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+// 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
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