Add the two-dimensional subspace search to DoglegStrategy Change-Id: I5163744c100cdf07dd93343d0734ffe0e80364f3
diff --git a/examples/bundle_adjuster.cc b/examples/bundle_adjuster.cc index 5173e79..68458a0 100644 --- a/examples/bundle_adjuster.cc +++ b/examples/bundle_adjuster.cc
@@ -86,6 +86,7 @@ "Options are: suitesparse and cxsparse"); DEFINE_string(ordering_type, "schur", "Options are: schur, user, natural"); +DEFINE_string(dogleg_type, "traditional", "Options are: traditional, subspace"); DEFINE_bool(use_block_amd, true, "Use a block oriented fill reducing " "ordering."); @@ -255,6 +256,14 @@ LOG(FATAL) << "Unknown trust region strategy: " << FLAGS_trust_region_strategy; } + if (FLAGS_dogleg_type == "traditional") { + options->dogleg_type = TRADITIONAL_DOGLEG; + } else if (FLAGS_dogleg_type == "subspace") { + options->dogleg_type = SUBSPACE_DOGLEG; + } else { + LOG(FATAL) << "Unknown dogleg type: " + << FLAGS_dogleg_type; + } } void SetSolverOptionsFromFlags(BALProblem* bal_problem,
diff --git a/include/ceres/solver.h b/include/ceres/solver.h index ef6c617..16c7387 100644 --- a/include/ceres/solver.h +++ b/include/ceres/solver.h
@@ -58,6 +58,7 @@ // Default constructor that sets up a generic sparse problem. Options() { trust_region_strategy_type = LEVENBERG_MARQUARDT; + dogleg_type = TRADITIONAL_DOGLEG; use_nonmonotonic_steps = false; max_consecutive_nonmonotonic_steps = 5; max_num_iterations = 50; @@ -121,6 +122,9 @@ TrustRegionStrategyType trust_region_strategy_type; + // Type of dogleg strategy to use. + DoglegType dogleg_type; + // The classical trust region methods are descent methods, in that // they only accept a point if it strictly reduces the value of // the objective function.
diff --git a/include/ceres/types.h b/include/ceres/types.h index d6474cc..3980885 100644 --- a/include/ceres/types.h +++ b/include/ceres/types.h
@@ -187,6 +187,24 @@ DOGLEG }; +// Ceres supports two different dogleg strategies. +// The "traditional" dogleg method by Powell and the +// "subspace" method described in +// R. H. Byrd, R. B. Schnabel, and G. A. Shultz, +// "Approximate solution of the trust region problem by minimization +// over two-dimensional subspaces", Mathematical Programming, +// 40 (1988), pp. 247--263 +enum DoglegType { + // The traditional approach constructs a dogleg path + // consisting of two line segments and finds the furthest + // point on that path that is still inside the trust region. + TRADITIONAL_DOGLEG, + + // The subspace approach finds the exact minimum of the model + // constrained to the subspace spanned by the dogleg path. + SUBSPACE_DOGLEG +}; + enum SolverTerminationType { // The minimizer did not run at all; usually due to errors in the user's // Problem or the solver options.
