mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-30 00:50:37 +08:00
Update docs for 2.2.0.
Change-Id: Ib8fd3918d7bfda52212aa02c3c7573eb4dace270
This commit is contained in:
Sameer Agarwal
@@ -379,62 +379,65 @@ gives us:
|
||||
|
||||
Initial x1 = 3, x2 = -1, x3 = 0, x4 = 1
|
||||
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
|
||||
0 1.075000e+02 0.00e+00 1.55e+02 0.00e+00 0.00e+00 1.00e+04 0 4.95e-04 2.30e-03
|
||||
1 5.036190e+00 1.02e+02 2.00e+01 2.16e+00 9.53e-01 3.00e+04 1 4.39e-05 2.40e-03
|
||||
2 3.148168e-01 4.72e+00 2.50e+00 6.23e-01 9.37e-01 9.00e+04 1 9.06e-06 2.43e-03
|
||||
3 1.967760e-02 2.95e-01 3.13e-01 3.08e-01 9.37e-01 2.70e+05 1 8.11e-06 2.45e-03
|
||||
4 1.229900e-03 1.84e-02 3.91e-02 1.54e-01 9.37e-01 8.10e+05 1 6.91e-06 2.48e-03
|
||||
5 7.687123e-05 1.15e-03 4.89e-03 7.69e-02 9.37e-01 2.43e+06 1 7.87e-06 2.50e-03
|
||||
6 4.804625e-06 7.21e-05 6.11e-04 3.85e-02 9.37e-01 7.29e+06 1 5.96e-06 2.52e-03
|
||||
7 3.003028e-07 4.50e-06 7.64e-05 1.92e-02 9.37e-01 2.19e+07 1 5.96e-06 2.55e-03
|
||||
8 1.877006e-08 2.82e-07 9.54e-06 9.62e-03 9.37e-01 6.56e+07 1 5.96e-06 2.57e-03
|
||||
9 1.173223e-09 1.76e-08 1.19e-06 4.81e-03 9.37e-01 1.97e+08 1 7.87e-06 2.60e-03
|
||||
10 7.333425e-11 1.10e-09 1.49e-07 2.40e-03 9.37e-01 5.90e+08 1 6.20e-06 2.63e-03
|
||||
11 4.584044e-12 6.88e-11 1.86e-08 1.20e-03 9.37e-01 1.77e+09 1 6.91e-06 2.65e-03
|
||||
12 2.865573e-13 4.30e-12 2.33e-09 6.02e-04 9.37e-01 5.31e+09 1 5.96e-06 2.67e-03
|
||||
13 1.791438e-14 2.69e-13 2.91e-10 3.01e-04 9.37e-01 1.59e+10 1 7.15e-06 2.69e-03
|
||||
0 1.075000e+02 0.00e+00 1.55e+02 0.00e+00 0.00e+00 1.00e+04 0 2.91e-05 3.40e-04
|
||||
1 5.036190e+00 1.02e+02 2.00e+01 0.00e+00 9.53e-01 3.00e+04 1 4.98e-05 3.99e-04
|
||||
2 3.148168e-01 4.72e+00 2.50e+00 6.23e-01 9.37e-01 9.00e+04 1 2.15e-06 4.06e-04
|
||||
3 1.967760e-02 2.95e-01 3.13e-01 3.08e-01 9.37e-01 2.70e+05 1 9.54e-07 4.10e-04
|
||||
4 1.229900e-03 1.84e-02 3.91e-02 1.54e-01 9.37e-01 8.10e+05 1 1.91e-06 4.14e-04
|
||||
5 7.687123e-05 1.15e-03 4.89e-03 7.69e-02 9.37e-01 2.43e+06 1 1.91e-06 4.18e-04
|
||||
6 4.804625e-06 7.21e-05 6.11e-04 3.85e-02 9.37e-01 7.29e+06 1 1.19e-06 4.21e-04
|
||||
7 3.003028e-07 4.50e-06 7.64e-05 1.92e-02 9.37e-01 2.19e+07 1 1.91e-06 4.25e-04
|
||||
8 1.877006e-08 2.82e-07 9.54e-06 9.62e-03 9.37e-01 6.56e+07 1 9.54e-07 4.28e-04
|
||||
9 1.173223e-09 1.76e-08 1.19e-06 4.81e-03 9.37e-01 1.97e+08 1 9.54e-07 4.32e-04
|
||||
10 7.333425e-11 1.10e-09 1.49e-07 2.40e-03 9.37e-01 5.90e+08 1 9.54e-07 4.35e-04
|
||||
11 4.584044e-12 6.88e-11 1.86e-08 1.20e-03 9.37e-01 1.77e+09 1 9.54e-07 4.38e-04
|
||||
12 2.865573e-13 4.30e-12 2.33e-09 6.02e-04 9.37e-01 5.31e+09 1 2.15e-06 4.42e-04
|
||||
13 1.791438e-14 2.69e-13 2.91e-10 3.01e-04 9.37e-01 1.59e+10 1 1.91e-06 4.45e-04
|
||||
14 1.120029e-15 1.68e-14 3.64e-11 1.51e-04 9.37e-01 4.78e+10 1 2.15e-06 4.48e-04
|
||||
|
||||
Solver Summary (v 2.2.0-eigen-(3.4.0)-lapack-suitesparse-(7.1.0)-metis-(5.1.0)-acceleratesparse-eigensparse)
|
||||
