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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/manifold.h"
#include <cmath>
#include <limits>
#include <memory>
#include <utility>
#include "Eigen/Core"
#include "Eigen/Geometry"
#include "ceres/constants.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/port.h"
#include "ceres/line_manifold.h"
#include "ceres/manifold_test_utils.h"
#include "ceres/product_manifold.h"
#include "ceres/rotation.h"
#include "ceres/sphere_manifold.h"
#include "ceres/types.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"
namespace ceres::internal {
constexpr int kNumTrials = 1000;
constexpr double kTolerance = 1e-9;
TEST(EuclideanManifold, StaticNormalFunctionTest) {
EuclideanManifold<3> manifold;
EXPECT_EQ(manifold.AmbientSize(), 3);
EXPECT_EQ(manifold.TangentSize(), 3);
Vector zero_tangent = Vector::Zero(manifold.TangentSize());
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(manifold.AmbientSize());
const Vector y = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
Vector x_plus_delta = Vector::Zero(manifold.AmbientSize());
manifold.Plus(x.data(), delta.data(), x_plus_delta.data());
EXPECT_NEAR((x_plus_delta - x - delta).norm() / (x + delta).norm(),
0.0,
kTolerance);
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(EuclideanManifold, DynamicNormalFunctionTest) {
EuclideanManifold<DYNAMIC> manifold(3);
EXPECT_EQ(manifold.AmbientSize(), 3);
EXPECT_EQ(manifold.TangentSize(), 3);
Vector zero_tangent = Vector::Zero(manifold.TangentSize());
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(manifold.AmbientSize());
const Vector y = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
Vector x_plus_delta = Vector::Zero(manifold.AmbientSize());
manifold.Plus(x.data(), delta.data(), x_plus_delta.data());
EXPECT_NEAR((x_plus_delta - x - delta).norm() / (x + delta).norm(),
0.0,
kTolerance);
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(SubsetManifold, EmptyConstantParameters) {
SubsetManifold manifold(3, {});
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(3);
const Vector y = Vector::Random(3);
Vector delta = Vector::Random(3);
Vector x_plus_delta = Vector::Zero(3);
manifold.Plus(x.data(), delta.data(), x_plus_delta.data());
EXPECT_NEAR((x_plus_delta - x - delta).norm() / (x + delta).norm(),
0.0,
kTolerance);
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(SubsetManifold, NegativeParameterIndexDeathTest) {
EXPECT_DEATH_IF_SUPPORTED(SubsetManifold manifold(2, {-1}),
"greater than equal to zero");
}
TEST(SubsetManifold, GreaterThanSizeParameterIndexDeathTest) {
EXPECT_DEATH_IF_SUPPORTED(SubsetManifold manifold(2, {2}),
"less than the size");
}
TEST(SubsetManifold, DuplicateParametersDeathTest) {
EXPECT_DEATH_IF_SUPPORTED(SubsetManifold manifold(2, {1, 1}), "duplicates");
}
TEST(SubsetManifold, NormalFunctionTest) {
const int kAmbientSize = 4;
const int kTangentSize = 3;
for (int i = 0; i < kAmbientSize; ++i) {
SubsetManifold manifold_with_ith_parameter_constant(kAmbientSize, {i});
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(kAmbientSize);
Vector y = Vector::Random(kAmbientSize);
// x and y must have the same i^th coordinate to be on the manifold.
