10 ^ 8变量的矩阵求解或方程求解 [英] Matrix Solving or Equation solving for 10^8 variables

问题描述

我正在开发一个模拟软件，它涉及解决大约10 ^ 8个联立线性方程。方程式稀疏。我已经制作了一个原型，我自己实现了LU分解。但由于性能和内存限制，我的实现只能解决小于10 ^ 4的等式。我从未使用任何CAS系统。任何人都可以从我可以开始的地方建议一些好的CAS系统吗？即使经过长时间的网络搜索，我也无法对现有的CAS系统进行良好的比较，无论是它可以处理的数据大小还是性能比较。

我使用的开发环境是C＃使用.Net 4.0，但我可以在我的系统中使用任何C ++，C或C＃库。



我发现许多CAS系统，如Mathematica，Boost，Sage，Intel的MKL图书馆。但我无法从中找出比较结果。他们可以处理多少数据并具有显着的性能。



我期待的答案如我已经使用xxx库解决了1,00,000个变量中的1,00,000个等式在xxxx中使用x核心和xGB Ram的机器使用xThreads

I am developing a simulation software which involves solving around 10^8 simultaneous linear equations. Equations are sparse. I already made a prototype in which I implemented LU decomposition myself. But my implementation can only address less than 10^4 equation due to performance and memory constraints. I never worked with any CAS systems. Can anyone suggest some good CAS system from where I can start? Even after a long web search I was not able to get a good comparison of existing CAS systems in terms of the size of data it can process and also a performance comparison.
Development environment I am using is C# with .Net 4.0, but I can use any C++ , C or C# libraries in my system.

I found many CAS systems like Mathematica, Boost, Sage, Intel's MKL library. But i am not able to sort out a comparison from that. And how much data they can handle with a significant performance.

I am expecting answers like "I have solved 1,00,000 equations in 1,00,000 variables with xxx Library with in xxxx time in a machine with x cores and xGB Ram using xThreads"

推荐答案

我不知道CAS系统是什么，谷歌的信息似乎不一样有帮助。您需要提供更多详细信息并在您的问题中解释。



这个大小的数据（即使稀疏）可能需要在64位机器上完成，只需提供扩展的地址空间。您使用的编程语言（从列出的选项中）不应该那么重要。如果问题可以解决，可以用C＃解决。



确保你的系统上有足够的交换文件空间。由于存在大量数据，因此在运行计算时会有大量的分页/交换活动。

I don't know what a CAS system is and info from Google doesn't seem to be helpful. You need to provide more detail and explain that in your question.

Data of this size (even if sparse) likely needs to be done on a 64 bit machine, simply to provide the expanded address space. The programming language you use (from the choices listed) should not be that important. If the problem can be can be solved, it can be solved in C#.

Make sure that you have adequate swapfile space defined on your system. Because of the huge amount of data, there will be a lot of paging/swapping activity as you run your calculation.

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