426 lines
15 KiB
C++
426 lines
15 KiB
C++
// 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: keir@google.com (Keir Mierle)
|
|
// sameeragarwal@google.com (Sameer Agarwal)
|
|
//
|
|
// This tests the TrustRegionMinimizer loop using a direct Evaluator
|
|
// implementation, rather than having a test that goes through all the
|
|
// Program and Problem machinery.
|
|
|
|
#include <cmath>
|
|
#include "ceres/autodiff_cost_function.h"
|
|
#include "ceres/cost_function.h"
|
|
#include "ceres/dense_qr_solver.h"
|
|
#include "ceres/dense_sparse_matrix.h"
|
|
#include "ceres/evaluator.h"
|
|
#include "ceres/internal/port.h"
|
|
#include "ceres/linear_solver.h"
|
|
#include "ceres/minimizer.h"
|
|
#include "ceres/problem.h"
|
|
#include "ceres/trust_region_minimizer.h"
|
|
#include "ceres/trust_region_strategy.h"
|
|
#include "gtest/gtest.h"
|
|
|
|
namespace ceres {
|
|
namespace internal {
|
|
|
|
// Templated Evaluator for Powell's function. The template parameters
|
|
// indicate which of the four variables/columns of the jacobian are
|
|
// active. This is equivalent to constructing a problem and using the
|
|
// SubsetLocalParameterization. This allows us to test the support for
|
|
// the Evaluator::Plus operation besides checking for the basic
|
|
// performance of the trust region algorithm.
|
|
template <bool col1, bool col2, bool col3, bool col4>
|
|
class PowellEvaluator2 : public Evaluator {
|
|
public:
|
|
PowellEvaluator2()
|
|
: num_active_cols_(
|
|
(col1 ? 1 : 0) +
|
|
(col2 ? 1 : 0) +
|
|
(col3 ? 1 : 0) +
|
|
(col4 ? 1 : 0)) {
|
|
VLOG(1) << "Columns: "
|
|
<< col1 << " "
|
|
<< col2 << " "
|
|
<< col3 << " "
|
|
<< col4;
|
|
}
|
|
|
|
virtual ~PowellEvaluator2() {}
|
|
|
|
// Implementation of Evaluator interface.
|
|
virtual SparseMatrix* CreateJacobian() const {
|
|
CHECK(col1 || col2 || col3 || col4);
|
|
DenseSparseMatrix* dense_jacobian =
|
|
new DenseSparseMatrix(NumResiduals(), NumEffectiveParameters());
|
|
dense_jacobian->SetZero();
|
|
return dense_jacobian;
|
|
}
|
|
|
|
virtual bool Evaluate(const Evaluator::EvaluateOptions& evaluate_options,
|
|
const double* state,
|
|
double* cost,
|
|
double* residuals,
|
|
double* gradient,
|
|
SparseMatrix* jacobian) {
|
|
const double x1 = state[0];
|
|
const double x2 = state[1];
|
|
const double x3 = state[2];
|
|
const double x4 = state[3];
|
|
|
|
VLOG(1) << "State: "
|
|
<< "x1=" << x1 << ", "
|
|
<< "x2=" << x2 << ", "
|
|
<< "x3=" << x3 << ", "
|
|
<< "x4=" << x4 << ".";
|
|
|
|
const double f1 = x1 + 10.0 * x2;
|
|
const double f2 = sqrt(5.0) * (x3 - x4);
|
|
const double f3 = pow(x2 - 2.0 * x3, 2.0);
|
|
const double f4 = sqrt(10.0) * pow(x1 - x4, 2.0);
|
|
|
|
VLOG(1) << "Function: "
|
|
<< "f1=" << f1 << ", "
|
|
<< "f2=" << f2 << ", "
|
|
<< "f3=" << f3 << ", "
|
|
<< "f4=" << f4 << ".";
|
|
|
|
*cost = (f1*f1 + f2*f2 + f3*f3 + f4*f4) / 2.0;
|
