Re: a big limit of mathematica?

On 12 Sep 2005 19:43:38 -0700, "Daniel Lichtblau" <danl@xxxxxxxxxxx>
wrote:



>
>(One might wonder where and why the breakdown occurs. It happens when
>we go from 215 to 216 rows. Packed arrays can handle 2^31 elements in
>total, and we are crossing the threshhold of 2^(31/2) elements here,
>which I'm sure will figure into the diagnosis.)

Is this limit of the packedArrays worth for Mathem 5.2?

Where these accurate information can be retrieved on the limits of the
packeds array ...etc
If they are in the documentation what time I don't have available I
apologize me. In contrary case can you point out me where to be able
to deepen the kernel of mathematica?
On the texts I am sure that nothing of this doesn't exist. It serves
me because I would like to create a program fem that should undertake
itself to develop heavy numerical computations



>Next question is what happens if you do obtain a packed array, and then
>try to take the determinant. There are a few ways in which one can run
>out of memory. One is that most 32 bit Mathematica platforms have a 2
>Gb limit on total space.

Just for this motive I have not marveled when the calculation is
arrested on Mathematica 5.1 + XP(32Bit)
I have marveled instead when the calculation is arrested on
Mathematica 5.2 + WinXP(64Bit) 2GB Ram 400GB HD


> The determinant computation will require at
>least one full sized copy of the matrix (using the Lapack functions
>appropriate for computing such things). I'm not certain that only one
>copy is utilized; there may be a need for more workspace. Also the
>800,000,000 byte matrices each need contiguous storage, which may or
>may not be available. Also Mathematica itself occupies space. The
>upshot is it is not hard to see memory being an issue.
>
>As of version 5.2 there is support for 64-bit platforms, with greater
>memory capabilities. We have confirmed that on 64 bit systems with
>sufficient RAM the example above can be handled (tested thus far on a
>Linux and a Windows machine). Specifically, one can allocate the matrix
>and compute its (possibly ill conditioned) determinant.

Could I know how much RAM could be necessary to create a matrix (if it
is possible ) of 10^5 * 10^5 elements and to operate one single
products (Blas1) of the type m[[i]]. m[[j]] ? (Mathem 5.2 + XP(64) or
Linux Suse 64)



>I'll mention that we tried creating a 8000 x 8000 matrix of random
>reals in one of the other languages you indicate, in order to test the
>claim that it can handle matrices in that size range. We got an
>out-of-memory message. It is not clear to me what exactly you do to get
>different behavior. Quite likely this, too, hinges on configuration
>specifics such as available RAM.


Personally I have experimented in positive sense using Gnu gcc +
UbuntuLinux 5.04 (64Bit) + ACML (amd) (Blas+Lapack) 2GB RAM+ 400GB HD
+Athlon64
>
>
>For the record, whatever you may think you did, you did not do it on a
>desktop machine with a matrix occupying 160 Gb of memory. Maybe you
>meant 1.6 Gb?

Attention in this case I have well specified that I create only the
matrix and I don't calculate the determinant


However thanks of heart. I have finally understood the true essence of
the problem. I believe that without understanding well as the
technology packed array has been implemented both useless to try to
make analytical calculations on the dimension of memory used during
the calculation


Cheers
Rob

.

Relevant Pages

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