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Add relative and absolute tolerance for rank. #29926

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Dec 6, 2018
Merged

Add relative and absolute tolerance for rank. #29926

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4b66716
Add reltol and abstol in rank
Nov 4, 2018
1730b39
Add reltol and abstol in rank
Nov 4, 2018
0373eee
Add reltol and abstol
Nov 4, 2018
2a22d18
Add space
Nov 4, 2018
a134702
Add rtol,atol to rank
Nov 4, 2018
99b50c8
Add rel and abs tol
Nov 8, 2018
eaa5a65
Add documentation
Nov 8, 2018
40a0b6c
Add rtol, atol
Nov 8, 2018
17bc946
fix test
Nov 9, 2018
d88dd89
Add check for 0 dimension case
Nov 10, 2018
5623b9f
resolve comments
Nov 10, 2018
9bf234b
typo
Nov 10, 2018
d952739
typo
Nov 10, 2018
87cf3ce
deprecate tol in rank
Dec 2, 2018
c9ba74d
remove depwarn
simonbyrne Dec 5, 2018
c5e6a38
Add default values of tolerances and future deprecated method to docs
simonbyrne Dec 5, 2018
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25 changes: 17 additions & 8 deletions stdlib/LinearAlgebra/src/generic.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -712,13 +712,13 @@ end
###########################################################################################

"""
rank(A[, tol::Real])
rank(A::AbstractArray, atol::Real, rtol::Real)
rank(A[, tol::Real]) = rank(A, rtol=tol)
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Compute the rank of a matrix by counting how many singular
values of `A` have magnitude greater than `tol*σ₁` where `σ₁` is
`A`'s largest singular values. By default, the value of `tol` is the smallest
dimension of `A` multiplied by the [`eps`](@ref)
of the [`eltype`](@ref) of `A`.
values of `A` have magnitude greater than `max(atol, rtol*σ₁)` where `σ₁` is
`A`'s largest singular value, `atol` and `rtol` are the absolute and relative
tolerance, respectively.
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# Examples
```jldoctest
Expand All @@ -731,14 +731,23 @@ julia> rank(diagm(0 => [1, 0, 2]))
julia> rank(diagm(0 => [1, 0.001, 2]), 0.1)
2

julia> rank(diagm(0 => [1, 0.001, 2]), 0.00001)
julia> rank(diagm(0 => [1, 0.001, 2]), rtol=0.1)
2

julia> rank(diagm(0 => [1, 0.001, 2]), rtol=0.00001)
3

julia> rank(diagm(0 => [1, 0.001, 2]), atol=1.5)
1
```
"""
function rank(A::AbstractMatrix, tol::Real = min(size(A)...)*eps(real(float(one(eltype(A))))))
function rank(A::AbstractMatrix; atol::Real = 0.0, rtol::Real = (min(size(A)...)*eps(real(float(one(eltype(A))))))*iszero(atol))
isempty(A) && return 0 # 0-dimensional case
s = svdvals(A)
count(x -> x > tol*s[1], s)
tol = max(atol, rtol*s[1])
count(x -> x > tol, s)
end
rank(A::AbstractMatrix, tol::Real) = rank(A,rtol=tol) # TODO: deprecate tol in 2.0
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rank(x::Number) = x == 0 ? 0 : 1

"""
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3 changes: 3 additions & 0 deletions stdlib/LinearAlgebra/test/generic.jl
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Expand Up @@ -195,6 +195,9 @@ end

@test rank(fill(0, 0, 0)) == 0
@test rank([1.0 0.0; 0.0 0.9],0.95) == 1
@test rank([1.0 0.0; 0.0 0.9],rtol=0.95) == 1
@test rank([1.0 0.0; 0.0 0.9],atol=0.95) == 1
@test rank([1.0 0.0; 0.0 0.9],atol=0.95,rtol=0.95)==1
@test qr(big.([0 1; 0 0])).R == [0 1; 0 0]

@test norm([2.4e-322, 4.4e-323]) ≈ 2.47e-322
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