|
|
|
VLOG(1) << "Cost: " << *cost;
|
|
|
|
if (residuals != NULL) {
|
|
residuals[0] = f1;
|
|
residuals[1] = f2;
|
|
residuals[2] = f3;
|
|
residuals[3] = f4;
|
|
}
|
|
|
|
if (jacobian != NULL) {
|
|
DenseSparseMatrix* dense_jacobian;
|
|
dense_jacobian = down_cast<DenseSparseMatrix*>(jacobian);
|
|
dense_jacobian->SetZero();
|
|
|
|
ColMajorMatrixRef jacobian_matrix = dense_jacobian->mutable_matrix();
|
|
CHECK_EQ(jacobian_matrix.cols(), num_active_cols_);
|
|
|
|
int column_index = 0;
|
|
if (col1) {
|
|
jacobian_matrix.col(column_index++) <<
|
|
1.0,
|
|
0.0,
|
|
0.0,
|
|
sqrt(10.0) * 2.0 * (x1 - x4) * (1.0 - x4);
|
|
}
|
|
if (col2) {
|
|
jacobian_matrix.col(column_index++) <<
|
|
10.0,
|
|
0.0,
|
|
2.0*(x2 - 2.0*x3)*(1.0 - 2.0*x3),
|
|
0.0;
|
|
}
|
|
|
|
if (col3) {
|
|
jacobian_matrix.col(column_index++) <<
|
|
0.0,
|
|
sqrt(5.0),
|
|
2.0*(x2 - 2.0*x3)*(x2 - 2.0),
|
|
0.0;
|
|
}
|
|
|
|
if (col4) {
|
|
jacobian_matrix.col(column_index++) <<
|
|
0.0,
|
|
-sqrt(5.0),
|
|
0.0,
|
|
sqrt(10.0) * 2.0 * (x1 - x4) * (x1 - 1.0);
|
|
}
|
|
VLOG(1) << "\n" << jacobian_matrix;
|
|
}
|
|
|
|
if (gradient != NULL) {
|
|
int column_index = 0;
|
|
if (col1) {
|
|
gradient[column_index++] = f1 + f4 * sqrt(10.0) * 2.0 * (x1 - x4);
|
|
}
|
|
|
|
if (col2) {
|
|
gradient[column_index++] = f1 * 10.0 + f3 * 2.0 * (x2 - 2.0 * x3);
|
|
}
|
|
|
|
if (col3) {
|
|
gradient[column_index++] =
|
|
f2 * sqrt(5.0) + f3 * (2.0 * 2.0 * (2.0 * x3 - x2));
|
|
}
|
|
|
|
if (col4) {
|
|
gradient[column_index++] =
|
|
-f2 * sqrt(5.0) + f4 * sqrt(10.0) * 2.0 * (x4 - x1);
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
virtual bool Plus(const double* state,
|
|
const double* delta,
|
|
double* state_plus_delta) const {
|
|
int delta_index = 0;
|
|
state_plus_delta[0] = (col1 ? state[0] + delta[delta_index++] : state[0]);
|
|
state_plus_delta[1] = (col2 ? state[1] + delta[delta_index++] : state[1]);
|
|
state_plus_delta[2] = (col3 ? state[2] + delta[delta_index++] : state[2]);
|
|
state_plus_delta[3] = (col4 ? state[3] + delta[delta_index++] : state[3]);
|
|
return true;
|
|
}
|
|
|
|
virtual int NumEffectiveParameters() const { return num_active_cols_; }
|
|
virtual int NumParameters() const { return 4; }
|
|
virtual int NumResiduals() const { return 4; }
|
|
|
|
private:
|
|
const int num_active_cols_;
|
|
};
|
|
|
|
// Templated function to hold a subset of the columns fixed and check
|
|
// if the solver converges to the optimal values or not.
|
|
template<bool col1, bool col2, bool col3, bool col4>
|
|
void IsTrustRegionSolveSuccessful(TrustRegionStrategyType strategy_type) {
|
|
Solver::Options solver_options;
|
|
LinearSolver::Options linear_solver_options;
|
|
DenseQRSolver linear_solver(linear_solver_options);
|
|
|
|
double parameters[4] = { 3, -1, 0, 1.0 };
|
|
|
|
// If the column is inactive, then set its value to the optimal
|
|
// value.
