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faster implementation of rank(::QRPivoted) fixes #1128 #1129

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Merged
merged 7 commits into from
Dec 2, 2024
Merged

faster implementation of rank(::QRPivoted) fixes #1128 #1129

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9cf5df3
added rank method for SVD object alongwith unit tests for the method.…
ajinkya-k Nov 29, 2024
7764601
faster implementation of rank(::QRPivoted)
ajinkya-k Nov 29, 2024
d7942fb
added stevengj's suggestion to qr. reversed changes in svd
ajinkya-k Nov 29, 2024
d270bda
minor edit to qr(::QRPivoted)
ajinkya-k Nov 30, 2024
c4aa5f3
simplified rank(::QRPivoted) implementation
ajinkya-k Dec 1, 2024
d1c35e6
simplified the rtol default eps call in rank(::QRPivoted)
ajinkya-k Dec 1, 2024
3ee69e6
using eltype(A) instead of eltype(A.Q) in the default val for rtol in…
ajinkya-k Dec 1, 2024
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6 changes: 3 additions & 3 deletions src/qr.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -535,11 +535,11 @@ function ldiv!(A::QRCompactWY{T}, B::AbstractMatrix{T}) where {T}
return B
end

function rank(A::QRPivoted; atol::Real=0, rtol::Real=min(size(A)...) * eps(real(float(one(eltype(A.Q))))) * iszero(atol))
function rank(A::QRPivoted; atol::Real=0, rtol::Real=min(size(A)...) * eps(real(float(eltype(A)))) * iszero(atol))
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@stevengj stevengj Dec 2, 2024 •
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Note that one(eltype(A)) would be better here, in principle, in order to handle the case of dimensionful matrices — the rtol should always be dimensionless, and one strips any units.

(I'm not sure if we support dimensionful matrices yet in QRPivoted — I'm guessing we don't — but it's nice to think about the possibility of unitful numbers when implementing algorithms.)

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Sorry, I made that change based on a comment in #1127 . Before making the change I compared eps(eltype(A)) and eps(one(eltype(A))) and verified they give the same answer. I can submit another PR to put back the one in there. Also I dont think I understand what you mean by dimensionful here. Can you point me to a resource to read?

m = min(size(A)...)
m == 0 && return 0
tol = max(atol, rtol*abs(A.R[1,1]))
return something(findfirst(i -> abs(A.R[i,i]) <= tol, 1:m), m+1) - 1
tol = max(atol, rtol*abs(A.factors[1,1]))
return something(findfirst(i -> abs(A.factors[i,i]) <= tol, 1:m), m+1) - 1
end

# Julia implementation similar to xgelsy
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