admfem.hpp

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// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.

#ifndef ADMFEM_HPP
#define ADMFEM_HPP

#include "mfem.hpp"
#include "../../linalg/dual.hpp"
#include "tadvector.hpp"
#include "taddensemat.hpp"

#ifdef MFEM_USE_CODIPACK
#include <codi.hpp>

namespace mfem
{

namespace ad
{
#ifdef MFEM_USE_ADFORWARD
/// Forward AD type declaration
typedef codi::RealForward ADFloatType;
/// Vector type for AD-numbers
typedef TAutoDiffVector<ADFloatType> ADVectorType;
/// Matrix type for AD-numbers
typedef TAutoDiffDenseMatrix<ADFloatType> ADMatrixType;
#else
/// Reverse AD type declaration
typedef codi::RealReverse ADFloatType;
/// Vector type for AD-numbers
typedef TAutoDiffVector<ADFloatType> ADVectorType;
/// Matrix type for AD-numbers
typedef TAutoDiffDenseMatrix<ADFloatType> ADMatrixType;
#endif
}

/// The class provides an evaluation of the Jacobian of a templated vector
/// function provided in the constructor. The Jacobian is evaluated with the
/// help of automatic differentiation (AD). The template parameters specify the
/// size of the return vector (vector_size), the size of the input vector
/// (state_size), and the size of the parameters supplied to the function.
template<int vector_size=1, int state_size=1, int param_size=0>
class VectorFuncAutoDiff
{
public:
   /// F_ is user implemented function to be differentiated by
   /// VectorFuncAutoDiff. The signature of the function is: F_(mfem::Vector&
   /// parameters, ad::ADVectorType& state_vector, ad::ADVectorType& result).
   /// The parameters vector should have size param_size. The state_vector
   /// should have size state_size, and the result vector should have size
   /// vector_size. All size parameters are teplate parameters in
   /// VectorFuncAutoDiff.
   VectorFuncAutoDiff(
      std::function<void(mfem::Vector&, ad::ADVectorType&, ad::ADVectorType&)> F_)
   {
      F=F_;
   }

   /// Evaluates the Jacobian of the vector function F_ for a set of parameters
   /// (vparam) and state vector vstate. The Jacobian (jac) has dimensions
   /// [vector_size x state_size].
   void Jacobian(mfem::Vector &vparam, mfem::Vector &vstate,
                 mfem::DenseMatrix &jac)
   {
#ifdef MFEM_USE_ADFORWARD
      // use forward mode
      jac.SetSize(vector_size, state_size);
      jac = 0.0;
      {
         ad::ADVectorType ad_state(state_size);
         ad::ADVectorType ad_result(vector_size);
         for (int i=0; i<state_size; i++)
         {
            ad_state[i].setValue(vstate[i]);
            ad_state[i].setGradient(0.0);
         }
         for (int ii=0; ii<state_size; ii++)
         {
            ad_state[ii].setGradient(1.0);
            F(vparam,ad_state,ad_result);
            for (int jj=0; jj<vector_size; jj++)
            {
               jac(jj,ii)=ad_result[jj].getGradient();
            }
            ad_state[ii].setGradient(0.0);
         }
      }
#else // use reverse mode
      jac.SetSize(vector_size, state_size);
      jac = 0.0;
      {
         ad::ADVectorType ad_state(state_size);
         ad::ADVectorType ad_result(vector_size);
         for (int i=0; i<state_size; i++)
         {
            ad_state[i]=vstate[i];
         }

         ad::ADFloatType::TapeType& tape =ad::ADFloatType::getGlobalTape();
         typename ad::ADFloatType::TapeType::Position pos=tape.getPosition();

         tape.setActive();
         for (int ii=0; ii<state_size; ii++) { tape.registerInput(ad_state[ii]); }
         F(vparam,ad_state,ad_result);
         for (int ii=0; ii<vector_size; ii++) { tape.registerOutput(ad_result[ii]); }
         tape.setPassive();

         for (int jj=0; jj<vector_size; jj++)
         {
            ad_result[jj].setGradient(1.0);
            tape.evaluate();
            for (int ii=0; ii<state_size; ii++)
            {
               jac(jj,ii)=ad_state[ii].getGradient();
            }
            tape.clearAdjoints();
            ad_result[jj].setGradient(0.0);
         }
         tape.reset(pos);
      }
#endif
   }
private:
   std::function<void(mfem::Vector&, ad::ADVectorType&, ad::ADVectorType&)> F;
}; // VectorFuncAutoDiff

