blocks|key|3225863|text|选择数学库的一个常见陷阱是，我们希望存在一个适用于一切的数学库。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|3225864|在找到一个库之前，你应该首先问“我想要什么样的数学库？”然后你会有一个标准列表，比如开源与否，高性能与否，可移植性与否，易用性与否。|3225865|以下是我对您列表中的库的评论(我还没有使用后两个库)：|3225866|1)+DotNumerics|offset|length|style|BOLD|3225867|(http://www.dotnumerics.com/)|3225868|它们使用一个将Lapack过程代码转换成C#类的fortran2C#转换器。用户友好的C#包装器是为原始的Lapack类编写的。|3225869|2)+Alglib+()|3225870|该库有多种语言版本，如delphi、c%2B%2B和c#。我相信它比你列出的任何其他库都有更长的历史。|3225871|大多数函数都是从Lapack翻译过来的。而且它的界面并不是那么用户友好。(但您可以灵活地使用Lapack风格的界面。)使用lapack风格的界面意味着您需要更多地了解矩阵及其操作。|3225872|3)+dnAnalytics+(http://dnanalytics.codeplex.com/)|3225873|这个库现在正在合并到Math.Net中。合并似乎还没有完成。dnA中的一些函数在Math.Net中仍然不可用。|3225874|4)+Math.NET+(http://www.mathdotnet.com/)它的实现是从头开始的，也就是说，它不是从Lapack直接翻译过来的。他们的目标是为.Net平台提供一个纯托管库。这意味着易用性和可移植性是两个主要目标。一个令人担忧的问题是，他们自己的实现是否正确。一个好的方面是，这个库是可移植的，你可以很轻松地在Mono，XNA，Windows+Mobile手机上使用它。|3225875|上面的库并不关注F#。然而，Math.Net的一名团队成员在剑桥MS+Research工作，是一名F#专家。就像库达说的那样，他们将为这个库设计一个F#接口。此外，它们还将提供本机包装器。但也许你会等待很长时间，比“几个月”更长:)|3225876|出于对高性能的考虑，上面的库没有提供本机包装器(至少现在是这样)。如果你想要原生性能%2B+.Net，你最好使用商业化的库。有一些开源的解决方案：|3225877|1.+这是一个类似.Net的numpy解决方案。他们PInvoke到Lapack+dll(例如，netlib上的未优化的lapack，来自AMD和英特尔的优化版本)。|3225878|2.+F#中的数学提供程序。在this+question中读取我的答案。因为F#源代码现在是开源的。我可能会修订库并发布我的更新:)|3225879|通常你不需要一个大的数学库。你只需要一些功能，例如，如果你需要一个快速的矩阵乘法过程，使用PInovke到一个平台优化的BLAS+dll是最简单的方法。如果你需要为孩子们做一个面向教育的数学软件，那么Math.net的质量就足够了。如果你在一家公司开发可靠的数学组件，那么为什么不使用由高质量团队支持的商业组件呢？|3225880|找到一个完美的数学库是很困难的。但是为你的问题找到一个库解决方案通常很容易。|3225881|entityMap|0|LINK|mutability|MUTABLE|url|http://www.dotnumerics.com/|1|http://dnanalytics.codeplex.com/|2|http://www.mathdotnet.com/|3|https://stackoverflow.com/questions/3227647/open-source-math-library-for-f^0|0|0|0|3|B|0|1|R|0|0|0|3|9|0|0|0|3|B|G|W|1|0|0|3|8|D|Q|2|0|0|0|0|2|0|0|E|F|D|3|0|0|0^^$0|@$1|2|3|4|5|6|7|1R|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|1S|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|1T|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|1U|8|@$H|1V|I|1W|J|K]]|9|@]|A|$]]|$1|L|3|M|5|6|7|1X|8|@]|9|@$H|1Y|I|1Z|1|20]]|A|$]]|$1|N|3|O|5|6|7|21|8|@]|9|@]|A|$]]|$1|P|3|Q|5|6|7|22|8|@$H|23|I|24|J|K]]|9|@]|A|$]]|$1|R|3|S|5|6|7|25|8|@]|9|@]|A|$]]|$1|T|3|U|5|6|7|26|8|@]|9|@]|A|$]]|$1|V|3|W|5|6|7|27|8|@$H|28|I|29|J|K]]|9|@$H|2A|I|2B|1|2C]]|A|$]]|$1|X|3|Y|5|6|7|2D|8|@]|9|@]|A|$]]|$1|Z|3|10|5|6|7|2E|8|@$H|2F|I|2G|J|K]]|9|@$H|2H|I|2I|1|2J]]|A|$]]|$1|11|3|12|5|6|7|2K|8|@]|9|@]|A|$]]|$1|13|3|14|5|6|7|2L|8|@]|9|@]|A|$]]|$1|15|3|16|5|6|7|2M|8|@$H|2N|I|2O|J|K]]|9|@]|A|$]]|$1|17|3|18|5|6|7|2P|8|@$H|2Q|I|2R|J|K]]|9|@$H|2S|I|2T|1|2U]]|A|$]]|$1|19|3|1A|5|6|7|2V|8|@]|9|@]|A|$]]|$1|1B|3|1C|5|6|7|2W|8|@]|9|@]|A|$]]|$1|1D|3|-4|5|6|7|2X|8|@]|9|@]|A|$]]]|1E|$1F|$5|1G|1H|1I|A|$1J|1K]]|1L|$5|1G|1H|1I|A|$1J|1M]]|1N|$5|1G|1H|1I|A|$1J|1O]]|1P|$5|1G|1H|1I|A|$1J|1Q]]]]

