426 lines
15 KiB
C++
426 lines
15 KiB
C++
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: keir@google.com (Keir Mierle)
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// sameeragarwal@google.com (Sameer Agarwal)
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//
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// This tests the TrustRegionMinimizer loop using a direct Evaluator
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// implementation, rather than having a test that goes through all the
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// Program and Problem machinery.
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#include <cmath>
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#include "ceres/autodiff_cost_function.h"
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#include "ceres/cost_function.h"
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#include "ceres/dense_qr_solver.h"
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#include "ceres/dense_sparse_matrix.h"
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#include "ceres/evaluator.h"
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#include "ceres/internal/port.h"
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#include "ceres/linear_solver.h"
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#include "ceres/minimizer.h"
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#include "ceres/problem.h"
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#include "ceres/trust_region_minimizer.h"
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#include "ceres/trust_region_strategy.h"
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#include "gtest/gtest.h"
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namespace ceres {
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namespace internal {
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// Templated Evaluator for Powell's function. The template parameters
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// indicate which of the four variables/columns of the jacobian are
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// active. This is equivalent to constructing a problem and using the
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// SubsetLocalParameterization. This allows us to test the support for
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// the Evaluator::Plus operation besides checking for the basic
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// performance of the trust region algorithm.
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template <bool col1, bool col2, bool col3, bool col4>
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class PowellEvaluator2 : public Evaluator {
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public:
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PowellEvaluator2()
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: num_active_cols_(
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(col1 ? 1 : 0) +
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(col2 ? 1 : 0) +
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(col3 ? 1 : 0) +
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(col4 ? 1 : 0)) {
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VLOG(1) << "Columns: "
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<< col1 << " "
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<< col2 << " "
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<< col3 << " "
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<< col4;
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}
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virtual ~PowellEvaluator2() {}
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// Implementation of Evaluator interface.
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virtual SparseMatrix* CreateJacobian() const {
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CHECK(col1 || col2 || col3 || col4);
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DenseSparseMatrix* dense_jacobian =
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new DenseSparseMatrix(NumResiduals(), NumEffectiveParameters());
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dense_jacobian->SetZero();
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return dense_jacobian;
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}
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virtual bool Evaluate(const Evaluator::EvaluateOptions& evaluate_options,
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const double* state,
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double* cost,
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double* residuals,
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double* gradient,
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SparseMatrix* jacobian) {
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const double x1 = state[0];
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const double x2 = state[1];
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const double x3 = state[2];
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const double x4 = state[3];
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VLOG(1) << "State: "
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<< "x1=" << x1 << ", "
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<< "x2=" << x2 << ", "
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<< "x3=" << x3 << ", "
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<< "x4=" << x4 << ".";
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const double f1 = x1 + 10.0 * x2;
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const double f2 = sqrt(5.0) * (x3 - x4);
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const double f3 = pow(x2 - 2.0 * x3, 2.0);
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const double f4 = sqrt(10.0) * pow(x1 - x4, 2.0);
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VLOG(1) << "Function: "
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<< "f1=" << f1 << ", "
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<< "f2=" << f2 << ", "
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<< "f3=" << f3 << ", "
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<< "f4=" << f4 << ".";
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*cost = (f1*f1 + f2*f2 + f3*f3 + f4*f4) / 2.0;
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VLOG(1) << "Cost: " << *cost;
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if (residuals != NULL) {
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residuals[0] = f1;
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residuals[1] = f2;
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residuals[2] = f3;
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residuals[3] = f4;
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}
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if (jacobian != NULL) {
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DenseSparseMatrix* dense_jacobian;
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dense_jacobian = down_cast<DenseSparseMatrix*>(jacobian);
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dense_jacobian->SetZero();
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ColMajorMatrixRef jacobian_matrix = dense_jacobian->mutable_matrix();
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CHECK_EQ(jacobian_matrix.cols(), num_active_cols_);
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int column_index = 0;
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if (col1) {
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jacobian_matrix.col(column_index++) <<
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1.0,
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0.0,
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0.0,
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sqrt(10.0) * 2.0 * (x1 - x4) * (1.0 - x4);
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}
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if (col2) {
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jacobian_matrix.col(column_index++) <<
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10.0,
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0.0,
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2.0*(x2 - 2.0*x3)*(1.0 - 2.0*x3),
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0.0;
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}
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if (col3) {
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jacobian_matrix.col(column_index++) <<
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0.0,
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sqrt(5.0),
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2.0*(x2 - 2.0*x3)*(x2 - 2.0),
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0.0;
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}
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if (col4) {
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jacobian_matrix.col(column_index++) <<
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0.0,
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-sqrt(5.0),
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0.0,
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sqrt(10.0) * 2.0 * (x1 - x4) * (x1 - 1.0);
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}
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VLOG(1) << "\n" << jacobian_matrix;
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}
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if (gradient != NULL) {
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int column_index = 0;
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if (col1) {
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gradient[column_index++] = f1 + f4 * sqrt(10.0) * 2.0 * (x1 - x4);
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}
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if (col2) {
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gradient[column_index++] = f1 * 10.0 + f3 * 2.0 * (x2 - 2.0 * x3);
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}
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if (col3) {
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gradient[column_index++] =
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f2 * sqrt(5.0) + f3 * (2.0 * 2.0 * (2.0 * x3 - x2));
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}
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if (col4) {
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gradient[column_index++] =
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-f2 * sqrt(5.0) + f4 * sqrt(10.0) * 2.0 * (x4 - x1);
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}
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}
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return true;
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}
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virtual bool Plus(const double* state,
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const double* delta,
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double* state_plus_delta) const {
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int delta_index = 0;
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state_plus_delta[0] = (col1 ? state[0] + delta[delta_index++] : state[0]);
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state_plus_delta[1] = (col2 ? state[1] + delta[delta_index++] : state[1]);
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state_plus_delta[2] = (col3 ? state[2] + delta[delta_index++] : state[2]);
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state_plus_delta[3] = (col4 ? state[3] + delta[delta_index++] : state[3]);
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return true;
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}
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virtual int NumEffectiveParameters() const { return num_active_cols_; }
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virtual int NumParameters() const { return 4; }
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virtual int NumResiduals() const { return 4; }
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private:
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const int num_active_cols_;
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};
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// Templated function to hold a subset of the columns fixed and check
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// if the solver converges to the optimal values or not.
