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// ===================================================================================
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// Copyright ScalFmm 2011 INRIA, Olivier Coulaud, Bérenger Bramas, Matthias Messner
// olivier.coulaud@inria.fr, berenger.bramas@inria.fr
// This software is a computer program whose purpose is to compute the FMM.
//
// This software is governed by the CeCILL-C and LGPL licenses and
// abiding by the rules of distribution of free software.  
// 
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public and CeCILL-C Licenses for more details.
// "http://www.cecill.info". 
// "http://www.gnu.org/licenses".
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// ===================================================================================
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#ifndef FCHEBINTERPOLATOR_HPP
#define FCHEBINTERPOLATOR_HPP


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#include "./../Interpolation/FInterpMapping.hpp"
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#include "./../Interpolation/FInterpMatrixKernel.hpp" //PB
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#include "./FChebTensor.hpp"
#include "./FChebRoots.hpp"

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#include "../../Utils/FBlas.hpp"
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/**
 * @author Matthias Messner (matthias.matthias@inria.fr)
 * Please read the license
 */

/**
 * @class FChebInterpolator
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 *
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 * The class @p FChebInterpolator defines the anterpolation (M2M) and
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 * interpolation (L2L) concerning operations.
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 * 
 * PB: MatrixKernelClass is passed as template in order to inform interpolator 
 * of the size of the vectorial interpolators. Default is the scalar 
 * matrix kernel class of type ONE_OVER_R (NRHS=NLHS=1).
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 */
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template <int ORDER, class MatrixKernelClass = struct FInterpMatrixKernelR>
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class FChebInterpolator : FNoCopyable
{
  // compile time constants and types
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  enum {nnodes = TensorTraits<ORDER>::nnodes,
        nRhs = MatrixKernelClass::NRHS,
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        nLhs = MatrixKernelClass::NLHS,
        nPV = MatrixKernelClass::NPV};
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  typedef FChebRoots< ORDER>  BasisType;
  typedef FChebTensor<ORDER> TensorType;

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protected: // PB for OptiDis

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  FReal T_of_roots[ORDER][ORDER];
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  FReal T[ORDER * (ORDER-1)];
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    unsigned int node_ids[nnodes][3];
    FReal* ChildParentInterpolator[8];

    // permutations (only needed in the tensor product interpolation case)
    unsigned int perm[3][nnodes];

    ////////////////////////////////////////////////////////////////////
    // needed for P2M
    struct IMN2MNI {
        enum {size = ORDER * (ORDER-1) * (ORDER-1)};
        unsigned int imn[size], mni[size];
        IMN2MNI() {
            unsigned int counter = 0;
            for (unsigned int i=0; i<ORDER; ++i) {
                for (unsigned int m=0; m<ORDER-1; ++m) {
                    for (unsigned int n=0; n<ORDER-1; ++n) {
                        imn[counter] = n*(ORDER-1)*ORDER + m*ORDER + i;
                        mni[counter] = i*(ORDER-1)*(ORDER-1) + n*(ORDER-1) + m;
                        counter++;
                    }
                }
            }
        }
    } perm0;

    struct JNI2NIJ {
        enum {size = ORDER * ORDER * (ORDER-1)};
        unsigned int jni[size], nij[size];
        JNI2NIJ() {
            unsigned int counter = 0;
            for (unsigned int i=0; i<ORDER; ++i) {
                for (unsigned int j=0; j<ORDER; ++j) {
                    for (unsigned int n=0; n<ORDER-1; ++n) {
                        jni[counter] = i*(ORDER-1)*ORDER + n*ORDER + j;
                        nij[counter] = j*ORDER*(ORDER-1) + i*(ORDER-1) + n;
                        counter++;
                    }
                }
            }
        }
    } perm1;

    struct KIJ2IJK {
        enum {size = ORDER * ORDER * ORDER};
        unsigned int kij[size], ijk[size];
        KIJ2IJK() {
            unsigned int counter = 0;
            for (unsigned int i=0; i<ORDER; ++i) {
                for (unsigned int j=0; j<ORDER; ++j) {
                    for (unsigned int k=0; k<ORDER; ++k) {
                        kij[counter] = j*ORDER*ORDER + i*ORDER + k;
                        ijk[counter] = k*ORDER*ORDER + j*ORDER + i;
                        counter++;
                    }
                }
            }
        }
    } perm2;
    ////////////////////////////////////////////////////////////////////

    ////////////////////////////////////////////////////////////////////
    // needed for L2P
    struct IJK2JKI {
        enum {size = ORDER * ORDER * ORDER};
        unsigned int ijk[size], jki[size];
        IJK2JKI() {
            unsigned int counter = 0;
            for (unsigned int i=0; i<ORDER; ++i) {
                for (unsigned int j=0; j<ORDER; ++j) {
                    for (unsigned int k=0; k<ORDER; ++k) {
                        ijk[counter] = k*ORDER*ORDER + j*ORDER + i;
                        jki[counter] = i*ORDER*ORDER + k*ORDER + j;
                        counter++;
                    }
                }
            }
        }
        void permute(const FReal *const IN, FReal *const OUT) const
        { for (unsigned int i=0; i<size; ++i) OUT[jki[i]] = IN[ijk[i]]; }
    } perm3;

    struct IJK2KIJ {
        enum {size = ORDER * ORDER * ORDER};
        unsigned int ijk[size], kij[size];
        IJK2KIJ() {
            unsigned int counter = 0;
            for (unsigned int i=0; i<ORDER; ++i) {
                for (unsigned int j=0; j<ORDER; ++j) {
                    for (unsigned int k=0; k<ORDER; ++k) {
                        ijk[counter] = k*ORDER*ORDER + j*ORDER + i;
                        kij[counter] = j*ORDER*ORDER + i*ORDER + k;
                        counter++;
                    }
                }
            }
        }
        void permute(const FReal *const IN, FReal *const OUT) const
        { for (unsigned int i=0; i<size; ++i) OUT[kij[i]] = IN[ijk[i]]; }
    } perm4;

    struct LJK2JKL {
        enum {size = (ORDER-1) * ORDER * ORDER};
        unsigned int ljk[size], jkl[size];
        LJK2JKL() {
            unsigned int counter = 0;
            for (unsigned int l=0; l<ORDER-1; ++l) {
                for (unsigned int j=0; j<ORDER; ++j) {
                    for (unsigned int k=0; k<ORDER; ++k) {
                        ljk[counter] = k*ORDER*(ORDER-1) + j*(ORDER-1) + l;
                        jkl[counter] = l*ORDER*ORDER + k*ORDER + j;
                        counter++;
                    }
                }
            }
        }
        void permute(const FReal *const IN, FReal *const OUT) const
        { for (unsigned int i=0; i<size; ++i) OUT[jkl[i]] = IN[ljk[i]]; }
    } perm5;

    struct LJK2KLJ {
        enum {size = (ORDER-1) * ORDER * ORDER};
        unsigned int ljk[size], klj[size];
        LJK2KLJ() {
            unsigned int counter = 0;
            for (unsigned int l=0; l<ORDER-1; ++l) {
                for (unsigned int j=0; j<ORDER; ++j) {
                    for (unsigned int k=0; k<ORDER; ++k) {
                        ljk[counter] = k*ORDER*(ORDER-1) + j*(ORDER-1) + l;
                        klj[counter] = j*(ORDER-1)*ORDER + l*ORDER + k;
                        counter++;
                    }
                }
            }
        }
        void permute(const FReal *const IN, FReal *const OUT) const
        { for (unsigned int i=0; i<size; ++i) OUT[klj[i]] = IN[ljk[i]]; }
    } perm6;

    struct MKI2KIM {
        enum {size = (ORDER-1) * ORDER * ORDER};
        unsigned int mki[size], kim[size];
        MKI2KIM() {
            unsigned int counter = 0;
            for (unsigned int m=0; m<ORDER-1; ++m) {
                for (unsigned int k=0; k<ORDER; ++k) {
                    for (unsigned int i=0; i<ORDER; ++i) {
                        mki[counter] = i*ORDER*(ORDER-1) + k*(ORDER-1) + m;
                        kim[counter] = m*ORDER*ORDER + i*ORDER + k;
                        counter++;
                    }
                }
            }
        }
        void permute(const FReal *const IN, FReal *const OUT) const
        { for (unsigned int i=0; i<size; ++i) OUT[kim[i]] = IN[mki[i]]; }
    } perm7;

