forked from bartvdbraak/blender
75ea4b8a1f
We already were using one of earlier RC of the library, so there is no expected big changes. Just making the update official, using official version and stating it in the readme file.
115 lines
3.8 KiB
C++
115 lines
3.8 KiB
C++
// 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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// Solve dense rectangular systems Ax = b using the QR factorization.
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#ifndef CERES_INTERNAL_DENSE_QR_SOLVER_H_
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#define CERES_INTERNAL_DENSE_QR_SOLVER_H_
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#include "ceres/internal/eigen.h"
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#include "ceres/internal/port.h"
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#include "ceres/linear_solver.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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// The solution strategy is based on computing the QR decomposition of
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// A, i.e.
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//
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// A = QR
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//
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// Where Q is an orthonormal matrix and R is an upper triangular
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// matrix. Then
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//
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// Ax = b
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// QRx = b
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// Q'QRx = Q'b
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// Rx = Q'b
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// x = R^{-1} Q'b
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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 dense QR 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 CERES_EXPORT_INTERNAL DenseQRSolver : public DenseSparseMatrixSolver {
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public:
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explicit DenseQRSolver(const LinearSolver::Options& options);
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private:
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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) final;
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LinearSolver::Summary SolveUsingEigen(
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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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LinearSolver::Summary SolveUsingLAPACK(
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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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ColMajorMatrix lhs_;
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Vector rhs_;
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Vector work_;
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};
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_DENSE_QR_SOLVER_H_
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