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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 - 1 + pow(1+x,2) + 2*sqrt(y*y+0) - 4 * sin(0+x) + 2 * cos(y+0) - exp(-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];
}
}
}
};
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!
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)) ));
}
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));
}
void 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>() );
}
}
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