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

const std::string solver_name = "Hypre"
auto solver = Solver::create(solver_name, "");

// Configuration parameters like iteration or accuracy for iterative solvers
// solver->set_parameters(params);

// System sparse matrix
Eigen::SparseMatrix<double> A;

// Right-hand side
Eigen::VectorXd b;

// Solution
Eigen::VectorXd x(b.size());

solver->analyze_pattern(A, A.rows());
solver->factorize(A);
solver->solve(b, x);

You can use Solver::available_solvers() 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 points, and a more detailed explanation of the parameters is below.

{
    "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_iter controls the solver's iterations, default 1000
• conv_tol, tolerance controls the convergence tolerance, default 1e-10

Hypre Only

• pre_max_iter, number of pre iterations, default 1

AMGCL Only

The default parameters of the AMGCL solver are:

{
    "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 |

Troubleshooting

Compilation error: use of undeclared identifier 'SuiteSparse_config'

This error is cause by having a more recent version of SuiteSparse (≥ v7.0.0) installed on your system than the version we download and build. We use @sergiud's fork of SuiteSparse which includes CMake support. However, the fork is not up to date with the latest version of SuiteSparse (currently v5.12.0 while the official release is at version v7.0.1). Version v7.0.0 changed the SuiteSparse_config.h header and no longer includes the necessary struct definitions.

Solution

For now, if you can, please downgrade (< v7.0.0) or uninstall your system version of SuiteSparse. In the meantime, we will work with the SuiteSparse developers to resolve this issue.