mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-30 00:50:37 +08:00
Sameer Agarwal
b9f15a5936
For problems with a small number of variables, but a large number of residuals, it is sometimes beneficial to use the Cholesky factorization on the normal equations, instead of the dense QR factorization of the Jacobian, even though it is numerically the better thing to do. Change-Id: I3506b006195754018deec964e6e190b7e8c9ac8f
96 lines
3.5 KiB
C++
96 lines
3.5 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2012 Google Inc. All rights reserved.
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// http://code.google.com/p/ceres-solver/
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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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// Solve dense rectangular systems Ax = b by forming the normal
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// equations and solving them using the Cholesky factorization.
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#ifndef CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_
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#define CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_
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#include "ceres/linear_solver.h"
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#include "ceres/internal/macros.h"
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namespace ceres {
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namespace internal {
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class DenseSparseMatrix;
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// This class implements the LinearSolver interface for solving
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// rectangular/unsymmetric (well constrained) linear systems of the
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// form
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//
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// Ax = b
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//
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// Since there does not usually exist a solution that satisfies these
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// equations, the solver instead solves the linear least squares
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// problem
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//
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// min_x |Ax - b|^2
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//
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// Setting the gradient of the above optimization problem to zero
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// gives us the normal equations
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//
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// A'Ax = A'b
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//
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// A'A is a positive definite matrix (hopefully), and the resulting
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// linear system can be solved using Cholesky factorization.
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//
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// If the PerSolveOptions struct has a non-null array D, then the
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// augmented/regularized linear system
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//
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// [ A ]x = [b]
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// [ diag(D) ] [0]
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//
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// is solved.
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//
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// This class uses the LDLT factorization routines from the Eigen
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// library. This solver always returns a solution, it is the user's
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// responsibility to judge if the solution is good enough for their
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// purposes.
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class DenseNormalCholeskySolver: public DenseSparseMatrixSolver {
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public:
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explicit DenseNormalCholeskySolver(const LinearSolver::Options& options);
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private:
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virtual LinearSolver::Summary SolveImpl(
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DenseSparseMatrix* A,
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const double* b,
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const LinearSolver::PerSolveOptions& per_solve_options,
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double* x);
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const LinearSolver::Options options_;
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CERES_DISALLOW_COPY_AND_ASSIGN(DenseNormalCholeskySolver);
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};
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_
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