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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2021 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.
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// used to endorse or promote products derived from this software without
// specific prior written permission.
//
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// 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
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// 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 "ceres/manifold.h"
#include <cmath>
#include <limits>
#include <memory>
#include "Eigen/Geometry"
#include "ceres/dynamic_numeric_diff_cost_function.h"
#include "ceres/internal/eigen.h"
#include "ceres/numeric_diff_options.h"
#include "ceres/rotation.h"
#include "ceres/types.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
// TODO(sameeragarwal): Once these helpers and matchers converge, it would be
// helpful to expose them as testing utilities which can be used by the user
// when implementing their own manifold objects.
// The tests in this file are in two parts.
//
// 1. Manifold::Plus is doing what is expected. This requires per manifold
// logic.
// 2. The other methods of the manifold have mathematical properties that
// make it compatible with Plus, as described in
// https://arxiv.org/pdf/1107.1119.pdf. These tests are implemented using
// generic matchers defined below which can all be called by the macro
// EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y)
constexpr int kNumTrials = 1000;
constexpr double kEpsilon = 1e-9;
// Checks that the invariant Plus(x, 0) == x holds.
MATCHER_P(XPlusZeroIsXAt, x, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Vector actual = Vector::Zero(ambient_size);
Vector zero = Vector::Zero(tangent_size);
EXPECT_TRUE(arg.Plus(x.data(), zero.data(), actual.data()));
const double n = (actual - x).norm();
const double d = x.norm();
const double diffnorm = (d == 0.0) ? n : (n / d);
if (diffnorm > kEpsilon) {
*result_listener << "\nexpected (x): " << x.transpose()
<< "\nactual: " << actual.transpose()
<< "\ndiffnorm: " << diffnorm;
return false;
}
return true;
}
// Checks that the invariant Minus(x, x) == 0 holds.
MATCHER_P(XMinusXIsZeroAt, x, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Vector actual = Vector::Zero(tangent_size);
EXPECT_TRUE(arg.Minus(x.data(), x.data(), actual.data()));
const double diffnorm = actual.norm();
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose() //
<< "\nexpected: 0 0 0"
<< "\nactual: " << actual.transpose()
<< "\ndiffnorm: " << diffnorm;
return false;
}
return true;
}
// Helper struct to curry Plus(x, .) so that it can be numerically
// differentiated.
struct PlusFunctor {
PlusFunctor(const Manifold& manifold, const double* x)
: manifold(manifold), x(x) {}
bool operator()(double const* const* parameters, double* x_plus_delta) const {
return manifold.Plus(x, parameters[0], x_plus_delta);
}
const Manifold& manifold;
const double* x;
};
// Checks that the output of PlusJacobian matches the one obtained by
// numerically evaluating D_2 Plus(x,0).
MATCHER_P(HasCorrectPlusJacobianAt, x, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
NumericDiffOptions options;
options.ridders_relative_initial_step_size = 1e-4;
DynamicNumericDiffCostFunction<PlusFunctor, RIDDERS> cost_function(
new PlusFunctor(arg, x.data()), TAKE_OWNERSHIP, options);
cost_function.AddParameterBlock(tangent_size);
cost_function.SetNumResiduals(ambient_size);
Vector zero = Vector::Zero(tangent_size);
double* parameters[1] = {zero.data()};
Vector x_plus_zero = Vector::Zero(ambient_size);
Matrix expected = Matrix::Zero(ambient_size, tangent_size);
double* jacobians[1] = {expected.data()};
EXPECT_TRUE(
cost_function.Evaluate(parameters, x_plus_zero.data(), jacobians));
Matrix actual = Matrix::Random(ambient_size, tangent_size);
EXPECT_TRUE(arg.PlusJacobian(x.data(), actual.data()));
const double n = (actual - expected).norm();
const double d = expected.norm();
const double diffnorm = (d == 0.0) ? n : n / d;
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose() << "\nexpected: \n"
<< expected << "\nactual:\n"
<< actual << "\ndiff:\n"
<< expected - actual << "\ndiffnorm : " << diffnorm;
return false;
}
return true;
}
// Checks that the invariant Minus(Plus(x, delta), x) == delta holds.
