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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2018 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: mierle@gmail.com (Keir Mierle)
+
+#include "ceres/solver.h"
+
+#include <cmath>
+#include <limits>
+#include <vector>
+
+#include "gtest/gtest.h"
+#include "ceres/sized_cost_function.h"
+#include "ceres/problem.h"
+#include "ceres/problem_impl.h"
+
+namespace ceres {
+namespace internal {
+
+// Use an inline hash function to avoid portability wrangling. Algorithm from
+// Daniel Bernstein, known as the "djb2" hash.
+template<typename T>
+uint64_t Djb2Hash(const T* data, const int size) {
+ uint64_t hash = 5381;
+ const uint8_t* data_as_bytes = reinterpret_cast<const uint8_t*>(data);
+ for (int i = 0; i < sizeof(*data) * size; ++i) {
+ hash = hash * 33 + data_as_bytes[i];
+ }
+ return hash;
+}
+
+const double kUninitialized = 0;
+
+// Generally multiple inheritance is a terrible idea, but in this (test)
+// case it makes for a relatively elegant test implementation.
+struct WigglyBowlCostFunctionAndEvaluationCallback :
+ SizedCostFunction<2, 2>,
+ EvaluationCallback {
+
+ explicit WigglyBowlCostFunctionAndEvaluationCallback(double *parameter)
+ : EvaluationCallback(),
+ user_parameter_block(parameter),
+ prepare_num_calls(0),
+ prepare_requested_jacobians(false),
+ prepare_new_evaluation_point(false),
+ prepare_parameter_hash(kUninitialized),
+ evaluate_num_calls(0),
+ evaluate_last_parameter_hash(kUninitialized) {}
+
+ virtual ~WigglyBowlCostFunctionAndEvaluationCallback() {}
+
+ // Evaluation callback interface. This checks that all the preconditions are
+ // met at the point that Ceres calls into it.
+ virtual void PrepareForEvaluation(bool evaluate_jacobians,
+ bool new_evaluation_point) {
+ // At this point, the incoming parameters are implicitly pushed by Ceres
+ // into the user parameter blocks; in contrast to in Evaluate().
+ uint64_t incoming_parameter_hash = Djb2Hash(user_parameter_block, 2);
+
+ // Check: Prepare() & Evaluate() come in pairs, in that order. Before this
+ // call, the number of calls excluding this one should match.
+ EXPECT_EQ(prepare_num_calls, evaluate_num_calls);
+
+ // Check: new_evaluation_point indicates that the parameter has changed.
+ if (new_evaluation_point) {
+ // If it's a new evaluation point, then the parameter should have
+ // changed. Technically, it's not required that it must change but
+ // in practice it does, and that helps with testing.
+ EXPECT_NE(evaluate_last_parameter_hash, incoming_parameter_hash);
+ EXPECT_NE(prepare_parameter_hash, incoming_parameter_hash);
+ } else {
+ // If this is the same evaluation point as last time, ensure that
+ // the parameters match both from the previous evaluate, the
+ // previous prepare, and the current prepare.
+ EXPECT_EQ(evaluate_last_parameter_hash, prepare_parameter_hash);
+ EXPECT_EQ(evaluate_last_parameter_hash, incoming_parameter_hash);
+ }
+
+ // Save details for to check at the next call to Evaluate().
+ prepare_num_calls++;
+ prepare_requested_jacobians = evaluate_jacobians;
+ prepare_new_evaluation_point = new_evaluation_point;
+ prepare_parameter_hash = incoming_parameter_hash;
+ }
+
+ // Cost function interface. This checks that preconditions that were
+ // set as part of the PrepareForEvaluation() call are met in this one.
+ virtual bool Evaluate(double const* const* parameters,
+ double* residuals,
+ double** jacobians) const {
+ // Cost function implementation of the "Wiggly Bowl" function:
+ //
+ // 1/2 * [(y - a*sin(x))^2 + x^2],
+ //
+ // expressed as a Ceres cost function with two residuals:
+ //
+ // r[0] = y - a*sin(x)
+ // r[1] = x.
+ //
+ // This is harder to optimize than the Rosenbrock function because the
+ // minimizer has to navigate a sine-shaped valley while descending the 1D
+ // parabola formed along the y axis. Note that the "a" needs to be more
+ // than 5 to get a strong enough wiggle effect in the cost surface to
+ // trigger failed iterations in the optimizer.
