// 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/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
#include <cmath>
#include "ceres/fpclassify.h"
#include "ceres/internal/autodiff.h"
#include "ceres/internal/eigen.h"
#include "ceres/local_parameterization.h"
#include "ceres/rotation.h"
#include "gtest/gtest.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_IF_SUPPORTED(
SubsetParameterization parameterization(1, constant_parameters),
"at least");
constant_parameters.push_back(0);
EXPECT_DEATH_IF_SUPPORTED(
SubsetParameterization parameterization(1, constant_parameters),
"Number of parameters");
constant_parameters.push_back(1);
EXPECT_DEATH_IF_SUPPORTED(
SubsetParameterization parameterization(2, constant_parameters),
"Number of parameters");
constant_parameters.push_back(1);
EXPECT_DEATH_IF_SUPPORTED(
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