It seems that Eigen's LLT factorization is broken on ARM.
This patch enables the use of LDLT factorization instead of LLT
factorization. The switch is controlled at compile time using a
preprocessor define - CERES_USE_EIGEN_LDLT.
By default we continue to use LLT factorization though.
To make the switching easier without introducing the Cholesky factorization
based inversion and linear system solve routines have been abstracted into
two new functions.
Android.mk has been updated to enable the LDLT factorization, but
the cmake file has not been updated as I will leave it to Alex's
capable hands to do proper detection of ARM as a target platform.
Change-Id: Iffe3abd2ce894de2a388b454df3da909b482d5e5
Since Ceres is moving to using GitHub for issues, and the Google
Code URL in the current copyright header will soon become invalid,
update all the headers.
Change-Id: I1fce70375d1bcf098591f07b4d8f01a5c1e0789c
For historical reasons we had a "using namespace std;" in port.h. This
is generally a bad idea. So removing it and along the way doing a bunch
of cpplint cleanup.
Change-Id: Ia125601a55ae62695e247fb0250df4c6f86c46c6
Up till now ITERATIVE_SCHUR evaluates matrix-vector products
between the Schur complement and a vector implicitly by exploiting
the algebraic expression for the Schur complement.
This cost of this evaluation scales with the number of non-zeros
in the Jacobian.
For small to medium sized problems there is a sweet spot where
computing the Schur complement is cheap enough that it is much
more efficient to explicitly compute it and use it for evaluating
the matrix-vector products.
This changes implements support for an explicit Schur complement
in ITERATIVE_SCHUR in combination with the SCHUR_JACOBI preconditioner.
API wise a new bool Solver::Options::use_explicit_schur_complement
has been added.
The implementation extends the SparseSchurComplementSolver to use
Conjugate Gradients.
Example speedup:
use_explicit_schur_complement = false
Time (in seconds):
Preprocessor 0.585
Residual evaluation 0.319
Jacobian evaluation 1.590
Linear solver 25.685
Minimizer 27.990
Postprocessor 0.010
Total 28.585
use_explicit_schur_complement = true
Time (in seconds):
Preprocessor 0.638
Residual evaluation 0.318
Jacobian evaluation 1.507
Linear solver 5.930
Minimizer 8.144
Postprocessor 0.010
Total 8.791
Which indicates an end-to-end speedup of more than 3x, with the linear
solver being sped up by > 4x.
The idea to explore this optimization was inspired by the recent paper:
Mining structure fragments for smart bundle adjustment
L. Carlone, P. Alcantarilla, H. Chiu, K. Zsolt, F. Dellaert
British Machine Vision Conference, 2014
which uses a more complicated algorithm to compute parts of the
Schur complement to speed up the matrix-vector product.
Change-Id: I95324af0ab351faa1600f5204039a1d2a64ae61d
The instrumentation revealed that EIGEN_SPARSE can be upto
an order of magnitude slower than CX_SPARSE on some bundle
adjustment problems.
The problem comes down to the quality of AMD ordering that
CXSparse/Eigen implements. It does particularly badly
on the Schur complement. In the CXSparse implementation
we got around this by considering the block sparsity structure
and computing the AMD ordering on it and lifting it to the
full matrix.
This is currently not possible with the release version of
Eigen, as the support for using preordered/natural orderings
is in the master branch but has not been released yet.
Change-Id: I25588d3e723e50606f327db5759f174f58439e29
SPARSE_NORMAL_CHOLESKY and SPARSE_SCHUR can now be used
with EIGEN_SPARSE as the backend.
The performance is not as good as CXSparse. This needs to be
investigated. Is it because the quality of AMD ordering that
we are computing is not as good as the one for CXSparse? This
could be because we are working with the scalar matrix instead
of the block matrix.
Also, the upper/lower triangular story is not completely clear.
Both of these issues will be benchmarked and tackled in the
near future.
Also included in this change is a bunch of cleanup to the
SparseNormalCholeskySolver and SparseSchurComplementSolver
classes around the use of the of defines used to conditionally
compile out parts of the code.
The system_test has been updated to test EIGEN_SPARSE also.
Change-Id: I46a57e9c4c97782696879e0b15cfc7a93fe5496a
cholmod_lhs was not being freed before
the SolveImpl function returned if the
underlying linear solver failed.
Change-Id: Id45db4f69a2821e43dc00fc975718584d426f44d
A lot of error checking cruft has accumulated over the years
in the various linear solvers. This change makes the error reporting
more robust and consistent across the various solvers.
Preconditioners are not covered by this change and will be the
subject of a future change.
