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+// 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");
+ return static_cast<Scalar>(x*2 - pow(x,2) + 2*sqrt(y*y) - 4 * sin(x) + 2 * cos(y) - exp(-0.5*x*x));
+ //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];
+ }
+ }
+ }
+};
+
+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);
+// std::cerr << y.transpose() << "\n\n";;
+// std::cerr << j << "\n\n";;
+
+ j.setZero();
+ y.setZero();
+ AutoDiffJacobian<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);
+}
+
+
+// TODO also check actual derivatives!
+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!
+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));
+}
+
+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)) ));
+}
+
+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();
+}
+
+void test_autodiff()
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( test_autodiff_scalar() );
+ CALL_SUBTEST_2( test_autodiff_vector() );
+ CALL_SUBTEST_3( test_autodiff_jacobian() );
+ }
+
+ bug_1222();
+}
+