/// The class provides an evaluation of the Jacobian of a templated vector
/// function provided as a functor TFunctor. The Jacobian is evaluated with the
/// help of automatic differentiation (AD). The template parameters specify the
/// size of the return vector (vector_size), the size of the input vector
/// (state_size), and the size of the parameters supplied to the function. The
/// TFunctor functor is a template class with parameters [Float data type],
/// [Vector type for the additional parameters], [Vector type for the state
/// vector and the return residual]. The integer template parameters are the
/// same ones passed to QVectorFuncAutoDiff.
template<template<typename, typename, typename, int, int, int> class TFunctor
         , int vector_size=1, int state_size=1, int param_size=0>
class QVectorFuncAutoDiff
{
public:
   /// Evaluates the vector function for given set of parameters and state
   /// values in vector uu. The result is returned in vector rr.
   void VectorFunc(const mfem::Vector &vparam, mfem::Vector &uu, mfem::Vector& rr)
   {
      rf(vparam,uu,rr);
   }

   /// Returns the gradient of TFunctor(...) in the dense matrix jac. The
   /// dimensions of jac are vector_size x state_size, where state_size is the
   /// length of vector uu.
   void Jacobian(mfem::Vector &vparam, mfem::Vector &uu, mfem::DenseMatrix &jac)
   {
#ifdef MFEM_USE_ADFORWARD
      // use forward mode
      jac.SetSize(vector_size, state_size);
      jac = 0.0;
      {
         ad::ADVectorType aduu(state_size);
         ad::ADVectorType rr(vector_size);
         for (int i=0; i<state_size; i++)
         {
            aduu[i].setValue(uu[i]);
            aduu[i].setGradient(0.0);
         }

         for (int ii=0; ii<state_size; ii++)
         {
            aduu[ii].setGradient(1.0);
            tf(vparam,aduu,rr);
            for (int jj=0; jj<vector_size; jj++)
            {
               jac(jj,ii)=rr[jj].getGradient();
            }
            aduu[ii].setGradient(0.0);
         }
      }
#else // end MFEM_USE_ADFORWARD
      // use reverse mode
      jac.SetSize(vector_size, state_size);
      jac = 0.0;
      {
         ad::ADVectorType aduu(state_size);
         ad::ADVectorType rr(vector_size);
         for (int i=0; i<state_size; i++)
         {
            aduu[i]=uu[i];
         }

         ad::ADFloatType::TapeType& tape =ad::ADFloatType::getGlobalTape();
         typename ad::ADFloatType::TapeType::Position pos=tape.getPosition();

         tape.setActive();
         for (int ii=0; ii<state_size; ii++) { tape.registerInput(aduu[ii]); }
         tf(vparam,aduu,rr);
         for (int ii=0; ii<vector_size; ii++) { tape.registerOutput(rr[ii]); }
         tape.setPassive();
         for (int jj=0; jj<vector_size; jj++)
         {
            rr[jj].setGradient(1.0);
            tape.evaluate();
            for (int ii=0; ii<state_size; ii++)
            {
               jac(jj,ii)=aduu[ii].getGradient();
            }
            tape.clearAdjoints();
            rr[jj].setGradient(0.0);
         }
         tape.reset(pos);
      }
#endif
   }
private:


   TFunctor<ad::ADFloatType, const Vector, ad::ADVectorType,
            vector_size, state_size, param_size> tf;

   TFunctor<double,const mfem::Vector, mfem::Vector,
            vector_size, state_size, param_size> rf;

};

/// The class provides an evaluation of the first derivatives and the Hessian of
/// a templated scalar function provided as a functor TFunctor. Both the first
/// and the second derivatives are evaluated with the help of automatic
/// differentiation (AD). The template parameters specify the size of the input
/// vector (state_size) and the size of the parameters supplied to the
/// function. The TFunctor functor is a template class with parameters [Float
/// data type], [Vector type for the additional parameters], [Vector type for
/// the state vector and the return residual].  The integer template parameters
/// are the same ones passed to QFunctionAutoDiff.
template<template<typename, typename, typename, int, int> class TFunctor
         , int state_size=1, int param_size=0>
class QFunctionAutoDiff
{
public:

