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https://github.com/ceres-solver/ceres-solver.git
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Joydeep Biswas
42352e2e2a
* Added CudaCpuPreconditionerWrapper, a templated wrapper to leverage
existing CPU preconditioners that provide CompressedRowSparse
representation, for use with CudaCgnrSolver.
* Added CudaJacobiPreconditioner as a specific instantiation of
CudaCpuPreconditionerWrapper over BlockCRSJacobiPreconditioner.
The resulting Jacobi-preconditioned CudaCgnrSolver exhibits moderate
increase in speed with a healthy increase in numerical stability.
Examples of running CudaCgnrSolver with Jacobi vs. Identity
preconditioner for bundle adjustment on problem-13682-4456117-pre.txt
on a desktop computer with an Intel(R) Core(TM) i9-9940X CPU @ 3.30GHz
and an Nvidia Quadro RTX 6000 GPU.
A known issue is that the Jacobi preconditioner update is slow - this
can be sped up in the future by multithreading on the CPU, or by
computing the preconditioner on the GPU.
====================================================================
CUDA CGNR + IDENTITY Preconditioner
====================================================================
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
0 1.126372e+09 0.00e+00 3.02e+15 0.00e+00 0.00e+00 1.00e+04 0 9.17e+00 2.70e+01
1 3.796903e+07 1.09e+09 1.08e+15 6.48e+03 9.95e-01 3.00e+04 49 1.55e+01 4.24e+01
2 3.529024e+21 -3.53e+21 1.08e+15 1.93e+04 -2.25e+14 1.50e+04 500 3.79e+01 8.03e+01
3 7.952482e+09 -7.91e+09 1.08e+15 1.63e+04 -5.16e+02 3.75e+03 386 2.96e+01 1.10e+02
4 8.842366e+08 -8.46e+08 1.08e+15 1.18e+04 -5.87e+01 4.69e+02 312 2.47e+01 1.35e+02
5 2.935800e+07 8.61e+06 1.24e+13 3.93e+03 8.19e-01 6.32e+02 129 1.96e+01 1.54e+02
6 2.529342e+07 4.06e+06 3.22e+12 3.39e+03 9.93e-01 1.90e+03 148 2.16e+01 1.76e+02
7 2.343028e+07 1.86e+06 1.27e+13 6.00e+03 9.37e-01 5.68e+03 387 3.79e+01 2.14e+02
8 2.332405e+07 1.06e+05 7.92e+12 6.47e+01 8.26e-01 7.87e+03 46 1.48e+01 2.28e+02
9 3.591512e+14 -3.59e+14 7.92e+12 5.19e+03 -4.09e+08 3.94e+03 500 3.83e+01 2.67e+02
10 2.956078e+07 -6.24e+06 7.92e+12 3.94e+03 -8.34e+00 9.84e+02 447 3.40e+01 3.01e+02
Solver Summary (v 2.2.0-eigen-(3.3.7)-lapack-suitesparse-(5.7.1)-metis-(5.1.0)-eigensparse-no_openmp-cuda-(11070))
Original Reduced
Parameter blocks 4469799 4469799
Parameters 13491489 13491489
Residual blocks 28987644 28987644
Residuals 57975288 57975288
Minimizer TRUST_REGION
Trust region strategy LEVENBERG_MARQUARDT
Sparse linear algebra library CUDA_SPARSE
Given Used
Linear solver CGNR CGNR
Preconditioner IDENTITY IDENTITY
Threads 24 24
Linear solver ordering 4456117,13682 4456117,13682
Cost:
Initial 1.126372e+09
Final 2.332405e+07
Change 1.103048e+09
Minimizer iterations 11
Successful steps 6
Unsuccessful steps 5
Time (in seconds):
Preprocessor 17.798455
Residual only evaluation 8.656350 (10)
Jacobian & residual evaluation 35.794169 (6)
Linear solver 208.586109 (10)
Minimizer 283.593882
Postprocessor 1.985112
Total 303.377449
====================================================================
CUDA CGNR + JACOBI Preconditioner
====================================================================
iter cost cost_change |gradient| |step| tr_ratio tr_radius ls_iter iter_time total_time
0 1.126372e+09 0.00e+00 3.02e+15 0.00e+00 0.00e+00 1.00e+04 0 9.18e+00 2.68e+01
1 1.491225e+14 -1.49e+14 3.02e+15 8.73e+05 -1.36e+05 5.00e+03 6 1.07e+01 3.74e+01
2 7.461790e+12 -7.46e+12 3.02e+15 4.78e+05 -6.78e+03 1.25e+03 6 8.88e+00 4.63e+01
3 4.357438e+07 1.08e+09 5.41e+13 1.57e+05 9.87e-01 3.75e+03 6 1.62e+01 6.25e+01
4 2.928453e+07 1.43e+07 6.85e+13 3.81e+05 6.97e-01 3.99e+03 23 1.82e+01 8.08e+01
5 5.977433e+14 -5.98e+14 6.85e+13 4.97e+05 -8.70e+07 2.00e+03 9 9.93e+00 9.07e+01
6 6.423965e+10 -6.42e+10 6.85e+13 2.45e+05 -9.61e+03 4.99e+02 7 8.95e+00 9.97e+01
7 2.337471e+07 5.91e+06 1.49e+12 8.24e+04 9.31e-01 1.39e+03 4 1.60e+01 1.16e+02
8 2.257524e+07 7.99e+05 8.71e+12 1.62e+05 8.99e-01 2.81e+03 54 2.03e+01 1.36e+02
9 2.285090e+07 -2.76e+05 8.71e+12 3.56e+05 -6.13e-01 1.41e+03 104 1.65e+01 1.52e+02
10 5.909983e+12 -5.91e+12 8.71e+12 1.78e+05 -1.83e+07 3.52e+02 74 1.36e+01 1.66e+02
Solver Summary (v 2.2.0-eigen-(3.3.7)-lapack-suitesparse-(5.7.1)-metis-(5.1.0)-eigensparse-no_openmp-cuda-(11070))
Original Reduced
Parameter blocks 4469799 4469799
Parameters 13491489 13491489
Residual blocks 28987644 28987644
Residuals 57975288 57975288
Minimizer TRUST_REGION
Trust region strategy LEVENBERG_MARQUARDT
Sparse linear algebra library CUDA_SPARSE
Given Used
Linear solver CGNR CGNR
Preconditioner JACOBI JACOBI
Threads 24 24
Linear solver ordering 4456117,13682 4456117,13682
Cost:
Initial 1.126372e+09
Final 2.257524e+07
Change 1.103796e+09
Minimizer iterations 11
Successful steps 5
Unsuccessful steps 6
Time (in seconds):
Preprocessor 17.575990
Residual only evaluation 8.461414 (10)
Jacobian & residual evaluation 30.055383 (5)
Linear solver 82.550675 (10)
Minimizer 149.137856
Postprocessor 1.994014
Total 168.707860
Change-Id: I458d2445bf062e54de44fc91517ed11a300c7182
Ceres Solver
Ceres Solver is an open source C++ library for modeling and solving large, complicated optimization problems. It is a feature rich, mature and performant library which has been used in production at Google since 2010. Ceres Solver can solve two kinds of problems.
- Non-linear Least Squares problems with bounds constraints.
- General unconstrained optimization problems.
Please see ceres-solver.org for more information.