LinearSystem.cpp

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*/
 
#include "LinearSystem.hpp"
 
#include <iostream>
#include <cassert>
#include <algorithm>
#include <boost/scoped_array.hpp>
 
#include "PetscException.hpp"
#include "OutputFileHandler.hpp"
#include "PetscTools.hpp"
#include "HeartEventHandler.hpp"
#include "Timer.hpp"
#include "Warnings.hpp"
 
// Implementation
 
LinearSystem::LinearSystem(PetscInt lhsVectorSize, unsigned rowPreallocation)
   :mPrecondMatrix(nullptr),
    mSize(lhsVectorSize),
    mMatNullSpace(nullptr),
    mDestroyMatAndVec(true),
    mKspIsSetup(false),
    mNonZerosUsed(0.0),
    mMatrixIsConstant(false),
    mTolerance(1e-6),
    mUseAbsoluteTolerance(false),
    mDirichletBoundaryConditionsVector(nullptr),
    mpBlockDiagonalPC(nullptr),
    mpLDUFactorisationPC(nullptr),
    mpTwoLevelsBlockDiagonalPC(nullptr),
    mpBathNodes( boost::shared_ptr<std::vector<PetscInt> >() ),
    mPrecondMatrixIsNotLhs(false),
    mRowPreallocation(rowPreallocation),
    mUseFixedNumberIterations(false),
    mEvaluateNumItsEveryNSolves(UINT_MAX),
    mpConvergenceTestContext(nullptr),
    mEigMin(DBL_MAX),
    mEigMax(DBL_MIN),
    mForceSpectrumReevaluation(false)
{
    assert(lhsVectorSize > 0);
    if (mRowPreallocation == UINT_MAX)
    {
        // Automatic preallocation if it's a small matrix
        if (lhsVectorSize<15)
        {
            mRowPreallocation=lhsVectorSize;
        }
        else
        {
            EXCEPTION("You must provide a rowPreallocation argument for a large sparse system");
        }
    }
 
    mRhsVector = PetscTools::CreateVec(mSize);
    PetscTools::SetupMat(mLhsMatrix, mSize, mSize, mRowPreallocation, PETSC_DECIDE, PETSC_DECIDE);
 
    VecGetOwnershipRange(mRhsVector, &mOwnershipRangeLo, &mOwnershipRangeHi);
 
    mKspType = "gmres";
    mPcType = "jacobi";
 
    mNumSolves = 0;
#ifdef TRACE_KSP
    mTotalNumIterations = 0;
    mMaxNumIterations = 0;
#endif
}
 
LinearSystem::LinearSystem(PetscInt lhsVectorSize, Mat lhsMatrix, Vec rhsVector)
   :mPrecondMatrix(nullptr),
    mSize(lhsVectorSize),
    mMatNullSpace(nullptr),
    mDestroyMatAndVec(true),
    mKspIsSetup(false),
    mNonZerosUsed(0.0),
    mMatrixIsConstant(false),
    mTolerance(1e-6),
    mUseAbsoluteTolerance(false),
    mDirichletBoundaryConditionsVector(nullptr),
    mpBlockDiagonalPC(nullptr),
    mpLDUFactorisationPC(nullptr),
    mpTwoLevelsBlockDiagonalPC(nullptr),
    mpBathNodes( boost::shared_ptr<std::vector<PetscInt> >() ),
    mPrecondMatrixIsNotLhs(false),
    mUseFixedNumberIterations(false),
    mEvaluateNumItsEveryNSolves(UINT_MAX),
    mpConvergenceTestContext(nullptr),
    mEigMin(DBL_MAX),
    mEigMax(DBL_MIN),
    mForceSpectrumReevaluation(false)
{
    assert(lhsVectorSize > 0);
    // Conveniently, PETSc Mats and Vecs are actually pointers
    mLhsMatrix = lhsMatrix;
    mRhsVector = rhsVector;
 
    VecGetOwnershipRange(mRhsVector, &mOwnershipRangeLo, &mOwnershipRangeHi);
 
    mNumSolves = 0;
#ifdef TRACE_KSP
    mTotalNumIterations = 0;
    mMaxNumIterations = 0;
#endif
}
 
LinearSystem::LinearSystem(Vec templateVector, unsigned rowPreallocation, bool newAllocationError)
   :mPrecondMatrix(nullptr),
    mMatNullSpace(nullptr),
    mDestroyMatAndVec(true),
    mKspIsSetup(false),
    mMatrixIsConstant(false),
    mTolerance(1e-6),
    mUseAbsoluteTolerance(false),
    mDirichletBoundaryConditionsVector(nullptr),
    mpBlockDiagonalPC(nullptr),
    mpLDUFactorisationPC(nullptr),
    mpTwoLevelsBlockDiagonalPC(nullptr),
    mpBathNodes( boost::shared_ptr<std::vector<PetscInt> >() ),
    mPrecondMatrixIsNotLhs(false),
    mRowPreallocation(rowPreallocation),
    mUseFixedNumberIterations(false),
    mEvaluateNumItsEveryNSolves(UINT_MAX),
    mpConvergenceTestContext(nullptr),
    mEigMin(DBL_MAX),
    mEigMax(DBL_MIN),
    mForceSpectrumReevaluation(false)
{
    VecDuplicate(templateVector, &mRhsVector);
    VecGetSize(mRhsVector, &mSize);
    VecGetOwnershipRange(mRhsVector, &mOwnershipRangeLo, &mOwnershipRangeHi);
    PetscInt local_size = mOwnershipRangeHi - mOwnershipRangeLo;
 
    PetscTools::SetupMat(mLhsMatrix, mSize, mSize, mRowPreallocation, local_size, local_size, true, newAllocationError);
 
    mKspType = "gmres";
    mPcType = "jacobi";
 
    mNumSolves = 0;
#ifdef TRACE_KSP
    mTotalNumIterations = 0;
    mMaxNumIterations = 0;
#endif
}
 
