| 1 | //
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| 2 | // qnewton.cc
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| 3 | //
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| 4 | // Copyright (C) 1996 Limit Point Systems, Inc.
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| 5 | //
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| 6 | // Author: Curtis Janssen <cljanss@limitpt.com>
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| 7 | // Maintainer: LPS
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| 8 | //
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| 9 | // This file is part of the SC Toolkit.
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| 10 | //
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| 11 | // The SC Toolkit is free software; you can redistribute it and/or modify
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| 12 | // it under the terms of the GNU Library General Public License as published by
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| 13 | // the Free Software Foundation; either version 2, or (at your option)
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| 14 | // any later version.
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| 15 | //
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| 16 | // The SC Toolkit is distributed in the hope that it will be useful,
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| 17 | // but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 18 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 19 | // GNU Library General Public License for more details.
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| 20 | //
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| 21 | // You should have received a copy of the GNU Library General Public License
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| 22 | // along with the SC Toolkit; see the file COPYING.LIB. If not, write to
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| 23 | // the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
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| 24 | //
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| 25 | // The U.S. Government is granted a limited license as per AL 91-7.
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| 26 | //
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| 27 |
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| 28 | #ifdef __GNUC__
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| 29 | #pragma implementation
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| 30 | #endif
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| 31 |
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| 32 | #include <math.h>
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| 33 | #include <float.h>
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| 34 |
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| 35 | #include <util/state/stateio.h>
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| 36 | #include <math/optimize/qnewton.h>
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| 37 | #include <util/keyval/keyval.h>
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| 38 | #include <util/misc/formio.h>
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| 39 |
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| 40 | using namespace std;
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| 41 | using namespace sc;
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| 42 |
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| 43 | /////////////////////////////////////////////////////////////////////////
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| 44 | // QNewtonOpt
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| 45 |
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| 46 | static ClassDesc QNewtonOpt_cd(
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| 47 | typeid(QNewtonOpt),"QNewtonOpt",2,"public Optimize",
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| 48 | 0, create<QNewtonOpt>, create<QNewtonOpt>);
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| 49 |
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| 50 | QNewtonOpt::QNewtonOpt(const Ref<KeyVal>&keyval):
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| 51 | Optimize(keyval)
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| 52 | {
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| 53 |
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| 54 | if (function_.null()) {
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| 55 | ExEnv::err0() << "QNewtonOpt requires a function keyword" << endl;
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| 56 | abort();
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| 57 | }
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| 58 |
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| 59 | init();
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| 60 |
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| 61 | update_ << keyval->describedclassvalue("update");
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| 62 | if (update_.nonnull()) update_->set_inverse();
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| 63 | lineopt_ << keyval->describedclassvalue("lineopt");
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| 64 | accuracy_ = keyval->doublevalue("accuracy");
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| 65 | if (keyval->error() != KeyVal::OK) accuracy_ = 0.0001;
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| 66 | print_x_ = keyval->booleanvalue("print_x");
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| 67 | print_hessian_ = keyval->booleanvalue("print_hessian");
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| 68 | print_gradient_ = keyval->booleanvalue("print_gradient");
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| 69 | linear_ = keyval->booleanvalue("linear");
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| 70 | if (keyval->error() != KeyVal::OK) linear_ = 0;
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| 71 | restrict_ = keyval->booleanvalue("restrict");
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| 72 | if (keyval->error() != KeyVal::OK) restrict_ = 1;
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| 73 | dynamic_grad_acc_ = keyval->booleanvalue("dynamic_grad_acc");
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| 74 | if (keyval->error() != KeyVal::OK) dynamic_grad_acc_ = 1;
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| 75 | force_search_ = keyval->booleanvalue("force_search");
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| 76 | if (keyval->error() != KeyVal::OK) force_search_ = 0;
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| 77 | restart_ = keyval->booleanvalue("restart");
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| 78 | if (keyval->error() != KeyVal::OK) restart_ = 1;
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| 79 |
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| 80 | RefSymmSCMatrix hessian(dimension(),matrixkit());
