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/blas.h" 37 #include "ceres/dense_sparse_matrix.h" 38 #include "ceres/internal/eigen.h" 39 #include "ceres/internal/scoped_ptr.h" 40 #include "ceres/lapack.h" 41 #include "ceres/linear_solver.h" 42 #include "ceres/types.h" 43 #include "ceres/wall_time.h" 44 45 namespace ceres { 46 namespace internal { 47 48 DenseNormalCholeskySolver::DenseNormalCholeskySolver( 49 const LinearSolver::Options& options) 50 : options_(options) {} 51 52 LinearSolver::Summary DenseNormalCholeskySolver::SolveImpl( 53 DenseSparseMatrix* A, 54 const double* b, 55 const LinearSolver::PerSolveOptions& per_solve_options, 56 double* x) { 57 if (options_.dense_linear_algebra_library_type == EIGEN) { 58 return SolveUsingEigen(A, b, per_solve_options, x); 59 } else { 60 return SolveUsingLAPACK(A, b, per_solve_options, x); 61 } 62 } 63 64 LinearSolver::Summary DenseNormalCholeskySolver::SolveUsingEigen( 65 DenseSparseMatrix* A, 66 const double* b, 67 const LinearSolver::PerSolveOptions& per_solve_options, 68 double* x) { 69 EventLogger event_logger("DenseNormalCholeskySolver::Solve"); 70 71 const int num_rows = A->num_rows(); 72 const int num_cols = A->num_cols(); 73 74 ConstColMajorMatrixRef Aref = A->matrix(); 75 Matrix lhs(num_cols, num_cols); 76 lhs.setZero(); 77 78 event_logger.AddEvent("Setup"); 79 80 // lhs += A'A 81 // 82 // Using rankUpdate instead of GEMM, exposes the fact that its the 83 // same matrix being multiplied with itself and that the product is 84 // symmetric. 85 lhs.selfadjointView<Eigen::Upper>().rankUpdate(Aref.transpose()); 86 87 // rhs = A'b 88 Vector rhs = Aref.transpose() * ConstVectorRef(b, num_rows); 89 90 if (per_solve_options.D != NULL) { 91 ConstVectorRef D(per_solve_options.D, num_cols); 92 lhs += D.array().square().matrix().asDiagonal(); 93 } 94 event_logger.AddEvent("Product"); 95 96 LinearSolver::Summary summary; 97 summary.num_iterations = 1; 98 summary.termination_type = LINEAR_SOLVER_SUCCESS; 99 Eigen::LLT<Matrix, Eigen::Upper> llt = 100 lhs.selfadjointView<Eigen::Upper>().llt(); 101 102 if (llt.info() != Eigen::Success) { 103 summary.termination_type = LINEAR_SOLVER_FAILURE; 104 summary.message = "Eigen LLT decomposition failed."; 105 } else { 106 summary.termination_type = LINEAR_SOLVER_SUCCESS; 107 summary.message = "Success."; 108 } 109 110 VectorRef(x, num_cols) = llt.solve(rhs); 111 event_logger.AddEvent("Solve"); 112 return summary; 113 } 114 115 LinearSolver::Summary DenseNormalCholeskySolver::SolveUsingLAPACK( 116 DenseSparseMatrix* A, 117 const double* b, 118 const LinearSolver::PerSolveOptions& per_solve_options, 119 double* x) { 120 EventLogger event_logger("DenseNormalCholeskySolver::Solve"); 121 122 if (per_solve_options.D != NULL) { 123 // Temporarily append a diagonal block to the A matrix, but undo 124 // it before returning the matrix to the user. 125 A->AppendDiagonal(per_solve_options.D); 126 } 127 128 const int num_cols = A->num_cols(); 129 Matrix lhs(num_cols, num_cols); 130 event_logger.AddEvent("Setup"); 131 132 // lhs = A'A 133 // 134 // Note: This is a bit delicate, it assumes that the stride on this 135 // matrix is the same as the number of rows. 136 BLAS::SymmetricRankKUpdate(A->num_rows(), 137 num_cols, 138 A->values(), 139 true, 140 1.0, 141 0.0, 142 lhs.data()); 143 144 if (per_solve_options.D != NULL) { 145 // Undo the modifications to the matrix A. 146 A->RemoveDiagonal(); 147 } 148 149 // TODO(sameeragarwal): Replace this with a gemv call for true blasness. 150 // rhs = A'b 151 VectorRef(x, num_cols) = 152 A->matrix().transpose() * ConstVectorRef(b, A->num_rows()); 153 event_logger.AddEvent("Product"); 154 155 LinearSolver::Summary summary; 156 summary.num_iterations = 1; 157 summary.termination_type = 158 LAPACK::SolveInPlaceUsingCholesky(num_cols, 159 lhs.data(), 160 x, 161 &summary.message); 162 event_logger.AddEvent("Solve"); 163 return summary; 164 } 165 } // namespace internal 166 } // namespace ceres 167
