tree 449a579bdc7e34f4fd2a306578878c44b9aeb811
parent 290b34ef058eb83aae64236b26742867a7a9431d
author Joydeep Biswas <joydeepb@cs.utexas.edu> 1654391826 -0500
committer Joydeep Biswas <joydeepb@cs.utexas.edu> 1657713331 -0500

Mixed-precision Iterative Refinement Cholesky With CUDA

* Created a new class CUDADenseCholeskyMixedPrecision, which performs
  Cholesky factorization and solving in single (fp32) precision, and
  optionally performs iterative refinement.
* Added CUDA kernels for mixed-precision solve operations
* Added more detailed timing information to the FullReport about Schur
  elimination, reduced system solves, and back-substitution.

Some test performance numbers follow.
All tests were performed on an Ubuntu 20.04 desktop with an
Intel Core i9-9940X CPU and Nvidia Quadro RTX 6000 GPU.

Tests were launched as:
./bin/bundle_adjuster --input (problem_file) \
    --num_iterations 20
    --num_threads 28
    --linear_solver dense_schur
    --dense_linear_algebra_library (cuda|lapack)
    [--mixed_precision_solves]

==================================================
problem-21-11315-pre.txt
==================================================

--------------------------------------------------
Cuda Mixed Precision
--------------------------------------------------
Cost:
Initial                          4.413239e+06
Final                            3.037864e+04
Change                           4.382861e+06
  Linear solver                      0.250703 (14)
  ├ Schur eliminate                  0.234025 (14)
  ├ Reduced solve                    0.006643 (14)
  └ Backsubstitute                   0.006598 (12)

--------------------------------------------------
Cuda
--------------------------------------------------
Cost:
Initial                          4.413239e+06
Final                            3.037864e+04
Change                           4.382861e+06
  Linear solver                      0.257517 (12)
  ├ Schur eliminate                  0.233518 (12)
  ├ Reduced solve                    0.010621 (12)
  └ Backsubstitute                   0.007124 (12)

--------------------------------------------------
Lapack (OpenBLAS)
--------------------------------------------------
Cost:
Initial                          4.413239e+06
Final                            3.037864e+04
Change                           4.382861e+06
  Linear solver                      0.332349 (12)
  ├ Schur eliminate                  0.274748 (12)
  ├ Reduced solve                    0.015966 (12)
  └ Backsubstitute                   0.034192 (12)

==================================================
problem-257-65132-pre.txt
==================================================

--------------------------------------------------
Cuda Mixed Precision
--------------------------------------------------
Cost:
Initial                          2.456242e+07
Final                            9.677593e+04
Change                           2.446565e+07
  Linear solver                      1.332367 (20)
  ├ Schur eliminate                  1.021365 (20)
  ├ Reduced solve                    0.195472 (20)
  └ Backsubstitute                   0.075582 (20)

--------------------------------------------------
Cuda
--------------------------------------------------
Cost:
Initial                          2.456242e+07
Final                            9.677547e+04
Change                           2.446565e+07
  Linear solver                      1.810176 (20)
  ├ Schur eliminate                  1.012862 (20)
  ├ Reduced solve                    0.678704 (20)
  └ Backsubstitute                   0.083925 (20)

--------------------------------------------------
Lapack (OpenBLAS)
--------------------------------------------------
Cost:
Initial                          2.456242e+07
Final                            9.677547e+04
Change                           2.446565e+07
  Linear solver                      2.376273 (20)
  ├ Schur eliminate                  0.987613 (20)
  ├ Reduced solve                    1.043873 (20)
  └ Backsubstitute                   0.310402 (20)

==================================================
problem-744-543562-pre.txt
==================================================

--------------------------------------------------
Cuda Mixed Precision
--------------------------------------------------
Cost:
Initial                          1.434881e+08
Final                            1.546895e+06
Change                           1.419412e+08
  Linear solver                     27.010088 (20)
  ├ Schur eliminate                 24.362433 (20)
  ├ Reduced solve                    1.428542 (20)
  └ Backsubstitute                   0.814266 (20)

--------------------------------------------------
Cuda
--------------------------------------------------
Cost:
Initial                          1.434881e+08
Final                            1.546895e+06
Change                           1.419412e+08
  Linear solver                     32.342513 (20)
  ├ Schur eliminate                 24.638819 (20)
  ├ Reduced solve                    6.492090 (20)
  └ Backsubstitute                   0.802184 (20)

--------------------------------------------------
Lapack (OpenBLAS)
--------------------------------------------------
Cost:
Initial                          1.434881e+08
Final                            1.546895e+06
Change                           1.419412e+08
  Linear solver                     34.152224 (20)
  ├ Schur eliminate                 24.183723 (20)
  ├ Reduced solve                    8.784413 (20)
  └ Backsubstitute                   0.795044 (20)

Change-Id: I178887e776d8f4a1e8abb99bbc205bf8c278bf79