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
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20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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28//
29// Author: keir@google.com (Keir Mierle)
30
31#ifndef CERES_INTERNAL_CGNR_LINEAR_OPERATOR_H_
32#define CERES_INTERNAL_CGNR_LINEAR_OPERATOR_H_
33
34#include <algorithm>
35#include "ceres/linear_operator.h"
36#include "ceres/internal/scoped_ptr.h"
37#include "ceres/internal/eigen.h"
38
39namespace ceres {
40namespace internal {
41
42class SparseMatrix;
43
44// A linear operator which takes a matrix A and a diagonal vector D and
45// performs products of the form
46//
47//   (A^T A + D^T D)x
48//
49// This is used to implement iterative general sparse linear solving with
50// conjugate gradients, where A is the Jacobian and D is a regularizing
51// parameter. A brief proof that D^T D is the correct regularizer:
52//
53// Given a regularized least squares problem:
54//
55//   min  ||Ax - b||^2 + ||Dx||^2
56//    x
57//
58// First expand into matrix notation:
59//
60//   (Ax - b)^T (Ax - b) + xD^TDx
61//
62// Then multiply out to get:
63//
64//   = xA^TAx - 2b^T Ax + b^Tb + xD^TDx
65//
66// Take the derivative:
67//
68//   0 = 2A^TAx - 2A^T b + 2 D^TDx
69//   0 = A^TAx - A^T b + D^TDx
70//   0 = (A^TA + D^TD)x - A^T b
71//
72// Thus, the symmetric system we need to solve for CGNR is
73//
74//   Sx = z
75//
76// with S = A^TA + D^TD
77//  and z = A^T b
78//
79// Note: This class is not thread safe, since it uses some temporary storage.
80class CgnrLinearOperator : public LinearOperator {
81 public:
82  CgnrLinearOperator(const LinearOperator& A, const double *D)
83      : A_(A), D_(D), z_(new double[A.num_rows()]) {
84  }
85  virtual ~CgnrLinearOperator() {}
86
87  virtual void RightMultiply(const double* x, double* y) const {
88    std::fill(z_.get(), z_.get() + A_.num_rows(), 0.0);
89
90    // z = Ax
91    A_.RightMultiply(x, z_.get());
92
93    // y = y + Atz
94    A_.LeftMultiply(z_.get(), y);
95
96    // y = y + DtDx
97    if (D_ != NULL) {
98      int n = A_.num_cols();
99      VectorRef(y, n).array() += ConstVectorRef(D_, n).array().square() *
100                                 ConstVectorRef(x, n).array();
101    }
102  }
103
104  virtual void LeftMultiply(const double* x, double* y) const {
105    RightMultiply(x, y);
106  }
107
108  virtual int num_rows() const { return A_.num_cols(); }
109  virtual int num_cols() const { return A_.num_cols(); }
110
111 private:
112  const LinearOperator& A_;
113  const double* D_;
114  scoped_array<double> z_;
115};
116
117}  // namespace internal
118}  // namespace ceres
119
120#endif  // CERES_INTERNAL_CGNR_LINEAR_OPERATOR_H_
121