diff --git a/internal/ceres/dogleg_strategy.cc b/internal/ceres/dogleg_strategy.cc index 4b1f074..131de39 100644 --- a/internal/ceres/dogleg_strategy.cc +++ b/internal/ceres/dogleg_strategy.cc
@@ -31,10 +31,11 @@ #include "ceres/dogleg_strategy.h" #include <cmath> -#include "Eigen/Core" +#include "Eigen/Dense" #include "ceres/array_utils.h" #include "ceres/internal/eigen.h" #include "ceres/linear_solver.h" +#include "ceres/polynomial_solver.h" #include "ceres/sparse_matrix.h" #include "ceres/trust_region_strategy.h" #include "ceres/types.h" @@ -60,7 +61,8 @@ increase_threshold_(0.75), decrease_threshold_(0.25), dogleg_step_norm_(0.0), - reuse_(false) { + reuse_(false), + dogleg_type_(options.dogleg_type) { CHECK_NOTNULL(linear_solver_); CHECK_GT(min_diagonal_, 0.0); CHECK_LT(min_diagonal_, max_diagonal_); @@ -83,8 +85,17 @@ const int n = jacobian->num_cols(); if (reuse_) { // Gauss-Newton and gradient vectors are always available, only a - // new interpolant need to be computed. - ComputeDoglegStep(step); + // new interpolant need to be computed. For the subspace case, + // the subspace and the two-dimensional model are also still valid. + switch(dogleg_type_) { + case TRADITIONAL_DOGLEG: + ComputeTraditionalDoglegStep(step); + break; + + case SUBSPACE_DOGLEG: + ComputeSubspaceDoglegStep(step); + break; + } TrustRegionStrategy::Summary summary; summary.num_iterations = 0; summary.termination_type = TOLERANCE; @@ -109,8 +120,8 @@ jacobian->SquaredColumnNorm(diagonal_.data()); for (int i = 0; i < n; ++i) { diagonal_[i] = min(max(diagonal_[i], min_diagonal_), max_diagonal_); - diagonal_[i] = std::sqrt(diagonal_[i]); } + diagonal_ = diagonal_.array().sqrt(); ComputeGradient(jacobian, residuals); ComputeCauchyPoint(jacobian); @@ -118,15 +129,30 @@ LinearSolver::Summary linear_solver_summary = ComputeGaussNewtonStep(jacobian, residuals); - // Interpolate the Cauchy point and the Gauss-Newton step. - if (linear_solver_summary.termination_type != FAILURE) { - ComputeDoglegStep(step); - } - TrustRegionStrategy::Summary summary; summary.residual_norm = linear_solver_summary.residual_norm; summary.num_iterations = linear_solver_summary.num_iterations; summary.termination_type = linear_solver_summary.termination_type; + + if (linear_solver_summary.termination_type != FAILURE) { + switch(dogleg_type_) { + // Interpolate the Cauchy point and the Gauss-Newton step. + case TRADITIONAL_DOGLEG: + ComputeTraditionalDoglegStep(step); + break; + + // Find the minimum in the subspace defined by the + // Cauchy point and the (Gauss-)Newton step. + case SUBSPACE_DOGLEG: + if (!ComputeSubspaceModel(jacobian)) { + summary.termination_type = FAILURE; + break; + } + ComputeSubspaceDoglegStep(step); + break; + } + } + return summary; } @@ -145,6 +171,8 @@ gradient_.array() /= diagonal_.array(); } +// The Cauchy point is the global minimizer of the quadratic model +// along the one-dimensional subspace spanned by the gradient. void DoglegStrategy::ComputeCauchyPoint(SparseMatrix* jacobian) { // alpha * -gradient is the Cauchy point. Vector Jg(jacobian->num_rows()); @@ -157,7 +185,12 @@ alpha_ = gradient_.squaredNorm() / Jg.squaredNorm(); } -void DoglegStrategy::ComputeDoglegStep(double* dogleg) { +// The dogleg step is defined as the intersection of the trust region +// boundary with the piecewise linear path from the origin to the Cauchy +// point and then from there to the Gauss-Newton point (global minimizer +// of the model function). The Gauss-Newton point is taken if it lies +// within the trust region. +void DoglegStrategy::ComputeTraditionalDoglegStep(double* dogleg) { VectorRef dogleg_step(dogleg, gradient_.rows()); // Case 1. The Gauss-Newton step lies inside the trust region, and @@ -207,13 +240,272 @@ (c <= 0) ? (d - c) / b_minus_a_squared_norm : (radius_ * radius_ - a_squared_norm) / (d + c); - dogleg_step = (-alpha_ * (1.0 - beta)) * gradient_ + beta * gauss_newton_step_; + dogleg_step = (-alpha_ * (1.0 - beta)) * gradient_ + + beta * gauss_newton_step_; dogleg_step_norm_ = dogleg_step.norm(); dogleg_step.array() /= diagonal_.array(); VLOG(3) << "Dogleg step size: " << dogleg_step_norm_ << " radius: " << radius_; } +// The subspace method finds the minimum of the two-dimensional problem +// +// min. 1/2 x' B' H B x + g' B x +// s.t. || B x ||^2 <= r^2 +// +// where r is the trust region radius and B is the matrix with unit columns +// spanning the subspace defined by the steepest descent and Newton direction. +// This subspace by definition includes the Gauss-Newton point, which is +// therefore taken if it lies within the trust region. +void DoglegStrategy::ComputeSubspaceDoglegStep(double* dogleg) { + VectorRef dogleg_step(dogleg, gradient_.rows()); + + // The Gauss-Newton point is inside the trust region if |GN| <= radius_. + // This test is valid even though radius_ is a length in the two-dimensional + // subspace while gauss_newton_step_ is expressed in the (scaled) + // higher dimensional original space. This is because + // + // 1. gauss_newton_step_ by definition lies in the subspace, and + // 2. the subspace basis is orthonormal. + // + // As a consequence, the norm of the gauss_newton_step_ in the subspace is + // the same as its norm in the original space. + const double gauss_newton_norm = gauss_newton_step_.norm(); + if (gauss_newton_norm <= radius_) { + dogleg_step = gauss_newton_step_; + dogleg_step_norm_ = gauss_newton_norm; + dogleg_step.array() /= diagonal_.array(); + VLOG(3) << "GaussNewton step size: " << dogleg_step_norm_ + << " radius: " << radius_; + return; + } + + // The optimum lies on the boundary of the trust region. The above problem + // therefore becomes + // + // min. 1/2 x^T B^T H B x + g^T B x + // s.t. || B x ||^2 = r^2 + // + // Notice the equality in the constraint. + // + // This can be solved by forming the Lagrangian, solving for x(y), where + // y is the Lagrange multiplier, using the gradient of the objective, and + // putting x(y) back into the constraint. This results in a fourth order + // polynomial in y, which can be solved using e.g. the companion matrix. + // See the description of MakePolynomialForBoundaryConstrainedProblem for + // details. The result is up to four real roots y*, not all of which + // correspond to feasible points. The feasible points x(y*) have to be + // tested for optimality. + + if (subspace_is_one_dimensional_) { + // The subspace is one-dimensional, so both the gradient and + // the Gauss-Newton step point towards the same direction. + // In this case, we move along the gradient until we reach the trust + // region boundary. + dogleg_step = -(radius_ / gradient_.norm()) * gradient_; + dogleg_step_norm_ = radius_; + dogleg_step.array() /= diagonal_.array(); + VLOG(3) << "Dogleg subspace step size (1D): " << dogleg_step_norm_ + << " radius: " << radius_; + return; + } + + Vector2d minimum(0.0, 0.0); + if (!FindMinimumOnTrustRegionBoundary(&minimum)) { + // For the positive semi-definite case, a traditional dogleg step + // is taken in this case. + LOG(WARNING) << "Failed to compute polynomial roots. " + << "Taking traditional dogleg step instead."; + ComputeTraditionalDoglegStep(dogleg); + return; + } + + // Test first order optimality at the minimum. + // The first order KKT conditions state that the minimum x* + // has to satisfy either || x* ||^2 < r^2 (i.e. has to lie within + // the trust region), or + // + // (B x* + g) + y x* = 0 + // + // for some positive scalar y. + // Here, as it is already known that the minimum lies on the boundary, the + // latter condition is tested. To allow for small imprecisions, we test if + // the angle between (B x* + g) and -x* is smaller than acos(0.99). + // The exact value of the cosine is arbitrary but should be close to 1. + // + // This condition should not be violated. If it is, the minimum was not + // correctly determined. + const double kCosineThreshold = 0.99; + const Vector2d grad_minimum = subspace_B_ * minimum + subspace_g_; + const double cosine_angle = -minimum.dot(grad_minimum) / + (minimum.norm() * grad_minimum.norm()); + if (cosine_angle < kCosineThreshold) { + LOG(WARNING) << "First order optimality seems to be violated " + << "in the subspace method!\n" + << "Cosine of angle between x and B x + g is " + << cosine_angle << ".