PolySolve¶
This library contains a cross-platform Eigen wrapper for many different external linear solvers including (but not limited to):
- CHOLMOD
- Hypre
- AMGCL
- Pardiso
Example Usage¶
```c++ const std::string solver_name = “Hypre” auto solver = LinearSolver::create(solver_name, “”);
// Configuration parameters like iteration or accuracy for iterative solvers // solver->setParameters(params);
// System sparse matrix
Eigen::SparseMatrix
// Right-hand side Eigen::VectorXd b;
// Solution Eigen::VectorXd x(b.size());
solver->analyzePattern(A, A.rows()); solver->factorize(A); solver->solve(b, x); ```
You can use LinearSolver::availableSolvers() to obtain the list of available solvers.
Parameters¶
Polysolve uses a JSON file to provide parameters to the individual solvers. The following template can be used as a starting point, and a more detailed explanation of the parameters is below.
json
{
"Eigen::LeastSquaresConjugateGradient": {
"max_iter": 1000,
"tolerance": 1e-6
},
"Eigen::DGMRES": {
"max_iter": 1000,
"tolerance": 1e-6
},
"Eigen::ConjugateGradient": {
"max_iter": 1000,
"tolerance": 1e-6
},
"Eigen::BiCGSTAB": {
"max_iter": 1000,
"tolerance": 1e-6
},
"Eigen::GMRES": {
"max_iter": 1000,
"tolerance": 1e-6
},
"Eigen::MINRES": {
"max_iter": 1000,
"tolerance": 1e-6
},
"Pardiso": {
"mtype": -1
},
"Hypre": {
"max_iter": 1000,
"pre_max_iter": 1000,
"tolerance": 1e-6
},
"AMGCL": {
"precond": {
"relax": {
"degree": 16,
"type": "chebyshev",
"power_iters": 100,
"higher": 2,
"lower": 0.008333333333,
"scale": true
},
"class": "amg",
"max_levels": 6,
"direct_coarse": false,
"ncycle": 2,
"coarsening": {
"type": "smoothed_aggregation",
"estimate_spectral_radius": true,
"relax": 1,
"aggr": {
"eps_strong": 0
}
}
},
"solver": {
"tol": 1e-10,
"maxiter": 1000,
"type": "cg"
}
}
}
Iterative solvers (AMGCL, Eigen Internal Solvers, HYPRE)¶
max_itercontrols the solver’s iterations, default1000conv_tol,tolerancecontrols the convergence tolerance, default1e-10
Hypre Only¶
pre_max_iter, number of pre iterations, default1
AMGCL Only¶
The default parameters of the AMGCL solver are:
json
{
"precond": {
"relax": {
"degree": 16,
"type": "chebyshev",
"power_iters": 100,
"higher": 2,
"lower": 0.008333333333,
"scale": true
},
"class": "amg",
"max_levels": 6,
"direct_coarse": false,
"ncycle": 2,
"coarsening": {
"type": "smoothed_aggregation",
"estimate_spectral_radius": true,
"relax": 1,
"aggr": {
"eps_strong": 0
}
}
},
"solver": {
"tol": 1e-10,
"maxiter": 1000,
"type": "cg"
}
}
For a more details and options refer to the AMGCL documentation.
Pardiso¶
mtype, sets the matrix type, default 11
| mtype | Description |
|---|---|
| 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 |