|
|
parameters[0] = (col1 ? parameters[0] : 0.0);
|
|
parameters[1] = (col2 ? parameters[1] : 0.0);
|
|
parameters[2] = (col3 ? parameters[2] : 0.0);
|
|
parameters[3] = (col4 ? parameters[3] : 0.0);
|
|
|
|
Minimizer::Options minimizer_options(solver_options);
|
|
minimizer_options.gradient_tolerance = 1e-26;
|
|
minimizer_options.function_tolerance = 1e-26;
|
|
minimizer_options.parameter_tolerance = 1e-26;
|
|
minimizer_options.evaluator.reset(
|
|
new PowellEvaluator2<col1, col2, col3, col4>);
|
|
minimizer_options.jacobian.reset(
|
|
minimizer_options.evaluator->CreateJacobian());
|
|
|
|
TrustRegionStrategy::Options trust_region_strategy_options;
|
|
trust_region_strategy_options.trust_region_strategy_type = strategy_type;
|
|
trust_region_strategy_options.linear_solver = &linear_solver;
|
|
trust_region_strategy_options.initial_radius = 1e4;
|
|
trust_region_strategy_options.max_radius = 1e20;
|
|
trust_region_strategy_options.min_lm_diagonal = 1e-6;
|
|
trust_region_strategy_options.max_lm_diagonal = 1e32;
|
|
minimizer_options.trust_region_strategy.reset(
|
|
TrustRegionStrategy::Create(trust_region_strategy_options));
|
|
|
|
TrustRegionMinimizer minimizer;
|
|
Solver::Summary summary;
|
|
minimizer.Minimize(minimizer_options, parameters, &summary);
|
|
|
|
// The minimum is at x1 = x2 = x3 = x4 = 0.
|
|
EXPECT_NEAR(0.0, parameters[0], 0.001);
|
|
EXPECT_NEAR(0.0, parameters[1], 0.001);
|
|
EXPECT_NEAR(0.0, parameters[2], 0.001);
|
|
EXPECT_NEAR(0.0, parameters[3], 0.001);
|
|
}
|
|
|
|
TEST(TrustRegionMinimizer, PowellsSingularFunctionUsingLevenbergMarquardt) {
|
|
// This case is excluded because this has a local minimum and does
|
|
// not find the optimum. This should not affect the correctness of
|
|
// this test since we are testing all the other 14 combinations of
|
|
// column activations.
|
|
//
|
|
// IsSolveSuccessful<true, true, false, true>();
|
|
|
|
const TrustRegionStrategyType kStrategy = LEVENBERG_MARQUARDT;
|
|
IsTrustRegionSolveSuccessful<true, true, true, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, true, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, true, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, true, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, true, false, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, false, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, false, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, false, true, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, false, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, false, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, false, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, false, false, true >(kStrategy);
|
|
}
|
|
|
|
TEST(TrustRegionMinimizer, PowellsSingularFunctionUsingDogleg) {
|
|
// The following two cases are excluded because they encounter a
|
|
// local minimum.