LinearSystem::LinearSystem(Vec residualVector, Mat jacobianMatrix)
   :mPrecondMatrix(nullptr),
    mMatNullSpace(nullptr),
    mDestroyMatAndVec(false),
    mKspIsSetup(false),
    mMatrixIsConstant(false),
    mTolerance(1e-6),
    mUseAbsoluteTolerance(false),
    mDirichletBoundaryConditionsVector(nullptr),
    mpBlockDiagonalPC(nullptr),
    mpLDUFactorisationPC(nullptr),
    mpTwoLevelsBlockDiagonalPC(nullptr),
    mpBathNodes( boost::shared_ptr<std::vector<PetscInt> >() ),
    mPrecondMatrixIsNotLhs(false),
    mRowPreallocation(UINT_MAX),
    mUseFixedNumberIterations(false),
    mEvaluateNumItsEveryNSolves(UINT_MAX),
    mpConvergenceTestContext(nullptr),
    mEigMin(DBL_MAX),
    mEigMax(DBL_MIN),
    mForceSpectrumReevaluation(false)
{
    assert(residualVector || jacobianMatrix);
    mRhsVector = residualVector;
    mLhsMatrix = jacobianMatrix;
 
    PetscInt mat_size=0, vec_size=0;
    if (mRhsVector)
    {
        VecGetSize(mRhsVector, &vec_size);
        mSize = (unsigned)vec_size;
        VecGetOwnershipRange(mRhsVector, &mOwnershipRangeLo, &mOwnershipRangeHi);
    }
    if (mLhsMatrix)
    {
        PetscInt mat_cols;
        MatGetSize(mLhsMatrix, &mat_size, &mat_cols);
        assert(mat_size == mat_cols);
        mSize = (unsigned)mat_size;
        MatGetOwnershipRange(mLhsMatrix, &mOwnershipRangeLo, &mOwnershipRangeHi);
 
        MatInfo matrix_info;
        MatGetInfo(mLhsMatrix, MAT_GLOBAL_MAX, &matrix_info);
 
        /*
         * Assuming that mLhsMatrix was created with PetscTools::SetupMat, the value
         * below should be equivalent to what was used as preallocation in that call.
         */
        mRowPreallocation = (unsigned) matrix_info.nz_allocated / mSize;
    }
    assert(!mRhsVector || !mLhsMatrix || vec_size == mat_size);
 
    mKspType = "gmres";
    mPcType = "jacobi";
 
    mNumSolves = 0;
#ifdef TRACE_KSP
    mTotalNumIterations = 0;
    mMaxNumIterations = 0;
#endif
}
 
LinearSystem::~LinearSystem()
{
    delete mpBlockDiagonalPC;
    delete mpLDUFactorisationPC;
    delete mpTwoLevelsBlockDiagonalPC;
 
    if (mDestroyMatAndVec)
    {
        PetscTools::Destroy(mRhsVector);
        PetscTools::Destroy(mLhsMatrix);
    }
 
    if (mPrecondMatrixIsNotLhs)
    {
        PetscTools::Destroy(mPrecondMatrix);
    }
 
    if (mMatNullSpace)
    {
        MatNullSpaceDestroy(PETSC_DESTROY_PARAM(mMatNullSpace));
    }
 
    if (mKspIsSetup)
    {
        KSPDestroy(PETSC_DESTROY_PARAM(mKspSolver));
    }
 
    if (mDirichletBoundaryConditionsVector)
    {
        PetscTools::Destroy(mDirichletBoundaryConditionsVector);
    }
 
#if (PETSC_VERSION_MAJOR == 3) //PETSc 3.x.x
    if (mpConvergenceTestContext)
    {
#if (PETSC_VERSION_MINOR >= 5) //PETSc 3.5 or later
        KSPConvergedDefaultDestroy(mpConvergenceTestContext);
#else
        KSPDefaultConvergedDestroy(mpConvergenceTestContext);
#endif
    }
#endif
 
#ifdef TRACE_KSP
    if (PetscTools::AmMaster())
    {
        if (mNumSolves > 0)
        {
            double ave_num_iterations = mTotalNumIterations/(double)mNumSolves;
 
            std::cout << std::endl << "KSP iterations report:" << std::endl;
            std::cout << "mNumSolves" << "\t" << "mTotalNumIterations" << "\t" << "mMaxNumIterations" << "\t" << "mAveNumIterations" << std::endl;
            std::cout << mNumSolves << "\t" << mTotalNumIterations << "\t" << mMaxNumIterations << "\t" << ave_num_iterations << std::endl;
        }
    }
#endif
}
 
void LinearSystem::SetMatrixElement(PetscInt row, PetscInt col, double value)
{
    PetscMatTools::SetElement(mLhsMatrix, row, col, value);
}
 
void LinearSystem::AddToMatrixElement(PetscInt row, PetscInt col, double value)
{
    PetscMatTools::AddToElement(mLhsMatrix, row, col, value);
}
 
void LinearSystem::AssembleFinalLinearSystem()
{
    FinaliseLhsMatrix();
    FinaliseRhsVector();
}
 
void LinearSystem::AssembleIntermediateLinearSystem()
{
    SwitchWriteModeLhsMatrix();
    FinaliseRhsVector();
}
 
void LinearSystem::FinaliseLhsMatrix()
{
    PetscMatTools::Finalise(mLhsMatrix);
}
 
void LinearSystem::SwitchWriteModeLhsMatrix()
{
    PetscMatTools::SwitchWriteMode(mLhsMatrix);
}
 
void LinearSystem::FinalisePrecondMatrix()
{
    PetscMatTools::Finalise(mPrecondMatrix);
}
 
void LinearSystem::FinaliseRhsVector()
{
    PetscVecTools::Finalise(mRhsVector);
}
 
void LinearSystem::SetRhsVectorElement(PetscInt row, double value)
{
    PetscVecTools::SetElement(mRhsVector, row, value);
}
 
void LinearSystem::AddToRhsVectorElement(PetscInt row, double value)
{
    PetscVecTools::AddToElement(mRhsVector, row, value);
}
 
void LinearSystem::DisplayMatrix()
{
    PetscMatTools::Display(mLhsMatrix);
}
 
void LinearSystem::DisplayRhs()
{
    PetscVecTools::Display(mRhsVector);
}
 
void LinearSystem::SetMatrixRow(PetscInt row, double value)
{
    PetscMatTools::SetRow(mLhsMatrix, row, value);
}
 