|
||||
Ceres Solver v1.12.0 Solve Report
|
||||
----------------------------------
|
||||
Original Reduced
|
||||
Parameter blocks 4 4
|
||||
Parameters 4 4
|
||||
Residual blocks 4 4
|
||||
Residual 4 4
|
||||
Residuals 4 4
|
||||
|
||||
Minimizer TRUST_REGION
|
||||
|
||||
Dense linear algebra library EIGEN
|
||||
Trust region strategy LEVENBERG_MARQUARDT
|
||||
|
||||
Given Used
|
||||
Linear solver DENSE_QR DENSE_QR
|
||||
Threads 1 1
|
||||
Linear solver threads 1 1
|
||||
Linear solver ordering AUTOMATIC 4
|
||||
|
||||
Cost:
|
||||
Initial 1.075000e+02
|
||||
Final 1.791438e-14
|
||||
Final 1.120029e-15
|
||||
Change 1.075000e+02
|
||||
|
||||
Minimizer iterations 14
|
||||
Successful steps 14
|
||||
Minimizer iterations 15
|
||||
Successful steps 15
|
||||
Unsuccessful steps 0
|
||||
|
||||
Time (in seconds):
|
||||
Preprocessor 0.002
|
||||
Preprocessor 0.000311
|
||||
|
||||
Residual evaluation 0.000
|
||||
Jacobian evaluation 0.000
|
||||
Linear solver 0.000
|
||||
Minimizer 0.001
|
||||
Residual only evaluation 0.000002 (14)
|
||||
Jacobian & residual evaluation 0.000023 (15)
|
||||
Linear solver 0.000043 (14)
|
||||
Minimizer 0.000163
|
||||
|
||||
Postprocessor 0.000
|
||||
Total 0.005
|
||||
Postprocessor 0.000012
|
||||
Total 0.000486
|
||||
|
||||
Termination: CONVERGENCE (Gradient tolerance reached. Gradient max norm: 3.642190e-11 <= 1.000000e-10)
|
||||
|
||||
Final x1 = 0.000292189, x2 = -2.92189e-05, x3 = 4.79511e-05, x4 = 4.79511e-05
|
||||
Final x1 = 0.000146222, x2 = -1.46222e-05, x3 = 2.40957e-05, x4 = 2.40957e-05
|
||||
|
||||
|
||||
|
||||
|
||||
It is easy to see that the optimal solution to this problem is at
|
||||
:math:`x_1=0, x_2=0, x_3=0, x_4=0` with an objective function value of
|
||||
@@ -864,23 +867,23 @@ directory contains a number of other examples:
|
||||
measurement and the predicted measurement is:
|
||||
|
||||
.. math:: r_{ab} =
|
||||
\left[
|
||||
\begin{array}{c}
|
||||
R_a^T\left(p_b - p_a\right) - \hat{p}_{ab} \\
|
||||
\mathrm{Normalize}\left(\psi_b - \psi_a - \hat{\psi}_{ab}\right)
|
||||
\end{array}
|
||||
\right]
|
||||
\left[
|
||||
\begin{array}{c}
|
||||
R_a^T\left(p_b - p_a\right) - \hat{p}_{ab} \\
|
||||
\mathrm{Normalize}\left(\psi_b - \psi_a - \hat{\psi}_{ab}\right)
|
||||
\end{array}
|
||||
\right]
|
||||
|
||||
where the function :math:`\mathrm{Normalize}()` normalizes the angle in the range
|
||||
:math:`[-\pi,\pi)`, and :math:`R` is the rotation matrix given by
|
||||
|
||||
.. math:: R_a =
|
||||
\left[
|
||||
\begin{array}{cc}
|
||||
\cos \psi_a & -\sin \psi_a \\
|
||||
\sin \psi_a & \cos \psi_a \\
|
||||
\end{array}
|
||||
\right]
|
||||
\left[
|
||||
\begin{array}{cc}
|
||||
\cos \psi_a & -\sin \psi_a \\
|
||||
\sin \psi_a & \cos \psi_a \\
|
||||
\end{array}
|
||||
\right]
|
||||
|
||||
To finish the cost function, we need to weight the residual by the
|
||||
uncertainty of the measurement. Hence, we pre-multiply the residual by the
|
||||
|
||||
Reference in New Issue
Block a user