RFC: treat small negative λ as 0 for sqrt(::Hermitian) #35057
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stevengj
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linear algebra
stevengj
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Oh, I guess this doesn't make sense in the case of a matrix Note that this can change the output of |
stevengj
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needs docs
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@andreasnoack, I updated the test tolerances some time ago and tests are passing. Good to merge? |
eschnett
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May 11, 2020
* treat small negative λ as 0 for sqrt(::Hermitian) and log(::Hermitian) * typo * added tests, docs; removed rtol argument for log * don't ask for rtol so close to eps(Float64)
Roger-luo
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May 14, 2020
* treat small negative λ as 0 for sqrt(::Hermitian) and log(::Hermitian) * typo * added tests, docs; removed rtol argument for log * don't ask for rtol so close to eps(Float64)
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This PR treats sufficiently small negative eigenvalues as "zero" for the purpose of taking matrix
sqrtand, as otherwise one gets spurious complex results from semidefinite matrices due to roundoff errors. (See also discourse discussion.)logIt works by adding an
rtolkeyword parameter tosqrt(::Hermitian)and, specifying a relative tolerance for negative eigenvalues to ignore, which defaults to the same relative tolerance that we use for thelog(::Hermitian)pinvfunction.This is currently just a rough draft to get reactions.To do:rtolargument forlog, where semidefinite matrices don't make sense