Vec LinearSystem::GetMatrixRowDistributed(unsigned rowIndex)
{
    return PetscMatTools::GetMatrixRowDistributed(mLhsMatrix, rowIndex);
}
 
void LinearSystem::ZeroMatrixRowsWithValueOnDiagonal(std::vector<unsigned>& rRows, double diagonalValue)
{
    PetscMatTools::ZeroRowsWithValueOnDiagonal(mLhsMatrix, rRows, diagonalValue);
}
 
void LinearSystem::ZeroMatrixRowsAndColumnsWithValueOnDiagonal(std::vector<unsigned>& rRowColIndices, double diagonalValue)
{
    PetscMatTools::ZeroRowsAndColumnsWithValueOnDiagonal(mLhsMatrix, rRowColIndices, diagonalValue);
}
 
void LinearSystem::ZeroMatrixColumn(PetscInt col)
{
    PetscMatTools::ZeroColumn(mLhsMatrix, col);
}
 
void LinearSystem::ZeroRhsVector()
{
    PetscVecTools::Zero(mRhsVector);
}
 
void LinearSystem::ZeroLhsMatrix()
{
    PetscMatTools::Zero(mLhsMatrix);
}
 
void LinearSystem::ZeroLinearSystem()
{
    ZeroRhsVector();
    ZeroLhsMatrix();
}
 
unsigned LinearSystem::GetSize() const
{
    return (unsigned) mSize;
}
 
void LinearSystem::SetNullBasis(Vec nullBasis[], unsigned numberOfBases)
{
#ifndef NDEBUG
    // Check all the vectors of the base are normal
    for (unsigned vec_index=0; vec_index<numberOfBases; vec_index++)
    {
        PetscReal l2_norm;
        VecNorm(nullBasis[vec_index], NORM_2, &l2_norm);
        if (fabs(l2_norm-1.0) > 1e-08)
        {
            EXCEPTION("One of the vectors in the null space is not normalised");
        }
    }
 
    // Check all the vectors of the base are orthogonal
    for (unsigned vec_index=1; vec_index<numberOfBases; vec_index++)
    {
        // The strategy is to check the (i-1)-th vector against vectors from i to n with VecMDot. This should be the most efficient way of doing it.
        unsigned num_vectors_ahead = numberOfBases-vec_index;
        boost::scoped_array<PetscScalar> dot_products(new PetscScalar[num_vectors_ahead]);
#if (PETSC_VERSION_MAJOR == 2 && PETSC_VERSION_MINOR == 2) //PETSc 2.2
        VecMDot(num_vectors_ahead, nullBasis[vec_index-1], &nullBasis[vec_index], dot_products.get());
#else
        VecMDot(nullBasis[vec_index-1], num_vectors_ahead, &nullBasis[vec_index], dot_products.get());
#endif
        for (unsigned index=0; index<num_vectors_ahead; index++)
        {
            if (fabs(dot_products[index]) > 1e-08 )
            {
                EXCEPTION("The null space is not orthogonal.");
            }
        }
    }
 
#endif
 
    PETSCEXCEPT( MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_FALSE, numberOfBases, nullBasis, &mMatNullSpace) );
}
 
void LinearSystem::RemoveNullSpace()
{
    // Only remove if previously set
    if (mMatNullSpace)
    {
        PETSCEXCEPT( MatNullSpaceDestroy(PETSC_DESTROY_PARAM(mMatNullSpace)) );
        PETSCEXCEPT( MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_FALSE, 0, nullptr, &mMatNullSpace) );
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 3) //PETSc 3.3 or later
        // Setting null space in the KSP was deprecated in PETSc 3.6, but setting the null space
        // for the matrix appeared in PETSc 3.3 so 3.3, 3.4, 3.5 can do either
        PETSCEXCEPT( MatSetNullSpace(mLhsMatrix, mMatNullSpace) );
        /* This is heavy-handed:
         * Changing the Null-space appears to only work if we reset the KSP
         * Adding null-space to the matrix has to happen *before* KSPSetOperators
         */
        ResetKspSolver();
#else
        if (mKspIsSetup)
        {
            PETSCEXCEPT( KSPSetNullSpace(mKspSolver, mMatNullSpace) );
        }
        //else: it will be set next time Solve() is called
#endif
    }
}
 
void LinearSystem::GetOwnershipRange(PetscInt& lo, PetscInt& hi)
{
    lo = mOwnershipRangeLo;
    hi = mOwnershipRangeHi;
}
 
double LinearSystem::GetMatrixElement(PetscInt row, PetscInt col)
{
    return PetscMatTools::GetElement(mLhsMatrix, row, col);
}
 
double LinearSystem::GetRhsVectorElement(PetscInt row)
{
    return PetscVecTools::GetElement(mRhsVector, row);
}
 
unsigned LinearSystem::GetNumIterations() const
{
    assert(this->mKspIsSetup);
 
