unsupported/test/autodiff.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 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 <unsupported/Eigen/AutoDiff>

template <typename Scalar>
EIGEN_DONT_INLINE Scalar foo(const Scalar& x, const Scalar& y) {
  using namespace std;
  //   return x+std::sin(y);
  EIGEN_ASM_COMMENT("mybegin");
  // pow(float, int) promotes to pow(double, double)
  return x * 2 - 1 + static_cast<Scalar>(pow(1 + x, 2)) + 2 * sqrt(y * y + 0) - 4 * sin(0 + x) + 2 * cos(y + 0) -
         exp(Scalar(-0.5) * x * x + 0);
  // return x+2*y*x;//x*2 -std::pow(x,2);//(2*y/x);// - y*2;
  EIGEN_ASM_COMMENT("myend");
}

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() * p.array()).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];
      }
    }
  }
};

/* Test functor for the C++11 features. */
template <typename Scalar>
struct integratorFunctor {
  typedef Matrix<Scalar, 2, 1> InputType;
  typedef Matrix<Scalar, 2, 1> ValueType;

  /*
   * Implementation starts here.
   */
  integratorFunctor(const Scalar gain) : _gain(gain) {}
  integratorFunctor(const integratorFunctor& f) : _gain(f._gain) {}
  const Scalar _gain;

  template <typename T1, typename T2>
  void operator()(const T1& input, T2* output, const Scalar dt) const {
    T2& o = *output;

    /* Integrator to test the AD. */
    o[0] = input[0] + input[1] * dt * _gain;
    o[1] = input[1] * _gain;
  }

  /* Only needed for the test */
  template <typename T1, typename T2, typename T3>
  void operator()(const T1& input, T2* output, T3* jacobian, const Scalar dt) const {
    T2& o = *output;

    /* Integrator to test the AD. */
    o[0] = input[0] + input[1] * dt * _gain;
    o[1] = input[1] * _gain;

    if (jacobian) {
      T3& j = *jacobian;

      j(0, 0) = 1;
      j(0, 1) = dt * _gain;
      j(1, 0) = 0;
      j(1, 1) = _gain;
    }
  }
};

template <typename Func>
void forward_jacobian_cpp11(const Func& f) {
  typedef typename Func::ValueType::Scalar Scalar;
  typedef typename Func::ValueType ValueType;
  typedef typename Func::InputType InputType;
  typedef typename AutoDiffJacobian<Func>::JacobianType JacobianType;

  InputType x = InputType::Random(InputType::RowsAtCompileTime);
  ValueType y, yref;
  JacobianType j, jref;

  const Scalar dt = internal::random<double>();

  jref.setZero();
  yref.setZero();
  f(x, &yref, &jref, dt);

  // std::cerr << "y, yref, jref: " << "\n";
  // std::cerr << y.transpose() << "\n\n";
  // std::cerr << yref << "\n\n";
  // std::cerr << jref << "\n\n";

  AutoDiffJacobian<Func> autoj(f);
  autoj(x, &y, &j, dt);

  // std::cerr << "y j (via autodiff): " << "\n";
  // std::cerr << y.transpose() << "\n\n";
  // std::cerr << j << "\n\n";

  VERIFY_IS_APPROX(y, yref);
  VERIFY_IS_APPROX(j, jref);
}

template <typename Func>
void 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);

  j.setZero();
  y.setZero();
  AutoDiffJacobian<Func> autoj(f);
  autoj(x, &y, &j);

  VERIFY_IS_APPROX(y, yref);
  VERIFY_IS_APPROX(j, jref);
}

// TODO also check actual derivatives!
template <int>
void test_autodiff_scalar() {
  Vector2f p = Vector2f::Random();
  typedef AutoDiffScalar<Vector2f> AD;
  AD ax(p.x(), Vector2f::UnitX());
  AD ay(p.y(), Vector2f::UnitY());
  AD res = foo<AD>(ax, ay);
  VERIFY_IS_APPROX(res.value(), foo(p.x(), p.y()));
}

// TODO also check actual derivatives!
template <int>
void test_autodiff_vector() {
  Vector2f p = Vector2f::Random();
  typedef AutoDiffScalar<Vector2f> AD;
  typedef Matrix<AD, 2, 1> VectorAD;
  VectorAD ap = p.cast<AD>();
  ap.x().derivatives() = Vector2f::UnitX();
  ap.y().derivatives() = Vector2f::UnitY();

  AD res = foo<VectorAD>(ap);
  VERIFY_IS_APPROX(res.value(), foo(p));
}

template <int>
void test_autodiff_jacobian() {
  CALL_SUBTEST((forward_jacobian(TestFunc1<double, 2, 2>())));
  CALL_SUBTEST((forward_jacobian(TestFunc1<double, 2, 3>())));
  CALL_SUBTEST((forward_jacobian(TestFunc1<double, 3, 2>())));
  CALL_SUBTEST((forward_jacobian(TestFunc1<double, 3, 3>())));
  CALL_SUBTEST((forward_jacobian(TestFunc1<double>(3, 3))));
  CALL_SUBTEST((forward_jacobian_cpp11(integratorFunctor<double>(10))));
}

template <int>
void test_autodiff_hessian() {
  typedef AutoDiffScalar<VectorXd> AD;
  typedef Matrix<AD, Eigen::Dynamic, 1> VectorAD;
  typedef AutoDiffScalar<VectorAD> ADD;
  typedef Matrix<ADD, Eigen::Dynamic, 1> VectorADD;
  VectorADD x(2);
  double s1 = internal::random<double>(), s2 = internal::random<double>(), s3 = internal::random<double>(),
         s4 = internal::random<double>();
  x(0).value() = s1;
  x(1).value() = s2;

