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added missing matrix exponentiation methods #29782

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merged 6 commits into from
Oct 30, 2018
Merged

added missing matrix exponentiation methods #29782

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61d6384
added missing matrix exponentiation methods
ExpandingMan Oct 23, 2018
9881db3
added some tests
ExpandingMan Oct 23, 2018
0c483a8
moved new methods to LinearAlgebra
ExpandingMan Oct 23, 2018
72266ad
added general method and cleaned up tests
ExpandingMan Oct 24, 2018
9def8c7
moved methods
ExpandingMan Oct 24, 2018
6b9f486
eliminate spurious allocation
ExpandingMan Oct 29, 2018
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4 changes: 4 additions & 0 deletions stdlib/LinearAlgebra/src/dense.jl
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Expand Up @@ -489,6 +489,10 @@ julia> exp(A)
exp(A::StridedMatrix{<:BlasFloat}) = exp!(copy(A))
exp(A::StridedMatrix{<:Union{Integer,Complex{<:Integer}}}) = exp!(float.(A))

Base.:^(b::Number, A::AbstractMatrix) = exp!(log(b)*A)
# method for ℯ to explicitly elide the log(b) multiplication
Base.:^(::Irrational{:ℯ}, A::AbstractMatrix) = exp(A)

## Destructive matrix exponential using algorithm from Higham, 2008,
## "Functions of Matrices: Theory and Computation", SIAM
function exp!(A::StridedMatrix{T}) where T<:BlasFloat
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7 changes: 7 additions & 0 deletions stdlib/LinearAlgebra/test/dense.jl
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Expand Up @@ -428,6 +428,13 @@ end
end
end

@testset "^ tests" for elty in (Float32, Float64, ComplexF32, ComplexF64, Int32, Int64)
# should all be exact as the lhs functions are simple aliases
@test ℯ^(fill(elty(2), (4,4))) == exp(fill(elty(2), (4,4)))
@test 2^(fill(elty(2), (4,4))) == exp(log(2)*fill(elty(2), (4,4)))
@test 2.0^(fill(elty(2), (4,4))) == exp(log(2.0)*fill(elty(2), (4,4)))
end

A8 = 100 * [-1+1im 0 0 1e-8; 0 1 0 0; 0 0 1 0; 0 0 0 1]
@test exp(log(A8)) ≈ A8
end
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