    PetscInt num_its;
    KSPGetIterationNumber(this->mKspSolver, &num_its);
 
    return (unsigned) num_its;
}
 
Vec& LinearSystem::rGetRhsVector()
{
    return mRhsVector;
}
 
Vec LinearSystem::GetRhsVector() const
{
    return mRhsVector;
}
 
Mat& LinearSystem::rGetLhsMatrix()
{
    return mLhsMatrix;
}
 
Mat LinearSystem::GetLhsMatrix() const
{
    return mLhsMatrix;
}
 
Mat& LinearSystem::rGetPrecondMatrix()
{
    if (!mPrecondMatrixIsNotLhs)
    {
        EXCEPTION("LHS matrix used for preconditioner construction");
    }
 
    return mPrecondMatrix;
}
 
Vec& LinearSystem::rGetDirichletBoundaryConditionsVector()
{
    return mDirichletBoundaryConditionsVector;
}
 
void LinearSystem::SetMatrixIsSymmetric(bool isSymmetric)
{
 
    if (isSymmetric)
    {
        PetscMatTools::SetOption(mLhsMatrix, MAT_SYMMETRIC);
        PetscMatTools::SetOption(mLhsMatrix, MAT_SYMMETRY_ETERNAL);
    }
    else
    {
// don't have a PetscMatTools method for setting options to false
#if (PETSC_VERSION_MAJOR == 3) //PETSc 3.x.x
        MatSetOption(mLhsMatrix, MAT_SYMMETRIC, PETSC_FALSE);
        MatSetOption(mLhsMatrix, MAT_STRUCTURALLY_SYMMETRIC, PETSC_FALSE);
        MatSetOption(mLhsMatrix, MAT_SYMMETRY_ETERNAL, PETSC_FALSE);
#else
        MatSetOption(mLhsMatrix, MAT_NOT_SYMMETRIC);
        MatSetOption(mLhsMatrix, MAT_NOT_STRUCTURALLY_SYMMETRIC);
        MatSetOption(mLhsMatrix, MAT_NOT_SYMMETRY_ETERNAL);
#endif
    }
}
 
bool LinearSystem::IsMatrixSymmetric()
{
    PetscBool symmetry_flag_is_set;
    PetscBool symmetry_flag;
 
    MatIsSymmetricKnown(mLhsMatrix, &symmetry_flag_is_set, &symmetry_flag);
 
    // If the flag is not set we assume is a non-symmetric matrix
    return symmetry_flag_is_set && symmetry_flag;
}
 
void LinearSystem::SetMatrixIsConstant(bool matrixIsConstant)
{
    mMatrixIsConstant = matrixIsConstant;
}
 
void LinearSystem::SetRelativeTolerance(double relativeTolerance)
{
    mTolerance = relativeTolerance;
    mUseAbsoluteTolerance = false;
    if (mKspIsSetup)
    {
        KSPSetTolerances(mKspSolver, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);
    }
}
 
void LinearSystem::SetAbsoluteTolerance(double absoluteTolerance)
{
    mTolerance = absoluteTolerance;
    mUseAbsoluteTolerance = true;
    if (mKspIsSetup)
    {
        KSPSetTolerances(mKspSolver, DBL_EPSILON, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT);
    }
}
 
void LinearSystem::SetKspType(const char *kspType)
{
    mKspType = kspType;
    if (mKspIsSetup)
    {
        KSPSetType(mKspSolver, kspType);
        KSPSetFromOptions(mKspSolver);
    }
}
 
void LinearSystem::SetPcType(const char* pcType, boost::shared_ptr<std::vector<PetscInt> > pBathNodes)
{
    mPcType = pcType;
    mpBathNodes = pBathNodes;
 
    if (mKspIsSetup)
    {
        if (mPcType == "blockdiagonal")
        {
            // If the previous preconditioner was purpose-built we need to free the appropriate pointer.
            delete mpBlockDiagonalPC;
            mpBlockDiagonalPC = nullptr;
            delete mpLDUFactorisationPC;
            mpLDUFactorisationPC = nullptr;
            delete mpTwoLevelsBlockDiagonalPC;
            mpTwoLevelsBlockDiagonalPC = nullptr;
 
            mpBlockDiagonalPC = new PCBlockDiagonal(mKspSolver);
        }
        else if (mPcType == "ldufactorisation")
        {
            // If the previous preconditioner was purpose-built we need to free the appropriate pointer.
            delete mpBlockDiagonalPC;
            mpBlockDiagonalPC = nullptr;
            delete mpLDUFactorisationPC;
            mpLDUFactorisationPC = nullptr;
            delete mpTwoLevelsBlockDiagonalPC;
            mpTwoLevelsBlockDiagonalPC = nullptr;
 
            mpLDUFactorisationPC = new PCLDUFactorisation(mKspSolver);
        }
        else if (mPcType == "twolevelsblockdiagonal")
        {
            // If the previous preconditioner was purpose-built we need to free the appropriate pointer.
            delete mpBlockDiagonalPC;
            mpBlockDiagonalPC = nullptr;
            delete mpLDUFactorisationPC;
            mpLDUFactorisationPC = nullptr;
            delete mpTwoLevelsBlockDiagonalPC;
            mpTwoLevelsBlockDiagonalPC = nullptr;
 
            if (!mpBathNodes)
            {
                TERMINATE("You must provide a list of bath nodes when using TwoLevelsBlockDiagonalPC"); // LCOV_EXCL_LINE
            }
            mpTwoLevelsBlockDiagonalPC = new PCTwoLevelsBlockDiagonal(mKspSolver, *mpBathNodes);
        }
        else
        {
            PC prec;
            KSPGetPC(mKspSolver, &prec);
            PCSetType(prec, pcType);
        }
        KSPSetFromOptions(mKspSolver);
    }
}
 
Vec LinearSystem::Solve(Vec lhsGuess)
{
    /*
     * The following lines are very useful for debugging:
     *    MatView(mLhsMatrix,    PETSC_VIEWER_STDOUT_WORLD);
     *    VecView(mRhsVector,    PETSC_VIEWER_STDOUT_WORLD);
     */
 
