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79 lines
3.2 KiB
79 lines
3.2 KiB
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2017 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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#ifndef CERES_INTERNAL_INVERT_PSD_MATRIX_H_
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#define CERES_INTERNAL_INVERT_PSD_MATRIX_H_
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#include "ceres/internal/eigen.h"
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#include "glog/logging.h"
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#include "Eigen/Dense"
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namespace ceres {
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namespace internal {
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// Helper routine to compute the inverse or pseudo-inverse of a
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// symmetric positive semi-definite matrix.
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//
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// assume_full_rank controls whether a Cholesky factorization or an
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// Singular Value Decomposition is used to compute the inverse and the
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// pseudo-inverse respectively.
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//
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// The template parameter kSize can either be Eigen::Dynamic or a
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// positive integer equal to the number of rows of m.
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template <int kSize>
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typename EigenTypes<kSize, kSize>::Matrix InvertPSDMatrix(
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const bool assume_full_rank,
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const typename EigenTypes<kSize, kSize>::Matrix& m) {
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const int size = m.rows();
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// If the matrix can be assumed to be full rank, then just use the
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// Cholesky factorization to invert it.
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if (assume_full_rank) {
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return m.template selfadjointView<Eigen::Upper>().llt().solve(
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Matrix::Identity(size, size));
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}
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Eigen::JacobiSVD<Matrix> svd(m, Eigen::ComputeThinU | Eigen::ComputeThinV);
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const double tolerance =
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std::numeric_limits<double>::epsilon() * size * svd.singularValues()(0);
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return svd.matrixV() *
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(svd.singularValues().array() > tolerance)
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.select(svd.singularValues().array().inverse(), 0)
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.matrix()
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.asDiagonal() *
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svd.matrixU().adjoint();
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}
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_INVERT_PSD_MATRIX_H_
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