SVD cleanup by mgates3 · Pull Request #46 · icl-utk-edu/plasma

mgates3 · 2025-03-19T00:23:16Z

Cleanup the SVD code, applying changes similar to the eigenvalue code (#40).

Note that the 2-stage reduction goes to upper or lower triangular band (tb) form, not general band (gb) form. The LAPACK routine gbbrd takes a general band matrix that can have non-zero upper (ku > 0) and lower (kl > 0) bandwidths. Hence renaming PLASMA's routines to tbbrd.

Also add diagrams to the eigenvalue bulge chasing kernels.

Since both SVD and eig use proper atomic operations, remove the volatile variables. (See discussion on atomics vs. volatile in the PLASMA style guide and Scott Meyers book, Effective Modern C++.)

mgates3 · 2025-03-21T18:21:38Z

+            'S', seed,
+            'N', Sigma_ref, mode, rcond,
+            dmax, kl, ku,
+            pack, Aband + nb, ldab, work);


This works fine with OpenBLAS 0.3.27 (using Netlib LAPACK), but fails with MKL 2024.2.0. I can disable checks in that case.

################################################################################ # Test with OpenBLAS, using Netlib LAPACK. sh methane build-openblas> ./run_tests.py tbbrd Fri Mar 21 18:15:55 2025 ./plasmatest stbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, OpenBLAS 0.3.27 , 2025-03-21 18:15:55 % input: ./plasmatest stbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 5.52e-09 0.0008 0.0000 l 100 64 pass 2.95e-08 0.0028 0.0000 l 200 64 pass 3.28e-08 0.0054 0.0000 l 300 64 pass 3.99e-08 0.0081 0.0000 l 400 64 pass 4.28e-08 0.0115 0.0000 l 500 64 pass 5.00e-09 0.0008 0.0000 u 100 64 pass 2.90e-08 0.0036 0.0000 u 200 64 pass 3.22e-08 0.0080 0.0000 u 300 64 pass 4.30e-08 0.0137 0.0000 u 400 64 pass 4.23e-08 0.0184 0.0000 u 500 64 % All tests passed pass ./plasmatest dtbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, OpenBLAS 0.3.27 , 2025-03-21 18:15:55 % input: ./plasmatest dtbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 1.05e-17 0.0011 0.0000 l 100 64 pass 4.82e-17 0.0035 0.0000 l 200 64 pass 6.41e-17 0.0070 0.0000 l 300 64 pass 8.26e-17 0.0104 0.0000 l 400 64 pass 8.59e-17 0.0150 0.0000 l 500 64 pass 1.08e-17 0.0010 0.0000 u 100 64 pass 4.91e-17 0.0046 0.0000 u 200 64 pass 6.49e-17 0.0099 0.0000 u 300 64 pass 8.08e-17 0.0155 0.0000 u 400 64 pass 8.40e-17 0.0219 0.0000 u 500 64 % All tests passed pass ./plasmatest ctbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, OpenBLAS 0.3.27 , 2025-03-21 18:15:56 % input: ./plasmatest ctbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 5.32e-09 0.0016 0.0000 l 100 64 pass 3.11e-08 0.0044 0.0000 l 200 64 pass 4.55e-08 0.0084 0.0000 l 300 64 pass 5.56e-08 0.0128 0.0000 l 400 64 pass 6.48e-08 0.0181 0.0000 l 500 64 pass 5.56e-09 0.0012 0.0000 u 100 64 pass 3.15e-08 0.0053 0.0000 u 200 64 pass 4.85e-08 0.0112 0.0000 u 300 64 pass 5.79e-08 0.0182 0.0000 u 400 64 pass 6.24e-08 0.0264 0.0000 u 500 64 % All tests passed pass ./plasmatest ztbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, OpenBLAS 0.3.27 , 2025-03-21 18:15:57 % input: ./plasmatest ztbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 1.24e-17 0.0016 0.0000 l 100 64 pass 6.00e-17 0.0058 0.0000 l 200 64 pass 7.32e-17 0.0117 0.0000 l 300 64 pass 8.68e-17 0.0181 0.0000 l 400 64 pass 9.71e-17 0.0250 0.0000 l 500 64 pass 1.00e-17 0.0015 0.0000 u 100 64 pass 5.95e-17 0.0065 0.0000 u 200 64 pass 7.58e-17 0.0136 0.0000 u 300 64 pass 8.89e-17 0.0224 0.0000 u 400 64 pass 9.06e-17 0.0313 0.0000 u 500 64 % All tests passed pass -------------------------------------------------------------------------------- All routines passed. Elapsed 3.35 sec Fri Mar 21 18:15:58 2025 ################################################################################ # Test with Intel MKL. sh methane