// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// modification, are permitted provided that the following conditions are met:
//
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//
// 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/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 double* state,
double* cost,
double* residuals,
double* /* gradient */,
SparseMatrix* jacobian) {
double x1 = state[0];
double x2 = state[1];
double x3 = state[2];
double x4 = state[3];
VLOG(1) << "State: "
<< "x1=" << x1 << ", "
<< "x2=" << x2 << ", "
<< "x3=" << x3 << ", "
<< "x4=" << x4 << ".";
double f1 = x1 + 10.0 * x2;
double f2 = sqrt(5.0) * (x3 - x4);
double f3 = pow(x2 - 2.0 * x3, 2.0);
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();
AlignedMatrixRef 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;
}
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);
PowellEvaluator2<col1, col2, col3, col4> powell_evaluator;
scoped_ptr<SparseMatrix> jacobian(powell_evaluator.CreateJacobian());
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 = &powell_evaluator;
minimizer_options.jacobian = jacobian.get();
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.lm_min_diagonal = 1e-6;
trust_region_strategy_options.lm_max_diagonal = 1e32;
scoped_ptr<TrustRegionStrategy> strategy(
TrustRegionStrategy::Create(trust_region_strategy_options));
minimizer_options.trust_region_strategy = strategy.get();
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];
}
}
} // namespace internal
} // namespace ceres