LMonestep.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
5 //
6 // This code initially comes from MINPACK whose original authors are:
7 // Copyright Jorge More - Argonne National Laboratory
8 // Copyright Burt Garbow - Argonne National Laboratory
9 // Copyright Ken Hillstrom - Argonne National Laboratory
10 //
11 // This Source Code Form is subject to the terms of the Minpack license
12 // (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
13 
14 #ifndef EIGEN_LMONESTEP_H
15 #define EIGEN_LMONESTEP_H
16 
17 namespace Eigen {
18 
19 template<typename FunctorType>
20 LevenbergMarquardtSpace::Status
21 LevenbergMarquardt<FunctorType>::minimizeOneStep(FVectorType &x)
22 {
23  using std::abs;
24  using std::sqrt;
25  RealScalar temp, temp1,temp2;
26  RealScalar ratio;
27  RealScalar pnorm, xnorm, fnorm1, actred, dirder, prered;
28  eigen_assert(x.size()==n); // check the caller is not cheating us
29 
30  temp = 0.0; xnorm = 0.0;
31  /* calculate the jacobian matrix. */
32  Index df_ret = m_functor.df(x, m_fjac);
33  if (df_ret<0)
34  return LevenbergMarquardtSpace::UserAsked;
35  if (df_ret>0)
36  // numerical diff, we evaluated the function df_ret times
37  m_nfev += df_ret;
38  else m_njev++;
39 
40  /* compute the qr factorization of the jacobian. */
41  for (int j = 0; j < x.size(); ++j)
42  m_wa2(j) = m_fjac.col(j).blueNorm();
43  QRSolver qrfac(m_fjac);
44  if(qrfac.info() != Success) {
45  m_info = NumericalIssue;
46  return LevenbergMarquardtSpace::ImproperInputParameters;
47  }
48  // Make a copy of the first factor with the associated permutation
49  m_rfactor = qrfac.matrixR();
50  m_permutation = (qrfac.colsPermutation());
51 
52  /* on the first iteration and if external scaling is not used, scale according */
53  /* to the norms of the columns of the initial jacobian. */
54  if (m_iter == 1) {
55  if (!m_useExternalScaling)
56  for (Index j = 0; j < n; ++j)
57  m_diag[j] = (m_wa2[j]==0.)? 1. : m_wa2[j];
58 
59  /* on the first iteration, calculate the norm of the scaled x */
60  /* and initialize the step bound m_delta. */
61  xnorm = m_diag.cwiseProduct(x).stableNorm();
62  m_delta = m_factor * xnorm;
63  if (m_delta == 0.)
64  m_delta = m_factor;
65  }
66 
67  /* form (q transpose)*m_fvec and store the first n components in */
68  /* m_qtf. */
69  m_wa4 = m_fvec;
70  m_wa4 = qrfac.matrixQ().adjoint() * m_fvec;
71  m_qtf = m_wa4.head(n);
72 
73  /* compute the norm of the scaled gradient. */
74  m_gnorm = 0.;
75  if (m_fnorm != 0.)
76  for (Index j = 0; j < n; ++j)
77  if (m_wa2[m_permutation.indices()[j]] != 0.)
