// 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: sameeragarwal@google.com (Sameer Agarwal)

#include <cmath>

#include "ceres/autodiff_local_parameterization.h"

#include "ceres/fpclassify.h"

#include "ceres/local_parameterization.h"

#include "ceres/rotation.h"

#include "gtest/gtest.h"

namespace ceres {

namespace internal {

struct IdentityPlus {

  template <typename T>

  bool operator()(const T* x, const T* delta, T* x_plus_delta) const {

    for (int i = 0; i < 3; ++i) {

      x_plus_delta[i] = x[i] + delta[i];

    }

    return true;

  }

};

TEST(AutoDiffLocalParameterizationTest, IdentityParameterization) {

  AutoDiffLocalParameterization<IdentityPlus, 3, 3>

      parameterization;

  double x[3] = {1.0, 2.0, 3.0};

  double delta[3] = {0.0, 1.0, 2.0};

  double x_plus_delta[3] = {0.0, 0.0, 0.0};

  parameterization.Plus(x, delta, x_plus_delta);

  EXPECT_EQ(x_plus_delta[0], 1.0);

  EXPECT_EQ(x_plus_delta[1], 3.0);

  EXPECT_EQ(x_plus_delta[2], 5.0);

  double jacobian[9];

  parameterization.ComputeJacobian(x, jacobian);

  int k = 0;

  for (int i = 0; i < 3; ++i) {

    for (int j = 0; j < 3; ++j, ++k) {

      EXPECT_EQ(jacobian[k], (i == j) ? 1.0 : 0.0);

    }

  }

}

struct ScaledPlus {

  explicit ScaledPlus(const double &scale_factor)

     : scale_factor_(scale_factor)

  {}

  template <typename T>

  bool operator()(const T* x, const T* delta, T* x_plus_delta) const {

    for (int i = 0; i < 3; ++i) {

      x_plus_delta[i] = x[i] + T(scale_factor_) * delta[i];

    }

    return true;

  }

  const double scale_factor_;

};

TEST(AutoDiffLocalParameterizationTest, ScaledParameterization) {

  const double kTolerance = 1e-14;

  AutoDiffLocalParameterization<ScaledPlus, 3, 3>

      parameterization(new ScaledPlus(1.2345));

  double x[3] = {1.0, 2.0, 3.0};

  double delta[3] = {0.0, 1.0, 2.0};

  double x_plus_delta[3] = {0.0, 0.0, 0.0};

  parameterization.Plus(x, delta, x_plus_delta);

  EXPECT_NEAR(x_plus_delta[0], 1.0, kTolerance);

  EXPECT_NEAR(x_plus_delta[1], 3.2345, kTolerance);

  EXPECT_NEAR(x_plus_delta[2], 5.469, kTolerance);

  double jacobian[9];

  parameterization.ComputeJacobian(x, jacobian);

  int k = 0;

  for (int i = 0; i < 3; ++i) {

    for (int j = 0; j < 3; ++j, ++k) {

      EXPECT_NEAR(jacobian[k], (i == j) ? 1.2345 : 0.0, kTolerance);

    }

  }

}

struct QuaternionPlus {

  template<typename T>

  bool operator()(const T* x, const T* delta, T* x_plus_delta) const {

    const T squared_norm_delta =

        delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2];

    T q_delta[4];

    if (squared_norm_delta > T(0.0)) {

      T norm_delta = sqrt(squared_norm_delta);

      const T sin_delta_by_delta = sin(norm_delta) / norm_delta;

      q_delta[0] = cos(norm_delta);

      q_delta[1] = sin_delta_by_delta * delta[0];

      q_delta[2] = sin_delta_by_delta * delta[1];

      q_delta[3] = sin_delta_by_delta * delta[2];

    } else {

      // We do not just use q_delta = [1,0,0,0] here because that is a

      // constant and when used for automatic differentiation will

      // lead to a zero derivative. Instead we take a first order

      // approximation and evaluate it at zero.

      q_delta[0] = T(1.0);

      q_delta[1] = delta[0];

      q_delta[2] = delta[1];

      q_delta[3] = delta[2];

    }

    QuaternionProduct(q_delta, x, x_plus_delta);

    return true;

  }

};

void QuaternionParameterizationTestHelper(const double* x,

                                          const double* delta) {

  const double kTolerance = 1e-14;

  double x_plus_delta_ref[4] = {0.0, 0.0, 0.0, 0.0};

  double jacobian_ref[12];

  QuaternionParameterization ref_parameterization;

  ref_parameterization.Plus(x, delta, x_plus_delta_ref);

  ref_parameterization.ComputeJacobian(x, jacobian_ref);

  double x_plus_delta[4] = {0.0, 0.0, 0.0, 0.0};

  double jacobian[12];

  AutoDiffLocalParameterization<QuaternionPlus, 4, 3> parameterization;

  parameterization.Plus(x, delta, x_plus_delta);

  parameterization.ComputeJacobian(x, jacobian);

  for (int i = 0; i < 4; ++i) {

    EXPECT_NEAR(x_plus_delta[i], x_plus_delta_ref[i], kTolerance);

  }

  const double x_plus_delta_norm =

      sqrt(x_plus_delta[0] * x_plus_delta[0] +

           x_plus_delta[1] * x_plus_delta[1] +

           x_plus_delta[2] * x_plus_delta[2] +

           x_plus_delta[3] * x_plus_delta[3]);

  EXPECT_NEAR(x_plus_delta_norm, 1.0, kTolerance);

  for (int i = 0; i < 12; ++i) {

    EXPECT_TRUE(IsFinite(jacobian[i]));

    EXPECT_NEAR(jacobian[i], jacobian_ref[i], kTolerance)

        << "Jacobian mismatch: i = " << i

        << "\n Expected \n" << ConstMatrixRef(jacobian_ref, 4, 3)

        << "\n Actual \n" << ConstMatrixRef(jacobian, 4, 3);

  }

}

TEST(AutoDiffLocalParameterization, QuaternionParameterizationZeroTest) {

  double x[4] = {0.5, 0.5, 0.5, 0.5};

  double delta[3] = {0.0, 0.0, 0.0};

  QuaternionParameterizationTestHelper(x, delta);

}

TEST(AutoDiffLocalParameterization, QuaternionParameterizationNearZeroTest) {

  double x[4] = {0.52, 0.25, 0.15, 0.45};

  double norm_x = sqrt(x[0] * x[0] +

                       x[1] * x[1] +

                       x[2] * x[2] +

                       x[3] * x[3]);

  for (int i = 0; i < 4; ++i) {

    x[i] = x[i] / norm_x;

  }

  double delta[3] = {0.24, 0.15, 0.10};

  for (int i = 0; i < 3; ++i) {

    delta[i] = delta[i] * 1e-14;

  }

  QuaternionParameterizationTestHelper(x, delta);

}

TEST(AutoDiffLocalParameterization, QuaternionParameterizationNonZeroTest) {

  double x[4] = {0.52, 0.25, 0.15, 0.45};

  double norm_x = sqrt(x[0] * x[0] +

                       x[1] * x[1] +

                       x[2] * x[2] +

                       x[3] * x[3]);

  for (int i = 0; i < 4; ++i) {

    x[i] = x[i] / norm_x;

  }

  double delta[3] = {0.24, 0.15, 0.10};

  QuaternionParameterizationTestHelper(x, delta);

}

}  // namespace internal

}  // namespace ceres