diff options
Diffstat (limited to 'extern/ceres/include/ceres/internal/householder_vector.h')
-rw-r--r-- | extern/ceres/include/ceres/internal/householder_vector.h | 88 |
1 files changed, 88 insertions, 0 deletions
diff --git a/extern/ceres/include/ceres/internal/householder_vector.h b/extern/ceres/include/ceres/internal/householder_vector.h new file mode 100644 index 00000000000..55f68e526a0 --- /dev/null +++ b/extern/ceres/include/ceres/internal/householder_vector.h @@ -0,0 +1,88 @@ +// 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_INTERNAL_HOUSEHOLDER_VECTOR_H_ +#define CERES_PUBLIC_INTERNAL_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. +// +// 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; +} + +} // namespace internal +} // namespace ceres + +#endif // CERES_PUBLIC_INTERNAL_HOUSEHOLDER_VECTOR_H_ |