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Re: issue with LinearSolve[] when using SparseArray when size close

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  • Subject: [mg113626] Re: issue with LinearSolve[] when using SparseArray when size close
  • From: "Nasser M. Abbasi" <nma at 12000.org>
  • Date: Fri, 5 Nov 2010 05:11:45 -0500 (EST)
  • Reply-to: nma at 12000.org

Sorry, I forgot to mention that I am using Mathematica 7.0, on windows 
7, 64 bit OS, intel i7 930, with 8 GB installed physical RAM.

could someone with 7.01 version please try this? If it works with n=511 
when using 7.01, I can try to upgrade.


On 11/4/2010 11:40 AM, Nasser M. Abbasi wrote:
> There is some serious problem I am getting when trying to use
> Mathematica LinearSolve[] to solve  Au=f when using SparseArray when the
> size of non-zero elements gets close to 1 GB.
>
> The non-zero elements in A that I am building is of the order n^3.
>
> Therefore, for n=255, memory needed should be around 130 Mega Bytes
> (255^2*8) (using 8 bytes for each value, I am using numerical everything).
>
> For n=511, memory used should be a little over 1 Giga Bytes.
>
> I have 8 GB Ram. Windows 7, new Intel CPU.
>
> When I run the solver for n=31 or 63 or 127 or 255, it all works, and
> Mathematica is fast solving Au=f, takes few seconds, and no problem.
> These are the CPU times reported by Mathemtica Timing command for the
> LinearSolve[] call
>
> n=63, cpu=0.03
> n=127, cpu=0.078
> n=255, cpu=0.437
> n=511, been running for many hrs, memory problem.
>
> When I changed to n=511, I see memory of the Mathematica Kernel going up
> to almost 100% of the PC memory, using almost 7 GB, and I have waited
> for 9 hrs, and Mathematica is still not done.
>
> There seems, on the face of it, something really wrong here. It seems
> SparseArray behavior or how LinearSolve[] uses it, does not scale well
> at all? or is this a windows OS issue? if it is a bug in my code, but it
> works so well for all the other n values?
>
> I am posting the code, it is really small code, to see if someone can
> please try it on their PC and see if they get the same behavior.
>
> ------------ code -----------------
> $MinPrecision=$MachinePrecision;$MaxPrecision=$MachinePrecision;
> Share[];
>
> (* make sparse A*)
> makeA[n_?(IntegerQ[#]&&Positive[#]&)]:=Module[{r,off,block},
> r=Table[-4,{i,n}];
> off=Table[1,{i,n-1}];
>
> block =DiagonalMatrix[r,0]+DiagonalMatrix[off,1]+DiagonalMatrix[off,-1];
>
> SparseArray[{Band[{1,1}]->ConstantArray[block,{n}],Band[{1,n+1}]->1,Band[{n+1,1}]->1}]
> ];
>
> (* f(x,y) *)
> force[i_?(IntegerQ[#]&),j_?(IntegerQ[#]&),h_?(NumericQ[#]&&Positive[#]
> &)]:=Module[{x=i*h,y=j*h},
> N@Exp[-(x-0.25)^2-(y-0.6)^2]
> ];
>
> (*n=127; h=2^-7;*)    (*these values are OK *)
> (*n=255; h=2^-8;*)    (*these values are OK *)
> n=511; h=2^-9;  (*these cause problem *)
>
> A=N[makeA[n]];
>
> (* fill in f vector, in correct order for problem*)
> f=Table[0,{i,n^2}];
> For[j=1,j<=n,j++,
> For[i=1,i<=n,i++,
> f[[j+n*(i-1)]]=force[i,j,h]
> ]
> ];
>
> Print["before solver, MemoryInUse[]=",MemoryInUse[]];
> {cpu,sol}=Timing[LinearSolve[A,f]];
> Print["after solver, MemoryInUse[]=",MemoryInUse[]];
> Print["after solver, cpu=",cpu];
>
> ---------------- end code -----------------
>
> thanks
> --Nasser



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