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Re: memory issues

• To: mathgroup at smc.vnet.net
• Subject: [mg68811] Re: memory issues
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 19 Aug 2006 00:41:24 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <ec3pme$2a0$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Christoph Lhotka wrote:
> Hi!
> 
> Running Mathematica 5.2 on 64Bit (AMD) with 2GB of RAM Memory OS: WindowsXP 64
> Pro. I get the message: No more memory available. Mathematica Kernel has shut
> down...
> 
> How do I find out:
 > [ ... ]
> 5) Why does my dual core processor does not work higher than with 50%

The thread "Illusory Multicore Support in 5.2?", April 2006, should 
answer your question,
http://forums.wolfram.com/mathgroup/archive/2006/Apr/msg00673.html

> 
> Doing some tests on my own I got the following riddle:
> 
> In[]:=ByteCount[1]
> Out[]:=16
> 
> In[]:=2000000000/16
> Out[]:=125000000
> 
> In[]:=DAT=Table[i,{i,1,125000000}];
> 
> In[]:=ByteCount[DAT]
> Out[]:=500000056
> 
> In[]:=MaxMemoryUsed[]
> Out[]:= 502133312
> 
> Why is a list of 125 000 000 different integers (a 16 Byte) only 500 000 000
> Bytes long? How should I estimate the memory limits in my algorithms, when
> designing them on this basis?

Mathematica uses packed arrays: "When appropriate, large lists and 
nested lists of numbers are automatically stored as packed arrays of 
machine-sized integers or real numbers [1], [2]."

Regards,
Jean-Marc

[1] "A.9.2 Data Structures and Memory Management"
http://documents.wolfram.com/mathematica/book/section-A.9.2

[2] "Packed Array Summary"
http://documents.wolfram.com/mathematica/Built-inFunctions/AdvancedDocumentation/LinearAlgebra/LinearAlgebraInMathematica/Performance/PackedArrays/AdvancedDocumentationLinearAlgebra5.0.2.html