| // 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: richie.stebbing@gmail.com (Richard Stebbing) |
| // |
| // This fits points randomly distributed on an ellipse with an approximate |
| // line segment contour. This is done by jointly optimizing the control points |
| // of the line segment contour along with the preimage positions for the data |
| // points. The purpose of this example is to show an example use case for |
| // dynamic_sparsity, and how it can benefit problems which are numerically |
| // dense but dynamically sparse. |
| |
| #include <cmath> |
| #include <vector> |
| #include "ceres/ceres.h" |
| #include "glog/logging.h" |
| |
| // Data generated with the following Python code. |
| // import numpy as np |
| // np.random.seed(1337) |
| // t = np.linspace(0.0, 2.0 * np.pi, 212, endpoint=False) |
| // t += 2.0 * np.pi * 0.01 * np.random.randn(t.size) |
| // theta = np.deg2rad(15) |
| // a, b = np.cos(theta), np.sin(theta) |
| // R = np.array([[a, -b], |
| // [b, a]]) |
| // Y = np.dot(np.c_[4.0 * np.cos(t), np.sin(t)], R.T) |
| |
| const int kYRows = 212; |
| const int kYCols = 2; |
| const double kYData[kYRows * kYCols] = { |
| +3.871364e+00, +9.916027e-01, |
| +3.864003e+00, +1.034148e+00, |
| +3.850651e+00, +1.072202e+00, |
| +3.868350e+00, +1.014408e+00, |
| +3.796381e+00, +1.153021e+00, |
| +3.857138e+00, +1.056102e+00, |
| +3.787532e+00, +1.162215e+00, |
| +3.704477e+00, +1.227272e+00, |
| +3.564711e+00, +1.294959e+00, |
| +3.754363e+00, +1.191948e+00, |
| +3.482098e+00, +1.322725e+00, |
| +3.602777e+00, +1.279658e+00, |
| +3.585433e+00, +1.286858e+00, |
| +3.347505e+00, +1.356415e+00, |
| +3.220855e+00, +1.378914e+00, |
| +3.558808e+00, +1.297174e+00, |
| +3.403618e+00, +1.343809e+00, |
| +3.179828e+00, +1.384721e+00, |
| +3.054789e+00, +1.398759e+00, |
| +3.294153e+00, +1.366808e+00, |
| +3.247312e+00, +1.374813e+00, |
| +2.988547e+00, +1.404247e+00, |
| +3.114508e+00, +1.392698e+00, |
| +2.899226e+00, +1.409802e+00, |
| +2.533256e+00, +1.414778e+00, |
| +2.654773e+00, +1.415909e+00, |
| +2.565100e+00, +1.415313e+00, |
| +2.976456e+00, +1.405118e+00, |
| +2.484200e+00, +1.413640e+00, |
| +2.324751e+00, +1.407476e+00, |
| +1.930468e+00, +1.378221e+00, |
| +2.329017e+00, +1.407688e+00, |
| +1.760640e+00, +1.360319e+00, |
| +2.147375e+00, +1.396603e+00, |
| +1.741989e+00, +1.358178e+00, |
| +1.743859e+00, +1.358394e+00, |
| +1.557372e+00, +1.335208e+00, |
| +1.280551e+00, +1.295087e+00, |
| +1.429880e+00, +1.317546e+00, |
| +1.213485e+00, +1.284400e+00, |
| +9.168172e-01, +1.232870e+00, |
| +1.311141e+00, +1.299839e+00, |
| +1.231969e+00, +1.287382e+00, |
| +7.453773e-01, +1.200049e+00, |
| +6.151587e-01, +1.173683e+00, |
| +5.935666e-01, +1.169193e+00, |
| +2.538707e-01, +1.094227e+00, |
| +6.806136e-01, +1.187089e+00, |
| +2.805447e-01, +1.100405e+00, |
| +6.184807e-01, +1.174371e+00, |
| +1.170550e-01, +1.061762e+00, |