    // Double check that the non-zero pattern hasn't changed
    MatInfo mat_info;
    MatGetInfo(mLhsMatrix, MAT_GLOBAL_SUM, &mat_info);
 
    if (!mKspIsSetup)
    {
        // Create PETSc Vec that may be required if we use a Chebyshev solver
        Vec chebyshev_lhs_vector = nullptr;
 
        HeartEventHandler::BeginEvent(HeartEventHandler::COMMUNICATION);
        mNonZerosUsed=mat_info.nz_used;
        //MatNorm(mLhsMatrix, NORM_FROBENIUS, &mMatrixNorm);
        PC prec; //Type of pre-conditioner
 
        KSPCreate(PETSC_COMM_WORLD, &mKspSolver);
 
        if (mMatNullSpace) // Adding null-space to the matrix (new style) has to happen *before* KSPSetOperators
        {
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 3) //PETSc 3.3 or later
            // Setting null space in the KSP was deprecated in PETSc 3.6, but setting the null space
            // for the matrix appeared in PETSc 3.3 so 3.3, 3.4, 3.5 can do either
 
            PETSCEXCEPT(MatSetNullSpace(mLhsMatrix, mMatNullSpace));
#else
            PETSCEXCEPT(KSPSetNullSpace(mKspSolver, mMatNullSpace));
#endif
        }
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 5) //PETSc 3.5 or later
        // Do nothing.  Note that reusing the pre-conditioner in later PETSc versions is done after the pre-conditioner is formed
        // (This comment is retained here so that the #if logic is consistent.)
#else
        /*
         * The preconditioner flag (last argument) in the following calls says
         * how to reuse the preconditioner on subsequent iterations.
         */
        MatStructure preconditioner_over_successive_calls;
 
        if (mMatrixIsConstant)
        {
            preconditioner_over_successive_calls = SAME_PRECONDITIONER;
        }
        else
        {
            preconditioner_over_successive_calls = SAME_NONZERO_PATTERN;
        }
#endif
 
        if (mPrecondMatrixIsNotLhs)
        {
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 5) //PETSc 3.5 or later
            KSPSetOperators(mKspSolver, mLhsMatrix, mPrecondMatrix);
#else
            KSPSetOperators(mKspSolver, mLhsMatrix, mPrecondMatrix, preconditioner_over_successive_calls);
#endif
        }
        else
        {
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 5) //PETSc 3.5 or later
            KSPSetOperators(mKspSolver, mLhsMatrix, mLhsMatrix);
#else
            KSPSetOperators(mKspSolver, mLhsMatrix, mLhsMatrix, preconditioner_over_successive_calls);
#endif
        }
#if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR >= 5) //PETSc 3.5 or later
        if (mMatrixIsConstant)
        {
            // Emulate SAME_PRECONDITIONER as above
            KSPSetReusePreconditioner(mKspSolver, PETSC_TRUE);
        }
#endif
 
        // Set either absolute or relative tolerance of the KSP solver.
        // The default is to use relative tolerance (1e-6)
        if (mUseAbsoluteTolerance)
        {
            KSPSetTolerances(mKspSolver, DBL_EPSILON, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT);
        }
        else
        {
            KSPSetTolerances(mKspSolver, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);
        }
 
        // Set ksp and pc types
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 3) //PETSc 3.3 or later
        if (mKspType == "chebychev")
        {
            KSPSetType(mKspSolver, "chebyshev");
        }
        else
        {
            KSPSetType(mKspSolver, mKspType.c_str());
        }
#else
        KSPSetType(mKspSolver, mKspType.c_str());
#endif
        KSPGetPC(mKspSolver, &prec);
 
        // Turn off pre-conditioning if the system size is very small
        const bool is_small = (mSize <= 6); 
        if (is_small)
        {
            PCSetType(prec, PCNONE);
        }
        else
        {
#ifdef TRACE_KSP
            Timer::Reset();
#endif
            if (mPcType == "blockdiagonal")
            {
                mpBlockDiagonalPC = new PCBlockDiagonal(mKspSolver);
#ifdef TRACE_KSP
                if (PetscTools::AmMaster())
                {
                    Timer::Print("Purpose-build preconditioner creation");
                }
#endif
            }
            else if (mPcType == "ldufactorisation")
            {
                mpLDUFactorisationPC = new PCLDUFactorisation(mKspSolver);
#ifdef TRACE_KSP
                if (PetscTools::AmMaster())
                {
                    Timer::Print("Purpose-build preconditioner creation");
                }
#endif
            }
            else if (mPcType == "twolevelsblockdiagonal")
            {
                if (!mpBathNodes)
                {
                    TERMINATE("You must provide a list of bath nodes when using TwoLevelsBlockDiagonalPC"); // LCOV_EXCL_LINE
                }
                mpTwoLevelsBlockDiagonalPC = new PCTwoLevelsBlockDiagonal(mKspSolver, *mpBathNodes);
#ifdef TRACE_KSP
                if (PetscTools::AmMaster())
                {
                    Timer::Print("Purpose-build preconditioner creation");
                }
#endif
 
            }
            else
            {
                PCSetType(prec, mPcType.c_str());
            }
        }
 
        KSPSetFromOptions(mKspSolver);
 
        if (lhsGuess)
        {
            // Assume that the user of this method will always be kind enough to give us a reasonable guess.
            KSPSetInitialGuessNonzero(mKspSolver,PETSC_TRUE);
        }
        /*
         * Non-adaptive Chebyshev: the required spectrum approximation is computed just once
         * at the beginning of the simulation. This is done with two extra CG solves.
         */
        if (mKspType == "chebychev" && !mUseFixedNumberIterations)
        {
#ifdef TRACE_KSP
            Timer::Reset();
#endif
            // Preconditioned matrix spectrum is approximated with CG
            KSPSetType(mKspSolver,"cg");
            KSPSetComputeEigenvalues(mKspSolver, PETSC_TRUE);
            KSPSetUp(mKspSolver);
 
