The Pardiso.jl package provides an interface for using PARDISO 5.0 from the Julia language. You cannot use Pardiso.jl without having a valid license for PARDISO. This package is available free of charge and in no way replaces or alters any functionality of PARDISO.
Notes: This package does currently not support MKL's PARDISO solver.
Pardiso.jl expects the following libraries to be loadable from within Julia with dlopen.
libpardiso.so- The PARDISO library.libgfortran.so- The gfortran library. Should correspond to the same version as PARDISO is compiled against.libgomp.so- Library for OpenMP
Pardiso.jl has currently only been tested to work on Linux.
This section will explain how to use solve equations using Pardiso.jl with the default settings of the library. For more advanced usage there is a section further down.
The matrix type (default 11) should be set before calling the solve functions. This is done with set_mtype(key) where the key has the following meaning:
| key | Matrix type |
|---|---|
| 1 | real and structurally symmetric |
| 2 | real and symmetric positive definite |
| -2 | real and symmetric indefinite |
| 3 | complex and structurally symmetric |
| 4 | complex and Hermitian positive definite |
| -4 | complex and Hermitian indefinite |
| 6 | complex and symmetric |
| 11 | real and nonsymmetric |
| 13 | complex and nonsymmetric |
The number of processors to use is set by defining the environment variable OMP_NUM_THREADS before loading the package. If this variable does not exist, the number of cores on the machine will be used.
Four different versions are provided. The syntax now is not very beautiful but they are currently named this way to be similar to the Julia Base versions.
pA_ldiv_B!(X, A, B)solvesAX = Band stores the result inX.pA_ldiv_B(A, B)solvesAX = Band returns a newly allocatedX.pAt_ldiv_B!(X, A, B)solvesA^T X = Band stores the result inX.pAt_ldiv_B(A, B)solvesA^T X = Band returns a newly allocatedX.
For terminology in this section please refer to the PARDISO manual.
Pardiso.jl operates like a state machine where the properties of the solver is set before the call to the solve functions. After the solve function has completed, different types of data can be extracted.
PARDISO supports direct and iterative solvers. The solver is set with set_solver(key) where the key has the following meaning:
| key | Solver |
|---|---|
| 0 | sparse direct solver |
| 1 | multi-recursive iterative solver |
Depending on the phase calls to pardiso does different things. The phase is set with set_phase(key::Int) where key has the meaning:
| key | Solver Execution Steps |
|---|---|
| 11 | Analysis |
| 12 | Analysis, numerical factorization |
| 13 | Analysis, numerical factorization, solve, iterative refinement |
| 22 | Numerical factorization |
| -22 | Selected Inversion |
| 23 | Numerical factorization, solve, iterative refinement |
| 33 | Solve, iterative refinement |
| 0 | Release internal memory for L and U matrix number MNUM |
| -1 | Release all internal memory for all matrices |
Advanced users might want to explicitly set and retrieve the DPARM and IPARM settings.
This can be done with the getters get_iparm(), get_dparm() and the setters set_iparm(v::Int, i::Int), set_dparm(v::FloatingPoint, i::Int), where the first argument is the value to set and the second is the index at which to set it.
To set the default values of IPARM and DPARM for a given matrix type and solver call init_pardiso().
When setting IPARM and DPARM explicitly, calls should now be made directly to
pardiso(X, A, B)
which will not modify the IPARM and DPARM values.
If you have suggestions or idea of improving this package, please file an issue or even better, create a PR!