| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2022 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
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| // |
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| // |
| // Author: vitus@google.com (Mike Vitus) |
| // jodebo_beck@gmx.de (Johannes Beck) |
| |
| #ifndef CERES_PUBLIC_INTERNAL_SPHERE_MANIFOLD_HELPERS_H_ |
| #define CERES_PUBLIC_INTERNAL_SPHERE_MANIFOLD_HELPERS_H_ |
| |
| #include "ceres/internal/householder_vector.h" |
| |
| // This module contains functions to compute the SphereManifold plus and minus |
| // operator and their Jacobians. |
| // |
| // As the parameters to these functions are shared between them, they are |
| // described here: The following variable names are used: |
| // Plus(x, delta) = x + delta = x_plus_delta, |
| // Minus(y, x) = y - x = y_minus_x. |
| // |
| // The remaining ones are v and beta which describe the Householder |
| // transformation of x, and norm_delta which is the norm of delta. |
| // |
| // The types of x, y, x_plus_delta and y_minus_x need to be equivalent to |
| // Eigen::Matrix<double, AmbientSpaceDimension, 1> and the type of delta needs |
| // to be equivalent to Eigen::Matrix<double, TangentSpaceDimension, 1>. |
| // |
| // The type of Jacobian plus needs to be equivalent to Eigen::Matrix<double, |
| // AmbientSpaceDimension, TangentSpaceDimension, Eigen::RowMajor> and for |
| // Jacobian minus Eigen::Matrix<double, TangentSpaceDimension, |
| // AmbientSpaceDimension, Eigen::RowMajor>. |
| // |
| // For all vector / matrix inputs and outputs, template parameters are |
| // used in order to allow also Eigen::Ref and Eigen block expressions to |
| // be passed to the function. |
| |
| namespace ceres { |
| namespace internal { |
| |
| template <typename VT, typename XT, typename DeltaT, typename XPlusDeltaT> |
| inline void ComputeSphereManifoldPlus(const VT& v, |
| double beta, |
| const XT& x, |
| const DeltaT& delta, |
| double norm_delta, |
| XPlusDeltaT* x_plus_delta) { |
| constexpr int AmbientDim = VT::RowsAtCompileTime; |
| |
| // Map the delta from the minimum representation to the over parameterized |
| // homogeneous vector. See B.2 p.25 equation (106) - (107) for more details. |
| const double norm_delta_div_2 = 0.5 * norm_delta; |
| const double sin_delta_by_delta = |
| std::sin(norm_delta_div_2) / norm_delta_div_2; |
| |
| Eigen::Matrix<double, AmbientDim, 1> y(v.size()); |
| y << 0.5 * sin_delta_by_delta * delta, std::cos(norm_delta_div_2); |
| |
| // Apply the delta update to remain on the sphere. |
| *x_plus_delta = x.norm() * ApplyHouseholderVector(y, v, beta); |
| } |
| |
| template <typename VT, typename JacobianT> |
| inline void ComputeSphereManifoldPlusJacobian(const VT& x, |
| JacobianT* jacobian) { |
| constexpr int AmbientSpaceDim = VT::RowsAtCompileTime; |
| using AmbientVector = Eigen::Matrix<double, AmbientSpaceDim, 1>; |
| const int ambient_size = x.size(); |
| const int tangent_size = x.size() - 1; |
| |
| AmbientVector v(ambient_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. |
| ComputeHouseholderVector<VT, double, AmbientSpaceDim>(x, &v, &beta); |
| |
| // The Jacobian is equal to J = 0.5 * H.leftCols(size_ - 1) where H is the |
| // Householder matrix (H = I - beta * v * v'). |
| for (int i = 0; i < tangent_size; ++i) { |
| (*jacobian).col(i) = -0.5 * beta * v(i) * v; |
| (*jacobian)(i, i) += 0.5; |
| } |
| (*jacobian) *= x.norm(); |
| } |
| |
| template <typename VT, typename XT, typename YT, typename YMinusXT> |
| inline void ComputeSphereManifoldMinus( |
| const VT& v, double beta, const XT& x, const YT& y, YMinusXT* y_minus_x) { |
| constexpr int AmbientSpaceDim = VT::RowsAtCompileTime; |
| constexpr int TangentSpaceDim = |
| AmbientSpaceDim == Eigen::Dynamic ? Eigen::Dynamic : AmbientSpaceDim - 1; |
| using AmbientVector = Eigen::Matrix<double, AmbientSpaceDim, 1>; |
| |
| const int tanget_size = v.size() - 1; |
| |
| const AmbientVector hy = ApplyHouseholderVector(y, v, beta) / x.norm(); |
| |
| // Calculate y - x. See B.2 p.25 equation (108). |
| double y_last = hy[tanget_size]; |
| double hy_norm = hy.template head<TangentSpaceDim>(tanget_size).norm(); |
| if (hy_norm == 0.0) { |
| y_minus_x->setZero(); |
| } else { |
| *y_minus_x = 2.0 * std::atan2(hy_norm, y_last) / hy_norm * |
| hy.template head<TangentSpaceDim>(tanget_size); |
| } |
| } |
| |
| template <typename VT, typename JacobianT> |
| inline void ComputeSphereManifoldMinusJacobian(const VT& x, |
| JacobianT* jacobian) { |
| constexpr int AmbientSpaceDim = VT::RowsAtCompileTime; |
| using AmbientVector = Eigen::Matrix<double, AmbientSpaceDim, 1>; |
| const int ambient_size = x.size(); |
| const int tangent_size = x.size() - 1; |
| |
| AmbientVector v(ambient_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. |
| ComputeHouseholderVector<VT, double, AmbientSpaceDim>(x, &v, &beta); |
| |
| // The Jacobian is equal to J = 2.0 * H.leftCols(size_ - 1) where H is the |
| // Householder matrix (H = I - beta * v * v'). |
| for (int i = 0; i < tangent_size; ++i) { |
| (*jacobian).row(i) = -2.0 * beta * v(i) * v; |
| (*jacobian)(i, i) += 2.0; |
| } |
| (*jacobian) /= x.norm(); |
| } |
| |
| } // namespace internal |
| } // namespace ceres |
| |
| #endif |