    struct MKL2KLM {
        enum {size = (ORDER-1) * ORDER * (ORDER-1)};
        unsigned int mkl[size], klm[size];
        MKL2KLM() {
            unsigned int counter = 0;
            for (unsigned int m=0; m<ORDER-1; ++m) {
                for (unsigned int k=0; k<ORDER; ++k) {
                    for (unsigned int l=0; l<ORDER-1; ++l) {
                        mkl[counter] = l*ORDER*(ORDER-1) + k*(ORDER-1) + m;
                        klm[counter] = m*(ORDER-1)*ORDER + l*ORDER + k;
                        counter++;
                    }
                }
            }
        }
        void permute(const FReal *const IN, FReal *const OUT) const
        { for (unsigned int i=0; i<size; ++i) OUT[klm[i]] = IN[mkl[i]]; }
    } perm8;

    struct NLM2LMN {
        enum {size = (ORDER-1) * (ORDER-1) * (ORDER-1)};
        unsigned int nlm[size], lmn[size];
        NLM2LMN() {
            unsigned int counter = 0;
            for (unsigned int n=0; n<ORDER-1; ++n) {
                for (unsigned int l=0; l<ORDER-1; ++l) {
                    for (unsigned int m=0; m<ORDER-1; ++m) {
                        nlm[counter] = m*(ORDER-1)*(ORDER-1) + l*(ORDER-1) + n;
                        lmn[counter] = n*(ORDER-1)*(ORDER-1) + m*(ORDER-1) + l;
                        counter++;
                    }
                }
            }
        }
        void permute(const FReal *const IN, FReal *const OUT) const
        { for (unsigned int i=0; i<size; ++i) OUT[lmn[i]] = IN[nlm[i]]; }
    } perm9;

    ////////////////////////////////////////////////////////////////////



    /**
     * Initialize the child - parent - interpolator, it is basically the matrix
     * S which is precomputed and reused for all M2M and L2L operations, ie for
     * all non leaf inter/anterpolations.
     */
    void initM2MandL2L()
    {
        FPoint ParentRoots[nnodes], ChildRoots[nnodes];
        const FReal ParentWidth(2.);
        const FPoint ParentCenter(0., 0., 0.);
        FChebTensor<ORDER>::setRoots(ParentCenter, ParentWidth, ParentRoots);

        FPoint ChildCenter;
        const FReal ChildWidth(1.);

        // loop: child cells
        for (unsigned int child=0; child<8; ++child) {

            // allocate memory
            ChildParentInterpolator[child] = new FReal [nnodes * nnodes];

            // set child info
            FChebTensor<ORDER>::setRelativeChildCenter(child, ChildCenter);
            FChebTensor<ORDER>::setRoots(ChildCenter, ChildWidth, ChildRoots);

            // assemble child - parent - interpolator
            assembleInterpolator(nnodes, ChildRoots, ChildParentInterpolator[child]);
        }
    }

    /**
     * Initialize the child - parent - interpolator, it is basically the matrix
     * S which is precomputed and reused for all M2M and L2L operations, ie for
     * all non leaf inter/anterpolations.
     */
    void initTensorM2MandL2L()
    {
        FPoint ParentRoots[nnodes];
        FReal ChildCoords[3][ORDER];
        const FReal ParentWidth(2.);
        const FPoint ParentCenter(0., 0., 0.);
        FChebTensor<ORDER>::setRoots(ParentCenter, ParentWidth, ParentRoots);

        FPoint ChildCenter;
        const FReal ChildWidth(1.);

        // loop: child cells
        for (unsigned int child=0; child<8; ++child) {

            // set child info
            FChebTensor<ORDER>::setRelativeChildCenter(child, ChildCenter);
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            FChebTensor<ORDER>::setPolynomialsRoots(ChildCenter, ChildWidth, ChildCoords);
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            // allocate memory
            ChildParentInterpolator[child] = new FReal [3 * ORDER*ORDER];
            assembleInterpolator(ORDER, ChildCoords[0], ChildParentInterpolator[child]);
            assembleInterpolator(ORDER, ChildCoords[1], ChildParentInterpolator[child] + 1 * ORDER*ORDER);
            assembleInterpolator(ORDER, ChildCoords[2], ChildParentInterpolator[child] + 2 * ORDER*ORDER);
        }


        // init permutations
        for (unsigned int i=0; i<ORDER; ++i) {
            for (unsigned int j=0; j<ORDER; ++j) {
                for (unsigned int k=0; k<ORDER; ++k) {
                    const unsigned int index = k*ORDER*ORDER + j*ORDER + i;
                    perm[0][index] = k*ORDER*ORDER + j*ORDER + i;
                    perm[1][index] = i*ORDER*ORDER + k*ORDER + j;
                    perm[2][index] = j*ORDER*ORDER + i*ORDER + k;
                }
            }
        }

    }
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    /**
     * Constructor: Initialize the Chebyshev polynomials at the Chebyshev
     * roots/interpolation point
     */
    explicit FChebInterpolator()
    {
        // initialize chebyshev polynomials of root nodes: T_o(x_j)
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    for (unsigned int o=1; o<ORDER; ++o)
      for (unsigned int j=0; j<ORDER; ++j)
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        T_of_roots[o][j] = FReal(BasisType::T(o, FReal(BasisType::roots[j])));
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        // initialize chebyshev polynomials of root nodes: T_o(x_j)
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    for (unsigned int o=1; o<ORDER; ++o)
      for (unsigned int j=0; j<ORDER; ++j)
        T[(o-1)*ORDER + j] = FReal(BasisType::T(o, FReal(BasisType::roots[j])));
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        // initialize root node ids
        TensorType::setNodeIds(node_ids);

        // initialize interpolation operator for non M2M and L2L (non leaf
        // operations)
        //this -> initM2MandL2L();     // non tensor-product interpolation
        this -> initTensorM2MandL2L(); // tensor-product interpolation
    }


    /**
     * Destructor: Delete dynamically allocated memory for M2M and L2L operator
     */
    ~FChebInterpolator()
    {
        for (unsigned int child=0; child<8; ++child)
            delete [] ChildParentInterpolator[child];
    }


    /**
     * Assembles the interpolator \f$S_\ell\f$ of size \f$N\times
     * \ell^3\f$. Here local points is meant as points whose global coordinates
     * have already been mapped to the reference interval [-1,1].
     *
     * @param[in] NumberOfLocalPoints
     * @param[in] LocalPoints
     * @param[out] Interpolator
     */
    void assembleInterpolator(const unsigned int NumberOfLocalPoints,
                  const FPoint *const LocalPoints,
                  FReal *const Interpolator) const
    {
        // values of chebyshev polynomials of source particle: T_o(x_i)
        FReal T_of_x[ORDER][3];
        // loop: local points (mapped in [-1,1])
        for (unsigned int m=0; m<NumberOfLocalPoints; ++m) {
            // evaluate chebyshev polynomials at local points
            for (unsigned int o=1; o<ORDER; ++o) {
                T_of_x[o][0] = BasisType::T(o, LocalPoints[m].getX());
                T_of_x[o][1] = BasisType::T(o, LocalPoints[m].getY());
                T_of_x[o][2] = BasisType::T(o, LocalPoints[m].getZ());
            }

            // assemble interpolator
            for (unsigned int n=0; n<nnodes; ++n) {
                //Interpolator[n*nnodes + m] = FReal(1.);
                Interpolator[n*NumberOfLocalPoints + m] = FReal(1.);
                for (unsigned int d=0; d<3; ++d) {
                    const unsigned int j = node_ids[n][d];
                    FReal S_d = FReal(1.) / ORDER;
                    for (unsigned int o=1; o<ORDER; ++o)
                        S_d += FReal(2.) / ORDER * T_of_x[o][d] * T_of_roots[o][j];
                    //Interpolator[n*nnodes + m] *= S_d;
                    Interpolator[n*NumberOfLocalPoints + m] *= S_d;
                }

            }

        }

    }


    void assembleInterpolator(const unsigned int M, const FReal *const x, FReal *const S) const
    {
        // values of chebyshev polynomials of source particle: T_o(x_i)
        FReal T_of_x[ORDER];