MATCHER_P2(MinusPlusIsIdentityAt, x, delta, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Vector x_plus_delta = Vector::Zero(ambient_size);
EXPECT_TRUE(arg.Plus(x.data(), delta.data(), x_plus_delta.data()));
Vector actual = Vector::Zero(tangent_size);
EXPECT_TRUE(arg.Minus(x_plus_delta.data(), x.data(), actual.data()));
const double n = (actual - delta).norm();
const double d = delta.norm();
const double diffnorm = (d == 0.0) ? n : (n / d);
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose()
<< "\nexpected: " << delta.transpose()
<< "\nactual:" << actual.transpose()
<< "\ndiff:" << (delta - actual).transpose()
<< "\ndiffnorm: " << diffnorm;
return false;
}
return true;
}
// Checks that the invariant Plus(Minus(y, x), x) == y holds.
MATCHER_P2(PlusMinusIsIdentityAt, x, y, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Vector y_minus_x = Vector::Zero(tangent_size);
EXPECT_TRUE(arg.Minus(y.data(), x.data(), y_minus_x.data()));
Vector actual = Vector::Zero(ambient_size);
EXPECT_TRUE(arg.Plus(x.data(), y_minus_x.data(), actual.data()));
const double n = (actual - y).norm();
const double d = y.norm();
const double diffnorm = (d == 0.0) ? n : (n / d);
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose()
<< "\nexpected: " << y.transpose()
<< "\nactual:" << actual.transpose()
<< "\ndiff:" << (y - actual).transpose()
<< "\ndiffnorm: " << diffnorm;
return false;
}
return true;
}
// Helper struct to curry Minus(., x) so that it can be numerically
// differentiated.
struct MinusFunctor {
MinusFunctor(const Manifold& manifold, const double* x)
: manifold(manifold), x(x) {}
bool operator()(double const* const* parameters, double* y_minus_x) const {
return manifold.Minus(parameters[0], x, y_minus_x);
}
const Manifold& manifold;
const double* x;
};
// Checks that the output of MinusJacobian matches the one obtained by
// numerically evaluating D_1 Minus(x,x).
MATCHER_P(HasCorrectMinusJacobianAt, x, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Vector y = x;
Vector y_minus_x = Vector::Zero(tangent_size);
NumericDiffOptions options;
options.ridders_relative_initial_step_size = 1e-4;
DynamicNumericDiffCostFunction<MinusFunctor, RIDDERS> cost_function(
new MinusFunctor(arg, x.data()), TAKE_OWNERSHIP, options);
cost_function.AddParameterBlock(ambient_size);
cost_function.SetNumResiduals(tangent_size);
double* parameters[1] = {y.data()};
Matrix expected = Matrix::Zero(tangent_size, ambient_size);
double* jacobians[1] = {expected.data()};
EXPECT_TRUE(cost_function.Evaluate(parameters, y_minus_x.data(), jacobians));
Matrix actual = Matrix::Random(tangent_size, ambient_size);
EXPECT_TRUE(arg.MinusJacobian(x.data(), actual.data()));
const double n = (actual - expected).norm();
const double d = expected.norm();
const double diffnorm = (d == 0.0) ? n : (n / d);
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose() << "\nexpected: \n"
<< expected << "\nactual:\n"
<< actual << "\ndiff:\n"
<< expected - actual << "\ndiffnorm: " << diffnorm;
return false;
}
return true;
}
// Checks that D_delta Minus(Plus(x, delta), x) at delta = 0 is an identity
// matrix.