y[i] = x[i];
Vector delta = Vector::Random(kTangentSize);
Vector x_plus_delta = Vector::Zero(kAmbientSize);
x_plus_delta.setZero();
manifold_with_ith_parameter_constant.Plus(
x.data(), delta.data(), x_plus_delta.data());
int k = 0;
for (int j = 0; j < kAmbientSize; ++j) {
if (j == i) {
EXPECT_EQ(x_plus_delta[j], x[j]);
} else {
EXPECT_EQ(x_plus_delta[j], x[j] + delta[k++]);
}
}
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(
manifold_with_ith_parameter_constant, x, delta, y, kTolerance);
}
}
}
TEST(ProductManifold, Size2) {
SubsetManifold manifold1(5, {2});
SubsetManifold manifold2(3, {0, 1});
ProductManifold<SubsetManifold, SubsetManifold> manifold(manifold1,
manifold2);
EXPECT_EQ(manifold.AmbientSize(),
manifold1.AmbientSize() + manifold2.AmbientSize());
EXPECT_EQ(manifold.TangentSize(),
manifold1.TangentSize() + manifold2.TangentSize());
}
TEST(ProductManifold, Size3) {
SubsetManifold manifold1(5, {2});
SubsetManifold manifold2(3, {0, 1});
SubsetManifold manifold3(4, {1});
ProductManifold<SubsetManifold, SubsetManifold, SubsetManifold> manifold(
manifold1, manifold2, manifold3);
EXPECT_EQ(manifold.AmbientSize(),
manifold1.AmbientSize() + manifold2.AmbientSize() +
manifold3.AmbientSize());
EXPECT_EQ(manifold.TangentSize(),
manifold1.TangentSize() + manifold2.TangentSize() +
manifold3.TangentSize());
}
TEST(ProductManifold, Size4) {
SubsetManifold manifold1(5, {2});
SubsetManifold manifold2(3, {0, 1});
SubsetManifold manifold3(4, {1});
SubsetManifold manifold4(2, {0});
ProductManifold<SubsetManifold,
SubsetManifold,
SubsetManifold,
SubsetManifold>
manifold(manifold1, manifold2, manifold3, manifold4);
EXPECT_EQ(manifold.AmbientSize(),
manifold1.AmbientSize() + manifold2.AmbientSize() +
manifold3.AmbientSize() + manifold4.AmbientSize());
EXPECT_EQ(manifold.TangentSize(),
manifold1.TangentSize() + manifold2.TangentSize() +
manifold3.TangentSize() + manifold4.TangentSize());
}
TEST(ProductManifold, NormalFunctionTest) {
SubsetManifold manifold1(5, {2});
SubsetManifold manifold2(3, {0, 1});
SubsetManifold manifold3(4, {1});
SubsetManifold manifold4(2, {0});
ProductManifold<SubsetManifold,
SubsetManifold,
SubsetManifold,
SubsetManifold>
manifold(manifold1, manifold2, manifold3, manifold4);
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
Vector x_plus_delta = Vector::Zero(manifold.AmbientSize());
Vector x_plus_delta_expected = Vector::Zero(manifold.AmbientSize());
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), x_plus_delta.data()));
int ambient_cursor = 0;
int tangent_cursor = 0;
EXPECT_TRUE(manifold1.Plus(&x[ambient_cursor],
&delta[tangent_cursor],
&x_plus_delta_expected[ambient_cursor]));
ambient_cursor += manifold1.AmbientSize();
tangent_cursor += manifold1.TangentSize();
EXPECT_TRUE(manifold2.Plus(&x[ambient_cursor],
&delta[tangent_cursor],
&x_plus_delta_expected[ambient_cursor]));
ambient_cursor += manifold2.AmbientSize();
tangent_cursor += manifold2.TangentSize();
EXPECT_TRUE(manifold3.Plus(&x[ambient_cursor],
&delta[tangent_cursor],
&x_plus_delta_expected[ambient_cursor]));
ambient_cursor += manifold3.AmbientSize();
tangent_cursor += manifold3.TangentSize();
EXPECT_TRUE(manifold4.Plus(&x[ambient_cursor],
&delta[tangent_cursor],
&x_plus_delta_expected[ambient_cursor]));
ambient_cursor += manifold4.AmbientSize();
tangent_cursor += manifold4.TangentSize();
for (int i = 0; i < x.size(); ++i) {
EXPECT_EQ(x_plus_delta[i], x_plus_delta_expected[i]);
}
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(
manifold, x, delta, x_plus_delta, kTolerance);
}
}
