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#ifndef VIGRA_WIGNER_MATRIX_HXX
#define VIGRA_WIGNER_MATRIX_HXX

#include <complex>
#include "config.hxx"
#include "error.hxx"
#include "utilities.hxx"
#include "mathutil.hxx"
#include "array_vector.hxx"
#include "matrix.hxx"
#include "tinyvector.hxx"
#include "quaternion.hxx"
#include "clebsch-gordan.hxx"

namespace vigra {

    /**
     *  \class WignerMatrix 
     *  \brief computation of Wigner D matrix + rotation functions 
     *         in SH,VH and R³
     *
     * All rotations in Euler zyz' convention   
     *
     * WARNING: not thread safe! use a new instance of WignerMatrix
     * for each thread!!!
     */
template <class Real>
class WignerMatrix
{   
  public:
  
    // FIXME: should we rather use FFTWComplex?
    typedef std::complex<Real> Complex;
    typedef ArrayVector<ArrayVector<ArrayVector<Complex> > > NestedArray;
    
         /** \brief constructor
          * 
          * \param l_max    maximum expansion band (used to pre-compute 
          *         the D matrix)
          *
          */
    WignerMatrix(int l_max);
    
         /** \brief Compute D with fixed theta = pi/2, phi=0, psi=0.
          *
          * \param band expansion band
          *
             FIXME: compute_D(l, 0.0, M_PI / 2.0, 0.0) creates the transposed matrix!
          */
    void compute_D(int band);

         /** \brief Compute D for arbitrary rotations.
          *
          * \param l        expansion band
          * \param phi  rotation angle  
          * \param theta    rotation angle
          * \param psi  rotation angle
          *
          */
    void compute_D(int l, Real phi, Real theta, Real psi);

         /** \brief  Get the (n,m) entry of D.
          *
          * \param l        expansion band
          * \param n        
          * \param m    
          */
    Complex get_D(int l, int n, int m) const
    {
        if (l>0)
        {
            std::string message = std::string("WignerMatrix::get_D(): index out of bounds: l=");
            message << l << " l_max=" << D.size() << " m=" << m << " n=" << n << "\n";
                                  
            vigra_precondition(l < D.size() && m+l <= 2*l+1 &&
                               n+l <= 2*l+1 && m+l >= 0 && n+l >= 0,
                               message.c_str());
            return D[l](n+l, m+l);
        }
        else 
        {
            return Complex(Real(1.0));
        }
    }

         /** \brief Return the rotation matrix D for the lth band.
          *
          * \param l        expansion band
          */
    Matrix<Complex> const & get_D(int l) const
    {
        std::string message = std::string("WignerMatrix::get_D(): index out of bounds: l=");
        message << l << " l_max=" << l_max << "\n";
                              
        vigra_precondition(l > 0 && l <= l_max, message.c_str());
        return D[l];
    }

         /** \brief Rotate in PH.
          *
          * \param PH       input PH expansion 
          * \param phi      rotation angle
          * \param theta    rotation angle
          * \param psi      rotation angle
          *
          * \retval PHresult PH expansion   
          */
    void rotatePH(NestedArray const & PH, Real phi, Real theta, Real psi,
                  NestedArray & PHresult);


  private:
    // FIXME: is function is not called (and cannot be called from outside the class)
    TinyVector<double,3> 
    rot(TinyVector<double,3> const & vec, TinyVector<double,3> const & axis, double angle)
    {
        typedef Quaternion<double> Q;
        Q qr = Q::createRotation(angle, axis),
          qv(0.0, vec);
        return (qr * qv * conj(qr)).v();
    }

    int l_max;
    int cg1cnt;
    ArrayVector<double> CGcoeff;
    ArrayVector<Matrix<Complex> > D;
};

template <class Real>
WignerMatrix<Real>::WignerMatrix(int band)
: l_max(0),
  cg1cnt(0)
{
    //precompute clebschGordan coeffs
    for (int l = 2; l <= band+1; l++)
    {
        for(int m = -l; m <= l ; m++)
        {
            for(int n = -l; n <= l ; n++)
            {
                for (int m2 = -1; m2 <= 1; m2++)
                {
                    for (int n2 = -1; n2 <= 1; n2++)
                    {
                        int m1 = m-m2;
                        int n1 = n-n2;
                        if (m1 > -l && m1 < l && n1 > -l && n1 < l)
                        {
                            CGcoeff.push_back((clebschGordan(l-1,m1,1,m2,l,m))*(clebschGordan(l-1,n1,1,n2,l,n)));
                        }
                    }
                }
            }
        }
    }
}

template <class Real>
void
WignerMatrix<Real>::compute_D(int l, Real phi, Real theta, Real psi)
{
    double s = std::sin(theta);
    double c = std::cos(theta);
    