\n" + << "Taking a regular dogleg step instead.\n" + << "Please consider filing a bug report if this " + << "happens frequently or consistently.\n"; + ComputeTraditionalDoglegStep(dogleg); + return; + } + + // Create the full step from the optimal 2d solution. + dogleg_step = subspace_basis_ * minimum; + dogleg_step_norm_ = radius_; + dogleg_step.array() /= diagonal_.array(); + VLOG(3) << "Dogleg subspace step size: " << dogleg_step_norm_ + << " radius: " << radius_; +} + +// Build the polynomial that defines the optimal Lagrange multipliers. +// Let the Lagrangian be +// +// L(x, y) = 0.5 x^T B x + x^T g + y (0.5 x^T x - 0.5 r^2). (1) +// +// Stationary points of the Lagrangian are given by +// +// 0 = d L(x, y) / dx = Bx + g + y x (2) +// 0 = d L(x, y) / dy = 0.5 x^T x - 0.5 r^2 (3) +// +// For any given y, we can solve (2) for x as +// +// x(y) = -(B + y I)^-1 g . (4) +// +// As B + y I is 2x2, we form the inverse explicitly: +// +// (B + y I)^-1 = (1 / det(B + y I)) adj(B + y I) (5) +// +// where adj() denotes adjugation. This should be safe, as B is positive +// semi-definite and y is necessarily positive, so (B + y I) is indeed +// invertible. +// Plugging (5) into (4) and the result into (3), then dividing by 0.5 we +// obtain +// +// 0 = (1 / det(B + y I))^2 g^T adj(B + y I)^T adj(B + y I) g - r^2 +// (6) +// +// or +// +// det(B + y I)^2 r^2 = g^T adj(B + y I)^T adj(B + y I) g (7a) +// = g^T adj(B)^T adj(B) g +// + 2 y g^T adj(B)^T g + y^2 g^T g (7b) +// +// as +// +// adj(B + y I) = adj(B) + y I = adj(B)^T + y I . (8) +// +// The left hand side can be expressed explicitly using +// +// det(B + y I) = det(B) + y tr(B) + y^2 . (9) +// +// So (7) is a polynomial in y of degree four. +// Bringing everything back to the left hand side, the coefficients can +// be read off as +// +// y^4 r^2 +// + y^3 2 r^2 tr(B) +// + y^2 (r^2 tr(B)^2 + 2 r^2 det(B) - g^T g) +// + y^1 (2 r^2 det(B) tr(B) - 2 g^T adj(B)^T g) +// + y^0 (r^2 det(B)^2 - g^T adj(B)^T adj(B) g) +// +Vector DoglegStrategy::MakePolynomialForBoundaryConstrainedProblem() const { + const double detB = subspace_B_.determinant(); + const double trB = subspace_B_.trace(); + const double r2 = radius_ * radius_; + Matrix2d B_adj; + B_adj << subspace_B_(1,1) , -subspace_B_(0,1), + -subspace_B_(1,0) , subspace_B_(0,0); + + Vector polynomial(5); + polynomial(0) = r2; + polynomial(1) = 2.0 * r2 * trB; + polynomial(2) = r2 * ( trB * trB + 2.0 * detB ) - subspace_g_.squaredNorm(); + polynomial(3) = -2.0 * ( subspace_g_.transpose() * B_adj * subspace_g_ + - r2 * detB * trB ); + polynomial(4) = r2 * detB * detB - (B_adj * subspace_g_).squaredNorm(); + + return polynomial; +} + +// Given a Lagrange multiplier y that corresponds to a stationary point +// of the Lagrangian L(x, y), compute the corresponding x from the +// equation +// +// 0 = d L(x, y) / dx +// = B * x + g + y * x +// = (B + y * I) * x + g +// +DoglegStrategy::Vector2d DoglegStrategy::ComputeSubspaceStepFromRoot( + double y) const { + const Matrix2d B_i = subspace_B_ + y * Matrix2d::Identity(); + return -B_i.partialPivLu().solve(subspace_g_); +} + +// This function evaluates the quadratic model at a point x in the +// subspace spanned by subspace_basis_. +double DoglegStrategy::EvaluateSubspaceModel(const Vector2d& x) const { + return 0.5 * x.dot(subspace_B_ * x) + subspace_g_.dot(x); +} + +// This function attempts to solve the boundary-constrained subspace problem +// +// min. 1/2 x^T B^T H B x + g^T B x +// s.t. || B x ||^2 = r^2 +// +// where B is an orthonormal subspace basis and r is the trust-region radius. +// +// This is done by finding the roots of a fourth degree polynomial. If the +// root finding fails, the function returns false and minimum will be set +// to (0, 0). If it succeeds, true is returned. +// +// In the failure case, another step should be taken, such as the traditional +// dogleg step. +bool DoglegStrategy::FindMinimumOnTrustRegionBoundary(Vector2d* minimum) const { + CHECK_NOTNULL(minimum); + + // Return (0, 0) in all error cases. + minimum->setZero(); + + // Create the fourth-degree polynomial that is a necessary condition