA], pp. 367-383.

<b>[12]</b> Marius Hofert and Christiane Lemieux (2019). qrng: (Randomized) Quasi-Random Number Generators. R package version 0.0-7. [https://CRAN.R-project.org/package=qrng](https://CRAN.R-project.org/package=qrng).

<b>[13]</b> Faure, Henri, and Christiane Lemieux. “Implementation of Irreducible Sobol’ Sequences in Prime Power Bases,” Mathematics and Computers in Simulation 161 (2019): 13–22.

<b>[14]</b> M. B. Giles. "Multi-level Monte Carlo path simulation," Operations Research, 56(3):607-617, 2008. [http://people.maths.ox.ac.uk/~gilesm/files/OPRE_2008.pdf](http://people.maths.ox.ac.uk/~gilesm/files/OPRE_2008.pdf).

<b>[15]</b> M. B. Giles. "Improved multilevel Monte Carlo convergence using the Milstein scheme," 343-358, in Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, 2008. [http://people.maths.ox.ac.uk/~gilesm/files/mcqmc06.pdf](http://people.maths.ox.ac.uk/~gilesm/files/mcqmc06.pdf).

<b>[16]</b> M. B. Giles and B. J. Waterhouse. "Multilevel quasi-Monte Carlo path simulation," pp.165-181 in Advanced Financial Modelling, in Radon Series on Computational and Applied Mathematics, de Gruyter, 2009. [http://people.maths.ox.ac.uk/~gilesm/files/radon.pdf](http://people.maths.ox.ac.uk/~gilesm/files/radon.pdf).

<b>[17]</b> Owen, A. B. "A randomized Halton algorithm in R," 2017. arXiv:1706.02808 [stat.CO]

<b>[18]</b> B. D. Keister, Multidimensional Quadrature Algorithms, 'Computers in Physics', *10*, pp. 119-122, 1996.

<b>[19]</b> L’Ecuyer, Pierre & Munger, David. (2015). LatticeBuilder: A General Software Tool for Constructing Rank-1 Lattice Rules. ACM Transactions on Mathematical Software. 42. 10.1145/2754929.

<b>[20]</b> Fischer, Gregory & Carmon, Ziv & Zauberman, Gal & L’Ecuyer, Pierre. (1999). Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators. Operations Research. 47. 159-164. 10.1287/opre.47.1.159.

<b>[21]</b> I.M. Sobol', V.I. Turchaninov, Yu.L. Levitan, B.V. Shukhman: "Quasi-Random Sequence Generators" Keldysh Institute of Applied Mathematics, Russian Acamdey of Sciences, Moscow (1992).

<b>[22]</b> Sobol, Ilya & Asotsky, Danil & Kreinin, Alexander & Kucherenko, Sergei. (2011). Construction and Comparison of High-Dimensional Sobol' Generators. Wilmott. 2011. 10.1002/wilm.10056.

<b>[23]</b> Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., … Chintala, S. (2019). PyTorch: An Imperative Style, High-Performance Deep Learning Library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d extquotesingle Alch&#39;e-Buc, E. Fox, & R. Garnett (Eds.), Advances in Neural Information Processing Systems 32 (pp. 8024–8035). Curran Associates, Inc. Retrieved from http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf

----

## Sponsors

Illinois Tech
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## QMCPy Citation

If you find QMCPy helpful in your work, please support us by citing the following work:

**BibTex**

~~~
@misc{QMCPy,
Author = {S.-C. T. Choi and F. J. Hickernell and M. McCourt and A. Sorokin},
Date-Added = {2020-04-15 15:19:14 -0500},
Date-Modified = {2020-04-26 17:13:25 -0500},
Title = {{QMCPy}: A quasi-{M}onte {C}arlo {P}ython Library},
Url = {https://github.com/QMCSoftware/QMCSoftware},
Year = {2020+},
Bdsk-Url-1 = {https://github.com/QMCSoftware/QMCSoftware}}
~~~

**Plain Text**

~~~
Choi, S.-C. T., Hickernell, F. J., McCourt, M., Rathinavel, J. & Sorokin, A.
QMCPy: A quasi-Monte Carlo Python Library. Working. 2020.
https://qmcsoftware.github.io/QMCSoftware/
~~~

----

## References

<b>[1]</b> F. Y. Kuo and D. Nuyens. "Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation," Foundations of Computational Mathematics, 16(6):1631-1696, 2016. ([springer link](https://link.springer.com/article/10.1007/s10208-016-9329-5), [arxiv link](https://arxiv.org/abs/1606.06613))

<b>[2]</b> 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

<b>[3]</b> Sou-Cheng T. Choi, Yuhan Ding, Fred J. Hickernell, Lan Jiang, Lluis Antoni Jimenez Rugama, Da Li, Jagadeeswaran Rathinavel, Xin Tong, Kan Zhang, Yizhi Zhang, and Xuan Zhou, GAIL: Guaranteed Automatic Integration Library (Version 2.3.1) [MATLAB Software], 2020. Available from [http://gailgithub.github.io/GAIL_Dev/](http://gailgithub.github.io/GAIL_Dev/).

