I think this is all of the cases. These cases arise because pow(a,b) is limited
to real valued results, if the argument and result were complex valued then
these cases would disappear.
NOTE: Since there is so much special casing here, it is worth checking to see
if cpow() is implemented in terms of pow(), and what might be the consequences
of using cpow() on the type std::complex<Jet<double, N> >. It is *possible*
that a separate implementation of cpow might be required also.
Also some comment fixes.
Change-Id: Ia1e38df4cdcb548f778304c2854cacba6e1556ff
1. Add documentation for cubic_interpolation.h
2. Remove the list of publications. It is an incomplete list which is
a pain to maintain.
3. Add a note about the interaction between manifolds and
NumericDiffCostFunction.
4. Fix some of the comments in cubic_interpolation.h to better reflect reality.
5. Updated the version history.
Change-Id: I0b4a5a6f3361d3fc85f1b4aec685cd80540934f1
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
This CL is required to build Tango.
Inspired by this commit in RedwoodInternal repository:
commit 09dde53c248e04f432b5eccceea5daeedb706aea
Author: Mike Vitus <mike@hidof.com>
Date: Wed Apr 23 11:05:17 2014 -0700
Change-Id: I328b6634969de4ccdd71947945aa67a49ee9073f
MSVC 2013 compiler crashed when not specifying the
template parameter of CubicHermiteSpline explicitly.
Change-Id: I6ab79aea47f55373df5cb7b89e38f8b326ff21c9
This has a measurable impact on interpolation performance.
Also remove an accidentally named enum with an anonymous enum.
Change-Id: Ied6a4b2b06bb27a7f004bd0e01353742e1f84034
The key change is that there is a new layer of abstract,
a Array object that the interpolator depends on.
The Array provides a one dimension or two dimensional
array like interface independent of the underlying representation
of the data.
Also included here is support for vector valued functions.
Change-Id: Ica68f03778cf0d84192db00cd55653f8b4124d51
Delete code needed by old versions of the NDK. We do not build
with these versions of the NDK and do not use STLPort anymore.
Change-Id: I61092db0aa3980cfae6ff57f3f318482027e627f
Example code demonstrates how a sampled function can be
minimized. Also, in the process uncovered some deficiencies
in the CubicInterpolator and BicubicInterpolator interfaces and
fixed them.
Change-Id: I18c8f670fbee076bf1e94d1f45c7477fd71640e8
This bi-cubic interpolation implementation is based
on the cubic convolution algorithm of keys, which allows
us to implement a bi-cubic spline like interpolation scheme
using five one dimensional cubic spline operations.
Change-Id: I116aa8036191c3e654af788323fc8298ae8252a6
Add a cubic interpolator based on the Catmull-Rom spline,
with support for automatic differentiation.
Change-Id: I02ae4c4ea37805ff1f717b05ea805989b474bd59
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
- Previously we had no defined default value for
sparse_linear_algebra_library_type in Solver::Options if Ceres
was compiled with no sparse library available. Thus in that case,
the default value (dependent upon the compiler) would indicate that
one was available.
- Now we have an explicit option that means no sparse library is
available, which is now the default value in Solver::Options in this
case.
- Add a warning in CMake when the user disables all sparse libraries.
- Fix typos in trust_region_preprocessor_test:
(SUITE/CX)_SPARSE -> (SUITE/CX)SPARSE that induced failures when
no sparse libraries were available.
Change-Id: I869c399a12d42bfc44220cbb25ce6d6dd80236bd
- We now compute & report the cumulative time spent performing the
following tasks as part of a line search:
- Evaluation of the univariate cost function value & gradient.
- Minimization of the interpolating polynomial.
- Total time spent performing line searches.
- This information is now reported for all minimizers, although only in
the case of a constrained problem for the TR minimizer.
- Remove LineSearch::Function abstraction in place of using
LineSearchFunction implementation directly, and remove virtual
functions from LineSearchFunction.
-- LineSearch::Function added an unnecessary level of abstraction since
the user always had to create a LineSearchFunction anyway to use a
Ceres Evaluator, and it added an unncessary virtual function call.
Change-Id: Ia4e1921d78f351ae119875aa97a3ea5e8b5d9877
1. Remove an unused private member in TukeyLoss.
2. The test for RotationMatrixToAngle had an indexing error.
Change-Id: I7decc9448ae0abef53aa435005f739e9e0931e80
Use this function to implement RotationMatrixToAngleAxis.
This simplifies the implementation of RotationMatrixToAngleAxis,
just like Eigen does. It is also autodiff compatible, unlike the
Eigen based version.
Also significantly improve the test coverage of
RotationMatrixToAngleAxis.
Change-Id: Ic192a12fb5de952197ee24b0deedc45f195477f1
Use Eigen's much more complicated conversion routine
when we encounter cases where the angle of rotation is
close to Pi.
Along the way also fix the way angle_axis vectors are
compared by making the matcher more robust.
Thanks to Tobias Strauss for reporting this.
Change-Id: Ia7e65dafad92c48d29d5f3cd22c4d6534789c183
1. Complete restructuring of the documentation to account for
GradientProblemSolver.