| +2.890507e-01, +1.102365e+00, |
| +3.834234e-01, +1.123772e+00, |
| +3.980161e-04, +1.033061e+00, |
| -3.651680e-01, +9.370367e-01, |
| -8.386351e-01, +7.987201e-01, |
| -8.105704e-01, +8.073702e-01, |
| -8.735139e-01, +7.878886e-01, |
| -9.913836e-01, +7.506100e-01, |
| -8.784011e-01, +7.863636e-01, |
| -1.181440e+00, +6.882566e-01, |
| -1.229556e+00, +6.720191e-01, |
| -1.035839e+00, +7.362765e-01, |
| -8.031520e-01, +8.096470e-01, |
| -1.539136e+00, +5.629549e-01, |
| -1.755423e+00, +4.817306e-01, |
| -1.337589e+00, +6.348763e-01, |
| -1.836966e+00, +4.499485e-01, |
| -1.913367e+00, +4.195617e-01, |
| -2.126467e+00, +3.314900e-01, |
| -1.927625e+00, +4.138238e-01, |
| -2.339862e+00, +2.379074e-01, |
| -1.881736e+00, +4.322152e-01, |
| -2.116753e+00, +3.356163e-01, |
| -2.255733e+00, +2.754930e-01, |
| -2.555834e+00, +1.368473e-01, |
| -2.770277e+00, +2.895711e-02, |
| -2.563376e+00, +1.331890e-01, |
| -2.826715e+00, -9.000818e-04, |
| -2.978191e+00, -8.457804e-02, |
| -3.115855e+00, -1.658786e-01, |
| -2.982049e+00, -8.678322e-02, |
| -3.307892e+00, -2.902083e-01, |
| -3.038346e+00, -1.194222e-01, |
| -3.190057e+00, -2.122060e-01, |
| -3.279086e+00, -2.705777e-01, |
| -3.322028e+00, -2.999889e-01, |
| -3.122576e+00, -1.699965e-01, |
| -3.551973e+00, -4.768674e-01, |
| -3.581866e+00, -5.032175e-01, |
| -3.497799e+00, -4.315203e-01, |
| -3.565384e+00, -4.885602e-01, |
| -3.699493e+00, -6.199815e-01, |
| -3.585166e+00, -5.061925e-01, |
| -3.758914e+00, -6.918275e-01, |
| -3.741104e+00, -6.689131e-01, |
| -3.688331e+00, -6.077239e-01, |
| -3.810425e+00, -7.689015e-01, |
| -3.791829e+00, -7.386911e-01, |
| -3.789951e+00, -7.358189e-01, |
| -3.823100e+00, -7.918398e-01, |
| -3.857021e+00, -8.727074e-01, |
| -3.858250e+00, -8.767645e-01, |
| -3.872100e+00, -9.563174e-01, |
| -3.864397e+00, -1.032630e+00, |
| -3.846230e+00, -1.081669e+00, |
| -3.834799e+00, -1.102536e+00, |
| -3.866684e+00, -1.022901e+00, |
| -3.808643e+00, -1.139084e+00, |
| -3.868840e+00, -1.011569e+00, |
| -3.791071e+00, -1.158615e+00, |
| -3.797999e+00, -1.151267e+00, |
| -3.696278e+00, -1.232314e+00, |
| -3.779007e+00, -1.170504e+00, |
| -3.622855e+00, -1.270793e+00, |
| -3.647249e+00, -1.259166e+00, |
| -3.655412e+00, -1.255042e+00, |
| -3.573218e+00, -1.291696e+00, |
| -3.638019e+00, -1.263684e+00, |
| -3.498409e+00, -1.317750e+00, |
| -3.304143e+00, -1.364970e+00, |
| -3.183001e+00, -1.384295e+00, |
| -3.202456e+00, -1.381599e+00, |
| -3.244063e+00, -1.375332e+00, |
| -3.233308e+00, -1.377019e+00, |
| -3.060112e+00, -1.398264e+00, |
| -3.078187e+00, -1.396517e+00, |
| -2.689594e+00, -1.415761e+00, |
| -2.947662e+00, -1.407039e+00, |
| -2.854490e+00, -1.411860e+00, |
| -2.660499e+00, -1.415900e+00, |
| -2.875955e+00, -1.410930e+00, |
| -2.675385e+00, -1.415848e+00, |
| -2.813155e+00, -1.413363e+00, |
| -2.417673e+00, -1.411512e+00, |
| -2.725461e+00, -1.415373e+00, |
| -2.148334e+00, -1.396672e+00, |
