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JuliaIntervals / IntervalLinearAlgebra.jl

Linear algebra done rigorously
MIT License
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Implemented Theorem 7 in Miya14 #129

Open orkolorko opened 2 years ago

orkolorko commented 2 years ago

PR description

Implemented Algorithm M1 based on Theorem 7 of https://link.springer.com/article/10.1007/s13160-014-0145-5

After

The, not exported function svdbox, allows to compute rigorous enclosures of the singular values of a matrix (rectangular and square)

Checklist

Other

I did not export the function yet

lucaferranti commented 2 years ago

thank you very much! This is a very nice and welcome addition! I'll try to investigate the failing tests in the next couple of days

orkolorko commented 2 years ago

I'm doing some further work on the branch

codecov-commenter commented 2 years ago

Codecov Report

Base: 97.19% // Head: 96.72% // Decreases project coverage by -0.48% :warning:

Coverage data is based on head (17f6aae) compared to base (fe87dd4). Patch coverage: 94.21% of modified lines in pull request are covered.

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Additional details and impacted files ```diff @@ Coverage Diff @@ ## main #129 +/- ## ========================================== - Coverage 97.19% 96.72% -0.48% ========================================== Files 17 19 +2 Lines 642 763 +121 ========================================== + Hits 624 738 +114 - Misses 18 25 +7 ``` | [Impacted Files](https://codecov.io/gh/JuliaIntervals/IntervalLinearAlgebra.jl/pull/129?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaIntervals) | Coverage Δ | | |---|---|---| | [src/IntervalLinearAlgebra.jl](https://codecov.io/gh/JuliaIntervals/IntervalLinearAlgebra.jl/pull/129?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaIntervals#diff-c3JjL0ludGVydmFsTGluZWFyQWxnZWJyYS5qbA==) | `73.68% <66.66%> (-26.32%)` | :arrow_down: | | [src/eigenvalues/miyajima\_svd.jl](https://codecov.io/gh/JuliaIntervals/IntervalLinearAlgebra.jl/pull/129?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaIntervals#diff-c3JjL2VpZ2VudmFsdWVzL21peWFqaW1hX3N2ZC5qbA==) | `97.53% <97.53%> (ø)` | | | [src/multiplication.jl](https://codecov.io/gh/JuliaIntervals/IntervalLinearAlgebra.jl/pull/129?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaIntervals#diff-c3JjL211bHRpcGxpY2F0aW9uLmps) | `100.00% <100.00%> (ø)` | | | [src/numerical\_test/multithread.jl](https://codecov.io/gh/JuliaIntervals/IntervalLinearAlgebra.jl/pull/129?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaIntervals#diff-c3JjL251bWVyaWNhbF90ZXN0L211bHRpdGhyZWFkLmps) | `100.00% <100.00%> (ø)` | | Help us with your feedback. Take ten seconds to tell us [how you rate us](https://about.codecov.io/nps?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaIntervals). Have a feature suggestion? [Share it here.](https://app.codecov.io/gh/feedback/?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaIntervals)

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orkolorko commented 2 years ago

thank you very much! This is a very nice and welcome addition! I'll try to investigate the failing tests in the next couple of days

@lucaferranti I'm happy is it interesting! Happy to contribute!

I am thinking about implementing Miyajima's estimates for eigenvalues later on, also.

I will also check if Miyajima's svd estimate works for complex matrices (Rump estimate works, so it should, but the theorems in his paper are only stated for real matrices.)