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| 81 | // get a guess hessian from the function
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| 82 | function()->guess_hessian(hessian);
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| 83 |
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| 84 | // see if any hessian matrix elements have been given in the input
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| 85 | if (keyval->exists("hessian")) {
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| 86 | int n = hessian.n();
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| 87 | for (int i=0; i<n; i++) {
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| 88 | if (keyval->exists("hessian",i)) {
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| 89 | for (int j=0; j<=i; j++) {
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| 90 | double tmp = keyval->doublevalue("hessian",i,j);
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| 91 | if (keyval->error() == KeyVal::OK) hessian(i,j) = tmp;
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| 92 | }
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| 93 | }
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| 94 | }
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| 95 | }
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| 96 | ihessian_ = function()->inverse_hessian(hessian);
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| 97 | }
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| 98 |
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| 99 | QNewtonOpt::QNewtonOpt(StateIn&s):
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| 100 | SavableState(s),
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| 101 | Optimize(s)
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| 102 | {
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| 103 | ihessian_ = matrixkit()->symmmatrix(dimension());
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| 104 | ihessian_.restore(s);
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| 105 | update_ << SavableState::restore_state(s);
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| 106 | s.get(accuracy_);
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| 107 | s.get(take_newton_step_);
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| 108 | s.get(maxabs_gradient);
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| 109 | if (s.version(::class_desc<QNewtonOpt>()) > 1) {
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| 110 | s.get(print_hessian_);
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| 111 | s.get(print_x_);
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| 112 | s.get(print_gradient_);
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| 113 | }
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| 114 | else {
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| 115 | print_hessian_ = 0;
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| 116 | print_x_ = 0;
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| 117 | print_gradient_ = 0;
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| 118 | }
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| 119 | lineopt_ << SavableState::restore_state(s);
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| 120 | }
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| 121 |
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| 122 | QNewtonOpt::~QNewtonOpt()
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| 123 | {
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| 124 | }
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| 125 |
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| 126 | void
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| 127 | QNewtonOpt::save_data_state(StateOut&s)
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| 128 | {
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| 129 | Optimize::save_data_state(s);
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| 130 | ihessian_.save(s);
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| 131 | SavableState::save_state(update_.pointer(),s);
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| 132 | s.put(accuracy_);
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| 133 | s.put(take_newton_step_);
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| 134 | s.put(maxabs_gradient);
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| 135 | s.put(print_hessian_);
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| 136 | s.put(print_x_);
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| 137 | s.put(print_gradient_);
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| 138 | SavableState::save_state(lineopt_.pointer(),s);
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| 139 | }
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| 140 |
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| 141 | void
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| 142 | QNewtonOpt::init()
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| 143 | {
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| 144 | Optimize::init();
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| 145 | take_newton_step_ = 1;
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| 146 | maxabs_gradient = -1.0;
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| 147 | }
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| 148 |
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| 149 | int
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| 150 | QNewtonOpt::update()
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| 151 | {
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| 152 | // these are good candidates to be input options
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| 153 | const double maxabs_gradient_to_desired_accuracy = 0.05;
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| 154 | const double maxabs_gradient_to_next_desired_accuracy = 0.005;
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| 155 | const double roundoff_error_factor = 1.1;
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| 156 |
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| 157 | // the gradient convergence criterion.
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| 158 | double old_maxabs_gradient = maxabs_gradient;
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| 159 | RefSCVector xcurrent;
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| 160 | RefSCVector gcurrent;
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| 161 |
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| 162 | if( dynamic_grad_acc_ ) {
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| 163 | // get the next gradient at the required level of accuracy.
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| 164 | // usually only one pass is needed, unless we happen to find
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| 165 | // that the accuracy was set too low.