TEST(ProductManifold, ZeroTangentSizeAndEuclidean) {
SubsetManifold subset_manifold(1, {0});
EuclideanManifold<2> euclidean_manifold;
ProductManifold<SubsetManifold, EuclideanManifold<2>> manifold(
subset_manifold, euclidean_manifold);
EXPECT_EQ(manifold.AmbientSize(), 3);
EXPECT_EQ(manifold.TangentSize(), 2);
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(3);
Vector y = Vector::Random(3);
y[0] = x[0];
Vector delta = Vector::Random(2);
Vector x_plus_delta = Vector::Zero(3);
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), x_plus_delta.data()));
EXPECT_EQ(x_plus_delta[0], x[0]);
EXPECT_EQ(x_plus_delta[1], x[1] + delta[0]);
EXPECT_EQ(x_plus_delta[2], x[2] + delta[1]);
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(ProductManifold, EuclideanAndZeroTangentSize) {
SubsetManifold subset_manifold(1, {0});
EuclideanManifold<2> euclidean_manifold;
ProductManifold<EuclideanManifold<2>, SubsetManifold> manifold(
euclidean_manifold, subset_manifold);
EXPECT_EQ(manifold.AmbientSize(), 3);
EXPECT_EQ(manifold.TangentSize(), 2);
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(3);
Vector y = Vector::Random(3);
y[2] = x[2];
Vector delta = Vector::Random(2);
Vector x_plus_delta = Vector::Zero(3);
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), x_plus_delta.data()));
EXPECT_EQ(x_plus_delta[0], x[0] + delta[0]);
EXPECT_EQ(x_plus_delta[1], x[1] + delta[1]);
EXPECT_EQ(x_plus_delta[2], x[2]);
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
struct CopyableManifold : ceres::Manifold {
CopyableManifold() = default;
CopyableManifold(const CopyableManifold&) = default;
// Do not care about copy-assignment
CopyableManifold& operator=(const CopyableManifold&) = delete;
// Not moveable
CopyableManifold(CopyableManifold&&) = delete;
CopyableManifold& operator=(CopyableManifold&&) = delete;
int AmbientSize() const override { return 3; }
int TangentSize() const override { return 2; }
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const override {
return true;
}
bool PlusJacobian(const double* x, double* jacobian) const override {
return true;
}
bool RightMultiplyByPlusJacobian(const double* x,
const int num_rows,
const double* ambient_matrix,
double* tangent_matrix) const override {
return true;
}
bool Minus(const double* y,
const double* x,
double* y_minus_x) const override {
return true;
}
bool MinusJacobian(const double* x, double* jacobian) const override {
return true;
}
};
struct MoveableManifold : ceres::Manifold {
MoveableManifold() = default;
MoveableManifold(MoveableManifold&&) = default;
// Do not care about move-assignment
MoveableManifold& operator=(MoveableManifold&&) = delete;
// Not copyable
MoveableManifold(const MoveableManifold&) = delete;
MoveableManifold& operator=(const MoveableManifold&) = delete;
int AmbientSize() const override { return 3; }
int TangentSize() const override { return 2; }
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const override {
return true;
}
bool PlusJacobian(const double* x, double* jacobian) const override {
return true;
}
bool RightMultiplyByPlusJacobian(const double* x,
const int num_rows,
const double* ambient_matrix,
double* tangent_matrix) const override {
return true;
}
bool Minus(const double* y,
const double* x,
double* y_minus_x) const override {
return true;
}
bool MinusJacobian(const double* x, double* jacobian) const override {
return true;
}
};
TEST(ProductManifold, CopyableOnly) {
ProductManifold<CopyableManifold, EuclideanManifold<3>> manifold1{
CopyableManifold{}, EuclideanManifold<3>{}};
CopyableManifold inner2;
