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ceres-solver/internal/ceres/line_search_minimizer.cc
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Sameer Agarwal 8bfdb02fb1 Rewrite uses of VLOG_IF and LOG_IF. 
VLOG_IF's evaluation order is ambiguous - does it mean
`if (cond) VLOG(lvl)` or `if (VLOG_IS_ON(lvl) && cond) LOG(INFO)`?
In particular, the way it works now is inconsistent with the way the
rest of the LOG macros evaluate their arguments.
Fixing this would be hard, and the macro's behavior would still surprise
some people. Replacing it with an if statement is simple, clear, and unambiguous.

Change-Id: I97a92d17a932c0a5344a1bf98d676308793ba877
2020-10-12 18:34:24 +00:00

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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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)
//
// Generic loop for line search based optimization algorithms.
//
// This is primarily inpsired by the minFunc packaged written by Mark
// Schmidt.
//
// http://www.di.ens.fr/~mschmidt/Software/minFunc.html
//
// For details on the theory and implementation see "Numerical
// Optimization" by Nocedal & Wright.
#include "ceres/line_search_minimizer.h"
#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <memory>
#include <string>
#include <vector>
#include "Eigen/Dense"
#include "ceres/array_utils.h"
#include "ceres/evaluator.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/port.h"
#include "ceres/line_search.h"
#include "ceres/line_search_direction.h"
#include "ceres/stringprintf.h"
#include "ceres/types.h"
#include "ceres/wall_time.h"
#include "glog/logging.h"
namespace ceres {
namespace internal {
namespace {
bool EvaluateGradientNorms(Evaluator* evaluator,
const Vector& x,
LineSearchMinimizer::State* state,
std::string* message) {
Vector negative_gradient = -state->gradient;
Vector projected_gradient_step(x.size());
if (!evaluator->Plus(
x.data(), negative_gradient.data(), projected_gradient_step.data())) {
*message = "projected_gradient_step = Plus(x, -gradient) failed.";
return false;
}
state->gradient_squared_norm = (x - projected_gradient_step).squaredNorm();
state->gradient_max_norm =
(x - projected_gradient_step).lpNorm<Eigen::Infinity>();
return true;
}
} // namespace
void LineSearchMinimizer::Minimize(const Minimizer::Options& options,
double* parameters,
Solver::Summary* summary) {
const bool is_not_silent = !options.is_silent;
double start_time = WallTimeInSeconds();
double iteration_start_time = start_time;
CHECK(options.evaluator != nullptr);
Evaluator* evaluator = options.evaluator.get();
const int num_parameters = evaluator->NumParameters();
const int num_effective_parameters = evaluator->NumEffectiveParameters();
summary->termination_type = NO_CONVERGENCE;
summary->num_successful_steps = 0;
summary->num_unsuccessful_steps = 0;
VectorRef x(parameters, num_parameters);
State current_state(num_parameters, num_effective_parameters);
State previous_state(num_parameters, num_effective_parameters);
IterationSummary iteration_summary;
iteration_summary.iteration = 0;
iteration_summary.step_is_valid = false;
iteration_summary.step_is_successful = false;
iteration_summary.cost_change = 0.0;
iteration_summary.gradient_max_norm = 0.0;
iteration_summary.gradient_norm = 0.0;
iteration_summary.step_norm = 0.0;
iteration_summary.linear_solver_iterations = 0;
iteration_summary.step_solver_time_in_seconds = 0;
// Do initial cost and gradient evaluation.
