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Computational Kernels for Preconditioned Iterative Methods


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PreAlps is a library that implements communication avoiding solvers based on enlarged Krylov subspace methods and robust preconditioners.

In its current state the library contains routines for solving symmetric positive definite (SPD) linear systems. The current version provides an efficient implementation of ECG and LORASC preconditioner. ECG is based on enriching the Krylov subspace used in classic methods that allows to reduce drastically the communication cost of the iterative solver (see [1]). LORASC is a robust algebraic preconditioner based on low rank approximation of the Schur complement (see [3]).

ECG can be used as an iterative solver and can be combined with block Jacobi, LORASC, or any other efficient preconditioner. It is based on reverse communication such that it can be used also for matrix-free problems. LORASC can be used in combination with ECG but also with any other Krylov solver.

Running instructions

  1. Make sure all these libraries are installed on your system or install them:
    1.1 MPI
    1.2 MKL
    1.3 METIS (can be downloaded from

  2. If you want to enable LORASC preconditioner in preAlps, make sure all these libraries are installed or install them:
    2.1 ParMETIS (can be downloaded from )
    2.2 MUMPS (can be downloaded from
    2.3 PARPACK (can be downloaded from

  3. If you will like to compare ECG results with PETSc, make sure PETSc is installed.
    3.1 PETSc ( can be downloaded from )

  4. Get the latest version of preAlps.
    $ git clone preAlps

  5. Edit the file at the top level of the root directory, check compiler directives and flags.

  6. Copy an example of from the directory MAKES.

In order to use ECG Solver only, type:  
$ cp MAKES/
For the full installation of preAlps, type:
$ cp MAKES/  
  1. Edit the file to enable the libraries used and installed in 1,2 and 3. Make sure the LD_FLAGS of these libraries are correctly set. Disable unused libraries.

  2. Type 'make' to compile the library.
    $ make

  3. To run the example program

9.1 for a test on a provided elasticity 3D matrix (see [1,3]):  

  9.1.1 run ECG + Block Jacobi with 8 processors with an enlarging factor of 4.  
  $ mpirun -np 8 ./bin/test_ecg_prealps_op -m matrix/elasticity3d_12x10x10_var.mtx -o 0 -r 0 -e 4  
  9.1.1 run ECG + Lorasc Multilevel with 8 processors with enlarging factor of 2, use 4 domains at the first level of the parallelism for LORASC.  
  $ mpirun -np 8 bin/test_lorasc -m matrix/elasticity3d_12x10x10_var.mtx  -t 2 -p 2 -npLevel1 4  
9.2 for obtaining the help about all the options provided with the test programs.
  $ ./bin/test_ecg_prealps_op -h  
  $ ./bin/test_lorasc -h  
9.3 for a general case:  
  $ mpirun -np <nb_processors> mpirun ./test_ecg_prealps_op -e/--enlarging-factor <int> [-h/--help] [-i/--iteration-maximum <int>] -m/--matrix <matrix_file.mtx> -o/--ortho-alg <int> -r/--search-dir-red <int> [-t/--tolerance <double>]  

  $ mpirun -np <nb_processors> ./bin/test_lorasc -m <matrix_file.mtx> -t <enlarging factor> -p <preconditionner_number> -npLevel1 <number_domains_first_level>  


PreAlps is free software licensed under the BSD-3 License.

The preAlps software contains proprietary of Inria.

Version V1.0, August 2018
Authors: Simplice Donfack, Olivier Tissot, Laura Grigori, Sebastien Cayrols, Alan Ayala Obregon Copyright (C) 2018, Inria


  1. Laura Grigori, Sophie Moufawad, and Frederic Nataf. Enlarged Krylov subspace conjugate gradient methods for reducing communication. SIAM J. Matrix Anal. Appl., 2016.

  2. Laura Grigori and Olivier Tissot. Reducing the communication and computational costs of enlarged krylov subspaces conjugate gradient. In submission.

  3. Laura Grigori , Frederic Nataf, Soleiman Yousef. Robust algebraic schur complement based on low rank correction. Technical report, ALPINES-INRIA, Paris-Rocquencourt, 6 2014.

  4. Laura Grigori , Frederic Nataf, Soleiman Yousef, Simplice Donfack, Remi Lacroix. Robust algebraic schur complement based on low rank correction. In submission.


Simplice Donfack Olivier Tissot Laura Grigori Sebastien Cayrols Alan Ayala Obregon


For any question, please contact {simplice.donfack, olivier.tissot, laura.grigori} .


Computational Kernels for Preconditioned Iterative Methods







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