#include <WarpXConst.H>
#include <SpectralKSpace.H>
#include <cmath>

using namespace amrex;
using namespace Gpu;

SpectralKSpace::SpectralKSpace( const BoxArray& realspace_ba,
                                const DistributionMapping& dm,
                                const RealVect realspace_dx )
{
    // Store the cell size
    dx = realspace_dx;

    // Create the box array that corresponds to spectral space
    BoxList spectral_bl; // Create empty box list
    // Loop over boxes and fill the box list
    for (int i=0; i < realspace_ba.size(); i++ ) {
        // For local FFTs, boxes in spectral space start at 0 in each direction
        // and have the same number of points as the real space box
        // TODO: this will be different for the hybrid FFT scheme
        Box realspace_bx = realspace_ba[i];
        Box bx = Box( IntVect::TheZeroVector(),
                      realspace_bx.bigEnd() - realspace_bx.smallEnd() );
        spectral_bl.push_back( bx );
    }
    spectralspace_ba.define( spectral_bl );

    // Allocate the components of the k vector: kx, ky (only in 3D), kz
    for (int i_dim=0; i_dim<AMREX_SPACEDIM; i_dim++) {
        k_vec[i_dim] = getKComponent( dm, i_dim );
    }
}

KVectorComponent
SpectralKSpace::getKComponent( const DistributionMapping& dm,
                               const int i_dim ) const
{
    // Initialize an empty ManagedVector in each box
    KVectorComponent k_comp = KVectorComponent(spectralspace_ba, dm);
    // Loop over boxes
    for ( MFIter mfi(spectralspace_ba, dm); mfi.isValid(); ++mfi ){
        Box bx = spectralspace_ba[mfi];
        ManagedVector<Real>& k = k_comp[mfi];

        // Allocate k to the right size
        int N = bx.length( i_dim );
        k.resize( N );

        // Fill the k vector
        const Real dk = 2*MathConst::pi/(N*dx[i_dim]);
        AMREX_ALWAYS_ASSERT_WITH_MESSAGE( bx.smallEnd(i_dim) == 0,
            "Expected box to start at 0, in spectral space.");
        AMREX_ALWAYS_ASSERT_WITH_MESSAGE( bx.bigEnd(i_dim) == N-1,
            "Expected different box end index in spectral space.");
        // Fill positive values of k (FFT conventions: first half is positive)
        for (int i=0; i<(N+1)/2; i++ ){
            k[i] = i*dk;
        }
        // Fill negative values of k (FFT conventions: second half is negative)
        for (int i=(N+1)/2; i<N; i++){
            k[i] = (N-i)*dk;
        }
        // TODO: this will also be different for the real-to-complex transform
        // TODO: this will be different for the hybrid FFT scheme
    }
    return k_comp;
}

SpectralShiftFactor
SpectralKSpace::getSpectralShiftFactor( const DistributionMapping& dm,
                                        const int i_dim,
                                        const int shift_type ) const
{
    // Initialize an empty ManagedVector in each box
    SpectralShiftFactor shift_factor = SpectralShiftFactor( spectralspace_ba, dm );
    // Loop over boxes
    for ( MFIter mfi(spectralspace_ba, dm); mfi.isValid(); ++mfi ){
        const ManagedVector<Real>& k = k_vec[i_dim][mfi];
        ManagedVector<Complex>& shift = shift_factor[mfi];

        // Allocate shift coefficients
        shift.resize( k.size() );

        // Fill the shift coefficients
        Real sign = 0;
        switch (shift_type){
            case ShiftType::TransformFromCellCentered: sign = 1.; break;
            case ShiftType::TransformToCellCentered: sign = -1.;
        }
        constexpr Complex I{0,1};
        for (int i=0; i<k.size(); i++ ){
            shift[i] = std::exp( I*sign*k[i]*0.5*dx[i_dim] );
        }
    }
    return shift_factor;
}

KVectorComponent
SpectralKSpace::getModifiedKComponent( const DistributionMapping& dm,
                                       const int i_dim,
                                       const int n_order,
                                       const bool nodal ) const
{
    // Initialize an empty ManagedVector in each box
    KVectorComponent modified_k_comp = KVectorComponent( spectralspace_ba, dm );

    // Compute real-space stencil coefficients
    Vector<Real> stencil_coef = getFonbergStencilCoefficients(n_order, nodal);

    // Loop over boxes
    for ( MFIter mfi(spectralspace_ba, dm); mfi.isValid(); ++mfi ){
        Real delta_x = dx[i_dim];
        const ManagedVector<Real>& k = k_vec[i_dim][mfi];
        ManagedVector<Real>& modified_k = modified_k_comp[mfi];

        // Allocate modified_k to the same size as k
        modified_k.resize( k.size() );

        // Fill the modified k vector
        for (int i=0; i<k.size(); i++ ){
            for (int n=1; n<stencil_coef.size(); n++){
                if (nodal){
                    modified_k[i] = stencil_coef[n]* \
                        std::sin( k[i]*n*delta_x )/( n*delta_x );
                } else {
                    modified_k[i] = stencil_coef[n]* \
                        std::sin( k[i]*(n-0.5)*delta_x )/( (n-0.5)*delta_x );
                }
            }
        }
    }
    return modified_k_comp;
}

/* TODO: Documentation: point to Fonberg paper ; explain recurrence relation
 */
Vector<Real>
getFonbergStencilCoefficients( const int n_order, const bool nodal )
{
    AMREX_ALWAYS_ASSERT_WITH_MESSAGE( n_order%2 == 0,
                                      "n_order should be even.");
    const int m = n_order/2;
    Vector<Real> coefs;
    coefs.resize( m+1 );

    // Coefficients for nodal (a.k.a. centered) finite-difference
    if (nodal == true) {
        coefs[0] = -2.; // First coefficient
        for (int n=1; n<m+1; n++){ // Get the other coefficients by recurrence
            coefs[n] = - (m+1-n)*1./(m+n)*coefs[n-1];
        }
    }
    // Coefficients for staggered finite-difference
    else {
        Real prod = 1.;
        for (int k=1; k<m+1; k++){
            prod *= (m+k)*1./(4*k);
        }
        coefs[0] = 4*m*prod*prod; // First coefficient
        for (int n=1; n<m+1; n++){ // Get the other coefficients by recurrence
            coefs[n] = - ((2*n-3)*(m+1-n))*1./((2*n-1)*(m-1+n))*coefs[n-1];
        }
    }
    return coefs;
}