        // loop: local points (mapped in [-1,1])
        for (unsigned int m=0; m<M; ++m) {
            // evaluate chebyshev polynomials at local points
            for (unsigned int o=1; o<ORDER; ++o)
                T_of_x[o] = BasisType::T(o, x[m]);

            for (unsigned int n=0; n<ORDER; ++n) {
                S[n*M + m] = FReal(1.) / ORDER;
                for (unsigned int o=1; o<ORDER; ++o)
                    S[n*M + m] += FReal(2.) / ORDER * T_of_x[o] * T_of_roots[o][n];
            }

        }

    }



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    const FReal *const * getChildParentInterpolator() const
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    { return ChildParentInterpolator; }
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    const unsigned int * getPermutationsM2ML2L(unsigned int i) const
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    { return perm[i]; }






    /**
     * Particle to moment: application of \f$S_\ell(y,\bar y_n)\f$
     * (anterpolation, it is the transposed interpolation)
     */
    template <class ContainerClass>
    void applyP2M(const FPoint& center,
                                const FReal width,
                                FReal *const multipoleExpansion,
                                const ContainerClass *const sourceParticles) const;



    /**
     * Local to particle operation: application of \f$S_\ell(x,\bar x_m)\f$ (interpolation)
     */
    template <class ContainerClass>
    void applyL2P(const FPoint& center,
                                const FReal width,
                                const FReal *const localExpansion,
                                ContainerClass *const localParticles) const;


    /**
     * Local to particle operation: application of \f$\nabla_x S_\ell(x,\bar x_m)\f$ (interpolation)
     */
    template <class ContainerClass>
    void applyL2PGradient(const FPoint& center,
                                                const FReal width,
                                                const FReal *const localExpansion,
                                                ContainerClass *const localParticles) const;

    /**
     * Local to particle operation: application of \f$S_\ell(x,\bar x_m)\f$ and
     * \f$\nabla_x S_\ell(x,\bar x_m)\f$ (interpolation)
     */
    template <class ContainerClass>
    void applyL2PTotal(const FPoint& center,
                                         const FReal width,
                                         const FReal *const localExpansion,
                                         ContainerClass *const localParticles) const;


    /*
    void applyM2M(const unsigned int ChildIndex,
                                const FReal *const ChildExpansion,
                                FReal *const ParentExpansion) const
    {
        FBlas::gemtva(nnodes, nnodes, FReal(1.),
                                    ChildParentInterpolator[ChildIndex],
                                    const_cast<FReal*>(ChildExpansion), ParentExpansion);
    }

    void applyL2L(const unsigned int ChildIndex,
                                const FReal *const ParentExpansion,
                                FReal *const ChildExpansion) const
    {
        FBlas::gemva(nnodes, nnodes, FReal(1.),
                                 ChildParentInterpolator[ChildIndex],
                                 const_cast<FReal*>(ParentExpansion), ChildExpansion);
    }
    */



    void applyM2M(const unsigned int ChildIndex,
                                const FReal *const ChildExpansion,
                                FReal *const ParentExpansion) const
    {
        FReal Exp[nnodes], PermExp[nnodes];
        // ORDER*ORDER*ORDER * (2*ORDER-1)
        FBlas::gemtm(ORDER, ORDER, ORDER*ORDER, FReal(1.),
                                 ChildParentInterpolator[ChildIndex], ORDER,
                                 const_cast<FReal*>(ChildExpansion), ORDER, PermExp, ORDER);

        for (unsigned int n=0; n<nnodes; ++n)	Exp[n] = PermExp[perm[1][n]];
        // ORDER*ORDER*ORDER * (2*ORDER-1)
        FBlas::gemtm(ORDER, ORDER, ORDER*ORDER, FReal(1.),
                                 ChildParentInterpolator[ChildIndex] + 2 * ORDER*ORDER, ORDER,
                                 Exp, ORDER, PermExp, ORDER);

        for (unsigned int n=0; n<nnodes; ++n)	Exp[perm[1][n]] = PermExp[perm[2][n]];
        // ORDER*ORDER*ORDER * (2*ORDER-1)
        FBlas::gemtm(ORDER, ORDER, ORDER*ORDER, FReal(1.),
                                 ChildParentInterpolator[ChildIndex] + 1 * ORDER*ORDER, ORDER,
                                 Exp, ORDER, PermExp, ORDER);

        for (unsigned int n=0; n<nnodes; ++n)	ParentExpansion[perm[2][n]] += PermExp[n];
    }


    void applyL2L(const unsigned int ChildIndex,
                                const FReal *const ParentExpansion,
                                FReal *const ChildExpansion) const
    {
        FReal Exp[nnodes], PermExp[nnodes];
        // ORDER*ORDER*ORDER * (2*ORDER-1)
        FBlas::gemm(ORDER, ORDER, ORDER*ORDER, FReal(1.),
                                ChildParentInterpolator[ChildIndex], ORDER,
                                const_cast<FReal*>(ParentExpansion), ORDER, PermExp, ORDER);

        for (unsigned int n=0; n<nnodes; ++n)	Exp[n] = PermExp[perm[1][n]];
        // ORDER*ORDER*ORDER * (2*ORDER-1)
        FBlas::gemm(ORDER, ORDER, ORDER*ORDER, FReal(1.),
                                ChildParentInterpolator[ChildIndex] + 2 * ORDER*ORDER, ORDER,
                                Exp, ORDER, PermExp, ORDER);

        for (unsigned int n=0; n<nnodes; ++n)	Exp[perm[1][n]] = PermExp[perm[2][n]];
        // ORDER*ORDER*ORDER * (2*ORDER-1)
        FBlas::gemm(ORDER, ORDER, ORDER*ORDER, FReal(1.),
                                ChildParentInterpolator[ChildIndex] + 1 * ORDER*ORDER, ORDER,
                                Exp, ORDER, PermExp, ORDER);

        for (unsigned int n=0; n<nnodes; ++n)	ChildExpansion[perm[2][n]] += PermExp[n];
    }
    // total flops count: 3 * ORDER*ORDER*ORDER * (2*ORDER-1)
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};
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/**
 * Particle to moment: application of \f$S_\ell(y,\bar y_n)\f$
 * (anterpolation, it is the transposed interpolation)
 */
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template <int ORDER, class MatrixKernelClass>
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template <class ContainerClass>
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inline void FChebInterpolator<ORDER,MatrixKernelClass>::applyP2M(const FPoint& center,
                                                                 const FReal width,
                                                                 FReal *const multipoleExpansion,
                                                                 const ContainerClass *const inParticles) const
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{
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    // set all multipole expansions to zero
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    FBlas::setzero(2*nRhs*nnodes, multipoleExpansion);
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    // allocate stuff
    const map_glob_loc map(center, width);
    FPoint localPosition;

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//    FReal W1 = FReal(0.);
    FReal W1[nRhs];
    FReal W2[nRhs][3][ ORDER-1];
    FReal W4[nRhs][3][(ORDER-1)*(ORDER-1)];
    FReal W8[nRhs][   (ORDER-1)*(ORDER-1)*(ORDER-1)];
    for(int idxRhs = 0 ; idxRhs < nRhs ; ++idxRhs){
      W1[idxRhs] = FReal(0.);
      for(unsigned int i=0; i<(ORDER-1); ++i) W2[idxRhs][0][i] = W2[idxRhs][1][i] = W2[idxRhs][2][i] = FReal(0.);
      for(unsigned int i=0; i<(ORDER-1)*(ORDER-1); ++i)	W4[idxRhs][0][i] = W4[idxRhs][1][i] = W4[idxRhs][2][i] = FReal(0.);
      for(unsigned int i=0; i<(ORDER-1)*(ORDER-1)*(ORDER-1); ++i)	W8[idxRhs][i] = FReal(0.);
    }

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    // loop over source particles
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//    const FReal*const physicalValues = inParticles->getPhysicalValues();
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    const FReal*const positionsX = inParticles->getPositions()[0];
    const FReal*const positionsY = inParticles->getPositions()[1];
    const FReal*const positionsZ = inParticles->getPositions()[2];
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    for(int idxPart = 0 ; idxPart < inParticles->getNbParticles() ; ++idxPart){
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        // map global position to [-1,1]
612
        map(FPoint(positionsX[idxPart],positionsY[idxPart],positionsZ[idxPart]), localPosition); // 15 flops
613 614 615 616 617 618 619 620 621 622 623 624 625

