ddTensor2_symmetric.hpp

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/* Takes a second derivative of a Tensor2_symmetric, yielding a
   Ddg. */
 
#pragma once
 
namespace FTensor
{
  template <class T, int Dim01, int Dim23, char i, char j, char k, char l>
  class ddTensor2_symmetric
  {
    const Tensor2_symmetric<T *, Dim01> &a;
    const Tensor1<int, Dim23> &d_ijk;
    const Tensor1<double, Dim23> &d_xyz;
 
  public:
    typename promote<T, double>::V
    operator()(const int N1, const int N2, const int N3, const int N4) const
    {
      return N3 == N4 ? (*(a.ptr(N1, N2) + d_ijk(N3)) - 2 * a(N1, N2)
                         + *(a.ptr(N1, N2) - d_ijk(N3)))
                          * d_xyz(N3) * d_xyz(N3)
                      : (*(a.ptr(N1, N2) + d_ijk(N3) + d_ijk(N4))
                         - *(a.ptr(N1, N2) - d_ijk(N3) + d_ijk(N4))
                         - *(a.ptr(N1, N2) + d_ijk(N3) - d_ijk(N4))
                         + *(a.ptr(N1, N2) - d_ijk(N3) - d_ijk(N4)))
                          * d_xyz(N3) * d_xyz(N4) * 0.25;
    }
    ddTensor2_symmetric(const Tensor2_symmetric<T *, Dim01> &A,
                        const Tensor1<int, Dim23> &D_ijk,
                        const Tensor1<double, Dim23> &D_xyz)
        : a(A), d_ijk(D_ijk), d_xyz(D_xyz)
    {}
  };
 
  template <class T, int Dim01, int Dim23, char i, char j, char k, char l>
  const Ddg_Expr<const ddTensor2_symmetric<T, Dim01, Dim23, i, j, k, l>,
                 typename promote<T, double>::V, Dim01, Dim23, i, j, k, l>
  dd(const Tensor2_symmetric<T *, Dim01> &a, const Index<i, Dim01> index1,
     const Index<j, Dim01> index2, const Index<k, Dim23> index3,
     const Index<l, Dim23> index4, const Tensor1<int, Dim23> &d_ijk,
     const Tensor1<double, Dim23> &d_xyz)
  {
    using Tensor_Expr = ddTensor2_symmetric<T, Dim01, Dim23, i, j, k, l>;
    return Ddg_Expr<Tensor_Expr, typename promote<T, double>::V, Dim01, Dim23,
                    i, j, k, l>(Tensor_Expr(a, d_ijk, d_xyz));
  }
}