我正在尝试使用 Ceres 编写 BA 优化器，并希望计算优化结果的协方差。但是该程序停留在covariance.Compute(covariance_blocks, &problem)，它似乎永远不会停止计算并永远运行。我在covariance.Compute()函数内部进行了深入调试，并注意到它卡在Eigen::SparseQR求解器上。优化步骤工作正常。这是我在谷神星的完整报告。
Solver Summary (v 1.14.0-eigen-(3.3.5)-no_lapack-eigensparse-openmp-no_tbb)
Original Reduced
Parameter blocks 1335 1335
Parameters 20025 20025
Residual blocks 1780 1780
Residuals 22677 22677
Minimizer TRUST_REGION
Sparse linear algebra library EIGEN_SPARSE
Trust region strategy LEVENBERG_MARQUARDT
Given Used
Linear solver SPARSE_NORMAL_CHOLESKY SPARSE_NORMAL_CHOLESKY
Threads 1 1
Linear solver ordering AUTOMATIC 1335
Cost:
Initial 2.021075e+09
Final 5.734662e+03
Change 2.021070e+09
Minimizer iterations 25
Successful steps 25
Unsuccessful steps 0
Time (in seconds):
Preprocessor 0.000846
Residual only evaluation 0.021398 (25)
Jacobian & residual evaluation 0.699060 (25)
Linear solver 0.557998 (25)
Minimizer 1.327035
Postprocessor 0.000104
Total 1.327986
Termination: CONVERGENCE (Function tolerance reached. |cost_change|/cost: 2.763070e-10 <= 1.000000e-06)
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
0 3.179329e+07 0.00e+00 3.91e+10 0.00e+00 0.00e+00 1.00e+04 0 1.08e-01 1.20e-01
1 1.517378e+06 3.03e+07 7.50e+06 9.20e+01 1.00e+00 3.00e+04 1 8.24e-01 9.44e-01
2 1.578857e+05 1.36e+06 1.26e+06 3.50e+01 1.00e+00 9.00e+04 1 7.31e-01 1.68e+00
3 7.079412e+04 8.71e+04 2.09e+05 1.59e+01 1.00e+00 2.70e+05 1 7.24e-01 2.40e+00
4 6.395899e+04 6.84e+03 7.87e+04 9.33e+00 1.02e+00 8.10e+05 1 7.21e-01 3.12e+00
5 5.746863e+04 6.49e+03 7.13e+04 4.92e+00 1.02e+00 2.43e+06 1 7.25e-01 3.84e+00
6 4.865750e+04 8.81e+03 8.72e+04 3.41e+00 1.01e+00 7.29e+06 1 7.23e-01 4.57e+00
7 4.089894e+04 7.76e+03 9.71e+04 6.98e+00 1.02e+00 2.19e+07 1 7.22e-01 5.29e+00
8 3.531157e+04 5.59e+03 1.07e+05 1.63e+01 1.05e+00 6.56e+07 1 7.25e-01 6.02e+00
9 2.937695e+04 5.93e+03 1.88e+05 2.85e+01 1.04e+00 1.97e+08 1 7.28e-01 6.74e+00
10 2.435229e+04 5.02e+03 3.88e+05 3.19e+01 9.59e-01 5.90e+08 1 7.23e-01 7.47e+00
11 2.065070e+04 3.70e+03 2.95e+05 2.39e+01 1.04e+00 1.77e+09 1 7.22e-01 8.19e+00
12 1.886882e+04 1.78e+03 9.54e+04 1.43e+01 1.13e+00 5.31e+09 1 7.23e-01 8.91e+00
13 1.828538e+04 5.83e+02 1.20e+05 1.16e+01 1.08e+00 1.59e+10 1 7.24e-01 9.64e+00
14 1.790181e+04 3.84e+02 7.20e+04 1.79e+01 1.04e+00 4.78e+10 1 7.19e-01 1.04e+01
15 1.759101e+04 3.11e+02 1.18e+05 2.76e+01 1.03e+00 1.43e+11 1 7.20e-01 1.11e+01
16 1.739361e+04 1.97e+02 2.49e+05 3.36e+01 1.03e+00 4.30e+11 1 7.21e-01 1.18e+01
17 1.733176e+04 6.19e+01 9.70e+04 2.12e+01 1.10e+00 1.29e+12 1 7.22e-01 1.25e+01
18 1.732284e+04 8.92e+00 1.19e+04 6.60e+00 1.15e+00 3.87e+12 1 7.21e-01 1.32e+01
19 1.732184e+04 9.95e-01 3.75e+03 1.57e+00 1.26e+00 1.16e+13 1 7.29e-01 1.40e+01
20 1.732163e+04 2.10e-01 2.29e+03 9.22e-01 1.62e+00 3.49e+13 1 7.26e-01 1.47e+01
21 1.732153e+04 1.04e-01 1.51e+03 4.64e-01 1.75e+00 1.05e+14 1 7.23e-01 1.54e+01
22 1.732147e+04 6.23e-02 1.06e+03 9.74e-02 1.80e+00 3.14e+14 1 7.27e-01 1.61e+01
23 1.732143e+04 4.05e-02 7.78e+02 2.55e-02 1.82e+00 9.41e+14 1 7.24e-01 1.69e+01
24 1.732140e+04 2.78e-02 5.92e+02 1.87e-02 1.84e+00 2.82e+15 1 7.19e-01 1.76e+01
25 1.732138e+04 1.97e-02 4.56e+02 1.48e-02 1.85e+00 8.47e+15 1 7.17e-01 1.83e+01
Solver Summary (v 1.14.0-eigen-(3.3.5)-no_lapack-eigensparse-openmp-no_tbb)
Original Reduced
Parameter blocks 2552 2552
Parameters 23679 23679
Residual blocks 26098 26098
Residuals 71313 71313
Minimizer TRUST_REGION
Sparse linear algebra library EIGEN_SPARSE
Trust region strategy LEVENBERG_MARQUARDT
Given Used
Linear solver SPARSE_NORMAL_CHOLESKY SPARSE_NORMAL_CHOLESKY
Threads 1 1
Linear solver ordering AUTOMATIC 2552
Cost:
Initial 3.179329e+07
Final 1.732138e+04
Change 3.177597e+07
Minimizer iterations 26
Successful steps 26
Unsuccessful steps 0
Time (in seconds):
Preprocessor 0.012063
Residual only evaluation 0.135580 (26)
Jacobian & residual evaluation 3.066419 (26)
Linear solver 15.525091 (26)
Minimizer 18.891099
Postprocessor 0.001107
Total 18.904269
Termination: CONVERGENCE (Function tolerance reached. |cost_change|/cost: 7.930327e-07 <= 1.000000e-06)
用于设置协方差的代码为
ceres::Covariance::Options options_cov;
ceres::Covariance covariance(options_cov);
std::vector<std::pair<const double*, const double*> > covariance_blocks;
covariance_blocks.push_back(std::make_pair(cameraIntrinsic, cameraIntrinsic));
covariance_blocks.push_back(std::make_pair(delta_theta_ci.data(), delta_theta_ci.data()));
covariance_blocks.push_back(std::make_pair(cameraIntrinsic, delta_theta_ci.data()));
cameraIntrinsic和delta_theta_ci是我要计算协方差的两个数组。 谁能帮我？
好吧，我自己发现了问题。问题恰恰出在 QR 求解器Eigen_Sparse。我构建的优化问题没有错。如果我切换到另一个线性代数库，例如options_cov.sparse_linear_algebra_library_type = ceres::SparseLinearAlgebraLibraryType::SUITE_SPARSE;可以计算协方差。