ProductManifold<CopyableManifold, EuclideanManifold<3>> manifold2{
inner2, EuclideanManifold<3>{}};
EXPECT_EQ(manifold1.AmbientSize(), manifold2.AmbientSize());
EXPECT_EQ(manifold1.TangentSize(), manifold2.TangentSize());
}
TEST(ProductManifold, MoveableOnly) {
ProductManifold<MoveableManifold, EuclideanManifold<3>> manifold1{
MoveableManifold{}, EuclideanManifold<3>{}};
MoveableManifold inner2;
ProductManifold<MoveableManifold, EuclideanManifold<3>> manifold2{
std::move(inner2), EuclideanManifold<3>{}};
EXPECT_EQ(manifold1.AmbientSize(), manifold2.AmbientSize());
EXPECT_EQ(manifold1.TangentSize(), manifold2.TangentSize());
}
TEST(ProductManifold, CopyableOrMoveable) {
const CopyableManifold inner12{};
ProductManifold<MoveableManifold, CopyableManifold> manifold1{
MoveableManifold{}, inner12};
MoveableManifold inner21;
CopyableManifold inner22;
ProductManifold<MoveableManifold, CopyableManifold> manifold2{
std::move(inner21), inner22};
EXPECT_EQ(manifold1.AmbientSize(), manifold2.AmbientSize());
EXPECT_EQ(manifold1.TangentSize(), manifold2.TangentSize());
}
struct NonDefaultConstructibleManifold : ceres::Manifold {
NonDefaultConstructibleManifold(int, int) {}
int AmbientSize() const override { return 4; }
int TangentSize() const override { return 3; }
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const override {
return true;
}
bool PlusJacobian(const double* x, double* jacobian) const override {
return true;
}
bool RightMultiplyByPlusJacobian(const double* x,
const int num_rows,
const double* ambient_matrix,
double* tangent_matrix) const override {
return true;
}
bool Minus(const double* y,
const double* x,
double* y_minus_x) const override {
return true;
}
bool MinusJacobian(const double* x, double* jacobian) const override {
return true;
}
};
TEST(ProductManifold, NonDefaultConstructible) {
ProductManifold<NonDefaultConstructibleManifold, QuaternionManifold>
manifold1{NonDefaultConstructibleManifold{1, 2}, QuaternionManifold{}};
ProductManifold<QuaternionManifold, NonDefaultConstructibleManifold>
manifold2{QuaternionManifold{}, NonDefaultConstructibleManifold{1, 2}};
EXPECT_EQ(manifold1.AmbientSize(), manifold2.AmbientSize());
EXPECT_EQ(manifold1.TangentSize(), manifold2.TangentSize());
}
TEST(ProductManifold, DefaultConstructible) {
ProductManifold<EuclideanManifold<3>, SphereManifold<4>> manifold1;
ProductManifold<SphereManifold<4>, EuclideanManifold<3>> manifold2;
EXPECT_EQ(manifold1.AmbientSize(), manifold2.AmbientSize());
EXPECT_EQ(manifold1.TangentSize(), manifold2.TangentSize());
}
TEST(ProductManifold, Pointers) {
auto p = std::make_unique<QuaternionManifold>();
auto q = std::make_shared<EuclideanManifold<3>>();
ProductManifold<std::unique_ptr<Manifold>,
EuclideanManifold<3>,
std::shared_ptr<EuclideanManifold<3>>>
manifold1{
std::make_unique<QuaternionManifold>(), EuclideanManifold<3>{}, q};
ProductManifold<QuaternionManifold*,
EuclideanManifold<3>,
std::shared_ptr<EuclideanManifold<3>>>
manifold2{p.get(), EuclideanManifold<3>{}, q};
EXPECT_EQ(manifold1.AmbientSize(), manifold2.AmbientSize());
EXPECT_EQ(manifold1.TangentSize(), manifold2.TangentSize());
}
TEST(QuaternionManifold, PlusPiBy2) {
QuaternionManifold manifold;
Vector x = Vector::Zero(4);
x[0] = 1.0;
for (int i = 0; i < 3; ++i) {
Vector delta = Vector::Zero(3);
delta[i] = constants::pi / 2;
Vector x_plus_delta = Vector::Zero(4);
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), x_plus_delta.data()));
// Expect that the element corresponding to pi/2 is +/- 1. All other
// elements should be zero.