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template<bool col1, bool col2, bool col3, bool col4>
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void IsTrustRegionSolveSuccessful(TrustRegionStrategyType strategy_type) {
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Solver::Options solver_options;
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LinearSolver::Options linear_solver_options;
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DenseQRSolver linear_solver(linear_solver_options);
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double parameters[4] = { 3, -1, 0, 1.0 };
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// If the column is inactive, then set its value to the optimal
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// value.
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parameters[0] = (col1 ? parameters[0] : 0.0);
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parameters[1] = (col2 ? parameters[1] : 0.0);
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parameters[2] = (col3 ? parameters[2] : 0.0);
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parameters[3] = (col4 ? parameters[3] : 0.0);
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Minimizer::Options minimizer_options(solver_options);
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minimizer_options.gradient_tolerance = 1e-26;
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minimizer_options.function_tolerance = 1e-26;
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minimizer_options.parameter_tolerance = 1e-26;
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minimizer_options.evaluator.reset(
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new PowellEvaluator2<col1, col2, col3, col4>);
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minimizer_options.jacobian.reset(
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minimizer_options.evaluator->CreateJacobian());
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TrustRegionStrategy::Options trust_region_strategy_options;
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trust_region_strategy_options.trust_region_strategy_type = strategy_type;
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trust_region_strategy_options.linear_solver = &linear_solver;
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trust_region_strategy_options.initial_radius = 1e4;
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trust_region_strategy_options.max_radius = 1e20;
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trust_region_strategy_options.min_lm_diagonal = 1e-6;
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trust_region_strategy_options.max_lm_diagonal = 1e32;
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minimizer_options.trust_region_strategy.reset(
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TrustRegionStrategy::Create(trust_region_strategy_options));
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TrustRegionMinimizer minimizer;
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Solver::Summary summary;
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minimizer.Minimize(minimizer_options, parameters, &summary);
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// The minimum is at x1 = x2 = x3 = x4 = 0.
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EXPECT_NEAR(0.0, parameters[0], 0.001);
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EXPECT_NEAR(0.0, parameters[1], 0.001);
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EXPECT_NEAR(0.0, parameters[2], 0.001);
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EXPECT_NEAR(0.0, parameters[3], 0.001);
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}
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TEST(TrustRegionMinimizer, PowellsSingularFunctionUsingLevenbergMarquardt) {
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// This case is excluded because this has a local minimum and does
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// not find the optimum. This should not affect the correctness of
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// this test since we are testing all the other 14 combinations of
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// column activations.
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//
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// IsSolveSuccessful<true, true, false, true>();
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const TrustRegionStrategyType kStrategy = LEVENBERG_MARQUARDT;
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IsTrustRegionSolveSuccessful<true, true, true, true >(kStrategy);
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IsTrustRegionSolveSuccessful<true, true, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, true, true >(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, true, true >(kStrategy);
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IsTrustRegionSolveSuccessful<true, true, false, false>(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, false, true >(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, false, true >(kStrategy);
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IsTrustRegionSolveSuccessful<false, false, true, true >(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, false, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, false, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, false, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, false, false, true >(kStrategy);
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}
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TEST(TrustRegionMinimizer, PowellsSingularFunctionUsingDogleg) {
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// The following two cases are excluded because they encounter a
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// local minimum.
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//
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// IsTrustRegionSolveSuccessful<true, true, false, true >(kStrategy);
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// IsTrustRegionSolveSuccessful<true, true, true, true >(kStrategy);
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const TrustRegionStrategyType kStrategy = DOGLEG;
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IsTrustRegionSolveSuccessful<true, true, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, true, true >(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, true, true >(kStrategy);
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IsTrustRegionSolveSuccessful<true, true, false, false>(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, false, true >(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, false, true >(kStrategy);
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IsTrustRegionSolveSuccessful<false, false, true, true >(kStrategy);
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IsTrustRegionSolveSuccessful<true, false, false, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, true, false, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, false, true, false>(kStrategy);
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IsTrustRegionSolveSuccessful<false, false, false, true >(kStrategy);
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}
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class CurveCostFunction : public CostFunction {
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public:
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CurveCostFunction(int num_vertices, double target_length)
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: num_vertices_(num_vertices), target_length_(target_length) {
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set_num_residuals(1);
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for (int i = 0; i < num_vertices_; ++i) {
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mutable_parameter_block_sizes()->push_back(2);
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}
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}
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bool Evaluate(double const* const* parameters,
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double* residuals,
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double** jacobians) const {
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residuals[0] = target_length_;
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for (int i = 0; i < num_vertices_; ++i) {
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int prev = (num_vertices_ + i - 1) % num_vertices_;
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double length = 0.0;
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for (int dim = 0; dim < 2; dim++) {
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const double diff = parameters[prev][dim] - parameters[i][dim];
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length += diff * diff;
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}
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residuals[0] -= sqrt(length);
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}
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if (jacobians == NULL) {
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return true;
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}
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for (int i = 0; i < num_vertices_; ++i) {
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if (jacobians[i] != NULL) {
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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
|