build> ./run_tests.py tbbrd Fri Mar 21 18:16:07 2025 ./plasmatest stbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, Intel MKL 2024.0.2, 2025-03-21 18:16:07 % input: ./plasmatest stbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 5.54e-09 0.0011 0.0000 l 100 64 pass 2.80e-08 0.0028 0.0000 l 200 64 pass 3.58e-08 0.0055 0.0000 l 300 64 pass 4.58e-08 0.0085 0.0000 l 400 64 pass 4.70e-08 0.0117 0.0000 l 500 64 pass 6.42e-09 0.0008 0.0000 u 100 64 Intel oneMKL ERROR: Parameter 4 was incorrect on entry to SLAROT. #### cut 161545 duplicate lines #### Intel oneMKL ERROR: Parameter 4 was incorrect on entry to SLAROT. FAILED 7.01e-03 0.0163 0.0000 u 500 64 % 4 tests failed FAILED: exit code 4 ./plasmatest dtbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, Intel MKL 2024.0.2, 2025-03-21 18:16:08 % input: ./plasmatest dtbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 9.60e-18 0.0011 0.0000 l 100 64 pass 5.29e-17 0.0031 0.0000 l 200 64 pass 6.15e-17 0.0062 0.0000 l 300 64 pass 8.12e-17 0.0097 0.0000 l 400 64 pass 8.45e-17 0.0135 0.0000 l 500 64 pass 1.04e-17 0.0009 0.0000 u 100 64 pass 5.35e-17 0.0043 0.0000 u 200 64 pass 6.30e-17 0.0094 0.0000 u 300 64 pass 8.36e-17 0.0151 0.0000 u 400 64 pass 8.80e-17 0.0209 0.0000 u 500 64 % All tests passed pass ./plasmatest ctbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, Intel MKL 2024.0.2, 2025-03-21 18:16:08 % input: ./plasmatest ctbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 6.03e-09 0.0014 0.0000 l 100 64 pass 3.48e-08 0.0039 0.0000 l 200 64 pass 5.00e-08 0.0073 0.0000 l 300 64 pass 6.17e-08 0.0113 0.0000 l 400 64 pass 7.33e-08 0.0154 0.0000 l 500 64 pass 4.30e-09 0.0011 0.0000 u 100 64 pass 3.43e-08 0.0051 0.0000 u 200 64 pass 5.48e-08 0.0110 0.0000 u 300 64 pass 5.91e-08 0.0171 0.0000 u 400 64 pass 7.58e-08 0.0304 0.0000 u 500 64 % All tests passed pass ./plasmatest ztbbrd --nb=64 --dim=100:500:100 --uplo=l,u % PLASMA 24.8.7, OpenMP num threads 10, Intel MKL 2024.0.2, 2025-03-21 18:16:09 % input: ./plasmatest ztbbrd --nb=64 --dim=100:500:100 --uplo=l,u Status Error Time Gflop/s uplo n nb pass 1.29e-17 0.0015 0.0000 l 100 64 pass 5.38e-17 0.0053 0.0000 l 200 64 pass 7.83e-17 0.0101 0.0000 l 300 64 pass 8.72e-17 0.0164 0.0000 l 400 64 pass 9.68e-17 0.0210 0.0000 l 500 64 pass 1.51e-17 0.0014 0.0000 u 100 64 pass 5.60e-17 0.0059 0.0000 u 200 64 pass 8.63e-17 0.0128 0.0000 u 300 64 pass 8.76e-17 0.0212 0.0000 u 400 64 pass 9.63e-17 0.0272 0.0000 u 500 64 % All tests passed pass -------------------------------------------------------------------------------- 1 routines FAILED: tbbrd Elapsed 3.67 sec Fri Mar 21 18:16:10 2025

This is concerning that the tests are not passing with all optimized BLAS. Do you think is it related to threading or the OpenMP tasking runtime?

Don't know; never finished investigating.

mgates3 added 5 commits March 18, 2025 20:18

svd: rename functions. Band form is triangular (tb), not general (gb).

cdf0c7a

svd: style

da1f675

svd: docs

d0678b8

svd: clean bulge chasing

738b692

svd/eig: remove volatile and unused static scheduler variables

2f03537

mgates3 commented Mar 21, 2025

View reviewed changes

mgates3 added 3 commits March 21, 2025 16:35

svd: add test_tbbrd

87f5351

eig: update docs with diagram

5f21c41

svd: cleanup and rename bulge-chasing header

e5ede0a

mgates3 force-pushed the svd branch from 928cdf0 to e5ede0a Compare March 21, 2025 20:36

mgates3 added 3 commits February 11, 2026 20:57

simplify and document findVTpos code

c432ba8

update gitignore

3736546

WIP

faab1f1

mgates3 marked this pull request as draft April 7, 2026 21:46

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SVD cleanup#46

SVD cleanup#46
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