https://github.com/ceres-solver/ceres-solver/issues/270
Detailed list of changes:
1. Add SUBSET to the PreconditionerType enum.
2. Add Solver::Options::residual_blocks_for_subset_preconditioner
3. Integrate SubsetPreconditioner into the CGNR solver.
4. Add the reordering logic needed for this to TrustRegionPreprocessor.
5. Expect CreateJacobianBlockTranspose to take the starting row block
so that we can work with subparts of the Jacobian matrix.
6. Extend the denoising example to use this preconditioner.
As an illustration of its performance, we consider the performance of
denoising -input ../data/ceres_noisy.pgm --foe_file ../data/5x5.foe
tl;dr
For the same cost,
SPARSE_NORMAL_CHOLESKY - 81s
CGNR + JACOBI - 718s
CGNR + SUBSET - 57s
SPARSE_NORMAL_CHOLESKY
======================
Cost:
Initial 2.317806e+05
Final 2.232323e+04
Change 2.094574e+05
Minimizer iterations 10
Successful steps 10
Unsuccessful steps 0
Time (in seconds):
Preprocessor 2.999746
Residual only evaluation 2.306811 (10)
Jacobian & residual evaluation 7.421727 (10)
Linear solver 65.517273 (10)
Minimizer 78.731011
Postprocessor 0.026079
Total 81.756836
Termination: CONVERGENCE (Function tolerance reached. |cost_change|/cost: 8.573046e-04 <= 1.000000e-03)
CGNR + JACOBI
=============
Cost:
Initial 2.317806e+05
Final 2.232344e+04
Change 2.094572e+05
Minimizer iterations 10
Successful steps 10
Unsuccessful steps 0
Time (in seconds):
Preprocessor 0.648814
Residual only evaluation 2.297607 (10)
Jacobian & residual evaluation 7.327886 (10)
Linear solver 699.601248 (10)
Minimizer 712.419493
Postprocessor 0.024014
Total 713.092321
Termination: CONVERGENCE (Function tolerance reached. |cost_change|/cost: 8.528538e-04 <= 1.000000e-03)
CGNR + SUBSET (random 20% residuals used for the preconditioner)
===============================================================
Cost:
Initial 2.317806e+05
Final 2.232327e+04
Change 2.094574e+05
Minimizer iterations 10
Successful steps 10
Unsuccessful steps 0
Time (in seconds):
Preprocessor 1.472743
Residual only evaluation 2.428315 (10)
Jacobian & residual evaluation 7.367796 (10)
Linear solver 42.585999 (10)
Minimizer 55.664459
Postprocessor 0.024098
Total 57.161301
Termination: CONVERGENCE (Function tolerance reached. |cost_change|/cost: 8.538277e-04 <= 1.000000e-03)
Change-Id: Ifb011408bd53edbb9439b0b7345649a38f999e18
1. Add Solver::Options::use_mixed_precision_solves,
and Solver::Options::max_num_refinement_iterations.
2. Make SparseCholesky::Create return a unique_ptr.
3. SparseCholesky::Create now takes LinearSolver::Options
as an argument.
4. IterativeRefiner's constructor does not require num_cols
as an argument.
5. SparseNormalCholeskySolver now uses a separate rhs vector.
This basic implementation results in a 10% reduction in solver time
and 30% reduction in linear solver memory usage.
Change-Id: I6830f32cae2febf082d2733262eb2c9f0482b0ea
Migrate all Option and Summary structs to use
inline member initialization syntax.
This reduces the amount of code, and collocates the
default values with the documentation for the corresponding
member variable.
Change-Id: I8e6b9ee3b31464699d678667f6166ace5fc137c9
A Ceres Context holds common global state that can be re-used within
Ceres. The Context current contains a thread pool if compiling with
C++11 threading support. Threads are expensive to create and destroy so
it is good to maintain across multiple Ceres solves.
Tested by compiling with and without TBB support and ran unit tests. Ran
bazel as well.
Change-Id: I82f598dfae642aa0e81a6039dc174608a5e8dbfb
1. Replace two maps by 1.
2. Update number of calls and the time for the call at the cost
of a single map lookup.
