A more robust error bound for the determinant. #5902

andreasnoack · 2014-02-22T10:43:07Z

The old test for the determinant has caused a lot of trouble. The new test depends on the condition number of the matrix and should therefore work for arbitrary matrices.

I would appreciate if someone with a 32 bit machine could try this out.

Related: JuliaLang/LinearAlgebra.jl#67, JuliaLang/LinearAlgebra.jl#79

rickhg12hs · 2014-02-23T11:09:37Z

Xref #5472 , JuliaLang/LinearAlgebra.jl#67 , JuliaLang/LinearAlgebra.jl#79

Looks like your changed test passed, but there are still problems in test/linalg1.jl (and test/linalg2.jl) for 32-bit machines ...

Before applying Pull Request:

$ ./julia -e 'versioninfo()'
Julia Version 0.3.0-prerelease+1692
Commit 736251d* (2014-02-23 06:21 UTC)
Platform Info:
  System: Linux (i686-redhat-linux)
  CPU: Genuine Intel(R) CPU           T2250  @ 1.73GHz
  WORD_SIZE: 32
  BLAS: libopenblas (DYNAMIC_ARCH NO_AFFINITY)
  LAPACK: libopenblas
  LIBM: libopenlibm
$ make test-linalg1
    JULIA test/linalg1
     * linalg1
exception on 1: ERROR: assertion failed: |det(capd) - det(apd)| <= 0.002384185791015625
  det(capd) = 1.626428240984628e9
  det(apd) = 1.6264282409980435e9
  difference = 0.01341557502746582 > 0.002384185791015625
 in error at error.jl:22
 in test_approx_eq at test.jl:68
 in anonymous at no file:54
 in runtests at /usr/local/src/julia/julia/test/testdefs.jl:5
 in anonymous at multi.jl:629
 in run_work_thunk at multi.jl:590
 in remotecall_fetch at multi.jl:663
 in remotecall_fetch at multi.jl:678
 in anonymous at task.jl:1320
while loading linalg1.jl, in expression starting on line 23
ERROR: assertion failed: |det(capd) - det(apd)| <= 0.002384185791015625
  det(capd) = 1.626428240984628e9
  det(apd) = 1.6264282409980435e9
  difference = 0.01341557502746582 > 0.002384185791015625
 in error at error.jl:22
 in test_approx_eq at test.jl:68
 in anonymous at no file:54
 in runtests at /usr/local/src/julia/julia/test/testdefs.jl:5
 in anonymous at multi.jl:629
 in run_work_thunk at multi.jl:590
 in remotecall_fetch at multi.jl:663
 in remotecall_fetch at multi.jl:678
 in anonymous at task.jl:1320
while loading linalg1.jl, in expression starting on line 23
while loading /usr/local/src/julia/julia/test/runtests.jl, in expression starting on line 34

make[1]: *** [linalg1] Error 1
make: *** [test-linalg1] Error 2
$

After applying PR:

$ git cherry-pick -n 98cc8df
$ git status
# On branch master
# Changes to be committed:
#   (use "git reset HEAD <file>..." to unstage)
#
#   modified:   test/linalg1.jl
$ make test-linalg1
    JULIA test/linalg1
     * linalg1
exception on 1: ERROR: assertion failed: |apd * inv(capd) - eye(n)| <= 2.220446049250313e-10
  apd * inv(capd) = .9999999999690772   15279510989785194e-26   3637978807091713e-26    -8185452315956354e-27   -4729372449219227e-26   18189894035458565e-27   12732925824820995e-26   -9094947017729282e-27   -21827872842550278e-27  -6821210263296962e-28
-11823431123048067e-27  1.0000000002073648  -15643308870494366e-26  28194335754960775e-27   16370904631912708e-26   3637978807091713e-27    14551915228366852e-26   -18189894035458565e-28  -54569682106375694e-27  6821210263296962e-27
-54569682106375694e-27  1673470251262188e-25    1.000000000010914   9094947017729282e-27    5820766091346741e-26    -836735125631094e-25    9094947017729282e-26    -54569682106375694e-27  -14915713109076023e-26  54569682106375694e-28
-54569682106375694e-28  13460521586239338e-26   -29103830456733704e-27  .9999999999818101   9822542779147625e-26    -6184563972055912e-26   6184563972055912e-26    -4001776687800884e-26   -2546585164964199e-26   -13642420526593924e-28
-5820766091346741e-26   2837623469531536e-25    -21827872842550278e-27  7275957614183426e-27    1.0000000000800355  -54569682106375694e-27  1418811734765768e-25    -29103830456733704e-27  -15643308870494366e-26  22737367544323206e-28
-4547473508864641e-26   11641532182693481e-26   -9458744898438454e-26   8185452315956354e-27    6548361852765083e-26    .9999999999436113   1127773430198431e-25    -27284841053187847e-27  -14551915228366852e-26  5229594535194337e-27
-48203219193965197e-27  17462298274040222e-26   5093170329928398e-26    2000888343900442e-26    12005330063402653e-26   -10550138540565968e-26  1.0000000000363798  -29103830456733704e-27  -5820766091346741e-26   6821210263296962e-28
-4729372449219227e-26   23283064365386963e-26   -54569682106375694e-27  18189894035458565e-27   12005330063402653e-26   -12732925824820995e-26  1964508555829525e-25    .9999999998981366   -1382431946694851e-25   8412825991399586e-27
-6002665031701326e-26   2255546860396862e-25    -1127773430198431e-25   54569682106375694e-28   16370904631912708e-26   -9276845958083868e-26   1000444171950221e-25    -8003553375601768e-26   .999999999836291    12732925824820995e-27
-5093170329928398e-26   2255546860396862e-25    29103830456733704e-27   -2091837814077735e-26   7639755494892597e-26    -3637978807091713e-27   6548361852765083e-26    -16370904631912708e-27  -5093170329928398e-26   .9999999999947704

