Hello,
I have reworked my old Parallel Gauss-Seidel with relaxation iterative
program gsp.pas into a Parallel Gauss-Seidel with relaxation iterative
algorithm library version 1.1
Description
The Parallel iterative with relaxation method that i programmed here is designed
to be used to solve large sparse systems of linear equations where the direct methods
can exceed available machine memory and/or be extremely time-consuming. for example
the direct method of the Gauss algorithm takes O(n^2) in the back substitution process
and is dominated by the O(n^3) forward elimination process, that means, if for example
an operation takes 10^-9 second and we have 1000 equations , the elimination process
in the Gauss algorithm will takes 0.7 second, but if we have 10000 equations in the system ,
the elimination process in the Gauss algorithm will take 11 minutes !. This is why i have
develloped for you the Parallel Gauss-Seidel with relaxation iterative algorithm in Object Pascal,
that is very fast.
And please take a look at my article on my Parallel Gauss-Seidel with relaxation algorithm: GSRP.
The benchmarks are here:
http://pages.videotron.com/aminer/ParallelGaussSeidel/gsrp.htmAnd here is how to use the library, as you have noticed you have to initialize
your vector x first , and set your lambda inside the call to Solve(), i have set lambda to 0.01 ,
and set the number of cores in the constructor, and pass you matrix and vector b to the Solve() method,
and that's all:
Here is the example:
---------------------
program test;
uses parallelgaussseidel,timer;
var gsp:TParallelGaussSeidel;
i,j,size:integer;
matrows: arrarrext;
vecb,vecx: arrext;
begin
gsp:=TParallelGaussSeidel.create(4); // number of cores to use
size:=10000; // set it as you wish...
SetLength(matrows, size);
SetLength(vecb, size);
SetLength(vecx, size);
for I := Low(matrows) to High(matrows) do
begin
setlength(matrows
,High(matrows)+1);
end;
for I := Low(matrows) to High(matrows)
do
begin
vecb:=100000000;
vecx:=22222222;
for J := Low(matrows) to High(matrows) do
matrows[J] := 77770000777;
end;
if gsp.testconvergence(matrows)
then writeln('The system converge...')
else writeln('The system may or may not converge...');
HPT.Timestart;
if gsp.Solve(matrows,vecb,vecx,0.01)
then
begin
writeln('Time in microseconds: ',hpt.TimePeriod);
writeln('The system converge...');
writeln('The system solved...');
writeln(vecx[0],' ',vecx[1],' ',vecx[2]); // write here you vecx...
end
else
begin
writeln('The system doesn''t converge...');
end;
SetLength(matrows, 0);
SetLength(vecb, 0);
SetLength(vecx, 0);
gsp.free;
end.
------
Please look at my parallel program test.pas inside the zip file , compile and execute it ... -
Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freepascal.org/
Operating Systems: Win , Linux and Mac (x86).
Required FPC switches: -O3 -Sd -dFPC -dWin32 -dFreePascal
-Sd for delphi mode....
Required Delphi switches: -DMSWINDOWS -$H+ -DDelphi
Thank you,
Amine Moulay Ramdane.
Recent
