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// 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
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// 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
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//
// Author: jodebo_beck@gmx.de (Johannes Beck)
//
#ifndef CERES_PUBLIC_LINE_MANIFOLD_H_
#define CERES_PUBLIC_LINE_MANIFOLD_H_
#include <Eigen/Core>
#include <algorithm>
#include <array>
#include <memory>
#include <vector>
#include "ceres/internal/disable_warnings.h"
#include "ceres/internal/export.h"
#include "ceres/internal/householder_vector.h"
#include "ceres/internal/sphere_manifold_functions.h"
#include "ceres/manifold.h"
#include "ceres/types.h"
#include "glog/logging.h"
namespace ceres {
// This provides a manifold for lines, where the line is
// over-parameterized by an origin point and a direction vector. So the
// parameter vector size needs to be two times the ambient space dimension,
// where the first half is interpreted as the origin point and the second half
// as the direction.
//
// The plus operator for the line direction is the same as for the
// SphereManifold. The update of the origin point is
// perpendicular to the line direction before the update.
//
// This manifold is a special case of the affine Grassmannian
// manifold (see https://en.wikipedia.org/wiki/Affine_Grassmannian_(manifold))
// for the case Graff_1(R^n).
//
// The class works with dynamic and static ambient space dimensions. If the
// ambient space dimensions is known at compile time use
//
// LineManifold<3> manifold;
//
// If the ambient space dimensions is not known at compile time the template
// parameter needs to be set to ceres::DYNAMIC and the actual dimension needs
// to be provided as a constructor argument:
//
// LineManifold<ceres::DYNAMIC> manifold(ambient_dim);
//
template <int AmbientSpaceDimension>
class LineManifold final : public Manifold {
public:
static_assert(AmbientSpaceDimension == DYNAMIC || AmbientSpaceDimension >= 2,
"The ambient space must be at least 2.");
static_assert(ceres::DYNAMIC == Eigen::Dynamic,
"ceres::DYNAMIC needs to be the same as Eigen::Dynamic.");
LineManifold();
explicit LineManifold(int size);
int AmbientSize() const override { return 2 * size_; }
int TangentSize() const override { return 2 * (size_ - 1); }
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const override;
bool PlusJacobian(const double* x, double* jacobian) const override;
bool Minus(const double* y,
const double* x,
double* y_minus_x) const override;
bool MinusJacobian(const double* x, double* jacobian) const override;
private:
static constexpr bool IsDynamic = (AmbientSpaceDimension == ceres::DYNAMIC);
static constexpr int TangentSpaceDimension =
IsDynamic ? ceres::DYNAMIC : AmbientSpaceDimension - 1;
static constexpr int DAmbientSpaceDimension =
IsDynamic ? ceres::DYNAMIC : 2 * AmbientSpaceDimension;
static constexpr int DTangentSpaceDimension =
IsDynamic ? ceres::DYNAMIC : 2 * TangentSpaceDimension;
using AmbientVector = Eigen::Matrix<double, AmbientSpaceDimension, 1>;
using TangentVector = Eigen::Matrix<double, TangentSpaceDimension, 1>;
using MatrixPlusJacobian = Eigen::Matrix<double,
DAmbientSpaceDimension,
DTangentSpaceDimension,
Eigen::RowMajor>;
using MatrixMinusJacobian = Eigen::Matrix<double,
DTangentSpaceDimension,
DAmbientSpaceDimension,
Eigen::RowMajor>;
const int size_{AmbientSpaceDimension};
};
template <int AmbientSpaceDimension>
LineManifold<AmbientSpaceDimension>::LineManifold()
: size_{AmbientSpaceDimension} {
static_assert(
AmbientSpaceDimension != Eigen::Dynamic,
"The size is set to dynamic. Please call the constructor with a size.");
}
template <int AmbientSpaceDimension>
LineManifold<AmbientSpaceDimension>::LineManifold(int size) : size_{size} {
if (AmbientSpaceDimension != Eigen::Dynamic) {
CHECK_EQ(AmbientSpaceDimension, size)
<< "Specified size by template parameter differs from the supplied "
"one.";
} else {
CHECK_GT(size_, 1)
<< "The size of the manifold needs to be greater than 1.";
}
}
template <int AmbientSpaceDimension>
bool LineManifold<AmbientSpaceDimension>::Plus(const double* x_ptr,
const double* delta_ptr,
double* x_plus_delta_ptr) const {
// We seek a box plus operator of the form
//
// [o*, d*] = Plus([o, d], [delta_o, delta_d])
//
// where o is the origin point, d is the direction vector, delta_o is
// the delta of the origin point and delta_d the delta of the direction and
// o* and d* is the updated origin point and direction.
//
// We separate the Plus operator into the origin point and directional part
// d* = Plus_d(d, delta_d)
// o* = Plus_o(o, d, delta_o)
//
// The direction update function Plus_d is the same as as the SphereManifold:
//
// d* = H_{v(d)} [sinc(|delta_d|) delta_d, cos(|delta_d|)]^T
//
// where H is the householder matrix
// H_{v} = I - (2 / |v|^2) v v^T
// and
// v(d) = d - sign(d_n) |d| e_n.