for + // optimality. + const Vector polynomial = MakePolynomialForBoundaryConstrainedProblem(); + + // Find the real parts y_i of its roots (not only the real roots). + Vector roots_real; + if (!FindPolynomialRoots(polynomial, &roots_real, NULL)) { + // Failed to find the roots of the polynomial, i.e. the candidate + // solutions of the constrained problem. Report this back to the caller. + return false; + } + + // For each root y, compute B x(y) and check for feasibility. + // Notice that there should always be four roots, as the leading term of + // the polynomial is r^2 and therefore non-zero. However, as some roots + // may be complex, the real parts are not necessarily unique. + double minimum_value = std::numeric_limits<double>::max(); + bool valid_root_found = false; + for (int i = 0; i < roots_real.size(); ++i) { + const Vector2d x_i = ComputeSubspaceStepFromRoot(roots_real(i)); + + // Not all roots correspond to points on the trust region boundary. + // There are at most four candidate solutions. As we are interested + // in the minimum, it is safe to consider all of them after projecting + // them onto the trust region boundary. + if (x_i.norm() > 0) { + const double f_i = EvaluateSubspaceModel((radius_ / x_i.norm()) * x_i); + valid_root_found = true; + if (f_i < minimum_value) { + minimum_value = f_i; + *minimum = x_i; + } + } + } + + return valid_root_found; +} + LinearSolver::Summary DoglegStrategy::ComputeGaussNewtonStep( SparseMatrix* jacobian, const double* residuals) { @@ -239,6 +531,7 @@ // // When a step is declared successful, the multiplier is decreased // by half of mu_increase_factor_. + while (mu_ < max_mu_) { // Dogleg, as far as I (sameeragarwal) understand it, requires a // reasonably good estimate of the Gauss-Newton step. This means @@ -278,19 +571,22 @@ break; } - // The scaled Gauss-Newton step is D * GN: - // - // - (D^-1 J^T J D^-1)^-1 (D^-1 g) - // = - D (J^T J)^-1 D D^-1 g - // = D -(J^T J)^-1 g - // - gauss_newton_step_.array() *= -diagonal_.array(); + if (linear_solver_summary.termination_type != FAILURE) { + // The scaled Gauss-Newton step is D * GN: + // + // - (D^-1 J^T J D^-1)^-1 (D^-1 g) + // = - D (J^T J)^-1 D D^-1 g + // = D -(J^T J)^-1 g + // + gauss_newton_step_.array() *= -diagonal_.array(); + } return linear_solver_summary; } void DoglegStrategy::StepAccepted(double step_quality) { CHECK_GT(step_quality, 0.0); + if (step_quality < decrease_threshold_) { radius_ *= 0.5; } @@ -320,5 +616,76 @@ return radius_; } +bool DoglegStrategy::ComputeSubspaceModel(SparseMatrix* jacobian) { + // Compute an orthogonal basis for the subspace using QR decomposition. + Matrix basis_vectors(jacobian->num_cols(), 2); + basis_vectors.col(0) = gradient_; + basis_vectors.col(1) = gauss_newton_step_; + Eigen::ColPivHouseholderQR<Matrix> basis_qr(basis_vectors); + + switch (basis_qr.rank()) { + case 0: + // This should never happen, as it implies that both the gradient + // and the Gauss-Newton step are zero. In this case, the minimizer should + // have stopped due to the gradient being too small. + LOG(ERROR) << "Rank of subspace basis is 0. " + << "This means that the gradient at the current iterate is " + << "zero but the optimization has not been terminated. " + << "You may have found a bug in Ceres."; + return false; + + case 1: + // Gradient and Gauss-Newton step coincide, so we lie on one of the + // major axes of the quadratic problem. In this case, we simply move + // along the gradient until we reach the trust region boundary. + subspace_is_one_dimensional_ = true; + return true; + + case 2: + subspace_is_one_dimensional_ = false; + break; + + default: + LOG(ERROR) << "Rank of the subspace basis matrix is reported to be " + << "greater than 2. As the matrix contains only two " + << "columns this cannot be true and is indicative of " + << "a bug."; + return false; + } + + // The subspace is two-dimensional, so compute the subspace model. + // Given the basis U, this is + // + // subspace_g_ = g_scaled^T U + // + // and + // + // subspace_B_ = U^T (J_scaled^T J_scaled) U + // + // As J_scaled = J * D^-1, the latter becomes + // + // subspace_B_ = ((U^T D^-1) J^T) (J (D^-1 U)) + // = (J (D^-1 U))^T (J (D^-1 U)) + + subspace_basis_ = + basis_qr.householderQ() * Matrix::Identity(jacobian->num_cols(), 2); + + subspace_g_ = subspace_basis_.transpose() * gradient_; + + Eigen::Matrix<double, 2, Eigen::Dynamic, Eigen::RowMajor> + Jb(2, jacobian->num_rows()); + Jb.setZero(); + + Vector tmp; + tmp = (subspace_basis_.col(0).array() / diagonal_.array()).matrix(); + jacobian->RightMultiply(tmp.data(), Jb.row(0).data()); + tmp = (subspace_basis_.col(1).array() / diagonal_.array()).matrix(); + jacobian->RightMultiply(tmp.data(), Jb.row(1).data()); + + subspace_B_ = Jb * Jb.transpose(); + + return true; +} + } // namespace internal } // namespace ceres
diff --git a/internal/ceres/dogleg_strategy.h b/internal/ceres/dogleg_strategy.h index 8c2ff7b..ad3257c 100644 --- a/internal/ceres/dogleg_strategy.h +++ b/internal/ceres/dogleg_strategy.h
@@ -47,6 +47,11 @@ // Gauss-Newton step, we compute a regularized version of it. This is // because the Jacobian is often rank-deficient and in such cases // using a direct solver leads to numerical failure. +// +// If SUBSPACE is passed as the type argument to the constructor, the +// DoglegStrategy follows the approach by Shultz, Schnabel, Byrd. +// This finds the exact optimum over the two-dimensional subspace +// spanned by the two Dogleg vectors. class DoglegStrategy : public TrustRegionStrategy { public: DoglegStrategy(const TrustRegionStrategy::Options& options); @@ -64,11 +69,21 @@ virtual double Radius() const; private: + typedef Eigen::Matrix<double, 2, 1, Eigen::DontAlign> Vector2d; + typedef Eigen::Matrix<double, 2, 2, Eigen::DontAlign> Matrix2d; + LinearSolver::Summary ComputeGaussNewtonStep(SparseMatrix* jacobian, const double* residuals); void ComputeCauchyPoint(SparseMatrix* jacobian); void ComputeGradient(SparseMatrix* jacobian, const double* residuals); - void ComputeDoglegStep(double* step); + void ComputeTraditionalDoglegStep(double* step); + bool ComputeSubspaceModel(SparseMatrix* jacobian); + void ComputeSubspaceDoglegStep(double* step); + + bool FindMinimumOnTrustRegionBoundary(Vector2d* minimum) const; + Vector MakePolynomialForBoundaryConstrainedProblem() const; + Vector2d ComputeSubspaceStepFromRoot(double lambda) const; + double EvaluateSubspaceModel(const Vector2d& x) const; LinearSolver* linear_solver_; double radius_; @@ -122,6 +137,17 @@ // increased and a new solve should be done when ComputeStep is // called again, thus reuse is set to false. bool reuse_; + + // The dogleg type determines how the minimum of the local + // quadratic model is found. + DoglegType dogleg_type_; + + // If the type is SUBSPACE_DOGLEG, the two-dimensional + // model 1/2 x^T B x + g^T x has to be computed and stored. + bool subspace_is_one_dimensional_; + Matrix subspace_basis_; + Vector2d subspace_g_; + Matrix2d subspace_B_; }; } // namespace internal
diff --git a/internal/ceres/solver_impl.cc b/internal/ceres/solver_impl.cc index 530b47c..072f8bb 100644 --- a/internal/ceres/solver_impl.cc +++ b/internal/ceres/solver_impl.cc
@@ -183,6 +183,7 @@ trust_region_strategy_options.lm_max_diagonal = options.lm_max_diagonal; trust_region_strategy_options.trust_region_strategy_type = options.trust_region_strategy_type; + trust_region_strategy_options.dogleg_type = options.dogleg_type; scoped_ptr<TrustRegionStrategy> strategy( TrustRegionStrategy::Create(trust_region_strategy_options)); minimizer_options.trust_region_strategy = strategy.get();
diff --git a/internal/ceres/trust_region_strategy.h b/internal/ceres/trust_region_strategy.h index 7d94ca2..391da97 100644 --- a/internal/ceres/trust_region_strategy.h +++ b/internal/ceres/trust_region_strategy.h
@@ -59,7 +59,8 @@ initial_radius(1e4), max_radius(1e32), lm_min_diagonal(1e-6), - lm_max_diagonal(1e32) { + lm_max_diagonal(1e32), + dogleg_type(TRADITIONAL_DOGLEG) { } TrustRegionStrategyType trust_region_strategy_type; @@ -74,6 +75,9 @@ // that the Gauss-Newton step computation is of full rank. double lm_min_diagonal; double lm_max_diagonal; + + // Further specify which dogleg method to use + DoglegType dogleg_type; }; // Per solve options.