One common pitfall of choosing math library is that we hope there exists a math library for everything. 

Before finding a library, you should first ask "what kind of math library do I want?". Then you will have a list of criteria, such as open source or not, high performance or not, portable or not, easy to use or not. 

Following are my comments on the libraries in your list (I haven't used the last two):

1) DotNumerics

(<a href="http://www.dotnumerics.com/" rel="nofollow noreferrer">http://www.dotnumerics.com/</a>)

They use a fortran2C# translator that translates the Lapack procedures code into C# classes. User friendly C# wrappers are written for the raw Lapack classes. 

2) Alglib (<a href="http://www.alglib.net/" rel="nofollow noreferrer">http://www.alglib.net/</a>)

This library is available in several languages, like delphi, c++ and c#. I believe it has longer history than any other libraries you listed. 

Most of the functions are translated from Lapack. And its interface is not so user friendly. (But you have the flexibility of Lapack style interface.) Using lapack style interface means that you need to know more about the matrix and its operations. 

3) dnAnalytics (<a href="http://dnanalytics.codeplex.com/" rel="nofollow noreferrer">http://dnanalytics.codeplex.com/</a>)

This library is merging into Math.Net now. It seems that the merging is not done yet. A few functions in dnA is still not available in Math.Net. 

4) Math.NET (<a href="http://www.mathdotnet.com/" rel="nofollow noreferrer">http://www.mathdotnet.com/</a>)
Its implementation is from scratch, i.e., it is not a direct translation from Lapack. They aim to provide a purely managed library for .Net platform. That means easy usage and portability are two primary goals. One concern is that whether their own implementation is correct or not. One good thing is that this library is portable in the sense that you can use it on Mono, XNA, Windows Mobile Phone with little effort. 

The above libraries dont' focus on F#. However one of the team members in Math.Net works for MS Research Cambridge and is an F# expert. Like Cuda said, they will work out an F# interface for the library. Also they will provide native wrappers. But maybe you will wait a long time, longer than "several months" :)

For the concern of high performance, the above libraries don't provide native wrappers (at least now). If you want native performance + .Net, you had better use a commercial library. There are some open source solutions:

1. <a href="http://ilnumerics.net/" rel="nofollow noreferrer">http://ilnumerics.net/</a> This is a numpy like solution for .Net. They PInvoke to Lapack dlls (e.g. the non-optimized lapack at netlib, the optimized versions from AMD and Intel.)

2. math provider in F#. read my answer in <a href="https://stackoverflow.com/questions/3227647/open-source-math-library-for-f">this question</a>. Since F# source code is now open sourced. I may revise the library and release my updates :)

Usually you don't need a big math library. You just need some functionality, e.g., if you need a fast matrix multiplication procedure, using PInovke to a platform optimized BLAS dll is the easiest way. If you need do a education oriented math software for kids, then the quality of Math.net is enough. If you are in a company and developing reliable math components, then why don't use a commercial one backed by a high-quality team? 