            VecDuplicate(mRhsVector, &chebyshev_lhs_vector);
            if (lhsGuess)
            {
                VecCopy(lhsGuess, chebyshev_lhs_vector);
            }
 
            // Smallest eigenvalue is approximated to default tolerance
            KSPSolve(mKspSolver, mRhsVector, chebyshev_lhs_vector);
 
            PetscReal *r_eig = new PetscReal[mSize];
            PetscReal *c_eig = new PetscReal[mSize];
            PetscInt eigs_computed;
            KSPComputeEigenvalues(mKspSolver, mSize, r_eig, c_eig, &eigs_computed);
 
            mEigMin = r_eig[0];
 
            // Largest eigenvalue is approximated to machine precision
            KSPSetTolerances(mKspSolver, DBL_EPSILON, DBL_EPSILON, PETSC_DEFAULT, PETSC_DEFAULT);
            KSPSetUp(mKspSolver);
            if (lhsGuess)
            {
                VecCopy(lhsGuess, chebyshev_lhs_vector);
            }
 
            KSPSolve(mKspSolver, mRhsVector, chebyshev_lhs_vector);
            KSPComputeEigenvalues(mKspSolver, mSize, r_eig, c_eig, &eigs_computed);
 
            mEigMax = r_eig[eigs_computed-1];
 
#ifdef TRACE_KSP
            /*
             * Under certain circumstances (see Golub&Overton 1988), underestimating
             * the spectrum of the preconditioned operator improves convergence rate.
             * See publication for a discussion and for definition of alpha and sigma_one.
             */
            if (PetscTools::AmMaster())
            {
                std::cout << "EIGS: ";
                for (int index=0; index<eigs_computed; index++)
                {
                    std::cout << r_eig[index] << ", ";
                }
                std::cout << std::endl;
            }
 
            if (PetscTools::AmMaster()) std::cout << "EIGS "<< mEigMax << " " << mEigMin <<std::endl;
            double alpha = 2/(mEigMax+mEigMin);
            double sigma_one = 1 - alpha*mEigMin;
            if (PetscTools::AmMaster()) std::cout << "sigma_1 = 1 - alpha*mEigMin = "<< sigma_one <<std::endl;
#endif
 
            // Set Chebyshev solver and max/min eigenvalues
            assert(mKspType == "chebychev");
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 3) //PETSc 3.3 or later
            KSPSetType(mKspSolver, "chebyshev");
            KSPChebyshevSetEigenvalues(mKspSolver, mEigMax, mEigMin);
#else
            KSPSetType(mKspSolver, mKspType.c_str());
            KSPChebychevSetEigenvalues(mKspSolver, mEigMax, mEigMin);
#endif
            KSPSetComputeEigenvalues(mKspSolver, PETSC_FALSE);
            if (mUseAbsoluteTolerance)
            {
                KSPSetTolerances(mKspSolver, DBL_EPSILON, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT);
            }
            else
            {
                KSPSetTolerances(mKspSolver, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);
            }
 
            delete[] r_eig;
            delete[] c_eig;
 
#ifdef TRACE_KSP
            if (PetscTools::AmMaster())
            {
                Timer::Print("Computing extremal eigenvalues");
            }
#endif
        }
 
#ifdef TRACE_KSP
        Timer::Reset();
#endif
 
        KSPSetUp(mKspSolver);
 
        if (chebyshev_lhs_vector)
        {
            PetscTools::Destroy(chebyshev_lhs_vector);
        }
 
#ifdef TRACE_KSP
        if (PetscTools::AmMaster())
        {
            Timer::Print("KSPSetUP (contains preconditioner creation for PETSc preconditioners)");
        }
#endif
 
        mKspIsSetup = true;
 
        HeartEventHandler::EndEvent(HeartEventHandler::COMMUNICATION);
    }
    else
    {
        if (mNonZerosUsed!=mat_info.nz_used)
        {
            WARNING("LinearSystem doesn't like the non-zero pattern of a matrix to change. (I think you changed it).");
            mNonZerosUsed = mat_info.nz_used;
        }
//        PetscScalar norm;
//        MatNorm(mLhsMatrix, NORM_FROBENIUS, &norm);
//        if (fabs(norm - mMatrixNorm) > 0)
//        {
//            EXCEPTION("LinearSystem doesn't allow the matrix norm to change");
//        }
    }
 
    HeartEventHandler::BeginEvent(HeartEventHandler::COMMUNICATION);
    // Create solution vector
    Vec lhs_vector;
    VecDuplicate(mRhsVector, &lhs_vector); // Sets the same size (doesn't copy)
    if (lhsGuess)
    {
        VecCopy(lhsGuess, lhs_vector);
        // If this wasn't done at construction time then it may be too late for this:
        // KSPSetInitialGuessNonzero(mKspSolver, PETSC_TRUE);
        // Is it possible to warn the user?
    }
 
    // Check if the right hand side is small (but non-zero), PETSc can diverge immediately
    // with a non-zero initial guess. Here we check for this and alter the initial guess to zero.
    PetscReal rhs_norm;
    VecNorm(mRhsVector, NORM_1, &rhs_norm);
    double rhs_zero_tol = 1e-15;
 
    if (rhs_norm < rhs_zero_tol && rhs_norm > 0.0)
    {
        WARNING("Using zero initial guess due to small right hand side vector");
        PetscVecTools::Zero(lhs_vector);
    }
 
