用于稀疏酉矩阵的最佳C ++矩阵库 [英] Best C++ Matrix Library for sparse unitary matrices

问题描述

我在寻找一个好的（在最好的情况下积极维护）C ++矩阵库。因此，它应该模板化，因为我想使用一个复杂的理性作为数字类型。我处理的矩阵主要是稀疏和单一的。

你能建议图书馆，并给一个小解释为什么使用它们，因为我知道如何找到他们，但我不能真正决定什么是适合我，因为我缺少与他们的经验。

编辑：

我要处理的主要操作是矩阵乘法，与向量和 kronecker乘积的标量乘法。矩阵的大小是指数的，我想至少能处理高达1024x1024个条目的矩阵。

解决方案

做严重的矩阵素材，依靠 BLAS ，添加 LAPACK / ATLAS （正则矩阵）或 UMFPACK （稀疏矩阵）以获得更高级的数学。原因是这个代码经过了良好的测试，稳定，可靠，并且相当快。此外，您可以直接从供应商处购买（例如 Intel MKL ）对你的建筑，而且也免费获得他们。 uBLAS 在 Manuel的回答可能是标准的C ++ BLAS实现。如果您稍后需要类似LAPACK的软件，则可以绑定执行此操作。

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 （我以前使用 NewMat 过去）。优点：

• 在英特尔架构上相当快，可能是最小的矩阵


• nice interface


• 几乎可以从矩阵库中获得所有预期


• ，您可以轻松地添加新类型

缺点（IMO）：

• 单一处理器[编辑：部分固定在 Eigen 3.0 ]


• 较大的矩阵和一些高级数学比ATLAS或Intel MKL Edit：在Eigen 3.0中也有所改善]


• 只有稀疏矩阵的实验性支持[ Edit： / li>
  

编辑：即将推出的Eigen 3.1允许一些功能使用英特尔MKL（或任何其他BLAS / LAPACK实施）。

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.

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.

EDIT:

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.

解决方案

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.

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.

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:

• quite fast on Intel architecture, probably the fastest for smaller matrices
• nice interface
• almost everything you expect from a matrix library
• you can easily add new types

Disadvantages (IMO):

• single-processor [Edit: partly fixed in Eigen 3.0]
• slower for larger matrices and some advanced math than ATLAS or Intel MKL (e.g. LU decomposition) [Edit: also improved in Eigen 3.0]
• only experimental support for sparse matrices [Edit: improved in upcoming version 3.1].

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

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