        FReal T_of_x[3][ORDER];
        T_of_x[0][0] = FReal(1.); T_of_x[0][1] = localPosition.getX();
        T_of_x[1][0] = FReal(1.); T_of_x[1][1] = localPosition.getY();
        T_of_x[2][0] = FReal(1.); T_of_x[2][1] = localPosition.getZ();
        const FReal x2 = FReal(2.) * T_of_x[0][1]; // 1 flop
        const FReal y2 = FReal(2.) * T_of_x[1][1]; // 1 flop
        const FReal z2 = FReal(2.) * T_of_x[2][1]; // 1 flop
        for (unsigned int j=2; j<ORDER; ++j) {
            T_of_x[0][j] = x2 * T_of_x[0][j-1] - T_of_x[0][j-2]; // 2 flops
            T_of_x[1][j] = y2 * T_of_x[1][j-1] - T_of_x[1][j-2]; // 2 flops
            T_of_x[2][j] = z2 * T_of_x[2][j-1] - T_of_x[2][j-2]; // 2 flops
        }
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        for(int idxRhs = 0 ; idxRhs < nRhs ; ++idxRhs){
          const FReal*const physicalValues = inParticles->getPhysicalValues(idxRhs);
628

629 630 631
          const FReal weight = physicalValues[idxPart];
          W1[idxRhs] += weight; // 1 flop
          for (unsigned int i=1; i<ORDER; ++i) {
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            const FReal wx = weight * T_of_x[0][i]; // 1 flop
            const FReal wy = weight * T_of_x[1][i]; // 1 flop
            const FReal wz = weight * T_of_x[2][i]; // 1 flop
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            W2[idxRhs][0][i-1] += wx; // 1 flop
            W2[idxRhs][1][i-1] += wy; // 1 flop
            W2[idxRhs][2][i-1] += wz; // 1 flop
638
            for (unsigned int j=1; j<ORDER; ++j) {
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              const FReal wxy = wx * T_of_x[1][j]; // 1 flop
              const FReal wxz = wx * T_of_x[2][j]; // 1 flop
              const FReal wyz = wy * T_of_x[2][j]; // 1 flop
              W4[idxRhs][0][(j-1)*(ORDER-1) + (i-1)] += wxy; // 1 flop
              W4[idxRhs][1][(j-1)*(ORDER-1) + (i-1)] += wxz; // 1 flop
              W4[idxRhs][2][(j-1)*(ORDER-1) + (i-1)] += wyz; // 1 flop
              for (unsigned int k=1; k<ORDER; ++k) {
                const FReal wxyz = wxy * T_of_x[2][k]; // 1 flop
                W8[idxRhs][(k-1)*(ORDER-1)*(ORDER-1) + (j-1)*(ORDER-1) + (i-1)] += wxyz; // 1 flop
              } // flops: (ORDER-1) * 2
649
            } // flops: (ORDER-1) * (6 + (ORDER-1) * 2)
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          } // flops: (ORDER-1) * (6 + (ORDER-1) * (6 + (ORDER-1) * 2))
        } // flops: ... * NRHS 
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    } // flops: N * (18 + (ORDER-2) * 6 + (ORDER-1) * (6 + (ORDER-1) * (6 + (ORDER-1) * 2)))

    ////////////////////////////////////////////////////////////////////

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    for(int idxRhs = 0 ; idxRhs < nRhs ; ++idxRhs){

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    // loop over interpolation points
    FReal F2[3][ORDER];
    FReal F4[3][ORDER*ORDER];
    FReal F8[   ORDER*ORDER*ORDER];
    {
        // compute W2: 3 * ORDER*(2*(ORDER-1)-1) flops
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        FBlas::gemv(ORDER, ORDER-1, FReal(1.), const_cast<FReal*>(T), W2[idxRhs][0], F2[0]);
        FBlas::gemv(ORDER, ORDER-1, FReal(1.), const_cast<FReal*>(T), W2[idxRhs][1], F2[1]);
        FBlas::gemv(ORDER, ORDER-1, FReal(1.), const_cast<FReal*>(T), W2[idxRhs][2], F2[2]);
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        // compute W4: 3 * [ORDER*(ORDER-1)*(2*(ORDER-1)-1) + ORDER*ORDER*(2*(ORDER-1)-1)]
        FReal C[ORDER * (ORDER-1)];
671
        FBlas::gemmt(ORDER, ORDER-1, ORDER-1, FReal(1.), const_cast<FReal*>(T), ORDER, W4[idxRhs][0], ORDER-1, C,     ORDER);
672
        FBlas::gemmt(ORDER, ORDER-1, ORDER,   FReal(1.), const_cast<FReal*>(T), ORDER, C,     ORDER,   F4[0], ORDER);
673
        FBlas::gemmt(ORDER, ORDER-1, ORDER-1, FReal(1.), const_cast<FReal*>(T), ORDER, W4[idxRhs][1], ORDER-1, C,     ORDER);
674
        FBlas::gemmt(ORDER, ORDER-1, ORDER,   FReal(1.), const_cast<FReal*>(T), ORDER, C,     ORDER,   F4[1], ORDER);
675
        FBlas::gemmt(ORDER, ORDER-1, ORDER-1, FReal(1.), const_cast<FReal*>(T), ORDER, W4[idxRhs][2], ORDER-1, C,     ORDER);
676 677 678 679
        FBlas::gemmt(ORDER, ORDER-1, ORDER,   FReal(1.), const_cast<FReal*>(T), ORDER, C,     ORDER,   F4[2], ORDER);

        // compute W8: 3 * (2*(ORDER-1)-1) * [ORDER*(ORDER-1)*(ORDER-1) + ORDER*ORDER*(ORDER-1) + ORDER*ORDER*ORDER]
        FReal D[ORDER * (ORDER-1) * (ORDER-1)];
680
        FBlas::gemm(ORDER, ORDER-1, (ORDER-1)*(ORDER-1), FReal(1.),	const_cast<FReal*>(T), ORDER, W8[idxRhs], ORDER-1, D, ORDER);
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        FReal E[(ORDER-1) * (ORDER-1) * ORDER];
        for (unsigned int s=0; s<perm0.size; ++s)	E[perm0.mni[s]] = D[perm0.imn[s]];
        FReal F[ORDER * (ORDER-1) * ORDER];
        FBlas::gemm(ORDER, ORDER-1, ORDER*(ORDER-1), FReal(1.), const_cast<FReal*>(T), ORDER, E, ORDER-1, F, ORDER);
        FReal G[(ORDER-1) * ORDER * ORDER];
        for (unsigned int s=0; s<perm1.size; ++s)	G[perm1.nij[s]] = F[perm1.jni[s]];
        FReal H[ORDER * ORDER * ORDER];
        FBlas::gemm(ORDER, ORDER-1, ORDER*ORDER, FReal(1.), const_cast<FReal*>(T), ORDER, G, ORDER-1, H, ORDER);
        for (unsigned int s=0; s<perm2.size; ++s)	F8[perm2.ijk[s]] = H[perm2.kij[s]];
    }

    // assemble multipole expansions
    for (unsigned int i=0; i<ORDER; ++i) {
        for (unsigned int j=0; j<ORDER; ++j) {
            for (unsigned int k=0; k<ORDER; ++k) {
                const unsigned int idx = k*ORDER*ORDER + j*ORDER + i;
697
                multipoleExpansion[2*idxRhs*nnodes + idx] = (W1[idxRhs] +
698 699 700 701 702 703
                                                                     FReal(2.) * (F2[0][i] + F2[1][j] + F2[2][k]) +
                                                                     FReal(4.) * (F4[0][j*ORDER+i] + F4[1][k*ORDER+i] + F4[2][k*ORDER+j]) +
                                                                     FReal(8.) *  F8[idx]) / nnodes; // 11 * ORDER*ORDER*ORDER flops
            }
        }
    }
704