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| 166 | int accurate_enough;
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| 167 | do {
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| 168 | // compute the current point
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| 169 | function()->set_desired_gradient_accuracy(accuracy_);
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| 170 | xcurrent = function()->get_x();
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| 171 | gcurrent = function()->gradient().copy();
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| 172 |
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| 173 | // compute the gradient convergence criterion now so i can see if
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| 174 | // the accuracy needs to be tighter
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| 175 | maxabs_gradient = gcurrent.maxabs();
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| 176 | // compute the required accuracy
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| 177 | accuracy_ = maxabs_gradient * maxabs_gradient_to_desired_accuracy;
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| 178 |
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| 179 | if (accuracy_ < DBL_EPSILON) accuracy_ = DBL_EPSILON;
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| 180 |
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| 181 | // The roundoff_error_factor is thrown in to allow for round off making
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| 182 | // the current gcurrent.maxabs() a bit smaller than the previous,
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| 183 | // which would make the current required accuracy less than the
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| 184 | // gradient's actual accuracy and cause everything to be recomputed.
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| 185 | accurate_enough = (
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| 186 | function()->actual_gradient_accuracy()
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| 187 | <= accuracy_*roundoff_error_factor);
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| 188 |
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| 189 | if (!accurate_enough) {
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| 190 | ExEnv::out0().unsetf(ios::fixed);
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| 191 | ExEnv::out0() << indent <<
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| 192 | "NOTICE: function()->actual_gradient_accuracy() > accuracy_:\n"
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| 193 | << indent
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| 194 | << scprintf(
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| 195 | " function()->actual_gradient_accuracy() = %15.8e",
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| 196 | function()->actual_gradient_accuracy()) << endl << indent
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| 197 | << scprintf(
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| 198 | " accuracy_ = %15.8e",
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| 199 | accuracy_) << endl;
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| 200 | }
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| 201 | } while(!accurate_enough);
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| 202 | // increase accuracy, since the next gradient will be smaller
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| 203 | accuracy_ = maxabs_gradient * maxabs_gradient_to_next_desired_accuracy;
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| 204 | }
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| 205 | else {
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| 206 | xcurrent = function()->get_x();
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| 207 | gcurrent = function()->gradient().copy();
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| 208 | }
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| 209 |
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| 210 | if (old_maxabs_gradient >= 0.0 && old_maxabs_gradient < maxabs_gradient) {
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| 211 | ExEnv::out0() << indent
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| 212 | << scprintf("NOTICE: maxabs_gradient increased from %8.4e to %8.4e",
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| 213 | old_maxabs_gradient, maxabs_gradient) << endl;
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| 214 | }
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| 215 |
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| 216 | // update the hessian
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| 217 | if(update_.nonnull())
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| 218 | update_->update(ihessian_,function(),xcurrent,gcurrent);
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| 219 |
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| 220 | conv_->reset();
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| 221 | conv_->get_grad(function());
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| 222 | conv_->get_x(function());
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| 223 |
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| 224 | // compute the quadratic step
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| 225 | RefSCVector xdisp = -1.0*(ihessian_ * gcurrent);
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| 226 | RefSCVector xnext = xcurrent + xdisp;
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| 227 |
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| 228 | // either do a lineopt or check stepsize
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| 229 | double tot;
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| 230 | if(lineopt_.nonnull()) {
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| 231 | if (dynamic_cast<Backtrack*>(lineopt_.pointer()) != 0) {
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| 232 | // The Backtrack line search is a special case.