MATCHER_P(MinusPlusJacobianIsIdentityAt, x, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
Matrix plus_jacobian(ambient_size, tangent_size);
EXPECT_TRUE(arg.PlusJacobian(x.data(), plus_jacobian.data()));
Matrix minus_jacobian(tangent_size, ambient_size);
EXPECT_TRUE(arg.MinusJacobian(x.data(), minus_jacobian.data()));
const Matrix actual = minus_jacobian * plus_jacobian;
const Matrix expected = Matrix::Identity(tangent_size, tangent_size);
const double n = (actual - expected).norm();
const double d = expected.norm();
const double diffnorm = n / d;
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose() << "\nexpected: \n"
<< expected << "\nactual:\n"
<< actual << "\ndiff:\n"
<< expected - actual << "\ndiffnorm: " << diffnorm;
return false;
}
return true;
}
// Verify that the output of RightMultiplyByPlusJacobian is ambient_matrix *
// plus_jacobian.
MATCHER_P(HasCorrectRightMultiplyByPlusJacobianAt, x, "") {
const int ambient_size = arg.AmbientSize();
const int tangent_size = arg.TangentSize();
constexpr int kMinNumRows = 0;
constexpr int kMaxNumRows = 3;
for (int num_rows = kMinNumRows; num_rows <= kMaxNumRows; ++num_rows) {
Matrix plus_jacobian = Matrix::Random(ambient_size, tangent_size);
EXPECT_TRUE(arg.PlusJacobian(x.data(), plus_jacobian.data()));
Matrix ambient_matrix = Matrix::Random(num_rows, ambient_size);
Matrix expected = ambient_matrix * plus_jacobian;
Matrix actual = Matrix::Random(num_rows, tangent_size);
EXPECT_TRUE(arg.RightMultiplyByPlusJacobian(
x.data(), num_rows, ambient_matrix.data(), actual.data()));
const double n = (actual - expected).norm();
const double d = expected.norm();
const double diffnorm = (d == 0.0) ? n : (n / d);
if (diffnorm > kEpsilon) {
*result_listener << "\nx: " << x.transpose() << "\nambient_matrix : \n"
<< ambient_matrix << "\nplus_jacobian : \n"
<< plus_jacobian << "\nexpected: \n"
<< expected << "\nactual:\n"
<< actual << "\ndiff:\n"
<< expected - actual << "\ndiffnorm : " << diffnorm;
return false;
}
}
return true;
}
#define EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y) \
Vector zero_tangent = Vector::Zero(manifold.TangentSize()); \
EXPECT_THAT(manifold, XPlusZeroIsXAt(x)); \
EXPECT_THAT(manifold, XMinusXIsZeroAt(x)); \
EXPECT_THAT(manifold, MinusPlusIsIdentityAt(x, delta)); \
EXPECT_THAT(manifold, MinusPlusIsIdentityAt(x, zero_tangent)); \
EXPECT_THAT(manifold, PlusMinusIsIdentityAt(x, x)); \
EXPECT_THAT(manifold, PlusMinusIsIdentityAt(x, y)); \
EXPECT_THAT(manifold, HasCorrectPlusJacobianAt(x)); \
EXPECT_THAT(manifold, HasCorrectMinusJacobianAt(x)); \
EXPECT_THAT(manifold, MinusPlusJacobianIsIdentityAt(x)); \
EXPECT_THAT(manifold, HasCorrectRightMultiplyByPlusJacobianAt(x));
TEST(EuclideanManifold, NormalFunctionTest) {
EuclideanManifold 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, kEpsilon);
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
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, kEpsilon);
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
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);
}
}
}
TEST(ProductManifold, Size2) {
Manifold* manifold1 = new SubsetManifold(5, {2});
Manifold* manifold2 = new SubsetManifold(3, {0, 1});
ProductManifold manifold(manifold1, manifold2);
EXPECT_EQ(manifold.AmbientSize(),
manifold1->AmbientSize() + manifold2->AmbientSize());
EXPECT_EQ(manifold.TangentSize(),
manifold1->TangentSize() + manifold2->TangentSize());
}
TEST(ProductManifold, Size3) {
Manifold* manifold1 = new SubsetManifold(5, {2});
Manifold* manifold2 = new SubsetManifold(3, {0, 1});
Manifold* manifold3 = new SubsetManifold(4, {1});
ProductManifold 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) {