705 706
    } // NRHS

707 708 709
}


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///**
// * Particle to moment: application of \f$S_\ell(y,\bar y_n)\f$
// * (anterpolation, it is the transposed interpolation)
// */
//template <int ORDER>
//template <class ContainerClass>
//inline void FChebInterpolator<ORDER>::applyP2M(const FPoint& center,
//																							 const FReal width,
//																							 FReal *const multipoleExpansion,
//																							 const ContainerClass *const sourceParticles) const
//{
//	// set all multipole expansions to zero
//	FBlas::setzero(nnodes, multipoleExpansion);
//
//	// allocate stuff
//	const map_glob_loc map(center, width);
//	FPoint localPosition;
//	FReal T_of_x[ORDER][3];
//	FReal S[3], c1;
//	//
//	FReal xpx,ypy,zpz ;
//	c1 = FReal(8.) / nnodes ; // 1 flop
//	// loop over source particles
//	typename ContainerClass::ConstBasicIterator iter(*sourceParticles);
//	while(iter.hasNotFinished()){
//
//		// map global position to [-1,1]
//		map(iter.data().getPosition(), localPosition); // 15 flops
//
//		// evaluate chebyshev polynomials of source particle: T_o(x_i)
//		T_of_x[0][0] = FReal(1.);	T_of_x[1][0] = localPosition.getX();
//		T_of_x[0][1] = FReal(1.);	T_of_x[1][1] = localPosition.getY();
//		T_of_x[0][2] = FReal(1.);	T_of_x[1][2] = localPosition.getZ();
//		xpx = FReal(2.) * localPosition.getX() ; // 1 flop
//		ypy = FReal(2.) * localPosition.getY() ; // 1 flop
//		zpz = FReal(2.) * localPosition.getZ() ; // 1 flop
//
//		for (unsigned int o=2; o<ORDER; ++o) {
//			T_of_x[o][0] = xpx * T_of_x[o-1][0] - T_of_x[o-2][0]; // 2 flops
//			T_of_x[o][1] = ypy * T_of_x[o-1][1] - T_of_x[o-2][1];	// 2 flops
//			T_of_x[o][2] = zpz * T_of_x[o-1][2] - T_of_x[o-2][2]; // 2 flops
//		} // flops: (ORDER-1) * 6
//		
//		// anterpolate
//		const FReal sourceValue = iter.data().getPhysicalValue();
//		for (unsigned int n=0; n<nnodes; ++n) {
//			const unsigned int j[3] = {node_ids[n][0], node_ids[n][1], node_ids[n][2]};
//			S[0] = FReal(0.5) + T_of_x[1][0] * T_of_roots[1][j[0]]; // 2 flops 
//			S[1] = FReal(0.5) + T_of_x[1][1] * T_of_roots[1][j[1]]; // 2 flops
//			S[2] = FReal(0.5) + T_of_x[1][2] * T_of_roots[1][j[2]]; // 2 flops
//			for (unsigned int o=2; o<ORDER; ++o) {
//				S[0] += T_of_x[o][0] * T_of_roots[o][j[0]]; // 2 flops
//				S[1] += T_of_x[o][1] * T_of_roots[o][j[1]]; // 2 flops
//				S[2] += T_of_x[o][2] * T_of_roots[o][j[2]]; // 2 flops
//			} // flops: (ORDER-2) * 6
//
//			// gather contributions
//			multipoleExpansion[n]	+= c1 *	S[0] * S[1] * S[2] *	sourceValue; // 4 flops
//		} // flops: ORDER*ORDER*ORDER * (10 + (ORDER-2) * 6)
//
//		// increment source iterator
//		iter.gotoNext();
//	} // flops: M * (18 + (ORDER-1) * 6 + ORDER*ORDER*ORDER * (10 + (ORDER-2) * 6))
//}



777 778 779
/**
 * Local to particle operation: application of \f$S_\ell(x,\bar x_m)\f$ (interpolation)
 */
780
template <int ORDER, class MatrixKernelClass>
781
template <class ContainerClass>
782
inline void FChebInterpolator<ORDER,MatrixKernelClass>::applyL2P(const FPoint& center,
783 784 785
                                             const FReal width,
                                             const FReal *const localExpansion,
                                             ContainerClass *const inParticles) const
786
{
787 788 789 790 791 792 793 794 795 796 797 798
    FReal f1[nLhs];
    FReal W2[nLhs][3][ ORDER-1];
    FReal W4[nLhs][3][(ORDER-1)*(ORDER-1)];
    FReal W8[nLhs][   (ORDER-1)*(ORDER-1)*(ORDER-1)];
    { 
      for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs){

      // sum over interpolation points
        f1[idxLhs] = FReal(0.);
        for(unsigned int i=0; i<ORDER-1; ++i)	                   W2[idxLhs][0][i] = W2[idxLhs][1][i] = W2[idxLhs][2][i] = FReal(0.);
        for(unsigned int i=0; i<(ORDER-1)*(ORDER-1); ++i)        W4[idxLhs][0][i] = W4[idxLhs][1][i] = W4[idxLhs][2][i] = FReal(0.);
        for(unsigned int i=0; i<(ORDER-1)*(ORDER-1)*(ORDER-1); ++i)	W8[idxLhs][i] = FReal(0.);
799 800 801 802 803 804

        for (unsigned int idx=0; idx<nnodes; ++idx) {
            const unsigned int i = node_ids[idx][0];
            const unsigned int j = node_ids[idx][1];
            const unsigned int k = node_ids[idx][2];

805
            f1[idxLhs] += localExpansion[2*idxLhs*nnodes + idx]; // 1 flop
806 807

            for (unsigned int l=0; l<ORDER-1; ++l) {
808 809 810 811 812 813
                const FReal wx = T[l*ORDER+i] * localExpansion[2*idxLhs*nnodes + idx]; // 1 flops
                const FReal wy = T[l*ORDER+j] * localExpansion[2*idxLhs*nnodes + idx]; // 1 flops
                const FReal wz = T[l*ORDER+k] * localExpansion[2*idxLhs*nnodes + idx]; // 1 flops
                W2[idxLhs][0][l] += wx; // 1 flops
                W2[idxLhs][1][l] += wy; // 1 flops
                W2[idxLhs][2][l] += wz; // 1 flops
814 815 816 817
                for (unsigned int m=0; m<ORDER-1; ++m) {
                    const FReal wxy = wx * T[m*ORDER + j]; // 1 flops
                    const FReal wxz = wx * T[m*ORDER + k]; // 1 flops
                    const FReal wyz = wy * T[m*ORDER + k]; // 1 flops
818 819 820
                    W4[idxLhs][0][m*(ORDER-1)+l] += wxy; // 1 flops
                    W4[idxLhs][1][m*(ORDER-1)+l] += wxz; // 1 flops
                    W4[idxLhs][2][m*(ORDER-1)+l] += wyz; // 1 flops
821 822
                    for (unsigned int n=0; n<ORDER-1; ++n) {
                        const FReal wxyz = wxy * T[n*ORDER + k]; // 1 flops
823
                        W8[idxLhs][n*(ORDER-1)*(ORDER-1) + m*(ORDER-1) + l]	+= wxyz; // 1 flops
824 825 826 827
                    } // (ORDER-1) * 2 flops
                } // (ORDER-1) * (6 + (ORDER-1)*2) flops
            } // (ORDER-1) * (6 + (ORDER-1) * (6 + (ORDER-1)*2)) flops
        } // ORDER*ORDER*ORDER * (1 + (ORDER-1) * (6 + (ORDER-1) * (6 + (ORDER-1)*2))) flops
828
      } // NLHS
829 830 831 832 833 834
    }


    // loop over particles
    const map_glob_loc map(center, width);
    FPoint localPosition;
835 836 837 838 839 840 841 842

    //const FReal*const physicalValues = inParticles->getPhysicalValues();
    const FReal*const positionsX = inParticles->getPositions()[0];
    const FReal*const positionsY = inParticles->getPositions()[1];
    const FReal*const positionsZ = inParticles->getPositions()[2];
    //FReal*const forcesX = inParticles->getForcesX();
    //FReal*const forcesY = inParticles->getForcesY();
    //FReal*const forcesZ = inParticles->getForcesZ();
843
//    FReal*const potentials = inParticles->getPotentials();
844 845

    for(int idxPart = 0 ; idxPart < inParticles->getNbParticles() ; ++ idxPart){
846

847 848
      // map global position to [-1,1]
      map(FPoint(positionsX[idxPart],positionsY[idxPart],positionsZ[idxPart]), localPosition); // 15 flops
849

850 851 852 853 854 855 856 857 858 859 860 861
      FReal T_of_x[3][ORDER];
      {
        T_of_x[0][0] = FReal(1.); T_of_x[0][1] = localPosition.getX();
        T_of_x[1][0] = FReal(1.); T_of_x[1][1] = localPosition.getY();
        T_of_x[2][0] = FReal(1.); T_of_x[2][1] = localPosition.getZ();
        const FReal x2 = FReal(2.) * T_of_x[0][1]; // 1 flop
        const FReal y2 = FReal(2.) * T_of_x[1][1]; // 1 flop
        const FReal z2 = FReal(2.) * T_of_x[2][1]; // 1 flop
        for (unsigned int j=2; j<ORDER; ++j) {
          T_of_x[0][j] = x2 * T_of_x[0][j-1] - T_of_x[0][j-2]; // 2 flops
          T_of_x[1][j] = y2 * T_of_x[1][j-1] - T_of_x[1][j-2]; // 2 flops
          T_of_x[2][j] = z2 * T_of_x[2][j-1] - T_of_x[2][j-2]; // 2 flops
862
        }
863 864
      }