| -2.108972e+00, -1.393738e+00, |
| -2.029905e+00, -1.387302e+00, |
| -2.046214e+00, -1.388687e+00, |
| -2.057402e+00, -1.389621e+00, |
| -1.650250e+00, -1.347160e+00, |
| -1.806764e+00, -1.365469e+00, |
| -1.206973e+00, -1.283343e+00, |
| -8.029259e-01, -1.211308e+00, |
| -1.229551e+00, -1.286993e+00, |
| -1.101507e+00, -1.265754e+00, |
| -9.110645e-01, -1.231804e+00, |
| -1.110046e+00, -1.267211e+00, |
| -8.465274e-01, -1.219677e+00, |
| -7.594163e-01, -1.202818e+00, |
| -8.023823e-01, -1.211203e+00, |
| -3.732519e-01, -1.121494e+00, |
| -1.918373e-01, -1.079668e+00, |
| -4.671988e-01, -1.142253e+00, |
| -4.033645e-01, -1.128215e+00, |
| -1.920740e-01, -1.079724e+00, |
| -3.022157e-01, -1.105389e+00, |
| -1.652831e-01, -1.073354e+00, |
| +4.671625e-01, -9.085886e-01, |
| +5.940178e-01, -8.721832e-01, |
| +3.147557e-01, -9.508290e-01, |
| +6.383631e-01, -8.591867e-01, |
| +9.888923e-01, -7.514088e-01, |
| +7.076339e-01, -8.386023e-01, |
| +1.326682e+00, -6.386698e-01, |
| +1.149834e+00, -6.988221e-01, |
| +1.257742e+00, -6.624207e-01, |
| +1.492352e+00, -5.799632e-01, |
| +1.595574e+00, -5.421766e-01, |
| +1.240173e+00, -6.684113e-01, |
| +1.706612e+00, -5.004442e-01, |
| +1.873984e+00, -4.353002e-01, |
| +1.985633e+00, -3.902561e-01, |
| +1.722880e+00, -4.942329e-01, |
| +2.095182e+00, -3.447402e-01, |
| +2.018118e+00, -3.768991e-01, |
| +2.422702e+00, -1.999563e-01, |
| +2.370611e+00, -2.239326e-01, |
| +2.152154e+00, -3.205250e-01, |
| +2.525121e+00, -1.516499e-01, |
| +2.422116e+00, -2.002280e-01, |
| +2.842806e+00, +9.536372e-03, |
| +3.030128e+00, +1.146027e-01, |
| +2.888424e+00, +3.433444e-02, |
| +2.991609e+00, +9.226409e-02, |
| +2.924807e+00, +5.445844e-02, |
| +3.007772e+00, +1.015875e-01, |
| +2.781973e+00, -2.282382e-02, |
| +3.164737e+00, +1.961781e-01, |
| +3.237671e+00, +2.430139e-01, |
| +3.046123e+00, +1.240014e-01, |
| +3.414834e+00, +3.669060e-01, |
| +3.436591e+00, +3.833600e-01, |
| +3.626207e+00, +5.444311e-01, |
| +3.223325e+00, +2.336361e-01, |
| +3.511963e+00, +4.431060e-01, |
| +3.698380e+00, +6.187442e-01, |
| +3.670244e+00, +5.884943e-01, |
| +3.558833e+00, +4.828230e-01, |
| +3.661807e+00, +5.797689e-01, |
| +3.767261e+00, +7.030893e-01, |
| +3.801065e+00, +7.532650e-01, |
| +3.828523e+00, +8.024454e-01, |
| +3.840719e+00, +8.287032e-01, |
| +3.848748e+00, +8.485921e-01, |
| +3.865801e+00, +9.066551e-01, |
| +3.870983e+00, +9.404873e-01, |
| +3.870263e+00, +1.001884e+00, |
| +3.864462e+00, +1.032374e+00, |
| +3.870542e+00, +9.996121e-01, |
| +3.865424e+00, +1.028474e+00 |
| }; |
| ceres::ConstMatrixRef kY(kYData, kYRows, kYCols); |
| |
| class PointToLineSegmentContourCostFunction : public ceres::CostFunction { |
| public: |
| PointToLineSegmentContourCostFunction(const int num_segments, |
| const Eigen::Vector2d& y) |
| : num_segments_(num_segments), y_(y) { |
| // The first parameter is the preimage position. |