Finding a perfect math library is hard. But finding a library solution to your problem is usually easy.

blocks|key|3011824|text|F#+for+Numerics是我公司的一个产品，用100%25的F#编写。我们的重点是一般技术(从FFT到随机数生成)，而不是特定的线性代数，尽管提供了基本的线性代数例程(Cholesky，LU，QR，SVD+on各种矩阵/元素类型)，我们对F#的易用性特别感兴趣。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|3011825|如果你想要全面的LAPACK，那么我的建议是Alglib，如果你有预算，或者Extreme+Optimization，如果你能负担得起。Alglib是一个完全托管的代码，它有一个“怪异”的API，所以它运行起来相对较慢，使用起来也比较麻烦。Extreme+Optimization是一个更好的API，它包装了英特尔MKL和一些额外的例程，因此它更易于使用，运行速度也更快。|3011826|我应该警告你，如果你来自开源背景，.NET库(免费的，商业的，甚至框架本身)的总体质量是相对较差的。我尝试了您提到的许多其他库，但对它们一点也不感兴趣。|3011827|entityMap|0|LINK|mutability|MUTABLE|url|http://ffconsultancy.com/products/fsharp_for_numerics/index.html|1|http://www.alglib.net/|2|http://www.extremeoptimization.com/^0|0|F|0|0|M|6|1|12|K|2|0|0^^$0|@$1|2|3|4|5|6|7|T|8|@]|9|@$A|U|B|V|1|W]]|C|$]]|$1|D|3|E|5|6|7|X|8|@]|9|@$A|Y|B|Z|1|10]|$A|11|B|12|1|13]]|C|$]]|$1|F|3|G|5|6|7|14|8|@]|9|@]|C|$]]|$1|H|3|-4|5|6|7|15|8|@]|9|@]|C|$]]]|I|$J|$5|K|L|M|C|$N|O]]|P|$5|K|L|M|C|$N|Q]]|R|$5|K|L|M|C|$N|S]]]]

<a href="http://ffconsultancy.com/products/fsharp_for_numerics/index.html">F# for Numerics</a> is a product of my company, written in 100% F#. Our emphasis is on general techniques (everything from FFTs to random number generation) and not specifically linear algebra although basic linear algebra routines are provided (Cholesky, LU, QR, SVD on various matrix/element types) and we are particularly interested in ease of use from F#.

If you're after the full breadth of LAPACK then my recommendations are <a href="http://www.alglib.net/">Alglib</a> if you're on a budget or <a href="http://www.extremeoptimization.com/">Extreme Optimization</a> if you can afford it. Alglib is entirely managed code with an, umm, "quirky" API so it is relatively slow to run and cumbersome to use. Extreme Optimization is a nicer API wrapping the Intel MKL and some extra routines so it is easier to use and much faster to run.

I should warn you that the general quality of .NET libraries (free, commercial and even the framework itself) is comparatively poor if you are coming from an open source background. I tried many of the other libraries that you mentioned and was not at all impressed with them.

blocks|key|3226069|text|我还可以建议查看新的名为FinMath的.net数值库，我在开发中使用了它。它为许多MKL+(Intel+Math+Kernel+Library+)功能提供了易于使用的.net类包装，例如线性代数(BLAS和LAPACK)、统计和快速傅立叶变换。此外，它还包含一些高级方法，如线性和二次规划求解器，聚类分析等。它还包括各种.net到本机c编组的优化，这导致了高性能和易于使用的单一dll解决方案。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|3226070|但不幸的是，它不是开源的，也不是免费的，而且与LAPACK相比，大多数方法只支持双精度浮点reals。对于很少使用的LAPACK方法，没有提供包装器。|3226071|entityMap|0|LINK|mutability|MUTABLE|url|https://rtmath.net/products/finmath/^0|C|7|0|0|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@$A|O|B|P|1|Q]]|C|$]]|$1|D|3|E|5|6|7|R|8|@]|9|@]|C|$]]|$1|F|3|-4|5|6|7|S|8|@]|9|@]|C|$]]]|G|$H|$5|I|J|K|C|$L|M]]]]