+ const double a = 10.0;
+ double x = (*parameters)[0];
+ double y = (*parameters)[1];
+ residuals[0] = y - a * sin(x);
+ residuals[1] = x;
+ if (jacobians != NULL) {
+ (*jacobians)[2 * 0 + 0] = - a * cos(x); // df1/dx
+ (*jacobians)[2 * 0 + 1] = 1.0; // df1/dy
+ (*jacobians)[2 * 1 + 0] = 1.0; // df2/dx
+ (*jacobians)[2 * 1 + 1] = 0.0; // df2/dy
+ }
+
+ uint64_t incoming_parameter_hash = Djb2Hash(*parameters, 2);
+
+ // Check: PrepareForEvaluation() & Evaluate() come in pairs, in that order.
+ EXPECT_EQ(prepare_num_calls, evaluate_num_calls + 1);
+
+ // Check: if new_evaluation_point indicates that the parameter has
+ // changed, it has changed; otherwise it is the same.
+ if (prepare_new_evaluation_point) {
+ EXPECT_NE(evaluate_last_parameter_hash, incoming_parameter_hash);
+ } else {
+ EXPECT_NE(evaluate_last_parameter_hash, kUninitialized);
+ EXPECT_EQ(evaluate_last_parameter_hash, incoming_parameter_hash);
+ }
+
+ // Check: Parameter matches value in in parameter blocks during prepare.
+ EXPECT_EQ(prepare_parameter_hash, incoming_parameter_hash);
+
+ // Check: jacobians are requested if they were in PrepareForEvaluation().
+ EXPECT_EQ(prepare_requested_jacobians, jacobians != NULL);
+
+ evaluate_num_calls++;
+ evaluate_last_parameter_hash = incoming_parameter_hash;
+ return true;
+ }
+
+ // Pointer to the parameter block associated with this cost function.
+ // Contents should get set by Ceres before calls to PrepareForEvaluation()
+ // and Evaluate().
+ double* user_parameter_block;
+
+ // Track state: PrepareForEvaluation().
+ //
+ // These track details from the PrepareForEvaluation() call (hence the
+ // "prepare_" prefix), which are checked for consistency in Evaluate().
+ int prepare_num_calls;
+ bool prepare_requested_jacobians;
+ bool prepare_new_evaluation_point;
+ uint64_t prepare_parameter_hash;
+
+ // Track state: Evaluate().
+ //
+ // These track details from the Evaluate() call (hence the "evaluate_"
+ // prefix), which are then checked for consistency in the calls to
+ // PrepareForEvaluation(). Mutable is reasonable for this case.
+ mutable int evaluate_num_calls;
+ mutable uint64_t evaluate_last_parameter_hash;
+};
+
+TEST(EvaluationCallback, WithTrustRegionMinimizer) {
+ double parameters[2] = {50.0, 50.0};
+ const uint64_t original_parameters_hash = Djb2Hash(parameters, 2);
+
+ WigglyBowlCostFunctionAndEvaluationCallback cost_function(parameters);
+ Problem::Options problem_options;
+ problem_options.cost_function_ownership = DO_NOT_TAKE_OWNERSHIP;
+ Problem problem(problem_options);
+ problem.AddResidualBlock(&cost_function, NULL, parameters);
+
+ Solver::Options options;
+ options.linear_solver_type = DENSE_QR;
+ options.max_num_iterations = 300; // Cost function is hard.
+ options.evaluation_callback = &cost_function;
+
+ // Run the solve. Checking is done inside the cost function / callback.
+ Solver::Summary summary;
+ Solve(options, &problem, &summary);
+
+ // Ensure that this was a hard cost function (not all steps succeed).
+ EXPECT_GT(summary.num_successful_steps, 10);
+ EXPECT_GT(summary.num_unsuccessful_steps, 10);
+
+ // Ensure PrepareForEvaluation() is called the appropriate number of times.
+ EXPECT_EQ(cost_function.prepare_num_calls,
+ // Unsuccessful steps are evaluated only once (no jacobians).
+ summary.num_unsuccessful_steps +
+ // Successful steps are evaluated twice: with and without jacobians.
+ 2 * summary.num_successful_steps
+ // Final iteration doesn't re-evaluate the jacobian.
+ // Note: This may be sensitive to tweaks to the TR algorithm; if
+ // this becomes too brittle, remove this EXPECT_EQ() entirely.
+ - 1);
+
+ // Ensure the callback calls ran a reasonable number of times.