   /// Evaluates a function for arguments vparam and uu. The evaluation is
   /// based on the operator() in the user provided functor TFunctor.
   double Eval(const mfem::Vector &vparam, mfem::Vector &uu)
   {
      return rf(vparam,uu);
   }

   /// Provides the same functionality as Grad.
   void VectorFunc(const mfem::Vector &vparam, mfem::Vector &uu, mfem::Vector &rr)
   {
      Grad(vparam,uu,rr);
   }

   /// Returns the first derivative of TFunctor(...) with respect to the active
   /// arguments proved in vector uu. The length of rr is the same as for uu.
   void Grad(const mfem::Vector &vparam, mfem::Vector &uu, mfem::Vector &rr)
   {

#ifdef MFEM_USE_ADFORWARD
      // use forward mode
      rr.SetSize(state_size);
      {
         ad::ADVectorType aduu(state_size);
         for (int i=0; i<state_size; i++)
         {
            aduu[i].setValue(uu[i]);
            aduu[i].setGradient(0.0);
         }

         ad::ADFloatType rez;

         for (int ii=0; ii<state_size; ii++)
         {
            aduu[ii].setGradient(1.0);
            rez=tf(vparam,aduu);
            rr[ii]=rez.getGradient();
            aduu[ii].setGradient(0.0);
         }
      }
#else
      {
         ad::ADVectorType aduu(state_size);
         ad::ADFloatType rez;
         for (int i=0; i<state_size; i++)
         {
            aduu[i]=uu[i];
         }

         ad::ADFloatType::TapeType& tape =ad::ADFloatType::getGlobalTape();
         typename ad::ADFloatType::TapeType::Position pos=tape.getPosition();

         tape.setActive();
         for (int ii=0; ii<state_size; ii++) { tape.registerInput(aduu[ii]); }

         rez=tf(vparam,aduu);
         tape.registerOutput(rez);
         tape.setPassive();

         rez.setGradient(1.0);
         tape.evaluate();
         for (int i=0; i<state_size; i++)
         {
            rr[i]=aduu[i].getGradient();
         }
         tape.reset(pos);
      }
#endif
   }

   /// Provides same functionality as Hessian.
   void Jacobian(mfem::Vector &vparam, mfem::Vector &uu, mfem::DenseMatrix &jac)
   {
      Hessian(vparam,uu,jac);
   }

#ifdef MFEM_USE_ADFORWARD
   // use forward-forward mode
   typedef codi::RealForwardGen<double>    ADFType;
   typedef TAutoDiffVector<ADFType>        ADFVector;
   typedef TAutoDiffDenseMatrix<ADFType>   ADFDenseMatrix;

   typedef codi::RealForwardGen<ADFType>   ADSType;
   typedef TAutoDiffVector<ADSType>        ADSVector;
   typedef TAutoDiffDenseMatrix<ADSType>   ADSDenseMatrix;
#else
   //use mixed forward and reverse mode
   typedef codi::RealForwardGen<double>    ADFType;
   typedef TAutoDiffVector<ADFType>        ADFVector;
   typedef TAutoDiffDenseMatrix<ADFType>   ADFDenseMatrix;

   typedef codi::RealReverseGen<ADFType>   ADSType;
   typedef TAutoDiffVector<ADSType>        ADSVector;
   typedef TAutoDiffDenseMatrix<ADSType>   ADSDenseMatrix;
#endif


   /// Returns the Hessian of TFunctor(...) in the dense matrix jac. The
   /// dimensions of jac are state_size x state_size, where state_size is the
   /// length of vector uu.
   void Hessian(mfem::Vector &vparam, mfem::Vector &uu, mfem::DenseMatrix &jac)
   {
#ifdef MFEM_USE_ADFORWARD
      // use forward-forward mode
      jac.SetSize(state_size);
      jac=0.0;
      {
         ADSVector aduu(state_size);
         for (int ii = 0;  ii < state_size; ii++)
         {
            aduu[ii].value().value()=uu[ii];
            aduu[ii].value().gradient()=0.0;
            aduu[ii].gradient().value()=0.0;
            aduu[ii].gradient().gradient()=0.0;
         }

         for (int ii = 0; ii < state_size; ii++)
         {
            aduu[ii].value().gradient()=1.0;
            for (int jj=0; jj<(ii+1); jj++)
            {
               aduu[jj].gradient().value()=1.0;
               ADSType rez=sf(vparam,aduu);
               jac(ii,jj)=rez.gradient().gradient();
               jac(jj,ii)=jac(ii,jj);
               aduu[jj].gradient().value()=0.0;
            }
            aduu[ii].value().gradient()=0.0;
         }
      }
#else
      // use mixed forward and reverse mode
      jac.SetSize(state_size);
      jac=0.0;
      {
         ADSVector aduu(state_size);
         for (int ii=0; ii < state_size ; ii++)
         {
            aduu[ii].value().value()=uu[ii];
         }