    HeartEventHandler::EndEvent(HeartEventHandler::COMMUNICATION);
//    // Double check that the mRhsVector contains sensible values
//    double* p_rhs,* p_guess;
//    VecGetArray(mRhsVector, &p_rhs);
//    VecGetArray(lhsGuess, &p_guess);
//    for (int global_index=mOwnershipRangeLo; global_index<mOwnershipRangeHi; global_index++)
//    {
//        int local_index = global_index - mOwnershipRangeLo;
//        assert(!std::isnan(p_rhs[local_index]));
//        assert(!std::isnan(p_guess[local_index]));
//        if (p_rhs[local_index] != p_rhs[local_index])
//        {
//            std::cout << "********* PETSc nan\n";
//            assert(0);
//        }
//    }
//    std::cout << "b[0] = " << p_rhs[0] << ", guess[0] = " << p_guess[0] << "\n";
//    VecRestoreArray(mRhsVector, &p_rhs);
//    VecRestoreArray(lhsGuess, &p_guess);
//    // Test A*guess
//    Vec temp;
//    VecDuplicate(mRhsVector, &temp);
//    MatMult(mLhsMatrix, lhs_vector, temp);
//    double* p_temp;
//    VecGetArray(temp, &p_temp);
//    std::cout << "temp[0] = " << p_temp[0] << "\n";
//    VecRestoreArray(temp, &p_temp);
//    PetscTools::Destroy(temp);
//    // Dump the matrix to file
//    PetscViewer viewer;
//    PetscViewerASCIIOpen(PETSC_COMM_WORLD,"mat.output",&viewer);
//    MatView(mLhsMatrix, viewer);
//    PetscViewerFlush(viewer);
//    PetscViewerDestroy(PETSC_DESTROY_PARAM(viewer);
//    // Dump the rhs vector to file
//    PetscViewerASCIIOpen(PETSC_COMM_WORLD,"vec.output",&viewer);
//    PetscViewerSetFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
//    VecView(mRhsVector, viewer);
//    PetscViewerFlush(viewer);
//    PetscViewerDestroy(PETSC_DESTROY_PARAM(viewer);
 
    try
    {
        HeartEventHandler::BeginEvent(HeartEventHandler::SOLVE_LINEAR_SYSTEM);
 
#ifdef TRACE_KSP
        Timer::Reset();
#endif
 
        // Current solve has to be done with tolerance-based stop criteria in order to record iterations taken
        if (mUseFixedNumberIterations && (mNumSolves%mEvaluateNumItsEveryNSolves==0 || mForceSpectrumReevaluation))
        {
#if ((PETSC_VERSION_MAJOR == 2 && PETSC_VERSION_MINOR == 2) || (PETSC_VERSION_MAJOR == 2 && PETSC_VERSION_MINOR == 3 && PETSC_VERSION_SUBMINOR <= 2))
            KSPSetNormType(mKspSolver, KSP_PRECONDITIONED_NORM);
#else
            KSPSetNormType(mKspSolver, KSP_NORM_PRECONDITIONED);
#endif
 
#if (PETSC_VERSION_MAJOR == 3) //PETSc 3.x.x
            if (!mpConvergenceTestContext)
            {
    #if (PETSC_VERSION_MINOR >= 5) //PETSc 3.5 or later
                KSPConvergedDefaultCreate(&mpConvergenceTestContext);
    #else
                KSPDefaultConvergedCreate(&mpConvergenceTestContext);
    #endif
            }
    #if (PETSC_VERSION_MINOR >= 5) //PETSc 3.5 or later
            // From PETSc 3.5, KSPDefaultConverged became KSPConvergedDefault.
            KSPSetConvergenceTest(mKspSolver, KSPConvergedDefault, &mpConvergenceTestContext, CHASTE_PETSC_NULLPTR);
    #else
            KSPSetConvergenceTest(mKspSolver, KSPDefaultConverged, &mpConvergenceTestContext, CHASTE_PETSC_NULLPTR);
    #endif
 
#else
            KSPSetConvergenceTest(mKspSolver, KSPDefaultConverged, CHASTE_PETSC_NULLPTR);
#endif
 
            if (mUseAbsoluteTolerance)
            {
                KSPSetTolerances(mKspSolver, DBL_EPSILON, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT);
            }
            else
            {
                KSPSetTolerances(mKspSolver, mTolerance, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);
            }
 
            std::stringstream num_it_str;
            num_it_str << 1000;
            PetscTools::SetOption("-ksp_max_it", num_it_str.str().c_str());
 
            // Adaptive Chebyshev: reevaluate spectrum with cg
            if (mKspType == "chebychev")
            {
                // You can estimate preconditioned matrix spectrum with CG
                KSPSetType(mKspSolver,"cg");
                KSPSetComputeEigenvalues(mKspSolver, PETSC_TRUE);
            }
 
            KSPSetFromOptions(mKspSolver);
            KSPSetUp(mKspSolver);
        }
 
        PETSCEXCEPT(KSPSolve(mKspSolver, mRhsVector, lhs_vector));
        HeartEventHandler::EndEvent(HeartEventHandler::SOLVE_LINEAR_SYSTEM);
 
#ifdef TRACE_KSP
        PetscInt num_it;
        KSPGetIterationNumber(mKspSolver, &num_it);
        if (PetscTools::AmMaster())
        {
            std::cout << "++ Solve: " << mNumSolves << " NumIterations: " << num_it << " "; // don't add std::endl so we get Timer::Print output in the same line (better for grep-ing)
            Timer::Print("Solve");
        }
 
        mTotalNumIterations += num_it;
        if ((unsigned) num_it > mMaxNumIterations)
        {
            mMaxNumIterations = num_it;
        }
#endif
 