//
// The origin point update function Plus_o is defined as
//
// o* = o + H_{v(d)} [delta_o, 0]^T.
Eigen::Map<const AmbientVector> o(x_ptr, size_);
Eigen::Map<const AmbientVector> d(x_ptr + size_, size_);
Eigen::Map<const TangentVector> delta_o(delta_ptr, size_ - 1);
Eigen::Map<const TangentVector> delta_d(delta_ptr + size_ - 1, size_ - 1);
Eigen::Map<AmbientVector> o_plus_delta(x_plus_delta_ptr, size_);
Eigen::Map<AmbientVector> d_plus_delta(x_plus_delta_ptr + size_, size_);
const double norm_delta_d = delta_d.norm();
o_plus_delta = o;
// Shortcut for zero delta direction.
if (norm_delta_d == 0.0) {
d_plus_delta = d;
if (delta_o.isZero(0.0)) {
return true;
}
}
// Calculate the householder transformation which is needed for f_d and f_o.
AmbientVector v(size_);
double beta;
// NOTE: The explicit template arguments are needed here because
// ComputeHouseholderVector is templated and some versions of MSVC
// have trouble deducing the type of v automatically.
internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
double,
AmbientSpaceDimension>(d, &v, &beta);
if (norm_delta_d != 0.0) {
internal::ComputeSphereManifoldPlus(
v, beta, d, delta_d, norm_delta_d, &d_plus_delta);
}
// The null space is in the direction of the line, so the tangent space is
// perpendicular to the line direction. This is achieved by using the
// householder matrix of the direction and allow only movements
// perpendicular to e_n.
AmbientVector y(size_);
y << delta_o, 0;
o_plus_delta += internal::ApplyHouseholderVector(y, v, beta);
return true;
}
template <int AmbientSpaceDimension>
bool LineManifold<AmbientSpaceDimension>::PlusJacobian(
const double* x_ptr, double* jacobian_ptr) const {
Eigen::Map<const AmbientVector> d(x_ptr + size_, size_);
Eigen::Map<MatrixPlusJacobian> jacobian(
jacobian_ptr, 2 * size_, 2 * (size_ - 1));
// Clear the Jacobian as only half of the matrix is not zero.
jacobian.setZero();
auto jacobian_d =
jacobian
.template topLeftCorner<AmbientSpaceDimension, TangentSpaceDimension>(
size_, size_ - 1);
auto jacobian_o = jacobian.template bottomRightCorner<AmbientSpaceDimension,
TangentSpaceDimension>(
size_, size_ - 1);
internal::ComputeSphereManifoldPlusJacobian(d, &jacobian_d);
jacobian_o = jacobian_d;
return true;
}
template <int AmbientSpaceDimension>
bool LineManifold<AmbientSpaceDimension>::Minus(const double* y_ptr,
const double* x_ptr,
double* y_minus_x) const {
Eigen::Map<const AmbientVector> y_o(y_ptr, size_);
Eigen::Map<const AmbientVector> y_d(y_ptr + size_, size_);
Eigen::Map<const AmbientVector> x_o(x_ptr, size_);
Eigen::Map<const AmbientVector> x_d(x_ptr + size_, size_);
Eigen::Map<TangentVector> y_minus_x_o(y_minus_x, size_ - 1);
Eigen::Map<TangentVector> y_minus_x_d(y_minus_x + size_ - 1, size_ - 1);
AmbientVector v(size_);
double beta;
// NOTE: The explicit template arguments are needed here because
// ComputeHouseholderVector is templated and some versions of MSVC
// have trouble deducing the type of v automatically.
internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
double,
AmbientSpaceDimension>(x_d, &v, &beta);
internal::ComputeSphereManifoldMinus(v, beta, x_d, y_d, &y_minus_x_d);
AmbientVector delta_o = y_o - x_o;
const AmbientVector h_delta_o =
internal::ApplyHouseholderVector(delta_o, v, beta);
y_minus_x_o = h_delta_o.template head<TangentSpaceDimension>(size_ - 1);
return true;
}
template <int AmbientSpaceDimension>
bool LineManifold<AmbientSpaceDimension>::MinusJacobian(
const double* x_ptr, double* jacobian_ptr) const {
Eigen::Map<const AmbientVector> d(x_ptr + size_, size_);
Eigen::Map<MatrixMinusJacobian> jacobian(
jacobian_ptr, 2 * (size_ - 1), 2 * size_);
// Clear the Jacobian as only half of the matrix is not zero.
jacobian.setZero();
auto jacobian_d =
jacobian
.template topLeftCorner<TangentSpaceDimension, AmbientSpaceDimension>(
size_ - 1, size_);
auto jacobian_o = jacobian.template bottomRightCorner<TangentSpaceDimension,
AmbientSpaceDimension>(
size_ - 1, size_);
internal::ComputeSphereManifoldMinusJacobian(d, &jacobian_d);
jacobian_o = jacobian_d;
return true;
}
} // namespace ceres
// clang-format off
#include "ceres/internal/reenable_warnings.h"
// clang-format on
#endif // CERES_PUBLIC_LINE_MANIFOLD_H_