internal/ceres/local_parameterization_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include <cmath>
#include "gtest/gtest.h"
#include "ceres/internal/autodiff.h"
#include "ceres/internal/eigen.h"
#include "ceres/local_parameterization.h"
#include "ceres/rotation.h"

namespace ceres {
namespace internal {

TEST(IdentityParameterization, EverythingTest) {
  IdentityParameterization parameterization(3);
  EXPECT_EQ(parameterization.GlobalSize(), 3);
  EXPECT_EQ(parameterization.LocalSize(), 3);

  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);
    }
  }
}

TEST(SubsetParameterization, DeathTests) {
  vector<int> constant_parameters;
  EXPECT_DEATH(SubsetParameterization parameterization(1, constant_parameters),
               "at least");

  constant_parameters.push_back(0);
  EXPECT_DEATH(SubsetParameterization parameterization(1, constant_parameters),
               "Number of parameters");

  constant_parameters.push_back(1);
  EXPECT_DEATH(SubsetParameterization parameterization(2, constant_parameters),
               "Number of parameters");

  constant_parameters.push_back(1);
  EXPECT_DEATH(SubsetParameterization parameterization(2, constant_parameters),
               "duplicates");
}

TEST(SubsetParameterization, NormalFunctionTest) {
  double x[4] = {1.0, 2.0, 3.0, 4.0};
  for (int i = 0; i < 4; ++i) {
    vector<int> constant_parameters;
    constant_parameters.push_back(i);
    SubsetParameterization parameterization(4, constant_parameters);
    double delta[3] = {1.0, 2.0, 3.0};
    double x_plus_delta[4] = {0.0, 0.0, 0.0};

    parameterization.Plus(x, delta, x_plus_delta);
    int k = 0;
    for (int j = 0; j < 4; ++j) {
      if (j == i)  {
        EXPECT_EQ(x_plus_delta[j], x[j]);
      } else {
        EXPECT_EQ(x_plus_delta[j], x[j] + delta[k++]);
      }
    }

    double jacobian[4 * 3];
    parameterization.ComputeJacobian(x, jacobian);
    int delta_cursor = 0;
    int jacobian_cursor = 0;
    for (int j = 0; j < 4; ++j) {
      if (j != i) {
        for (int k = 0; k < 3; ++k, jacobian_cursor++) {
          EXPECT_EQ(jacobian[jacobian_cursor], delta_cursor == k ? 1.0 : 0.0);
        }
        ++delta_cursor;
      } else {
        for (int k = 0; k < 3; ++k, jacobian_cursor++) {
          EXPECT_EQ(jacobian[jacobian_cursor], 0.0);
        }
      }
    }
  };
}

// Functor needed to implement automatically differentiated Plus for
// quaternions.
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* q_delta) {
  const double kTolerance = 1e-14;
  double x_plus_delta_ref[4] = {0.0, 0.0, 0.0, 0.0};
  QuaternionProduct(q_delta, x, x_plus_delta_ref);

  double x_plus_delta[4] = {0.0, 0.0, 0.0, 0.0};
  QuaternionParameterization param;
  param.Plus(x, delta, x_plus_delta);
  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);

  double jacobian_ref[12];
  double zero_delta[3] = {0.0, 0.0, 0.0};
  const double* parameters[2] = {x, zero_delta};
  double* jacobian_array[2] = { NULL, jacobian_ref };

  // Autodiff jacobian at delta_x = 0.
  internal::AutoDiff<QuaternionPlus, double, 4, 3>::Differentiate(
      QuaternionPlus(), parameters, 4, x_plus_delta, jacobian_array);

  double jacobian[12];
  param.ComputeJacobian(x, jacobian);
  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(QuaternionParameterization, ZeroTest) {
  double x[4] = {0.5, 0.5, 0.5, 0.5};
  double delta[3] = {0.0, 0.0, 0.0};
  double q_delta[4] = {1.0, 0.0, 0.0, 0.0};
  QuaternionParameterizationTestHelper(x, delta, q_delta);
}


TEST(QuaternionParameterization, NearZeroTest) {
  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;
  }

  double q_delta[4];
  q_delta[0] = 1.0;
  q_delta[1] = delta[0];
  q_delta[2] = delta[1];
  q_delta[3] = delta[2];

  QuaternionParameterizationTestHelper(x, delta, q_delta);
}

TEST(QuaternionParameterization, AwayFromZeroTest) {
  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};
  const double delta_norm = sqrt(delta[0] * delta[0] +
                                 delta[1] * delta[1] +
                                 delta[2] * delta[2]);
  double q_delta[4];
  q_delta[0] = cos(delta_norm);
  q_delta[1] = sin(delta_norm) / delta_norm * delta[0];
  q_delta[2] = sin(delta_norm) / delta_norm * delta[1];
  q_delta[3] = sin(delta_norm) / delta_norm * delta[2];

  QuaternionParameterizationTestHelper(x, delta, q_delta);
}


}  // namespace internal
}  // namespace ceres