865 866 867 868 869 870 871 872 873
      for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs){      
        // distribution over potential components:
        // We sum the multidim contribution of PhysValue
        // This was originally done at M2L step but moved here 
        // because their storage is required by the force computation.
        // In fact : f_{ik}(x)=w_j(x) \nabla_{x_i} K_{ij}(x,y)w_j(y))
        const unsigned int idxPot = idxLhs / nPV; 

        FReal*const potentials = inParticles->getPotentials(idxPot);
874 875

        // interpolate and increment target value
876
        FReal targetValue = potentials[idxPart];
877
        {
878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899
          FReal f2, f4, f8;
          {
            f2 = f4 = f8 = FReal(0.);
            for (unsigned int l=1; l<ORDER; ++l) {
              f2 +=
                T_of_x[0][l] * W2[idxLhs][0][l-1] +
                T_of_x[1][l] * W2[idxLhs][1][l-1] +
                T_of_x[2][l] * W2[idxLhs][2][l-1]; // 6 flops
              for (unsigned int m=1; m<ORDER; ++m) {
                f4 +=
                  T_of_x[0][l] * T_of_x[1][m] * W4[idxLhs][0][(m-1)*(ORDER-1)+(l-1)] +
                  T_of_x[0][l] * T_of_x[2][m] * W4[idxLhs][1][(m-1)*(ORDER-1)+(l-1)] +
                  T_of_x[1][l] * T_of_x[2][m] * W4[idxLhs][2][(m-1)*(ORDER-1)+(l-1)]; // 9 flops
                for (unsigned int n=1; n<ORDER; ++n) {
                  f8 +=
                    T_of_x[0][l] * T_of_x[1][m] * T_of_x[2][n] *
                    W8[idxLhs][(n-1)*(ORDER-1)*(ORDER-1) + (m-1)*(ORDER-1) + (l-1)];
                } // ORDER * 4 flops
              } // ORDER * (9 + ORDER * 4) flops
            } // ORDER * (ORDER * (9 + ORDER * 4)) flops
          }
          targetValue = (f1[idxLhs] + FReal(2.)*f2 + FReal(4.)*f4 + FReal(8.)*f8) / nnodes; // 7 flops
900 901
        } // 7 + ORDER * (ORDER * (9 + ORDER * 4)) flops

902
          // set potential
903
        potentials[idxPart] += (targetValue);
904 905
      } // NLHS
    } // N * (7 + ORDER * (ORDER * (9 + ORDER * 4))) flops
906 907 908
}


909 910 911 912 913 914 915
//	FReal F2[3][ORDER-1];
//	FBlas::gemtv(ORDER, ORDER-1, FReal(1.), const_cast<FReal*>(T), const_cast<FReal*>(localExpansion), F2[0]);
//	for (unsigned int i=1; i<ORDER*ORDER; ++i)
//		FBlas::gemtva(ORDER, ORDER-1, FReal(1.), const_cast<FReal*>(T),
//									const_cast<FReal*>(localExpansion) + ORDER*i, F2[0]);
//	for (unsigned int i=0; i<ORDER-1; ++i)
//		std::cout << W2[0][i] << "\t" << F2[0][i] << std::endl;
916

917 918 919 920 921 922 923 924
//	FReal F2[(ORDER-1) * ORDER*ORDER];
//	FBlas::gemtm(ORDER, ORDER-1, ORDER*ORDER, FReal(1.), const_cast<FReal*>(T), ORDER,
//							 const_cast<FReal*>(localExpansion), ORDER, F2, ORDER-1);
//	FReal F[ORDER-1]; FBlas::setzero(ORDER-1, F);
//	for (unsigned int i=0; i<ORDER-1; ++i)
//		for (unsigned int j=0; j<ORDER*ORDER; ++j) F[i] += F2[j*(ORDER-1) + i];
//	for (unsigned int i=0; i<ORDER-1; ++i)
//		std::cout << W2[0][i] << "\t" << F[i] << std::endl;
925 926


927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991
///**
// * Local to particle operation: application of \f$S_\ell(x,\bar x_m)\f$ (interpolation)
// */
//template <int ORDER>
//template <class ContainerClass>
//inline void FChebInterpolator<ORDER>::applyL2P(const FPoint& center,
//																							 const FReal width,
//																							 const FReal *const localExpansion,
//																							 ContainerClass *const localParticles) const
//{
//	// allocate stuff
//	const map_glob_loc map(center, width);
//	FPoint localPosition;
//	FReal T_of_x[ORDER][3];
//	FReal xpx,ypy,zpz ;
//	FReal S[3],c1;
//	//
//	c1 = FReal(8.) / nnodes ;
//	typename ContainerClass::BasicIterator iter(*localParticles);
//	while(iter.hasNotFinished()){
//			
//		// map global position to [-1,1]
//		map(iter.data().getPosition(), localPosition); // 15 flops
//
//		// evaluate chebyshev polynomials of source particle: T_o(x_i)
//		T_of_x[0][0] = FReal(1.);	T_of_x[1][0] = localPosition.getX();
//		T_of_x[0][1] = FReal(1.);	T_of_x[1][1] = localPosition.getY();
//		T_of_x[0][2] = FReal(1.);	T_of_x[1][2] = localPosition.getZ();
//		xpx = FReal(2.) * localPosition.getX() ; // 1 flop
//		ypy = FReal(2.) * localPosition.getY() ; // 1 flop
//		zpz = FReal(2.) * localPosition.getZ() ; // 1 flop
//		for (unsigned int o=2; o<ORDER; ++o) {
//			T_of_x[o][0] = xpx * T_of_x[o-1][0] - T_of_x[o-2][0]; // 2 flop
//			T_of_x[o][1] = ypy * T_of_x[o-1][1] - T_of_x[o-2][1]; // 2 flop
//			T_of_x[o][2] = zpz * T_of_x[o-1][2] - T_of_x[o-2][2]; // 2 flop
//		} // (ORDER-2) * 6 flops
//
//		// interpolate and increment target value
//		FReal targetValue = iter.data().getPotential();
//		for (unsigned int n=0; n<nnodes; ++n) {
//			const unsigned int j[3] = {node_ids[n][0], node_ids[n][1], node_ids[n][2]};
//			S[0] = T_of_x[1][0] * T_of_roots[1][j[0]]; // 1 flops
//			S[1] = T_of_x[1][1] * T_of_roots[1][j[1]]; // 1 flops
//			S[2] = T_of_x[1][2] * T_of_roots[1][j[2]]; // 1 flops
//			for (unsigned int o=2; o<ORDER; ++o) {
//				S[0] += T_of_x[o][0] * T_of_roots[o][j[0]]; // 2 flops
//				S[1] += T_of_x[o][1] * T_of_roots[o][j[1]]; // 2 flops
//				S[2] += T_of_x[o][2] * T_of_roots[o][j[2]]; // 2 flops
//			} // (ORDER-2) * 6 flops 
//			// gather contributions
//			S[0] += FReal(0.5); // 1 flops
//			S[1] += FReal(0.5); // 1 flops
//			S[2] += FReal(0.5); // 1 flops
//			targetValue	+= S[0] * S[1] * S[2] * localExpansion[n]; // 4 flops
//		} // ORDER*ORDER*ORDER * (10 + (ORDER-2) * 6) flops
//		// scale
//		targetValue *= c1; // 1 flops
//
//		// set potential
//		iter.data().setPotential(targetValue);
//
//		// increment target iterator
//		iter.gotoNext();
//	} // N * ORDER*ORDER*ORDER * (10 + (ORDER-2) * 6) flops
//}
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/**
 * Local to particle operation: application of \f$\nabla_x S_\ell(x,\bar x_m)\f$ (interpolation)
 */
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template <int ORDER, class MatrixKernelClass>
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template <class ContainerClass>
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inline void FChebInterpolator<ORDER,MatrixKernelClass>::applyL2PGradient(const FPoint& center,
                                                                         const FReal width,
                                                                         const FReal *const localExpansion,
                                                                         ContainerClass *const inParticles) const
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{
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    ////////////////////////////////////////////////////////////////////
    // TENSOR-PRODUCT INTERPOLUTION NOT IMPLEMENTED YET HERE!!! ////////
    ////////////////////////////////////////////////////////////////////