| mutable_parameter_block_sizes()->push_back(1); |
| // The next parameters are the control points for the line segment contour. |
| for (int i = 0; i < num_segments_; ++i) { |
| mutable_parameter_block_sizes()->push_back(2); |
| } |
| set_num_residuals(2); |
| } |
| |
| virtual bool Evaluate(const double* const* x, |
| double* residuals, |
| double** jacobians) const { |
| // Convert the preimage position `t` into a segment index `i0` and the |
| // line segment interpolation parameter `u`. `i1` is the index of the next |
| // control point. |
| const double t = ModuloNumSegments(*x[0]); |
| CHECK_GE(t, 0.0); |
| CHECK_LT(t, num_segments_); |
| const int i0 = floor(t), i1 = (i0 + 1) % num_segments_; |
| const double u = t - i0; |
| |
| // Linearly interpolate between control points `i0` and `i1`. |
| residuals[0] = y_[0] - ((1.0 - u) * x[1 + i0][0] + u * x[1 + i1][0]); |
| residuals[1] = y_[1] - ((1.0 - u) * x[1 + i0][1] + u * x[1 + i1][1]); |
| |
| if (jacobians == NULL) { |
| return true; |
| } |
| |
| if (jacobians[0] != NULL) { |
| jacobians[0][0] = x[1 + i0][0] - x[1 + i1][0]; |
| jacobians[0][1] = x[1 + i0][1] - x[1 + i1][1]; |
| } |
| for (int i = 0; i < num_segments_; ++i) { |
| if (jacobians[i + 1] != NULL) { |
| ceres::MatrixRef(jacobians[i + 1], 2, 2).setZero(); |
| if (i == i0) { |
| jacobians[i + 1][0] = -(1.0 - u); |
| jacobians[i + 1][3] = -(1.0 - u); |
| } else if (i == i1) { |
| jacobians[i + 1][0] = -u; |
| jacobians[i + 1][3] = -u; |
| } |
| } |
| } |
| return true; |
| } |
| |
| static ceres::CostFunction* Create(const int num_segments, |
| const Eigen::Vector2d& y) { |
| return new PointToLineSegmentContourCostFunction(num_segments, y); |
| } |
| |
| private: |
| inline double ModuloNumSegments(const double t) const { |
| return t - num_segments_ * floor(t / num_segments_); |
| } |
| |
| const int num_segments_; |
| const Eigen::Vector2d y_; |
| }; |
| |
| class EuclideanDistanceFunctor { |
| public: |
| explicit EuclideanDistanceFunctor(const double& sqrt_weight) |
| : sqrt_weight_(sqrt_weight) {} |
| |
| template <typename T> |
| bool operator()(const T* x0, const T* x1, T* residuals) const { |
| residuals[0] = sqrt_weight_ * (x0[0] - x1[0]); |
| residuals[1] = sqrt_weight_ * (x0[1] - x1[1]); |
| return true; |
| } |
| |
| static ceres::CostFunction* Create(const double sqrt_weight) { |
| return new ceres::AutoDiffCostFunction<EuclideanDistanceFunctor, 2, 2, 2>( |
| new EuclideanDistanceFunctor(sqrt_weight)); |
| } |
| |
| private: |
| const double sqrt_weight_; |
| }; |
| |
| static bool SolveWithFullReport(ceres::Solver::Options options, |
| ceres::Problem* problem, |
| bool dynamic_sparsity) { |
| options.dynamic_sparsity = dynamic_sparsity; |
| |
| ceres::Solver::Summary summary; |
| ceres::Solve(options, problem, &summary); |
| |
| std::cout << "####################" << std::endl; |
| std::cout << "dynamic_sparsity = " << dynamic_sparsity << std::endl; |