2. Update the version history to account for changes since 1.9.0.
3. Add links and document the various examples that ship with ceres.
4. Documentation for GradientProblem GradientProblemSolver.
Change-Id: If3a18f2850cbc98be1bc34435e9ea468785b8b27
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 line search minimizer in Ceres does not require that the
problems that is solving is a sum of squares. Over the past
year there have been multiple requests to expose this algorithm
on its own so that it can be used to solve unconstrained
non-linear minimization problems on its own.
With this change, a new optimization problem called
GradientProblem is introduced which is basically a thin
wrapper around a user defined functor that evaluates cost
and gradients (FirstOrderFunction) and an optional LocalParameterization.
Corresponding to it, a GradientProblemSolver and its associated
options and summary structs are introduced too.
An example that uses the new API to find the minimum of Rosenbrock's
function is also added.
Change-Id: I42bf687540da25de991e9bdb00e321239244e8b4
Problem::GetCostFunctionForResidualBlock
Problem::GetLossFunctionForResidualBlock
are added, so that users do not have to maintain this mapping
outside the Problem.
Change-Id: I38356dfa094b2c7eec90651dafeaf3a33c5f5f56
Its API was broken, and its implementation was an unnecessary
layer of abstraction over CostFunctionToFunctor.
Change-Id: I18fc261fc6a3620b51a9eeb4dde0af03d753af69
The code itself was perfectly capable of handling residuals, but there
was an overly strict runtime check that had to be removed.
Thanks to Domink Reitzle for reporting this.
Change-Id: I6a6d000a7c5203dd5945a61b4caeda1b8aeb09c9
If the parameter block size is 1, asking Eigen to create
a row-major matrix triggers a compile time error. Previously
we were handling the case where the number of rows in the
jacobian block was known statically, but the problem is present
when the nummber of rows is dynamic.
This CL fixes this problem.
Thanks to Dominik Reitzle for reporting this.
Change-Id: I99c3eec3558e66ebf4efa51c4dee8ce292ffe0c1
1. Fix a build breakage in graph_test.
2. Respect Solver::Options::min_num_linear_solver_iterations in
conjugate_gradients_solver.cc
Thanks to Johannes Schönberger for reporting these.
Change-Id: Ib32e3929bf5d92dd576ae5b53d4d88797095136e
Replace SolverImpl with
a. A minimizer specific preprocessor class.
b. A generic Solve function inside solver.cc
c. Presummarize and Postsummarize functions to handle
updates to the summary object.
The existing SolverImpl class was a mixture of the above three
things and was increasingly complicated code to follow. This change,
breaks it into its three separate constituents, with the aims of
better separation of concerns and thus better testability and
reliability.
The call to Solver::Solve() now consists of
1. Presummarize - summarize the given state of the problem and solver
options.
2. Preprocess - Setup everything that is needed to call the minimizer.
This includes, removing redundant parameter and residual blocks,
setting up the reordering for the linear solver, creating the
linear solver, evaluator, inner iteration minimizer etc.
3. Minimize.
4. Post summarize - summarize the result of the preprocessing and the
solve.
Change-Id: I80f35cfc9f2cbf78f1df4aceace27075779d8a3a
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
Sparse Cholesky factorization is not rank revealing. Therefore
this algorithm cannot reliably tell when the Jacobian matrix is
rank deficient or so poorly conditioned that the covariance matrix
cannot be estimated.
Making things worse, this algorithm works on the normal equations,
which makes the conditioning problem much worse.
This change, deletes the SPARSE_CHOLESKY algorithm in the covariance
estimation code. Also to make the naming consistent, it renames
SPARSE_QR -> SUITE_SPARSE_QR
so that it parallels EIGEN_SPARSE_QR.
Also, since we now have EIGEN_SPARSE_QR, we can default to using
it when SuiteSparse is not available instead of DENSE_SVD, which
generally speaking should only be used by folks who are dealing
with small rank deficient jacobians.
Change-Id: I8b134c7e8a2e86ca374371f185b19f1c3e74349c
For smaller problems Eigen is faster than SuiteSparseQR. This has been
tested with Eigen 3.2.1. Below are detailed timings. Problem 1 is the
smallest and problem 3 is the largest. The timings below are:
mean +- standard deviation.
Problem 1:
Eigen 0.0009218 +- 0.0002755
SuiteSparse 0.001406 +- 0.001610
Problem 2:
Eigen 0.002338 +- 0.001005
SuiteSparse 0.001910 +- 0.0004513
Problem 3:
Eigen 0.005455 +- 0.001759
SuiteSparse 0.002411 +- 0.0004974
Detailed problem descriptions:
Problem 1 size:
Original Reduced
Parameter blocks 533 54
Parameters 368 104
Effective parameters 1201 94
Residual blocks 233 77
Residual 1194 258
Problem 2 size:
Original Reduced
Parameter blocks 573 84
Parameters 1458 184
Effective parameters 1281 164
Residual blocks 263 107
Residual 1314 378
Problem 3 size:
Original Reduced
Parameter blocks 613 114
Parameters 1548 264
Effective parameters 1361 234
Residual blocks 293 137
Residual 1434 498
Change-Id: I884a67e2f728fe2992812148d82ccf5f27864fd7
Tal Ben-Nun