+ EXPECT_GT(cost_function.prepare_num_calls, 0);
+ EXPECT_GT(cost_function.evaluate_num_calls, 0);
+ EXPECT_EQ(cost_function.prepare_num_calls,
+ cost_function.evaluate_num_calls);
+
+ // Ensure that the parameters did actually change.
+ EXPECT_NE(Djb2Hash(parameters, 2), original_parameters_hash);
+}
+
+void WithLineSearchMinimizerImpl(
+ LineSearchType line_search,
+ LineSearchDirectionType line_search_direction,
+ LineSearchInterpolationType line_search_interpolation) {
+ double parameters[2] = {50.0, 50.0};
+ const uint64_t original_parameters_hash = Djb2Hash(parameters, 2);
+
+ WigglyBowlCostFunctionAndEvaluationCallback cost_function(parameters);
+ Problem::Options problem_options;
+ problem_options.cost_function_ownership = DO_NOT_TAKE_OWNERSHIP;
+ Problem problem(problem_options);
+ problem.AddResidualBlock(&cost_function, NULL, parameters);
+
+ Solver::Options options;
+ options.linear_solver_type = DENSE_QR;
+ options.max_num_iterations = 300; // Cost function is hard.
+ options.minimizer_type = ceres::LINE_SEARCH;
+ options.evaluation_callback = &cost_function;
+ options.line_search_type = line_search;
+ options.line_search_direction_type = line_search_direction;
+ options.line_search_interpolation_type = line_search_interpolation;
+
+ // Run the solve. Checking is done inside the cost function / callback.
+ Solver::Summary summary;
+ Solve(options, &problem, &summary);
+
+ // Ensure the callback calls ran a reasonable number of times.
+ EXPECT_GT(summary.num_line_search_steps, 10);
+ EXPECT_GT(cost_function.prepare_num_calls, 30);
+ EXPECT_EQ(cost_function.prepare_num_calls,
+ cost_function.evaluate_num_calls);
+
+ // Ensure that the parameters did actually change.
+ EXPECT_NE(Djb2Hash(parameters, 2), original_parameters_hash);
+}
+
+// Note: These tests omit combinations of Wolfe line search with bisection.
+// Due to an implementation quirk in Wolfe line search with bisection, there
+// are calls to re-evaluate an existing point with new_point = true. That
+// causes the (overly) strict tests to break, since they check the new_point
+// preconditions in an if-and-only-if way. Strictly speaking, if new_point =
+// true, the interface does not *require* that the point has changed; only that
+// if new_point = false, the same point is reused.
+//
+// Since the strict checking is useful to verify that there aren't missed
+// optimizations, omit tests of the Wolfe with bisection cases.
+
+// Wolfe with L-BFGS.
+TEST(EvaluationCallback, WithLineSearchMinimizerWolfeLbfgsCubic) {
+ WithLineSearchMinimizerImpl(WOLFE, LBFGS, CUBIC);
+}
+TEST(EvaluationCallback, WithLineSearchMinimizerWolfeLbfgsQuadratic) {
+ WithLineSearchMinimizerImpl(WOLFE, LBFGS, QUADRATIC);
+}
+
+// Wolfe with full BFGS.
+TEST(EvaluationCallback, WithLineSearchMinimizerWolfeBfgsCubic) {
+ WithLineSearchMinimizerImpl(WOLFE, BFGS, CUBIC);
+}
+
+TEST(EvaluationCallback, WithLineSearchMinimizerWolfeBfgsQuadratic) {
+ WithLineSearchMinimizerImpl(WOLFE, BFGS, QUADRATIC);
+}
+
+// Armijo with nonlinear conjugate gradient.
+TEST(EvaluationCallback, WithLineSearchMinimizerArmijoCubic) {
+ WithLineSearchMinimizerImpl(ARMIJO, NONLINEAR_CONJUGATE_GRADIENT, CUBIC);
+}
+
+TEST(EvaluationCallback, WithLineSearchMinimizerArmijoBisection) {
+ WithLineSearchMinimizerImpl(ARMIJO, NONLINEAR_CONJUGATE_GRADIENT, BISECTION);
+}
+
+TEST(EvaluationCallback, WithLineSearchMinimizerArmijoQuadratic) {
+ WithLineSearchMinimizerImpl(ARMIJO, NONLINEAR_CONJUGATE_GRADIENT, QUADRATIC);
+}
+
+} // namespace internal
+} // namespace ceres