         ADSType rez;

         ADSType::TapeType& tape = ADSType::getGlobalTape();
         typename ADSType::TapeType::Position pos;
         for (int ii = 0; ii < state_size ; ii++)
         {
            pos=tape.getPosition();
            tape.setActive();

            for (int jj=0; jj < state_size; jj++)
            {
               if (jj==ii) {aduu[jj].value().gradient()=1.0;}
               else {aduu[jj].value().gradient()=0.0;}
               tape.registerInput(aduu[jj]);
            }

            rez=sf(vparam,aduu);
            tape.registerOutput(rez);
            tape.setPassive();

            rez.gradient().value()=1.0;
            tape.evaluate();

            for (int jj=0; jj<(ii+1); jj++)
            {
               jac(ii,jj)=aduu[jj].gradient().gradient();
               jac(jj,ii)=jac(ii,jj);
            }
            tape.reset(pos);
         }

      }
#endif
   }
private:
   TFunctor<double, const mfem::Vector,
            mfem::Vector, state_size, param_size> rf;

   TFunctor<ad::ADFloatType, const mfem::Vector,
            ad::ADVectorType, state_size, param_size> tf;

   TFunctor<ADSType, const mfem::Vector, ADSVector,
            state_size, param_size> sf;
};

}
#else // end MFEM_USE_CODIPACK

// USE NATIVE IMPLEMENTATION
namespace mfem
{

namespace ad
{
/// MFEM native forward AD-type
typedef internal::dual<double, double> ADFloatType;
/// Vector type for AD-type numbers
typedef TAutoDiffVector<ADFloatType> ADVectorType;
/// Matrix type for AD-type numbers
typedef TAutoDiffDenseMatrix<ADFloatType> ADMatrixType;
}

/// The class provides an evaluation of the Jacobian of a templated vector
/// function provided in the constructor. The Jacobian is evaluated with the
/// help of automatic differentiation (AD). The template parameters specify the
/// size of the return vector (vector_size), the size of the input vector
/// (state_size), and the size of the parameters supplied to the function.
template<int vector_size=1, int state_size=1, int param_size=0>
class VectorFuncAutoDiff
{
public:
   /// F_ is user implemented function to be differentiated by
   /// VectorFuncAutoDiff. The signature of the function is: F_(mfem::Vector&
   /// parameters, ad::ADVectroType& state_vector, ad::ADVectorType& result).
   /// The parameters vector should have size param_size. The state_vector
   /// should have size state_size, and the result vector should have size
   /// vector_size. All size parameters are teplate parameters in
   /// VectorFuncAutoDiff.
   VectorFuncAutoDiff(
      std::function<void(mfem::Vector&, ad::ADVectorType&, ad::ADVectorType&)> F_)
   {
      F=F_;
   }

   /// Evaluates the Jacobian of the vector function F_ for a set of parameters
   /// (vparam) and state vector uu. The Jacobian (jac) has dimensions
   /// [vector_size x state_size].
   void Jacobian(mfem::Vector &vparam, mfem::Vector &uu, mfem::DenseMatrix &jac)
   {
      jac.SetSize(vector_size, state_size);
      jac = 0.0;
      {
         ad::ADVectorType aduu(uu); // all dual numbers are initialized to zero
         ad::ADVectorType rr(vector_size);

         for (int ii = 0; ii < state_size; ii++)
         {
            aduu[ii].gradient = 1.0;
            F(vparam,aduu,rr);
            for (int jj = 0; jj < vector_size; jj++)
            {
               jac(jj, ii) = rr[jj].gradient;
            }
            aduu[ii].gradient = 0.0;
         }
      }
   }

private:
   std::function<void(mfem::Vector&, ad::ADVectorType&, ad::ADVectorType&)> F;

};

