| // 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) | |
| 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. | |
| // | |
| // NOTE: Some versions of MSVC have trouble deducing the type of v if | |
| // you do not specify all the template arguments explicitly. | |
| template <typename XVectorType, typename Scalar, int N> | |
| void ComputeHouseholderVector(const XVectorType& x, | |
| Eigen::Matrix<Scalar, N, 1>* v, | |
| Scalar* beta) { | |
| CHECK(beta != nullptr); | |
| CHECK(v != nullptr); | |
| 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; | |
| } | |
| template <typename XVectorType, typename Derived> | |
| typename Derived::PlainObject ApplyHouseholderVector( | |
| const XVectorType& y, | |
| const Eigen::MatrixBase<Derived>& v, | |
| const typename Derived::Scalar& beta) { | |
| return (y - v * (beta * (v.transpose() * y))); | |
| } | |
| } // namespace internal | |
| } // namespace ceres | |