        // Check that solver converged and throw if not
        KSPConvergedReason reason;
        KSPGetConvergedReason(mKspSolver, &reason);
 
        if (mUseFixedNumberIterations && PETSC_VERSION_MAJOR < 3)
        {
            WARNING("Not explicitly checking convergence reason when using fixed number of iterations and PETSc 2");
        }
        else
        {
            KSPEXCEPT(reason);
        }
 
        if (mUseFixedNumberIterations && (mNumSolves%mEvaluateNumItsEveryNSolves==0 || mForceSpectrumReevaluation))
        {
            // Adaptive Chebyshev: reevaluate spectrum with cg
            if (mKspType == "chebychev")
            {
                PetscReal *r_eig = new PetscReal[mSize];
                PetscReal *c_eig = new PetscReal[mSize];
                PetscInt eigs_computed;
                KSPComputeEigenvalues(mKspSolver, mSize, r_eig, c_eig, &eigs_computed);
 
                mEigMin = r_eig[0];
                /*
                 * Using max() covers a borderline case found in TestChasteBenchmarksForPreDiCT where there's a big
                 * gap in the spectrum between ~1.2 and ~2.5. Some reevaluations pick up 2.5 and others don't. If it
                 * is not picked up, Chebyshev will diverge after 10 solves or so.
                 */
                mEigMax = std::max(mEigMax,r_eig[eigs_computed-1]);
 
                delete[] r_eig;
                delete[] c_eig;
 
                assert(mKspType == "chebychev");
#if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 3) //PETSc 3.3 or later
                KSPSetType(mKspSolver, "chebyshev");
                KSPChebyshevSetEigenvalues(mKspSolver, mEigMax, mEigMin);
#else
                KSPSetType(mKspSolver, mKspType.c_str());
                KSPChebychevSetEigenvalues(mKspSolver, mEigMax, mEigMin);
#endif
                KSPSetComputeEigenvalues(mKspSolver, PETSC_FALSE);
            }
 
#if ((PETSC_VERSION_MAJOR == 2 && PETSC_VERSION_MINOR == 2) || (PETSC_VERSION_MAJOR == 2 && PETSC_VERSION_MINOR == 3 && PETSC_VERSION_SUBMINOR <= 2))
            if (mKspType == "chebychev")
            {
                // See #1695 for more details.
                EXCEPTION("Chebyshev with fixed number of iterations is known to be broken in PETSc <= 2.3.2");
            }
 
            KSPSetNormType(mKspSolver, KSP_NO_NORM);
#elif (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 2) //PETSc 3.2 or later
            KSPSetNormType(mKspSolver, KSP_NORM_NONE);
    #if (PETSC_VERSION_MAJOR == 3 && PETSC_VERSION_MINOR >= 7) //PETSc 3.7 or later
              /*
             * Up to PETSc 3.7.2 the above call also turned off the default convergence test.
             * However, in PETSc 3.7.3 (subminor release) this behaviour was removed and so, here,
             * we explicitly add it back again.
             * See
             * https://bitbucket.org/petsc/petsc/commits/eb70c44be3430b039effa3de7e1ca2fab9f75a57
             * This following line of code is actually valid from PETSc 3.5.
             */
            KSPSetConvergenceTest(mKspSolver, KSPConvergedSkip, CHASTE_PETSC_NULLPTR, CHASTE_PETSC_NULLPTR);
    #endif
#else
            KSPSetNormType(mKspSolver, KSP_NORM_NO);
#endif
 
#if (PETSC_VERSION_MAJOR == 2)
            KSPSetConvergenceTest(mKspSolver, KSPSkipConverged, CHASTE_PETSC_NULLPTR);
#endif
 
            PetscInt num_it;
            KSPGetIterationNumber(mKspSolver, &num_it);
            std::stringstream num_it_str;
            num_it_str << num_it;
            PetscTools::SetOption("-ksp_max_it", num_it_str.str().c_str());
 
            KSPSetFromOptions(mKspSolver);
            KSPSetUp(mKspSolver);
 
            mForceSpectrumReevaluation=false;
        }
 
        mNumSolves++;
 
    }
    catch (const Exception& e)
    {
        // Destroy solution vector on error to avoid memory leaks
        PetscTools::Destroy(lhs_vector);
        throw e;
    }
 
    return lhs_vector;
}
 
void LinearSystem::SetPrecondMatrixIsDifferentFromLhs(bool precondIsDifferent)
{
    mPrecondMatrixIsNotLhs = precondIsDifferent;
 
    if (mPrecondMatrixIsNotLhs)
    {
        if (mRowPreallocation == UINT_MAX)
        {
            /*
             * At the time of writing, this line will be reached if the constructor
             * with signature LinearSystem(Vec residualVector, Mat jacobianMatrix) is
             * called with jacobianMatrix=NULL and preconditioning matrix different
             * from lhs is used.
             *
             * If this combination is ever required you will need to work out
             * matrix allocation (mRowPreallocation) here.
             */
            NEVER_REACHED;
        }
 
        PetscInt local_size = mOwnershipRangeHi - mOwnershipRangeLo;
        PetscTools::SetupMat(mPrecondMatrix, mSize, mSize, mRowPreallocation, local_size, local_size);
    }
}
 
void LinearSystem::SetUseFixedNumberIterations(bool useFixedNumberIterations, unsigned evaluateNumItsEveryNSolves)
{
 
    mUseFixedNumberIterations = useFixedNumberIterations;
    mEvaluateNumItsEveryNSolves = evaluateNumItsEveryNSolves;
}
 
void LinearSystem::ResetKspSolver()
{
    if (mKspIsSetup)
    {
        KSPDestroy(PETSC_DESTROY_PARAM(mKspSolver));
    }
 
    mKspIsSetup = false;
    mForceSpectrumReevaluation = true;
 
    /*
     * Reset max number of iterations. This option is stored in the configuration database and
     * explicitely read in with KSPSetFromOptions() everytime a KSP object is created. Therefore,
     * destroying the KSP object will not ensure that it is set back to default.
     */
    std::stringstream num_it_str;
    num_it_str << 1000;
    PetscTools::SetOption("-ksp_max_it", num_it_str.str().c_str());
}
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(LinearSystem)