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
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24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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28 //
29 // Author: sameeragarwal@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
DenseNormalCholeskySolver(const LinearSolver::Options & options)45 DenseNormalCholeskySolver::DenseNormalCholeskySolver(
46 const LinearSolver::Options& options)
47 : options_(options) {}
48
SolveImpl(DenseSparseMatrix * A,const double * b,const LinearSolver::PerSolveOptions & per_solve_options,double * x)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