mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-29 16:40:38 +08:00
Alex Stewart
297 lines
10 KiB
C++
297 lines
10 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
|
|
// Copyright 2022 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
|
|
// 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 "ceres/autodiff_manifold.h"
|
|
|
|
#include <cmath>
|
|
|
|
#include "ceres/manifold.h"
|
|
#include "ceres/manifold_test_utils.h"
|
|
#include "ceres/rotation.h"
|
|
#include "gtest/gtest.h"
|
|
|
|
namespace ceres {
|
|
namespace internal {
|
|
|
|
namespace {
|
|
|
|
constexpr int kNumTrials = 1000;
|
|
constexpr double kTolerance = 1e-9;
|
|
|
|
Vector RandomQuaternion() {
|
|
Vector x = Vector::Random(4);
|
|
x.normalize();
|
|
return x;
|
|
}
|
|
|
|
} // namespace
|
|
|
|
struct EuclideanFunctor {
|
|
template <typename T>
|
|
bool Plus(const T* x, const T* delta, T* x_plus_delta) const {
|
|
for (int i = 0; i < 3; ++i) {
|
|
x_plus_delta[i] = x[i] + delta[i];
|
|
}
|
|
return true;
|
|
}
|
|
|
|
template <typename T>
|
|
bool Minus(const T* y, const T* x, T* y_minus_x) const {
|
|
for (int i = 0; i < 3; ++i) {
|
|
y_minus_x[i] = y[i] - x[i];
|
|
}
|
|
return true;
|
|
}
|
|
};
|
|
|
|
TEST(AutoDiffLManifoldTest, EuclideanManifold) {
|
|
AutoDiffManifold<EuclideanFunctor, 3, 3> manifold;
|
|
EXPECT_EQ(manifold.AmbientSize(), 3);
|
|
EXPECT_EQ(manifold.TangentSize(), 3);
|
|
|
|
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);
|
|
}
|
|
}
|
|
|
|
struct ScaledFunctor {
|
|
explicit ScaledFunctor(const double s) : s(s) {}
|
|
|
|
template <typename T>
|
|
bool Plus(const T* x, const T* delta, T* x_plus_delta) const {
|
|
for (int i = 0; i < 3; ++i) {
|
|
x_plus_delta[i] = x[i] + s * delta[i];
|
|
}
|
|
return true;
|
|
}
|
|
|
|
template <typename T>
|
|
bool Minus(const T* y, const T* x, T* y_minus_x) const {
|
|
for (int i = 0; i < 3; ++i) {
|
|
y_minus_x[i] = (y[i] - x[i]) / s;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
const double s;
|
|
};
|
|
|
|
TEST(AutoDiffManifoldTest, ScaledManifold) {
|
|
constexpr double kScale = 1.2342;
|
|
AutoDiffManifold<ScaledFunctor, 3, 3> manifold(new ScaledFunctor(kScale));
|
|
EXPECT_EQ(manifold.AmbientSize(), 3);
|
|
EXPECT_EQ(manifold.TangentSize(), 3);
|
|
|
|
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 * kScale).norm() /
|
|
(x + delta * kScale).norm(),
|
|
0.0,
|
|
kTolerance);
|
|
|
|
EXPECT_THAT_MANIFOLD_INVARIANTS_HOLD(manifold, x, delta, y, kTolerance);
|
|
}
|
|
}
|
|
|
|
// Templated functor that implements the Plus and Minus operations on the
|
|
// Quaternion manifold.
|
|
struct QuaternionFunctor {
|
|
template <typename T>
|
|
bool Plus(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;
|
|
}
|
|
|
|
template <typename T>
|
|
bool Minus(const T* y, const T* x, T* y_minus_x) const {
|
|
T minus_x[4] = {x[0], -x[1], -x[2], -x[3]};
|
|
T ambient_y_minus_x[4];
|
|
QuaternionProduct(y, minus_x, ambient_y_minus_x);
|
|
T u_norm = sqrt(ambient_y_minus_x[1] * ambient_y_minus_x[1] +
|
|
ambient_y_minus_x[2] * ambient_y_minus_x[2] +
|
|
ambient_y_minus_x[3] * ambient_y_minus_x[3]);
|
|
if (u_norm > 0.0) {
|
|
T theta = atan2(u_norm, ambient_y_minus_x[0]);
|
|
y_minus_x[0] = theta * ambient_y_minus_x[1] / u_norm;
|
|
y_minus_x[1] = theta * ambient_y_minus_x[2] / u_norm;
|
|
y_minus_x[2] = theta * ambient_y_minus_x[3] / u_norm;
|
|
} else {
|
|
// We do not use [0,0,0] here because even though the value part is
|
|
// a constant, the derivative part is not.
|
|
y_minus_x[0] = ambient_y_minus_x[1];
|
|
y_minus_x[1] = ambient_y_minus_x[2];
|
|
y_minus_x[2] = ambient_y_minus_x[3];
|
|
}
|
|
return true;
|
|
}
|
|
};
|
|
|
|
TEST(AutoDiffManifoldTest, QuaternionPlusPiBy2) {
|
|
AutoDiffManifold<QuaternionFunctor, 4, 3> 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, kTolerance);
|
|
}
|
|
}
|
|
|
|
// 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 > 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;
|
|
}
|
|
|
|
TEST(AutoDiffManifoldTest, QuaternionGenericDelta) {
|
|
AutoDiffManifold<QuaternionFunctor, 4, 3> 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, kTolerance);
|
|
}
|
|
}
|
|
|
|
TEST(AutoDiffManifoldTest, QuaternionSmallDelta) {
|
|
AutoDiffManifold<QuaternionFunctor, 4, 3> 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, kTolerance);
|
|
}
|
|
}
|
|
|
|
TEST(AutoDiffManifold, QuaternionDeltaJustBelowPi) {
|
|
AutoDiffManifold<QuaternionFunctor, 4, 3> 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, kTolerance);
|
|
}
|
|
}
|
|
|
|
} // namespace internal
|
|
} // namespace ceres
|