// Ceres Solver - A fast non-linear least squares minimizer

// Copyright 2015 Google Inc. All rights reserved.

// http://ceres-solver.org/

//

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// Author: moll.markus@arcor.de (Markus Moll)

#include <limits>

#include "ceres/internal/eigen.h"

#include "ceres/internal/scoped_ptr.h"

#include "ceres/dense_qr_solver.h"

#include "ceres/dogleg_strategy.h"

#include "ceres/linear_solver.h"

#include "ceres/trust_region_strategy.h"

#include "glog/logging.h"

#include "gtest/gtest.h"

namespace ceres {

namespace internal {

namespace {

class Fixture : public testing::Test {

 protected:

  scoped_ptr<DenseSparseMatrix> jacobian_;

  Vector residual_;

  Vector x_;

  TrustRegionStrategy::Options options_;

};

// A test problem where

//

//   J^T J = Q diag([1 2 4 8 16 32]) Q^T

//

// where Q is a randomly chosen orthonormal basis of R^6.

// The residual is chosen so that the minimum of the quadratic function is

// at (1, 1, 1, 1, 1, 1). It is therefore at a distance of sqrt(6) ~ 2.45

// from the origin.

class DoglegStrategyFixtureEllipse : public Fixture {

 protected:

  virtual void SetUp() {

    Matrix basis(6, 6);

    // The following lines exceed 80 characters for better readability.

    basis << -0.1046920933796121, -0.7449367449921986, -0.4190744502875876, -0.4480450716142566,  0.2375351607929440, -0.0363053418882862,  // NOLINT

              0.4064975684355914,  0.2681113508511354, -0.7463625494601520, -0.0803264850508117, -0.4463149623021321,  0.0130224954867195,  // NOLINT

             -0.5514387729089798,  0.1026621026168657, -0.5008316122125011,  0.5738122212666414,  0.2974664724007106,  0.1296020877535158,  // NOLINT

              0.5037835370947156,  0.2668479925183712, -0.1051754618492798, -0.0272739396578799,  0.7947481647088278, -0.1776623363955670,  // NOLINT

             -0.4005458426625444,  0.2939330589634109, -0.0682629380550051, -0.2895448882503687, -0.0457239396341685, -0.8139899477847840,  // NOLINT

             -0.3247764582762654,  0.4528151365941945, -0.0276683863102816, -0.6155994592510784,  0.1489240599972848,  0.5362574892189350;  // NOLINT

    Vector Ddiag(6);

    Ddiag << 1.0, 2.0, 4.0, 8.0, 16.0, 32.0;

    Matrix sqrtD = Ddiag.array().sqrt().matrix().asDiagonal();

    Matrix jacobian = sqrtD * basis;

    jacobian_.reset(new DenseSparseMatrix(jacobian));

    Vector minimum(6);

    minimum << 1.0, 1.0, 1.0, 1.0, 1.0, 1.0;

    residual_ = -jacobian * minimum;

    x_.resize(6);

    x_.setZero();

    options_.min_lm_diagonal = 1.0;

    options_.max_lm_diagonal = 1.0;

  }

};

// A test problem where

//

//   J^T J = diag([1 2 4 8 16 32]) .

//

// The residual is chosen so that the minimum of the quadratic function is

// at (0, 0, 1, 0, 0, 0). It is therefore at a distance of 1 from the origin.

// The gradient at the origin points towards the global minimum.

class DoglegStrategyFixtureValley : public Fixture {

 protected:

  virtual void SetUp() {

    Vector Ddiag(6);

    Ddiag << 1.0, 2.0, 4.0, 8.0, 16.0, 32.0;

    Matrix jacobian = Ddiag.asDiagonal();

    jacobian_.reset(new DenseSparseMatrix(jacobian));

    Vector minimum(6);

    minimum << 0.0, 0.0, 1.0, 0.0, 0.0, 0.0;

    residual_ = -jacobian * minimum;

    x_.resize(6);

    x_.setZero();

    options_.min_lm_diagonal = 1.0;

    options_.max_lm_diagonal = 1.0;

  }

};

const double kTolerance = 1e-14;

const double kToleranceLoose = 1e-5;

const double kEpsilon = std::numeric_limits<double>::epsilon();

}  // namespace

// The DoglegStrategy must never return a step that is longer than the current

// trust region radius.

TEST_F(DoglegStrategyFixtureEllipse, TrustRegionObeyedTraditional) {

  scoped_ptr<LinearSolver> linear_solver(

      new DenseQRSolver(LinearSolver::Options()));

  options_.linear_solver = linear_solver.get();

  // The global minimum is at (1, 1, ..., 1), so the distance to it is

  // sqrt(6.0).  By restricting the trust region to a radius of 2.0,

  // we test if the trust region is actually obeyed.

  options_.dogleg_type = TRADITIONAL_DOGLEG;

  options_.initial_radius = 2.0;

  options_.max_radius = 2.0;

  DoglegStrategy strategy(options_);

  TrustRegionStrategy::PerSolveOptions pso;

  TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,

                                                              jacobian_.get(),

                                                              residual_.data(),

                                                              x_.data());

  EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);

  EXPECT_LE(x_.norm(), options_.initial_radius * (1.0 + 4.0 * kEpsilon));

