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#include "ceres/manifold.h"
#include <algorithm>
#include <cmath>
#include "ceres/internal/eigen.h"
#include "ceres/internal/fixed_array.h"
#include "glog/logging.h"
namespace ceres {
namespace {
struct CeresQuaternionOrder {
static constexpr int kW = 0;
static constexpr int kX = 1;
static constexpr int kY = 2;
static constexpr int kZ = 3;
};
struct EigenQuaternionOrder {
static constexpr int kW = 3;
static constexpr int kX = 0;
static constexpr int kY = 1;
static constexpr int kZ = 2;
};
template <typename Order>
inline void QuaternionPlusImpl(const double* x,
const double* delta,
double* x_plus_delta) {
// x_plus_delta = QuaternionProduct(q_delta, x), where q_delta is the
// quaternion constructed from delta.
const double norm_delta = std::sqrt(
delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2]);
if (norm_delta == 0.0) {
for (int i = 0; i < 4; ++i) {
x_plus_delta[i] = x[i];
}
return;
}
const double sin_delta_by_delta = (std::sin(norm_delta) / norm_delta);
double q_delta[4];
q_delta[Order::kW] = std::cos(norm_delta);
q_delta[Order::kX] = sin_delta_by_delta * delta[0];
q_delta[Order::kY] = sin_delta_by_delta * delta[1];
q_delta[Order::kZ] = sin_delta_by_delta * delta[2];
x_plus_delta[Order::kW] =
q_delta[Order::kW] * x[Order::kW] - q_delta[Order::kX] * x[Order::kX] -
q_delta[Order::kY] * x[Order::kY] - q_delta[Order::kZ] * x[Order::kZ];
x_plus_delta[Order::kX] =
q_delta[Order::kW] * x[Order::kX] + q_delta[Order::kX] * x[Order::kW] +
q_delta[Order::kY] * x[Order::kZ] - q_delta[Order::kZ] * x[Order::kY];
x_plus_delta[Order::kY] =
q_delta[Order::kW] * x[Order::kY] - q_delta[Order::kX] * x[Order::kZ] +
q_delta[Order::kY] * x[Order::kW] + q_delta[Order::kZ] * x[Order::kX];
x_plus_delta[Order::kZ] =
q_delta[Order::kW] * x[Order::kZ] + q_delta[Order::kX] * x[Order::kY] -
q_delta[Order::kY] * x[Order::kX] + q_delta[Order::kZ] * x[Order::kW];
}
template <typename Order>
inline void QuaternionPlusJacobianImpl(const double* x, double* jacobian_ptr) {
Eigen::Map<Eigen::Matrix<double, 4, 3, Eigen::RowMajor>> jacobian(
jacobian_ptr);
jacobian(Order::kW, 0) = -x[Order::kX];
jacobian(Order::kW, 1) = -x[Order::kY];
jacobian(Order::kW, 2) = -x[Order::kZ];
jacobian(Order::kX, 0) = x[Order::kW];
jacobian(Order::kX, 1) = x[Order::kZ];
jacobian(Order::kX, 2) = -x[Order::kY];
jacobian(Order::kY, 0) = -x[Order::kZ];
jacobian(Order::kY, 1) = x[Order::kW];
jacobian(Order::kY, 2) = x[Order::kX];
jacobian(Order::kZ, 0) = x[Order::kY];
jacobian(Order::kZ, 1) = -x[Order::kX];
jacobian(Order::kZ, 2) = x[Order::kW];
}
template <typename Order>
inline void QuaternionMinusImpl(const double* y,
const double* x,
double* y_minus_x) {
// ambient_y_minus_x = QuaternionProduct(y, -x) where -x is the conjugate of
// x.