if (!evaluator->Evaluate(x.data(),
&(current_state.cost),
nullptr,
current_state.gradient.data(),
nullptr)) {
summary->termination_type = FAILURE;
summary->message = "Initial cost and jacobian evaluation failed.";
if (is_not_silent) {
LOG(WARNING) << "Terminating: " << summary->message;
}
return;
}
if (!EvaluateGradientNorms(evaluator, x, &current_state, &summary->message)) {
summary->termination_type = FAILURE;
summary->message =
"Initial cost and jacobian evaluation failed. More details: " +
summary->message;
if (is_not_silent) {
LOG(WARNING) << "Terminating: " << summary->message;
}
return;
}
summary->initial_cost = current_state.cost + summary->fixed_cost;
iteration_summary.cost = current_state.cost + summary->fixed_cost;
iteration_summary.gradient_norm = sqrt(current_state.gradient_squared_norm);
iteration_summary.gradient_max_norm = current_state.gradient_max_norm;
if (iteration_summary.gradient_max_norm <= options.gradient_tolerance) {
summary->message =
StringPrintf("Gradient tolerance reached. Gradient max norm: %e <= %e",
iteration_summary.gradient_max_norm,
options.gradient_tolerance);
summary->termination_type = CONVERGENCE;
if (is_not_silent) {
VLOG(1) << "Terminating: " << summary->message;
}
return;
}
iteration_summary.iteration_time_in_seconds =
WallTimeInSeconds() - iteration_start_time;
iteration_summary.cumulative_time_in_seconds =
WallTimeInSeconds() - start_time + summary->preprocessor_time_in_seconds;
summary->iterations.push_back(iteration_summary);
LineSearchDirection::Options line_search_direction_options;
line_search_direction_options.num_parameters = num_effective_parameters;
line_search_direction_options.type = options.line_search_direction_type;
line_search_direction_options.nonlinear_conjugate_gradient_type =
options.nonlinear_conjugate_gradient_type;
line_search_direction_options.max_lbfgs_rank = options.max_lbfgs_rank;
line_search_direction_options.use_approximate_eigenvalue_bfgs_scaling =
options.use_approximate_eigenvalue_bfgs_scaling;
std::unique_ptr<LineSearchDirection> line_search_direction(
LineSearchDirection::Create(line_search_direction_options));
LineSearchFunction line_search_function(evaluator);
LineSearch::Options line_search_options;
line_search_options.interpolation_type =
options.line_search_interpolation_type;
line_search_options.min_step_size = options.min_line_search_step_size;
line_search_options.sufficient_decrease =
options.line_search_sufficient_function_decrease;
line_search_options.max_step_contraction =
options.max_line_search_step_contraction;
line_search_options.min_step_contraction =
options.min_line_search_step_contraction;
line_search_options.max_num_iterations =
options.max_num_line_search_step_size_iterations;
line_search_options.sufficient_curvature_decrease =
options.line_search_sufficient_curvature_decrease;
line_search_options.max_step_expansion =
options.max_line_search_step_expansion;
line_search_options.is_silent = options.is_silent;
line_search_options.function = &line_search_function;
std::unique_ptr<LineSearch> line_search(LineSearch::Create(
options.line_search_type, line_search_options, &summary->message));
if (line_search.get() == nullptr) {
summary->termination_type = FAILURE;
if (is_not_silent) {
LOG(ERROR) << "Terminating: " << summary->message;
}
return;
}
LineSearch::Summary line_search_summary;
int num_line_search_direction_restarts = 0;
while (true) {
if (!RunCallbacks(options, iteration_summary, summary)) {
break;
}
iteration_start_time = WallTimeInSeconds();
if (iteration_summary.iteration >= options.max_num_iterations) {
summary->message = "Maximum number of iterations reached.";
summary->termination_type = NO_CONVERGENCE;
if (is_not_silent) {
VLOG(1) << "Terminating: " << summary->message;
}
break;
}
const double total_solver_time = iteration_start_time - start_time +
summary->preprocessor_time_in_seconds;
if (total_solver_time >= options.max_solver_time_in_seconds) {
summary->message = "Maximum solver time reached.";
summary->termination_type = NO_CONVERGENCE;
if (is_not_silent) {
VLOG(1) << "Terminating: " << summary->message;
}
break;
}
iteration_summary = IterationSummary();
iteration_summary.iteration = summary->iterations.back().iteration + 1;
iteration_summary.step_is_valid = false;
iteration_summary.step_is_successful = false;
bool line_search_status = true;
if (iteration_summary.iteration == 1) {
current_state.search_direction = -current_state.gradient;
} else {
line_search_status = line_search_direction->NextDirection(
previous_state, current_state, &current_state.search_direction);
}
if (!line_search_status &&
num_line_search_direction_restarts >=
options.max_num_line_search_direction_restarts) {
// Line search direction failed to generate a new direction, and we
// have already reached our specified maximum number of restarts,
// terminate optimization.
