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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
#ifndef CERES_NO_LINE_SEARCH_MINIMIZER
#include "ceres/line_search.h"
#include <glog/logging.h>
#include "ceres/fpclassify.h"
#include "ceres/evaluator.h"
#include "ceres/internal/eigen.h"
#include "ceres/polynomial.h"
namespace ceres {
namespace internal {
namespace {
FunctionSample ValueSample(const double x, const double value) {
FunctionSample sample;
sample.x = x;
sample.value = value;
sample.value_is_valid = true;
return sample;
};
FunctionSample ValueAndGradientSample(const double x,
const double value,
const double gradient) {
FunctionSample sample;
sample.x = x;
sample.value = value;
sample.gradient = gradient;
sample.value_is_valid = true;
sample.gradient_is_valid = true;
return sample;
};
} // namespace
LineSearchFunction::LineSearchFunction(Evaluator* evaluator)
: evaluator_(evaluator),
position_(evaluator->NumParameters()),
direction_(evaluator->NumEffectiveParameters()),
evaluation_point_(evaluator->NumParameters()),
scaled_direction_(evaluator->NumEffectiveParameters()),
gradient_(evaluator->NumEffectiveParameters()) {
}
void LineSearchFunction::Init(const Vector& position,
const Vector& direction) {
position_ = position;
direction_ = direction;
}
bool LineSearchFunction::Evaluate(const double x, double* f, double* g) {
scaled_direction_ = x * direction_;
if (!evaluator_->Plus(position_.data(),
scaled_direction_.data(),
evaluation_point_.data())) {
return false;
}
if (g == NULL) {
return (evaluator_->Evaluate(evaluation_point_.data(),
f, NULL, NULL, NULL) &&
IsFinite(*f));
}
if (!evaluator_->Evaluate(evaluation_point_.data(),
f,
NULL,
gradient_.data(), NULL)) {
return false;
}
*g = direction_.dot(gradient_);
return IsFinite(*f) && IsFinite(*g);
}
void ArmijoLineSearch::Search(const LineSearch::Options& options,
const double initial_step_size,
const double initial_cost,
const double initial_gradient,
Summary* summary) {
*CHECK_NOTNULL(summary) = LineSearch::Summary();
Function* function = options.function;
double previous_step_size = 0.0;
double previous_cost = 0.0;
double previous_gradient = 0.0;
bool previous_step_size_is_valid = false;
double step_size = initial_step_size;
double cost = 0.0;
double gradient = 0.0;
bool step_size_is_valid = false;
++summary->num_evaluations;
step_size_is_valid =
function->Evaluate(step_size,
&cost,
options.interpolation_degree < 2 ? NULL : &gradient);
while (!step_size_is_valid || cost > (initial_cost
+ options.sufficient_decrease
* initial_gradient
* step_size)) {
// If step_size_is_valid is not true we treat it as if the cost at
// that point is not large enough to satisfy the sufficient
// decrease condition.
const double current_step_size = step_size;
// Backtracking search. Each iteration of this loop finds a new point
if ((options.interpolation_degree == 0) || !step_size_is_valid) {
// Backtrack by halving the step_size;
step_size *= 0.5;
} else {
// Backtrack by interpolating the function and gradient values
// and minimizing the corresponding polynomial.
vector<FunctionSample> samples;
samples.push_back(ValueAndGradientSample(0.0,
initial_cost,
initial_gradient));
if (options.interpolation_degree == 1) {
// Two point interpolation using function values and the
// initial gradient.
samples.push_back(ValueSample(step_size, cost));
if (options.use_higher_degree_interpolation_when_possible &&
summary->num_evaluations > 1 &&
previous_step_size_is_valid) {
// Three point interpolation, using function values and the
// initial gradient.
samples.push_back(ValueSample(previous_step_size, previous_cost));
}
} else {
// Two point interpolation using the function values and the gradients.
samples.push_back(ValueAndGradientSample(step_size,
cost,
gradient));
if (options.use_higher_degree_interpolation_when_possible &&
summary->num_evaluations > 1 &&
previous_step_size_is_valid) {
// Three point interpolation using the function values and
// the gradients.
samples.push_back(ValueAndGradientSample(previous_step_size,
previous_cost,
previous_gradient));
}
}
double min_value;
MinimizeInterpolatingPolynomial(samples, 0.0, current_step_size,
&step_size, &min_value);
step_size =
min(max(step_size,
options.min_relative_step_size_change * current_step_size),
options.max_relative_step_size_change * current_step_size);
}
previous_step_size = current_step_size;
previous_cost = cost;
previous_gradient = gradient;
if (fabs(initial_gradient) * step_size < options.step_size_threshold) {
LOG(WARNING) << "Line search failed: step_size too small: " << step_size;
return;
}
++summary->num_evaluations;
step_size_is_valid =
function->Evaluate(step_size,
&cost,
options.interpolation_degree < 2 ? NULL : &gradient);
}
summary->optimal_step_size = step_size;
summary->success = true;
}
} // namespace internal
} // namespace ceres
#endif // CERES_NO_LINE_SEARCH_MINIMIZER
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