ceres-solver / ceres-solver / 863db948f381f74aea58a08a4b559facaf165ef0 / . / docs / source / solving_faqs.rst

.. _chapter-solving_faqs: | |

.. default-domain:: cpp | |

.. cpp:namespace:: ceres | |

======= | |

Solving | |

======= | |

#. How do I evaluate the Jacobian for a solved problem? | |

Using :func:`Problem::Evaluate`. | |

#. How do I choose the right linear solver? | |

When using the ``TRUST_REGION`` minimizer, the choice of linear | |

solver is an important decision. It affects solution quality and | |

runtime. Here is a simple way to reason about it. | |

1. For small (a few hundred parameters) or dense problems use | |

``DENSE_QR``. | |

2. For general sparse problems (i.e., the Jacobian matrix has a | |

substantial number of zeros) use | |

``SPARSE_NORMAL_CHOLESKY``. | |

3. For bundle adjustment problems with up to a hundred or so | |

cameras, use ``DENSE_SCHUR``. | |

4. For larger bundle adjustment problems with sparse Schur | |

Complement/Reduced camera matrices use ``SPARSE_SCHUR``. | |

If you do not have access to these libraries for whatever | |

reason, ``ITERATIVE_SCHUR`` with ``SCHUR_JACOBI`` is an | |

excellent alternative. | |

5. For large bundle adjustment problems (a few thousand cameras or | |

more) use the ``ITERATIVE_SCHUR`` solver. There are a number of | |

preconditioner choices here. ``SCHUR_JACOBI`` offers an | |

excellent balance of speed and accuracy. This is also the | |

recommended option if you are solving medium sized problems for | |

which ``DENSE_SCHUR`` is too slow but ``SuiteSparse`` is not | |

available. | |

.. NOTE:: | |

If you are solving small to medium sized problems, consider | |

setting ``Solver::Options::use_explicit_schur_complement`` to | |

``true``, it can result in a substantial performance boost. | |

If you are not satisfied with ``SCHUR_JACOBI``'s performance try | |

``CLUSTER_JACOBI`` and ``CLUSTER_TRIDIAGONAL`` in that | |

order. They require that you have ``SuiteSparse`` | |

installed. Both of these preconditioners use a clustering | |

algorithm. Use ``SINGLE_LINKAGE`` before ``CANONICAL_VIEWS``. | |

#. Use :func:`Solver::Summary::FullReport` to diagnose performance problems. | |

When diagnosing Ceres performance issues - runtime and convergence, | |

the first place to start is by looking at the output of | |

``Solver::Summary::FullReport``. Here is an example | |

.. code-block:: bash | |

./bin/bundle_adjuster --input ../data/problem-16-22106-pre.txt | |

iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time | |

0 4.185660e+06 0.00e+00 2.16e+07 0.00e+00 0.00e+00 1.00e+04 0 7.50e-02 3.58e-01 | |

1 1.980525e+05 3.99e+06 5.34e+06 2.40e+03 9.60e-01 3.00e+04 1 1.84e-01 5.42e-01 | |

2 5.086543e+04 1.47e+05 2.11e+06 1.01e+03 8.22e-01 4.09e+04 1 1.53e-01 6.95e-01 | |

3 1.859667e+04 3.23e+04 2.87e+05 2.64e+02 9.85e-01 1.23e+05 1 1.71e-01 8.66e-01 | |

4 1.803857e+04 5.58e+02 2.69e+04 8.66e+01 9.93e-01 3.69e+05 1 1.61e-01 1.03e+00 | |

5 1.803391e+04 4.66e+00 3.11e+02 1.02e+01 1.00e+00 1.11e+06 1 1.49e-01 1.18e+00 | |

Ceres Solver v1.12.0 Solve Report | |

---------------------------------- | |

Original Reduced | |

Parameter blocks 22122 22122 | |

Parameters 66462 66462 | |

Residual blocks 83718 83718 | |

Residual 167436 167436 | |

Minimizer TRUST_REGION | |

Sparse linear algebra library SUITE_SPARSE | |

Trust region strategy LEVENBERG_MARQUARDT | |

Given Used | |

Linear solver SPARSE_SCHUR SPARSE_SCHUR | |

Threads 1 1 | |

Linear solver threads 1 1 | |

Linear solver ordering AUTOMATIC 22106, 16 | |

Cost: | |

Initial 4.185660e+06 | |

Final 1.803391e+04 | |

Change 4.167626e+06 | |

Minimizer iterations 5 | |

Successful steps 5 | |

Unsuccessful steps 0 | |

Time (in seconds): | |

Preprocessor 0.283 | |

Residual evaluation 0.061 | |

Jacobian evaluation 0.361 | |

Linear solver 0.382 | |

Minimizer 0.895 | |

Postprocessor 0.002 | |

Total 1.220 | |

Termination: NO_CONVERGENCE (Maximum number of iterations reached.) | |

Let us focus on run-time performance. The relevant lines to look at | |

are | |

.. code-block:: bash | |

Time (in seconds): | |

Preprocessor 0.283 | |

Residual evaluation 0.061 | |

Jacobian evaluation 0.361 | |

Linear solver 0.382 | |

Minimizer 0.895 | |

Postprocessor 0.002 | |

Total 1.220 | |

Which tell us that of the total 1.2 seconds, about .3 seconds was | |

spent in the linear solver and the rest was mostly spent in | |

preprocessing and jacobian evaluation. | |

The preprocessing seems particularly expensive. Looking back at the | |

report, we observe | |

.. code-block:: bash | |

Linear solver ordering AUTOMATIC 22106, 16 | |

Which indicates that we are using automatic ordering for the | |

``SPARSE_SCHUR`` solver. This can be expensive at times. A straight | |

forward way to deal with this is to give the ordering manually. For | |

``bundle_adjuster`` this can be done by passing the flag | |

``-ordering=user``. Doing so and looking at the timing block of the | |

full report gives us | |

.. code-block:: bash | |

Time (in seconds): | |

Preprocessor 0.051 | |

Residual evaluation 0.053 | |

Jacobian evaluation 0.344 | |

Linear solver 0.372 | |

Minimizer 0.854 | |

Postprocessor 0.002 | |

Total 0.935 | |

The preprocessor time has gone down by more than 5.5x!. |