稀疏酉矩阵的最佳 C++ 矩阵库

2021-12-18 00:00:00 matrix sparse-matrix lapack c++ umfpack

我正在寻找一个好的(在积极维护的最好情况下)C++ 矩阵库.因此它应该被模板化，因为我想使用有理数的复数作为数值类型.我处理的矩阵主要是稀疏和幺正的.

I am looking for a good (in the best case actively maintained) C++ matrix library. Thereby it should be templated, because I want to use a complex of rationals as numerical type. The matrices what I am dealing with are mainly sparse and unitary.

能否请您推荐一些库并简要解释一下为什么要使用它们，因为我知道如何找到它们，但我无法真正决定什么适合我，因为我缺少使用它们的经验.

Can you please suggest libraries and also give a small explaination why to use them, because I know how to find them, but I cannot really decide what is suitable for me because I am missing the experience with them.

我处理的主要运算是矩阵乘法、向量的标量乘法和克罗内克积.矩阵的大小是指数级的，我希望至少能够处理多达 1024x1024 个条目的矩阵.

The main operations I am dealing with are matrix multiplication, scalar multiplication with a vector and kronecker product. The size of the matrices is exponential and I wanna at least be able to deal with matrices up to 1024x1024 entries.

推荐答案

很多人在做严肃"矩阵的事情，依赖 BLAS，添加 LAPACK/ATLAS(正态矩阵)或 UMFPACK(稀疏矩阵)用于更高级的数学.原因是此代码经过充分测试、稳定、可靠且速度相当快.此外，您可以直接从供应商处购买它们(例如 Intel MKL)调整到您的架构，但也可以免费获得它们.uBLAS在Manuel 的答案 可能是标准的 C++ BLAS 实现.如果您稍后需要类似 LAPACK 的东西，可以使用绑定来实现.

Many people doing "serious" matrix stuff, rely on BLAS, adding LAPACK / ATLAS (normal matrices) or UMFPACK (sparse matrices) for more advanced math. The reason is that this code is well-tested, stable, reliable, and quite fast. Furthermore, you can buy them directly from a vendor (e.g. Intel MKL) tuned towards your architecture, but also get them for free. uBLAS mentioned in Manuel's answer is probably the standard C++ BLAS implementation. And if you need something like LAPACK later on, there are bindings to do so.

然而，这些标准库(BLAS/LAPACK/ATLAS 或 uBLAS + bindings + LAPACK/ATLAS)都无法满足模板化和易于使用的要求(除非您只需要 uBLAS).实际上，我必须承认，当我使用 BLAS/LAPACK 实现时，我倾向于直接调用 C/Fortran 接口，因为我通常看不到 uBLAS + 绑定组合的太多额外优势.

However, none of these standard libraries (BLAS / LAPACK / ATLAS or uBLAS + bindings + LAPACK / ATLAS) ticks your box for being templated and easy to use (unless uBLAS is all you'll ever need). Actually, I must admit, that I tend to call the C / Fortran interface directly when I use a BLAS / LAPACK implementation, since I often don't see much additional advantage in the uBLAS + bindings combination.

如果我需要一个简单易用的通用 C++ 矩阵库，我倾向于使用 Eigen(我过去使用 NewMat).优点:

If I a need a simple-to-use, general-purpose C++ matrix library, I tend to use Eigen (I used to use NewMat in the past). Advantages:

  • 在英特尔架构上相当快，对于较小的矩阵可能是最快的
  • 漂亮的界面
  • 几乎满足您对矩阵库的所有期望
  • 您可以轻松添加新类型

缺点(国际海事组织):

Disadvantages (IMO):

  • 单处理器 [在 Eigen 中部分修复3.0]
  • 对于较大的矩阵和一些高级数学比 ATLAS 或 Intel MKL(例如 LU 分解)更慢[在 Eigen 3.0 中也有所改进]
  • 仅对稀疏矩阵提供实验性支持[在即将发布的 3.1 版中得到改进].
  • single-processor [ partly fixed in Eigen 3.0]
  • slower for larger matrices and some advanced math than ATLAS or Intel MKL (e.g. LU decomposition) [ also improved in Eigen 3.0]
  • only experimental support for sparse matrices [ improved in upcoming version 3.1].

即将推出的 Eigen 3.1 允许某些功能使用英特尔 MKL(或任何其他 BLAS/LAPACK 实现).

The upcoming Eigen 3.1 allows some functions to use the Intel MKL (or any other BLAS / LAPACK implementation).

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