internal/ceres/tiny_solver_autodiff_function_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2017 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: mierle@gmail.com (Keir Mierle)

#include "ceres/tiny_solver_autodiff_function.h"
#include "ceres/tiny_solver.h"
#include "ceres/tiny_solver_test_util.h"

#include <algorithm>
#include <cmath>
#include <limits>

#include "gtest/gtest.h"

namespace ceres {

struct AutoDiffTestFunctor {
  template<typename T>
  bool operator()(const T* const parameters, T* residuals) const {
    // Shift the parameters so the solution is not at the origin, to prevent
    // accidentally showing "PASS".
    const T& a = parameters[0] - T(1.0);
    const T& b = parameters[1] - T(2.0);
    const T& c = parameters[2] - T(3.0);
    residuals[0] = 2.*a + 0.*b + 1.*c;
    residuals[1] = 0.*a + 4.*b + 6.*c;
    return true;
  }
};

// Leave a factor of 10 slop since these tests tend to mysteriously break on
// other compilers or architectures if the tolerance is too tight.
static double const kTolerance = std::numeric_limits<double>::epsilon() * 10;

TEST(TinySolverAutoDiffFunction, SimpleFunction) {
  typedef TinySolverAutoDiffFunction<AutoDiffTestFunctor, 2, 3>
      AutoDiffTestFunction;
  AutoDiffTestFunctor autodiff_test_functor;
  AutoDiffTestFunction f(autodiff_test_functor);

  Eigen::Vector3d x(2.0, 1.0, 4.0);
  Eigen::Vector2d residuals;

  // Check the case with cost-only evaluation.
  residuals.setConstant(555);  // Arbitrary.
  EXPECT_TRUE(f(&x(0), &residuals(0), nullptr));
  EXPECT_NEAR(3.0, residuals(0), kTolerance);
  EXPECT_NEAR(2.0, residuals(1), kTolerance);

  // Check the case with cost and Jacobian evaluation.
  Eigen::Matrix<double, 2, 3> jacobian;
  residuals.setConstant(555);  // Arbitrary.
  jacobian.setConstant(555);
  EXPECT_TRUE(f(&x(0), &residuals(0), &jacobian(0, 0)));

  // Verify cost.
  EXPECT_NEAR(3.0, residuals(0), kTolerance);
  EXPECT_NEAR(2.0, residuals(1), kTolerance);

  // Verify Jacobian Row 1.
  EXPECT_NEAR(2.0, jacobian(0, 0), kTolerance);
  EXPECT_NEAR(0.0, jacobian(0, 1), kTolerance);
  EXPECT_NEAR(1.0, jacobian(0, 2), kTolerance);

  // Verify Jacobian row 2.
  EXPECT_NEAR(0.0, jacobian(1, 0), kTolerance);
  EXPECT_NEAR(4.0, jacobian(1, 1), kTolerance);
  EXPECT_NEAR(6.0, jacobian(1, 2), kTolerance);
}

class DynamicResidualsFunctor {
 public:
  typedef double Scalar;
  enum {
    NUM_RESIDUALS = Eigen::Dynamic,
    NUM_PARAMETERS = 3,
  };

  int NumResiduals() const {
    return 2;
  }

  template<typename T>
  bool operator()(const T* parameters, T* residuals) const {
    // Jacobian is not evaluated by cost function, but by autodiff.
    T* jacobian = nullptr;
    return EvaluateResidualsAndJacobians(parameters, residuals, jacobian);
  }
};

template<typename Function, typename Vector>
void TestHelper(const Function& f, const Vector& x0) {
  Vector x = x0;
  Eigen::Vector2d residuals;
  f(x.data(), residuals.data(), nullptr);
  EXPECT_GT(residuals.squaredNorm() / 2.0, 1e-10);

  TinySolver<Function> solver;
  solver.Solve(f, &x);
  EXPECT_NEAR(0.0, solver.summary.final_cost, 1e-10);
}

// A test case for when the number of residuals is
// dynamically sized and we use autodiff
TEST(TinySolverAutoDiffFunction, ResidualsDynamicAutoDiff) {
  Eigen::Vector3d x0(0.76026643, -30.01799744, 0.55192142);

  DynamicResidualsFunctor f;
  using AutoDiffCostFunctor =
      ceres::TinySolverAutoDiffFunction<DynamicResidualsFunctor,
                                        Eigen::Dynamic,
                                        3>;
  AutoDiffCostFunctor f_autodiff(f);

  Eigen::Vector2d residuals;
  f_autodiff(x0.data(), residuals.data(), nullptr);
  EXPECT_GT(residuals.squaredNorm() / 2.0, 1e-10);

  TinySolver<AutoDiffCostFunctor> solver;
  solver.Solve(f, &x0);
  EXPECT_NEAR(0.0, solver.summary.final_cost, 1e-10);
}

}  // namespace ceres