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| 233 |
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| 234 | // perform a search
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| 235 | double factor;
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| 236 | if( n_iterations_ == 0 && force_search_ )
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| 237 | factor = lineopt_->set_decrease_factor(1.0);
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| 238 | lineopt_->init(xdisp,function());
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| 239 | // reset value acc here so line search "precomputes" are
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| 240 | // accurate enough for subsequent gradient evals
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| 241 | function()->set_desired_value_accuracy(accuracy_/100);
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| 242 | int acceptable = lineopt_->update();
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| 243 | if( n_iterations_ == 0 && force_search_ )
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| 244 | lineopt_->set_decrease_factor( factor );
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| 245 |
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| 246 | if( !acceptable ) {
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| 247 | if( force_search_ ) factor = lineopt_->set_decrease_factor(1.0);
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| 248 |
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| 249 | // try a new guess hessian
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| 250 | if( restart_ ) {
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| 251 | ExEnv::out0() << endl << indent <<
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| 252 | "Restarting Hessian approximation" << endl;
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| 253 | RefSymmSCMatrix hessian(dimension(),matrixkit());
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| 254 | function()->guess_hessian(hessian);
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| 255 | ihessian_ = function()->inverse_hessian(hessian);
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| 256 | xdisp = -1.0 * (ihessian_ * gcurrent);
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| 257 | lineopt_->init(xdisp,function());
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| 258 | acceptable = lineopt_->update();
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| 259 | }
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| 260 |
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| 261 | // try steepest descent direction
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| 262 | if( !acceptable ) {
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| 263 | ExEnv::out0() << endl << indent <<
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| 264 | "Trying steepest descent direction." << endl;
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| 265 | xdisp = -1.0 * gcurrent;
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| 266 | lineopt_->init(xdisp,function());
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| 267 | acceptable = lineopt_->update();
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| 268 | }
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| 269 |
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| 270 | // give up and use steepest descent step
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| 271 | if( !acceptable ) {
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| 272 | ExEnv::out0() << endl << indent <<
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| 273 | "Resorting to unscaled steepest descent step." << endl;
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| 274 | function()->set_x(xcurrent + xdisp);
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| 275 | Ref<NonlinearTransform> t = function()->change_coordinates();
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| 276 | apply_transform(t);
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| 277 | }
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| 278 |
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| 279 | if( force_search_ ) lineopt_->set_decrease_factor( factor );
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| 280 | }
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| 281 | }
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| 282 | else {
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| 283 | // All line searches other than Backtrack use this
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| 284 | ExEnv::out0() << indent
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| 285 | << "......................................."
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| 286 | << endl
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| 287 | << indent
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| 288 | << "Starting line optimization."
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| 289 | << endl;
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| 290 | lineopt_->init(xdisp,function());
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| 291 | int nlineopt = 0;
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| 292 | int maxlineopt = 3;
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| 293 | for (int ilineopt=0; ilineopt<maxlineopt; ilineopt++) {
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| 294 | double maxabs_gradient = function()->gradient()->maxabs();
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| 295 |
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| 296 | int converged = lineopt_->update();
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| 297 |
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| 298 | ExEnv::out0() << indent
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| 299 | << "Completed line optimization step " << ilineopt+1
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| 300 | << (converged?" (converged)":" (not converged)")
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| 301 | << endl
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| 302 | << indent
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| 303 | << "......................................."
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| 304 | << endl;
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| 305 |
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| 306 | if (converged) break;
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| 307 |
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| 308 | // Improve accuracy, since we might be able to reuse the next
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| 309 | // gradient for the next quasi-Newton step.
