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387
cs440-acg/ext/eigen/unsupported/test/autodiff.cpp
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387
cs440-acg/ext/eigen/unsupported/test/autodiff.cpp
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <unsupported/Eigen/AutoDiff>
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template<typename Scalar>
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EIGEN_DONT_INLINE Scalar foo(const Scalar& x, const Scalar& y)
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{
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using namespace std;
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// return x+std::sin(y);
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EIGEN_ASM_COMMENT("mybegin");
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// pow(float, int) promotes to pow(double, double)
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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);
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//return x+2*y*x;//x*2 -std::pow(x,2);//(2*y/x);// - y*2;
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EIGEN_ASM_COMMENT("myend");
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}
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template<typename Vector>
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EIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p)
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{
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typedef typename Vector::Scalar Scalar;
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return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array() * p.array()).sum() + p.dot(p);
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}
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template<typename _Scalar, int NX=Dynamic, int NY=Dynamic>
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struct TestFunc1
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{
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typedef _Scalar Scalar;
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enum {
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InputsAtCompileTime = NX,
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ValuesAtCompileTime = NY
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};
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typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
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typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
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typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
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int m_inputs, m_values;
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TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
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TestFunc1(int inputs, int values) : m_inputs(inputs), m_values(values) {}
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int inputs() const { return m_inputs; }
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int values() const { return m_values; }
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template<typename T>
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void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const
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{
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Matrix<T,ValuesAtCompileTime,1>& v = *_v;
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v[0] = 2 * x[0] * x[0] + x[0] * x[1];
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v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1];
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if(inputs()>2)
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{
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v[0] += 0.5 * x[2];
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v[1] += x[2];
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}
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if(values()>2)
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{
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v[2] = 3 * x[1] * x[0] * x[0];
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}
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if (inputs()>2 && values()>2)
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v[2] *= x[2];
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}
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void operator() (const InputType& x, ValueType* v, JacobianType* _j) const
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{
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(*this)(x, v);
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if(_j)
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{
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JacobianType& j = *_j;
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j(0,0) = 4 * x[0] + x[1];
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j(1,0) = 3 * x[1];
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j(0,1) = x[0];
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j(1,1) = 3 * x[0] + 2 * 0.5 * x[1];
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if (inputs()>2)
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{
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j(0,2) = 0.5;
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j(1,2) = 1;
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}
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if(values()>2)
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{
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j(2,0) = 3 * x[1] * 2 * x[0];
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j(2,1) = 3 * x[0] * x[0];
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}
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if (inputs()>2 && values()>2)
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{
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j(2,0) *= x[2];
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j(2,1) *= x[2];
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j(2,2) = 3 * x[1] * x[0] * x[0];
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j(2,2) = 3 * x[1] * x[0] * x[0];
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}
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}
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}
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};
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#if EIGEN_HAS_VARIADIC_TEMPLATES
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/* Test functor for the C++11 features. */
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template <typename Scalar>
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struct integratorFunctor
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{
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typedef Matrix<Scalar, 2, 1> InputType;
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typedef Matrix<Scalar, 2, 1> ValueType;
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/*
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* Implementation starts here.
