Inversion of large sparse linear systems

pankos · June 23, 2010, 14:34

Can anyone tell me some libraries for C languange which inverts large sparse linear systems? It would be better if its install is for linux systems (gcc compiler).

DoHander · June 23, 2010, 16:55

GSL - GNU Scientific Library
Cblas
Clapack

and so on ... any Linux distribution should have the above.

Do

jed · June 23, 2010, 18:13

These suggestions are worthless for sparse systems. I recommend PETSc (http://mcs.anl.gov/petsc), it runs everywhere (Linux, Mac, Windows, exotic Unix, and even iPhone ;-)), scales to very large problems (5*10^11 unknowns, ~300k processors), and perhaps most importantly, is easy to extend with custom (physics-specific) solver components, or by composing existing components (including many third-party libraries) at runtime.

pankos · June 24, 2010, 02:03

OK. Thanks. I have installed PETCs library but i havent concerned it still. Yesterday, i try to use SuperLU library but cant invert matrices (only solve systems). In my problem use the same right large matrix more times. Therefore its not efficient to solve a system at each time. Of course, if i use iterative procedure maybe is ok.

jed · June 24, 2010, 06:24

Maybe you misunderstand the process of "solving". You don't want the inverse because it's dense and numerically unstable. Instead, you factor the matrix, and then solve with sparse triangular factors. This requires far fewer operations than actually creating the inverse, and the triangular solves are also much faster than multiplying by the inverse (roughly $O(n \log n)$ in 2D or $O(n^{4/3})$ in 3D vs.

, time and space). If you use PETSc, you just call KSPSolve() repeatedly (without updating the matrices), this will reuse the factorization that was computed on the first solve. A standard direct solver would be obtained with

Code:

-ksp_type preonly -pc_type lu -pc_factor_mat_solver_package superlu

(or mumps or umfpack, which are likely faster). Note that larger problems, especially in 3D, may be better suited to iterative methods (domain decomposition or multigrid), even if you need to solve many times.

June 23, 2010, 14:34	Inversion of large sparse linear systems	#1
pankos Member kostas Join Date: Jun 2010 Posts: 43 Rep Power: 15	Can anyone tell me some libraries for C languange which inverts large sparse linear systems? It would be better if its install is for linux systems (gcc compiler).

June 24, 2010, 06:24	You never want the inverse	#5
jed Member Jed Brown Join Date: Mar 2009 Posts: 56 Rep Power: 19	Maybe you misunderstand the process of "solving". You don't want the inverse because it's dense and numerically unstable. Instead, you factor the matrix, and then solve with sparse triangular factors. This requires far fewer operations than actually creating the inverse, and the triangular solves are also much faster than multiplying by the inverse (roughly $O(n \log n)$ in 2D or $O(n^{4/3})$ in 3D vs. , time and space). If you use PETSc, you just call KSPSolve() repeatedly (without updating the matrices), this will reuse the factorization that was computed on the first solve. A standard direct solver would be obtained with Code: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_package superlu (or mumps or umfpack, which are likely faster). Note that larger problems, especially in 3D, may be better suited to iterative methods (domain decomposition or multigrid), even if you need to solve many times.

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June 23, 2010, 16:55		#2
DoHander Senior Member Join Date: Nov 2009 Posts: 411 Rep Power: 19	GSL - GNU Scientific Library Cblas Clapack and so on ... any Linux distribution should have the above. Do

June 23, 2010, 18:13		#3
jed Member Jed Brown Join Date: Mar 2009 Posts: 56 Rep Power: 19	These suggestions are worthless for sparse systems. I recommend PETSc (http://mcs.anl.gov/petsc), it runs everywhere (Linux, Mac, Windows, exotic Unix, and even iPhone ;-)), scales to very large problems (5*10^11 unknowns, ~300k processors), and perhaps most importantly, is easy to extend with custom (physics-specific) solver components, or by composing existing components (including many third-party libraries) at runtime.

June 24, 2010, 02:03		#4
pankos Member kostas Join Date: Jun 2010 Posts: 43 Rep Power: 15	OK. Thanks. I have installed PETCs library but i havent concerned it still. Yesterday, i try to use SuperLU library but cant invert matrices (only solve systems). In my problem use the same right large matrix more times. Therefore its not efficient to solve a system at each time. Of course, if i use iterative procedure maybe is ok.