Change-Id: Ibeb2572a1e67758953dde8d12e3abc6d1df9052d
1. Move LinearSolverTerminationType to ceres::internal.
2. Add FATAL_ERROR as a new enum to LinearSolverTerminationType.
3. Pipe SuiteSparse errors via a LinearSolverTerminationType so
to distinguish between fatal and non-fatal errors.
4. Update levenberg marquardt and dogleg strategies to deal
with FATAL_ERROR.
5. Update trust_region_minimizer to terminate when FATAL_ERROR
is encountered.
6. Remove SuiteSparse::SolveCholesky as it screws up the error
handling.
7. Fix all clients calling SuiteSparse to handle the result of
SuiteSparse::Cholesky correctly.
8. Remove fatal failures in SuiteSparse when symbolic factorization
fails.
9. Fix all clients of SuiteSparse to deal with null symbolic factors.
This is a temporary fix to deal with some production problems. A more
extensive cleanup and testing regime will be put in place in a
subsequent CL.
Change-Id: I1f60d539799dd95db7ecc340911e261fa4824f92
Main purpose of this is to make implementation files free from
endless ifdef blocks every time this libraries are needed to be
included. This would hopefully prevent compilation errors in
the future caused by missing ifdef around header include.
This also includes some stubs added to suitesparse/cxsparse
headers to make code even more free from ifdefs.
Change-Id: Ic8554e7df31d8c4751583fe004b99e71b3c9087b
1. When a LAPACK implementation is present, then
DENSE_QR, DENSE_NORMAL_CHOLESKY and DENSE_SCHUR
can use it for doing dense linear algebra operations.
2. The user can switch dense linear algebra libraries
by setting Solver::Options::dense_linear_algebra_library_type.
3. Solver::Options::sparse_linear_algebra_library is now
Solver::Options::sparse_linear_algebra_library_type to be consistent
with all the other enums in Solver::Options.
4. Updated documentation as well as Solver::Summary::FullReport
to reflect these changes.
Change-Id: I5ab930bc15e90906b648bc399b551e6bd5d6498f
colPivHouseholderQR -> householderQR
ldlt -> llt.
The resulting performance differences are significant enough
to justify switching.
LAPACK's dgels routine used for solving linear least squares
problems does not use pivoting either.
Similarly, we are not actually using the fact that the matrix
being factorized can be indefinite when using LDLT factorization, so
its not clear that the performance hit is worth it.
These two changes result in Eigen being able to use blocking
algorithms, which for Cholesky factorization, brings the performance
closer to hardware optimized LAPACK. Similarly for dense QR
factorization, on intel there is a 2x speedup.
Change-Id: I4459ee0fc8eb87d58e2b299dfaa9e656d539dc5e
1. CX_SPARSE supports pre-ordering of the jacobian.
2. Add support for constrained approximate minimum degree ordering
for SuiteSparse versions >= 4.2.0
3. Using 2, support for pre-ordering for SPARSE_SCHUR when used
with SUITE_SPARSE.
4. Using 2, support for user orderings in SPARSE_NORMAL_CHOLESKY.
5. Minor cleanups in documentation and code all around.
6. Test update and refactoring.
Change-Id: Ibfe3ac95d59d54ab14d1d60a07f767688070f29f
Uptil now only SuiteSparse when used with SPARSE_SCHUR would use
the block structure of the reduced camera matrix to find a fill-reducing
ordering.
This leads to substantial speedup for some bundle adjustment
problems.
Credit for this technique goes to the authors of g2o. I learned
about it from reading their source code.
Change-Id: I5403efefd4d9552c9c6fc6e02a65498bdf171584
Sparse Cholesky factorization algorithms use a fill-reducing
ordering to permute the columns of the Jacobian matrix. There
are two ways of doing this.
1. Compute the Jacobian matrix in some order and then have the
factorization algorithm permute the columns of the Jacobian.
2. Compute the Jacobian with its columns already permuted.
The first option incurs a significant memory penalty. The
factorization algorithm has to make a copy of the permuted
Jacobian matrix.
Starting with this change Ceres pre-permutes the columns of the
Jacobian matrix and generally speaking, there is no performance
penalty for doing so.
In some rare cases, it is worth using a more complicated
reordering algorithm which has slightly better runtime
performance at the expense of an extra copy of the Jacobian
matrix. Setting Solver::Options::use_postordering to true
enables this tradeoff.
This change also removes Solver::Options::use_block_amd
as an option. All matrices are ordered using their block
structure. The ability to order them by their scalar
sparsity structure has been removed.