|
|
//
|
|
// IsTrustRegionSolveSuccessful<true, true, false, true >(kStrategy);
|
|
// IsTrustRegionSolveSuccessful<true, true, true, true >(kStrategy);
|
|
|
|
const TrustRegionStrategyType kStrategy = DOGLEG;
|
|
IsTrustRegionSolveSuccessful<true, true, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, true, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, true, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, true, false, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, false, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, false, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, false, true, true >(kStrategy);
|
|
IsTrustRegionSolveSuccessful<true, false, false, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, true, false, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, false, true, false>(kStrategy);
|
|
IsTrustRegionSolveSuccessful<false, false, false, true >(kStrategy);
|
|
}
|
|
|
|
|
|
class CurveCostFunction : public CostFunction {
|
|
public:
|
|
CurveCostFunction(int num_vertices, double target_length)
|
|
: num_vertices_(num_vertices), target_length_(target_length) {
|
|
set_num_residuals(1);
|
|
for (int i = 0; i < num_vertices_; ++i) {
|
|
mutable_parameter_block_sizes()->push_back(2);
|
|
}
|
|
}
|
|
|
|
bool Evaluate(double const* const* parameters,
|
|
double* residuals,
|
|
double** jacobians) const {
|
|
residuals[0] = target_length_;
|
|
|
|
for (int i = 0; i < num_vertices_; ++i) {
|
|
int prev = (num_vertices_ + i - 1) % num_vertices_;
|
|
double length = 0.0;
|
|
for (int dim = 0; dim < 2; dim++) {
|
|
const double diff = parameters[prev][dim] - parameters[i][dim];
|
|
length += diff * diff;
|
|
}
|
|
residuals[0] -= sqrt(length);
|
|
}
|
|
|
|
if (jacobians == NULL) {
|
|
return true;
|
|
}
|
|
|
|
for (int i = 0; i < num_vertices_; ++i) {
|
|
if (jacobians[i] != NULL) {
|
|
int prev = (num_vertices_ + i - 1) % num_vertices_;
|
|
int next = (i + 1) % num_vertices_;
|
|
|
|
double u[2], v[2];
|
|
double norm_u = 0., norm_v = 0.;
|
|
for (int dim = 0; dim < 2; dim++) {
|
|
u[dim] = parameters[i][dim] - parameters[prev][dim];
|
|
norm_u += u[dim] * u[dim];
|
|
v[dim] = parameters[next][dim] - parameters[i][dim];
|
|
norm_v += v[dim] * v[dim];
|
|
}
|
|
|
|
norm_u = sqrt(norm_u);
|
|
norm_v = sqrt(norm_v);
|
|
|
|
for (int dim = 0; dim < 2; dim++) {
|
|
jacobians[i][dim] = 0.;
|
|
|
|
if (norm_u > std::numeric_limits< double >::min()) {
|
|
jacobians[i][dim] -= u[dim] / norm_u;
|
|
}
|
|
|
|
if (norm_v > std::numeric_limits< double >::min()) {
|
|
jacobians[i][dim] += v[dim] / norm_v;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
private:
|
|
int num_vertices_;
|
|
double target_length_;
|
|
};
|
|
|
|
TEST(TrustRegionMinimizer, JacobiScalingTest) {
|
|
int N = 6;
|
|
std::vector<double*> y(N);
|
|
const double pi = 3.1415926535897932384626433;
|
|
for (int i = 0; i < N; i++) {
|
|
double theta = i * 2. * pi/ static_cast< double >(N);
|
|
y[i] = new double[2];
|
|
y[i][0] = cos(theta);
|
|
y[i][1] = sin(theta);
|
|
}
|
|
|
|
Problem problem;
|
|
problem.AddResidualBlock(new CurveCostFunction(N, 10.), NULL, y);
|
|
Solver::Options options;
|
|
options.linear_solver_type = ceres::DENSE_QR;
|
|
Solver::Summary summary;
|
|
Solve(options, &problem, &summary);
|
|
EXPECT_LE(summary.final_cost, 1e-10);
|
|
|
|
for (int i = 0; i < N; i++) {
|
|
delete []y[i];
|
|
}
|
|
}
|
|
|
|
struct ExpCostFunctor {
|
|
template <typename T>
|
|
bool operator()(const T* const x, T* residual) const {
|
|
residual[0] = T(10.0) - exp(x[0]);
|
|
return true;
|
|
}
|
|
|
|
static CostFunction* Create() {
|
|
return new AutoDiffCostFunction<ExpCostFunctor, 1, 1>(
|
|
new ExpCostFunctor);
|
|
}
|
|
};
|
|
|
|
TEST(TrustRegionMinimizer, GradientToleranceConvergenceUpdatesStep) {
|
|
double x = 5;
|
|
Problem problem;
|
|
problem.AddResidualBlock(ExpCostFunctor::Create(), NULL, &x);
|
|
problem.SetParameterLowerBound(&x, 0, 3.0);
|
|
Solver::Options options;
|
|
Solver::Summary summary;
|
|
Solve(options, &problem, &summary);
|
|
EXPECT_NEAR(3.0, x, 1e-12);
|
|
const double expected_final_cost = 0.5 * pow(10.0 - exp(3.0), 2);
|
|
EXPECT_NEAR(expected_final_cost, summary.final_cost, 1e-12);
|
|
}
|
|
|
|
} // namespace internal
|
|
} // namespace ceres
|