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| 310 | if (dynamic_grad_acc_) {
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| 311 | accuracy_ = maxabs_gradient*maxabs_gradient_to_next_desired_accuracy;
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| 312 | function()->set_desired_gradient_accuracy(accuracy_);
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| 313 | }
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| 314 | }
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| 315 | }
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| 316 | xnext = function()->get_x();
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| 317 | xdisp = xnext - xcurrent;
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| 318 | tot = sqrt(xdisp.scalar_product(xdisp));
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| 319 | }
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| 320 | else {
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| 321 |
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| 322 | tot = sqrt(xdisp.scalar_product(xdisp));
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| 323 |
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| 324 | if ( tot > max_stepsize_ ) {
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| 325 | if( restrict_ ) {
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| 326 | double scal = max_stepsize_/tot;
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| 327 | ExEnv::out0() << endl << indent <<
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| 328 | scprintf("stepsize of %f is too big, scaling by %f",tot,scal)
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| 329 | << endl;
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| 330 | xdisp.scale(scal);
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| 331 | tot *= scal;
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| 332 | }
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| 333 | else {
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| 334 | ExEnv::out0() << endl << indent <<
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| 335 | scprintf("stepsize of %f is too big, but scaling is disabled",tot)
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| 336 | << endl;
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| 337 | }
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| 338 | }
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| 339 | xnext = xcurrent + xdisp;
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| 340 | }
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| 341 |
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| 342 | if (print_hessian_) {
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| 343 | RefSymmSCMatrix hessian = ihessian_.gi();
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| 344 | ExEnv::out0() << indent << "hessian = [" << endl;
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| 345 | ExEnv::out0() << incindent;
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| 346 | int n = hessian.n();
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| 347 | for (int i=0; i<n; i++) {
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| 348 | ExEnv::out0() << indent << "[";
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| 349 | for (int j=0; j<=i; j++) {
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| 350 | ExEnv::out0() << scprintf(" % 10.6f",double(hessian(i,j)));
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| 351 | }
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| 352 | ExEnv::out0() << " ]" << endl;
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| 353 | }
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| 354 | ExEnv::out0() << decindent;
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| 355 | ExEnv::out0() << indent << "]" << endl;
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| 356 | }
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| 357 | if (print_x_) {
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| 358 | int n = xcurrent.n();
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| 359 | ExEnv::out0() << indent << "x = [";
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| 360 | for (int i=0; i<n; i++) {
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| 361 | ExEnv::out0() << scprintf(" % 16.12f",double(xcurrent(i)));
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| 362 | }
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| 363 | ExEnv::out0() << " ]" << endl;
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| 364 | }
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| 365 | if (print_gradient_) {
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| 366 | int n = gcurrent.n();
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| 367 | ExEnv::out0() << indent << "gradient = [";
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| 368 | for (int i=0; i<n; i++) {
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| 369 | ExEnv::out0() << scprintf(" % 16.12f",double(gcurrent(i)));
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| 370 | }
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| 371 | ExEnv::out0() << " ]" << endl;
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| 372 | }
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| 373 |
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| 374 | // check for convergence
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| 375 | conv_->set_nextx(xnext);
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| 376 | int converged = conv_->converged();
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| 377 | if (converged) return converged;
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| 378 |
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| 379 | ExEnv::out0() << indent
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| 380 | << scprintf("taking step of size %f", tot) << endl;
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| 381 | ExEnv::out0() << indent << "Optimization iteration "
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| 382 | << n_iterations_ + 1 << " complete" << endl;
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| 383 | ExEnv::out0() << indent
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| 384 | << "//////////////////////////////////////////////////////////////////////"
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| 385 | << endl;
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| 386 |
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| 387 | if( lineopt_.null() ) {
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| 388 | function()->set_x(xnext);
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| 389 | Ref<NonlinearTransform> t = function()->change_coordinates();
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| 390 | apply_transform(t);
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| 391 | }
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| 392 |
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| 393 | if( dynamic_grad_acc_ )
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| 394 | function()->set_desired_gradient_accuracy(accuracy_);
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| 395 |
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| 396 | return converged;
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| 397 | }
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| 398 |
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| 399 | void
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| 400 | QNewtonOpt::apply_transform(const Ref<NonlinearTransform> &t)
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| 401 | {
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| 402 | if (t.null()) return;
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| 403 | Optimize::apply_transform(t);
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| 404 | if (lineopt_.nonnull()) lineopt_->apply_transform(t);
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| 405 | if (ihessian_.nonnull()) t->transform_ihessian(ihessian_);
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| 406 | if (update_.nonnull()) update_->apply_transform(t);
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| 407 | }
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| 408 |
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| 409 | /////////////////////////////////////////////////////////////////////////////
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| 410 |
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| 411 | // Local Variables:
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| 412 | // mode: c++
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| 413 | // c-file-style: "ETS"
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| 414 | // End:
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