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Re: Intensive numerical calculations

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  • Subject: [mg80595] Re: Intensive numerical calculations
  • From: Cristian <LumisrobTogliquesto at>
  • Date: Sun, 26 Aug 2007 23:08:02 -0400 (EDT)
  • References: <f9s445$all$><fabgog$id8$> <fae9u4$ec7$> <> <faj4vu$8sk$> <> <far8u8$3r6$>

On Sun, 26 Aug 2007 07:08:56 +0000 (UTC), Daniel Lichtblau
<danl at> wrote:

>Cristian wrote:
>> On Thu, 23 Aug 2007 05:12:30 +0000 (UTC), Daniel Lichtblau
>> <danl at> wrote:
>>>Cristian wrote:
>> ]zac[
>>>Suffice it to say that a dense representation will cause problems for 
>>>most software on many machines. As for a sparse represntation, and 
>>>computational speed, it will depend on what specifically you want to do. 
>>>Mathematica uses some fairly good libraries for certain linear algebra 
>>>operations on such matrices. If what you require is not well supported 
>>>then you might need to go to some other approach, perhaps via MathLink.
>>>Daniel Lichtblau
>>>Wolfram Research
>> My problem is not the dimension of the matrixes. Certainly the
>> limitation on the packeds array (< 2^31)limits, but my true problem is
>> the slowness in to pass these matrixes to the form c++ by matlink.
>> That that profit inserting pieces in c++, I lose in the transfers
>> through matlink. I have to develop a form (structural fem)
>> personalized for the analysis of parts mechanics submitted to dynamic
>> solicitations and I was considering mathematica because I knew it from
>> the university. If I use c++ and MTL  for example it'is ok There is a
>> method for move more quickly big matrixes (unfortunately the matrixes
>> become full with the progress of the footsteps and it would be for me
>> too complicated to avoid this to the beginning)  from Mathematica to
>> an external form in c++?
>If you provide simple examples and take the trouble to use correct 
>terminology then you will more likely get useful responses.


> For example, 
>there is no "matlink" (the program you have in mind, I suspect, is 

I apologize for the error

>>Moreover you still have not specified what is your data 
>format when it resides in Mathematica. SparseArray[...]? Something else?
>Maybe what you will require is some form of Export. I believe that 
>function supports some matrix types but it is, as I note, unclear which 
>would be appropriate, as you gave no example.
>As for matrix fill-in, I'd be really surprised if your C++ library code 
>uses a dense method for solving linear systems of the sort generated for 
>FEM, with dimension around 10^5. 

I have never said to have to resolve a linear system.
What you have in mind ( I suspect), it is a wrong hypothesis

>As noted in a prior response, that 
>would be close to 100 Gb, and that is a large chunk of memory to work 
>with. Not to mention time, since you would likely have an O(n^3) 
>algorithm, or at best maybe O(n^2.4) or so from asymptotically fastest 
>approaches to matrix multiplication.

This to my notice is wrong. There are methodologies that reduce the
order of calculation ("Matrix Computation"  Golub/ Van Loan or
"Accuracy and stab..." Higham)
>Much more likely is that a Krylov type of method would be used. Similar 
>to what Mathematica might do in solving a sparse system using machine 
>double arithmetic.
>Daniel Lichtblau
>Wolfram Research

However thanks for the availability.  I now have however definite to
continue with the c++ and every doubt of mine I will turn t on the NGs
of such language


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