  // set unit vectors for the derivative directions (partial derivatives of the input vector)
  x(0).derivatives().resize(2);
  x(0).derivatives().setZero();
  x(0).derivatives()(0) = 1;
  x(1).derivatives().resize(2);
  x(1).derivatives().setZero();
  x(1).derivatives()(1) = 1;

  // repeat partial derivatives for the inner AutoDiffScalar
  x(0).value().derivatives() = VectorXd::Unit(2, 0);
  x(1).value().derivatives() = VectorXd::Unit(2, 1);

  // set the hessian matrix to zero
  for (int idx = 0; idx < 2; idx++) {
    x(0).derivatives()(idx).derivatives() = VectorXd::Zero(2);
    x(1).derivatives()(idx).derivatives() = VectorXd::Zero(2);
  }

  ADD y = sin(AD(s3) * x(0) + AD(s4) * x(1));

  VERIFY_IS_APPROX(y.value().derivatives()(0), y.derivatives()(0).value());
  VERIFY_IS_APPROX(y.value().derivatives()(1), y.derivatives()(1).value());
  VERIFY_IS_APPROX(y.value().derivatives()(0), s3 * std::cos(s1 * s3 + s2 * s4));
  VERIFY_IS_APPROX(y.value().derivatives()(1), s4 * std::cos(s1 * s3 + s2 * s4));
  VERIFY_IS_APPROX(y.derivatives()(0).derivatives(), -std::sin(s1 * s3 + s2 * s4) * Vector2d(s3 * s3, s4 * s3));
  VERIFY_IS_APPROX(y.derivatives()(1).derivatives(), -std::sin(s1 * s3 + s2 * s4) * Vector2d(s3 * s4, s4 * s4));

  ADD z = x(0) * x(1);
  VERIFY_IS_APPROX(z.derivatives()(0).derivatives(), Vector2d(0, 1));
  VERIFY_IS_APPROX(z.derivatives()(1).derivatives(), Vector2d(1, 0));
}

double bug_1222() {
  typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;
  const double _cv1_3 = 1.0;
  const AD chi_3 = 1.0;
  // this line did not work, because operator+ returns ADS<DerType&>, which then cannot be converted to ADS<DerType>
  const AD denom = chi_3 + _cv1_3;
  return denom.value();
}

double bug_1223() {
  using std::min;
  typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;

  const double _cv1_3 = 1.0;
  const AD chi_3 = 1.0;
  const AD denom = 1.0;

// failed because implementation of min attempts to construct ADS<DerType&> via constructor AutoDiffScalar(const Real&
// value) without initializing m_derivatives (which is a reference in this case)
#define EIGEN_TEST_SPACE
  const AD t = min EIGEN_TEST_SPACE(denom / chi_3, 1.0);

  const AD t2 = min EIGEN_TEST_SPACE(denom / (chi_3 * _cv1_3), 1.0);

  return t.value() + t2.value();
}

// regression test for some compilation issues with specializations of ScalarBinaryOpTraits
void bug_1260() {
  Matrix4d A = Matrix4d::Ones();
  Vector4d v = Vector4d::Ones();
  A* v;
}

// check a compilation issue with numext::max
double bug_1261() {
  typedef AutoDiffScalar<Matrix2d> AD;
  typedef Matrix<AD, 2, 1> VectorAD;

  VectorAD v(0., 0.);
  const AD maxVal = v.maxCoeff();
  const AD minVal = v.minCoeff();
  return maxVal.value() + minVal.value();
}

double bug_1264() {
  typedef AutoDiffScalar<Vector2d> AD;
  const AD s = 0.;
  const Matrix<AD, 3, 1> v1(0., 0., 0.);
  const Matrix<AD, 3, 1> v2 = (s + 3.0) * v1;
  return v2(0).value();
}

// check with expressions on constants
double bug_1281() {
  int n = 2;
  typedef AutoDiffScalar<VectorXd> AD;
  const AD c = 1.;
  AD x0(2, n, 0);
  AD y1 = (AD(c) + AD(c)) * x0;
  y1 = x0 * (AD(c) + AD(c));
  AD y2 = (-AD(c)) + x0;
  y2 = x0 + (-AD(c));
  AD y3 = (AD(c) * (-AD(c)) + AD(c)) * x0;
  y3 = x0 * (AD(c) * (-AD(c)) + AD(c));
  return (y1 + y2 + y3).value();
}

EIGEN_DECLARE_TEST(autodiff) {
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(test_autodiff_scalar<1>());
    CALL_SUBTEST_2(test_autodiff_vector<1>());
    CALL_SUBTEST_3(test_autodiff_jacobian<1>());
    CALL_SUBTEST_4(test_autodiff_hessian<1>());
  }

  CALL_SUBTEST_5(bug_1222());
  CALL_SUBTEST_5(bug_1223());
  CALL_SUBTEST_5(bug_1260());
  CALL_SUBTEST_5(bug_1261());
  CALL_SUBTEST_5(bug_1281());
}