summary->message = StringPrintf(
"Line search direction failure: specified "
"max_num_line_search_direction_restarts: %d reached.",
options.max_num_line_search_direction_restarts);
summary->termination_type = FAILURE;
if (is_not_silent) {
LOG(WARNING) << "Terminating: " << summary->message;
}
break;
} else if (!line_search_status) {
// Restart line search direction with gradient descent on first iteration
// as we have not yet reached our maximum number of restarts.
CHECK_LT(num_line_search_direction_restarts,
options.max_num_line_search_direction_restarts);
++num_line_search_direction_restarts;
if (is_not_silent) {
LOG(WARNING) << "Line search direction algorithm: "
<< LineSearchDirectionTypeToString(
options.line_search_direction_type)
<< ", failed to produce a valid new direction at "
<< "iteration: " << iteration_summary.iteration
<< ". Restarting, number of restarts: "
<< num_line_search_direction_restarts << " / "
<< options.max_num_line_search_direction_restarts
<< " [max].";
}
line_search_direction.reset(
LineSearchDirection::Create(line_search_direction_options));
current_state.search_direction = -current_state.gradient;
}
line_search_function.Init(x, current_state.search_direction);
current_state.directional_derivative =
current_state.gradient.dot(current_state.search_direction);
// TODO(sameeragarwal): Refactor this into its own object and add
// explanations for the various choices.
//
// Note that we use !line_search_status to ensure that we treat cases when
// we restarted the line search direction equivalently to the first
// iteration.
const double initial_step_size =
(iteration_summary.iteration == 1 || !line_search_status)
? std::min(1.0, 1.0 / current_state.gradient_max_norm)
: std::min(1.0,
2.0 * (current_state.cost - previous_state.cost) /
current_state.directional_derivative);
// By definition, we should only ever go forwards along the specified search
// direction in a line search, most likely cause for this being violated
// would be a numerical failure in the line search direction calculation.
if (initial_step_size < 0.0) {
summary->message = StringPrintf(
"Numerical failure in line search, initial_step_size is "
"negative: %.5e, directional_derivative: %.5e, "
"(current_cost - previous_cost): %.5e",
initial_step_size,
current_state.directional_derivative,
(current_state.cost - previous_state.cost));
summary->termination_type = FAILURE;
if (is_not_silent) {
LOG(WARNING) << "Terminating: " << summary->message;
}
break;
}
line_search->Search(initial_step_size,
current_state.cost,
current_state.directional_derivative,
&line_search_summary);
if (!line_search_summary.success) {
summary->message = StringPrintf(
"Numerical failure in line search, failed to find "
"a valid step size, (did not run out of iterations) "
"using initial_step_size: %.5e, initial_cost: %.5e, "
"initial_gradient: %.5e.",
initial_step_size,
current_state.cost,
current_state.directional_derivative);
if (is_not_silent) {
LOG(WARNING) << "Terminating: " << summary->message;
}
summary->termination_type = FAILURE;
break;
}
const FunctionSample& optimal_point = line_search_summary.optimal_point;
CHECK(optimal_point.vector_x_is_valid)
<< "Congratulations, you found a bug in Ceres. Please report it.";
current_state.step_size = optimal_point.x;
previous_state = current_state;
iteration_summary.step_solver_time_in_seconds =
WallTimeInSeconds() - iteration_start_time;
if (optimal_point.vector_gradient_is_valid) {
current_state.cost = optimal_point.value;
current_state.gradient = optimal_point.vector_gradient;
} else {
Evaluator::EvaluateOptions evaluate_options;
evaluate_options.new_evaluation_point = false;
if (!evaluator->Evaluate(evaluate_options,
optimal_point.vector_x.data(),
&(current_state.cost),
nullptr,
current_state.gradient.data(),
nullptr)) {
summary->termination_type = FAILURE;
summary->message = "Cost and jacobian evaluation failed.";
if (is_not_silent) {
LOG(WARNING) << "Terminating: " << summary->message;
}
return;
}
}
if (!EvaluateGradientNorms(evaluator,
optimal_point.vector_x,
&current_state,
&summary->message)) {
summary->termination_type = FAILURE;
summary->message =
"Step failed to evaluate. This should not happen as the step was "
"valid when it was selected by the line search. More details: " +
summary->message;
if (is_not_silent) {
LOG(WARNING) << "Terminating: " << summary->message;
}
break;
}
// Compute the norm of the step in the ambient space.