  eye(n) = 1    0   0   0   0   0   0   0   0   0
0   1   0   0   0   0   0   0   0   0
0   0   1   0   0   0   0   0   0   0
0   0   0   1   0   0   0   0   0   0
0   0   0   0   1   0   0   0   0   0
0   0   0   0   0   1   0   0   0   0
0   0   0   0   0   0   1   0   0   0
0   0   0   0   0   0   0   1   0   0
0   0   0   0   0   0   0   0   1   0
0   0   0   0   0   0   0   0   0   1

  difference = 2.837623469531536e-10 > 2.220446049250313e-10
 in error at error.jl:22
 in test_approx_eq at test.jl:68
 in anonymous at no file:54
 in runtests at /usr/local/src/julia/julia/test/testdefs.jl:5
 in anonymous at multi.jl:629
 in run_work_thunk at multi.jl:590
 in remotecall_fetch at multi.jl:663
 in remotecall_fetch at multi.jl:678
 in anonymous at task.jl:1320
while loading linalg1.jl, in expression starting on line 23
ERROR: assertion failed: |apd * inv(capd) - eye(n)| <= 2.220446049250313e-10
  apd * inv(capd) = .9999999999690772   15279510989785194e-26   3637978807091713e-26    -8185452315956354e-27   -4729372449219227e-26   18189894035458565e-27   12732925824820995e-26   -9094947017729282e-27   -21827872842550278e-27  -6821210263296962e-28
-11823431123048067e-27  1.0000000002073648  -15643308870494366e-26  28194335754960775e-27   16370904631912708e-26   3637978807091713e-27    14551915228366852e-26   -18189894035458565e-28  -54569682106375694e-27  6821210263296962e-27
-54569682106375694e-27  1673470251262188e-25    1.000000000010914   9094947017729282e-27    5820766091346741e-26    -836735125631094e-25    9094947017729282e-26    -54569682106375694e-27  -14915713109076023e-26  54569682106375694e-28
-54569682106375694e-28  13460521586239338e-26   -29103830456733704e-27  .9999999999818101   9822542779147625e-26    -6184563972055912e-26   6184563972055912e-26    -4001776687800884e-26   -2546585164964199e-26   -13642420526593924e-28
-5820766091346741e-26   2837623469531536e-25    -21827872842550278e-27  7275957614183426e-27    1.0000000000800355  -54569682106375694e-27  1418811734765768e-25    -29103830456733704e-27  -15643308870494366e-26  22737367544323206e-28
-4547473508864641e-26   11641532182693481e-26   -9458744898438454e-26   8185452315956354e-27    6548361852765083e-26    .9999999999436113   1127773430198431e-25    -27284841053187847e-27  -14551915228366852e-26  5229594535194337e-27
-48203219193965197e-27  17462298274040222e-26   5093170329928398e-26    2000888343900442e-26    12005330063402653e-26   -10550138540565968e-26  1.0000000000363798  -29103830456733704e-27  -5820766091346741e-26   6821210263296962e-28
-4729372449219227e-26   23283064365386963e-26   -54569682106375694e-27  18189894035458565e-27   12005330063402653e-26   -12732925824820995e-26  1964508555829525e-25    .9999999998981366   -1382431946694851e-25   8412825991399586e-27
-6002665031701326e-26   2255546860396862e-25    -1127773430198431e-25   54569682106375694e-28   16370904631912708e-26   -9276845958083868e-26   1000444171950221e-25    -8003553375601768e-26   .999999999836291    12732925824820995e-27
-5093170329928398e-26   2255546860396862e-25    29103830456733704e-27   -2091837814077735e-26   7639755494892597e-26    -3637978807091713e-27   6548361852765083e-26    -16370904631912708e-27  -5093170329928398e-26   .9999999999947704

