109 lines
4.6 KiB
C
109 lines
4.6 KiB
C
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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//
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// Limited memory positive definite approximation to the inverse
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// Hessian, using the LBFGS algorithm
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#ifndef CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_
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#define CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_
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#include <list>
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#include "ceres/internal/eigen.h"
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#include "ceres/linear_operator.h"
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namespace ceres {
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namespace internal {
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// LowRankInverseHessian is a positive definite approximation to the
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// Hessian using the limited memory variant of the
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// Broyden-Fletcher-Goldfarb-Shanno (BFGS)secant formula for
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// approximating the Hessian.
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//
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// Other update rules like the Davidon-Fletcher-Powell (DFP) are
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// possible, but the BFGS rule is considered the best performing one.
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//
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// The limited memory variant was developed by Nocedal and further
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// enhanced with scaling rule by Byrd, Nocedal and Schanbel.
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//
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// Nocedal, J. (1980). "Updating Quasi-Newton Matrices with Limited
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// Storage". Mathematics of Computation 35 (151): 773–782.
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//
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// Byrd, R. H.; Nocedal, J.; Schnabel, R. B. (1994).
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// "Representations of Quasi-Newton Matrices and their use in
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// Limited Memory Methods". Mathematical Programming 63 (4):
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class LowRankInverseHessian : public LinearOperator {
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public:
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// num_parameters is the row/column size of the Hessian.
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// max_num_corrections is the rank of the Hessian approximation.
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// use_approximate_eigenvalue_scaling controls whether the initial
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// inverse Hessian used during Right/LeftMultiply() is scaled by
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// the approximate eigenvalue of the true inverse Hessian at the
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// current operating point.
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// The approximation uses:
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// 2 * max_num_corrections * num_parameters + max_num_corrections
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// doubles.
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LowRankInverseHessian(int num_parameters,
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int max_num_corrections,
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bool use_approximate_eigenvalue_scaling);
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virtual ~LowRankInverseHessian() {}
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// Update the low rank approximation. delta_x is the change in the
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// domain of Hessian, and delta_gradient is the change in the
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// gradient. The update copies the delta_x and delta_gradient
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// vectors, and gets rid of the oldest delta_x and delta_gradient
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// vectors if the number of corrections is already equal to
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// max_num_corrections.
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bool Update(const Vector& delta_x, const Vector& delta_gradient);
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// LinearOperator interface
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virtual void RightMultiply(const double* x, double* y) const;
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virtual void LeftMultiply(const double* x, double* y) const {
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RightMultiply(x, y);
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}
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virtual int num_rows() const { return num_parameters_; }
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virtual int num_cols() const { return num_parameters_; }
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private:
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const int num_parameters_;
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const int max_num_corrections_;
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const bool use_approximate_eigenvalue_scaling_;
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double approximate_eigenvalue_scale_;
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ColMajorMatrix delta_x_history_;
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ColMajorMatrix delta_gradient_history_;
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Vector delta_x_dot_delta_gradient_;
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std::list<int> indices_;
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};
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_
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