iteration_summary.step_norm = (optimal_point.vector_x - x).norm();
const double x_norm = x.norm();
x = optimal_point.vector_x;
iteration_summary.gradient_max_norm = current_state.gradient_max_norm;
iteration_summary.gradient_norm = sqrt(current_state.gradient_squared_norm);
iteration_summary.cost_change = previous_state.cost - current_state.cost;
iteration_summary.cost = current_state.cost + summary->fixed_cost;
iteration_summary.step_is_valid = true;
iteration_summary.step_is_successful = true;
iteration_summary.step_size = current_state.step_size;
iteration_summary.line_search_function_evaluations =
line_search_summary.num_function_evaluations;
iteration_summary.line_search_gradient_evaluations =
line_search_summary.num_gradient_evaluations;
iteration_summary.line_search_iterations =
line_search_summary.num_iterations;
iteration_summary.iteration_time_in_seconds =
WallTimeInSeconds() - iteration_start_time;
iteration_summary.cumulative_time_in_seconds =
WallTimeInSeconds() - start_time +
summary->preprocessor_time_in_seconds;
summary->iterations.push_back(iteration_summary);
// Iterations inside the line search algorithm are considered
// 'steps' in the broader context, to distinguish these inner
// iterations from from the outer iterations of the line search
// minimizer. The number of line search steps is the total number
// of inner line search iterations (or steps) across the entire
// minimization.
summary->num_line_search_steps += line_search_summary.num_iterations;
summary->line_search_cost_evaluation_time_in_seconds +=
line_search_summary.cost_evaluation_time_in_seconds;
summary->line_search_gradient_evaluation_time_in_seconds +=
line_search_summary.gradient_evaluation_time_in_seconds;
summary->line_search_polynomial_minimization_time_in_seconds +=
line_search_summary.polynomial_minimization_time_in_seconds;
summary->line_search_total_time_in_seconds +=
line_search_summary.total_time_in_seconds;
++summary->num_successful_steps;
const double step_size_tolerance =
options.parameter_tolerance * (x_norm + options.parameter_tolerance);
if (iteration_summary.step_norm <= step_size_tolerance) {
summary->message = StringPrintf(
"Parameter tolerance reached. "
"Relative step_norm: %e <= %e.",
(iteration_summary.step_norm /
(x_norm + options.parameter_tolerance)),
options.parameter_tolerance);
summary->termination_type = CONVERGENCE;
if (is_not_silent) {
VLOG(1) << "Terminating: " << summary->message;
}
return;
}
if (iteration_summary.gradient_max_norm <= options.gradient_tolerance) {
summary->message = StringPrintf(
"Gradient tolerance reached. "
"Gradient max norm: %e <= %e",
iteration_summary.gradient_max_norm,
options.gradient_tolerance);
summary->termination_type = CONVERGENCE;
if (is_not_silent) {
VLOG(1) << "Terminating: " << summary->message;
}
break;
}
const double absolute_function_tolerance =
options.function_tolerance * std::abs(previous_state.cost);
if (std::abs(iteration_summary.cost_change) <=
absolute_function_tolerance) {
summary->message = StringPrintf(
"Function tolerance reached. "
"|cost_change|/cost: %e <= %e",
std::abs(iteration_summary.cost_change) / previous_state.cost,
options.function_tolerance);
summary->termination_type = CONVERGENCE;
if (is_not_silent) {
VLOG(1) << "Terminating: " << summary->message;
}
break;
}
}
}
} // namespace internal
} // namespace ceres
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