[Haskell-cafe] low-cost matrix rank?

[Audun Skaugen]

I found it a fun challenge, so I coded up a small demonstration in the  
attached file :)

På Fri, 24 Apr 2015 16:01:24 +0200, skrev Audun Skaugen  
<audunskaugen at gmail.com>:

> What about dumping the matrix into a C array using the storable instance  
> of the linear package's matrices, and then use a foreign->imported svd  
> call from lapack? I don't know whether you can count on lapack being  
> available in your systems. The lapack call is >very clumsy, requiring  
> lots of pointer inputs, but it should be doable in a few lines of code.
>
> The rank is then the number of nonzero singular values, for some  
> accuracy-dependent definition of "nonzero".
>
> På Fri, 24 Apr 2015 15:30:23 +0200, skrev Mike Meyer <mwm at mired.org>:
>
>> The bed-and-breakfast isn't to bad, except for needing TH. But it's  
>> apparently not being maintained. I've started the process of  
>> >>replacing the maintainer, but may roll my own instead.
>>
>> Thanks,
>> Mike
>>
>> On Fri, Apr 24, 2015 at 8:27 AM, Dennis J. McWherter, Jr.  
>> <dennis at deathbytape.com> wrote:
>>> I am not aware of any small library which does just this, but you  
>>> could easily roll your own. Though not the most efficient >>>method,  
>>> implementing gaussian elimination is a straightforward task (you can  
>>> even find the backtracking algorithm on google) >>>and then you can  
>>> find the rank from there.
>>>
>>> Dennis
>>>
>>> On Fri, Apr 24, 2015 at 6:50 AM, Mike Meyer <mwm at mired.org> wrote:
>>>> My apologies,but my use of "low-cost" was ambiguous.
>>>>
>>>> I meant the cost of having it available - installation, size of the  
>>>> package, extra packages brought in, etc. I don't the rank  
>>>> >>>>calculation to be fast, or even cheap to compute, as it's not  
>>>> used very often, and not for very large matrices. I'd rather >>>>not  
>>>> have the size of the software multiplied by integers in order to get  
>>>> that one function.
>>>>
>>>> hmatrix is highly optimized for performance and parallelization,  
>>>> built on top of a large C libraries with lots of >>>>functionality.  
>>>> Nice to have if you're doing any serious work with matrices, but  
>>>> massive overkill for what I need.
>>>>
>>>> On Fri, Apr 24, 2015 at 3:13 AM, Alberto Ruiz <aruiz at um.es> wrote:
>>>>> Hi Mike,
>>>>>
>>>>> If you need a robust numerical computation you can try "rcond" or  
>>>>> "rank" from hmatrix. (It is based on the singular values, >>>>>I  
>>>>> don't know if the cost is low enough for your application.)
>>>>>
>>>>> http://en.wikipedia.org/wiki/Rank_%28linear_algebra%29#Computation
>>>>>
>>>>> https://hackage.haskell.org/package/hmatrix-0.16.1.5/docs/Numeric-LinearAlgebra-HMatrix.html#g:10
>>>>>
>>>>> Alberto
>>>>>
>>>>> On 24/04/15 00:34, Mike Meyer wrote:
>>>>>> Noticing that diagrams 1.3 has moved from vector-space to linear, I
>>>>>> decided to check them both for a function to compute the rank of a
>>>>>> matrix. Neither seems to have it.
>>>>>>
>>>>>> While I'm doing quite a bit of work with 2 and 3-element vectors,  
>>>>>> the
>>>>>> only thing I do with matrices is take their rank, as part of  
>>>>>> verifying
>>>>>> that the faces of a polyhedron actually make a polyhedron.
>>>>>>
>>>>>> So I'm looking for a relatively light-weight way of doing so that  
>>>>>> will
>>>>>> work with a recent (7.8 or 7.10) ghc release. Or maybe getting such  
>>>>>> a
>>>>>> function added to an existing library. Anyone have any suggestions?
>>>>>>
>>>>>> Thanks,
>>>>>> Mike
>>>>
>>>>
>>>> _______________________________________________
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>>>> Haskell-Cafe at haskell.org
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>>>>
>>>
>>
>
>
>
> --Audun Skaugen



-- 
Audun Skaugen
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