for (int j = 0; j < 4; ++j) {
if (i == (j - 1)) {
EXPECT_LT(std::abs(x_plus_delta[j]) - 1,
std::numeric_limits<double>::epsilon())
<< "\ndelta = " << delta.transpose()
<< "\nx_plus_delta = " << x_plus_delta.transpose()
<< "\n expected the " << j
<< "th element of x_plus_delta to be +/- 1.";
} else {
EXPECT_LT(std::abs(x_plus_delta[j]),
std::numeric_limits<double>::epsilon())
<< "\ndelta = " << delta.transpose()
<< "\nx_plus_delta = " << x_plus_delta.transpose()
<< "\n expected the " << j << "th element of x_plus_delta to be 0.";
}
}
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(
manifold, x, delta, x_plus_delta, kTolerance);
}
}
// Compute the expected value of QuaternionManifold::Plus via functions in
// rotation.h and compares it to the one computed by QuaternionManifold::Plus.
MATCHER_P2(QuaternionManifoldPlusIsCorrectAt, x, delta, "") {
// This multiplication by 2 is needed because AngleAxisToQuaternion uses
// |delta|/2 as the angle of rotation where as in the implementation of
// QuaternionManifold for historical reasons we use |delta|.
const Vector two_delta = delta * 2;
Vector delta_q(4);
AngleAxisToQuaternion(two_delta.data(), delta_q.data());
Vector expected(4);
QuaternionProduct(delta_q.data(), x.data(), expected.data());
Vector actual(4);
EXPECT_TRUE(arg.Plus(x.data(), delta.data(), actual.data()));
const double n = (actual - expected).norm();
const double d = expected.norm();
const double diffnorm = n / d;
if (diffnorm > kTolerance) {
*result_listener << "\nx: " << x.transpose()
<< "\ndelta: " << delta.transpose()
<< "\nexpected: " << expected.transpose()
<< "\nactual: " << actual.transpose()
<< "\ndiff: " << (expected - actual).transpose()
<< "\ndiffnorm : " << diffnorm;
return false;
}
return true;
}
static Vector RandomQuaternion() {
Vector x = Vector::Random(4);
x.normalize();
return x;
}
TEST(QuaternionManifold, GenericDelta) {
QuaternionManifold manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
EXPECT_THAT(manifold, QuaternionManifoldPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(QuaternionManifold, SmallDelta) {
QuaternionManifold manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
delta.normalize();
delta *= 1e-6;
EXPECT_THAT(manifold, QuaternionManifoldPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(QuaternionManifold, DeltaJustBelowPi) {
QuaternionManifold manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
delta.normalize();
delta *= (constants::pi - 1e-6);
EXPECT_THAT(manifold, QuaternionManifoldPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
// Compute the expected value of EigenQuaternionManifold::Plus using Eigen and
// compares it to the one computed by QuaternionManifold::Plus.
MATCHER_P2(EigenQuaternionManifoldPlusIsCorrectAt, x, delta, "") {
// This multiplication by 2 is needed because AngleAxisToQuaternion uses
// |delta|/2 as the angle of rotation where as in the implementation of
// Quaternion for historical reasons we use |delta|.