  eye(n) = 1    0   0   0   0   0   0   0   0   0
0   1   0   0   0   0   0   0   0   0
0   0   1   0   0   0   0   0   0   0
0   0   0   1   0   0   0   0   0   0
0   0   0   0   1   0   0   0   0   0
0   0   0   0   0   1   0   0   0   0
0   0   0   0   0   0   1   0   0   0
0   0   0   0   0   0   0   1   0   0
0   0   0   0   0   0   0   0   1   0
0   0   0   0   0   0   0   0   0   1

  difference = 2.837623469531536e-10 > 2.220446049250313e-10
 in error at error.jl:22
 in test_approx_eq at test.jl:68
 in anonymous at no file:54
 in runtests at /usr/local/src/julia/julia/test/testdefs.jl:5
 in anonymous at multi.jl:629
 in run_work_thunk at multi.jl:590
 in remotecall_fetch at multi.jl:663
 in remotecall_fetch at multi.jl:678
 in anonymous at task.jl:1320
while loading linalg1.jl, in expression starting on line 23
while loading /usr/local/src/julia/julia/test/runtests.jl, in expression starting on line 34

make[1]: *** [linalg1] Error 1
make: *** [test-linalg1] Error 2
$

andreasnoack · 2014-02-24T22:55:08Z

I have added more condition number aware error bands and tried the tests on a 32 bit VB. The Woodbury test is now failing on 32 bit and is complicated solve. I haven't found a good error bound yet for that.

…nalg tests. Add fallback condition number method.

andreasnoack · 2014-03-07T20:42:55Z

@rickhg12hs I have updated this and now the tests pass on my 32 bit virtual box. Can you try it out on your machine?

rickhg12hs · 2014-03-08T18:47:55Z

Xref: #5472
Holy Mackerel! First time make test-linalg has passed since sometime in January!

$ patch -p1 -i ../tmp/5902.patch 
patching file base/linalg/factorization.jl
patching file test/linalg1.jl
patching file test/linalg2.jl
$ git status
# On branch master
# Changes not staged for commit:
#   (use "git add <file>..." to update what will be committed)
#   (use "git checkout -- <file>..." to discard changes in working directory)
#
#   modified:   base/linalg/factorization.jl
#   modified:   test/linalg1.jl
#   modified:   test/linalg2.jl
#
no changes added to commit (use "git add" and/or "git commit -a")
$ make -j2 && make -j2 debug && make
$ ./julia -e 'versioninfo()'
Julia Version 0.3.0-prerelease+1908
Commit e7c2f99* (2014-03-08 04:43 UTC)
Platform Info:
  System: Linux (i686-redhat-linux)
  CPU: Genuine Intel(R) CPU           T2250  @ 1.73GHz
  WORD_SIZE: 32
  BLAS: libopenblas (DYNAMIC_ARCH NO_AFFINITY)
  LAPACK: libopenblas
  LIBM: libopenlibm
$ make test-linalg
    JULIA test/linalg
    From worker 3:       * linalg2
    From worker 2:       * linalg1
    SUCCESS
$

andreasnoack · 2014-03-08T20:05:57Z

@jiahao It works and is better than hardcoded values, but it still needs improvement. However, it makes the tests pass on 32 bit systems so I think it would be good to get merged. Are you okay with that?

StefanKarpinski · 2014-03-08T20:31:34Z

Yes, please!

A more robust error bound for the determinant.

jiahao · 2014-03-08T22:07:31Z

Good enough for now

jiahao added the linear algebra label Feb 22, 2014

rickhg12hs mentioned this pull request Feb 23, 2014

make test-linalg fails #5472

Closed

andreasnoack mentioned this pull request Feb 24, 2014

is Float16 a real computational type or not? #5942

Closed

tkelman mentioned this pull request Mar 7, 2014

RFC: Windows CI #6028

Merged

A more robust error bound for the determinant. Remove Float16 from li…

b695c7a

…nalg tests. Add fallback condition number method.

jiahao added a commit that referenced this pull request Mar 8, 2014

Merge pull request #5902 from JuliaLang/anj/detbound

9d108f4

A more robust error bound for the determinant.

jiahao merged commit 9d108f4 into master Mar 8, 2014

andreasnoack deleted the anj/detbound branch March 9, 2014 05:40

mschauer mentioned this pull request Mar 18, 2014

Use single call to dsfmt_gv_genrand_uint32() for small ranges (Take 2) #5741

Merged

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A more robust error bound for the determinant. #5902

A more robust error bound for the determinant. #5902

andreasnoack commented Feb 22, 2014

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jiahao commented Mar 8, 2014

A more robust error bound for the determinant. #5902

A more robust error bound for the determinant. #5902

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