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*/
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integratorFunctor(const Scalar gain) : _gain(gain) {}
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integratorFunctor(const integratorFunctor& f) : _gain(f._gain) {}
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const Scalar _gain;
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template <typename T1, typename T2>
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void operator() (const T1 &input, T2 *output, const Scalar dt) const
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{
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T2 &o = *output;
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/* Integrator to test the AD. */
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o[0] = input[0] + input[1] * dt * _gain;
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o[1] = input[1] * _gain;
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}
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/* Only needed for the test */
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template <typename T1, typename T2, typename T3>
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void operator() (const T1 &input, T2 *output, T3 *jacobian, const Scalar dt) const
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{
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T2 &o = *output;
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/* Integrator to test the AD. */
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o[0] = input[0] + input[1] * dt * _gain;
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o[1] = input[1] * _gain;
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if (jacobian)
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{
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T3 &j = *jacobian;
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j(0, 0) = 1;
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j(0, 1) = dt * _gain;
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j(1, 0) = 0;
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j(1, 1) = _gain;
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}
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}
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};
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template<typename Func> void forward_jacobian_cpp11(const Func& f)
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{
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typedef typename Func::ValueType::Scalar Scalar;
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typedef typename Func::ValueType ValueType;
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typedef typename Func::InputType InputType;
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typedef typename AutoDiffJacobian<Func>::JacobianType JacobianType;
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InputType x = InputType::Random(InputType::RowsAtCompileTime);
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ValueType y, yref;
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JacobianType j, jref;
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const Scalar dt = internal::random<double>();
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jref.setZero();
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yref.setZero();
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f(x, &yref, &jref, dt);
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//std::cerr << "y, yref, jref: " << "\n";
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//std::cerr << y.transpose() << "\n\n";
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//std::cerr << yref << "\n\n";
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//std::cerr << jref << "\n\n";
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AutoDiffJacobian<Func> autoj(f);
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autoj(x, &y, &j, dt);
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//std::cerr << "y j (via autodiff): " << "\n";
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//std::cerr << y.transpose() << "\n\n";
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//std::cerr << j << "\n\n";
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VERIFY_IS_APPROX(y, yref);
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VERIFY_IS_APPROX(j, jref);
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}
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#endif
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template<typename Func> void forward_jacobian(const Func& f)
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{
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typename Func::InputType x = Func::InputType::Random(f.inputs());
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typename Func::ValueType y(f.values()), yref(f.values());
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typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs());
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jref.setZero();
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yref.setZero();
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f(x,&yref,&jref);
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// std::cerr << y.transpose() << "\n\n";;
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// std::cerr << j << "\n\n";;
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j.setZero();
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y.setZero();
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AutoDiffJacobian<Func> autoj(f);
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autoj(x, &y, &j);
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// std::cerr << y.transpose() << "\n\n";;
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// std::cerr << j << "\n\n";;
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VERIFY_IS_APPROX(y, yref);
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VERIFY_IS_APPROX(j, jref);
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}
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// TODO also check actual derivatives!
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template <int>
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void test_autodiff_scalar()
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{
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Vector2f p = Vector2f::Random();
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typedef AutoDiffScalar<Vector2f> AD;
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AD ax(p.x(),Vector2f::UnitX());
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AD ay(p.y(),Vector2f::UnitY());
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AD res = foo<AD>(ax,ay);
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VERIFY_IS_APPROX(res.value(), foo(p.x(),p.y()));
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}
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// TODO also check actual derivatives!
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template <int>
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void test_autodiff_vector()
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{
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Vector2f p = Vector2f::Random();
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typedef AutoDiffScalar<Vector2f> AD;
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typedef Matrix<AD,2,1> VectorAD;
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VectorAD ap = p.cast<AD>();
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ap.x().derivatives() = Vector2f::UnitX();
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ap.y().derivatives() = Vector2f::UnitY();
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AD res = foo<VectorAD>(ap);
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VERIFY_IS_APPROX(res.value(), foo(p));
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}
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template <int>
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void test_autodiff_jacobian()
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{
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CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,2>()) ));
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CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,3>()) ));
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CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,2>()) ));
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CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,3>()) ));
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CALL_SUBTEST(( forward_jacobian(TestFunc1<double>(3,3)) ));
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#if EIGEN_HAS_VARIADIC_TEMPLATES
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CALL_SUBTEST(( forward_jacobian_cpp11(integratorFunctor<double>(10)) ));
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#endif
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}
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template <int>
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void test_autodiff_hessian()
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{