const Vector two_delta = delta * 2;
Vector delta_q(4);
AngleAxisToQuaternion(two_delta.data(), delta_q.data());
Eigen::Quaterniond delta_eigen_q(
delta_q[0], delta_q[1], delta_q[2], delta_q[3]);
Eigen::Map<const Eigen::Quaterniond> x_eigen_q(x.data());
Eigen::Quaterniond expected = delta_eigen_q * x_eigen_q;
double actual[4];
EXPECT_TRUE(arg.Plus(x.data(), delta.data(), actual));
Eigen::Map<Eigen::Quaterniond> actual_eigen_q(actual);
const double n = (actual_eigen_q.coeffs() - expected.coeffs()).norm();
const double d = expected.norm();
const double diffnorm = n / d;
if (diffnorm > kTolerance) {
*result_listener
<< "\nx: " << x.transpose() << "\ndelta: " << delta.transpose()
<< "\nexpected: " << expected.coeffs().transpose()
<< "\nactual: " << actual_eigen_q.coeffs().transpose() << "\ndiff: "
<< (expected.coeffs() - actual_eigen_q.coeffs()).transpose()
<< "\ndiffnorm : " << diffnorm;
return false;
}
return true;
}
TEST(EigenQuaternionManifold, GenericDelta) {
EigenQuaternionManifold manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
EXPECT_THAT(manifold, EigenQuaternionManifoldPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(EigenQuaternionManifold, SmallDelta) {
EigenQuaternionManifold manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
delta.normalize();
delta *= 1e-6;
EXPECT_THAT(manifold, EigenQuaternionManifoldPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(EigenQuaternionManifold, DeltaJustBelowPi) {
EigenQuaternionManifold manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
delta.normalize();
delta *= (constants::pi - 1e-6);
EXPECT_THAT(manifold, EigenQuaternionManifoldPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
using Eigen::Vector2d;
using Eigen::Vector3d;
using Vector6d = Eigen::Matrix<double, 6, 1>;
using Eigen::Vector4d;
using Vector8d = Eigen::Matrix<double, 8, 1>;
TEST(SphereManifold, ZeroTest) {
Vector4d x{0.0, 0.0, 0.0, 1.0};
Vector3d delta = Vector3d::Zero();
Vector4d y = Vector4d::Zero();
SphereManifold<4> manifold;
manifold.Plus(x.data(), delta.data(), y.data());
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(SphereManifold, NearZeroTest1) {
Vector4d x{1e-5, 1e-5, 1e-5, 1.0};
x.normalize();
Vector3d delta{0.0, 1.0, 0.0};
Vector4d y = Vector4d::Zero();
SphereManifold<4> manifold;
manifold.Plus(x.data(), delta.data(), y.data());
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(SphereManifold, NearZeroTest2) {
Vector4d x{0.01, 0.0, 0.0, 0.0};
Vector3d delta{0.0, 1.0, 0.0};
Vector4d y = Vector4d::Zero();
SphereManifold<4> manifold;
manifold.Plus(x.data(), delta.data(), y.data());
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(SphereManifold, Plus2DTest) {
Eigen::Vector2d x{0.0, 1.0};
SphereManifold<2> manifold;
{
double delta[1]{constants::pi / 4};
Eigen::Vector2d y = Eigen::Vector2d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta, y.data()));
const Eigen::Vector2d gtY(std::sqrt(2.0) / 2.0, std::sqrt(2.0) / 2.0);
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
double delta[1]{constants::pi / 2};
Eigen::Vector2d y = Eigen::Vector2d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta, y.data()));
const Eigen::Vector2d gtY = Eigen::Vector2d::UnitX();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
double delta[1]{constants::pi};
Eigen::Vector2d y = Eigen::Vector2d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta, y.data()));
const Eigen::Vector2d gtY = -Eigen::Vector2d::UnitY();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
double delta[1]{2.0 * constants::pi};
Eigen::Vector2d y = Eigen::Vector2d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta, y.data()));
const Eigen::Vector2d gtY = Eigen::Vector2d::UnitY();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
}
TEST(SphereManifold, Plus3DTest) {
Eigen::Vector3d x{0.0, 0.0, 1.0};
SphereManifold<3> manifold;
{