double ambient_y_minus_x[4];
ambient_y_minus_x[Order::kW] =
y[Order::kW] * x[Order::kW] + y[Order::kX] * x[Order::kX] +
y[Order::kY] * x[Order::kY] + y[Order::kZ] * x[Order::kZ];
ambient_y_minus_x[Order::kX] =
-y[Order::kW] * x[Order::kX] + y[Order::kX] * x[Order::kW] -
y[Order::kY] * x[Order::kZ] + y[Order::kZ] * x[Order::kY];
ambient_y_minus_x[Order::kY] =
-y[Order::kW] * x[Order::kY] + y[Order::kX] * x[Order::kZ] +
y[Order::kY] * x[Order::kW] - y[Order::kZ] * x[Order::kX];
ambient_y_minus_x[Order::kZ] =
-y[Order::kW] * x[Order::kZ] - y[Order::kX] * x[Order::kY] +
y[Order::kY] * x[Order::kX] + y[Order::kZ] * x[Order::kW];
const double u_norm =
std::sqrt(ambient_y_minus_x[Order::kX] * ambient_y_minus_x[Order::kX] +
ambient_y_minus_x[Order::kY] * ambient_y_minus_x[Order::kY] +
ambient_y_minus_x[Order::kZ] * ambient_y_minus_x[Order::kZ]);
if (u_norm > 0.0) {
const double theta = std::atan2(u_norm, ambient_y_minus_x[Order::kW]);
y_minus_x[0] = theta * ambient_y_minus_x[Order::kX] / u_norm;
y_minus_x[1] = theta * ambient_y_minus_x[Order::kY] / u_norm;
y_minus_x[2] = theta * ambient_y_minus_x[Order::kZ] / u_norm;
} else {
y_minus_x[0] = 0.0;
y_minus_x[1] = 0.0;
y_minus_x[2] = 0.0;
}
}
template <typename Order>
inline void QuaternionMinusJacobianImpl(const double* x, double* jacobian_ptr) {
Eigen::Map<Eigen::Matrix<double, 3, 4, Eigen::RowMajor>> jacobian(
jacobian_ptr);
jacobian(0, Order::kW) = -x[Order::kX];
jacobian(0, Order::kX) = x[Order::kW];
jacobian(0, Order::kY) = -x[Order::kZ];
jacobian(0, Order::kZ) = x[Order::kY];
jacobian(1, Order::kW) = -x[Order::kY];
jacobian(1, Order::kX) = x[Order::kZ];
jacobian(1, Order::kY) = x[Order::kW];
jacobian(1, Order::kZ) = -x[Order::kX];
jacobian(2, Order::kW) = -x[Order::kZ];
jacobian(2, Order::kX) = -x[Order::kY];
jacobian(2, Order::kY) = x[Order::kX];
jacobian(2, Order::kZ) = x[Order::kW];
}
} // namespace
Manifold::~Manifold() = default;
bool Manifold::RightMultiplyByPlusJacobian(const double* x,
const int num_rows,
const double* ambient_matrix,
double* tangent_matrix) const {
const int tangent_size = TangentSize();
if (tangent_size == 0) {
return true;
}
const int ambient_size = AmbientSize();
Matrix plus_jacobian(ambient_size, tangent_size);
if (!PlusJacobian(x, plus_jacobian.data())) {
return false;
}
MatrixRef(tangent_matrix, num_rows, tangent_size) =
ConstMatrixRef(ambient_matrix, num_rows, ambient_size) * plus_jacobian;
return true;
}
SubsetManifold::SubsetManifold(const int size,
const std::vector<int>& constant_parameters)
: tangent_size_(size - constant_parameters.size()),
constancy_mask_(size, false) {
if (constant_parameters.empty()) {
return;
}
std::vector<int> constant = constant_parameters;
std::sort(constant.begin(), constant.end());
CHECK_GE(constant.front(), 0) << "Indices indicating constant parameter must "
"be greater than equal to zero.";
CHECK_LT(constant.back(), size)
<< "Indices indicating constant parameter must be less than the size "
<< "of the parameter block.";
CHECK(std::adjacent_find(constant.begin(), constant.end()) == constant.end())
<< "The set of constant parameters cannot contain duplicates";
for (auto index : constant_parameters) {
constancy_mask_[index] = true;
}
}
