| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://code.google.com/p/ceres-solver/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: vitus@google.com (Michael Vitus) |
| |
| #ifndef CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_ |
| #define CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_ |
| |
| #include "Eigen/Core" |
| #include "glog/logging.h" |
| |
| namespace ceres { |
| namespace internal { |
| |
| // Algorithm 5.1.1 from 'Matrix Computations' by Golub et al. (Johns Hopkins |
| // Studies in Mathematical Sciences) but using the nth element of the input |
| // vector as pivot instead of first. This computes the vector v with v(n) = 1 |
| // and beta such that H = I - beta * v * v^T is orthogonal and |
| // H * x = ||x||_2 * e_n. |
| template <typename Scalar> |
| void ComputeHouseholderVector(const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& x, |
| Eigen::Matrix<Scalar, Eigen::Dynamic, 1>* v, |
| Scalar* beta) { |
| CHECK_NOTNULL(beta); |
| CHECK_NOTNULL(v); |
| CHECK_GT(x.rows(), 1); |
| CHECK_EQ(x.rows(), v->rows()); |
| |
| Scalar sigma = x.head(x.rows() - 1).squaredNorm(); |
| *v = x; |
| (*v)(v->rows() - 1) = Scalar(1.0); |
| |
| *beta = Scalar(0.0); |
| const Scalar& x_pivot = x(x.rows() - 1); |
| |
| if (sigma <= Scalar(std::numeric_limits<double>::epsilon())) { |
| if (x_pivot < Scalar(0.0)) { |
| *beta = Scalar(2.0); |
| } |
| return; |
| } |
| |
| const Scalar mu = sqrt(x_pivot * x_pivot + sigma); |
| Scalar v_pivot = Scalar(1.0); |
| |
| if (x_pivot <= Scalar(0.0)) { |
| v_pivot = x_pivot - mu; |
| } else { |
| v_pivot = -sigma / (x_pivot + mu); |
| } |
| |
| *beta = Scalar(2.0) * v_pivot * v_pivot / (sigma + v_pivot * v_pivot); |
| |
| v->head(v->rows() - 1) /= v_pivot; |
| } |
| |
| } // namespace internal |
| } // namespace ceres |
| |
| #endif // CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_ |