    // setup local to global mapping
    const map_glob_loc map(center, width);
    FPoint Jacobian;
    map.computeJacobian(Jacobian);
    const FReal jacobian[3] = {Jacobian.getX(), Jacobian.getY(), Jacobian.getZ()};
    FPoint localPosition;
    FReal T_of_x[ORDER][3];
    FReal U_of_x[ORDER][3];
    FReal P[3];
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//    const FReal*const physicalValues = inParticles->getPhysicalValues();
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    const FReal*const positionsX = inParticles->getPositions()[0];
    const FReal*const positionsY = inParticles->getPositions()[1];
    const FReal*const positionsZ = inParticles->getPositions()[2];
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//    FReal*const forcesX = inParticles->getForcesX();
//    FReal*const forcesY = inParticles->getForcesY();
//    FReal*const forcesZ = inParticles->getForcesZ();
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    //FReal*const potentials = inParticles->getPotentials();

    for(int idxPart = 0 ; idxPart < inParticles->getNbParticles() ; ++ idxPart){
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        // map global position to [-1,1]
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        map(FPoint(positionsX[idxPart],positionsY[idxPart],positionsZ[idxPart]), localPosition);
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        // evaluate chebyshev polynomials of source particle
        // T_0(x_i) and T_1(x_i)
        T_of_x[0][0] = FReal(1.);	T_of_x[1][0] = localPosition.getX();
        T_of_x[0][1] = FReal(1.);	T_of_x[1][1] = localPosition.getY();
        T_of_x[0][2] = FReal(1.);	T_of_x[1][2] = localPosition.getZ();
        // U_0(x_i) and U_1(x_i)
        U_of_x[0][0] = FReal(1.);	U_of_x[1][0] = localPosition.getX() * FReal(2.);
        U_of_x[0][1] = FReal(1.);	U_of_x[1][1] = localPosition.getY() * FReal(2.);
        U_of_x[0][2] = FReal(1.);	U_of_x[1][2] = localPosition.getZ() * FReal(2.);
        for (unsigned int o=2; o<ORDER; ++o) {
            // T_o(x_i)
            T_of_x[o][0] = FReal(2.)*localPosition.getX()*T_of_x[o-1][0] - T_of_x[o-2][0];
            T_of_x[o][1] = FReal(2.)*localPosition.getY()*T_of_x[o-1][1] - T_of_x[o-2][1];
            T_of_x[o][2] = FReal(2.)*localPosition.getZ()*T_of_x[o-1][2] - T_of_x[o-2][2];
            // U_o(x_i)
            U_of_x[o][0] = FReal(2.)*localPosition.getX()*U_of_x[o-1][0] - U_of_x[o-2][0];
            U_of_x[o][1] = FReal(2.)*localPosition.getY()*U_of_x[o-1][1] - U_of_x[o-2][1];
            U_of_x[o][2] = FReal(2.)*localPosition.getZ()*U_of_x[o-1][2] - U_of_x[o-2][2];
        }

        // scale, because dT_o/dx = oU_{o-1}
        for (unsigned int o=2; o<ORDER; ++o) {
            U_of_x[o-1][0] *= FReal(o);
            U_of_x[o-1][1] *= FReal(o);
            U_of_x[o-1][2] *= FReal(o);
        }

        // apply P and increment forces
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        FReal forces[nLhs][3]; 
        for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs)
          for (unsigned int i=0; i<3; ++i)
            forces[idxLhs][i] = FReal(0.);

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        for (unsigned int n=0; n<nnodes; ++n) {

            // tensor indices of chebyshev nodes
            const unsigned int j[3] = {node_ids[n][0], node_ids[n][1], node_ids[n][2]};

            // f0 component //////////////////////////////////////
            P[0] = U_of_x[0][0] * T_of_roots[1][j[0]];
            P[1] = T_of_x[1][1] * T_of_roots[1][j[1]];
            P[2] = T_of_x[1][2] * T_of_roots[1][j[2]];
            for (unsigned int o=2; o<ORDER; ++o) {
                P[0] += U_of_x[o-1][0] * T_of_roots[o][j[0]];
                P[1] += T_of_x[o  ][1] * T_of_roots[o][j[1]];
                P[2] += T_of_x[o  ][2] * T_of_roots[o][j[2]];
            }
            P[0] *= FReal(2.);
            P[1] *= FReal(2.); P[1] += FReal(1.);
            P[2] *= FReal(2.); P[2] += FReal(1.);
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            for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs)
              forces[idxLhs][0]	+= P[0] * P[1] * P[2] * localExpansion[2*idxLhs*nnodes + n];
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            // f1 component //////////////////////////////////////
            P[0] = T_of_x[1][0] * T_of_roots[1][j[0]];
            P[1] = U_of_x[0][1] * T_of_roots[1][j[1]];
            P[2] = T_of_x[1][2] * T_of_roots[1][j[2]];
            for (unsigned int o=2; o<ORDER; ++o) {
                P[0] += T_of_x[o  ][0] * T_of_roots[o][j[0]];
                P[1] += U_of_x[o-1][1] * T_of_roots[o][j[1]];
                P[2] += T_of_x[o  ][2] * T_of_roots[o][j[2]];
            }
            P[0] *= FReal(2.); P[0] += FReal(1.);
            P[1] *= FReal(2.);
            P[2] *= FReal(2.); P[2] += FReal(1.);
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            for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs)
            forces[idxLhs][1]	+= P[0] * P[1] * P[2] * localExpansion[2*idxLhs*nnodes + n];
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            // f2 component //////////////////////////////////////
            P[0] = T_of_x[1][0] * T_of_roots[1][j[0]];
            P[1] = T_of_x[1][1] * T_of_roots[1][j[1]];
            P[2] = U_of_x[0][2] * T_of_roots[1][j[2]];
            for (unsigned int o=2; o<ORDER; ++o) {
                P[0] += T_of_x[o  ][0] * T_of_roots[o][j[0]];
                P[1] += T_of_x[o  ][1] * T_of_roots[o][j[1]];
                P[2] += U_of_x[o-1][2] * T_of_roots[o][j[2]];
            }
            P[0] *= FReal(2.); P[0] += FReal(1.);
            P[1] *= FReal(2.); P[1] += FReal(1.);
            P[2] *= FReal(2.);
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            for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs)
              forces[idxLhs][2]	+= P[0] * P[1] * P[2] * localExpansion[2*idxLhs*nnodes + n];
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        }

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        for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs){
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          const unsigned int idxPot = idxLhs / nPV; 
          const unsigned int idxPV  = idxLhs % nPV; 
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          // scale forces
          forces[idxLhs][0] *= jacobian[0] / nnodes;
          forces[idxLhs][1] *= jacobian[1] / nnodes;
          forces[idxLhs][2] *= jacobian[2] / nnodes;