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typedef AutoDiffScalar<VectorXd> AD;
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typedef Matrix<AD,Eigen::Dynamic,1> VectorAD;
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typedef AutoDiffScalar<VectorAD> ADD;
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typedef Matrix<ADD,Eigen::Dynamic,1> VectorADD;
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VectorADD x(2);
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double s1 = internal::random<double>(), s2 = internal::random<double>(), s3 = internal::random<double>(), s4 = internal::random<double>();
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x(0).value()=s1;
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x(1).value()=s2;
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//set unit vectors for the derivative directions (partial derivatives of the input vector)
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x(0).derivatives().resize(2);
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x(0).derivatives().setZero();
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x(0).derivatives()(0)= 1;
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x(1).derivatives().resize(2);
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x(1).derivatives().setZero();
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x(1).derivatives()(1)=1;
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//repeat partial derivatives for the inner AutoDiffScalar
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x(0).value().derivatives() = VectorXd::Unit(2,0);
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x(1).value().derivatives() = VectorXd::Unit(2,1);
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//set the hessian matrix to zero
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for(int idx=0; idx<2; idx++) {
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x(0).derivatives()(idx).derivatives() = VectorXd::Zero(2);
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x(1).derivatives()(idx).derivatives() = VectorXd::Zero(2);
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}
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ADD y = sin(AD(s3)*x(0) + AD(s4)*x(1));
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VERIFY_IS_APPROX(y.value().derivatives()(0), y.derivatives()(0).value());
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VERIFY_IS_APPROX(y.value().derivatives()(1), y.derivatives()(1).value());
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VERIFY_IS_APPROX(y.value().derivatives()(0), s3*std::cos(s1*s3+s2*s4));
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VERIFY_IS_APPROX(y.value().derivatives()(1), s4*std::cos(s1*s3+s2*s4));
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VERIFY_IS_APPROX(y.derivatives()(0).derivatives(), -std::sin(s1*s3+s2*s4)*Vector2d(s3*s3,s4*s3));
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VERIFY_IS_APPROX(y.derivatives()(1).derivatives(), -std::sin(s1*s3+s2*s4)*Vector2d(s3*s4,s4*s4));
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ADD z = x(0)*x(1);
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VERIFY_IS_APPROX(z.derivatives()(0).derivatives(), Vector2d(0,1));
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VERIFY_IS_APPROX(z.derivatives()(1).derivatives(), Vector2d(1,0));
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}
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double bug_1222() {
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typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;
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const double _cv1_3 = 1.0;
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const AD chi_3 = 1.0;
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// this line did not work, because operator+ returns ADS<DerType&>, which then cannot be converted to ADS<DerType>
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const AD denom = chi_3 + _cv1_3;
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return denom.value();
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}
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#ifdef EIGEN_TEST_PART_5
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double bug_1223() {
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using std::min;
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typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;
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const double _cv1_3 = 1.0;
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const AD chi_3 = 1.0;
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const AD denom = 1.0;
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// failed because implementation of min attempts to construct ADS<DerType&> via constructor AutoDiffScalar(const Real& value)
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// without initializing m_derivatives (which is a reference in this case)
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#define EIGEN_TEST_SPACE
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const AD t = min EIGEN_TEST_SPACE (denom / chi_3, 1.0);
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const AD t2 = min EIGEN_TEST_SPACE (denom / (chi_3 * _cv1_3), 1.0);
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return t.value() + t2.value();
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}
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// regression test for some compilation issues with specializations of ScalarBinaryOpTraits
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void bug_1260() {
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Matrix4d A = Matrix4d::Ones();
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Vector4d v = Vector4d::Ones();
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A*v;
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}
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// check a compilation issue with numext::max
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double bug_1261() {
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typedef AutoDiffScalar<Matrix2d> AD;
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typedef Matrix<AD,2,1> VectorAD;
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VectorAD v(0.,0.);
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const AD maxVal = v.maxCoeff();
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const AD minVal = v.minCoeff();
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return maxVal.value() + minVal.value();
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}
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double bug_1264() {
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typedef AutoDiffScalar<Vector2d> AD;
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const AD s = 0.;
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const Matrix<AD, 3, 1> v1(0.,0.,0.);
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const Matrix<AD, 3, 1> v2 = (s + 3.0) * v1;
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return v2(0).value();
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}
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// check with expressions on constants
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double bug_1281() {
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int n = 2;
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typedef AutoDiffScalar<VectorXd> AD;
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const AD c = 1.;
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AD x0(2,n,0);
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AD y1 = (AD(c)+AD(c))*x0;
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y1 = x0 * (AD(c)+AD(c));
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AD y2 = (-AD(c))+x0;
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y2 = x0+(-AD(c));
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AD y3 = (AD(c)*(-AD(c))+AD(c))*x0;
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y3 = x0 * (AD(c)*(-AD(c))+AD(c));
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return (y1+y2+y3).value();
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}
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#endif
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void test_autodiff()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( test_autodiff_scalar<1>() );
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CALL_SUBTEST_2( test_autodiff_vector<1>() );
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CALL_SUBTEST_3( test_autodiff_jacobian<1>() );
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CALL_SUBTEST_4( test_autodiff_hessian<1>() );
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}
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CALL_SUBTEST_5( bug_1222() );
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CALL_SUBTEST_5( bug_1223() );
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CALL_SUBTEST_5( bug_1260() );
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CALL_SUBTEST_5( bug_1261() );
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CALL_SUBTEST_5( bug_1281() );
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}
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