Re: Out Of Memory

*To*: mathgroup at smc.vnet.net*Subject*: [mg3155] Re: Out Of Memory*From*: withoff (David Withoff)*Date*: Fri, 9 Feb 1996 03:01:03 -0500*Sender*: owner-wri-mathgroup at wolfram.com

In article <4f960m$dp3 at dragonfly.wolfram.com> Rob Carscadden <carscadd at pps.pubpol.duke.edu> writes: > I'm trying to take the determinant of a 6 by 6 Jacobian, but I keep > getting an "Out of Memory" error. Mathematica grinds away, but finally > just stops. Mathematica is the only thing running in Windows3.1. My > machine grinds away with SAS no problem. Is there some way to help > mathematica (increase the kernel maybe?)? I don't want to take this > matrix apart and find the det by minors, so please don't suggest that > approach. > > Thanks for the help. > Rob In the absence of any special cancellations, the expanded determinant of a 6 x 6 symbolic matrix will have 6! terms in it, each a product of 6 matrix elements. If each matrix element uses 1 kB of memory, that's about four megabytes of memory. You probably won't be able to store very many determinants like that without running out of memory. I saw your example, though, (I think this is the example that you sent to technical support, support at wri.com), and from your example I don't believe that this is the problem. In your example, I think your computer is running out of memory while formatting the result. This is a common problem, and is not peculiar to Mathematica. There are many examples where the computer will have plenty of memory to store a result, but will not have enough memory to display it. In some situations, for example, if you paste 10 copies of the same page of text in a word processor, the word processor will only store one copy of the text, and will set up pointers to that one copy. If you print the document out on a printer, the printer will produce 10 separate copies of the same page, effectively using 10 times as much space as was needed to store the same information as is stored in the computer. The technical term for this is "sharing". The computer shares the single copy of the information between several places where it is needed. Another consideration is that displayed results are often larger than stored results even when there is only one copy. For example, a double-precision floating-point machine number is typically stored in 8 bytes of memory, but if you display a number like 1.234567890123456e-297 on your computer screen, 22 bytes of memory will be used to store the 22 characters in the output. Even more drastic memory requirements come up in formatting more complex output, such as formatting elaborate algebraic expressions. It is not uncommon to use 10 or 20 times as much memory to format a result as is required to store it. In Mathematica, you can use PrintForm to get a rough estimate of the amount of memory that will be required to format an expression. Here, for example, is a simple expression that is stored using about 260 bytes of memory. In[1]:= expr = Expand[(Sqrt[Sin[x]] + 1)^2]/2 1 + 2 Sqrt[Sin[x]] + Sin[x] Out[1]= --------------------------- 2 In[2]:= ByteCount[expr] Out[2]= 26O Over 7 times that amount of memory is used to display the result. In[3]:= ByteCount[PrintForm[expr]] Out[3]= 1900 Dave Withoff Research and Development Wolfram Research ==== [MESSAGE SEPARATOR] ====

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