1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2010, 2011, 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_qr_solver.h" 32 33 34 #include <cstddef> 35 #include "Eigen/Dense" 36 #include "ceres/dense_sparse_matrix.h" 37 #include "ceres/internal/eigen.h" 38 #include "ceres/internal/scoped_ptr.h" 39 #include "ceres/lapack.h" 40 #include "ceres/linear_solver.h" 41 #include "ceres/types.h" 42 #include "ceres/wall_time.h" 43 44 namespace ceres { 45 namespace internal { 46 47 DenseQRSolver::DenseQRSolver(const LinearSolver::Options& options) 48 : options_(options) { 49 work_.resize(1); 50 } 51 52 LinearSolver::Summary DenseQRSolver::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 DenseQRSolver::SolveUsingLAPACK( 65 DenseSparseMatrix* A, 66 const double* b, 67 const LinearSolver::PerSolveOptions& per_solve_options, 68 double* x) { 69 EventLogger event_logger("DenseQRSolver::Solve"); 70 71 const int num_rows = A->num_rows(); 72 const int num_cols = A->num_cols(); 73 74 if (per_solve_options.D != NULL) { 75 // Temporarily append a diagonal block to the A matrix, but undo 76 // it before returning the matrix to the user. 77 A->AppendDiagonal(per_solve_options.D); 78 } 79 80 // TODO(sameeragarwal): Since we are copying anyways, the diagonal 81 // can be appended to the matrix instead of doing it on A. 82 lhs_ = A->matrix(); 83 84 if (per_solve_options.D != NULL) { 85 // Undo the modifications to the matrix A. 86 A->RemoveDiagonal(); 87 } 88 89 // rhs = [b;0] to account for the additional rows in the lhs. 90 if (rhs_.rows() != lhs_.rows()) { 91 rhs_.resize(lhs_.rows()); 92 } 93 rhs_.setZero(); 94 rhs_.head(num_rows) = ConstVectorRef(b, num_rows); 95 96 if (work_.rows() == 1) { 97 const int work_size = 98 LAPACK::EstimateWorkSizeForQR(lhs_.rows(), lhs_.cols()); 99 VLOG(3) << "Working memory for Dense QR factorization: " 100 << work_size * sizeof(double); 101 work_.resize(work_size); 102 } 103 104 LinearSolver::Summary summary; 105 summary.num_iterations = 1; 106 summary.termination_type = LAPACK::SolveInPlaceUsingQR(lhs_.rows(), 107 lhs_.cols(), 108 lhs_.data(), 109 work_.rows(), 110 work_.data(), 111 rhs_.data(), 112 &summary.message); 113 event_logger.AddEvent("Solve"); 114 if (summary.termination_type == LINEAR_SOLVER_SUCCESS) { 115 VectorRef(x, num_cols) = rhs_.head(num_cols); 116 } 117 118 event_logger.AddEvent("TearDown"); 119 return summary; 120 } 121 122 LinearSolver::Summary DenseQRSolver::SolveUsingEigen( 123 DenseSparseMatrix* A, 124 const double* b, 125 const LinearSolver::PerSolveOptions& per_solve_options, 126 double* x) { 127 EventLogger event_logger("DenseQRSolver::Solve"); 128 129 const int num_rows = A->num_rows(); 130 const int num_cols = A->num_cols(); 131 132 if (per_solve_options.D != NULL) { 133 // Temporarily append a diagonal block to the A matrix, but undo 134 // it before returning the matrix to the user. 135 A->AppendDiagonal(per_solve_options.D); 136 } 137 138 // rhs = [b;0] to account for the additional rows in the lhs. 139 const int augmented_num_rows = 140 num_rows + ((per_solve_options.D != NULL) ? num_cols : 0); 141 if (rhs_.rows() != augmented_num_rows) { 142 rhs_.resize(augmented_num_rows); 143 rhs_.setZero(); 144 } 145 rhs_.head(num_rows) = ConstVectorRef(b, num_rows); 146 event_logger.AddEvent("Setup"); 147 148 // Solve the system. 149 VectorRef(x, num_cols) = A->matrix().householderQr().solve(rhs_); 150 event_logger.AddEvent("Solve"); 151 152 if (per_solve_options.D != NULL) { 153 // Undo the modifications to the matrix A. 154 A->RemoveDiagonal(); 155 } 156 157 // We always succeed, since the QR solver returns the best solution 158 // it can. It is the job of the caller to determine if the solution 159 // is good enough or not. 160 LinearSolver::Summary summary; 161 summary.num_iterations = 1; 162 summary.termination_type = LINEAR_SOLVER_SUCCESS; 163 summary.message = "Success."; 164 165 event_logger.AddEvent("TearDown"); 166 return summary; 167 } 168 169 } // namespace internal 170 } // namespace ceres 171