}

TEST_F(DoglegStrategyFixtureEllipse, TrustRegionObeyedSubspace) {

  scoped_ptr<LinearSolver> linear_solver(

      new DenseQRSolver(LinearSolver::Options()));

  options_.linear_solver = linear_solver.get();

  options_.dogleg_type = SUBSPACE_DOGLEG;

  options_.initial_radius = 2.0;

  options_.max_radius = 2.0;

  DoglegStrategy strategy(options_);

  TrustRegionStrategy::PerSolveOptions pso;

  TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,

                                                              jacobian_.get(),

                                                              residual_.data(),

                                                              x_.data());

  EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);

  EXPECT_LE(x_.norm(), options_.initial_radius * (1.0 + 4.0 * kEpsilon));

}

TEST_F(DoglegStrategyFixtureEllipse, CorrectGaussNewtonStep) {

  scoped_ptr<LinearSolver> linear_solver(

      new DenseQRSolver(LinearSolver::Options()));

  options_.linear_solver = linear_solver.get();

  options_.dogleg_type = SUBSPACE_DOGLEG;

  options_.initial_radius = 10.0;

  options_.max_radius = 10.0;

  DoglegStrategy strategy(options_);

  TrustRegionStrategy::PerSolveOptions pso;

  TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,

                                                              jacobian_.get(),

                                                              residual_.data(),

                                                              x_.data());

  EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);

  EXPECT_NEAR(x_(0), 1.0, kToleranceLoose);

  EXPECT_NEAR(x_(1), 1.0, kToleranceLoose);

  EXPECT_NEAR(x_(2), 1.0, kToleranceLoose);

  EXPECT_NEAR(x_(3), 1.0, kToleranceLoose);

  EXPECT_NEAR(x_(4), 1.0, kToleranceLoose);

  EXPECT_NEAR(x_(5), 1.0, kToleranceLoose);

}

// Test if the subspace basis is a valid orthonormal basis of the space spanned

// by the gradient and the Gauss-Newton point.

TEST_F(DoglegStrategyFixtureEllipse, ValidSubspaceBasis) {

  scoped_ptr<LinearSolver> linear_solver(

      new DenseQRSolver(LinearSolver::Options()));

  options_.linear_solver = linear_solver.get();

  options_.dogleg_type = SUBSPACE_DOGLEG;

  options_.initial_radius = 2.0;

  options_.max_radius = 2.0;

  DoglegStrategy strategy(options_);

  TrustRegionStrategy::PerSolveOptions pso;

  strategy.ComputeStep(pso, jacobian_.get(), residual_.data(), x_.data());

  // Check if the basis is orthonormal.

  const Matrix basis = strategy.subspace_basis();

  EXPECT_NEAR(basis.col(0).norm(), 1.0, kTolerance);

  EXPECT_NEAR(basis.col(1).norm(), 1.0, kTolerance);

  EXPECT_NEAR(basis.col(0).dot(basis.col(1)), 0.0, kTolerance);

  // Check if the gradient projects onto itself.

  const Vector gradient = strategy.gradient();

  EXPECT_NEAR((gradient - basis*(basis.transpose()*gradient)).norm(),

              0.0,

              kTolerance);

  // Check if the Gauss-Newton point projects onto itself.

  const Vector gn = strategy.gauss_newton_step();

  EXPECT_NEAR((gn - basis*(basis.transpose()*gn)).norm(),

              0.0,

              kTolerance);

}

// Test if the step is correct if the gradient and the Gauss-Newton step point

// in the same direction and the Gauss-Newton step is outside the trust region,

// i.e. the trust region is active.

TEST_F(DoglegStrategyFixtureValley, CorrectStepLocalOptimumAlongGradient) {

  scoped_ptr<LinearSolver> linear_solver(

      new DenseQRSolver(LinearSolver::Options()));

  options_.linear_solver = linear_solver.get();

  options_.dogleg_type = SUBSPACE_DOGLEG;

  options_.initial_radius = 0.25;

  options_.max_radius = 0.25;

  DoglegStrategy strategy(options_);

  TrustRegionStrategy::PerSolveOptions pso;

  TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,

                                                              jacobian_.get(),

                                                              residual_.data(),

                                                              x_.data());

  EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);

  EXPECT_NEAR(x_(0), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(1), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(2), options_.initial_radius, kToleranceLoose);

  EXPECT_NEAR(x_(3), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(4), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(5), 0.0, kToleranceLoose);

}

// Test if the step is correct if the gradient and the Gauss-Newton step point

// in the same direction and the Gauss-Newton step is inside the trust region,

// i.e. the trust region is inactive.

TEST_F(DoglegStrategyFixtureValley, CorrectStepGlobalOptimumAlongGradient) {

  scoped_ptr<LinearSolver> linear_solver(

      new DenseQRSolver(LinearSolver::Options()));

  options_.linear_solver = linear_solver.get();

  options_.dogleg_type = SUBSPACE_DOGLEG;

  options_.initial_radius = 2.0;

  options_.max_radius = 2.0;

  DoglegStrategy strategy(options_);

  TrustRegionStrategy::PerSolveOptions pso;

  TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,

                                                              jacobian_.get(),

                                                              residual_.data(),

                                                              x_.data());

  EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);

  EXPECT_NEAR(x_(0), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(1), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(2), 1.0, kToleranceLoose);

  EXPECT_NEAR(x_(3), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(4), 0.0, kToleranceLoose);

  EXPECT_NEAR(x_(5), 0.0, kToleranceLoose);

}

}  // namespace internal

}  // namespace ceres