I also can suggest to view new one .net numerical library called <a href="https://rtmath.net/products/finmath/" rel="nofollow">FinMath</a>, which I used in my development. It provides easy to use .net class wrappers for a lot of MKL (Intel Math Kernel Library on which it based) functionality, such as linear algebra (BLAS and LAPACK), statistics and FFT. Also, in addition it contains number of advanced methods such as linear and quadratic programming solver, cluster analysis and others. It also includes various .net to native c marshaling optimization which leads to high performance and easy to use single dll solution. 

But unfortunately it's not open source, not free and in contrast to LAPACK, most methods supports only double precision floating point reals. And for few rarely used LAPACK methods wrapper are not provided.

I’ve been searching Google and Stack Overflow like crazy for days and have yet to find any recent, completely relevant information to answer the following question: What are the best C#/F#/.NET math libraries (specifically, those that wrap or implement the same functionality as Lapack, etc.)?

One of the better posts on Stack Overflow that I did see was: <a href="https://stackoverflow.com/questions/3227647/open-source-math-library-for-f">https://stackoverflow.com/questions/3227647/open-source-math-library-for-f</a>

The reason that that post, and other previous posts, didn’t sufficiently answer my question was that no systematic comparison of user experiences with various libraries was given.

I’m interested in how completely the following libraries (in real-world usage) implement Lapack (or a broad set of equivalent linear algebra of functionality); and, I’m curious about their performance relative to each other particularly on very large matrices. Also, I’d like to hear about others’ experiences utilizing the various libraries: difficulties, ease of use, etc.

Below is a comprehensive list of the “free”/opensource/affordable .NET/F#/C# math libraries which – as far as I know – have a linear algebra feature set. I’d deeply appreciate it if the community here on Stack Overflow would chip in with any experiences they have with the following libraries:

<ul>
<li><a href="http://www.dotnumerics.com/" rel="nofollow noreferrer">DotNumerics</a></li>
<li><a href="http://www.alglib.net/" rel="nofollow noreferrer">Alglib</a></li>
<li><a href="http://dnanalytics.codeplex.com/" rel="nofollow noreferrer">dnAnalytics</a></li>
<li><a href="http://www.mathdotnet.com/" rel="nofollow noreferrer">Math.NET</a></li>
<li><a href="http://www.ffconsultancy.com/products/fsharp_for_numerics/?so" rel="nofollow noreferrer">F# for Numerics</a></li>
<li><a href="http://www.dewresearch.com/vs-mtxvec2.html" rel="nofollow noreferrer">MtxVec 2010</a></li>
</ul>

I’m interested in F# for Numerics (since I’m working with F#) but I’m having difficulty ascertaining the strengths and weaknesses of the various libraries. Like, which features are missing or included in various libraries, and how easily they are used and how well they perform.

DotNumerics seems like a comprehensive implementation of Lapack in C#, but I can’t find anyone who’s shared their experiences with it anywhere. Math.NET seems like it could eventually be an excellent, comprehensive math library for .NET, but it’s difficult to tell how active the project is and it seems that it’s very much in flux in its current stage. Alglib has been spoken of once or twice as being solid, but I’d like to hear more about them relative to others. I like the idea of supporting a native F# numerics library, but I’m not certain how committed the developer (Flying Frog Consultancy) is to supporting and developing F# for Numerics… and what functionality they plan to include in their 1.0 release and what their target date is for a 1.0 release.

DotNumerics, AlgLib, dnAnalytics, Math.net, F# for Numerics, Mtxvec?

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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我疯狂地搜索了谷歌和Stack Overflow好几天了，还没有找到任何最新的、完全相关的信息来回答以下问题：哪些是最好的C#/F#/.NET数学库(特别是那些包装或实现了与Lapack相同功能的库)？我在Stack Overflow上看到的一个更好的帖子是：这篇文章和其他之前的文章没有充分回答我的问题的原因是，没有给...

问DotNumerics、AlgLib、dnAnalytics、Math.net、用于数值计算的F#、Mtxvec？
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