86 lines
3.2 KiB
C
86 lines
3.2 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://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: vitus@google.com (Michael Vitus)
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#ifndef CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_
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#define CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_
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#include "Eigen/Core"
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#include "glog/logging.h"
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namespace ceres {
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namespace internal {
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// Algorithm 5.1.1 from 'Matrix Computations' by Golub et al. (Johns Hopkins
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// Studies in Mathematical Sciences) but using the nth element of the input
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// vector as pivot instead of first. This computes the vector v with v(n) = 1
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// and beta such that H = I - beta * v * v^T is orthogonal and
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// H * x = ||x||_2 * e_n.
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template <typename Scalar>
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void ComputeHouseholderVector(const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& x,
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Eigen::Matrix<Scalar, Eigen::Dynamic, 1>* v,
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Scalar* beta) {
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CHECK_NOTNULL(beta);
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CHECK_NOTNULL(v);
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CHECK_GT(x.rows(), 1);
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CHECK_EQ(x.rows(), v->rows());
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Scalar sigma = x.head(x.rows() - 1).squaredNorm();
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*v = x;
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(*v)(v->rows() - 1) = Scalar(1.0);
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*beta = Scalar(0.0);
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const Scalar& x_pivot = x(x.rows() - 1);
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if (sigma <= Scalar(std::numeric_limits<double>::epsilon())) {
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if (x_pivot < Scalar(0.0)) {
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*beta = Scalar(2.0);
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}
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return;
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}
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const Scalar mu = sqrt(x_pivot * x_pivot + sigma);
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Scalar v_pivot = Scalar(1.0);
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if (x_pivot <= Scalar(0.0)) {
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v_pivot = x_pivot - mu;
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} else {
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v_pivot = -sigma / (x_pivot + mu);
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}
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*beta = Scalar(2.0) * v_pivot * v_pivot / (sigma + v_pivot * v_pivot);
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v->head(v->rows() - 1) /= v_pivot;
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}
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} // namespace internal
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} // namespace ceres
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#endif // CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_
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