Here is what performance on looks like on some BAL problems.
Memory
======
HEAD pre-ordering
16-22106 137957376.0 113516544.0
49-7776 56688640.0 46628864.0
245-198739 1718005760.0 1383550976.0
257-65132 387715072.0 319512576.0
356-226730 2014826496.0 1626087424.0
744-543562 4903358464.0 3957878784.0
1024-110968 968626176.0 822071296.0
Time
====
HEAD pre-ordering
16-22106 3.8 3.7
49-7776 1.9 1.8
245-198739 82.6 81.9
257-65132 14.0 13.4
356-226730 98.8 95.8
744-543562 325.2 301.6
1024-110968 42.1 37.1
Change-Id: I6b2e25f3fed7310f88905386a7898ac94d37467e
1. Silence CHOLMOD's indefiniteness warnings.
2. Add a comment about how the error handling in suitesparse.cc
needs to be improved.
3. Move the analysis logging into suitesparse.cc and out of the
three callsites.
Change-Id: Idd396b8ea4bf59fc1ffc7f9fcbbc7b38ed71643c
1. Add -DLINE_SEARCH_MINIMIZER to CMake to make the line search
minimizer optional.
2. Better handling of -DSUITESPARSE/-DCXSPARSE in top level cmake
file.
3. Disable code which will never be used if SuiteSparse and/or
CXSparse is not available.
4. Update build docs.
5. Update jni/Android.mk
6. Minor lint cleanup from William Rucklidge.
Change-Id: If60460a858000df82faed7a6bb056dd2bfdde562
1. Add an ExecutionSummary object to record execution
information about Ceres objects.
2. Add an EventLogger object to log events in a function call.
3. Add a ScopedExecutionTimer object to log times in ExecutionSummary.
4. Instrument ProgramEvaluator and all the linear solvers
to report their timing statistics.
5. Connect the timing statistics to Summary::FullReport.
6. Add high precision timer on unix systems using
gettimeofday() call.
7. Various minor clean ups all around.
Change-Id: I5e09804b730b09535484124be7dbc1c58eccd1d4
Average factorization times for bundle adjustment test problem:
SuiteSparse: 0.2794 s.
CXSparse: 0.4039 s.
CXSparse cached: 0.2399 s.
CXSparse will still be slower, though, because it has to compute
the transpose and J^T * J.
Change-Id: If9cdaa3dd520bee84b56e5fd4953b56a93db6bde
Fix broken build and verbosity issues.
1. While cleaning up the last CL, I broke a macro.
2. cholmod_common_print was being called too often.
Change-Id: Ia76d8863c72f31b0c02977094b22035ceef835cf
By virtue of the modeling layer in Ceres being block oriented,
all the matrices used by Ceres are also block oriented.
When doing sparse direct factorization of these matrices, the
fill-reducing ordering algorithms can either be run on the
block or the scalar form of these matrices. Running it on the
block form exposes more of the super-nodal structure of the
matrix to the Cholesky factorization routines. This leads to
substantial gains in factorization performance.
This changelist adds support for approximate minimium degree
orderings to be computed on the block structure of the
Schur complement matrix. This affects, SchurComplementSolver
and VisibilityBasedPreconditioner and SparseNormalCholesky
when using SuiteSparse.
A bool, use_block_amd has been added to Solver::Options and
bundle_adjuster.cc has been updated to allow testing with it.
When combined with a multithreaded Schur elimination, speed ups
can be seen quite uniformly across the board. For some problems
this can be dramatic, reducing the factorization time from 70
seconds down to 17 seconds.
Change-Id: I15ebb0afcbc85ada032ec8d179ee3a2f7c8d3e46
1. Added support for CXSparse - SparseNormalCholesky and
SchurComplementSolver support SuiteSparse and CXSparse now.
I am not sure I will add suport for visibility based
preconditioning using CXSparse. Its not a high priority.
2. New enum SparseLinearAlgebraLibraryType which allows the user
to indicate which sparse linear algebra library should be used.
3. Updated tests for SolverImpl and system_test.
4. Build system changes to automatically detect CXSparse and
link to it by default -- just like SuiteSparse.
5. Minor bug fixes dealing in the cmake files and VBP.
6. Changed the order of the system test.
7. Deduped the unsymmetric linear solver test.
Change-Id: I33252a103c87b722ecb7ed7b5f0ae7fd91249244
unnecessarily complexity in the structure of linear solvers and preconditioners.
This is the first step towards cleaning up the Preconditioner interface.
2. Minor tweaks and cleanups to the various linear solvers.
Sameer Agarwal