<b>[4]</b> Sou-Cheng T. Choi, "MINRES-QLP Pack and Reliable Reproducible Research via Supportable Scientific Software," Journal of Open Research Software, Volume 2, Number 1, e22, pp. 1-7, 2014.

<b>[5]</b> Sou-Cheng T. Choi and Fred J. Hickernell, "IIT MATH-573 Reliable Mathematical Software" [Course Slides], Illinois Institute of Technology, Chicago, IL, 2013. Available from [http://gailgithub.github.io/GAIL_Dev/](http://gailgithub.github.io/GAIL_Dev/).

<b>[6]</b> Daniel S. Katz, Sou-Cheng T. Choi, Hilmar Lapp, Ketan Maheshwari, Frank Loffler, 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, Volume 2, Number 1, e6, pp. 1-21, 2014.

<b>[7]</b> Fang, K.-T., and Wang, Y. (1994). Number-theoretic Methods in Statistics. London, UK: CHAPMAN & HALL

<b>[8]</b> Lan Jiang, Guaranteed Adaptive Monte Carlo Methods for Estimating Means of Random Variables, PhD Thesis, Illinois Institute of Technology, 2016.

<b>[9]</b> Lluis Antoni Jimenez Rugama and Fred J. Hickernell, "Adaptive multidimensional integration based on rank-1 lattices," Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014 (R. Cools and D. Nuyens, eds.), Springer Proceedings in Mathematics and Statistics, vol. 163, Springer-Verlag, Berlin, 2016, arXiv:1411.1966, pp. 407-422.

<b>[10]</b> Kai-Tai Fang and Yuan Wang, Number-theoretic Methods in Statistics, Chapman & Hall, London, 1994.

<b>[11]</b> Fred J. Hickernell and Lluis Antoni Jimenez Rugama, "Reliable adaptive cubature using digital sequences," Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014 (R. Cools and D. Nuyens, eds.), Springer Proceedings in Mathematics and Statistics, vol. 163, Springer-Verlag, Berlin, 2016, arXiv:1410.8615 [math.NA], pp. 367-383.

<b>[12]</b> Marius Hofert and Christiane Lemieux (2019). qrng: (Randomized) Quasi-Random Number Generators. R package version 0.0-7. [https://CRAN.R-project.org/package=qrng](https://CRAN.R-project.org/package=qrng).

<b>[13]</b> Faure, Henri, and Christiane Lemieux. “Implementation of Irreducible Sobol’ Sequences in Prime Power Bases,” Mathematics and Computers in Simulation 161 (2019): 13–22.

<b>[14]</b> M. B. Giles. "Multi-level Monte Carlo path simulation," Operations Research, 56(3):607-617, 2008. [http://people.maths.ox.ac.uk/~gilesm/files/OPRE_2008.pdf](http://people.maths.ox.ac.uk/~gilesm/files/OPRE_2008.pdf).

<b>[15]</b> M. B. Giles. "Improved multilevel Monte Carlo convergence using the Milstein scheme," 343-358, in Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, 2008. [http://people.maths.ox.ac.uk/~gilesm/files/mcqmc06.pdf](http://people.maths.ox.ac.uk/~gilesm/files/mcqmc06.pdf).

<b>[16]</b> M. B. Giles and B. J. Waterhouse. "Multilevel quasi-Monte Carlo path simulation," pp.165-181 in Advanced Financial Modelling, in Radon Series on Computational and Applied Mathematics, de Gruyter, 2009. [http://people.maths.ox.ac.uk/~gilesm/files/radon.pdf](http://people.maths.ox.ac.uk/~gilesm/files/radon.pdf).

<b>[17]</b> Owen, A. B. "A randomized Halton algorithm in R," 2017. arXiv:1706.02808 [stat.CO]

<b>[18]</b> B. D. Keister, Multidimensional Quadrature Algorithms, 'Computers in Physics', *10*, pp. 119-122, 1996.

<b>[19]</b> L’Ecuyer, Pierre & Munger, David. (2015). LatticeBuilder: A General Software Tool for Constructing Rank-1 Lattice Rules. ACM Transactions on Mathematical Software. 42. 10.1145/2754929.

<b>[20]</b> Fischer, Gregory & Carmon, Ziv & Zauberman, Gal & L’Ecuyer, Pierre. (1999). Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators. Operations Research. 47. 159-164. 10.1287/opre.47.1.159.

<b>[21]</b> I.M. Sobol', V.I. Turchaninov, Yu.L. Levitan, B.V. Shukhman: "Quasi-Random Sequence Generators" Keldysh Institute of Applied Mathematics, Russian Acamdey of Sciences, Moscow (1992).

<b>[22]</b> Sobol, Ilya & Asotsky, Danil & Kreinin, Alexander & Kucherenko, Sergei. (2011). Construction and Comparison of High-Dimensional Sobol' Generators. Wilmott. 2011. 10.1002/wilm.10056.

<b>[23]</b> Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., … Chintala, S. (2019). PyTorch: An Imperative Style, High-Performance Deep Learning Library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d extquotesingle Alch&#39;e-Buc, E. Fox, & R. Garnett (Eds.), Advances in Neural Information Processing Systems 32 (pp. 8024–8035). Curran Associates, Inc. Retrieved from http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf

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