/// The class provides an evaluation of the Jacobian of a templated vector
/// function provided as a functor TFunctor. The Jacobian is evaluated with the
/// help of automatic differentiation (AD). The template parameters specify the
/// size of the return vector (vector_size), the size of the input vector
/// (state_size), and the size of the parameters supplied to the function. The
/// TFunctor functor is a template class with parameters [Float data type],
/// [Vector type for the additional parameters], [Vector type for the state
/// vector and the return residual].
/// The integer template parameters are the same ones
/// passed to QVectorFuncAutoDiff. \n
/// Example: f={sin(a*x*y), cos(b*x*y*z), x*x+y*x} \n
/// The vector function has vector_size=3, and state_size=3, i.e., it has
/// three arguments [x,y,z]. The parameters [a,b] size is 2.
/// The functor class will have the following form
/// \code{.cpp}
/// template<typename TDataType, typename TParamVector, typename TStateVector,
///         int residual_size, int state_size, int param_size>
/// class MyVectorFunction{
/// public:
/// TDataType operator() (TParamVector& vparam, TStateVector& uu, TStateVector& rr)
/// {
///    auto a=vparam[0];
///    auto b=vparam[1];
///    rr[0]=sin(a*uu[0]*uu[1]);
///    rr[1]=cos(b*uu[0]*uu[1]*uu[2]);
///    rr[2]=uu[0]*uu[0]+uu[0]*uu[1];
/// }
//
/// };
/// \endcode
template<template<typename, typename, typename, int, int, int> class TFunctor
         , int vector_size=1, int state_size=1, int param_size=0>
class QVectorFuncAutoDiff
{
private:
   /// MFEM native forward AD-type
   typedef internal::dual<double, double> ADFType;
   /// Vector type for AD-type numbers
   typedef TAutoDiffVector<ADFType> ADFVector;
   /// Matrix type for AD-type numbers
   typedef TAutoDiffDenseMatrix<ADFType> ADFDenseMatrix;

public:
   /// Returns a vector valued function rr for supplied passive arguments
   /// vparam and active arguments uu. The evaluation is based on the user
   /// supplied TFunctor template class.
   void VectorFunc(const Vector &vparam, Vector &uu, Vector &rr)
   {
      func(vparam, uu, rr);
   }

   /// Returns the gradient of TFunctor(...) residual in the dense matrix jac.
   /// The dimensions of jac are vector_size x state_size, where state_size is
   /// the length of vector uu.
   void Jacobian(mfem::Vector &vparam, mfem::Vector &uu, mfem::DenseMatrix &jac)
   {
      // use native AD package
      jac.SetSize(vector_size, state_size);
      jac = 0.0;
      {
         ADFVector aduu(uu); // all dual numbers are initialized to zero
         ADFVector rr(vector_size);

         for (int ii = 0; ii < state_size; ii++)
         {
            aduu[ii].gradient = 1.0;
            Eval(vparam, aduu, rr);
            for (int jj = 0; jj < vector_size; jj++)
            {
               jac(jj, ii) = rr[jj].gradient;
            }
            aduu[ii].gradient = 0.0;
         }
      }
   }

private:
   /// Evaluates the residual from TFunctor(...).
   /// Intended for internal use only.
   void Eval(const Vector &vparam, ADFVector &uu, ADFVector &rr)
   {
      tf(vparam, uu, rr);
   }

   TFunctor<double, const Vector, Vector,
            vector_size, state_size, param_size> func;

   TFunctor<ADFType, const Vector, ADFVector,
            vector_size, state_size, param_size> tf;

};