          // get pointers to PhysValues and force components
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          const FReal*const physicalValues = inParticles->getPhysicalValues(idxPV);
          FReal*const forcesX = inParticles->getForcesX(idxPot);
          FReal*const forcesY = inParticles->getForcesY(idxPot);
          FReal*const forcesZ = inParticles->getForcesZ(idxPot);
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          // set computed forces
          forcesX[idxPart] += forces[idxLhs][0] * physicalValues[idxPart];
          forcesY[idxPart] += forces[idxLhs][1] * physicalValues[idxPart];
          forcesZ[idxPart] += forces[idxLhs][2] * physicalValues[idxPart];
        }
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    }
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}
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/**
 * Local to particle operation: application of \f$S_\ell(x,\bar x_m)\f$ and
 * \f$\nabla_x S_\ell(x,\bar x_m)\f$ (interpolation)
 */
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template <int ORDER, class MatrixKernelClass>
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template <class ContainerClass>
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inline void FChebInterpolator<ORDER,MatrixKernelClass>::applyL2PTotal(const FPoint& center,
                                                                      const FReal width,
                                                                      const FReal *const localExpansion,
                                                                      ContainerClass *const inParticles) const
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{
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    FReal f1[nLhs];
    FReal W2[nLhs][3][ ORDER-1];
    FReal W4[nLhs][3][(ORDER-1)*(ORDER-1)];
    FReal W8[nLhs][   (ORDER-1)*(ORDER-1)*(ORDER-1)];
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    //{ // sum over interpolation points
    //	f1 = FReal(0.);
    //	for(unsigned int i=0; i<ORDER-1; ++i)	                   W2[0][i] = W2[1][i] = W2[2][i] = FReal(0.);
    //	for(unsigned int i=0; i<(ORDER-1)*(ORDER-1); ++i)        W4[0][i] = W4[1][i] = W4[2][i] = FReal(0.);
    //	for(unsigned int i=0; i<(ORDER-1)*(ORDER-1)*(ORDER-1); ++i)	W8[i] = FReal(0.);
    //
    //	for (unsigned int idx=0; idx<nnodes; ++idx) {
    //		const unsigned int i = node_ids[idx][0];
    //		const unsigned int j = node_ids[idx][1];
    //		const unsigned int k = node_ids[idx][2];
    //
    //		f1 += localExpansion[idx]; // 1 flop
    //
    //		for (unsigned int l=0; l<ORDER-1; ++l) {
    //			const FReal wx = T[l*ORDER+i] * localExpansion[idx]; // 1 flops
    //			const FReal wy = T[l*ORDER+j] * localExpansion[idx]; // 1 flops
    //			const FReal wz = T[l*ORDER+k] * localExpansion[idx]; // 1 flops
    //			W2[0][l] += wx; // 1 flops
    //			W2[1][l] += wy; // 1 flops
    //			W2[2][l] += wz; // 1 flops
    //			for (unsigned int m=0; m<ORDER-1; ++m) {
    //				const FReal wxy = wx * T[m*ORDER + j]; // 1 flops
    //				const FReal wxz = wx * T[m*ORDER + k]; // 1 flops
    //				const FReal wyz = wy * T[m*ORDER + k]; // 1 flops
    //				W4[0][m*(ORDER-1)+l] += wxy; // 1 flops
    //				W4[1][m*(ORDER-1)+l] += wxz; // 1 flops
    //				W4[2][m*(ORDER-1)+l] += wyz; // 1 flops
    //				for (unsigned int n=0; n<ORDER-1; ++n) {
    //					const FReal wxyz = wxy * T[n*ORDER + k]; // 1 flops
    //					W8[n*(ORDER-1)*(ORDER-1) + m*(ORDER-1) + l]	+= wxyz; // 1 flops
    //				} // (ORDER-1) * 2 flops
    //			} // (ORDER-1) * (6 + (ORDER-1)*2) flops
    //		} // (ORDER-1) * (6 + (ORDER-1) * (6 + (ORDER-1)*2)) flops
    //
    //	} // ORDER*ORDER*ORDER * (1 + (ORDER-1) * (6 + (ORDER-1) * (6 + (ORDER-1)*2))) flops
    //
    //}

    {
        // for W2
        FReal lE[nnodes];
        FReal F2[(ORDER-1) * ORDER*ORDER];
        // for W4
        FReal F4[ORDER * ORDER*(ORDER-1)];
        FReal G4[(ORDER-1) * ORDER*(ORDER-1)];
        // for W8
        FReal G8[ORDER * (ORDER-1)*(ORDER-1)];

        // sum local expansions
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        for(int idxLhs = 0 ; idxLhs < nLhs ; ++idxLhs){
          f1[idxLhs] = FReal(0.);
          for (unsigned int idx=0; idx<nnodes; ++idx)	f1[idxLhs] += localExpansion[2*idxLhs*nnodes + idx]; // 1 flop
        
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        //////////////////////////////////////////////////////////////////
        // IMPORTANT: NOT CHANGE ORDER OF COMPUTATIONS!!! ////////////////
        //////////////////////////////////////////////////////////////////

        // W2[0] ///////////////// (ORDER-1)*ORDER*ORDER * 2*ORDER
        FBlas::gemtm(ORDER, ORDER-1, ORDER*ORDER, FReal(1.), const_cast<FReal*>(T), ORDER,
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                                 const_cast<FReal*>(localExpansion) + 2*idxLhs*nnodes, ORDER, F2, ORDER-1);
        for (unsigned int l=0; l<ORDER-1; ++l) { W2[idxLhs][0][l] = F2[l];
            for (unsigned int j=1; j<ORDER*ORDER; ++j) W2[idxLhs][0][l] += F2[j*(ORDER-1) + l];	}
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        // W4[0] ///////////////// ORDER*(ORDER-1)*(ORDER-1) + 2*ORDER
        perm5.permute(F2, F4);
        FBlas::gemtm(ORDER, ORDER-1, ORDER*(ORDER-1), FReal(1.), const_cast<FReal*>(T), ORDER, F4, ORDER, G4, ORDER-1);
        for (unsigned int l=0; l<ORDER-1; ++l)
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            for (unsigned int m=0; m<ORDER-1; ++m) { W4[idxLhs][0][m*(ORDER-1)+l] = G4[l*ORDER*(ORDER-1) + m];
                for (unsigned int k=1; k<ORDER; ++k) W4[idxLhs][0][m*(ORDER-1)+l] += G4[l*ORDER*(ORDER-1) + k*(ORDER-1) + m];	}
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        // W8 //////////////////// (ORDER-1)*(ORDER-1)*(ORDER-1) * (2*ORDER-1)
        perm8.permute(G4, G8);
        FReal F8[(ORDER-1)*(ORDER-1)*(ORDER-1)];
        FBlas::gemtm(ORDER, ORDER-1, (ORDER-1)*(ORDER-1), FReal(1.), const_cast<FReal*>(T), ORDER, G8, ORDER, F8, ORDER-1);
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        perm9.permute(F8, W8[idxLhs]);
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        // W4[1] ///////////////// ORDER*(ORDER-1)*(ORDER-1) + 2*ORDER
        perm6.permute(F2, F4);
        FBlas::gemtm(ORDER, ORDER-1, (ORDER-1)*ORDER, FReal(1.), const_cast<FReal*>(T), ORDER, F4, ORDER, G4, ORDER-1);
        for (unsigned int l=0; l<ORDER-1; ++l)
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            for (unsigned int n=0; n<ORDER-1; ++n) { W4[idxLhs][1][n*(ORDER-1)+l] = G4[l*(ORDER-1) + n];
                for (unsigned int j=1; j<ORDER; ++j) W4[idxLhs][1][n*(ORDER-1)+l] += G4[j*(ORDER-1)*(ORDER-1) + l*(ORDER-1) + n];	}
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        // W2[1] ///////////////// (ORDER-1)*ORDER*ORDER * 2*ORDER
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        perm3.permute(localExpansion + 2*idxLhs*nnodes, lE);
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        FBlas::gemtm(ORDER, ORDER-1, ORDER*ORDER, FReal(1.), const_cast<FReal*>(T), ORDER, lE, ORDER, F2, ORDER-1);
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        for (unsigned int i=0; i<ORDER-1; ++i) { W2[idxLhs][1][i] = F2[i];
            for (unsigned int j=1; j<ORDER*ORDER; ++j) W2[idxLhs][1][i] += F2[j*(ORDER-1) + i]; }
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        // W4[2] ///////////////// ORDER*(ORDER-1)*(ORDER-1) + 2*ORDER
        perm7.permute(F2, F4);
        FBlas::gemtm(ORDER, ORDER-1, (ORDER-1)*ORDER, FReal(1.), const_cast<FReal*>(T), ORDER, F4, ORDER, G4, ORDER-1);
        for (unsigned int m=0; m<ORDER-1; ++m)
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            for (unsigned int n=0; n<ORDER-1; ++n) { W4[idxLhs][2][n*(ORDER-1)+m] = G4[m*ORDER*(ORDER-1) + n];
                for (unsigned int i=1; i<ORDER; ++i) W4[idxLhs][2][n*(ORDER-1)+m] += G4[m*ORDER*(ORDER-1) + i*(ORDER-1) + n];	}
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        // W2[2] ///////////////// (ORDER-1)*ORDER*ORDER * 2*ORDER
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        perm4.permute(localExpansion + 2*idxLhs*nnodes, lE);
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        FBlas::gemtm(ORDER, ORDER-1, ORDER*ORDER, FReal(1.), const_cast<FReal*>(T), ORDER, lE, ORDER, F2, ORDER-1);