225 lines
7.3 KiB
C++
225 lines
7.3 KiB
C++
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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#include <cmath>
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#include "ceres/autodiff_local_parameterization.h"
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#include "ceres/fpclassify.h"
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#include "ceres/local_parameterization.h"
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#include "ceres/rotation.h"
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#include "gtest/gtest.h"
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namespace ceres {
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namespace internal {
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struct IdentityPlus {
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template <typename T>
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bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
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for (int i = 0; i < 3; ++i) {
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x_plus_delta[i] = x[i] + delta[i];
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}
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return true;
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}
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};
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TEST(AutoDiffLocalParameterizationTest, IdentityParameterization) {
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AutoDiffLocalParameterization<IdentityPlus, 3, 3>
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parameterization;
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double x[3] = {1.0, 2.0, 3.0};
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double delta[3] = {0.0, 1.0, 2.0};
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double x_plus_delta[3] = {0.0, 0.0, 0.0};
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parameterization.Plus(x, delta, x_plus_delta);
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EXPECT_EQ(x_plus_delta[0], 1.0);
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EXPECT_EQ(x_plus_delta[1], 3.0);
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EXPECT_EQ(x_plus_delta[2], 5.0);
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double jacobian[9];
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parameterization.ComputeJacobian(x, jacobian);
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int k = 0;
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for (int i = 0; i < 3; ++i) {
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for (int j = 0; j < 3; ++j, ++k) {
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EXPECT_EQ(jacobian[k], (i == j) ? 1.0 : 0.0);
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}
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}
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}
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struct ScaledPlus {
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explicit ScaledPlus(const double &scale_factor)
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: scale_factor_(scale_factor)
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{}
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template <typename T>
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bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
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for (int i = 0; i < 3; ++i) {
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x_plus_delta[i] = x[i] + T(scale_factor_) * delta[i];
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}
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return true;
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}
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const double scale_factor_;
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};
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TEST(AutoDiffLocalParameterizationTest, ScaledParameterization) {
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const double kTolerance = 1e-14;
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AutoDiffLocalParameterization<ScaledPlus, 3, 3>
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parameterization(new ScaledPlus(1.2345));
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double x[3] = {1.0, 2.0, 3.0};
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double delta[3] = {0.0, 1.0, 2.0};
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double x_plus_delta[3] = {0.0, 0.0, 0.0};
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parameterization.Plus(x, delta, x_plus_delta);
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EXPECT_NEAR(x_plus_delta[0], 1.0, kTolerance);
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EXPECT_NEAR(x_plus_delta[1], 3.2345, kTolerance);
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EXPECT_NEAR(x_plus_delta[2], 5.469, kTolerance);
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double jacobian[9];
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parameterization.ComputeJacobian(x, jacobian);
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int k = 0;
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for (int i = 0; i < 3; ++i) {
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for (int j = 0; j < 3; ++j, ++k) {
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EXPECT_NEAR(jacobian[k], (i == j) ? 1.2345 : 0.0, kTolerance);
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}
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}
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}
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struct QuaternionPlus {
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template<typename T>
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bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
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const T squared_norm_delta =
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delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2];
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T q_delta[4];
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if (squared_norm_delta > T(0.0)) {
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T norm_delta = sqrt(squared_norm_delta);
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const T sin_delta_by_delta = sin(norm_delta) / norm_delta;
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q_delta[0] = cos(norm_delta);
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q_delta[1] = sin_delta_by_delta * delta[0];
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q_delta[2] = sin_delta_by_delta * delta[1];
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q_delta[3] = sin_delta_by_delta * delta[2];
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} else {
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// We do not just use q_delta = [1,0,0,0] here because that is a
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// constant and when used for automatic differentiation will
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// lead to a zero derivative. Instead we take a first order
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// approximation and evaluate it at zero.
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q_delta[0] = T(1.0);
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q_delta[1] = delta[0];
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q_delta[2] = delta[1];
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q_delta[3] = delta[2];
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}
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QuaternionProduct(q_delta, x, x_plus_delta);
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return true;
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}
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};
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void QuaternionParameterizationTestHelper(const double* x,
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const double* delta) {
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const double kTolerance = 1e-14;
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double x_plus_delta_ref[4] = {0.0, 0.0, 0.0, 0.0};
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double jacobian_ref[12];
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QuaternionParameterization ref_parameterization;
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ref_parameterization.Plus(x, delta, x_plus_delta_ref);
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ref_parameterization.ComputeJacobian(x, jacobian_ref);
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double x_plus_delta[4] = {0.0, 0.0, 0.0, 0.0};
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double jacobian[12];
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AutoDiffLocalParameterization<QuaternionPlus, 4, 3> parameterization;
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parameterization.Plus(x, delta, x_plus_delta);
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parameterization.ComputeJacobian(x, jacobian);
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for (int i = 0; i < 4; ++i) {
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EXPECT_NEAR(x_plus_delta[i], x_plus_delta_ref[i], kTolerance);
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}
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const double x_plus_delta_norm =
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sqrt(x_plus_delta[0] * x_plus_delta[0] +
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x_plus_delta[1] * x_plus_delta[1] +
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x_plus_delta[2] * x_plus_delta[2] +
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x_plus_delta[3] * x_plus_delta[3]);
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EXPECT_NEAR(x_plus_delta_norm, 1.0, kTolerance);
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for (int i = 0; i < 12; ++i) {
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EXPECT_TRUE(IsFinite(jacobian[i]));
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EXPECT_NEAR(jacobian[i], jacobian_ref[i], kTolerance)
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<< "Jacobian mismatch: i = " << i
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<< "\n Expected \n" << ConstMatrixRef(jacobian_ref, 4, 3)
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<< "\n Actual \n" << ConstMatrixRef(jacobian, 4, 3);
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}
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}
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TEST(AutoDiffLocalParameterization, QuaternionParameterizationZeroTest) {
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double x[4] = {0.5, 0.5, 0.5, 0.5};
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double delta[3] = {0.0, 0.0, 0.0};
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QuaternionParameterizationTestHelper(x, delta);
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}
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TEST(AutoDiffLocalParameterization, QuaternionParameterizationNearZeroTest) {
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double x[4] = {0.52, 0.25, 0.15, 0.45};
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double norm_x = sqrt(x[0] * x[0] +
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x[1] * x[1] +
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x[2] * x[2] +
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x[3] * x[3]);
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for (int i = 0; i < 4; ++i) {
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x[i] = x[i] / norm_x;
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}
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double delta[3] = {0.24, 0.15, 0.10};
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for (int i = 0; i < 3; ++i) {
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delta[i] = delta[i] * 1e-14;
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}
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QuaternionParameterizationTestHelper(x, delta);
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}
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TEST(AutoDiffLocalParameterization, QuaternionParameterizationNonZeroTest) {
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double x[4] = {0.52, 0.25, 0.15, 0.45};
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double norm_x = sqrt(x[0] * x[0] +
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x[1] * x[1] +
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x[2] * x[2] +
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x[3] * x[3]);
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for (int i = 0; i < 4; ++i) {
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x[i] = x[i] / norm_x;
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}
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double delta[3] = {0.24, 0.15, 0.10};
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QuaternionParameterizationTestHelper(x, delta);
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}
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} // namespace internal
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} // namespace ceres
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