| std::cout << "####################" << std::endl; |
| std::cout << summary.FullReport() << std::endl; |
| |
| return summary.termination_type == ceres::CONVERGENCE; |
| } |
| |
| int main(int argc, char** argv) { |
| google::InitGoogleLogging(argv[0]); |
| |
| // Problem configuration. |
| const int num_segments = 151; |
| const double regularization_weight = 1e-2; |
| |
| // Eigen::MatrixXd is column major so we define our own MatrixXd which is |
| // row major. Eigen::VectorXd can be used directly. |
| typedef Eigen::Matrix<double, |
| Eigen::Dynamic, Eigen::Dynamic, |
| Eigen::RowMajor> MatrixXd; |
| using Eigen::VectorXd; |
| |
| // `X` is the matrix of control points which make up the contour of line |
| // segments. The number of control points is equal to the number of line |
| // segments because the contour is closed. |
| // |
| // Initialize `X` to points on the unit circle. |
| VectorXd w(num_segments + 1); |
| w.setLinSpaced(num_segments + 1, 0.0, 2.0 * M_PI); |
| w.conservativeResize(num_segments); |
| MatrixXd X(num_segments, 2); |
| X.col(0) = w.array().cos(); |
| X.col(1) = w.array().sin(); |
| |
| // Each data point has an associated preimage position on the line segment |
| // contour. For each data point we initialize the preimage positions to |
| // the index of the closest control point. |
| const int num_observations = kY.rows(); |
| VectorXd t(num_observations); |
| for (int i = 0; i < num_observations; ++i) { |
| (X.rowwise() - kY.row(i)).rowwise().squaredNorm().minCoeff(&t[i]); |
| } |
| |
| ceres::Problem problem; |
| |
| // For each data point add a residual which measures its distance to its |
| // corresponding position on the line segment contour. |
| std::vector<double*> parameter_blocks(1 + num_segments); |
| parameter_blocks[0] = NULL; |
| for (int i = 0; i < num_segments; ++i) { |
| parameter_blocks[i + 1] = X.data() + 2 * i; |
| } |
| for (int i = 0; i < num_observations; ++i) { |
| parameter_blocks[0] = &t[i]; |
| problem.AddResidualBlock( |
| PointToLineSegmentContourCostFunction::Create(num_segments, kY.row(i)), |
| NULL, |
| parameter_blocks); |
| } |
| |
| // Add regularization to minimize the length of the line segment contour. |
| for (int i = 0; i < num_segments; ++i) { |
| problem.AddResidualBlock( |
| EuclideanDistanceFunctor::Create(sqrt(regularization_weight)), |
| NULL, |
| X.data() + 2 * i, |
| X.data() + 2 * ((i + 1) % num_segments)); |
| } |
| |
| ceres::Solver::Options options; |
| options.max_num_iterations = 100; |
| options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY; |
| |
| // First, solve `X` and `t` jointly with dynamic_sparsity = true. |
| MatrixXd X0 = X; |
| VectorXd t0 = t; |
| CHECK(SolveWithFullReport(options, &problem, true)); |
| |
| // Second, solve with dynamic_sparsity = false. |
| X = X0; |
| t = t0; |
| CHECK(SolveWithFullReport(options, &problem, false)); |
| |
| return 0; |
| } |
