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      1 // Ceres Solver - A fast non-linear least squares minimizer
      2 // Copyright 2012 Google Inc. All rights reserved.
      3 // http://code.google.com/p/ceres-solver/
      4 //
      5 // Redistribution and use in source and binary forms, with or without
      6 // modification, are permitted provided that the following conditions are met:
      7 //
      8 // * Redistributions of source code must retain the above copyright notice,
      9 //   this list of conditions and the following disclaimer.
     10 // * Redistributions in binary form must reproduce the above copyright notice,
     11 //   this list of conditions and the following disclaimer in the documentation
     12 //   and/or other materials provided with the distribution.
     13 // * Neither the name of Google Inc. nor the names of its contributors may be
     14 //   used to endorse or promote products derived from this software without
     15 //   specific prior written permission.
     16 //
     17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
     18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
     21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
     22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
     23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
     25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     27 // POSSIBILITY OF SUCH DAMAGE.
     28 //
     29 // Author: sameeragarwal (at) google.com (Sameer Agarwal)
     30 
     31 #include "ceres/dense_normal_cholesky_solver.h"
     32 
     33 #include <cstddef>
     34 
     35 #include "Eigen/Dense"
     36 #include "ceres/dense_sparse_matrix.h"
     37 #include "ceres/linear_solver.h"
     38 #include "ceres/internal/eigen.h"
     39 #include "ceres/internal/scoped_ptr.h"
     40 #include "ceres/types.h"
     41 
     42 namespace ceres {
     43 namespace internal {
     44 
     45 DenseNormalCholeskySolver::DenseNormalCholeskySolver(
     46     const LinearSolver::Options& options)
     47     : options_(options) {}
     48 
     49 LinearSolver::Summary DenseNormalCholeskySolver::SolveImpl(
     50     DenseSparseMatrix* A,
     51     const double* b,
     52     const LinearSolver::PerSolveOptions& per_solve_options,
     53     double* x) {
     54   const int num_rows = A->num_rows();
     55   const int num_cols = A->num_cols();
     56 
     57   ConstAlignedMatrixRef Aref = A->matrix();
     58   Matrix lhs(num_cols, num_cols);
     59   lhs.setZero();
     60 
     61   //   lhs += A'A
     62   //
     63   // Using rankUpdate instead of GEMM, exposes the fact that its the
     64   // same matrix being multiplied with itself and that the product is
     65   // symmetric.
     66   lhs.selfadjointView<Eigen::Upper>().rankUpdate(Aref.transpose());
     67 
     68   //   rhs = A'b
     69   Vector rhs = Aref.transpose() * ConstVectorRef(b, num_rows);
     70 
     71   if (per_solve_options.D != NULL) {
     72     ConstVectorRef D(per_solve_options.D, num_cols);
     73     lhs += D.array().square().matrix().asDiagonal();
     74   }
     75 
     76   VectorRef(x, num_cols) =
     77       lhs.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
     78 
     79   LinearSolver::Summary summary;
     80   summary.num_iterations = 1;
     81   summary.termination_type = TOLERANCE;
     82   return summary;
     83 }
     84 
     85 }   // namespace internal
     86 }   // namespace ceres
     87