int SubsetManifold::AmbientSize() const { return constancy_mask_.size(); }
int SubsetManifold::TangentSize() const { return tangent_size_; }
bool SubsetManifold::Plus(const double* x,
const double* delta,
double* x_plus_delta) const {
const int ambient_size = AmbientSize();
for (int i = 0, j = 0; i < ambient_size; ++i) {
if (constancy_mask_[i]) {
x_plus_delta[i] = x[i];
} else {
x_plus_delta[i] = x[i] + delta[j++];
}
}
return true;
}
bool SubsetManifold::PlusJacobian(const double* x,
double* plus_jacobian) const {
if (tangent_size_ == 0) {
return true;
}
const int ambient_size = AmbientSize();
MatrixRef m(plus_jacobian, ambient_size, tangent_size_);
m.setZero();
for (int r = 0, c = 0; r < ambient_size; ++r) {
if (!constancy_mask_[r]) {
m(r, c++) = 1.0;
}
}
return true;
}
bool SubsetManifold::RightMultiplyByPlusJacobian(const double* x,
const int num_rows,
const double* ambient_matrix,
double* tangent_matrix) const {
if (tangent_size_ == 0) {
return true;
}
const int ambient_size = AmbientSize();
for (int r = 0; r < num_rows; ++r) {
for (int idx = 0, c = 0; idx < ambient_size; ++idx) {
if (!constancy_mask_[idx]) {
tangent_matrix[r * tangent_size_ + c++] =
ambient_matrix[r * ambient_size + idx];
}
}
}
return true;
}
bool SubsetManifold::Minus(const double* y,
const double* x,
double* y_minus_x) const {
if (tangent_size_ == 0) {
return true;
}
const int ambient_size = AmbientSize();
for (int i = 0, j = 0; i < ambient_size; ++i) {
if (!constancy_mask_[i]) {
y_minus_x[j++] = y[i] - x[i];
}
}
return true;
}
bool SubsetManifold::MinusJacobian(const double* x,
double* minus_jacobian) const {
const int ambient_size = AmbientSize();
MatrixRef m(minus_jacobian, tangent_size_, ambient_size);
m.setZero();
for (int c = 0, r = 0; c < ambient_size; ++c) {
if (!constancy_mask_[c]) {
m(r++, c) = 1.0;
}
}
return true;
}
bool QuaternionManifold::Plus(const double* x,
const double* delta,
double* x_plus_delta) const {
QuaternionPlusImpl<CeresQuaternionOrder>(x, delta, x_plus_delta);
return true;
}
bool QuaternionManifold::PlusJacobian(const double* x, double* jacobian) const {
QuaternionPlusJacobianImpl<CeresQuaternionOrder>(x, jacobian);
return true;
}
bool QuaternionManifold::Minus(const double* y,
const double* x,
double* y_minus_x) const {
QuaternionMinusImpl<CeresQuaternionOrder>(y, x, y_minus_x);
return true;
}
bool QuaternionManifold::MinusJacobian(const double* x,
double* jacobian) const {
QuaternionMinusJacobianImpl<CeresQuaternionOrder>(x, jacobian);
return true;
}
bool EigenQuaternionManifold::Plus(const double* x,
const double* delta,
double* x_plus_delta) const {
QuaternionPlusImpl<EigenQuaternionOrder>(x, delta, x_plus_delta);
return true;
}
bool EigenQuaternionManifold::PlusJacobian(const double* x,
double* jacobian) const {
QuaternionPlusJacobianImpl<EigenQuaternionOrder>(x, jacobian);
return true;
}
bool EigenQuaternionManifold::Minus(const double* y,
const double* x,
double* y_minus_x) const {
QuaternionMinusImpl<EigenQuaternionOrder>(y, x, y_minus_x);
return true;
}
bool EigenQuaternionManifold::MinusJacobian(const double* x,
double* jacobian) const {
QuaternionMinusJacobianImpl<EigenQuaternionOrder>(x, jacobian);
return true;
}
} // namespace ceres
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