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

*To*: mathgroup at smc.vnet.net*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