78  m_gnorm = (std::max)(m_gnorm, abs( m_rfactor.col(j).head(j+1).dot(m_qtf.head(j+1)/m_fnorm) / m_wa2[m_permutation.indices()[j]]));
79 
80  /* test for convergence of the gradient norm. */
81  if (m_gnorm <= m_gtol) {
82  m_info = Success;
83  return LevenbergMarquardtSpace::CosinusTooSmall;
84  }
85 
86  /* rescale if necessary. */
87  if (!m_useExternalScaling)
88  m_diag = m_diag.cwiseMax(m_wa2);
89 
90  do {
91  /* determine the levenberg-marquardt parameter. */
92  internal::lmpar2(qrfac, m_diag, m_qtf, m_delta, m_par, m_wa1);
93 
94  /* store the direction p and x + p. calculate the norm of p. */
95  m_wa1 = -m_wa1;
96  m_wa2 = x + m_wa1;
97  pnorm = m_diag.cwiseProduct(m_wa1).stableNorm();
98 
99  /* on the first iteration, adjust the initial step bound. */
100  if (m_iter == 1)
101  m_delta = (std::min)(m_delta,pnorm);
102 
103  /* evaluate the function at x + p and calculate its norm. */
104  if ( m_functor(m_wa2, m_wa4) < 0)
105  return LevenbergMarquardtSpace::UserAsked;
106  ++m_nfev;
107  fnorm1 = m_wa4.stableNorm();
108 
109  /* compute the scaled actual reduction. */
110  actred = -1.;
111  if (Scalar(.1) * fnorm1 < m_fnorm)
112  actred = 1. - numext::abs2(fnorm1 / m_fnorm);
113 
114  /* compute the scaled predicted reduction and */
115  /* the scaled directional derivative. */
116  m_wa3 = m_rfactor.template triangularView<Upper>() * (m_permutation.inverse() *m_wa1);
117  temp1 = numext::abs2(m_wa3.stableNorm() / m_fnorm);
118  temp2 = numext::abs2(sqrt(m_par) * pnorm / m_fnorm);
119  prered = temp1 + temp2 / Scalar(.5);
120  dirder = -(temp1 + temp2);
121 
122  /* compute the ratio of the actual to the predicted */
123  /* reduction. */
124  ratio = 0.;
125  if (prered != 0.)
126  ratio = actred / prered;
127 
128  /* update the step bound. */
129  if (ratio <= Scalar(.25)) {
130  if (actred >= 0.)
131  temp = RealScalar(.5);
132  if (actred < 0.)
133  temp = RealScalar(.5) * dirder / (dirder + RealScalar(.5) * actred);
134  if (RealScalar(.1) * fnorm1 >= m_fnorm || temp < RealScalar(.1))
135  temp = Scalar(.1);
136  /* Computing MIN */
137  m_delta = temp * (std::min)(m_delta, pnorm / RealScalar(.1));
138  m_par /= temp;
139  } else if (!(m_par != 0. && ratio < RealScalar(.75))) {
140  m_delta = pnorm / RealScalar(.5);
141  m_par = RealScalar(.5) * m_par;
142  }
143 
144  /* test for successful iteration. */
145  if (ratio >= RealScalar(1e-4)) {
146  /* successful iteration. update x, m_fvec, and their norms. */
147  x = m_wa2;
148  m_wa2 = m_diag.cwiseProduct(x);
149  m_fvec = m_wa4;
150  xnorm = m_wa2.stableNorm();
151  m_fnorm = fnorm1;
152  ++m_iter;
153  }
154 
155  /* tests for convergence. */
156  if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1. && m_delta <= m_xtol * xnorm)
157  {
158  m_info = Success;
159  return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
160  }
161  if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1.)
162  {
163  m_info = Success;
164  return LevenbergMarquardtSpace::RelativeReductionTooSmall;
165  }
166  if (m_delta <= m_xtol * xnorm)
167  {
168  m_info = Success;
169  return LevenbergMarquardtSpace::RelativeErrorTooSmall;
170  }
171 
172  /* tests for termination and stringent tolerances. */
173  if (m_nfev >= m_maxfev)
174  {
175  m_info = NoConvergence;
176  return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
177  }
178  if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
179  {
180  m_info = Success;
181  return LevenbergMarquardtSpace::FtolTooSmall;
182  }
183  if (m_delta <= NumTraits<Scalar>::epsilon() * xnorm)
184  {
185  m_info = Success;
186  return LevenbergMarquardtSpace::XtolTooSmall;
187  }
188  if (m_gnorm <= NumTraits<Scalar>::epsilon())
189  {
190  m_info = Success;
191  return LevenbergMarquardtSpace::GtolTooSmall;
192  }
193 
194  } while (ratio < Scalar(1e-4));
195 
196  return LevenbergMarquardtSpace::Running;
197 }
198 
199 
200 } // end namespace Eigen
201 
202 #endif // EIGEN_LMONESTEP_H
Namespace containing all symbols from the Eigen library.
Definition: AdolcForward:45