text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #include "main.h"
  #include <Eigen/Dense>
  
  #define NUMBER_DIRECTIONS 16
  #include <unsupported/Eigen/AdolcForward>
  
  int adtl::ADOLC_numDir;
  
  template<typename Vector>
  EIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p)
  {
    typedef typename Vector::Scalar Scalar;
    return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array().sqrt().abs() * p.array().sin()).sum() + p.dot(p);
  }
  
  template<typename _Scalar, int NX=Dynamic, int NY=Dynamic>
  struct TestFunc1
  {
    typedef _Scalar Scalar;
    enum {
      InputsAtCompileTime = NX,
      ValuesAtCompileTime = NY
    };
    typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
    typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
    typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
  
    int m_inputs, m_values;
  
    TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
    TestFunc1(int inputs, int values) : m_inputs(inputs), m_values(values) {}
  
    int inputs() const { return m_inputs; }
    int values() const { return m_values; }
  
    template<typename T>
    void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const
    {
      Matrix<T,ValuesAtCompileTime,1>& v = *_v;
  
      v[0] = 2 * x[0] * x[0] + x[0] * x[1];
      v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1];
      if(inputs()>2)
      {
        v[0] += 0.5 * x[2];
        v[1] += x[2];
      }
      if(values()>2)
      {
        v[2] = 3 * x[1] * x[0] * x[0];
      }
      if (inputs()>2 && values()>2)
        v[2] *= x[2];
    }
  
    void operator() (const InputType& x, ValueType* v, JacobianType* _j) const
    {
      (*this)(x, v);
  
      if(_j)
      {
        JacobianType& j = *_j;
  
        j(0,0) = 4 * x[0] + x[1];
        j(1,0) = 3 * x[1];
  
        j(0,1) = x[0];
        j(1,1) = 3 * x[0] + 2 * 0.5 * x[1];
  
        if (inputs()>2)
        {
          j(0,2) = 0.5;
          j(1,2) = 1;
        }
        if(values()>2)
        {
          j(2,0) = 3 * x[1] * 2 * x[0];
          j(2,1) = 3 * x[0] * x[0];
        }
        if (inputs()>2 && values()>2)
        {
          j(2,0) *= x[2];
          j(2,1) *= x[2];
  
          j(2,2) = 3 * x[1] * x[0] * x[0];
          j(2,2) = 3 * x[1] * x[0] * x[0];
        }
      }
    }
  };
  
  template<typename Func> void adolc_forward_jacobian(const Func& f)
  {
      typename Func::InputType x = Func::InputType::Random(f.inputs());
      typename Func::ValueType y(f.values()), yref(f.values());
      typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs());
  
      jref.setZero();
      yref.setZero();
      f(x,&yref,&jref);
  //     std::cerr << y.transpose() << "\n\n";;
  //     std::cerr << j << "\n\n";;
  
      j.setZero();
      y.setZero();
      AdolcForwardJacobian<Func> autoj(f);
      autoj(x, &y, &j);
  //     std::cerr << y.transpose() << "\n\n";;
  //     std::cerr << j << "\n\n";;
  
      VERIFY_IS_APPROX(y, yref);
      VERIFY_IS_APPROX(j, jref);
  }
  
  void test_forward_adolc()
  {
    adtl::ADOLC_numDir = NUMBER_DIRECTIONS;
  
    for(int i = 0; i < g_repeat; i++) {
      CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,2>()) ));
      CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,3>()) ));
      CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,2>()) ));
      CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,3>()) ));
      CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double>(3,3)) ));
    }
  
    {
      // simple instanciation tests
      Matrix<adtl::adouble,2,1> x;
      foo(x);
      Matrix<adtl::adouble,Dynamic,Dynamic> A(4,4);;
      A.selfadjointView<Lower>().eigenvalues();
    }
  }
  