3. Add Solver::Summary::num_linear_solves.
Fixes https://github.com/ceres-solver/ceres-solver/issues/340
Change-Id: I71eb9be7fb363a8cb066591c4c1761f256c81677
SparseCholesky is an interface to sparse cholesky factorization
routines across sparse linear algebra libraries. Each sparse
linear algebra library is responsible for implementing its own
instance of this interface.
As a result the various places - SparseNormalCholeskySolver,
SparseSchurComplementSolver and VisibilityBasedPreconditioner
are significantly simplified.
Change-Id: I8b465705eae83bba9e1adfffcc741a05c70faf2e
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
Move functions that determine alternatives to Schur type linear
solver and preconditioners into the LinearSolver and Preconditioner
interfaces.
Change-Id: Iae900afb7db17cdbeb7753497005a48c3144e2d7
The standard sparse normal Cholesky solver assumes a fixed
sparsity pattern which is useful for a large number of problems
presented to Ceres. However, some problems are symbolically dense
but numerically sparse i.e. each residual is a function of a
large number of parameters but at any given state the residual
only depends on a sparse subset of them. For these class of
problems it is faster to re-analyse the sparsity pattern of the
jacobian at each iteration of the non-linear optimisation instead
of including all of the zero entries in the step computation.
The proposed solution adds the dynamic_sparsity option which can
be used with SPARSE_NORMAL_CHOLESKY. A
DynamicCompressedRowSparseMatrix type (which extends
CompressedRowSparseMatrix) has been introduced which allows
dynamic addition and removal of elements. A Finalize method is
provided which then consolidates the matrix so that it can be
used in place of a regular CompressedRowSparseMatrix. An
associated jacobian writer has also been provided.
Changes that were required to make this extension were adding the
SetMaxNumNonZeros method to CompressedRowSparseMatrix and adding
a JacobianFinalizer template parameter to the ProgramEvaluator.
Change-Id: Ia5a8a9523fdae8d5b027bc35e70b4611ec2a8d01
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
The original visibility based preconditioning paper and
implementation only used the canonical views algorithm.
This algorithm for large dense graphs can be particularly
expensive. As its worst case complexity is cubic in size
of the graph.
Further, for many uses the SCHUR_JACOBI preconditioner
was both effective enough while being cheap. It however
suffers from a fatal flaw. If the camera parameter blocks
are split between two or more parameter blocks, e.g,
extrinsics and intrinsics. The preconditioner because
it is block diagonal will not capture the interactions
between them.
Using CLUSTER_JACOBI or CLUSTER_TRIDIAGONAL will fix
this problem but as mentioned above this can be quite
expensive depending on the problem.
This change extends the visibility based preconditioner
to allow for multiple clustering algorithms. And adds
a simple thresholded single linkage clustering algorithm
which allows you to construct versions of CLUSTER_JACOBI
and CLUSTER_TRIDIAGONAL preconditioners that are cheap
to construct and are more effective than SCHUR_JACOBI.
Currently the constants controlling the threshold above
which edges are considered in the single linkage algorithm
are not exposed. This would be done in a future change.
Change-Id: I7ddc36790943f24b19c7f08b10694ae9a822f5c9
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
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. Introduce new typdefs in eigen.h to allow for column
major matrices.
2. Clean up old unused typedefs, and the aligned typedefs
since they do not actually add any real performance.
3. Made eigen.h conform to the google style guide by removing
the using directives. They were polluting the ceres namespace.
4. Made the template specialization generator work again.
Change-Id: Ic2268c784534b737ebd6e1a043e2a327adaeca37
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
report execution statistics of all kinds.
Currently a single map which maps arbitrary strings to doubles is supported,
which allows for precise timing information to be communicated.
Change-Id: Ibd930aca5c9e6cae89bcfeffe9b13e2887644881
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.
This adds a new LinearOperator which implements symmetric
products of a matrix, and a new CGNR solver to leverage
CG to directly solve the normal equations. This also
includes a block diagonal preconditioner. In experiments
on problem-16, the non-preconditioned version is about
1/5 the speed of SPARSE_SCHUR, and the preconditioned
version using block cholesky is about 20% slower than
SPARSE_SCHUR.
Sameer Agarwal