Eigen::Vector2d delta{constants::pi / 2, 0.0};
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY = Eigen::Vector3d::UnitX();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Eigen::Vector2d delta{constants::pi, 0.0};
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY = -Eigen::Vector3d::UnitZ();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Eigen::Vector2d delta{2.0 * constants::pi, 0.0};
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY = Eigen::Vector3d::UnitZ();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Eigen::Vector2d delta{0.0, constants::pi / 2};
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY = Eigen::Vector3d::UnitY();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Eigen::Vector2d delta{0.0, constants::pi};
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY = -Eigen::Vector3d::UnitZ();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Eigen::Vector2d delta{0.0, 2.0 * constants::pi};
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY = Eigen::Vector3d::UnitZ();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Eigen::Vector2d delta =
Eigen::Vector2d(1, 1).normalized() * constants::pi / 2;
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY(std::sqrt(2.0) / 2.0, std::sqrt(2.0) / 2.0, 0.0);
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Eigen::Vector2d delta = Eigen::Vector2d(1, 1).normalized() * constants::pi;
Eigen::Vector3d y = Eigen::Vector3d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
const Eigen::Vector3d gtY = -Eigen::Vector3d::UnitZ();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
}
TEST(SphereManifold, Minus2DTest) {
Eigen::Vector2d x{1.0, 0.0};
SphereManifold<2> manifold;
{
double delta[1];
const Eigen::Vector2d y(std::sqrt(2.0) / 2.0, std::sqrt(2.0) / 2.0);
const double gtDelta{constants::pi / 4};
EXPECT_TRUE(manifold.Minus(y.data(), x.data(), delta));
EXPECT_LT(std::abs(delta[0] - gtDelta), kTolerance);
}
{
double delta[1];
const Eigen::Vector2d y(-1, 0);
const double gtDelta{constants::pi};
EXPECT_TRUE(manifold.Minus(y.data(), x.data(), delta));
EXPECT_LT(std::abs(delta[0] - gtDelta), kTolerance);
}
}
TEST(SphereManifold, Minus3DTest) {
Eigen::Vector3d x{1.0, 0.0, 0.0};
SphereManifold<3> manifold;
{
Eigen::Vector2d delta;
const Eigen::Vector3d y(std::sqrt(2.0) / 2.0, 0.0, std::sqrt(2.0) / 2.0);
const Eigen::Vector2d gtDelta(constants::pi / 4, 0.0);
EXPECT_TRUE(manifold.Minus(y.data(), x.data(), delta.data()));
EXPECT_LT((delta - gtDelta).norm(), kTolerance);
}
{
Eigen::Vector2d delta;
const Eigen::Vector3d y(-1, 0, 0);
const Eigen::Vector2d gtDelta(0.0, constants::pi);
EXPECT_TRUE(manifold.Minus(y.data(), x.data(), delta.data()));
EXPECT_LT((delta - gtDelta).norm(), kTolerance);
}
}
TEST(SphereManifold, DeathTests) {
EXPECT_DEATH_IF_SUPPORTED(SphereManifold<Eigen::Dynamic> x(1), "size");
}
TEST(SphereManifold, NormalFunctionTest) {
SphereManifold<4> manifold;
EXPECT_EQ(manifold.AmbientSize(), 4);
EXPECT_EQ(manifold.TangentSize(), 3);
Vector zero_tangent = Vector::Zero(manifold.TangentSize());
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(manifold.AmbientSize());
Vector y = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
if (x.norm() == 0.0 || y.norm() == 0.0) {
continue;
}
// X and y need to have the same length.
y *= x.norm() / y.norm();
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(SphereManifold, NormalFunctionTestDynamic) {
SphereManifold<ceres::DYNAMIC> manifold(5);
EXPECT_EQ(manifold.AmbientSize(), 5);
EXPECT_EQ(manifold.TangentSize(), 4);
Vector zero_tangent = Vector::Zero(manifold.TangentSize());
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = Vector::Random(manifold.AmbientSize());
Vector y = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
if (x.norm() == 0.0 || y.norm() == 0.0) {
continue;
}
// X and y need to have the same length.
