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// Math.NET Numerics, part of the Math.NET Project
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using System;
using System.Collections.Generic;
using System.Linq;
using IStation.Numerics.LinearAlgebra.Solvers;

namespace IStation.Numerics.LinearAlgebra.Single.Solvers
{
    /// <summary>
    /// A composite matrix solver. The actual solver is made by a sequence of
    /// matrix solvers.
    /// </summary>
    /// <remarks>
    /// <para>
    /// Solver based on:<br />
    /// Faster PDE-based simulations using robust composite linear solvers<br />
    /// S. Bhowmicka, P. Raghavan a,*, L. McInnes b, B. Norris<br />
    /// Future Generation Computer Systems, Vol 20, 2004, pp 373�387<br />
    /// </para>
    /// <para>
    /// Note that if an iterator is passed to this solver it will be used for all the sub-solvers.
    /// </para>
    /// </remarks>
    public sealed class CompositeSolver : IIterativeSolver<float>
    {
        /// <summary>
        /// The collection of solvers that will be used
        /// </summary>
        readonly List<Tuple<IIterativeSolver<float>, IPreconditioner<float>>> _solvers;

        public CompositeSolver(IEnumerable<IIterativeSolverSetup<float>> solvers)
        {
            _solvers = solvers.Select(setup => new Tuple<IIterativeSolver<float>, IPreconditioner<float>>(setup.CreateSolver(), setup.CreatePreconditioner() ?? new UnitPreconditioner<float>())).ToList();
        }

        /// <summary>
        /// Solves the matrix equation Ax = b, where A is the coefficient matrix, b is the
        /// solution vector and x is the unknown vector.
        /// </summary>
        /// <param name="matrix">The coefficient matrix, <c>A</c>.</param>
        /// <param name="input">The solution vector, <c>b</c></param>
        /// <param name="result">The result vector, <c>x</c></param>
        /// <param name="iterator">The iterator to use to control when to stop iterating.</param>
        /// <param name="preconditioner">The preconditioner to use for approximations.</param>
        public void Solve(Matrix<float> matrix, Vector<float> input, Vector<float> result, Iterator<float> iterator, IPreconditioner<float> preconditioner)
        {
            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException("Matrix must be square.", nameof(matrix));
            }

            if (result.Count != input.Count)
            {
                throw new ArgumentException("All vectors must have the same dimensionality.");
            }

            if (iterator == null)
            {
                iterator = new Iterator<float>();
            }

            if (preconditioner == null)
            {
                preconditioner = new UnitPreconditioner<float>();
            }

            // Create a copy of the solution and result vectors so we can use them
            // later on
            var internalInput = input.Clone();
            var internalResult = result.Clone();

            foreach (var solver in _solvers)
            {
                // Store a reference to the solver so we can stop it.

                IterationStatus status;
                try
                {
                    // Reset the iterator and pass it to the solver
                    iterator.Reset();

                    // Start the solver
                    solver.Item1.Solve(matrix, internalInput, internalResult, iterator, solver.Item2 ?? preconditioner);
                    status = iterator.Status;
                }
                catch (Exception)
                {
                    // The solver broke down.
                    // Log a message about this
                    // Switch to the next preconditioner.
                    // Reset the solution vector to the previous solution
                    input.CopyTo(internalInput);
                    continue;
                }

                // There was no fatal breakdown so check the status
                if (status == IterationStatus.Converged)
                {
                    // We're done
                    internalResult.CopyTo(result);
                    break;
                }

                // We're not done
                // Either:
                // - calculation finished without convergence
                if (status == IterationStatus.StoppedWithoutConvergence)
                {
                    // Copy the internal result to the result vector and
                    // continue with the calculation.
                    internalResult.CopyTo(result);
                }
                else
                {
                    // - calculation failed --> restart with the original vector
                    // - calculation diverged --> restart with the original vector
                    // - Some unknown status occurred --> To be safe restart.
                    input.CopyTo(internalInput);
                }
            }
        }
    }
}