NOTE: Petsc4m is deprecated and no longer maintained. Please use petsc4m-lite instead.

OVERVIEW

Petsc4m is an interface of PETSc for MATLAB and GNU Octave. It supports solving large-scale sparse linear systems using PETSc in GNU Octave. Data exchanges between MATLAB/Octave and PETSc are done through memory.

Petsc4m is flexible and easy to use. Its top-most functions are composed of petscSolve and petscSolveCRS, plus nine other helper functions. These functions support accessing iterative solvers and preconditioners in PETSc directly from MATLAB or GNU Octave without much coding. Petsc4m also offers about 150 low-level PETSc API functions, so that you can also directly program in MATLAB and Octave using the PETSc API for prototyping. It supports both double-precision and single-precision versions of PETSc.

Petsc4m depends on ParaCoder for some basic MPI calls.

The high-level Petsc4m functions support two matrix formats: Sequential AIJ and MPI AIJ. These formats tend to deliver good performance and offer good interoperability with MATLAB and Octave. Other matrix formats, such as dense and MPI Block AIJ, are accessible through the low-level functions.

EXAMPLE

The following example illustrates how to use petscSolveCRS:

   % Set up a test matrix
   A = sprand(100,100,0.3);
   A = A + speye(100);
   [rowptr, colind, val] = crs_matrix(A);
   b = rand(100,1);

   % Solve using default KSP solver and preconditioner
   [x,flag,relres,reshis,iter] = petscSolveCRS(rowptr, colind, val, b);

   % Solve using GMRES with Jacobi preconditioner with default options
   [x,flag,relres,iter,reshis] = petscSolveCRS(rowptr, colind, val, b, ...
        PETSC_KSPGMRES, 0, int32(0), PETSC_PCJACOBI, 'right');

   % Solve using BiCGSTAB with Jacobi preconditioner as right preconditioner
   % with relative tolerance 1.e-10 and a maximum of 100 iterations
   [x,flag,relres,iter,reshis] = petscSolveCRS(rowptr, colind, val, b, ...
        PETSC_KSPBCGS, 1.e-10, int32(100), PETSC_PCJACOBI, 'right');

   % Solve using SuperLU as a direct solver (assuming SuperLU is installed)
   [x,flag,relres,iter,reshis] = petscSolveCRS(rowptr, colind, val, b, ...
        PETSC_KSPPREONLY, 0, int32(0), PETSC_PCLU, PETSC_MATSOLVERSUPERLU);

The top-level functions use the low-level PETSc function along with some basic MATLAB/Octave features.

TRYING OUT PETSC4M

Petsc4m is a very complicated piece of software with many dependencies. The easiest way to try it out is to use the Jupyter Notebook through Docker. It offers a very convenient way to try out different solvers in PETSc.

There are three simple steps to set it up:

• Make sure you have Python and Docker installed on your computer
• Download [petsc-notebook.ipynb](petsc-notebook](http://github.com/fastsolve/petsc4m/petsc-notebook.ipynb) and save it into a working directory
• Download petsc-jupyter.py and save it into your working directory

Now, you can run the Notebook by issuing the command:

petsc-jupyter.py petsc-notebook.ipynb

NAMING AND NUMBERING CONVENTIONS

Top-Level Functions

The top-level functions in Petsc4m have the prefix petsc, and are all in the Petsc4m root directory. The array indices of top-level functions are 1-based. The character strings for the top-level functions do not need to be null-terminated. These are consistent with the convention of MATLAB/Octave.

For most users, petscSolve and petscSolveCRS are the only two function you need to use. The former uses Octave's built-in sparse matrix format, and the latter uses the CRS format stored in three different arrays: row_ptr, col_ind, and val.

Low-Level Functions

The low-level functions in Petsc4m allow accessing virtually all features of PETSc in MATLAB. The indices for all low-level functions are 0-based, and all the strings must be null-terminated.

There are three types of low-level functions in Petsc4m.

• PETSc Functions: All functions have prefix petsc, such as petscMatCreate.
• PETSc Constants: All constants have prefix PETSC_, such as PETSC_COMM_WORLD.
• PETSc Data Types: All data types in Petsc4m have prefix Petsc, such as PetscMat, PetscVec, PetscKSP, etc. The first two types are useful for all users. The third types are for internal use.

When specifying KSPType, PCType, MatType, VecType, etc., it is the best to use the constants defined by Petsc4m instead of using character strings directly. These constants have the prefix PETSC_KSP, PETSC_PC, PETSC_MAT, and PETSC_VEC respectively. These names are all null-terminated strings, so you do not need to worry about null-terminating them manually.

The functions for Mat, Vec, KSP, and PC are all located in the sub-directory Mat/, Vec/, KSP/, and PC/, respectively. Most of these functions do not need to be used directly, except for the APIs for creating and destroying them. The other functions are helpful for prototyping new algorithms or experimenting with different matrix formats in PETSc.

The functions related to initialization, finalization, and options are in the sys/ subdirectory.

Basic MPI Functions

Petsc4m uses a few basic MPI functions provided by ParaCoder, including

   mpi_Init
   mpi_Initialized
   mpi_Comm_size
   mpi_Comm_rank
   mpi_Barrier
   mpi_Finalize
   mpi_Finalized

Additional MPI features are available through ParaCoder.

NOTES ON PETSC4M IN MATLAB

When using MATLAB, it is important for you to preset PETSC_DIR and also set LD_PRELOAD=/path/to/blas/libblas.so:/path/to/lapack/liblapack.so to prevent MATLAB from overriding the BLAS and LAPACK libraries used by PETSc and its third-party modules. In addition, use matlab -nojvm to prevent random crashing due to some apparent conflict between PETSc and Java.

LIMITATIONS

Virtually all features in PETSc are available through Petsc4m. However, Petsc4m does not support KSPRegister and PCRegister, so you cannot use Petsc4m to implement new solvers or preconditioners for PETSc.