y *= x.norm() / y.norm();
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(LineManifold, ZeroTest3D) {
const Vector6d x = Vector6d::Unit(5);
const Vector4d delta = Vector4d::Zero();
Vector6d y = Vector6d::Zero();
LineManifold<3> manifold;
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(LineManifold, ZeroTest4D) {
const Vector8d x = Vector8d::Unit(7);
const Vector6d delta = Vector6d::Zero();
Vector8d y = Vector8d::Zero();
LineManifold<4> manifold;
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(LineManifold, ZeroOriginPointTest3D) {
const Vector6d x = Vector6d::Unit(5);
Vector4d delta;
delta << 0.0, 0.0, 1.0, 2.0;
Vector6d y = Vector6d::Zero();
LineManifold<3> manifold;
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(LineManifold, ZeroOriginPointTest4D) {
const Vector8d x = Vector8d::Unit(7);
Vector6d delta;
delta << 0.0, 0.0, 0.0, 0.5, 1.0, 1.5;
Vector8d y = Vector8d::Zero();
LineManifold<4> manifold;
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(LineManifold, ZeroDirTest3D) {
Vector6d x = Vector6d::Unit(5);
Vector4d delta;
delta << 3.0, 2.0, 0.0, 0.0;
Vector6d y = Vector6d::Zero();
LineManifold<3> manifold;
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(LineManifold, ZeroDirTest4D) {
Vector8d x = Vector8d::Unit(7);
Vector6d delta;
delta << 3.0, 2.0, 1.0, 0.0, 0.0, 0.0;
Vector8d y = Vector8d::Zero();
LineManifold<4> manifold;
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
TEST(LineManifold, Plus) {
Vector6d x = Vector6d::Unit(5);
LineManifold<3> manifold;
{
Vector4d delta{0.0, 2.0, constants::pi / 2, 0.0};
Vector6d y = Vector6d::Random();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
Vector6d gtY;
gtY << 2.0 * Vector3d::UnitY(), Vector3d::UnitX();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Vector4d delta{3.0, 0.0, 0.0, constants::pi / 2};
Vector6d y = Vector6d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
Vector6d gtY;
gtY << 3.0 * Vector3d::UnitX(), Vector3d::UnitY();
EXPECT_LT((y - gtY).norm(), kTolerance);
}
{
Vector4d delta;
delta << Vector2d(1.0, 2.0),
Vector2d(1, 1).normalized() * constants::pi / 2;
Vector6d y = Vector6d::Zero();
EXPECT_TRUE(manifold.Plus(x.data(), delta.data(), y.data()));
Vector6d gtY;
gtY << Vector3d(1.0, 2.0, 0.0),
Vector3d(std::sqrt(2.0) / 2.0, std::sqrt(2.0) / 2.0, 0.0);
EXPECT_LT((y - gtY).norm(), kTolerance);
}
}
TEST(LineManifold, NormalFunctionTest) {
LineManifold<3> manifold;
EXPECT_EQ(manifold.AmbientSize(), 6);
EXPECT_EQ(manifold.TangentSize(), 4);
Vector zero_tangent = Vector::Zero(manifold.TangentSize());
for (int trial = 0; trial < kNumTrials; ++trial) {
Vector x = Vector::Random(manifold.AmbientSize());
Vector y = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
if (x.tail<3>().norm() == 0.0) {
continue;
}
x.tail<3>().normalize();
manifold.Plus(x.data(), delta.data(), y.data());
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
TEST(LineManifold, NormalFunctionTestDynamic) {
LineManifold<ceres::DYNAMIC> manifold(3);
EXPECT_EQ(manifold.AmbientSize(), 6);
EXPECT_EQ(manifold.TangentSize(), 4);
Vector zero_tangent = Vector::Zero(manifold.TangentSize());
for (int trial = 0; trial < kNumTrials; ++trial) {
Vector x = Vector::Random(manifold.AmbientSize());
Vector y = Vector::Random(manifold.AmbientSize());
Vector delta = Vector::Random(manifold.TangentSize());
if (x.tail<3>().norm() == 0.0) {
continue;
}
x.tail<3>().normalize();
manifold.Plus(x.data(), delta.data(), y.data());
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
}
}
} // namespace ceres::internal