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// Ceres Solver - A fast non-linear least squares minimizer
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// Author: jodebo_beck@gmx.de (Johannes Beck)
//
#ifndef CERES_PUBLIC_INTERNAL_LINE_MANIFOLD_H_
#define CERES_PUBLIC_INTERNAL_LINE_MANIFOLD_H_
#include "ceres/internal/householder_vector.h"
#include "ceres/internal/sphere_manifold_functions.h"
namespace ceres {
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)} [0.5 sinc(0.5 |delta_d|) delta_d, cos(0.5 |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)} [0.5 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.
//
// The factor of 0.5 is used to be consistent with the line direction
// update.
AmbientVector y(size_);
y << 0.5 * 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 =
2.0 * 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
#endif // CERES_PUBLIC_INTERNAL_LINE_MANIFOLD_H_