    Complex i(0.0, 1.0);
    Complex eiphi = std::exp(i*phi);
    Complex emiphi = std::exp(-i*phi);
    Complex eipsi = std::exp(i*psi);
    Complex emipsi = std::exp(-i*psi);
    
    if (D.size() < (std::size_t)(l+1)) 
        D.resize(l+1);
    D[1].reshape(MultiArrayShape<2>::type(3,3));
    
    D[1](0,0) = emipsi * Complex(Real(0.5*(1.0+c))) * emiphi;
    D[1](0,1) = Complex(Real(-s/M_SQRT2)) * emiphi;
    D[1](0,2) = eipsi * Complex(Real(0.5*(1.0-c))) * emiphi;
    D[1](1,0) = emipsi * Complex(Real(s/M_SQRT2));
    D[1](1,1) = Complex(Real(c));
    D[1](1,2) = eipsi * Complex(Real(-s/M_SQRT2));
    D[1](2,0) = emipsi * Complex(Real(0.5*(1.0-c))) * eiphi; 
    D[1](2,1) = Complex(Real(s/M_SQRT2)) * eiphi;
    D[1](2,2) = eipsi * Complex(Real(0.5*(1.0+c))) * eiphi;

    l_max = 1;
    cg1cnt = 0;
    if(l > 1)
        compute_D( l);
}


template <class Real>
void
WignerMatrix<Real>::compute_D(int l)
{
    if (D.size() < (std::size_t)(l+1) ) 
    {
        D.resize(l+1);
        l_max = 0;
    }

    if (l==1)
    {
        //precompute D0 =1 and D1 = (90 degree rot)
        // FIXME: signs are inconsistent with above explicit formula for 
        //        theta = pi/2, phi=0, psi=0 (sine terms should be negated)
        D[1].reshape(MultiArrayShape<2>::type(3,3));
        D[1](0,0) = Real(0.5);
        D[1](0,1) = Real(0.5*M_SQRT2);
        D[1](0,2) = Real(0.5);
        D[1](1,0) = Real(-0.5*M_SQRT2);
        D[1](1,1) = Real(0.0);
        D[1](1,2) = Real(0.5*M_SQRT2);
        D[1](2,0) = Real(0.5);
        D[1](2,1) = Real(-0.5*M_SQRT2);
        D[1](2,2) = Real(0.5);
        l_max = 1;
        cg1cnt = 0;
    }
    else
    {
        //compute D2-Dl_max recursive
        if (l>l_max+1)
        {
            compute_D(l-1);
        }

        D[l].reshape(MultiArrayShape<2>::type(2*l+1,2*l+1));
        D[l].init(Real(0.0));      
        
        for(int m = -l; m <= l ; m++)
        {
            for(int n = -l; n <= l ; n++)
            {
                for (int m2 = -1; m2 <= 1; m2++)
                {
                    for (int n2 = -1; n2 <= 1; n2++)
                    {
                        int m1 = m-m2;
                        int n1 = n-n2;
                        if ((m1 > -l) && (m1 < l) && (n1 > -l) && (n1 < l))
                        {
                            D[l](m+l,n+l) += D[1](m2+1,n2+1) * D[l-1](m1+l-1,n1+l-1) * Real(CGcoeff[cg1cnt++]);
                        }
                    }
                }
            }
        }

        l_max = l;
    }
}

template <class Real>
void 
WignerMatrix<Real>::rotatePH(NestedArray const & PH, Real phi, Real theta, Real psi,
                             NestedArray & PHresult)
{
    int band = PH[1].size()-1;
    compute_D(band, phi, theta, psi);

    PHresult.resize(PH.size());

    for(int n=1; n<=band; n++)
    {
        PHresult[n].resize(band+1);
        for (int l=0; l<=band; l++)
        {
            PHresult[n][l].resize(2*band+1);
            for(int m=-l; m<=l; m++)
            {
                Complex tmp = 0;
                for (int h=-l; h<=l; h++)
                {
                    tmp += get_D(l,h,m) * PH[n][l][h+l];
                }

                PHresult[n][l][m+l] = tmp;
            }
        }
    }
}

} // namespace vigra 

#endif // VIGRA_WIGNER_MATRIX_HXX
