ZMCintegral-v5.1: Support for multi-function integrations on GPUs

In this new version of ZMCintegral, we have added the functionality multi-function integrations, i.e. ability to integrate more than 103 different functions on GPUs. The Python API remains similar as previous versions. For integrands less 5 dimensions, it usually takes 10 minutes finish evaluation integrations one Tesla v100 card. performance scales linearly with increasing Program Title: ZMCintegral CPC Library link program files: https://doi.org/10.17632/p7wc7k6mpp.3 Licensing provisions: Apache-2.0 Programming language: Journal reference version: Hong-Zhong Wu, Jun-Jie Zhang, Long-Gang Pang, Qun Wang, Comput. Phys. Commun. 248 (2020) 106962 and 251 107240 Does supersede version?: Yes Reasons for When solving Boltzmann equation radiations [1], encounters collision integrals energy beams. relativistic QED plasma, terms involve various Feynman graphs [2] contribution from each graph is great interest. these circumstances needs many forms simultaneously. our versions [3,4], focused single integration high dimensions parameters. Therefore, necessary include integrating which domains. Summary revisions: • Multi-function Suppose a series defined as(1)fn(x)=ancos(kn⋅x)+bnsin(kn⋅x), where n=1,2,3,...,100. above can be treated set Harmonic bases if wishes evaluate mode. versions, cannot manipulated in convenient efficient way. It worth noting that domains or different, example(2)gn(x1,x2)=an|x1+x2|for 0<n<50gn(x1,x2,x3)=bn|x1+x2−x3|for 50≤n≤100. support multi-functions gives users full flexibility possible. Test GPUs As an illustrative example, report solution Eq. (1) x=(x1,x2,x3,x4), an=bn=1. ranges all components are taken [0,1] kn=(n+502π,n+502π,n+502π,n+502π) such highly fluctuating around zero line. hardware condition case be: Intel(R) Xeon(R) Silver 4110 [email protected] CPU processors + Nvidia V100 GPU. results shown Fig. 1. Nature problem: easy use package doing dimensional distributed GPU clusters. Using libraries Numba [5] Ray [6], well NVIDIA CUDA [7] capability, offers succinct interface numerical physical problems. updated version, mainly focus problems integrate. These take Solution method: This contains three classes. ZMCintegral_normal utilizes stratified-sampling heuristic-tree-search techniques, while ZMCintegral_functional ZMCintegral_multifunctions direct-Monte Carlo method integrand benefits heavily Additional comments including restrictions unusual features: If high-dimensional (e.g. dimensionality 8-12), encouraged ZMCintegral_normal. middle-dimensional 1-7) but large parameter space, suggest try ZMCintegral_functional. contain 104 integrations), then suggested. detailed instructions found here: [8]. J. Oxenius, Kinetic Theory Particles Photons, Springer Berlin Heidelberg, 1986, https://dx.doi.org/10.1007/978-3-642-70728-5. V. Morozov, G. Röpke, theory radiation non-equilibrium plasmas, Ann. 324 (6) (2009) 1261–1302, https://dx.doi.org/10.1016/j.aop.2009.02.001. H.-Z. J.-J. L.-G. Q. ZMCintegral: A multi-dimensional Monte multi-GPUs, (2019) https://dx.doi.org/10.1016/j.cpc.2019.106962. ZMCintegral-v5: Support scanning space 107240, https://dx.doi.org/10.1016/j.cpc.2020.107240. S. Kwan Lam, A. Pitrou, Seibert, Numba: llvm-based python jit compiler, 2015, pp. 1–6, https://dx.doi.org/10.1145/2833157.2833162. P. Moritz, R. Nishihara, Tumanov, Liaw, E. Liang, M. Elibol, Z. Yang, W. Paul, M.I. Jordan, I. Stoica, Ray: framework emerging AI applications, in: 13th USENIX Symposium Operating Systems Design Implementation (OSDI 18), Association, Carlsbad, CA, 2018, 561–577, https://www.usenix.org/conference/osdi18/presentation/moritz. Buck, T. Purcell, Toolkit Computation GPUs, 2004. https://github.com/Letianwu/ZMCintegral.git.