/// The class provides an evaluation of the first derivatives and the Hessian of
/// a templated scalar function provided as a functor TFunctor. Both the first
/// and the second derivatives are evaluated with the help of automatic
/// differentiation (AD). The template parameters specify the size of the input
/// vector (state_size) and the size of the parameters supplied to the
/// function. The TFunctor functor is a template class with parameters [Float
/// data type], [Vector type for the additional parameters], [Vector type for
/// the state vector and the return residual].  The integer template parameters
/// are the same ones passed to QFunctionAutoDiff. The class duplicates Grad and
/// Hessian, i.e., VectorFunc calls Grad, and Jacobian calls Hessian. The main
/// reason is to provide the same interface as the QVectorFuncAutoDiff class
/// used to differentiate vector functions. Such compatibility allows users to
/// start implementation of their problem based only on some energy or a weak
/// form. The gradients, computed with Grad/VectorFunc, of the function will
/// contribute to the FE residual. Computed with Hessian/Jacobian, the Hessian
/// will contribute to the tangent matrix in Newton's iterations. Once the
/// implementation is complete and tested, the users can start improving the
/// performance by replacing Grad/VectorFunc with a hand-coded version. The
/// gradient is a vector function and can be differentiated with the
/// functionality implemented in QVectorFuncAutoDiff. Thus, the user can
/// directly employ AD for computing the contributions to the global tangent
/// matrix. The main code will not require changes as the names Grad/VectorFunc
/// and Hessian/Jacobian are mirrored.
template<template<typename, typename, typename, int, int> class TFunctor
         , int state_size=1, int param_size=0>
class QFunctionAutoDiff
{
private:
   /// MFEM native AD-type for first derivatives
   typedef internal::dual<double, double> ADFType;
   /// Vector type for AD-numbers(first derivatives)
   typedef TAutoDiffVector<ADFType> ADFVector;
   /// Matrix type for AD-numbers(first derivatives)
   typedef TAutoDiffDenseMatrix<ADFType> ADFDenseMatrix;
   /// MFEM native AD-type for second derivatives
   typedef internal::dual<ADFType, ADFType> ADSType;
   /// Vector type for AD-numbers (second derivatives)
   typedef TAutoDiffVector<ADSType> ADSVector;
   /// Vector type for AD-numbers (second derivatives)
   typedef TAutoDiffDenseMatrix<ADSType> ADSDenseMatrix;

public:
   /// Evaluates a function for arguments vparam and uu. The evaluation is
   /// based on the operator() in the user provided functor TFunctor.
   double Eval(const Vector &vparam, Vector &uu)
   {
      return tf(vparam,uu);
   }

   /// Provides the same functionality as Grad.
   void VectorFunc(const Vector &vparam, Vector &uu, Vector &rr)
   {
      Grad(vparam,uu,rr);
   }

   /// Returns the first derivative of TFunctor(...) with respect to the active
   /// arguments proved in vector uu. The length of rr is the same as for uu.
   void Grad(const Vector &vparam, Vector &uu, Vector &rr)
   {
      int n = uu.Size();
      rr.SetSize(n);
      ADFVector aduu(uu);
      ADFType rez;
      for (int ii = 0; ii < n; ii++)
      {
         aduu[ii].gradient = 1.0;
         rez = ff(vparam, aduu);
         rr[ii] = rez.gradient;
         aduu[ii].gradient = 0.0;
      }
   }

   /// Provides same functionality as Hessian.
   void Jacobian(mfem::Vector &vparam, mfem::Vector &uu, mfem::DenseMatrix &jac)
   {
      Hessian(vparam,uu,jac);
   }

   /// Returns the Hessian of TFunctor(...) in the dense matrix jac. The
   /// dimensions of jac are state_size x state_size, where state_size is the
   /// length of vector uu.
   void Hessian(mfem::Vector &vparam, mfem::Vector &uu, mfem::DenseMatrix &jac)
   {
      int n = uu.Size();
      jac.SetSize(n);
      jac = 0.0;
      {
         ADSVector aduu(n);
         for (int ii = 0; ii < n; ii++)
         {
            aduu[ii].value = ADFType{uu[ii], 0.0};
            aduu[ii].gradient = ADFType{0.0, 0.0};
         }

         for (int ii = 0; ii < n; ii++)
         {
            aduu[ii].value = ADFType{uu[ii], 1.0};
            for (int jj = 0; jj < (ii + 1); jj++)
            {
               aduu[jj].gradient = ADFType{1.0, 0.0};
               ADSType rez = sf(vparam, aduu);
               jac(ii, jj) = rez.gradient.gradient;
               jac(jj, ii) = rez.gradient.gradient;
               aduu[jj].gradient = ADFType{0.0, 0.0};
            }
            aduu[ii].value = ADFType{uu[ii], 0.0};
         }
      }
   }

private:
   TFunctor<double, const Vector, Vector, state_size, param_size> tf;
   TFunctor<ADFType, const Vector, ADFVector, state_size, param_size> ff;
   TFunctor<ADSType, const Vector, ADSVector, state_size, param_size> sf;

};

} // end namespace mfem

#endif // NATIVE

#endif // ADMFEM_HPP