Manifold* manifold1 = new SubsetManifold(5, {2});
Manifold* manifold2 = new SubsetManifold(3, {0, 1});
Manifold* manifold3 = new SubsetManifold(4, {1});
Manifold* manifold4 = new SubsetManifold(2, {0});
ProductManifold 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) {
Manifold* manifold1 = new SubsetManifold(5, {2});
Manifold* manifold2 = new SubsetManifold(3, {0, 1});
Manifold* manifold3 = new SubsetManifold(4, {1});
Manifold* manifold4 = new SubsetManifold(2, {0});
ProductManifold 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);
}
}
TEST(ProductManifold, ZeroTangentSizeAndEuclidean) {
Manifold* subset_manifold = new SubsetManifold(1, {0});
Manifold* euclidean_manifold = new EuclideanManifold(2);
ProductManifold 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);
}
}
TEST(ProductManifold, EuclideanAndZeroTangentSize) {
Manifold* subset_manifold = new SubsetManifold(1, {0});
Manifold* euclidean_manifold = new EuclideanManifold(2);
ProductManifold 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);
}
}
TEST(Quaternion, PlusPiBy2) {
Quaternion manifold;
Vector x = Vector::Zero(4);
x[0] = 1.0;
for (int i = 0; i < 3; ++i) {
Vector delta = Vector::Zero(3);
delta[i] = M_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);
}
}
// Compute the expected value of Quaternion::Plus via functions in rotation.h
// and compares it to the one computed by Quaternion::Plus.
MATCHER_P2(QuaternionPlusIsCorrectAt, 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());
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 > kEpsilon) {
*result_listener << "\nx: " << x.transpose()
<< "\ndelta: " << delta.transpose()
<< "\nexpected: " << expected.transpose()
<< "\nactual: " << actual.transpose()
<< "\ndiff: " << (expected - actual).transpose()
<< "\ndiffnorm : " << diffnorm;
return false;
}
return true;
}
Vector RandomQuaternion() {
Vector x = Vector::Random(4);
x.normalize();
return x;
}
TEST(Quaternion, GenericDelta) {
Quaternion manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
EXPECT_THAT(manifold, QuaternionPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
TEST(Quaternion, SmallDelta) {
Quaternion 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, QuaternionPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
TEST(Quaternion, DeltaJustBelowPi) {
Quaternion manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
delta.normalize();
delta *= (M_PI - 1e-6);
EXPECT_THAT(manifold, QuaternionPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
// Compute the expected value of EigenQuaternion::Plus using Eigen and compares
// it to the one computed by Quaternion::Plus.
MATCHER_P2(EigenQuaternionPlusIsCorrectAt, 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 > kEpsilon) {
*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(EigenQuaternion, GenericDelta) {
EigenQuaternion manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
EXPECT_THAT(manifold, EigenQuaternionPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
TEST(EigenQuaternion, SmallDelta) {
EigenQuaternion 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, EigenQuaternionPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
TEST(EigenQuaternion, DeltaJustBelowPi) {
EigenQuaternion manifold;
for (int trial = 0; trial < kNumTrials; ++trial) {
const Vector x = RandomQuaternion();
const Vector y = RandomQuaternion();
Vector delta = Vector::Random(3);
delta.normalize();
delta *= (M_PI - 1e-6);
EXPECT_THAT(manifold, EigenQuaternionPlusIsCorrectAt(x, delta));
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y);
}
}
} // namespace internal
} // namespace ceres