| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2022 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
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| // |
| // Author: vitus@google.com (Mike Vitus) |
| // jodebo_beck@gmx.de (Johannes Beck) |
| |
| #include "ceres/internal/householder_vector.h" |
| |
| namespace ceres { |
| |
| template <int AmbientSpaceDimension> |
| SphereManifold<AmbientSpaceDimension>::SphereManifold() |
| : size_{AmbientSpaceDimension} { |
| static_assert( |
| AmbientSpaceDimension != Eigen::Dynamic, |
| "The size is set to dynamic. Please call the constructor with a size."); |
| } |
| |
| template <int AmbientSpaceDimension> |
| SphereManifold<AmbientSpaceDimension>::SphereManifold(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 SphereManifold<AmbientSpaceDimension>::Plus( |
| const double* x_ptr, |
| const double* delta_ptr, |
| double* x_plus_delta_ptr) const { |
| Eigen::Map<const AmbientVector> x(x_ptr, size_); |
| Eigen::Map<const TangentVector> delta(delta_ptr, size_ - 1); |
| Eigen::Map<AmbientVector> x_plus_delta(x_plus_delta_ptr, size_); |
| |
| const double norm_delta = delta.norm(); |
| |
| if (norm_delta == 0.0) { |
| x_plus_delta = x; |
| return true; |
| } |
| |
| // 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; |
| |
| AmbientVector y(size_); |
| y.head(size_ - 1) = 0.5 * sin_delta_by_delta * delta; |
| y(size_ - 1) = std::cos(norm_delta_div_2); |
| |
| 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, &v, &beta); |
| |
| // Apply the delta update to remain on the sphere. |
| x_plus_delta = x.norm() * internal::ApplyHouseholderVector(y, v, beta); |
| |
| return true; |
| } |
| |
| template <int AmbientSpaceDimension> |
| bool SphereManifold<AmbientSpaceDimension>::PlusJacobian( |
| const double* x_ptr, double* jacobian_ptr) const { |
| Eigen::Map<const AmbientVector> x(x_ptr, size_); |
| Eigen::Map<MatrixPlusJacobian> jacobian(jacobian_ptr, size_, 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, &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 < size_ - 1; ++i) { |
| jacobian.col(i) = -0.5 * beta * v(i) * v; |
| jacobian.col(i)(i) += 0.5; |
| } |
| jacobian *= x.norm(); |
| |
| return true; |
| } |
| |
| template <int AmbientSpaceDimension> |
| bool SphereManifold<AmbientSpaceDimension>::Minus(const double* y_ptr, |
| const double* x_ptr, |
| double* y_minus_x_ptr) const { |
| AmbientVector y = Eigen::Map<const AmbientVector>(y_ptr, size_); |
| Eigen::Map<const AmbientVector> x(x_ptr, size_); |
| Eigen::Map<TangentVector> y_minus_x(y_minus_x_ptr, size_ - 1); |
| |
| // Apply hoseholder transformation. |
| 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, &v, &beta); |
| |
| const AmbientVector hy = |
| internal::ApplyHouseholderVector(y, v, beta) / x.norm(); |
| |
| // Calculate y - x. See B.2 p.25 equation (108). |
| double y_last = hy[size_ - 1]; |
| double hy_norm = hy.head(size_ - 1).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.head(size_ - 1); |
| } |
| |
| return true; |
| } |
| |
| template <int AmbientSpaceDimension> |
| bool SphereManifold<AmbientSpaceDimension>::MinusJacobian( |
| const double* x_ptr, double* jacobian_ptr) const { |
| Eigen::Map<const AmbientVector> x(x_ptr, size_); |
| Eigen::Map<MatrixMinusJacobian> jacobian(jacobian_ptr, size_ - 1, size_); |
| |
| 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, &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 < size_ - 1; ++i) { |
| jacobian.row(i) = -2.0 * beta * v(i) * v; |
| jacobian.row(i)(i) += 2.0; |
| } |
| jacobian /= x.norm(); |
| |
| return true; |
| } |
| } // namespace ceres |