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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)
#ifndef CERES_PUBLIC_AUTODIFF_MANIFOLD_H_
#define CERES_PUBLIC_AUTODIFF_MANIFOLD_H_
#include <memory>
#include "ceres/internal/autodiff.h"
#include "ceres/manifold.h"
namespace ceres {
// Create a Manifold with Jacobians computed via automatic differentiation. For
// more information on manifolds, see include/ceres/manifold.h
//
// To get an auto differentiated manifold, you must define a class/struct with
// templated Plus and Minus functions that compute
//
// x_plus_delta = Plus(x, delta);
// y_minus_x = Minus(y, x);
//
// Where, x, y and x_plus_delta are vectors on the manifold in the ambient space
// (so they are kAmbientSize vectors) and delta, y_minus_x are vectors in the
// tangent space (so they are kTangentSize vectors).
//
// The Functor should have the signature:
//
// struct Functor {
// template <typename T>
// bool Plus(const T* x, const T* delta, T* x_plus_delta) const;
//
// template <typename T>
// bool Minus(const T* y, const T* x, T* y_minus_x) const;
// };
//
// Observe that the Plus and Minus operations are templated on the parameter T.
// The autodiff framework substitutes appropriate "Jet" objects for T in order
// to compute the derivative when necessary. This is the same mechanism that is
// used to compute derivatives when using AutoDiffCostFunction.
//
// Plus and Minus should return true if the computation is successful and false
// otherwise, in which case the result will not be used.
//
// Given this Functor, the corresponding Manifold can be constructed as:
//
// AutoDiffManifold<Functor, kAmbientSize, kTangentSize> manifold;
//
// As a concrete example consider the case of Quaternions. Quaternions form a
// three dimensional manifold embedded in R^4, i.e. they have an ambient
// dimension of 4 and their tangent space has dimension 3. The following Functor
// (taken from autodiff_manifold_test.cc) defines the Plus and Minus operations
// on the Quaternion manifold:
//
// NOTE: The following is only used for illustration purposes. Ceres Solver
// ships with optimized production grade QuaternionManifold implementation. See
// manifold.h.
//
// This functor assumes that the quaternions are laid out as [w,x,y,z] in
// memory, i.e. the real or scalar part is the first coordinate.
//
// 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;
// }
// };
//
// Then given this struct, the auto differentiated Quaternion Manifold can now
// be constructed as
//
// Manifold* manifold = new AutoDiffManifold<QuaternionFunctor, 4, 3>;
template <typename Functor, int kAmbientSize, int kTangentSize>
class AutoDiffManifold final : public Manifold {
public:
AutoDiffManifold() : functor_(std::make_unique<Functor>()) {}
// Takes ownership of functor.
explicit AutoDiffManifold(Functor* functor) : functor_(functor) {}
int AmbientSize() const override { return kAmbientSize; }
int TangentSize() const override { return kTangentSize; }
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const override {
return functor_->Plus(x, delta, x_plus_delta);
}
bool PlusJacobian(const double* x, double* jacobian) const override;
bool Minus(const double* y,
const double* x,
double* y_minus_x) const override {
return functor_->Minus(y, x, y_minus_x);
}
bool MinusJacobian(const double* x, double* jacobian) const override;
const Functor& functor() const { return *functor_; }
private:
std::unique_ptr<Functor> functor_;
};
namespace internal {
// The following two helper structs are needed to interface the Plus and Minus
// methods of the ManifoldFunctor with the automatic differentiation which
// expects a Functor with operator().
template <typename Functor>
struct PlusWrapper {
explicit PlusWrapper(const Functor& functor) : functor(functor) {}
template <typename T>
bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
return functor.Plus(x, delta, x_plus_delta);
}
const Functor& functor;
};
template <typename Functor>
struct MinusWrapper {
explicit MinusWrapper(const Functor& functor) : functor(functor) {}
template <typename T>
bool operator()(const T* y, const T* x, T* y_minus_x) const {
return functor.Minus(y, x, y_minus_x);
}
const Functor& functor;
};
} // namespace internal
template <typename Functor, int kAmbientSize, int kTangentSize>
bool AutoDiffManifold<Functor, kAmbientSize, kTangentSize>::PlusJacobian(
const double* x, double* jacobian) const {
double zero_delta[kTangentSize];
for (int i = 0; i < kTangentSize; ++i) {
zero_delta[i] = 0.0;
}
double x_plus_delta[kAmbientSize];
for (int i = 0; i < kAmbientSize; ++i) {
x_plus_delta[i] = 0.0;
}
const double* parameter_ptrs[2] = {x, zero_delta};
// PlusJacobian is D_2 Plus(x,0) so we only need to compute the Jacobian
// w.r.t. the second argument.
double* jacobian_ptrs[2] = {nullptr, jacobian};
return internal::AutoDifferentiate<
kAmbientSize,
internal::StaticParameterDims<kAmbientSize, kTangentSize>>(
internal::PlusWrapper<Functor>(*functor_),
parameter_ptrs,
kAmbientSize,
x_plus_delta,
jacobian_ptrs);
}
template <typename Functor, int kAmbientSize, int kTangentSize>
bool AutoDiffManifold<Functor, kAmbientSize, kTangentSize>::MinusJacobian(
const double* x, double* jacobian) const {
double y_minus_x[kTangentSize];
for (int i = 0; i < kTangentSize; ++i) {
y_minus_x[i] = 0.0;
}
const double* parameter_ptrs[2] = {x, x};
// MinusJacobian is D_1 Minus(x,x), so we only need to compute the Jacobian
// w.r.t. the first argument.
double* jacobian_ptrs[2] = {jacobian, nullptr};
return internal::AutoDifferentiate<
kTangentSize,
internal::StaticParameterDims<kAmbientSize, kAmbientSize>>(
internal::MinusWrapper<Functor>(*functor_),
parameter_ptrs,
kTangentSize,
y_minus_x,
jacobian_ptrs);
}
} // namespace ceres
#endif // CERES_PUBLIC_AUTODIFF_MANIFOLD_H_